Multivariate and Multiscale Data Assimilation in Terrestrial Systems: A Review
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paper_title: Improvements to the Community Land Model and their impact on the hydrological cycle: COMMUNITY LAND MODEL HYDROLOGY

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[1] The Community Land Model version 3 (CLM3) is the land component of the Community Climate System Model (CCSM). CLM3 has energy and water biases resulting from deficiencies in some of its canopy and soil parameterizations related to hydrological processes. Recent research by the community that utilizes CLM3 and the family of CCSM models has indicated several promising approaches to alleviating these biases. This paper describes the implementation of a selected set of these parameterizations and their effects on the simulated hydrological cycle. The modifications consist of surface data sets based on Moderate Resolution Imaging Spectroradiometer products, new parameterizations for canopy integration, canopy interception, frozen soil, soil water availability, and soil evaporation, a TOPMODEL-based model for surface and subsurface runoff, a groundwater model for determining water table depth, and the introduction of a factor to simulate nitrogen limitation on plant productivity. The results from a set of offline simulations were compared with observed data for runoff, river discharge, soil moisture, and total water storage to assess the performance of the new model (referred to as CLM3.5). CLM3.5 exhibits significant improvements in its partitioning of global evapotranspiration (ET) which result in wetter soils, less plant water stress, increased transpiration and photosynthesis, and an improved annual cycle of total water storage. Phase and amplitude of the runoff annual cycle is generally improved. Dramatic improvements in vegetation biogeography result when CLM3.5 is coupled to a dynamic global vegetation model. Lower than observed soil moisture variability in the rooting zone is noted as a remaining deficiency.
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paper_title: Soil moisture retrieval from space: the Soil Moisture and Ocean Salinity (SMOS) mission

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Microwave radiometry at low frequencies (L-band: 1.4 GHz, 21 cm) is an established technique for estimating surface soil moisture and sea surface salinity with a suitable sensitivity. However, from space, large antennas (several meters) are required to achieve an adequate spatial resolution at L-band. So as to reduce the problem of putting into orbit a large filled antenna, the possibility of using antenna synthesis methods has been investigated. Such a system, relying on a deployable structure, has now proved to be feasible and has led to the Soil Moisture and Ocean Salinity (SMOS) mission, which is described. The main objective of the SMOS mission is to deliver key variables of the land surfaces (soil moisture fields), and of ocean surfaces (sea surface salinity fields). The SMOS mission is based on a dual polarized L-band radiometer using aperture synthesis (two-dimensional [2D] interferometer) so as to achieve a ground resolution of 50 km at the swath edges coupled with multiangular acquisitions. The radiometer will enable frequent and global coverage of the globe and deliver surface soil moisture fields over land and sea surface salinity over the oceans. The SMOS mission was proposed to the European Space Agency (ESA) in the framework of the Earth Explorer Opportunity Missions. It was selected for a tentative launch in 2005. The goal of this paper is to present the main aspects of the baseline mission and describe how soil moisture will be retrieved from SMOS data.
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paper_title: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics

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A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The unbounded error growth found in the extended Kalman filter, which is caused by an overly simplified closure in the error covariance equation, is completely eliminated. Open boundaries can be handled as long as the ocean model is well posed. Well-known numerical instabilities associated with the error covariance equation are avoided because storage and evolution of the error covariance matrix itself are not needed. The results are also better than what is provided by the extended Kalman filter since there is no closure problem and the quality of the forecast error statistics therefore improves. The method should be feasible also for more sophisticated primitive equation models. The computational load for reasonable accuracy is only a fraction of what is required for the extended Kalman filter and is given by the storage of, say, 100 model states for an ensemble size of 100 and thus CPU requirements of the order of the cost of 100 model integrations. The proposed method can therefore be used with realistic nonlinear ocean models on large domains on existing computers, and it is also well suited for parallel computers and clusters of workstations where each processor integrates a few members of the ensemble.
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paper_title: Real-time groundwater flow modeling with the Ensemble Kalman Filter: Joint estimation of states and parameters and the filter inbreeding problem

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[1] Real-time groundwater flow modeling with filter methods is interesting for dynamical groundwater flow systems, for which measurement data in real-time are available. The Ensemble Kalman Filter (EnKF) approach is used here to update states together with parameters by adopting an augmented state vector approach. The performance of EnKF is investigated in a synthetic study with a two-dimensional transient groundwater flow model where (1) only the recharge rate is spatiotemporally variable, (2) only transmissivity is spatially variable with σlnT2 = 1.0 or (3) with σlnT2 = 2.7, and (4) both recharge rate and transmissivity are uncertain (a combination of (1) and (3)). The performance of EnKF for simultaneous state and parameter estimation in saturated groundwater flow problems is investigated in dependence of the number of stochastic realizations, the updating frequency and updating intensity of log-transmissivity, the amount of measurements in space and time, and the method (iterative versus noniterative EnKF), among others. Satisfactory results were also obtained if both transmissivity and recharge rate were uncertain. However, it was found that filter inbreeding is much more severe if hydraulic heads and transmissivities are jointly updated than if only hydraulic heads are updated. The filter inbreeding problem was investigated in more detail and could be strongly reduced with help of a damping parameter, which limits the intensity of the perturbation of the log-transmissivity field. An additional reduction of filter inbreeding could be achieved by combining two measures: (1) inflating the elements of the predicted state covariance matrix on the basis of a comparison between the model uncertainty and the observed errors at the measurement points and (2) starting the flow simulations with a very large number of realizations and then sampling the desired number of realizations after one simulation time step by minimizing the differences between the local cpdfs (and bivariate cpdfs) of hydraulic head for the large ensemble and the corresponding cpdfs for the reduced ensemble. The two measures, which cause very limited CPU costs, allowed making 100 stochastic realizations for the reproduction of the states as efficient as 200–500 untreated stochastic realizations.
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paper_title: Surface-subsurface flow modeling with path-based runoff routing, boundary condition-based coupling, and assimilation of multisource observation data

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Received 21 October 2008; revised 2 September 2009; accepted 16 September 2009; published 13 February 2010. [1] A distributed physically based model incorporating novel approaches for the representation of surface-subsurface processes and interactions is presented. A path-based description of surface flow across the drainage basin is used, with several options for identifying flow directions, for separating channel cells from hillslope cells, and for representing stream channel hydraulic geometry. Lakes and other topographic depressions are identified and specially treated as part of the preprocessing procedures applied to the digital elevation data for the catchment. Threshold-based boundary condition switching is used to partition potential (atmospheric) fluxes into actual fluxes across the land surface and changes in surface storage, thus resolving the exchange fluxes, or coupling, between the surface and subsurface modules. Nested time stepping allows smaller steps to be taken for typically faster and explicitly solved surface runoff routing, while a mesh coarsening option allows larger grid elements to be used for typically slower and more compute-intensive subsurface flow. Sequential data assimilation schemes allow the model predictions to be updated with spatiotemporal observation data of surface and subsurface variables. These approaches are discussed in detail, and the physical and numerical behavior of the model is illustrated over catchment scales ranging from 0.0027 to 356 km 2 , addressing different hydrological processes and highlighting the importance of describing coupled surfacesubsurface flow.
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paper_title: A Network of Terrestrial Environmental Observatories in Germany

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Multicompartment and multiscale long-term observation and research are important prerequisites to tackling the scientific challenges resulting from climate and global change. Long-term monitoring programs are cost intensive and require high analytical standards, however, and the gain of knowledge often requires longer observation times. Nevertheless, several environmental research networks have been established in recent years, focusing on the impact of climate and land use change on terrestrial ecosystems. From 2008 onward, a network of Terrestrial Environmental Observatories (TERENO) has been established in Germany as an interdisciplinary research program that aims to observe and explore the long-term ecological, social, and economic impacts of global change at the regional level. State-of-the-art methods from the field of environmental monitoring, geophysics, and remote sensing will be used to record and analyze states and fluxes for different environmental compartments from groundwater through the vadose zone, surface water, and biosphere, up to the lower atmosphere.
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paper_title: Radiance data assimilation for operational snow and streamflow forecasting

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Estimation of seasonal snowpack, in mountainous regions, is crucial for accurate streamflow prediction. This paper examines the ability of data assimilation (DA) of remotely sensed microwave radiance data to improve snow water equivalent prediction, and ultimately operational streamflow forecasts. Operational streamflow forecasts in the National Weather Service River Forecast Center (NWSRFC) are produced with a coupled SNOW17 (snow model) and SACramento Soil Moisture Accounting (SAC-SMA) model. A comparison of two assimilation techniques, the ensemble Kalman filter (EnKF) and the particle filter (PF), is made using a coupled SNOW17 and the microwave emission model for layered snow pack (MEMLS) model to assimilate microwave radiance data. Microwave radiance data, in the form of brightness temperature (TB), is gathered from the advanced microwave scanning radiometer-earth observing system (AMSR-E) at the 36.5 GHz channel. SWE prediction is validated in a synthetic experiment. The distribution of snowmelt from an experiment with real data is then used to run the SAC-SMA model. Several scenarios on state or joint state-parameter updating with TB data assimilation to SNOW-17 and SAC-SMA models were analyzed, and the results show potential benefit for operational streamflow forecasting.
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paper_title: An adjoint data assimilation approach for estimating parameters in a three-dimensional ecosystem model

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In this paper an ecosystem model, including phytoplankton, zooplankton, nitrate, ammonium, phosphate and detritus, is described. The model is driven by physical fields derived from a three-dimensional physical transport model. Simulation includes nitrate input from a river. Simulated results are then sampled and the sampled data are used in sequential numerical experiments to assess the ability of using an adjoint data assimilation approach for estimating the poorly known parameters of the ecosystem model, such as growth and death rate, half-saturation constant of nutrients, etc. Data with different spatial and temporal resolution over 1 week are assimilated into the ecosystem model. Assimilation of data at 30 grid stations with a sampling interval of 6 h is proved to be adequate for recovering all the parameters of the ecosystem model. Both the spatial and temporal resolution of the data are mutually complementary in the assimilative model. Thus, improvement of either of them can result in improvement of model parameter recoveries. The assimilation of phytoplankton data is essential to recover the model parameters. Phytoplankton is the core of the food web and without the information on phytoplankton, the structure of the ecosystem cannot be constructed correctly. The adjoint method can work well with the noisy data. In the twin experiments with noisy data, the parameters can be recovered but the error is increased. The results of the model and parameter recovery are sensitive to the initial conditions of state variables, so the determination of the initial condition is as important as that of the model parameter. The spatial and temporal resolution and the data type of the observations in Analysis and Modelling Research of the Ecosystem in the Bohai Sea (AMREB) are suitable for the recovery of the model parameters used in this study.
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paper_title: Calibration of the SUCROS emergence and early growth module for sugar beet using optical remote sensing data assimilation

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Crop models are useful for monitoring crop production on a local scale. Their application to a larger area, such as a region, is hampered by the difficulty in determining the value of some of their parameters, which may differ greatly between fields. The use of optical remote sensing helps to overcome this problem. Coupling a radiation transfer model to a crop model makes it possible to simulate reflectance for those times in crop growth for which remote sensing data are available. The inversion of the combined model on these data then makes it possible to estimate new values for certain sensitive parameters of the crop model. This paper describes the use of such a method on a local scale, for sugar beet, focusing on the parameters describing emergence and early crop growth. These processes vary greatly depending on the soil, climate and seedbed preparation, and affect yield significantly. The SUCROS crop model and the SAIL reflectance model were combined. The resulting model was calibrated under standard conditions and then evaluated under test conditions to which the emergence and early growth parameters of the SUCROS model were adjusted. The test conditions seedbed structure was coarser, and the sowing depth was greater than expected. Consequently, emergence occurred later, and the initial leaf area was smaller. The SUCROS simulation using standard values for emergence and early growth parameters did not accurately predict crop growth under these test conditions. The inversion of the combined model using a set of canopy reflectance measurements during crop establishment provided new parameter values that allowed us to accurately estimate crop yield. Application of this method on a regional scale, for yield prediction or agronomic diagnosis, should be of great value.
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paper_title: FLUXNET: A New Tool to Study the Temporal and Spatial Variability of Ecosystem–Scale Carbon Dioxide, Water Vapor, and Energy Flux Densities

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FLUXNET is a global network of micrometeorological flux measurement sites that measure the exchanges of carbon dioxide, water vapor, and energy between the biosphere and atmosphere. At present over 140 sites are operating on a long-term and continuous basis. Vegetation under study includes temperate conifer and broadleaved (deciduous and evergreen) forests, tropical and boreal forests, crops, grasslands, chaparral, wetlands, and tundra. Sites exist on five continents and their latitudinal distribution ranges from 70°N to 30°S. FLUXNET has several primary functions. First, it provides infrastructure for compiling, archiving, and distributing carbon, water, and energy flux measurement, and meteorological, plant, and soil data to the science community. (Data and site information are available online at the FLUXNET Web site, http://www-eosdis.ornl.gov/FLUXNET/.) Second, the project supports calibration and flux intercomparison activities. This activity ensures that data from the regional networks are intercomparable. And third, FLUXNET supports the synthesis, discussion, and communication of ideas and data by supporting project scientists, workshops, and visiting scientists. The overarching goal is to provide information for validating computations of net primary productivity, evaporation, and energy absorption that are being generated by sensors mounted on the NASA Terra satellite. Data being compiled by FLUXNET are being used to quantify and compare magnitudes and dynamics of annual ecosystem carbon and water balances, to quantify the response of stand-scale carbon dioxide and water vapor flux densities to controlling biotic and abiotic factors, and to validate a hierarchy of soil–plant–atmosphere trace gas exchange models. Findings so far include 1) net CO 2 exchange of temperate broadleaved forests increases by about 5.7 g C m −2 day −1 for each additional day that the growing season is extended; 2) the sensitivity of net ecosystem CO 2 exchange to sunlight doubles if the sky is cloudy rather than clear; 3) the spectrum of CO 2 flux density exhibits peaks at timescales of days, weeks, and years, and a spectral gap exists at the month timescale; 4) the optimal temperature of net CO 2 exchange varies with mean summer temperature; and 5) stand age affects carbon dioxide and water vapor flux densities.
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paper_title: Automatic state updating for operational streamflow forecasting via variational data assimilation.

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Summary In operational hydrologic forecasting, to account for errors in the initial and boundary conditions, and in parameters and structures of the hydrologic models, the forecasters routinely make adjustments in real-time to the hydrometeorological input, hydrologic model states and, in certain cases, model parameters based on streamflow observations. Though a great deal of effort has been made in recent years to automate such “run-time modifications” (MOD) by human forecasters to a possible extent, automatic state updating of hydrologic models is yet to be widely accepted or routinely practiced in operational hydrology for a range of reasons. In this paper, we describe a state updating procedure intended specifically for operational streamflow forecasting for gauged headwater basins, and compare its performance with human forecaster MOD through a real-time forecasting experiment. The procedure is based on variational assimilation (VAR) of streamflow, precipitation and potential evaporation (PE) data into lumped soil moisture accounting and routing models operating at a 1-h timestep. The procedure has been in experimental operation since 2003 at the National Weather Service’s (NWS) West Gulf River Forecast Center (WGRFC) in Fort Worth, TX. Also described is a novel parameter estimation and optimization tool, the Adjoint-Based OPTimizer (AB_OPT), used for lumped hydrologic modeling at a 1-h timestep necessary for VAR.
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paper_title: Coupled hydrogeophysical parameter estimation using a sequential Bayesian approach

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Abstract. Coupled hydrogeophysical methods infer hydrological and petrophysical parameters directly from geophysical measurements. Widespread methods do not explicitly recognize uncertainty in parameter estimates. Therefore, we apply a sequential Bayesian framework that provides updates of state, parameters and their uncertainty whenever measurements become available. We have coupled a hydrological and an electrical resistivity tomography (ERT) forward code in a particle filtering framework. First, we analyze a synthetic data set of lysimeter infiltration monitored with ERT. In a second step, we apply the approach to field data measured during an infiltration event on a full-scale dike model. For the synthetic data, the water content distribution and the hydraulic conductivity are accurately estimated after a few time steps. For the field data, hydraulic parameters are successfully estimated from water content measurements made with spatial time domain reflectometry and ERT, and the development of their posterior distributions is shown.
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paper_title: Novel approach to nonlinear/non-Gaussian Bayesian state estimation

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An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples, which are updated and propagated by the algorithm. The method is not restricted by assumptions of linear- ity or Gaussian noise: it may be applied to any state transition or measurement model. A simula- tion example of the bearings only tracking problem is presented. This simulation includes schemes for improving the efficiency of the basic algorithm. For this example, the performance of the bootstrap filter is greatly superior to the standard extended Kalman filter.
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paper_title: Data assimilation methods in the Earth sciences

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Abstract Although remote sensing data are often plentiful, they do not usually satisfy the users’ needs directly. Data assimilation is required to extract information about geophysical fields of interest from the remote sensing observations and to make the data more accessible to users. Remote sensing may provide, for example, measurements of surface soil moisture, snow water equivalent, snow cover, or land surface (skin) temperature. Data assimilation can then be used to estimate variables that are not directly observed from space but are needed for applications, for instance root zone soil moisture or land surface fluxes. The paper provides a brief introduction to modern data assimilation methods in the Earth sciences, their applications, and pertinent research questions. Our general overview is readily accessible to hydrologic remote sensing scientists. Within the general context of Earth science data assimilation, we point to examples of the assimilation of remotely sensed observations in land surface hydrology.
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paper_title: Provision of snow water equivalent from satellite data and the hydrological model PROMET using data assimilation techniques

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Information on snow cover and snow properties is an important factor for hydrology and runoff modelling. Frequent updates of snow cover information can help to improve water balance and discharge calculations. Within the frame of polar view, snow products from multisensoral satellite data are operationally provided to control and update water balance models for large parts of Southern Germany. Optical AVHRR sensors of the NOAA satellite are used for snow mapping and snow line delineation. Although these acquisitions are available several times per day, cloud cover hinders frequent updates of snow cover maps. As an additional remote sensing data source microwave data from ASAR on ENVISAT is used. Since C-band SAR sensors are only sensitive to snow with a high content of liquid water, the application of ASAR is limited to the melting periods. However under these conditions the developed procedure allows not only to delineate the snow cover in a comparable way as from optical data, also the additional information where the snow is melting is provided. In order to demonstrate how the remote sensing products can be used for improved water balance modelling, an application example for the watershed of the Upper Danube will be presented. This testsite is the research area of the integrative research project GLOWA-DANUBE that is conducted by the University of Munich. Model results using the PROMET-model of snow distributions with and without data assimilation of the remote sensing products will be given. Developed data assimilation concepts will be presented. Through data assimilation, the modelled snow cover agrees better with the mapped snow cover information from satellite. The optimised model provides maps of snow water equivalent, that can not directed be assessed by remote sensing. The impact of data assimilation on the modelled runoff will thus further be analysed.
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paper_title: Estimating transpiration and the sensitivity of carbon uptake to water availability in a subalpine forest using a simple ecosystem process model informed by measured net CO2 and H2O fluxes

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Modeling how the role of forests in the carbon cycle will respond to predicted changes in water availability hinges on an understanding of the processes controlling water use in ecosystems. Recent studies in forest ecosystem modeling have employed data-assimilation techniques to generate parameter sets that conform to observations, and predict net ecosystem CO2 exchange (NEE) and its component processes. Since the carbon and water cycles are linked, there should be additional process information available from ecosystem H2O exchange. We coupled SIPNET (Simple Photosynthesis EvapoTranspiration), a simplified model of ecosystem function, with a data-assimilation system to estimate parameters leading to model predictions most closely matching the net CO2 and H2O fluxes measured by eddy covariance in a high-elevation, subalpine forest ecosystem. When optimized using measurements of CO2 exchange, the model matched observed NEE (RMSE = 0.49 g C m−2) but underestimated transpiration calculated independently from sap flow measurements by a factor of 4. Consequently, the carbon-only optimization was insensitive to imposed changes in water availability. Including eddy flux data from both CO2 and H2O exchange to the optimization reduced the model fit to the observed NEE fluxes only slightly (RME = 0.53 g C m−2), however this parameterization also reproduced transpiration calculated from independent sap flow measurements (r2 = 0.67, slope = 0.6). A significant amount of information can be extracted from simultaneous analysis of CO2 and H2O exchange, which improved the accuracy of transpiration estimates from measured evapotranspiration. Conversely, failure to include both CO2 and H2O data streams can generate results that mask the responses of ecosystem carbon cycling to variation in the precipitation. In applying the model conditioned on both CO2 and H2O fluxes to the subalpine forest at the Niwot Ridge AmeriFlux site, we observed that the onset of transpiration is coincident with warm soil temperatures. However, after snow has covered the ground in the fall, we observed significant inter-annual variability in the fraction of evapotranspiration composed of transpiration; evapotranspiration was dominated by transpiration in years when late fall air temperatures were high enough to maintain photosynthesis, but by sublimation from the surface of the snowpack in years when late fall air temperatures were colder and forest photosynthetic activity had ceased. Data-assimilation techniques and simultaneous measurements of carbon and water exchange can be used to quantify the response of net carbon uptake to changes in water availability by using an ecosystem model where the carbon and water cycles are linked.
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paper_title: Hydraulic parameter estimation by remotely-sensed top soil moisture observations with the particle filter

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Summary In a synthetic study we explore the potential of using surface soil moisture measurements obtained from different satellite platforms to retrieve soil moisture profiles and soil hydraulic properties using a sequential data assimilation procedure and a 1D mechanistic soil water model. Four different homogeneous soil types were investigated including loamy sand, loam, silt, and clayey soils. The forcing data including precipitation and potential evapotranspiration were taken from the meteorological station of Aachen (Germany). With the aid of the forward model run, a synthetic data set was designed and observations were generated. The virtual top soil moisture observations were then assimilated to update the states and hydraulic parameters of the model by means of a particle filtering data assimilation method. Our analyses include the effect of assimilation strategy, measurement frequency, accuracy in surface soil moisture measurements, and soils differing in textural and hydraulic properties. With this approach we were able to assess the value of periodic spaceborne observations of top soil moisture for soil moisture profile estimation and identify the adequate conditions (e.g. temporal resolution and measurement accuracy) for remotely sensed soil moisture data assimilation. Updating of both hydraulic parameters and state variables allowed better predictions of top soil moisture contents as compared with updating of states only. An important conclusion is that the assimilation of remotely-sensed top soil moisture for soil hydraulic parameter estimation generates a bias depending on the soil type. Results indicate that the ability of a data assimilation system to correct the soil moisture state and estimate hydraulic parameters is driven by the non linearity between soil moisture and pressure head.
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paper_title: Retrieving soil temperature profile by assimilating MODIS LST products with ensemble Kalman filter

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Abstract Proper estimation of initial state variables and model parameters are vital importance for determining the accuracy of numerical model prediction. In this work, we develop a one-dimensional land data assimilation scheme based on ensemble Kalman filter and Common Land Model version 3.0 (CoLM). This scheme is used to improve the estimation of soil temperature profile. The leaf area index (LAI) is also updated dynamically by MODIS LAI production and the MODIS land surface temperature (LST) products are assimilated into CoLM. The scheme was tested and validated by observations from four automatic weather stations (BTS, DRS, MGS, and DGS) in Mongolian Reference Site of CEOP during the period of October 1, 2002 to September 30, 2003. Results indicate that data assimilation improves the estimation of soil temperature profile about 1 K. In comparison with simulation, the assimilation results of soil heat fluxes also have much improvement about 13 W m− 2 at BTS and DGS and 2 W m− 2 at DRS and MGS, respectively. In addition, assimilation of MODIS land products into land surface model is a practical and effective way to improve the estimation of land surface variables and fluxes.
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paper_title: The importance of the spatial patterns of remotely sensed soil moisture in the improvement of discharge predictions for small-scale basins through data assimilation

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Abstract In this paper, we investigate to which degree information concerning the spatial patterns of remotely sensed soil moisture data are needed in order to improve discharge predictions from hydrological models. For this purpose, we use the TOPMODEL-based Land–Atmosphere Transfer Scheme (TOPLATS). The remotely sensed soil moisture values are determined using C-band backscatter data from the European Space Agency (ESA) European Remote Sensing (ERS) Satellites. A baseline run, without soil moisture assimilation, is established for both the distributed and lumped versions of the land–atmosphere scheme. The modeled discharge matches the observations slightly better for the distributed model than for the lumped model. The remotely sensed soil moisture data are assimilated into the distributed version of the model through the ‘nudging to individual observations’ method, and the ‘statistical correction assimilation’ method. The remotely sensed soil moisture data are also assimilated into the lumped version of the model through the ‘statistical correction assimilation’ method. The statistical correction assimilation method leads to similar, and improved, discharge predictions for both the distributed and lumped models. The nudging to individual observations method leads, for the distributed model, to only slightly better results than the statistical correction assimilation method. As a consequence, it is suggested that it is sufficient to assimilate the statistics (spatial mean and variance) of remotely sensed soil moisture data into lumped hydrological models when one wants to improve hydrological model-based discharge predictions.
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paper_title: The representation of soil moisture freezing and its impact on the stable boundary layer

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The 1993 to 1996 version of the European Centre for Medium-Range Weather Forecasts model had a pronounced near-surface cold bias in winter over continental areas. the problem is illustrated in detail with help of tower observations. It is shown that a positive feedback exists in the land surface boundary-layer coupling that has the potential to amplify model biases. If the surface is cooled too much the boundary layer becomes too stable, reducing the downward heat flux and making the surface even colder. This positive feedback is believed to be stronger in the model than in the real atmosphere, resulting in diurnal temperature cycles that are too large and in excessive soil cooling on a seasonal time-scale in winter. ::: ::: ::: ::: An important contributor to the excessive winter cooling turns out to be the lack of soil moisture freezing in the model. the importance of this process is obvious from soil temperature observations. the seasonal soil temperature evolution shows a clear ‘barrier’ at 0°C due to the thermal inertia of freezing and thawing. A more quantitative illustration is the result of a simple calculation. This shows that the amount of energy necessary to freeze/thaw 1 m3 of wet soil, would cool/warm this soil by about 50 K if the phase transition was not taken into account. ::: ::: ::: ::: To reduce the winter cold bias in the model, three model changes have been tested and are described: (i) the introduction of the process of soil moisture freezing; (ii) revised stability functions to increase the turbulent diffusion of heat in stable situations; and (iii) an increase of the skin-layer conductivity. the effect of these changes on the seasonal evolution of soil and 2 m temperatures is investigated with long runs that have terms that relax towards the operational analysis above the boundary layer. In this way the impact can be studied on the temperature forecasts for the winter of 1995/1996, during which the operational model showed considerable soil temperature drift over Europe. Also, short periods of data assimilation (including 10-day forecasts) have been carried out to study the diurnal time-scales and the impact on model performance. ::: ::: ::: ::: The model changes eliminate to a large extent the systematic 2 m temperature biases for the winter of 1995/1996 over Europe and make the soil temperature evolution much more realistic. the soil moisture freezing, in particular, plays a crucial role by introducing thermal inertia near the freezing point, thereby reducing the annual temperature cycle in the soil. the process of soil moisture freezing leads to a considerable warming of the model's near-surface winter climate over continental areas.
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paper_title: The USDA Natural Resources Conservation Service Soil Climate Analysis Network (SCAN)

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Abstract Surface soil moisture plays an important role in the dynamics of land–atmosphere interactions and many current and upcoming models and satellite sensors. In situ data will be required to provide calibration and validation datasets. Therefore, there is a need for sensor networks at a variety of scales that provide near-real-time soil moisture and temperature data combined with other climate information for use in natural resource planning, drought assessment, water resource management, and resource inventory. The U.S. Department of Agriculture (USDA)–Natural Resources Conservation Service (NRCS)–National Water and Climate Center has established a continental-scale network to address this need, called the Soil Climate Analysis Network (SCAN). This ever-growing network has more than 116 stations located in 39 states, most of which have been installed since 1999. The stations are remotely located and collect hourly atmospheric, soil moisture, and soil temperature data that are available to the public...
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paper_title: Real-Time Data Assimilation for Operational Ensemble Streamflow Forecasting

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Abstract Operational flood forecasting requires that accurate estimates of the uncertainty associated with model-generated streamflow forecasts be provided along with the probable flow levels. This paper demonstrates a stochastic ensemble implementation of the Sacramento model used routinely by the National Weather Service for deterministic streamflow forecasting. The approach, the simultaneous optimization and data assimilation method (SODA), uses an ensemble Kalman filter (EnKF) for recursive state estimation allowing for treatment of streamflow data error, model structural error, and parameter uncertainty, while enabling implementation of the Sacramento model without major modification to its current structural form. Model parameters are estimated in batch using the shuffled complex evolution metropolis stochastic-ensemble optimization approach (SCEM-UA). The SODA approach was implemented using parallel computing to handle the increased computational requirements. Studies using data from the Leaf River...
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paper_title: Dual state-parameter estimation of hydrological models using ensemble Kalman filter

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Hydrologic models are twofold: models for understanding physical processes and models for prediction. This study addresses the latter, which modelers use to predict, for example, streamflow at some future time given knowledge of the current state of the system and model parameters. In this respect, good estimates of the parameters and state variables are needed to enable the model to generate accurate forecasts. In this paper, a dual state–parameter estimation approach is presented based on the Ensemble Kalman Filter (EnKF) for sequential estimation of both parameters and state variables of a hydrologic model. A systematic approach for identification of the perturbation factors used for ensemble generation and for selection of ensemble size is discussed. The dual EnKF methodology introduces a number of novel features: (1) both model states and parameters can be estimated simultaneously; (2) the algorithm is recursive and therefore does not require storage of all past information, as is the case in the batch calibration procedures; and (3) the various sources of uncertainties can be properly addressed, including input, output, and parameter uncertainties. The applicability and usefulness of the dual EnKF approach for ensemble streamflow forecasting is demonstrated using a conceptual rainfall-runoff model. 2004 Elsevier Ltd. All rights reserved.
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paper_title: Global Products Of Vegetation Leaf Area And Fraction Absorbed Par From Year One Of Modis Data

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An algorithm based on the physics of radiative transfer in vegetation canopies for the retrieval of vegetation green leaf area index (LAI) and fraction of absorbed photosynthetically active radiation (FPAR) from surface reflectances was developed and implemented for operational processing prior to the launch of the moderate resolution imaging spectroradiometer (MODIS) aboard the TERRA platform in December of 1999. The performance of the algorithm has been extensively tested in prototyping activities prior to operational production. Considerable attention was paid to characterizing the quality of the product and this information is available to the users as quality assessment (QA) accompanying the product. The MODIS LAI/FPAR product has been operationally produced from day one of science data processing from MODIS and is available free of charge to the users from the Earth Resources Observation System (EROS) Data Center Distributed Active Archive Center. Current and planned validation activities are aimed at evaluating the product at several field sites representative of the six structural biomes. Example results illustrating the physics and performance of the algorithm are presented together with initial QA and validation results. Potential users of the product are advised of the provisional nature of the product in view of changes to calibration, geolocation, cloud screening, atmospheric correction and ongoing validation activities. D 2002 Published by Elsevier Science Inc.
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paper_title: A data assimilation technique applied to a predator-prey model

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A new approach for data assimilation, which is based on the adjoint method, but allows the computer code for the adjoint to be constructed directly from the model computer code, is described. This technique is straightforward and reduces the chance of introducing errors in the construction of the adjoint code. Implementation of the technique is illustrated by applying it to a simple predator-prey model in a model fitting mode. A series of identical twin numerical experiments are used to show that this data assimilation approach can successfully recover model parameters as well as initial conditions. However, the ease with which these values are recovered is dependent on the form of the model equations as well as on the type and amount of data that are available. Additional numerical experiments show that sufficient coefficient and parameter recoveries are possible even when the assimilated data contain significant random noise. Thus, for biological systems that can be described by ecosystem models, the adjoint method represents a powerful approach for estimating values for little-known biological parameters, such as initial conditions, growth rates, and mortality rates.
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paper_title: Assimilation of SPOT/VEGETATION NDVI data into a sahelian vegetation dynamics model

paper_content:

Abstract This paper presents a method to monitor the dynamics of herbaceous vegetation in the Sahel. The approach is based on the assimilation of Normalized Difference Vegetation Index (NDVI) data acquired by the VEGETATION instrument on board SPOT 4/5 into a simple sahelian vegetation dynamics model. The study region is located in the Gourma region of Mali. The vegetation dynamics model is coupled with a radiative transfer model (the SAIL model). First, it is checked that the coupled models allow for a realistic simulation of the seasonal and interannual variability of NDVI over three sampling sites from 1999 to 2004. The data assimilation scheme relies on a parameter identification technique based on an Evolution Strategies algorithm. The simulated above-ground herbage mass resulting from NDVI assimilation is then compared to ground measurements performed over 13 study sites during the period 1999–2004. The assimilation scheme performs well with 404 kg DM/ha of average error ( n = 126 points) and a correlation coefficient of r = 0.80 (to be compared to the 463 kg DM/ha and r = 0.60 of the model performance without data assimilation). Finally, the sensitivity of the herbage mass model estimates to the quality of the meteorological forcing (rainfall and net radiation) is analyzed thanks to a stochastic approach.
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paper_title: Mapping of snow water equivalent and snow depth in boreal and sub-arctic zones by assimilating space-borne microwave radiometer data and ground-based observations

paper_content:

Abstract The monitoring of snow water equivalent (SWE) and snow depth (SD) in boreal forests is investigated by applying space-borne microwave radiometer data and synoptic snow depth observations. A novel assimilation technique based on (forward) modelling of observed brightness temperatures as a function of snow pack characteristics is introduced. The assimilation technique is a Bayesian approach that weighs the space-borne data and the reference field on SD interpolated from discrete synoptic observations with their estimated statistical accuracy. The results obtained using SSM/I and AMSR-E data for northern Eurasia and Finland indicate that the employment of space-borne data using the assimilation technique improves the SD and SWE retrieval accuracy when compared with the use of values interpolated from synoptic observations. Moreover, the assimilation technique is shown to reduce systematic SWE/SD estimation errors evident in the inversion of space-borne radiometer data.
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paper_title: Surface temperature and water vapour retrieval from MODIS data

paper_content:

This paper gives operational algorithms for retrieving sea (SST), land surface temperature (LST) and total atmospheric water vapour content (W) using Moderate Resolution Imaging Spectroradiometer (MODIS) data. To this end, the MODTRAN 3.5 radiative transfer program was used to predict radiances for MODIS channels 31, 32, 2, 17, 18 and 19. To analyse atmospheric effects, a simulation with a set of radiosonde observations was used to cover the variability of surface temperature and water vapour concentration on a worldwide scale. These simulated data were split into two sets (DB1 and DB2), the first one (DB1) was used to fit the coefficients of the algorithms, while the second one (DB2) was used to test the fitted coefficients. The results show that the algorithms are capable of producing SST and LST with a standard deviation of 0.3 K and 0.7 K if the satellite data are error free. The LST product has been validated with in situ data from a field campaign carried out in the Mississippi (USA), the results sh...
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paper_title: A strategy for operational implementation of 4D‐Var, using an incremental approach

paper_content:

SUMMARY An order of magnitude reduction in the cost of fourdimensional variational assimilation (4D-Var) is required before operational implementation is possible. Reconditioning is considered and, although it offers a signi6cant reduction in cost, it seems that it is unlikely to provide a reduction as large as an order of magnitude. An approximation to 4D-Var, namely the incremental approach, is then considered and is shown to produce the same result at the end of the assimilation window as an extended Kalman filter in which no approximations are made in the assimilating model but in which instead a simplitied evolution of the forecast error is introduced. This approach provides the flexibility for a cost-benefit trade-off of 4D-Var to be made. The development of variational four-dimensional assimilation (4D-Var) from the stage of being a theoretical possibility to being a practical reality is progressing at a rapid pace. The first results of four-dimensional variational assimilation using real observations were provided by Thbpaut et al. (1993b) using an adiabatic primitive-equation model at truncations "21 and T42. More recently Andersson ef al. (1994) used 4D-Var with a T63 model to assimilate remotely-sensed data such as infrared and microwave TOVS radiance measurements, while Thdpaut et d. (1993a) used 4D-Var with the same model to assimilate normalized radar backscatter cross-section measurements from the ERS-1 scatterometer.
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paper_title: A mechanistic modelling and data assimilation approach to estimate the carbon / chlorophyll and carbon / nitrogen ratios in a coupled hydrodynamical-biological model

paper_content:

The principal objective of hydrodynamical-biological models is to provide estimates of the main carbon fluxes such as total and export oceanic production. These models are nitrogen based, that is to say that the variables are expressed in terms of their nitrogen content. Moreover models are calibrated using chlorophyll data sets. Therefore carbon to chlorophyll (C:Chl) and carbon to nitrogen (C:N) ratios have to be assumed. This paper addresses the problem of the representation of these ratios. In a 1D framework at the DYFAMED station (NW Mediterranean Sea) we propose a model which enables the estimation of the basic biogeochemical fluxes and in which the spatio-temporal variability of the C:Chl and C:N ratios is fully represented in a mechanical way. This is achieved through the introduction of new state variables coming from the embedding of a phytoplankton growth model in a more classical Redfieldian NNPZD-DOM model (in which the C:N ratio is assumed to be a constant). Following this modelling step, the parameters of the model are estimated using the adjoint data assimilation method which enables the assimilation of chlorophyll and nitrate data sets collected at DYFAMED in 1997.Comparing the predictions of the new Mechanistic model with those of the classical Redfieldian NNPZD-DOM model which was calibrated with the same data sets, we find that both models reproduce the reference data in a comparable manner. Both fluxes and stocks can be equally well predicted by either model. However if the models are coinciding on an average basis, they are diverging from a variability prediction point of view. In the Mechanistic model biology adapts much faster to its environment giving rise to higher short term variations. Moreover the seasonal variability in total production differs from the Redfieldian NNPZD-DOM model to the Mechanistic model. In summer the Mechanistic model predicts higher production values in carbon unit than the Redfieldian NNPZD-DOM model. In winter the contrary holds.
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paper_title: Comparison of Data Assimilation Techniques for a Coupled Model of Surface and Subsurface Flow

paper_content:

Data assimilation in the geophysical sciences refers to methodologies to optimally merge model predictions and observations. The ensemble Kalman filter (EnKF) is a statistical sequential data assimilation technique explicitly developed for nonlinear filtering problems. It is based on a Monte Carlo approach that approximates the conditional probability densities of the variables of interest by a finite number of randomly generated model trajectories. In Newtonian relaxation or nudging (NN), which can be viewed as a special case of the classic Kalman filter, model variables are driven toward observations by adding to the model equations a forcing term, or relaxation component, that is proportional to the difference between simulation and observation. The forcing term contains four-dimensional weighting functions that can, ideally, incorporate prior knowledge about the characteristic scales of spatial and temporal variability of the state variable(s) being assimilated. In this study, we examined the EnKF and NN algorithms as implemented for a complex hydrologic model that simulates catchment dynamics, coupling a three-dimensional finite element Richards9 equation solver for variably saturated porous media and a finite difference diffusion wave approximation for surface water flow. We report on the retrieval performance of the two assimilation schemes for a small catchment in Belgium. The results of the comparison show that nudging, while more straightforward and less expensive computationally, is not as effective as the ensemble Kalman filter in retrieving the true system state. We discuss some of the strengths and weaknesses, both physical and numerical, of the NN and EnKF schemes.
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paper_title: Three-dimensional soil moisture profile retrieval by assimilation of near-surface measurements: Simplified Kalman filter covariance forecasting and field application: THREE-DIMENSIONAL SOIL MOISTURE ASSIMILATION

paper_content:

[1] The Kalman filter data assimilation technique is applied to a distributed three-dimensional soil moisture model for retrieval of the soil moisture profile in a 6 ha catchment using near-surface soil moisture measurements. A simplified Kalman filter covariance forecasting methodology is developed based on forecasting of the state correlations and imposed state variances. This covariance forecasting technique, termed the modified Kalman filter, was then used in a 1 month three-dimensional field application. Two updating scenarios were tested: (1) updating every 2 to 3 days and (2) a single update. The data used were from the Nerrigundah field site, near Newcastle, Australia. This study demonstrates the feasibility of data assimilation in a quasi three-dimensional distributed soil moisture model, provided simplified covariance forecasting techniques are used. It also identifies that (1) the soil moisture profile cannot be retrieved from near-surface soil moisture measurements when the near-surface and deep soil layers become decoupled, such as during extreme drying events; (2) if simulation of the soil moisture profile is already good, the assimilation can result in a slight degradation, but if the simulation is poor, assimilation can yield a significant improvement; (3) soil moisture profile retrieval results are independent of initial conditions; and (4) the required update frequency is a function of the errors in model physics and forcing data.
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paper_title: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics

paper_content:

A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The unbounded error growth found in the extended Kalman filter, which is caused by an overly simplified closure in the error covariance equation, is completely eliminated. Open boundaries can be handled as long as the ocean model is well posed. Well-known numerical instabilities associated with the error covariance equation are avoided because storage and evolution of the error covariance matrix itself are not needed. The results are also better than what is provided by the extended Kalman filter since there is no closure problem and the quality of the forecast error statistics therefore improves. The method should be feasible also for more sophisticated primitive equation models. The computational load for reasonable accuracy is only a fraction of what is required for the extended Kalman filter and is given by the storage of, say, 100 model states for an ensemble size of 100 and thus CPU requirements of the order of the cost of 100 model integrations. The proposed method can therefore be used with realistic nonlinear ocean models on large domains on existing computers, and it is also well suited for parallel computers and clusters of workstations where each processor integrates a few members of the ensemble.
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paper_title: Adaptive Ensemble Covariance Localization in Ensemble 4D-VAR State Estimation

paper_content:

An adaptive ensemble covariance localization technique, previously used in ‘‘local’’ forms of the ensemble Kalman filter, is extended to a global ensemble four-dimensional variational data assimilation (4D-VAR) scheme. The purely adaptive part of the localization matrix considered is given by the element-wise square of the correlation matrix of a smoothed ensemble of streamfunction perturbations. It is found that these purely adaptive localization functions have spurious far-field correlations as large as 0.1 with a 128-member ensemble. To attenuate the spurious features of the purely adaptive localization functions, the authors multiply the adaptive localization functions with very broadscale nonadaptive localization functions. Using the Navy’s operational ensemble forecasting system, it is shown that the covariance localization functions obtained by this approach adapt to spatially anisotropic aspects of the flow, move with the flow, and are free of far-field spurious correlations. The scheme is made computationally feasible by (i) a method for inexpensively generating the square root of an adaptively localized global four-dimensional error covariance model in terms of products or modulations of smoothed ensemble perturbations with themselves and with raw ensemble perturbations, and (ii) utilizing algorithms that speed ensemble covariance localization when localization functions are separable, variable-type independent, and/or large scale. In spite of the apparently useful characteristics of adaptive localization, single analysis/forecast experiments assimilating 583 200 observations over both 6- and 12-h data assimilation windows failed to identify any significant difference in the quality of the analyses and forecasts obtained using nonadaptive localization from that obtained using adaptive localization.
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paper_title: Novel approach to nonlinear/non-Gaussian Bayesian state estimation

paper_content:

An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples, which are updated and propagated by the algorithm. The method is not restricted by assumptions of linear- ity or Gaussian noise: it may be applied to any state transition or measurement model. A simula- tion example of the bearings only tracking problem is presented. This simulation includes schemes for improving the efficiency of the basic algorithm. For this example, the performance of the bootstrap filter is greatly superior to the standard extended Kalman filter.
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paper_title: Dual state-parameter estimation of hydrological models using ensemble Kalman filter

paper_content:

Hydrologic models are twofold: models for understanding physical processes and models for prediction. This study addresses the latter, which modelers use to predict, for example, streamflow at some future time given knowledge of the current state of the system and model parameters. In this respect, good estimates of the parameters and state variables are needed to enable the model to generate accurate forecasts. In this paper, a dual state–parameter estimation approach is presented based on the Ensemble Kalman Filter (EnKF) for sequential estimation of both parameters and state variables of a hydrologic model. A systematic approach for identification of the perturbation factors used for ensemble generation and for selection of ensemble size is discussed. The dual EnKF methodology introduces a number of novel features: (1) both model states and parameters can be estimated simultaneously; (2) the algorithm is recursive and therefore does not require storage of all past information, as is the case in the batch calibration procedures; and (3) the various sources of uncertainties can be properly addressed, including input, output, and parameter uncertainties. The applicability and usefulness of the dual EnKF approach for ensemble streamflow forecasting is demonstrated using a conceptual rainfall-runoff model. 2004 Elsevier Ltd. All rights reserved.
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paper_title: Assimilation of Active Microwave Measurements for Soil Moisture Profile Retrieval Under Laboratory Conditions

paper_content:

The authors discuss the potential of retrieving information on the soil moisture profile from measurements of the surface soil moisture content through active microwave observations. They use active microwave observations of the surface soil moisture content in a data assimilation framework to show that this allows the retrieval of the entire soil moisture profile. The data assimilation procedure demonstrated is based on the Kalman filter technique. Kalman filtering allows reconstruction of the state vector when at least part of the state variables are observed regularly. The dynamic model of the system used is based on the 1D Richards equation. The observation equation is based on the integral equation model of A. K. Fung et al. (1992) and is used to link the radar observations to surface soil moisture content. Recently, M. Mancini et al. (1999) reported about laboratory experiments investigating the use of active microwave observations to estimate surface soil moisture content. The present authors apply the data assimilation scheme to the radar measurements of these experiments to retrieve the entire soil moisture profile in the soil sample used, and compare these results with the soil moisture profile measurements (using TDR). It is shown that with a limited number of radar measurements accurate retrieval of the entire soil moisture profile is possible.
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paper_title: Assessment of local hydraulic properties from electrical resistivity tomography monitoring of a three-dimensional synthetic tracer test experiment

paper_content:

[1] In recent years geophysical methods have become increasingly popular for hydrological applications. Time-lapse electrical resistivity tomography (ERT) represents a potentially powerful tool for subsurface solute transport characterization since a full picture of the spatiotemporal evolution of the process can be obtained. However, the quantitative interpretation of tracer tests is difficult because of the uncertainty related to the geoelectrical inversion, the constitutive models linking geophysical and hydrological quantities, and the a priori unknown heterogeneous properties of natural formations. Here an approach based on the Lagrangian formulation of transport and the ensemble Kalman filter (EnKF) data assimilation technique is applied to assess the spatial distribution of hydraulic conductivity K by incorporating time-lapse cross-hole ERT data. Electrical data consist of three-dimensional cross-hole ERT images generated for a synthetic tracer test in a heterogeneous aquifer. Under the assumption that the solute spreads as a passive tracer, for high Peclet numbers the spatial moments of the evolving plume are dominated by the spatial distribution of the hydraulic conductivity. The assimilation of the electrical conductivity 4D images allows updating of the hydrological state as well as the spatial distribution of K. Thus, delineation of the tracer plume and estimation of the local aquifer heterogeneity can be achieved at the same time by means of this interpretation of time-lapse electrical images from tracer tests. We assess the impact on the performance of the hydrological inversion of (i) the uncertainty inherently affecting ERT inversions in terms of tracer concentration and (ii) the choice of the prior statistics of K. Our findings show that realistic ERT images can be integrated into a hydrological model even within an uncoupled inverse modeling framework. The reconstruction of the hydraulic conductivity spatial distribution is satisfactory in the portion of the domain directly covered by the passage of the tracer. Aside from the issues commonly affecting inverse models, the proposed approach is subject to the problem of the filter inbreeding and the retrieval performance is sensitive to the choice of K prior geostatistical parameters.
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paper_title: An Ensemble Kalman Smoother for Nonlinear Dynamics

paper_content:

It is formally proved that the general smoother for nonlinear dynamics can be formulated as a sequential method, that is, observations can be assimilated sequentially during a forward integration. The general filter can be derived from the smoother and it is shown that the general smoother and filter solutions at the final time become identical, as is expected from linear theory. Then, a new smoother algorithm based on ensemble statistics is presented and examined in an example with the Lorenz equations. The new smoother can be computed as a sequential algorithm using only forward-in-time model integrations. It bears a strong resemblance with the ensemble Kalman filter. The difference is that every time a new dataset is available during the forward integration, an analysis is computed for all previous times up to this time. Thus, the first guess for the smoother is the ensemble Kalman filter solution, and the smoother estimate provides an improvement of this, as one would expect a smoother to do. The method is demonstrated in this paper in an intercomparison with the ensemble Kalman filter and the ensemble smoother introduced by van Leeuwen and Evensen, and it is shown to be superior in an application with the Lorenz equations. Finally, a discussion is given regarding the properties of the analysis schemes when strongly non-Gaussian distributions are used. It is shown that in these cases more sophisticated analysis schemes based on Bayesian statistics must be used.
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paper_title: Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation

paper_content:

Hydrologic models use relatively simple mathematical equations to conceptualize and aggregate the complex, spatially distributed, and highly interrelated water, energy, and vegetation processes in a watershed. A consequence of process aggregation is that the model parameters often do not represent directly measurable entities and must therefore be estimated using measurements of the system inputs and outputs. During this process, known as model calibration, the parameters are adjusted so that the behavior of the model approximates, as closely and consistently as possible, the observed response of the hydrologic system over some historical period of time. In practice, however, because of errors in the model structure and the input (forcing) and output data, this has proven to be difficult, leading to considerable uncertainty in the model predictions. This paper surveys the limitations of current model calibration methodologies, which treat the uncertainty in the input-output relationship as being primarily attributable to uncertainty in the parameters and presents a simultaneous optimization and data assimilation (SODA) method, which improves the treatment of uncertainty in hydrologic modeling. The usefulness and applicability of SODA is demonstrated by means of a pilot study using data from the Leaf River watershed in Mississippi and a simple hydrologic model with typical conceptual components.
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paper_title: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics

paper_content:

A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The unbounded error growth found in the extended Kalman filter, which is caused by an overly simplified closure in the error covariance equation, is completely eliminated. Open boundaries can be handled as long as the ocean model is well posed. Well-known numerical instabilities associated with the error covariance equation are avoided because storage and evolution of the error covariance matrix itself are not needed. The results are also better than what is provided by the extended Kalman filter since there is no closure problem and the quality of the forecast error statistics therefore improves. The method should be feasible also for more sophisticated primitive equation models. The computational load for reasonable accuracy is only a fraction of what is required for the extended Kalman filter and is given by the storage of, say, 100 model states for an ensemble size of 100 and thus CPU requirements of the order of the cost of 100 model integrations. The proposed method can therefore be used with realistic nonlinear ocean models on large domains on existing computers, and it is also well suited for parallel computers and clusters of workstations where each processor integrates a few members of the ensemble.
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paper_title: Surface-subsurface flow modeling with path-based runoff routing, boundary condition-based coupling, and assimilation of multisource observation data

paper_content:

Received 21 October 2008; revised 2 September 2009; accepted 16 September 2009; published 13 February 2010. [1] A distributed physically based model incorporating novel approaches for the representation of surface-subsurface processes and interactions is presented. A path-based description of surface flow across the drainage basin is used, with several options for identifying flow directions, for separating channel cells from hillslope cells, and for representing stream channel hydraulic geometry. Lakes and other topographic depressions are identified and specially treated as part of the preprocessing procedures applied to the digital elevation data for the catchment. Threshold-based boundary condition switching is used to partition potential (atmospheric) fluxes into actual fluxes across the land surface and changes in surface storage, thus resolving the exchange fluxes, or coupling, between the surface and subsurface modules. Nested time stepping allows smaller steps to be taken for typically faster and explicitly solved surface runoff routing, while a mesh coarsening option allows larger grid elements to be used for typically slower and more compute-intensive subsurface flow. Sequential data assimilation schemes allow the model predictions to be updated with spatiotemporal observation data of surface and subsurface variables. These approaches are discussed in detail, and the physical and numerical behavior of the model is illustrated over catchment scales ranging from 0.0027 to 356 km 2 , addressing different hydrological processes and highlighting the importance of describing coupled surfacesubsurface flow.
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paper_title: Hydrologic Data Assimilation with the Ensemble Kalman Filter

paper_content:

Soil moisture controls the partitioning of moisture and energy fluxes at the land surface and is a key variable in weather and climate prediction. The performance of the ensemble Kalman filter (EnKF) for soil moisture estimation is assessed by assimilating L-band (1.4 GHz) microwave radiobrightness observations into a land surface model. An optimal smoother (a dynamic variational method) is used as a benchmark for evaluating the filter’s performance. In a series of synthetic experiments the effect of ensemble size and non-Gaussian forecast errors on the estimation accuracy of the EnKF is investigated. With a state vector dimension of 4608 and a relatively small ensemble size of 30 (or 100; or 500), the actual errors in surface soil moisture at the final update time are reduced by 55% (or 70%; or 80%) from the value obtained without assimilation (as compared to 84% for the optimal smoother). For robust error variance estimates, an ensemble of at least 500 members is needed. The dynamic evolution of the estimation error variances is dominated by wetting and drying events with high variances during drydown and low variances when the soil is either very wet or very dry. Furthermore, the ensemble distribution of soil moisture is typically symmetric except under very dry or wet conditions when the effects of the nonlinearities in the model become significant. As a result, the actual errors are consistently larger than ensemble-derived forecast and analysis error variances. This suggests that the update is suboptimal. However, the degree of suboptimality is relatively small and results presented here indicate that the EnKF is a flexible and robust data assimilation option that gives satisfactory estimates even for moderate ensemble sizes.
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paper_title: Data assimilation for transient flow in geologic formations via ensemble Kalman filter

paper_content:

Formation properties are one of the key factors in numerical modeling of flow and transport in geologic formations in spite of the fact that they may not be completely characterized. The incomplete knowledge or uncertainty in the description of the formation properties leads to uncertainty in simulation results. In this study, the ensemble Kalman filter (EnKF) approach is used for continuously updating model parameters such as hydraulic conductivity and model variables such as pressure head while simultaneously providing an estimate of the uncertainty through assimilating dynamic and static measurements, without resorting to the explicit computation of the covariance or the Jacobian of the state variables. A two-dimensional example is built to demonstrate the capability of EnKF and to analyze its sensitivity with respect to different factors such as the number of realizations, measurement timings, and initial guesses. An additional example is given to illustrate the applicability of EnKF to three-dimensional problems and to examine the model predictability after dynamic data assimilation. It is found from these examples that EnKF provides an efficient approach for obtaining satisfactory estimation of the hydraulic conductivity field with dynamic measurements. After data assimilation the conductivity field matches the reference field very well, and different kinds of incorrect prior knowledge of the formation properties may also be rectified to a certain extent.
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paper_title: An Iterative Ensemble Kalman Filter for Multiphase Fluid Flow Data Assimilation

paper_content:

Summary The dynamical equations for multiphase flow in porous media are highly non-linear and the number of variables required to characterize the medium is usually large, often two or more variables per simulator gridblock. Neither the extended Kalman filter nor the ensemble Kalman filter is suitable for assimilating data or for characterizing uncertainty for this type of problem. Although the ensemble Kalman filter handles the nonlinear dynamics correctly during the forecast step, it sometimes fails badly in the analysis (or updating) of saturations. This paper focuses on the use of an iterative ensemble Kalman filter for data assimilation in nonlinear problems, especially of the type related to multiphase flow in porous media. Two issues are key: (1) iteration to enforce constraints and (2) ensuring that the resulting ensemble is representative of the conditional pdf (i.e. that the uncertainty quantification is correct). The new algorithm is compared to the ensemble Kalman filter on several highly nonlinear example problems, and shown to be superior in the prediction of uncertainty.
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paper_title: A new data assimilation approach for improving runoff prediction using remotely-sensed soil moisture retrievals

paper_content:

A number of recent studies have focused on enhancing runoff prediction via the assimilation of remotely-sensed surface soil moisture retrievals into a hydrologic model. The majority of these approaches have viewed the problem from purely a state or parameter estimation perspective in which remotely-sensed soil moisture estimates are assimilated to improve the characterization of pre-storm soil moisture conditions in a hydrologic model, and consequently, its simulation of runoff response to subsequent rainfall. However, recent work has demonstrated that soil moisture retrievals can also be used to filter errors present in satellite-based rainfall accumulation products. This result implies that soil moisture retrievals have potential benefit for characterizing both antecedent moisture conditions (required to estimate sub-surface flow intensities and subsequent surface runoff efficiencies) and storm-scale rainfall totals (required to estimate the total surface runoff volume). In response, this work presents a new sequential data assimilation system that exploits remotely-sensed surface soil moisture retrievals to simultaneously improve estimates of both pre-storm soil moisture conditions and storm-scale rainfall accumulations. Preliminary testing of the system, via a synthetic twin data assimilation experiment based on the Sacramento hydrologic model and data collected from the Model Parameterization Experiment, suggests that the new approach is more efficient at improving stream flow predictions than data assimilation techniques focusing solely on the constraint of antecedent soil moisture conditions.
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paper_title: Surface heat flux estimation with the ensemble Kalman smoother: Joint estimation of state and parameters: ESTIMATION OF SURFACE FLUXES WITH ENKS

paper_content:

[1] The estimation of surface heat fluxes based on the assimilation of land surface temperature (LST) has been achieved within a variational data assimilation (VDA) framework. Variational approaches require the development of an adjoint model, which is difficult to derive and code in the presence of thresholds and discontinuities. Also, it is computationally expensive to obtain the background error covariance for the variational approaches. Moreover, the variational schemes cannot directly provide statistical information on the accuracy of their estimates. To overcome these shortcomings, we develop an alternative data assimilation (DA) procedure based on ensemble Kalman smoother (EnKS) with the state augmentation method. The unknowns of the assimilation scheme are neutral turbulent heat transfer coefficient (that scales the sum of turbulent heat fluxes) and evaporative fraction, EF (that represents partitioning among the turbulent fluxes). The new methodology is illustrated with an application to the First International Satellite Land Surface Climatology Project Field Experiment (FIFE) that includes areal average hydrometeorological forcings and flux observations. The results indicate that the EnKS model not only provides reasonably accurate estimates of EF and turbulent heat fluxes but also enables us to determine the uncertainty of estimations under various land surface hydrological conditions. The results of the EnKS model are also compared with those of an optimal smoother (a dynamic variational model). It is found that the EnKS model estimates are less than optimal. However, the degree of suboptimality is small, and its outcomes are roughly comparable to those of an optimal smoother. Overall, the results from this test indicate that EnKS is an efficient and flexible data assimilation procedure that is able to extract useful information on the partitioning of available surface energy from LST measurements and eventually provides reliable estimates of turbulent heat fluxes.
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paper_title: Advanced Data Assimilation for Strongly Nonlinear Dynamics

paper_content:

Advanced data assimilation methods become extremely complicated and challenging when used with strongly nonlinear models. Several previous works have reported various problems when applying existing popular data assimilation techniques with strongly nonlinear dynamics. Common for these techniques is that they can all be considered as extensions to methods that have proved to work well with linear dynamics. This paper examines the properties of three advanced data assimilation methods when used with the highly nonlinear Lorenz equations. The ensemble Kalman filter is used for sequential data assimilation and the recently proposed ensemble smoother method and a gradient descent method are used to minimize two different weak constraint formulations. The problems associated with the use of an approximate tangent linear model when solving the Euler‐Lagrange equations, or when the extended Kalman filter is used, are eliminated when using these methods. All three methods give reasonable consistent results with the data coverage and quality of measurements that are used here and overcome the traditional problems reported in many of the previous papers involving data assimilation with highly nonlinear dynamics.
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paper_title: The ensemble Kalman filter for combined state and parameter estimation: MONTE CARLO TECHNIQUES FOR DATA ASSIMILATION IN LARGE SYSTEMS

paper_content:

he ensemble Kalman filter (EnKF) [1] is a sequential Monte Carlo method that provides an alternative to the traditional Kalman filter (KF) [2], [3] and adjoint or four-dimensional variational (4DVAR) methods [4]-[6] to better handle large state spaces and nonlinear error evolution. EnKF provides a simple conceptual formulation and ease of implementation, since.
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paper_title: Impact of Multiresolution Active and Passive Microwave Measurements on Soil Moisture Estimation Using the Ensemble Kalman Smoother

paper_content:

An observing system simulation experiment is developed to test tradeoffs in resolution and accuracy for soil moisture estimation using active and passive L-band remote sensing. Concepts for combined radar and radiometer missions include designs that will provide multiresolution measurements. In this paper, the scientific impacts of instrument performance are analyzed to determine the measurement requirements for the mission concept. The ensemble Kalman smoother (EnKS) is used to merge these multiresolution observations with modeled soil moisture from a land surface model to estimate surface and subsurface soil moisture at 6-km resolution. The model used for assimilation is different from that used to generate "truth." Consequently, this experiment simulates how data assimilation performs in real applications when the model is not a perfect representation of reality. The EnKS is an extension of the ensemble Kalman filter (EnKF) in which observations are used to update states at previous times. Previous work demonstrated that it provides a computationally inexpensive means to improve the results from the EnKF, and that the limited memory in soil moisture can be exploited by employing it as a fixed lag smoother. Here, it is shown that the EnKS can be used in large problems with spatially distributed state vectors and spatially distributed multiresolution observations. The EnKS-based data assimilation framework is used to study the synergy between passive and active observations that have different resolutions and measurement error distributions. The extent to which the design parameters of the EnKS vary depending on the combination of observations assimilated is investigated
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paper_title: Land surface state and flux estimation using the ensemble Kalman smoother during the Southern Great Plains 1997 field experiment

paper_content:

[1] The ensemble Kalman smoother (EnKS) is employed to estimate surface and subsurface soil moisture and surface energy fluxes during the Southern Great Plains 1997 (SGP97) experiment through the assimilation of observed L band radiobrightness temperatures. Previous work using the ensemble Kalman filter (EnKF) and a simple smoother demonstrated that soil moisture estimation is a reanalysis-type problem. The EnKF uses observations as they become available to update the current state. The EnKS takes the EnKF estimate as its first guess. However, in addition to updating the current state it also updates the best estimate at previous times. The performance of the EnKS is compared to the EnKF and the ensemble open loop in which no measurements are assimilated. Estimated surface soil moisture is compared to gravimetric observations at three locations. Root zone (5–100 cm) soil moisture is evaluated by comparing the resultant latent heat flux to flux tower observations. In a fixed lag smoother, observations are used to update past estimates within a fixed time window. The EnKS can be implemented in a fixed lag formulation in problems with limited memory such as soil moisture estimation. It is shown that there is a trade-off to be made between the improved accuracy with longer lag and the increased computational cost incurred. It is demonstrated that the EnKS is a relatively inexpensive state estimation algorithm suited to operational data assimilation.
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paper_title: Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation

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Abstract The weak constraint inverse for nonlinear dynamical models is discussed and derived in term of a probabilistic formulation. The well-known result that for Gaussian error statistics the minimum of the weak constraint inverse is equal to the maximum-likelihood estimate is rederived. Then several methods based on ensemble statistics that can be used to find the smoother (as opposed to the filter) solution are introduced and compared to traditional methods. A strong point of the new methods is that they avoid the integration of adjoint equations, which is a complex task for real oceanographic or atmospheric applications. They also avoid iterative searches in a Hilbert space, and error estimates can be obtained without much additional computational effort. The feasibility of the new methods is illustrated in a two-layer quasigeostrophic ocean model.
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paper_title: A review on reflective remote sensing and data assimilation techniques for enhanced agroecosystem modeling

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Abstract During the last 50 years, the management of agroecosystems has been undergoing major changes to meet the growing demand for food, timber, fibre and fuel. As a result of this intensified use, the ecological status of many agroecosystems has been severely deteriorated. Modeling the behavior of agroecosystems is, therefore, of great help since it allows the definition of management strategies that maximize (crop) production while minimizing the environmental impacts. Remote sensing can support such modeling by offering information on the spatial and temporal variation of important canopy state variables which would be very difficult to obtain otherwise. In this paper, we present an overview of different methods that can be used to derive biophysical and biochemical canopy state variables from optical remote sensing data in the VNIR-SWIR regions. The overview is based on an extensive literature review where both statistical–empirical and physically based methods are discussed. Subsequently, the prevailing techniques of assimilating remote sensing data into agroecosystem models are outlined. The increasing complexity of data assimilation methods and of models describing agroecosystem functioning has significantly increased computational demands. For this reason, we include a short section on the potential of parallel processing to deal with the complex and computationally intensive algorithms described in the preceding sections. The studied literature reveals that many valuable techniques have been developed both for the retrieval of canopy state variables from reflective remote sensing data as for assimilating the retrieved variables in agroecosystem models. However, for agroecosystem modeling and remote sensing data assimilation to be commonly employed on a global operational basis, emphasis will have to be put on bridging the mismatch between data availability and accuracy on one hand, and model and user requirements on the other. This could be achieved by integrating imagery with different spatial, temporal, spectral, and angular resolutions, and the fusion of optical data with data of different origin, such as LIDAR and radar/microwave.
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paper_title: Assimilating remotely sensed snow observations into a macroscale hydrology model

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Abstract Accurate forecasting of snow properties is important for effective water resources management, especially in mountainous areas like the western United States. Current model-based forecasting approaches are limited by model biases and input data uncertainties. Remote sensing offers an opportunity for observation of snow properties, like areal extent and water equivalent, over larger areas. Data assimilation provides a framework for optimally merging information from remotely sensed observations and hydrologic model predictions. An ensemble Kalman filter (EnKF) was used to assimilate remotely sensed snow observations into the variable infiltration capacity (VIC) macroscale hydrologic model over the Snake River basin. The snow cover extent (SCE) product from the moderate resolution imaging spectroradiometer (MODIS) flown on the NASA Terra satellite was used to update VIC snow water equivalent (SWE), for a period of four consecutive winters (1999–2003). A simple snow depletion curve model was used for the necessary SWE–SCE inversion. The results showed that the EnKF is an effective and operationally feasible solution; the filter successfully updated model SCE predictions to better agree with the MODIS observations and ground surface measurements. Comparisons of the VIC SWE estimates following updating with surface SWE observations (from the NRCS SNOTEL network) indicated that the filter performance was a modest improvement over the open-loop (un-updated) simulations. This improvement was more evident for lower to middle elevations, and during snowmelt, while during accumulation the filter and open-loop estimates were very close on average. Subsequently, a preliminary assessment of the potential for assimilating the SWE product from the advanced microwave scanning radiometer (AMSR-E, flown on board the NASA Aqua satellite) was conducted. The results were not encouraging, and appeared to reflect large errors in the AMSR-E SWE product, which were also apparent in comparisons with SNOTEL data.
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paper_title: Identification of time-variant river bed properties with the ensemble Kalman filter

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[1] An adequate characterization of river bed hydraulic conductivities (L) is crucial for a proper assessment of river-aquifer interactions. However, river bed characteristics may change over time due to dynamic morphological processes like scouring or sedimentation what can lead to erroneous model predictions when static leakage parameters are assumed. Sequential data assimilation with the ensemble Kalman filter (EnKF) allows for an update of model parameters in real-time and may thus be capable of assessing the transient behavior of L. Synthetic experiments with a three-dimensional finite element model of the Limmat aquifer in Zurich were used to assess the performance of data assimilation in capturing time-variant river bed properties. Reference runs were generated where L followed different temporal and/or spatial patterns which should mimic real-world sediment dynamics. Hydraulic head (h) data from these reference runs were then used as input data for EnKF which jointly updated h and L. Results showed that EnKF is able to capture the different spatio-temporal patterns of L in the reference runs well. However, the adaptation time was relatively long which was attributed to the fast decrease of ensemble variance. To improve the performance of EnKF also an adaptive filtering approach with covariance inflation was applied that allowed a faster and more accurate adaptation of model parameters. A sensitivity analysis indicated that even for a low amount of observations a reasonable adaptation of L towards the reference values can be achieved and that EnKF is also able to correct for a biased initial ensemble of L.
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paper_title: Land data assimilation and estimation of soil moisture using measurements from the Southern Great Plains 1997 Field Experiment

paper_content:

Remotely sensed microwave measurements provide useful but indirect observations of surface soil moisture. Ground-based measurements are more direct but are very localized and limited in coverage. Model predictions providea more regional perspective but rely on many simplifications and approximations and depend on inputs that are difficult to obtain over extensive areas. The only effective way to achieve soil moisture estimates with the accuracy and coverage required for hydrologic and meteorological applications is to merge information from satellites, ground-based stations, and models. In this paper we describe a convenient data merging (or data assimilation) procedure based on an ensemble Kalman filter. This procedure is illustrated with an application to the Southern Great Plains 1997 (SGP97) field experiment. It uses land surface and radiative transfer models to derive soil moisture estimates from airborne L band microwave observations and ground-based measurements of micrometeorological variables, soil texture, and vegetation type. The ensemble filter approach is appealing because (1) it can accommodate a wide range of models, (2) it can account for input and measurement uncertainties, (3) it provides information on the accuracy of its estimates, and (4) it is relatively efficient, making large-scale applications feasible. Results from our SGP97 application of the ensemble Kalman filter include large-scale maps (∼10,000 km 2 ) of soil moisture estimates and estimation error standard deviations for the entire month long experiment and comparisons of filter soil moisture and latent heat estimates to ground truth measurements (gravimetric and flux tower observations). The ground truth comparisons show that the filter is able to track soil moisture fluctuations. The filter estimates are significantly better than those from an "open loop" simulation that includes the same ground-based data but does not incorporate radio brightness measurements. Overall, the results from this field test indicate that the ensemble Kalman filter is an accurate, efficient, and flexible data assimilation procedure that is able to extract useful information from remote sensing measurements.
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paper_title: Dual state-parameter estimation of hydrological models using ensemble Kalman filter

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Hydrologic models are twofold: models for understanding physical processes and models for prediction. This study addresses the latter, which modelers use to predict, for example, streamflow at some future time given knowledge of the current state of the system and model parameters. In this respect, good estimates of the parameters and state variables are needed to enable the model to generate accurate forecasts. In this paper, a dual state–parameter estimation approach is presented based on the Ensemble Kalman Filter (EnKF) for sequential estimation of both parameters and state variables of a hydrologic model. A systematic approach for identification of the perturbation factors used for ensemble generation and for selection of ensemble size is discussed. The dual EnKF methodology introduces a number of novel features: (1) both model states and parameters can be estimated simultaneously; (2) the algorithm is recursive and therefore does not require storage of all past information, as is the case in the batch calibration procedures; and (3) the various sources of uncertainties can be properly addressed, including input, output, and parameter uncertainties. The applicability and usefulness of the dual EnKF approach for ensemble streamflow forecasting is demonstrated using a conceptual rainfall-runoff model. 2004 Elsevier Ltd. All rights reserved.
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paper_title: Assimilation of GRACE Terrestrial Water Storage Data into a Land Surface Model: Results for the Mississippi River Basin

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Abstract Assimilation of data from the Gravity Recovery and Climate Experiment (GRACE) system of satellites yielded improved simulation of water storage and fluxes in the Mississippi River basin, as evaluated against independent measurements. The authors assimilated GRACE-derived monthly terrestrial water storage (TWS) anomalies for each of the four major subbasins of the Mississippi into the Catchment Land Surface Model (CLSM) using an ensemble Kalman smoother from January 2003 to May 2006. Compared with the open-loop CLSM simulation, assimilation estimates of groundwater variability exhibited enhanced skill with respect to measured groundwater in all four subbasins. Assimilation also significantly increased the correlation between simulated TWS and gauged river flow for all four subbasins and for the Mississippi River itself. In addition, model performance was evaluated for eight smaller watersheds within the Mississippi basin, all of which are smaller than the scale of GRACE observations. In seven of e...
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paper_title: Hydrological data assimilation with the ensemble Kalman filter: Use of streamflow observations to update states in a distributed hydrological model

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This paper describes an application of the ensemble Kalman filter (EnKF) in which streamflow observations are used to update states in a distributed hydrological model. We demonstrate that the standard implementation of the EnKF is inappropriate because of non-linear relationships between model states and observations. Transforming streamflow into log space before computing error covariances improves filter performance. We also demonstrate that model simulations improve when we use a variant of the EnKF that does not require perturbed observations. Our attempt to propagate information to neighbouring basins was unsuccessful, largely due to inadequacies in modelling the spatial variability of hydrological processes. New methods are needed to produce ensemble simulations that both reflect total model error and adequately simulate the spatial variability of hydrological states and fluxes.
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paper_title: The assimilation of remotely sensed soil brightness temperature imagery into a land surface model using Ensemble Kalman filtering: a case study based on ESTAR measurements during SGP97

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An Ensemble Kalman filter (EnKF) is used to assimilate airborne measurements of 1.4 GHz surface brightness temperature ðTBÞ acquired during the 1997 Southern Great Plains Hydrology Experiment (SGP97) into the TOPMODEL-based Land–Atmosphere Transfer Scheme (TOPLATS). In this way, the potential of using EnKF-assimilated remote measurements of TB to compensate land surface model predictions for errors arising from a climatological description of rainfall is assessed. The use of a real remotely sensed data source allows for a more complete examination of the challenges faced in implementing assimilation strategies than previous studies where observations were synthetically generated. Results demonstrate that the EnKF is an effective and computationally competitive strategy for the assimilation of remotely sensed TB measurements into land surface models. The EnKF is capable of extracting spatial and temporal trends in root-zone (40 cm) soil water content from TB measurements based solely on surface (5 cm) conditions. The accuracy of surface state and flux predictions made with the EnKF, ESTAR TB measurements, and climatological rainfall data within the Central Facility site during SGP97 are shown to be superior to predictions derived from open loop modeling driven by sparse temporal sampling of rainfall at frequencies consistent with expectations of future missions designed to measure rainfall from space (6–10 observations per day). Specific assimilation challenges posed by inadequacies in land surface model physics and spatial support contrasts between model predictions and sensor retrievals are discussed. 2002 Elsevier Science Ltd. All rights reserved.
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paper_title: Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation

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This review discusses recent advances in geophysical data assimilation beyond Gaussian statistical modeling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The non-Gaussian features are stressed rather than the nonlinearity of the dynamical models, although both aspects are entangled. Ideas recently proposed to deal with these non-Gaussian issues, in order to improve the state or parameter estimation, are emphasized. The general Bayesian solution to the estimation problem and the techniques to solve it are first presented, as well as the obstacles that hinder their use in high-dimensional and complex systems. Approximations to the Bayesian solution relying on Gaussian, or on second-order moment closure, have been wholly adopted in geophysical data assimilation (e.g., Kalman filters and quadratic variational solutions). Yet, nonlinear and non-Gaussian effects remain. They essentially originate in the nonlinear models and in the non-Gaussian priors. How these effects are handled within algorithms based on Gaussian assumptions is then described. Statistical tools that can diagnose them and measure deviations from Gaussianity are recalled. The following advanced techniques that seek to handle the estimation problem beyond Gaussianity are reviewed: maximum entropy filter, Gaussian anamorphosis, non-Gaussian priors, particle filter with an ensemble Kalman filter as a proposal distribution, maximum entropy on the mean, or strictly Bayesian inferences for large linear models, etc. Several ideas are illustrated with recent or original examples that possess some features of high-dimensional systems. Many of the new approaches are well understood only in special cases and have difficulties that remain to be circumvented. Some of the suggested approaches are quite promising, and sometimes already successful for moderately large though specific geophysical applications. Hints are given as to where progress might come from.
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paper_title: Particle Filters for State Estimation of Jump Markov Linear Systems

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Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. In this paper, our aim is to recursively compute optimal state estimates for this class of systems. We present efficient simulation-based algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixed-lag smoothing problem. Our algorithms combine sequential importance sampling, a selection scheme, and Markov chain Monte Carlo methods. They use several variance reduction methods to make the most of the statistical structure of JMLS. Computer simulations are carried out to evaluate the performance of the proposed algorithms. The problems of on-line deconvolution of impulsive processes and of tracking a maneuvering target are considered. It is shown that our algorithms outperform the current methods.
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paper_title: Estimation of regional terrestrial water cycle using multi-sensor remote sensing observations and data assimilation

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Abstract An integrated data assimilation system is implemented over the Red-Arkansas river basin to estimate the regional scale terrestrial water cycle driven by multiple satellite remote sensing data. These satellite products include the Tropical Rainfall Measurement Mission (TRMM), TRMM Microwave Imager (TMI), and Moderate Resolution Imaging Spectroradiometer (MODIS). Also, a number of previously developed assimilation techniques, including the ensemble Kalman filter (EnKF), the particle filter (PF), the water balance constrainer, and the copula error model, and as well as physically based models, including the Variable Infiltration Capacity (VIC), the Land Surface Microwave Emission Model (LSMEM), and the Surface Energy Balance System (SEBS), are tested in the water budget estimation experiments. This remote sensing based water budget estimation study is evaluated using ground observations driven model simulations. It is found that the land surface model driven by the bias-corrected TRMM rainfall produces reasonable water cycle states and fluxes, and the estimates are moderately improved by assimilating TMI 10.67 GHz microwave brightness temperature measurements that provides information on the surface soil moisture state, while it remains challenging to improve the results by assimilating evapotranspiration estimated from satellite-based measurements.
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paper_title: The ensemble Kalman filter for combined state and parameter estimation: MONTE CARLO TECHNIQUES FOR DATA ASSIMILATION IN LARGE SYSTEMS

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he ensemble Kalman filter (EnKF) [1] is a sequential Monte Carlo method that provides an alternative to the traditional Kalman filter (KF) [2], [3] and adjoint or four-dimensional variational (4DVAR) methods [4]-[6] to better handle large state spaces and nonlinear error evolution. EnKF provides a simple conceptual formulation and ease of implementation, since.
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paper_title: FLUXNET: A New Tool to Study the Temporal and Spatial Variability of Ecosystem–Scale Carbon Dioxide, Water Vapor, and Energy Flux Densities

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FLUXNET is a global network of micrometeorological flux measurement sites that measure the exchanges of carbon dioxide, water vapor, and energy between the biosphere and atmosphere. At present over 140 sites are operating on a long-term and continuous basis. Vegetation under study includes temperate conifer and broadleaved (deciduous and evergreen) forests, tropical and boreal forests, crops, grasslands, chaparral, wetlands, and tundra. Sites exist on five continents and their latitudinal distribution ranges from 70°N to 30°S. FLUXNET has several primary functions. First, it provides infrastructure for compiling, archiving, and distributing carbon, water, and energy flux measurement, and meteorological, plant, and soil data to the science community. (Data and site information are available online at the FLUXNET Web site, http://www-eosdis.ornl.gov/FLUXNET/.) Second, the project supports calibration and flux intercomparison activities. This activity ensures that data from the regional networks are intercomparable. And third, FLUXNET supports the synthesis, discussion, and communication of ideas and data by supporting project scientists, workshops, and visiting scientists. The overarching goal is to provide information for validating computations of net primary productivity, evaporation, and energy absorption that are being generated by sensors mounted on the NASA Terra satellite. Data being compiled by FLUXNET are being used to quantify and compare magnitudes and dynamics of annual ecosystem carbon and water balances, to quantify the response of stand-scale carbon dioxide and water vapor flux densities to controlling biotic and abiotic factors, and to validate a hierarchy of soil–plant–atmosphere trace gas exchange models. Findings so far include 1) net CO 2 exchange of temperate broadleaved forests increases by about 5.7 g C m −2 day −1 for each additional day that the growing season is extended; 2) the sensitivity of net ecosystem CO 2 exchange to sunlight doubles if the sky is cloudy rather than clear; 3) the spectrum of CO 2 flux density exhibits peaks at timescales of days, weeks, and years, and a spectral gap exists at the month timescale; 4) the optimal temperature of net CO 2 exchange varies with mean summer temperature; and 5) stand age affects carbon dioxide and water vapor flux densities.
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paper_title: Monte Carlo simulations on adsorptions of benzene and xylenes in sodium-Y zeolites

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Abstract The structures of benzene and C8 isomers ( o -xylene, m -xylene, p -xylene) in NaY simulated by the canonical Monte Carlo method were in good agreement with the experimental data of the available neutron diffraction analysis. All these sorbed compounds are stacked through the aromatic π-electron interaction on the cation of the SII site in the Sodium-Y. The experimental adsorption order ( m -xylene > o -xylene > p -xylene) of xylene isomers in the faujasite was also in good agreement with the order obtained from calculated heats of adsorption. It was shown that the difference in the interaction between the 4-ring sites and the methyl groups of xylene caused the better adsorption of m -xylene compared to those of the others. From these results, our conclusion is that the adsorption of the C8 isomers in the faujasite can be explained by considering only the interaction between the zeolite framework and the adsorbate approximated as a rigid model. Moreover, this type of simulation proved to be very useful to understand the mechanism of the adsorption of aromatic compounds in zeolites like faujasites.
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paper_title: Coupled hydrogeophysical parameter estimation using a sequential Bayesian approach

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Abstract. Coupled hydrogeophysical methods infer hydrological and petrophysical parameters directly from geophysical measurements. Widespread methods do not explicitly recognize uncertainty in parameter estimates. Therefore, we apply a sequential Bayesian framework that provides updates of state, parameters and their uncertainty whenever measurements become available. We have coupled a hydrological and an electrical resistivity tomography (ERT) forward code in a particle filtering framework. First, we analyze a synthetic data set of lysimeter infiltration monitored with ERT. In a second step, we apply the approach to field data measured during an infiltration event on a full-scale dike model. For the synthetic data, the water content distribution and the hydraulic conductivity are accurately estimated after a few time steps. For the field data, hydraulic parameters are successfully estimated from water content measurements made with spatial time domain reflectometry and ERT, and the development of their posterior distributions is shown.
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paper_title: Novel approach to nonlinear/non-Gaussian Bayesian state estimation

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An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples, which are updated and propagated by the algorithm. The method is not restricted by assumptions of linear- ity or Gaussian noise: it may be applied to any state transition or measurement model. A simula- tion example of the bearings only tracking problem is presented. This simulation includes schemes for improving the efficiency of the basic algorithm. For this example, the performance of the bootstrap filter is greatly superior to the standard extended Kalman filter.
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paper_title: Data assimilation methods in the Earth sciences

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Abstract Although remote sensing data are often plentiful, they do not usually satisfy the users’ needs directly. Data assimilation is required to extract information about geophysical fields of interest from the remote sensing observations and to make the data more accessible to users. Remote sensing may provide, for example, measurements of surface soil moisture, snow water equivalent, snow cover, or land surface (skin) temperature. Data assimilation can then be used to estimate variables that are not directly observed from space but are needed for applications, for instance root zone soil moisture or land surface fluxes. The paper provides a brief introduction to modern data assimilation methods in the Earth sciences, their applications, and pertinent research questions. Our general overview is readily accessible to hydrologic remote sensing scientists. Within the general context of Earth science data assimilation, we point to examples of the assimilation of remotely sensed observations in land surface hydrology.
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paper_title: Sequential Imputations and Bayesian Missing Data Problems

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Abstract For missing data problems, Tanner and Wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors. Their method of constructing the complete data sets is closely related to the Gibbs sampler. Both required iterations, and, similar to the EM algorithm, convergence can be slow. We introduce in this article an alternative procedure that involves imputing the missing data sequentially and computing appropriate importance sampling weights. In many applications this new procedure works very well without the need for iterations. Sensitivity analysis, influence analysis, and updating with new data can be performed cheaply. Bayesian prediction and model selection can also be incorporated. Examples taken from a wide range of applications are used for illustration.
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paper_title: Simultaneous estimation of both soil moisture and model parameters using particle filtering method through the assimilation of microwave signal

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[1] Soil moisture is a very important variable in land surface processes. Both field moisture measurements and estimates from modeling have their limitations when being used to estimate soil moisture on a large spatial scale. Remote sensing is becoming a practical method to estimate soil moisture globally; however, the quality of current soil surface moisture products needs to be improved in order to meet practical requirements. Data assimilation (DA) is a promising approach to merge model dynamics and remote sensing observations, thus having the potential to estimate soil moisture more accurately. In this study, a data assimilation algorithm, which couples the particle filter and the kernel smoothing technique, is presented to estimate soil moisture and soil parameters from microwave signals. A simple hydrological model with a daily time step is utilized to reduce the computational burden in the process of data assimilation. An observation operator based on the ratio of two microwave brightness temperatures at different frequencies is designed to link surface soil moisture with remote sensing measurements, and a sensitivity analysis of this operator is also conducted. Additionally, a variant of particle filtering method is developed for the joint estimation of soil moisture and soil parameters such as texture and porosity. This assimilation scheme is validated against field moisture measurements at the CEOP/Mongolia experiment site and is found to estimate near-surface soil moisture very well. The retrieved soil texture still contains large uncertainties as the retrieved values cannot converge to fixed points or narrow ranges when using different initial soil texture values, but the retrieved soil porosity has relatively small uncertainties.
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paper_title: Global Products Of Vegetation Leaf Area And Fraction Absorbed Par From Year One Of Modis Data

paper_content:

An algorithm based on the physics of radiative transfer in vegetation canopies for the retrieval of vegetation green leaf area index (LAI) and fraction of absorbed photosynthetically active radiation (FPAR) from surface reflectances was developed and implemented for operational processing prior to the launch of the moderate resolution imaging spectroradiometer (MODIS) aboard the TERRA platform in December of 1999. The performance of the algorithm has been extensively tested in prototyping activities prior to operational production. Considerable attention was paid to characterizing the quality of the product and this information is available to the users as quality assessment (QA) accompanying the product. The MODIS LAI/FPAR product has been operationally produced from day one of science data processing from MODIS and is available free of charge to the users from the Earth Resources Observation System (EROS) Data Center Distributed Active Archive Center. Current and planned validation activities are aimed at evaluating the product at several field sites representative of the six structural biomes. Example results illustrating the physics and performance of the algorithm are presented together with initial QA and validation results. Potential users of the product are advised of the provisional nature of the product in view of changes to calibration, geolocation, cloud screening, atmospheric correction and ongoing validation activities. D 2002 Published by Elsevier Science Inc.
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paper_title: Using data assimilation to identify diffuse recharge mechanisms from chemical and physical data in the unsaturated zone: RECHARGE MECHANISMS

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[1] It is difficult to estimate groundwater recharge in semiarid environments, where precipitation and evapotranspiration nearly balance. In such environments, groundwater supplies are sensitive to small changes in the processes that control recharge. Numerical modeling provides the temporal resolution needed to analyze these processes but is highly sensitive to model errors. Natural chloride tracer measurements in the unsaturated zone provide more robust indicators of low recharge rates but yield estimates at coarse time scales that mask most control mechanisms. This study presents a new probabilistic approach for analyzing diffuse recharge in semiarid environments, with an application to study sites in the U.S. southern High Plains. The approach uses data assimilation to combine model predictions and chloride-based recharge estimates. It has the advantage of providing probability distributions rather than point values for uncertain soil and vegetation properties. These can then be used to quantify recharge uncertainty. Estimates of moisture flux time series indicate that percolation (or potential recharge) at the data sites is episodic and exhibits interannual variability. Most percolation occurs during intense rains when crop roots are not fully developed and there is ample antecedent soil moisture. El Nino events can contribute to interannual variability of recharge if they bring rainy winters that provide wet antecedent conditions for spring precipitation. Data assimilation methods that combine modeling and chloride observations provide the high temporal resolution information needed to identify mechanisms controlling diffuse recharge and offer a way to examine the effects of land use change and climatic variability on groundwater resources.
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paper_title: Sequential Monte Carlo Methods for Dynamic Systems

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Abstract We provide a general framework for using Monte Carlo methods in dynamic systems and discuss its wide applications. Under this framework, several currently available techniques are studied and generalized to accommodate more complex features. All of these methods are partial combinations of three ingredients: importance sampling and resampling, rejection sampling, and Markov chain iterations. We provide guidelines on how they should be used and under what circumstance each method is most suitable. Through the analysis of differences and connections, we consolidate these methods into a generic algorithm by combining desirable features. In addition, we propose a general use of Rao-Blackwellization to improve performance. Examples from econometrics and engineering are presented to demonstrate the importance of Rao–Blackwellization and to compare different Monte Carlo procedures.
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paper_title: The importance of parameter resampling for soil moisture data assimilation into hydrologic models using the particle filter

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The Sequential Importance Sampling with Resampling (SISR) particle filter and the SISR with parameter resampling particle filter (SISR-PR) are evaluated for their performance in soil moisture assimilation and the consequent effect on baseflow generation. With respect to the resulting soil moisture time series, both filters perform appropriately. However, the SISR filter has a negative effect on the baseflow due to inconsistency between the parameter values and the states after the assimilation. In order to overcome this inconsistency, parameter resampling is applied along with the SISR filter, to obtain consistent parameter values with the analyzed soil moisture state. Extreme parameter replication, which could lead to a particle collapse, is avoided by the perturbation of the parameters with white noise. Both the modeled soil moisture and baseflow are improved if the complementary parameter resampling is applied. The SISR filter with parameter resampling offers an efficient way to deal with biased observations. The robustness of the methodology is evaluated for 3 model parameter sets and 3 assimilation frequencies. Overall, the results in this paper indicate that the particle filter is a promising tool for hydrologic modeling purposes, but that an additional parameter resampling may be necessary to consistently update all state variables and fluxes within the model.
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paper_title: Variational data assimilation of microwave radiobrightness observations for land surface hydrology applications

paper_content:

Our ability to accurately describe large-scale variations in soil moisture is severely restricted by process uncertainty and the limited availability of appropriate soil moisture data. Remotely sensed microwave radiobrightness observations can cover large scales but have limited resolution and are only indirectly related to the hydrologic variables of interest. The authors describe a four-dimensional (4D) variational assimilation algorithm that makes best use of available information while accounting for both measurement and model uncertainty. The representer method used is more efficient than a Kalman filter because it avoids explicit propagation of state error covariances. In a synthetic example, which is based on a field experiment, the authors demonstrate estimation performance by examining data residuals. Such tests provide a convenient way to check the statistical assumptions of the approach and to assess its operational feasibility. Internally computed covariances show that the estimation error decreases with increasing soil moisture. An adjoint analysis reveals that trends in model errors in the soil moisture equation can be estimated from daily L-band brightness measurements, whereas model errors in the soil and canopy temperature equations cannot be adequately retrieved from daily data alone. Nonetheless, state estimates obtained from the assimilation algorithm improve significantly on prior model predictions derived without assimilation of radiobrightness data.
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paper_title: A Microwave Satellite Observational Operator for Variational Data Assimilation of Soil Moisture

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An observational operator and its adjoint have been created that are suitable for use within variational data assimilation using polarized 6- and 10-GHz passive microwave satellite observations. When used within a variational data assimilation system, the operator will facilitate NWP soil moisture initialization using existing and future satellite datasets [e.g., NASA Advanced Microwave Scanning Radiometer‐Earth Observing System (AMSR-E), Advanced Earth Observing Satellite-II (ADEOS-II), Department of Defense (DoD) WindSat, and the National Polar Orbiter Environmental Satellite System (NPOESS) Conical Microwave Imager Sounder (CMIS)]. Five primary control variables are used within the operator, and surface soil moisture is explicitly included as one of the control variables. In future studies, this operator and its adjoint will be used to perform land surface model data assimilation experiments to better determine important NWP surface characteristics. In the current study, the adjoint model development and analysis of the potential information content of passive microwave measurements sensitive to the land surface and soil parameters are focused on. The multivariate results clarify the effects of masking phenomena upon the soil moisture signal. Also included is a useful transformation of the adjoint between real and complex number spaces. The transformations are necessary when higher-level mathematical operators, such as powers, use complex number arguments. This can be a common occurrence within radiative transfer models. Thus, the adjoint of this particular observational operator serves as an example of this behavior. Various observational operator results and sensitivity analyses are presented, demonstrating significant utility of the operator for NWP soil moisture data assimilation studies.
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paper_title: Constraining a physically based Soil-Vegetation-Atmosphere Transfer model with surface water content and thermal infrared brightness temperature measurements using a multiobjective approach: CONSTRAINING A PHYSICALLY BASED SVAT MODEL

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[1] This article reports on a multiobjective approach which is carried out on the physically based Soil-Vegetation-Atmosphere Transfer (SVAT) model. This approach is designed for (1) analyzing the model sensitivity to its input parameters under various environmental conditions and (2) assessing input parameters through the combined assimilation of the surface water content and the thermal infrared brightness temperature. To reach these goals, a multiobjective calibration iterative procedure (MCIP) is applied on the Simple Soil Plant Atmosphere Transfer–Remote Sensing (SiSPAT-RS) model. This new multiobjective approach consists of performing successive contractions of the feasible parameter space with the multiobjective generalized sensitivity analysis algorithm. Results show that the MCIP is an original and pertinent approach both for improving model calibration (i.e., reducing the a posteriori preferential ranges) and for driving a detailed SVAT model using various calibration data. The usefulness of the water content of the upper 5 cm and the thermal infrared brightness temperature for retrieving quantitative information about the main input surface parameters is also underlined. This study opens perspectives in the combined assimilation of various multispectral remotely sensed observations, such as passive microwaves and thermal infrared signals.
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paper_title: Variational inverse parameter estimation in a cohesive sediment transport model: An adjoint approach: VARIATIONAL INVERSE METHOD IN SEDIMENT TRANSPORT

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[1] Parameter estimation in the sediment deposition and resuspension process is an important issue in numerical modeling of suspended sediment transport. The sediment settling velocity and resuspension rate are two critical parameters controlling the sediment exchange process between the water column and sediment bed. In this paper a variational inverse data assimilation scheme for estimation of the sediment settling velocity and resuspension rate is developed and tested with a three-dimensional cohesive sediment transport model. The sediment settling velocity and resuspension rate are treated as poorly known parameters in the model and are estimated by the variational inverse scheme using an adjoint approach. A limited-memory quasi-Newtonian conjugate gradient algorithm is used in the minimization process. The variational inverse model is tested in the James River estuary in Virginia by identical twin experiments. Numerical experimental results show that variational inverse data assimilation is a useful tool for retrieving poorly known parameters in a cohesive sediment transport model.
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paper_title: Estimation of Surface Turbulent Fluxes through Assimilation of Radiometric Surface Temperature Sequences

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Abstract A model of land surface energy balance is used as a constraint on the estimation of factors characterizing land surface influences on evaporation and turbulent heat transfer from sequences of radiometric surface temperature measurements. The surface moisture control on evaporation is captured by the dimensionless evaporative fraction (ratio of latent heat flux to the sum of the turbulent fluxes), which is nearly constant for near-peak radiation hours on days without precipitation. The dimensionless parameter capturing the turbulent transfer characteristics (bulk heat transfer coefficient) includes the impacts of both forced and free convection. The mean diurnal pattern and seasonal trends are interpreted in the context of expected surface air layer static stability variations. The approach is tested over the First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE) site (Kansas) where verification data on surface fluxes are available. It is shown that sequent...
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paper_title: From Near-Surface to Root-Zone Soil Moisture Using Different Assimilation Techniques

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Abstract Root-zone soil moisture constitutes an important variable for hydrological and weather forecast models. Microwave radiometers like the L-band instrument on board the European Space Agency’s (ESA) future Soil Moisture and Ocean Salinity (SMOS) mission are being designed to provide estimates of near-surface soil moisture (0–5 cm). This quantity is physically related to root-zone soil moisture through diffusion processes, and both surface and root-zone soil layers are commonly simulated by land surface models (LSMs). Observed time series of surface soil moisture may be used to analyze the root-zone soil moisture using data assimilation systems. In this paper, various assimilation techniques derived from Kalman filters (KFs) and variational methods (VAR) are implemented and tested. The objective is to correct the modeled root-zone soil moisture deficiencies of the newest version of the Interaction between Soil, Biosphere, and Atmosphere scheme (ISBA) LSM, using the observations of the surface soil mo...
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paper_title: Estimation of Roughness Profile in Trapezoidal Open Channels

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In the well-known de Saint Venant equations, the bed roughness-coefficient cannot be measured directly and therefore needs to be estimated. The estimation process is referred to as “parameter identification,” which is a mathematical process based on using the difference between the solution of the model equations and the measured system response. This paper introduces an approach for solving the parameter identification problem in the de Saint Venant equations. The method proposed herein is widely used in gas dynamics; however, it has not been used before for unsteady problem identification of open channel flow parameters. Although the proposed solution procedure will be applied herein to the bed roughness-coefficient, it can be used for other parameters, e.g., cross-sectional area, bed width, etc. Starting with an initial guess of the roughness coefficient, the algorithm iteratively improves the guesses in the direction of the gradient of the least square criterion. The gradient is obtained by means of a variational approach, while the conditions of the criterion minimum are identified by the general method of indefinite Lagrangian multipliers.
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paper_title: Auto-calibration system developed to assimilate AMSR-E data into a land surface model for estimating soil moisture and the surface energy budget

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Low-frequency microwave brightness temperature is strongly affected by near-surface soil moisture; therefore, it can be assimilated into a land surface model to improve modeling of soil moisture and the surface energy budget. This study presents a new variational land system used to assimilate AMSR-E brightness temperature of vertical polarization of 6.9 GHz and 18.7 GHz. The system consists of a land surface model (LSM) used to calculate surface fluxes and soil moisture, a radiative transfer model (RTM) to estimate the microwave brightness temperature, and an optimization scheme to search for optimal values of soil moisture by minimizing the difference between modeled and observed brightness temperature. The LSM is an improved simple biosphere model for sparse vegetation modeling and the RTM is a Q-h model that can account for the effects of surface roughness and vegetation. Several parameters in the LSM and RTM can significantly affect the outputs of the land data assimilation system but their values are either highly variable or unavailable. To solve this problem, we developed a dual-pass assim
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paper_title: Future directions for advanced evapotranspiration modeling: Assimilation of remote sensing data into crop simulation models and SVAT models

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Soil-Vegetation-Atmosphere Transfer Models (SVAT) and Crop Simulation Models describe physical and physiological processes occurring in crop canopies. Remote sensing data may be used through assimilation procedures for constraining or driving SVAT and crop models. These models provide continuous simulation of processes such as evapotranspiration and, thus, direct means for interpolating evapotranspiration between remote sensing data acquisitions (which is not the case for classical evapotranspiration mapping methods). They also give access to variables other than evapotranspiration, such as soil moisture and crop production. We developed the coupling between crop, SVAT and radiative transfer models in order to implement assimilation procedures in various wavelength domains (solar, thermal and microwave). Such coupling makes it possible to transfer information from one model to another and then to use remote sensing information for retrieving model parameters which are not directly related to remote sensing data (such as soil initial water content, plant growth parameters, physical properties of soil and so on). Simple assimilation tests are presented to illustrate the main techniques that may be used for monitoring crop processes and evapotranspiration. An application to a small agricultural area is also performed showing the potential of such techniques for retrieving evapotranspiration and information on irrigation practices over wheat fields.
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paper_title: Estimation of Aquifer Parameters Under Transient and Steady State Conditions: 1. Maximum Likelihood Method Incorporating Prior Information

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In this series of three papers a method is presented to estimate the parameters of groundwater flow models under steady and nonsteady state conditions. The parameters include values and directions of principal hydraulic conductivities (or transmissivities) in anisotropic media, specific storage (or storativity), interior and boundary recharge or leakage rates, coefficients of head-dependent interior and boundary sources, and boundary heads. In transient situations, the initial head distribution can also be estimated if the system is originally at a steady state. Paper 1 of the series discusses some of the advantage in treating the inverse problem statistically and in regularizing its solution by means of penalty criteria based on prior estimates of the parameters. The inverse problem is posed in the framework of maximum likelihood theory cast in a manner that accounts for prior information about the parameters. Since not all the factors which contribute to the prior errors can be quantified statistically at the outset, the covariance matrices of these errors are expressed in terms of several parameters which, if unknown, can be estimated jointly with the hydraulic parameters by a stagewise optimization process. When transient head data are separated by a fixed time interval, the temporal structure of these data is approximated by a lag-one autoregressive model with a correlation coefficient that can be treated as another unknown parameter. Estimation errors are analyzed by examining the lower bound of their covariance matrix in the eigenspace. Paper 1 concludes by suggesting that certain model identification criteria developed in the time series literature, all of which are based on the maximum likelihood concept, might be useful for selecting the best groundwater model (or the best method of parameterizing a particular model) among a number of given alternatives.
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paper_title: Using a multiobjective approach to retrieve information on surface properties used in a SVAT model

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Abstract The reliability of model predictions used in meteorology, agronomy or hydrology is partly linked to an adequate representation of the water and energy balances which are described in so-called SVAT (Soil Vegetation Atmosphere Transfer) models. These models require the specification of many surface properties which can generally be obtained from laboratory or field experiments, using time consuming techniques, or can be derived from textural information. The required accuracy of the surface properties depends on the model complexity and their misspecification can affect model performance. At various time and spatial resolutions, remote sensing provides information related to surface parameters in SVAT models or state variables simulated by SVAT models. In this context, the Simple Soil-Plant-Atmosphere Transfer-Remote Sensing (SiSPAT-RS) model was developed for remote sensing data assimilation objectives. This new version of the physically based SiSPAT model simulates the main surface processes (energy fluxes, soil water content profiles, temperatures) and remote sensing data in the visible, infrared and thermal infrared spectral domains. As a preliminary step before data assimilation in the model, the objectives of this study were (1) to apply a multiobjective approach for retrieving quantitative information about the surface properties from different surface measurements and (2) to determine the potential of the SiSPAT-RS model to be applied with ‘little’ a priori information about input parameters. To reach these goals, the ability of the Multiobjective Generalized Sensitivity Analysis (MOGSA) algorithm to determine and quantify the most influential input parameters of the SiSPAT-RS model on several simulated output variables, was investigated. The results revealed the main influential input parameters according to different contrasted environmental conditions, and contributed to the reduction of their a priori uncertainty range. A procedure for specifying surface properties from MOGSA results was tested on the thermal and hydraulic soil parameters, and evaluated through the SiSPAT-RS model performance. Although slightly lower than a reference simulation, the performance were satisfactory and suggested that complex SVAT models can be driven with little a priori information on soil properties, as in a future context of remote sensing data assimilation. Measurement acquired on a winter wheat field of the ReSeDA (Remote Sensing Data Assimilation) experiment were used in this study.
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paper_title: Estimating root zone soil moisture from surface soil moisture data and soil-vegetation-atmosphere transfer modeling

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We studied the possibility of estimating root zone soil moisture through the combined use of a time series of observed surface soil moisture data and soil-vegetation-atmosphere transfer modeling. The analysis was based on the interactions between soil- biosphere-atmosphere surface scheme and two data sets obtained from soybean crops in 1989 and 1990. These data sets included detailed measurements of soil and vegetation characteristics and mass and energy transfer in the soil-plant-atmosphere system. The data measured during the 3-month experiment in 1989 are used to investigate the accuracy of soil reservoir retrievals, as a function of the time period and frequency of measurements of surface soil moisture involved in the retrieval process. This study contributes to better defining the requirements for the use of remotely sensed microwave measurements of surface soil moisture.
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paper_title: A simplified land data assimilation scheme and its application to soil moisture experiments in 2002 (SMEX02)

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[1] The influences of vegetation and its spatial and temporal heterogeneity on the detection of soil moisture can be significant and may limit the applicability of satellite passive microwave sensors. Sensitivity analysis of an applied soil moisture algorithm using ground-based measurements can show where problems can arise and how they may be circumvented. This paper investigates a method of retrieving a one-dimensional soil moisture profile and the surface and canopy temperature, under the influence of different vegetations and dynamics, by integrating numerical models and passive microwave, visible, and near-infrared measurements via a novel application of data assimilation. The land surface scheme (LSS), which is at the heart of the present land data assimilation scheme (LDAS), is a biophysically based model (simplified biosphere model 2: SiB2) of soil, vegetative and atmospheric interactions. The ground-based microwave radiometer (GBMR) measurements, gathered over the soil moisture experiments in 2002 (SMEX02) in Iowa, were assimilated into the LSS via a radiative transfer model (RTM) using LDAS. Compared to open loop simulations, the results of LDAS are in better agreement with observations.
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paper_title: Automatic differentiation : a tool for variational data assimilation and adjoint sensitivity analysis for flood modeling

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Flood modeling involves catchment scale hydrology and river hydraulics. Analysis and reduction of model uncertainties induce sensitivity analysis, reliable initial and boundary conditions, calibration of empirical parameters. A deterministic approach dealing with the aforementioned estimation and sensitivity analysis problems results in the need of computing the derivatives of a function of model output variables with respect to input variables. Modern automatic differentiation (ad) tools such as Tapenade provide an easier and safe way to fulfill this need. Two applications are presented in this paper: variational data assimilation and adjoint sensitivity analysis.
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paper_title: Recent progress of data assimilation methods in meteorology

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Data assimilation is a methodology for estimating accurately the state of a time-evolving complex system like the atmosphere from observational data and a numerical model of the system. It has become an indispensable tool for meteorological researches as well as for numerical weather prediction, as represented by extensive use of reanalysis datasets for research purposes. New advances of data assimilation methods emerged from the 1980s. This review paper presents the theoretical background and implementation of two advanced data assimilation methods: four-dimensional variational assimilation (4D-Var) and ensemble Kalman filtering (EnKF), which currently draw much attention in the meteorological community. Recent research results in Japan on those methods are reviewed, especially on mesoscale applications of 4D-Var and tests of the local ensemble transform Kalman filter (LETKF). Comparison of 4D-Var and EnKF is also briefly discussed. An outline of the mesoscale 4D-Var system of the Japan Meteorological Agency, which is the first operational 4D-Var for a mesoscale model, is given in Appendix.
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paper_title: From Near-Surface to Root-Zone Soil Moisture Using Year-Round Data

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Abstract Passive microwave remote sensing may provide quantitative information about the water content of a shallow near-surface soil layer. However, the variable of interest for applications such as short- and medium-term meteorological modeling and hydrological studies over vegetated areas is the root-zone soil moisture, which controls plant transpiration. Because near-surface soil moisture is related to root-zone soil moisture through diffusion processes, assimilation algorithms may enable one to retrieve the total soil moisture content from observed surface soil moisture. A variational assimilation method is applied to a new dataset obtained over a fallowland in southwestern France in 1997 and 1998. The new database includes continuous automatic measurements of water content within the top 6-cm soil layer during a 17-month period from January 1997 to May 1998. Once calibrated, the Interactions between Soil, Biosphere, and Atmosphere (ISBA) surface scheme is able to simulate properly the measured surfa...
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paper_title: Mantle circulation models with variational data assimilation: inferring past mantle flow and structure from plate motion histories and seismic tomography

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SUMMARY ::: ::: Mantle convection models require an initial condition some time in the past. Because this initial condition is unknown for Earth, we cannot infer the geological evolution of mantle flow from forward mantle convection calculations even for the most recent Mesozoic and Cenozoic geological history of our planet. Here we introduce a fluid dynamic inverse problem to constrain unknown mantle flow back in time from seismic tomographic observations of the mantle and reconstructions of past plate motions using variational data assimilation. We derive the generalized inverse of mantle convection and explore the initial condition problem in high-resolution, 3-D spherical mantle circulation models for a time period of 100 Myr, roughly comparable to half a mantle overturn. We present a synthetic modelling experiment to demonstrate that mid-Cretaceous mantle structure can be inferred accurately from fluid dynamic inverse modelling, assuming present-day mantle structure is well-known, even if an initial first guess assumption about the mid-Cretaceous mantle involved only a simple 1-D radial temperature profile. We also demonstrate that convecting present-day mantle structure back in time by reversing the time-stepping of the energy equation is insufficient to model the mantle structure of the past. The difficulty arises, because such backward convection calculations ignore thermal diffusion effects, and therefore cannot account for the generation of thermal buoyancy in boundary layers as we go back in time. Inverse mantle convection modelling should make it possible to infer a number of flow parameters from observational constraints of the mantle.
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paper_title: What Is an Adjoint Model?

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Adjoint models are powerful tools for many studies that require an estimate of sensitivity of model output (e.g., a forecast) with respect to input. Actual fields of sensitivity are produced directly and efficiently, which can then be used in a variety of applications, including data assimilation, parameter estimation, stability analysis, and synoptic studies. The use of adjoint models as tools for sensitivity analysis is described here using some simple mathematics. An example of sensitivity fields is presented along with a short description of adjoint applications. Limitations of the applications are discussed and some speculations about the future of adjoint models are offered.
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paper_title: Improvements to the Community Land Model and their impact on the hydrological cycle: COMMUNITY LAND MODEL HYDROLOGY

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[1] The Community Land Model version 3 (CLM3) is the land component of the Community Climate System Model (CCSM). CLM3 has energy and water biases resulting from deficiencies in some of its canopy and soil parameterizations related to hydrological processes. Recent research by the community that utilizes CLM3 and the family of CCSM models has indicated several promising approaches to alleviating these biases. This paper describes the implementation of a selected set of these parameterizations and their effects on the simulated hydrological cycle. The modifications consist of surface data sets based on Moderate Resolution Imaging Spectroradiometer products, new parameterizations for canopy integration, canopy interception, frozen soil, soil water availability, and soil evaporation, a TOPMODEL-based model for surface and subsurface runoff, a groundwater model for determining water table depth, and the introduction of a factor to simulate nitrogen limitation on plant productivity. The results from a set of offline simulations were compared with observed data for runoff, river discharge, soil moisture, and total water storage to assess the performance of the new model (referred to as CLM3.5). CLM3.5 exhibits significant improvements in its partitioning of global evapotranspiration (ET) which result in wetter soils, less plant water stress, increased transpiration and photosynthesis, and an improved annual cycle of total water storage. Phase and amplitude of the runoff annual cycle is generally improved. Dramatic improvements in vegetation biogeography result when CLM3.5 is coupled to a dynamic global vegetation model. Lower than observed soil moisture variability in the rooting zone is noted as a remaining deficiency.
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paper_title: Upscaling Hydraulic Properties and Soil Water Flow Processes in Heterogeneous Soils

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This review covers, in a comprehensive manner, the approaches available in the literature to upscale soil water processes and hydraulic parameters in the vadose zone. We distinguish two categories of upscaling methods: forward approaches requiring information about the spatial distribution of hydraulic parameters at a small scale, and inverse modeling approaches requiring information about the spatial and temporal variation of state variables at various scales, including so-called “soft data”. Geostatistical and scaling approaches are crucial to upscale soil water processes and to derive large-scale effective fluxes and parameters from small-scale information. Upscaling approaches include stochastic perturbation methods, the scaleway approach, the stream-tube approach, the aggregation concept, inverse modeling approaches, and data fusion. With all upscaling methods, the estimated effective parameters depend not only on the properties of the heterogeneous flow field but also on boundary conditions. The use of the Richards equation at the field and watershed scale is based more on pragmatism than on a sound physical basis. There are practically no data sets presently available that provide sufficient information to extensively validate existing upscaling approaches. Use of numerical case studies has therefore been most common. More recently and still under development, hydrogeophysical methods combined with ground-based remote sensing techniques promise significant contributions toward providing high-quality data sets. Finally, most of the upscaling literature in vadose zone research has dealt with bare soils or deep vadose zones. There is a need to develop upscaling methods for real world soils, considering root water uptake mechanisms and other soil–plant–atmosphere interactions.
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paper_title: Estimation of Radiative Transfer Parameters from L-Band Passive Microwave Brightness Temperatures Using Advanced Data Assimilation

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ESA's Soil Moisture and Ocean Salinity (SMOS) mission has been designed to extend our knowledge of the Earth's water cycle. Soil Moisture and Ocean Salinity records brightness temperatures at the L-band, which over land are sensitive to soil and vegetation parameters. On the basis of these measurements, soil moisture and vegetation opacity data sets have been derived operationally since 2009 for applications comprising hydrology, numerical weather prediction (NWP), and drought monitoring. We present a method to enhance the knowledge about the temporal evolution of radiative transfer parameters. The radiative transfer model L-Band Microwave Emission of the Biosphere (L-MEB) is used within a data assimilation framework to retrieve vegetation opacity and soil surface roughness. To analyze the ability of the data assimilation approach to track the temporal evolution of these parameters, scenario analyses were performed with increasing complexity. First, the HYDRUS-1D code was used to generate soil moisture and soil temperature time series. On the basis of these data, the L-MEB forward model was run to simulate brightness temperature observations. Finally, the coupled model system HYDRUS-1D and L-MEB were integrated into a data assimilation framework using a particle filter, which is able to update L-MEB states as well as L-MEB parameters. Time invariant and time variable radiative transfer parameters were estimated. Moreover, it was possible to estimate a "bias" term when model simulations show a systematic difference as compared to observations. An application to a USDA-NRCS Soil Climate Analysis Network (SCAN) site showed the good performance of the proposed approach under real conditions.
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paper_title: Assimilation of Disaggregated Microwave Soil Moisture into a Hydrologic Model Using Coarse-Scale Meteorological Data

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Abstract Near-surface soil moisture retrieved from Soil Moisture and Ocean Salinity (SMOS)-type data is downscaled and assimilated into a distributed soil–vegetation–atmosphere transfer (SVAT) model with the ensemble Kalman filter. Because satellite-based meteorological data (notably rainfall) are not currently available at finescale, coarse-scale data are used as forcing in both the disaggregation and the assimilation. Synthetic coarse-scale observations are generated from the Monsoon ‘90 data by aggregating the Push Broom Microwave Radiometer (PBMR) pixels covering the eight meteorological and flux (METFLUX) stations and by averaging the meteorological measurements. The performance of the disaggregation/assimilation coupling scheme is then assessed in terms of surface soil moisture and latent heat flux predictions over the 19-day period of METFLUX measurements. It is found that the disaggregation improves the assimilation results, and vice versa, the assimilation of the disaggregated microwave soil mois...
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paper_title: Dual state-parameter estimation of root zone soil moisture by optimal parameter estimation and extended Kalman filter data assimilation

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Abstract With well-determined hydraulic parameters in a hydrologic model, a traditional data assimilation method (such as the Kalman filter and its extensions) can be used to retrieve root zone soil moisture under uncertain initial state variables (e.g., initial soil moisture content) and good simulated results can be achieved. However, when the key soil hydraulic parameters are incorrect, the error is non-Gaussian, as the Kalman filter will produce a persistent bias in its predictions. In this paper, we propose a method coupling optimal parameters and extended Kalman filter data assimilation (OP-EKF) by combining optimal parameter estimation, the extended Kalman filter (EKF) assimilation method, a particle swarm optimization (PSO) algorithm, and Richards’ equation. We examine the accuracy of estimating root zone soil moisture through the optimal parameters and extended Kalman filter data assimilation method by using observed in situ data at the Meiling experimental station, China. Results indicate that merely using EKF for assimilating surface soil moisture content to obtain soil moisture content in the root zone will produce a persistent bias between simulated and observed values. Using the OP-EKF assimilation method, estimates were clearly improved. If the soil profile is heterogeneous, soil moisture retrieval is accurate in the 0–50 cm soil profile and is inaccurate at 100 cm depth. Results indicate that the method is useful for retrieving root zone soil moisture over large areas and long timescales even when available soil moisture data are limited to the surface layer, and soil moisture content are uncertain and soil hydraulic parameters are incorrect.
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paper_title: Multi-scale assimilation of root zone soil water predictions

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When hydrology model parameters are determined, a traditional data assimilation method (such as Kalman filter) and a hydrology model can estimate the root zone soil water with uncertain state variables (such as initial soil water content). The simulated result can be quite good. However, when a key soil hydraulic property, such as the saturated hydraulic conductivity, is overestimated or underestimated, the traditional soil water assimilation process will produce a persistent bias in its predictions. In this paper, we present and demonstrate a new multi-scale assimilation method by combining the direct insertion assimilation method, particle swarm optimisation (PSO) algorithm and Richards equation. We study the possibility of estimating root zone soil water with a multi-scale assimilation method by using observed in situ data from the Wudaogou experiment station, Huaihe River Basin, China. The results indicate there is a persistent bias between simulated and observed values when the direct insertion assimilation surface soil water content is used to estimate root zone soil water contents. Using a multi-scale assimilation method (PSO algorithm and direct insertion assimilation) and an assumed bottom boundary condition, the results show some obvious improvement, but the root mean square error is still relatively large. When the bottom boundary condition is similar to the actual situation, the multi-scale assimilation method can well represent the root zone soil water content. The results indicate that the method is useful in estimating root zone soil water when available soil water data are limited to the surface layer and the initial soil water content even when the soil hydraulic conductivities are uncertain. Copyright © 2011 John Wiley & Sons, Ltd.
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paper_title: Multi-scale assimilation of surface soil moisture data for robust root zone moisture predictions

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In the presence of uncertain initial conditions and soil hydraulic properties land surface model performance can be significantly improved by the assimilation of periodic observations of certain state variables, such as the near surface soil moisture as observed from a remote platform. Recently, Montaldo et al. [Water Resour Res 37 (2001) 2889] derived a framework that uses biases between observed and modeled time rates of change of surface soil moisture to quantify biases between modeled and actual root-zone-average soil moisture contents. For very large errors in the saturated conductivity the soil moisture assimilation procedure is continuously working against the drainage errors, resulting in a persistent bias in its predictions. In this paper, we adopt this persistent (directional) bias in soil moisture as evidence of an error in the saturated conductivity. From manipulations of soil water balance equations we derived an expression that quantitatively relates the persistent bias in soil moisture to the estimated error in the saturated hydraulic conductivity. We combined this result with the approach of Montaldo et al. [Water Resour Res 37 (2001) 2889] to form a multi-scale assimilation approach. The multi-scale assimilation system is shown to provide marked improvements in the prediction of root zone soil moisture for a case study using data taken from an experimental catchment near Cork, Ireland. In effect, the root zone moisture is updated to provide a temporal trajectory of the near surface moisture that follows the trajectory of the observed surface moisture, and the hydraulic conductivity is adjusted on the basis of the time averaged corrections applied to the root zone water content. It is anticipated that this approach would be useful in operational forecasting models over large domains, where system parameters would be uncertain and occasional distributed observations would be limited to the near surface zone.
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paper_title: How much improvement can precipitation data fusion achieve with a Multiscale Kalman Smoother-based framework?

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[1] With advancements in measuring techniques and modeling approaches, more and more precipitation data products, with different spatial resolutions and accuracies, become available. Therefore, there is an increasing need to produce a fused precipitation product that can take advantage of the strengths of each individual precipitation data product. This study systematically and quantitatively evaluates the improvements of the fused precipitation data as a result of using the Mulitscale Kalman Smoother-based (i.e., MKS-based) framework. Impacts of two types of errors, i.e., white noise and bias that are associated with individual precipitation products, are investigated through hypothetical experiments. Two measures, correlation and root-mean-square error, are used to evaluate the improvements of the fused precipitation data. Our study shows that the MKS-based framework can significantly recover the loss of precipitation's spatial patterns and magnitudes that are associated with the white noise and bias when the erroneous data at different spatial scales are fused together. Although the erroneous data at a finer resolution are generally more effective in improving the spatial patterns and magnitudes of the erroneous data at a coarser resolution, data at a coarser resolution can also provide valuable information in improving the quality of the data at a finer resolution when they are fused. This study provides insights on the values of the MKS-based framework and a guideline for determining a potentially optimal spatial scale over which improvements in both the spatial patterns and the magnitudes can be maximized based on given data with different spatial resolutions.
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paper_title: A Multiscale Ensemble Filtering System for Hydrologic Data Assimilation. Part I: Implementation and Synthetic Experiment

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Abstract The multiscale autoregressive (MAR) framework was introduced in the last decade to process signals that exhibit multiscale features. It provides the method for identifying the multiscale structure in signals and a filtering procedure, and thus is an efficient way to solve the optimal estimation problem for many high-dimensional dynamic systems. Later, an ensemble version of this multiscale filtering procedure, the ensemble multiscale filter (EnMSF), was developed for estimation systems that rely on Monte Carlo samples, making this technique suitable for a range of applications in geosciences. Following the prototype study that introduced EnMSF, a strategy is devised here to implement the multiscale method in a hydrologic data assimilation system, which runs a land surface model. Assimilation experiments are carried out over the Arkansas–Red River basin, located in the central United States (∼645 000 km2), using the Variable Infiltration Capacity (VIC) model with a computing grid of 1062 pixels. A...
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paper_title: Effects of uncertainty magnitude and accuracy on assimilation of multiscale measurements for snowpack characterization

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[1] Hydrologists regularly utilize data assimilation (DA) techniques to merge remote sensing measurements with physical models in order to characterize hydrologic reservoirs. DA methods generally require an estimate of the uncertainty of the various inputs to the models; in practice, however, the uncertainty of these quantities is often unknown. This paper explores the effects of the unknown uncertainty on the efficiency of a multifrequency, multiscale hydrologic DA scheme for snowpack characterization. Synthetic passive microwave (PM) measurements at 25 km and near-infrared (NIR) measurements at 1 km were assimilated, and both snow water equivalent (SWE) and grain size were estimated at 1 km resolution. It is found that the uncertainty magnitude had a significant effect on the efficiency of both SWE and grain size estimation, but that the uncertainty magnitude had very different effects on these two variables because of the different PM and NIR measurement scales. Secondly, it was found that the uncertainty accuracy had a very important role in this DA scheme and that the filter may degrade the estimate of SWE and grain size if key model inputs are misspecified. Finally, four metrics were used to assess the difference between the PM and NIR measurement innovations and their expected values. It was shown that these metrics could potentially be used in an adaptive filtering scheme to correct misspecified uncertainty. More investigation will be required before the feasibility of such an adaptive filtering scheme is established. These findings have important ramifications for snowpack estimation since it implies that in the context of DA schemes, better use will be made of remote sensing products when better physical characterization of the uncertainty of modeled estimates of snow states is available.
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paper_title: Multiscale assimilation of Advanced Microwave Scanning Radiometer-EOS snow water equivalent and Moderate Resolution Imaging Spectroradiometer snow cover fraction observations in northern Colorado: SATELLITE-OBSERVED SNOW DATA ASSIMILATION

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[1] Eight years (2002–2010) of Advanced Microwave Scanning Radiometer–EOS (AMSR-E) snow water equivalent (SWE) retrievals and Moderate Resolution Imaging Spectroradiometer (MODIS) snow cover fraction (SCF) observations are assimilated separately or jointly into the Noah land surface model over a domain in Northern Colorado. A multiscale ensemble Kalman filter (EnKF) is used, supplemented with a rule-based update. The satellite data are either left unscaled or are scaled for anomaly assimilation. The results are validated against in situ observations at 14 high-elevation Snowpack Telemetry (SNOTEL) sites with typically deep snow and at 4 lower-elevation Cooperative Observer Program (COOP) sites. Assimilation of coarse-scale AMSR-E SWE and fine-scale MODIS SCF observations both result in realistic spatial SWE patterns. At COOP sites with shallow snowpacks, AMSR-E SWE and MODIS SCF data assimilation are beneficial separately, and joint SWE and SCF assimilation yields significantly improved root-mean-square error and correlation values for scaled and unscaled data assimilation. In areas of deep snow where the SNOTEL sites are located, however, AMSR-E retrievals are typically biased low and assimilation without prior scaling leads to degraded SWE estimates. Anomaly SWE assimilation could not improve the interannual SWE variations in the assimilation results because the AMSR-E retrievals lack realistic interannual variability in deep snowpacks. SCF assimilation has only a marginal impact at the SNOTEL locations because these sites experience extended periods of near-complete snow cover. Across all sites, SCF assimilation improves the timing of the onset of the snow season but without a net improvement of SWE amounts.
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paper_title: Assimilation of Soil Wetness Index and Leaf Area Index into the ISBA-A-gs land surface model: grassland case study

paper_content:

Abstract. The performance of the joint assimilation in a land surface model of a Soil Wetness Index (SWI) product provided by an exponential filter together with Leaf Area Index (LAI) is investigated. The data assimilation is evaluated with different setups using the SURFEX modeling platform, for a period of seven years (2001–2007), at the SMOSREX grassland site in southwestern France. The results obtained with a Simplified Extended Kalman Filter demonstrate the effectiveness of a joint data assimilation scheme when both SWI and Leaf Area Index are merged into the ISBA-A-gs land surface model. The assimilation of a retrieved Soil Wetness Index product presents several challenges that are investigated in this study. A significant improvement of around 13 % of the root-zone soil water content is obtained by assimilating dimensionless root-zone SWI data. For comparison, the assimilation of in situ surface soil moisture is considered as well. A lower impact on the root zone is noticed. Under specific conditions, the transfer of the information from the surface to the root zone was found not accurate. Also, our results indicate that the assimilation of in situ LAI data may correct a number of deficiencies in the model, such as low LAI values in the senescence phase by using a seasonal-dependent error definition for background and observations. In order to verify the specification of the errors for SWI and LAI products, a posteriori diagnostics are employed. This approach highlights the importance of the assimilation design on the quality of the analysis. The impact of data assimilation scheme on CO2 fluxes is also quantified by using measurements of net CO2 fluxes gathered at the SMOSREX site from 2005 to 2007. An improvement of about 5 % in terms of rms error is obtained.
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paper_title: Multisensor snow data assimilation at the continental scale: The value of Gravity Recovery and Climate Experiment terrestrial water storage information

paper_content:

[1] This investigation establishes a multisensor snow data assimilation system over North America (from January 2002 to June 2007), toward the goal of better estimation of snowpack (in particular, snow water equivalent and snow depth) via incorporating both Gravity Recovery and Climate Experiment (GRACE) terrestrial water storage (TWS) and Moderate Resolution Imaging Spectroradiometer (MODIS) snow cover fraction (SCF) information into the Community Land Model. The different properties associated with the SCF and TWS observations are accommodated through a unified approach using the ensemble Kalman filter and smoother. Results show that this multisensor approach can provide significant improvements over a MODIS-only approach, for example, in the Saint Lawrence, Fraser, Mackenzie, Churchill & Nelson, and Yukon river basins and the southwestern rim of Hudson Bay. At middle latitudes, for example, the North Central and Missouri river basins, the inclusion of GRACE information preserves the advantages (compared with the open loop) shown in the MODIS-only run. However, in some high-latitude areas and given months the open loop run shows a comparable or even better performance, implying considerable room for refinements of the multisensor algorithm. In addition, ensemble-based metrics are calculated and interpreted domainwide. They indicate the potential importance of accurate representation of snow water equivalent autocovariance in assimilating TWS observations and the regional and/or seasonal dependence of GRACE’s capability to reduce ensemble variance. These analyses contribute to clarifying the effects of GRACE’s special features (e.g., a vertical integral of different land water changes, coarse spatial and temporal resolution) in the snow data assimilation system.
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paper_title: Improving Spatial Soil Moisture Representation Through Integration of AMSR-E and MODIS Products

paper_content:

The use of microwave observations has been highlighted as a complementary tool for evaluating land surface properties. Microwave observations are less affected by clouds, water vapor, and aerosol and also contain valuable soil moisture information. However, a critical limitation in microwave observations is the coarse spatial resolution attributed to the complex retrieval process. The objective of the current study is to develop an independent (from ground observations) downscaling approach that merges information from higher spatial resolution MODerate-resolution Imaging Spectroradiometer (MODIS) (~1 km) with lower spatial resolution AMSR-E (~25 km) to obtain soil moisture estimates at the MODIS scale (~1 km). We compare the developed (UCLA) method against a range of previous published approaches. Various key factors (i.e., surface temperature, vegetation indexes, and albedo) derived from MODIS provide information on relative variations in surface wetness conditions and contribute weighting parameters for downscaling the larger AMSR-E soil moisture footprints. Evaluation of the various downscaled soil moisture products is undertaken at the SMEX04 site in southern Arizona. Results show that the UCLA downscaling technique, as well as the previously published Merlin method, significantly improves the limited spatial variability of the current AMSR-E product. Spatial correlation (R) values improved from -0.08 to 0.34 and 0.27 for the Merlin and UCLA methods, respectively. The evaluated triangle-based methods show poorer performance over the study domain. Results from the current study yield insight on the integration of multiscale remote sensing data in various downscaling methods and the usefulness of MODIS observations in compensating for low-resolution microwave observations.
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paper_title: A Land Data Assimilation System for Soil Moisture and Temperature: An Information Content Study

paper_content:

Abstract A Canadian Land Data Assimilation System (CaLDAS) for the analysis of land surface prognostic variables is designed and implemented at the Meteorological Service of Canada for the initialization of numerical weather prediction and climate models. The assimilation of different data sources for the production of daily soil moisture and temperature analyses is investigated in a set of observing system simulation experiments over North America. A simplified variational technique is adapted to accommodate different observation types at their appropriate time in a 24-h time window. The screen-level observations of temperature and relative humidity, from conventional synoptic surface observations (SYNOP)/aviation routine weather report (METAR)/surface aviation observation (SA) reports, are considered together with presently available satellite observations provided by the Aqua satellite (microwave C-band), Geostationary Operational Environmental Satellite (GOES) [infrared (IR)], and observations availab...
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paper_title: Novel approach to nonlinear/non-Gaussian Bayesian state estimation

paper_content:

An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples, which are updated and propagated by the algorithm. The method is not restricted by assumptions of linear- ity or Gaussian noise: it may be applied to any state transition or measurement model. A simula- tion example of the bearings only tracking problem is presented. This simulation includes schemes for improving the efficiency of the basic algorithm. For this example, the performance of the bootstrap filter is greatly superior to the standard extended Kalman filter.
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paper_title: Three-dimensional soil moisture profile retrieval by assimilation of near-surface measurements: Simplified Kalman filter covariance forecasting and field application: THREE-DIMENSIONAL SOIL MOISTURE ASSIMILATION

paper_content:

[1] The Kalman filter data assimilation technique is applied to a distributed three-dimensional soil moisture model for retrieval of the soil moisture profile in a 6 ha catchment using near-surface soil moisture measurements. A simplified Kalman filter covariance forecasting methodology is developed based on forecasting of the state correlations and imposed state variances. This covariance forecasting technique, termed the modified Kalman filter, was then used in a 1 month three-dimensional field application. Two updating scenarios were tested: (1) updating every 2 to 3 days and (2) a single update. The data used were from the Nerrigundah field site, near Newcastle, Australia. This study demonstrates the feasibility of data assimilation in a quasi three-dimensional distributed soil moisture model, provided simplified covariance forecasting techniques are used. It also identifies that (1) the soil moisture profile cannot be retrieved from near-surface soil moisture measurements when the near-surface and deep soil layers become decoupled, such as during extreme drying events; (2) if simulation of the soil moisture profile is already good, the assimilation can result in a slight degradation, but if the simulation is poor, assimilation can yield a significant improvement; (3) soil moisture profile retrieval results are independent of initial conditions; and (4) the required update frequency is a function of the errors in model physics and forcing data.
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paper_title: Earth-Viewing L-Band Radiometer Sensing of Sea Surface Scattered Celestial Sky Radiation—Part II: Application to SMOS

paper_content:

We examine how the rough sea surface scattering of L-band celestial sky radiation might affect the measurements of the future European Space Agency Soil Moisture and Ocean Salinity (SMOS) mission. For this purpose, we combined data from several surveys to build a comprehensive all-sky L-band celestial sky brightness temperature map for the SMOS mission that includes the continuum radiation and the hydrogen line emission rescaled for the SMOS bandwidth. We also constructed a separate map of strong and very localized sources that may exhibit L-band brightness temperatures exceeding 1000 K. Scattering by the roughened ocean surface of radiation from even the strongest localized sources is found to reduce the contributions from these localized strong sources to negligible levels, and rough surface scattering solutions may be obtained with a map much coarser than the original continuum maps. In rough ocean surface conditions, the contribution of the scattered celestial noise to the reconstructed brightness temperatures is not significantly modified by the synthetic antenna weighting function, which makes integration over the synthetic beam unnecessary. The contamination of the reconstructed brightness temperatures by celestial noise exhibits a strong annual cycle with the largest contamination occurring in the descending swaths in September and October, when the specular projection of the field of view is aligned with the Galactic equator. Ocean surface roughness may alter the contamination by over 0.1 K in 30% of the SMOS measurements. Given this potentially large impact of surface roughness, an operational method is proposed to account for it in the SMOS level 2 sea surface salinity algorithm.
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paper_title: The Soil Moisture Active Passive (SMAP) Mission

paper_content:

The Soil Moisture Active Passive (SMAP) mission is one of the first Earth observation satellites being developed by NASA in response to the National Research Council's Decadal Survey. SMAP will make global measurements of the soil moisture present at the Earth's land surface and will distinguish frozen from thawed land surfaces. Direct observations of soil moisture and freeze/thaw state from space will allow significantly improved estimates of water, energy, and carbon transfers between the land and the atmosphere. The accuracy of numerical models of the atmosphere used in weather prediction and climate projections are critically dependent on the correct characterization of these transfers. Soil moisture measurements are also directly applicable to flood assessment and drought monitoring. SMAP observations can help monitor these natural hazards, resulting in potentially great economic and social benefits. SMAP observations of soil moisture and freeze/thaw timing will also reduce a major uncertainty in quantifying the global carbon balance by helping to resolve an apparent missing carbon sink on land over the boreal latitudes. The SMAP mission concept will utilize L-band radar and radiometer instruments sharing a rotating 6-m mesh reflector antenna to provide high-resolution and high-accuracy global maps of soil moisture and freeze/thaw state every two to three days. In addition, the SMAP project will use these observations with advanced modeling and data assimilation to provide deeper root-zone soil moisture and net ecosystem exchange of carbon. SMAP is scheduled for launch in the 2014-2015 time frame.
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paper_title: An Algorithm for Merging SMAP Radiometer and Radar Data for High-Resolution Soil-Moisture Retrieval

paper_content:

A robust and simple algorithm is developed to merge L-band radiometer retrievals and L-band radar observations to obtain high-resolution (9-km) soil-moisture estimates from data of the NASA Soil Moisture Active and Passive (SMAP) mission. The algorithm exploits the established accuracy of coarse-scale radiometer soil-moisture retrievals and blends this with the fine-scale spatial heterogeneity detectable by radar observations to produce a high-resolution optimal soil-moisture estimate at 9 km. The capability of the algorithm is demonstrated by implementing the approach using the airborne Passive and Active L-band System (PALS) instrument data set from Soil Moisture Experiments 2002 (SMEX02) and a four-month synthetic data set in an Observation System Simulation Experiment (OSSE) framework. The results indicate that the algorithm has the potential to obtain better soil-moisture accuracy at a high resolution and show an improvement in root-mean-square error of 0.015-0.02-cm3/cm3 volumetric soil moisture over the minimum performance taken to be retrievals based on radiometer measurements resampled to a finer scale. These results are based on PALS data from SMEX02 and a four-month OSSE data set and need to be further confirmed for different hydroclimatic regions using airborne data sets from prelaunch calibration/validation field campaigns of the SMAP mission.
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paper_title: Model-Based Satellite Image Fusion

paper_content:

A method is proposed for pixel-level satellite image fusion derived directly from a model of the imaging sensor. By design, the proposed method is spectrally consistent. It is argued that the proposed method needs regularization, as is the case for any method for this problem. A framework for pixel neighborhood regularization is presented. This framework enables the formulation of the regularization in a way that corresponds well with our prior assumptions of the image data. The proposed method is validated and compared with other approaches on several data sets. Lastly, the intensity-hue-saturation method is revisited in order to gain additional insight of what implications the spectral consistency has for an image fusion method.
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paper_title: Image Analysis, Classification, and Change Detection in Remote Sensing

paper_content:

Images, Arrays, and Vectors. Image Statistics. Transformations. Radiometric Enhancement. Topographic Modeling. Image Registration. Image Sharpening. Change Detection. Unsupervised Classification. Supervised Classification. Hyperspectral Analysis.
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paper_title: Multispectral imagery band sharpening study

paper_content:

The fusion of multisensor and multiresolution satellite imagery is an effective means of exploiting the complimentary nature of various image types. With band sharpening (a type of imagery fusion), higher spatial resolution panchromatic data is fused with lower resolution multispectral imagery (MSI). This fusion creates a product with the spectral characteristics of the MSI and a spatial resolution approaching that of the panchromatic image (effective ground-sample distance, or GSD). Others have fused 10-m SPOT panchromatic with 20-m SPOT MSI or 30-m Landsat TM (sharpening factors of 2:l and 3:1). In this study, MSI of 10 m to 30 m was sharpened with 5- to 15-m imagery (sharpening factors of 2:1 to 6:l) using four algorithms. The research goals were to (1) determine the validity of the concept of "effective GSD"; (2) determine the relative utility of band sharpening by different factors; and (3) compare the relative effectiveness of different band sharpening algorithms.
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paper_title: Context-driven fusion of high spatial and spectral resolution images based on oversampled multiresol

paper_content:

This paper compares two general and formal solutions to the problem of fusion of multispectral images with high-resolution panchromatic observations. The former exploits the undecimated discrete wavelet transform, which is an octave bandpass representation achieved from a conventional discrete wavelet transform by omitting all decimators and upsampling the wavelet filter bank. The latter relies on the generalized Laplacian pyramid, which is another oversampled structure obtained by recursively subtracting from an image an expanded decimated lowpass version. Both the methods selectively perform spatial-fre- quencies spectrum substitution from an image to another. In both schemes, context dependency is exploited by thresholding the local correlation coefficient between the images to be merged, to avoid injection of spatial details that are not likely to occur in the target image. Unlike other multiscale fusion schemes, both the present decompositions are not critically subsampled, thus avoiding possible impairments in the fused images, due to missing cancellation of aliasing terms. Results are presented and discussed on SPOT data.
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paper_title: Variational data assimilation of microwave radiobrightness observations for land surface hydrology applications

paper_content:

Our ability to accurately describe large-scale variations in soil moisture is severely restricted by process uncertainty and the limited availability of appropriate soil moisture data. Remotely sensed microwave radiobrightness observations can cover large scales but have limited resolution and are only indirectly related to the hydrologic variables of interest. The authors describe a four-dimensional (4D) variational assimilation algorithm that makes best use of available information while accounting for both measurement and model uncertainty. The representer method used is more efficient than a Kalman filter because it avoids explicit propagation of state error covariances. In a synthetic example, which is based on a field experiment, the authors demonstrate estimation performance by examining data residuals. Such tests provide a convenient way to check the statistical assumptions of the approach and to assess its operational feasibility. Internally computed covariances show that the estimation error decreases with increasing soil moisture. An adjoint analysis reveals that trends in model errors in the soil moisture equation can be estimated from daily L-band brightness measurements, whereas model errors in the soil and canopy temperature equations cannot be adequately retrieved from daily data alone. Nonetheless, state estimates obtained from the assimilation algorithm improve significantly on prior model predictions derived without assimilation of radiobrightness data.
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paper_title: Multiscale Recursive Estimation, Data Fusion, and Regularization

paper_content:

We describe a framework for modeling stochastic phenomena at multiple scales and for their efficient estimation or reconstruction given partial and/or noisy measurements which may also be at several scales. In particular multiscale signal representations lead naturally to pyramidal or tree-like data structures in which each level in the tree corresponds to a particular scale of representation. A class of multiscale dynamic models evolving on dyadic trees is introduced. The main focus of this paper is on the description, analysis, and application of an extremely efficient optimal estimation algorithm for this class of models. This algorithm consists of a fine-to-coarse filtering sweep, followed by a coarse-to-fine smoothing step, corresponding to the dyadic tree generalization of Kalman filtering and Rauch-Tung-Striebel smoothing. The Kalman filtering sweep consists of the recursive application of three steps: a measurement update step, a fine-to-coarse prediction step, and a fusion step. We illustrate the use of our methodology for the fusion of multiresolution data and for the efficient solution of "fractal regularizations" of ill-posed signal and image processing problems encountered. >
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paper_title: Soil moisture retrieval from space: the Soil Moisture and Ocean Salinity (SMOS) mission

paper_content:

Microwave radiometry at low frequencies (L-band: 1.4 GHz, 21 cm) is an established technique for estimating surface soil moisture and sea surface salinity with a suitable sensitivity. However, from space, large antennas (several meters) are required to achieve an adequate spatial resolution at L-band. So as to reduce the problem of putting into orbit a large filled antenna, the possibility of using antenna synthesis methods has been investigated. Such a system, relying on a deployable structure, has now proved to be feasible and has led to the Soil Moisture and Ocean Salinity (SMOS) mission, which is described. The main objective of the SMOS mission is to deliver key variables of the land surfaces (soil moisture fields), and of ocean surfaces (sea surface salinity fields). The SMOS mission is based on a dual polarized L-band radiometer using aperture synthesis (two-dimensional [2D] interferometer) so as to achieve a ground resolution of 50 km at the swath edges coupled with multiangular acquisitions. The radiometer will enable frequent and global coverage of the globe and deliver surface soil moisture fields over land and sea surface salinity over the oceans. The SMOS mission was proposed to the European Space Agency (ESA) in the framework of the Earth Explorer Opportunity Missions. It was selected for a tentative launch in 2005. The goal of this paper is to present the main aspects of the baseline mission and describe how soil moisture will be retrieved from SMOS data.
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paper_title: Bayesian statistical data assimilation for ecosystem models using Markov Chain Monte Carlo

paper_content:

Abstract This study considers advanced statistical approaches for sequential data assimilation. These are explored in the context of nowcasting and forecasting using nonlinear differential equation based marine ecosystem models assimilating sparse and noisy non-Gaussian multivariate observations. The statistical framework uses a state space model with the goal of estimating the time evolving probability distribution of the ecosystem state. Assimilation of observations relies on stochastic dynamic prediction and Bayesian principles. In this study, a new sequential data assimilation approach is introduced based on Markov Chain Monte Carlo (MCMC). The ecosystem state is represented by an ensemble, or sample, from which distributional properties, or summary statistical measures, can be derived. The Metropolis-Hastings based MCMC approach is compared and contrasted with two other sequential data assimilation approaches: sequential importance resampling, and the (approximate) ensemble Kalman filter (including computational comparisons). A simple illustrative application is provided based on a 0-D nonlinear plankton ecosystem model with multivariate non-Gaussian observations of the ecosystem state from a coastal ocean observatory. The MCMC approach is shown to be straightforward to implement and to effectively characterize the non-Gaussian ecosystem state in both nowcast and forecast experiments. Results are reported which illustrate how non-Gaussian information originates, and how it can be used to characterize ecosystem properties.
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paper_title: Using area-average remotely sensed surface soil moisture in multipatch land data assimilation systems

paper_content:

In coming years, Land Data Assimilation Systems (LDAS) two-dimensional (2-D) arrays of the relevant land-surface model) are likely to become the routine mechanism by which many predictive weather and climate models will be initiated. If this is so, it will be via assimilation into the LDAS that other data relevant to the land surface, such as remotely sensed estimates of soil moisture, will find value. This paper explores the potential for using low-resolution, remotely sensed observations of microwave brightness temperature to infer soil moisture in an LDAS with a "mosaic-patch" representation of land-surface heterogeneity, by coupling the land-surface model in the LDAS to a physically realistic microwave emission model. The past description of soil water movement by the LDAS is proposed as the most appropriate, LDAS-consistent basis for using remotely sensed estimates of surface soil moisture to infer soil moisture at depth, and the plausibility of this proposal is investigated. Three alternative methods are explored for partitioning soil moisture between modeled patches while altering the area-average soil moisture to correspond to the observed, pixel-average microwave brightness temperature, namely, 1) altering the soil moisture by a factor, which is the same for all the patches in the pixel, 2) altering the soil moisture by adding an amount that is the same for all the patches in the pixel, and 3) altering the change in soil moisture since the last assimilation cycle by a factor which is the same for all the patches in the pixel.
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paper_title: Estimation of Radiative Transfer Parameters from L-Band Passive Microwave Brightness Temperatures Using Advanced Data Assimilation

paper_content:

ESA's Soil Moisture and Ocean Salinity (SMOS) mission has been designed to extend our knowledge of the Earth's water cycle. Soil Moisture and Ocean Salinity records brightness temperatures at the L-band, which over land are sensitive to soil and vegetation parameters. On the basis of these measurements, soil moisture and vegetation opacity data sets have been derived operationally since 2009 for applications comprising hydrology, numerical weather prediction (NWP), and drought monitoring. We present a method to enhance the knowledge about the temporal evolution of radiative transfer parameters. The radiative transfer model L-Band Microwave Emission of the Biosphere (L-MEB) is used within a data assimilation framework to retrieve vegetation opacity and soil surface roughness. To analyze the ability of the data assimilation approach to track the temporal evolution of these parameters, scenario analyses were performed with increasing complexity. First, the HYDRUS-1D code was used to generate soil moisture and soil temperature time series. On the basis of these data, the L-MEB forward model was run to simulate brightness temperature observations. Finally, the coupled model system HYDRUS-1D and L-MEB were integrated into a data assimilation framework using a particle filter, which is able to update L-MEB states as well as L-MEB parameters. Time invariant and time variable radiative transfer parameters were estimated. Moreover, it was possible to estimate a "bias" term when model simulations show a systematic difference as compared to observations. An application to a USDA-NRCS Soil Climate Analysis Network (SCAN) site showed the good performance of the proposed approach under real conditions.
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paper_title: Computationally Efficient Stochastic Realization for Internal Multiscale Autoregressive Models

paper_content:

In this paper we develop a stochastic realization theory for multiscale autoregressive (MAR) processes that leads to computationally efficient realization algorithms. The utility of MAR processes has been limited by the fact that the previously known general purpose realization algorithm, based on canonical correlations, leads to model inconsistencies and has complexity quartic in problem size. Our realization theory and algorithms addresses these issues by focusing on the estimation-theoretic concept of predictive efficiency and by exploiting the scale-recursive structure of so-called internal MAR processes. Our realization algorithm has complexity quadratic in problem size and with an approximation we also obtain an algorithm that has complexity linear in problem size.
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paper_title: Validation of SMOS Brightness Temperatures During the HOBE Airborne Campaign, Western Denmark

paper_content:

The Soil Moisture and Ocean Salinity (SMOS) mission delivers global surface soil moisture fields at high temporal resolution which is of major relevance for water management and climate predictions. Between April 26 and May 9, 2010, an airborne campaign with the L-band radiometer EMIRAD-2 was carried out within one SMOS pixel (44 × 44 km) in the Skjern River Catchment, Denmark. Concurrently, ground sampling was conducted within three 2 × 2 km patches (EMIRAD footprint size) of differing land cover. By means of this data set, the objective of this study is to present the validation of SMOS L1C brightness temperatures TB of the selected node. Data is stepwise compared from point via EMIRAD to SMOS scale. From ground soil moisture samples, TB's are pointwise estimated through the L-band microwave emission of the biosphere model using land cover specific model settings. These TB's are patchwise averaged and compared with EMIRAD TB's. A simple uncertainty assessment by means of a set of model runs with the most influencing parameters varied within a most likely interval results in a considerable spread of TB's (5-20 K). However, for each land cover class, a combination of parameters could be selected to bring modeled and EMIRAD data in good agreement. Thereby, replacing the Dobson dielectric mixing model with the Mironov model decreases the overall RMSE from 11.5 K to 3.8 K. Similarly, EMIRAD data averaged at SMOS scale and corresponding SMOS TB 's show good accordance on the single day where comparison is not prevented by strong radio-frequency interference (RFI) (May 2, avg. RMSE = 9.7 K). While the advantages of solid data sets of high spatial coverage and density throughout spatial scales for SMOS validation could be clearly demonstrated, small temporal variability in soil moisture conditions and RFI contamination throughout the campaign limited the extent of the validation work. Further attempts over longer time frames are planned by means of soil moisture network data as well as studies on the impacts of organic layers under natural vegetation and higher open water fractions at surrounding grid nodes.
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paper_title: Assimilation of passive and active microwave soil moisture retrievals

paper_content:

[1] Near-surface soil moisture observations from the active microwave ASCAT and the passive microwave AMSR-E satellite instruments are assimilated, both separately and together, into the NASA Catchment land surface model over 3.5 years using an ensemble Kalman filter. The impact of each assimilation is evaluated using in situ soil moisture observations from 85 sites in the US and Australia, in terms of the anomaly time series correlation-coefficient, R. The skill gained by assimilating either ASCAT or AMSR-E was very similar, even when separated by land cover type. Over all sites, the mean root-zone R was significantly increased from 0.45 for an open-loop, to 0.55, 0.54, and 0.56 by the assimilation of ASCAT, AMSR-E, and both, respectively. Each assimilation also had a positive impact over each land cover type sampled. For maximum accuracy and coverage it is recommended that active and passive microwave observations be assimilated together.
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paper_title: Brightness Temperature and Soil Moisture Validation at Different Scales During the SMOS Validation Campaign in the Rur and Erft Catchments, Germany

paper_content:

The European Space Agency's Soil Moisture and Ocean Salinity (SMOS) satellite was launched in November 2009 and delivers now brightness temperature and soil moisture products over terrestrial areas on a regular three-day basis. In 2010, several airborne campaigns were conducted to validate the SMOS products with microwave emission radiometers at L-band (1.4 GHz). In this paper, we present results from measurements performed in the Rur and Erft catchments in May and June 2010. The measurement sites were situated in the very west of Germany close to the borders to Belgium and The Netherlands. We developed an approach to validate spatial and temporal SMOS brightness temperature products. An area-wide brightness temperature reference was generated by using an area-wide modeling of top soil moisture and soil temperature with the WaSiM-ETH model and radiative transfer calculation based on the L-band Microwave Emission of the Biosphere model. Measurements of the airborne L-band sensors EMIRAD and HUT-2D on-board a Skyvan aircraft as well as ground-based mobile measurements performed with the truck mounted JULBARA L-band radiometer were analyzed for calibration of the simulated brightness temperature reference. Radiative transfer parameters were estimated by a data assimilation approach. By this versatile reference data set, it is possible to validate the spaceborne brightness temperature and soil moisture data obtained from SMOS. However, comparisons with SMOS observations for the campaign period indicate severe differences between simulated and observed SMOS data.
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paper_title: An Ensemble Multiscale Filter for Large Nonlinear Data Assimilation Problems

paper_content:

Abstract Operational data assimilation problems tend to be very large, both in terms of the number of unknowns to be estimated and the number of measurements to be processed. This poses significant computational challenges, especially for ensemble methods, which are critically dependent on the number of replicates used to derive sample covariances and other statistics. Most efforts to deal with the related problems of computational effort and sampling error in ensemble estimation have focused on spatial localization. The ensemble multiscale Kalman filter described here offers an alternative approach that effectively replaces, at each update time, the prior (or background) sample covariance with a multiscale tree. The tree is composed of nodes distributed over a relatively small number of discrete scales. Global correlations between variables at different locations are described in terms of local relationships between nodes at adjacent scales (parents and children). The Kalman updating process can be carri...
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paper_title: Assimilation of Disaggregated Microwave Soil Moisture into a Hydrologic Model Using Coarse-Scale Meteorological Data

paper_content:

Abstract Near-surface soil moisture retrieved from Soil Moisture and Ocean Salinity (SMOS)-type data is downscaled and assimilated into a distributed soil–vegetation–atmosphere transfer (SVAT) model with the ensemble Kalman filter. Because satellite-based meteorological data (notably rainfall) are not currently available at finescale, coarse-scale data are used as forcing in both the disaggregation and the assimilation. Synthetic coarse-scale observations are generated from the Monsoon ‘90 data by aggregating the Push Broom Microwave Radiometer (PBMR) pixels covering the eight meteorological and flux (METFLUX) stations and by averaging the meteorological measurements. The performance of the disaggregation/assimilation coupling scheme is then assessed in terms of surface soil moisture and latent heat flux predictions over the 19-day period of METFLUX measurements. It is found that the disaggregation improves the assimilation results, and vice versa, the assimilation of the disaggregated microwave soil mois...
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paper_title: Optimal multiscale Kalman filter for assimilation of near-surface soil moisture into land surface models

paper_content:

[1] We undertake an alternative and novel approach to assimilation of near-surface soil moisture into land surface models by means of an extension of multiscale Kalman filtering (MKF). While most data assimilation studies rely on the assumption of spatially independent near-surface soil moisture observations to attain computational tractability in large-scale problems, MKF allows us to explicitly and very efficiently model the spatial dependence and scaling properties of near-surface soil moisture fields. Furthermore, MKF has the appealing ability to cope with model predictions and observations made at different spatial scales. Yet another essential feature of our approach is that we resort to the use of the expectation maximization (EM) algorithm in conjunction with MKF so that the statistical parameters inherent to MKF may be optimally determined directly from the data at hand and allowed to vary over time. This constitutes a significant advantage since these parameters (e.g., observation and model error noise variances) essentially determine the performance of the assimilation approach and have so far been most commonly prescribed heuristically and not allowed to evolve in time. We test our approach by assimilating the near-surface soil moisture fields derived from electronically scanned thinned array radiometer (ESTAR) during the Southern Great Plains Hydrology experiment of 1997 (SGP97) into the three-layer variable infiltration capacity (VIC-3L) land surface model. The results show that assimilation significantly improves the short-term predictions of soil moisture and energy fluxes from VIC-3L, especially with regard to capturing the spatial structure of these state variables. Additionally, we find that allowing the statistical parameters of the assimilation algorithm to evolve in time allows for an adequate representation of the time-varying uncertainties in land surface model predictions.
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paper_title: Thermal microwave emission depth and soil moisture remote sensing

paper_content:

This paper presents some additional theoretical and experimental results on the problem of estimating the soil depth to which soil moisture can be directly measured by VHF radiometers. The experimental work was implemented in August 1992 at the Research Farm of the Institute of Hydrotechnique and Amelioration, Sofia, Bulgaria. The soil thermal microwave emission was measured by an L-band Dicke-type radiometer at 1.65GHz at off-nadir angle from 20 to 60. It was found that the value obtained for the effective penetration depth depends on the definition used in the analysis: the definition of penetration depth is based on soil thermal emissivity or soil reflectivity. Further it was found that the depth to which the soil moisture can be directly measured exhibits a negligible dependence on polarization (horizontal, vertical) as well as on off-nadir observation angle. For the purpose of soil brightness temperature and soil reflectivity computing, a fast and robust method and algorithm were proposed which are b...
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paper_title: Modeling transient groundwater flow by coupling ensemble Kalman filtering and upscaling: COUPLING ENKF AND UPSCALING

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[1] The ensemble Kalman filter (EnKF) is coupled with upscaling to build an aquifer model at a coarser scale than the scale at which the conditioning data (conductivity and piezometric head) had been taken for the purpose of inverse modeling. Building an aquifer model at the support scale of observations is most often impractical since this would imply numerical models with many millions of cells. If, in addition, an uncertainty analysis is required involving some kind of Monte Carlo approach, the task becomes impossible. For this reason, a methodology has been developed that will use the conductivity data at the scale at which they were collected to build a model at a (much) coarser scale suitable for the inverse modeling of groundwater flow and mass transport. It proceeds as follows: (1) Generate an ensemble of realizations of conductivities conditioned to the conductivity data at the same scale at which conductivities were collected. (2) Upscale each realization onto a coarse discretization; on these coarse realizations, conductivities will become tensorial in nature with arbitrary orientations of their principal components. (3) Apply the EnKF to the ensemble of coarse conductivity upscaled realizations in order to condition the realizations to the measured piezometric head data. The proposed approach addresses the problem of how to deal with tensorial parameters, at a coarse scale, in ensemble Kalman filtering while maintaining the conditioning to the fine-scale hydraulic conductivity measurements. We demonstrate our approach in the framework of a synthetic worth-of-data exercise, in which the relevance of conditioning to conductivities, piezometric heads, or both is analyzed.
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paper_title: A data assimilation method for using low-resolution Earth observation data in heterogeneous ecosystems

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[1] We present an approach for dealing with coarse‐resolution Earth observations (EO) in terrestrial ecosystem data assimilation schemes. The use of coarse‐scale observations in ecological data assimilation schemes is complicated by spatial heterogeneity and nonlinear processes in natural ecosystems. If these complications are not appropriately dealt with, then the data assimilation will produce biased results. The “disaggregation” approach that we describe in this paper combines frequent coarse‐resolution observations with temporally sparse fine‐resolution measurements. We demonstrate the approach using a demonstration data set based on measurements of an Arctic ecosystem. In this example, normalized difference vegetation index observations are assimilated into a “zero‐order” model of leaf area index and carbon uptake. The disaggregation approach conserves key ecosystem characteristics regardless of the observation resolution and estimates the carbon uptake to within 1% of the demonstration data set “truth.” Assimilating the same data in the normal manner, but without the disaggregation approach, results in carbon uptake being underestimated by 58% at an observation resolution of 250 m. The disaggregation method allows the combination of multiresolution EO and improves in spatial resolution if observations are located on a grid that shifts from one observation time to the next. Additionally, the approach is not tied to a particular data assimilation scheme, model, or EO product and can cope with complex observation distributions, as it makes no implicit assumptions of normality.
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paper_title: ML estimation of a stochastic linear system with the EM algorithm and its application to speech recognition

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A nontraditional approach to the problem of estimating the parameters of a stochastic linear system is presented. The method is based on the expectation-maximization algorithm and can be considered as the continuous analog of the Baum-Welch estimation algorithm for hidden Markov models. The algorithm is used for training the parameters of a dynamical system model that is proposed for better representing the spectral dynamics of speech for recognition. It is assumed that the observed feature vectors of a phone segment are the output of a stochastic linear dynamical system, and it is shown how the evolution of the dynamics as a function of the segment length can be modeled using alternative assumptions. A phoneme classification task using the TIMIT database demonstrates that the approach is the first effective use of an explicit model for statistical dependence between frames of speech. >
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paper_title: Impact of Accuracy, Spatial Availability, and Revisit Time of Satellite-Derived Surface Soil Moisture in a Multiscale Ensemble Data Assimilation System

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This study evaluates the sensitivity of a multiscale ensemble assimilation system to different configurations of satellite soil moisture observations, namely the retrieval accuracy, spatial availability, and revisit time. We perform horizontally coupled assimilation experiments where pixels are updated not only by observations at the same location but also all in the study domain. Carrying out sensitivity studies within a multiscale assimilation system is a significant advancement over previous studies that used a 1-D assimilation framework where all horizontal grids are uncoupled. Twin experiments are performed with synthetic soil moisture retrievals. The hydrologic modeling system is forced with satellite estimated rainfall, and the assimilation performance is evaluated against model simulations using in-situ measured rainfall. The study shows that the assimilation performance is most sensitive to the spatial availability of soil moisture observations, then to revisit time and least sensitive to retrieval accuracy. The horizontally coupled assimilation system performs reasonably well even with large observation errors, and it is less sensitive to retrieval accuracy than the uncoupled system, as reported by previous studies. This suggests that more information may be extracted from satellite soil moisture observations using multiscale assimilation systems resulting in a potentially higher value of such satellite products.
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paper_title: A simple hydrologically based model of land surface water and energy fluxes for general circulation models

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A generalization of the single soil layer variable infiltration capacity (VIC) land surface hydrological model previously implemented in the Geophysical Fluid Dynamics Laboratory (GFDL) general circulation model (GCM) is described. The new model is comprised of a two-layer characterization of the soil column, and uses an aerodynamic representation of the latent and sensible heat fluxes at the land surface. The infiltration algorithm for the upper layer is essentially the same as for the single layer VIC model, while the lower layer drainage formulation is of the form previously implemented in the Max-Planck-Institut GCM. The model partitions the area of interest (e.g., grid cell) into multiple land surface cover types; for each land cover type the fraction of roots in the upper and lower zone is specified. Evapotranspiration consists of three components: canopy evaporation, evaporation from bare soils, and transpiration, which is represented using a canopy and architectural resistance formulation. Once the latent heat flux has been computed, the surface energy balance is iterated to solve for the land surface temperature at each time step. The model was tested using long-term hydrologic and climatological data for Kings Creek, Kansas to estimate and validate the hydrological parameters, and surface flux data frommore » three First International Satellite Land Surface Climatology Project Field Experiment (FIFE) intensive field campaigns in the summer-fall of 1987 to validate the surface energy fluxes.« less
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paper_title: A Multiscale Ensemble Filtering System for Hydrologic Data Assimilation. Part I: Implementation and Synthetic Experiment

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Abstract The multiscale autoregressive (MAR) framework was introduced in the last decade to process signals that exhibit multiscale features. It provides the method for identifying the multiscale structure in signals and a filtering procedure, and thus is an efficient way to solve the optimal estimation problem for many high-dimensional dynamic systems. Later, an ensemble version of this multiscale filtering procedure, the ensemble multiscale filter (EnMSF), was developed for estimation systems that rely on Monte Carlo samples, making this technique suitable for a range of applications in geosciences. Following the prototype study that introduced EnMSF, a strategy is devised here to implement the multiscale method in a hydrologic data assimilation system, which runs a land surface model. Assimilation experiments are carried out over the Arkansas–Red River basin, located in the central United States (∼645 000 km2), using the Variable Infiltration Capacity (VIC) model with a computing grid of 1062 pixels. A...
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paper_title: The Soil Moisture Active Passive (SMAP) Mission

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The Soil Moisture Active Passive (SMAP) mission is one of the first Earth observation satellites being developed by NASA in response to the National Research Council's Decadal Survey. SMAP will make global measurements of the soil moisture present at the Earth's land surface and will distinguish frozen from thawed land surfaces. Direct observations of soil moisture and freeze/thaw state from space will allow significantly improved estimates of water, energy, and carbon transfers between the land and the atmosphere. The accuracy of numerical models of the atmosphere used in weather prediction and climate projections are critically dependent on the correct characterization of these transfers. Soil moisture measurements are also directly applicable to flood assessment and drought monitoring. SMAP observations can help monitor these natural hazards, resulting in potentially great economic and social benefits. SMAP observations of soil moisture and freeze/thaw timing will also reduce a major uncertainty in quantifying the global carbon balance by helping to resolve an apparent missing carbon sink on land over the boreal latitudes. The SMAP mission concept will utilize L-band radar and radiometer instruments sharing a rotating 6-m mesh reflector antenna to provide high-resolution and high-accuracy global maps of soil moisture and freeze/thaw state every two to three days. In addition, the SMAP project will use these observations with advanced modeling and data assimilation to provide deeper root-zone soil moisture and net ecosystem exchange of carbon. SMAP is scheduled for launch in the 2014-2015 time frame.
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paper_title: Impact of Multiresolution Active and Passive Microwave Measurements on Soil Moisture Estimation Using the Ensemble Kalman Smoother

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An observing system simulation experiment is developed to test tradeoffs in resolution and accuracy for soil moisture estimation using active and passive L-band remote sensing. Concepts for combined radar and radiometer missions include designs that will provide multiresolution measurements. In this paper, the scientific impacts of instrument performance are analyzed to determine the measurement requirements for the mission concept. The ensemble Kalman smoother (EnKS) is used to merge these multiresolution observations with modeled soil moisture from a land surface model to estimate surface and subsurface soil moisture at 6-km resolution. The model used for assimilation is different from that used to generate "truth." Consequently, this experiment simulates how data assimilation performs in real applications when the model is not a perfect representation of reality. The EnKS is an extension of the ensemble Kalman filter (EnKF) in which observations are used to update states at previous times. Previous work demonstrated that it provides a computationally inexpensive means to improve the results from the EnKF, and that the limited memory in soil moisture can be exploited by employing it as a fixed lag smoother. Here, it is shown that the EnKS can be used in large problems with spatially distributed state vectors and spatially distributed multiresolution observations. The EnKS-based data assimilation framework is used to study the synergy between passive and active observations that have different resolutions and measurement error distributions. The extent to which the design parameters of the EnKS vary depending on the combination of observations assimilated is investigated
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paper_title: Optimal multiscale Kalman filter for assimilation of near-surface soil moisture into land surface models

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[1] We undertake an alternative and novel approach to assimilation of near-surface soil moisture into land surface models by means of an extension of multiscale Kalman filtering (MKF). While most data assimilation studies rely on the assumption of spatially independent near-surface soil moisture observations to attain computational tractability in large-scale problems, MKF allows us to explicitly and very efficiently model the spatial dependence and scaling properties of near-surface soil moisture fields. Furthermore, MKF has the appealing ability to cope with model predictions and observations made at different spatial scales. Yet another essential feature of our approach is that we resort to the use of the expectation maximization (EM) algorithm in conjunction with MKF so that the statistical parameters inherent to MKF may be optimally determined directly from the data at hand and allowed to vary over time. This constitutes a significant advantage since these parameters (e.g., observation and model error noise variances) essentially determine the performance of the assimilation approach and have so far been most commonly prescribed heuristically and not allowed to evolve in time. We test our approach by assimilating the near-surface soil moisture fields derived from electronically scanned thinned array radiometer (ESTAR) during the Southern Great Plains Hydrology experiment of 1997 (SGP97) into the three-layer variable infiltration capacity (VIC-3L) land surface model. The results show that assimilation significantly improves the short-term predictions of soil moisture and energy fluxes from VIC-3L, especially with regard to capturing the spatial structure of these state variables. Additionally, we find that allowing the statistical parameters of the assimilation algorithm to evolve in time allows for an adequate representation of the time-varying uncertainties in land surface model predictions.
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paper_title: A soil-vegetation-atmosphere transfer scheme for modeling spatially variable water and energy balance processes

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In support of the eventual goal to integrate remotely sensed observations with coupled land-atmosphere models, a soil-vegetation-atmosphere transfer scheme is presented which can represent spatially variable water and energy balance processes on timescales of minutes to months. This scheme differs from previous schemes developed to address similar objectives in that it: (1) represents horizontal heterogeneity and transport in a TOPMODEL framework, and (2) maintains computational efficiency while representing the processes most important for our applications. The model is based on the original TOPMODEL-based land surface-atmosphere transfer scheme [Famiglietti and Wood, 1994a] with modifications to correct for deficiencies in the representation of ground heat flux, soil column geometry, soil evaporation, transpiration, and the effect of atmospheric stability on energy fluxes. These deficiencies were found to cause errors in the model predictions in quantities such as the sensible heat flux, to which the development of the atmospheric boundary layer is particularly sensitive. Application of the model to the entire First International Satellite Land Surface Climatology Project Field Experiment 1987 experimental period, focusing on Intensive Field Campaigns 3 and 4, shows that it successfully represents the essential processes of interest.
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paper_title: How much improvement can precipitation data fusion achieve with a Multiscale Kalman Smoother-based framework?

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[1] With advancements in measuring techniques and modeling approaches, more and more precipitation data products, with different spatial resolutions and accuracies, become available. Therefore, there is an increasing need to produce a fused precipitation product that can take advantage of the strengths of each individual precipitation data product. This study systematically and quantitatively evaluates the improvements of the fused precipitation data as a result of using the Mulitscale Kalman Smoother-based (i.e., MKS-based) framework. Impacts of two types of errors, i.e., white noise and bias that are associated with individual precipitation products, are investigated through hypothetical experiments. Two measures, correlation and root-mean-square error, are used to evaluate the improvements of the fused precipitation data. Our study shows that the MKS-based framework can significantly recover the loss of precipitation's spatial patterns and magnitudes that are associated with the white noise and bias when the erroneous data at different spatial scales are fused together. Although the erroneous data at a finer resolution are generally more effective in improving the spatial patterns and magnitudes of the erroneous data at a coarser resolution, data at a coarser resolution can also provide valuable information in improving the quality of the data at a finer resolution when they are fused. This study provides insights on the values of the MKS-based framework and a guideline for determining a potentially optimal spatial scale over which improvements in both the spatial patterns and the magnitudes can be maximized based on given data with different spatial resolutions.
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paper_title: Data assimilation for transient flow in geologic formations via ensemble Kalman filter

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Formation properties are one of the key factors in numerical modeling of flow and transport in geologic formations in spite of the fact that they may not be completely characterized. The incomplete knowledge or uncertainty in the description of the formation properties leads to uncertainty in simulation results. In this study, the ensemble Kalman filter (EnKF) approach is used for continuously updating model parameters such as hydraulic conductivity and model variables such as pressure head while simultaneously providing an estimate of the uncertainty through assimilating dynamic and static measurements, without resorting to the explicit computation of the covariance or the Jacobian of the state variables. A two-dimensional example is built to demonstrate the capability of EnKF and to analyze its sensitivity with respect to different factors such as the number of realizations, measurement timings, and initial guesses. An additional example is given to illustrate the applicability of EnKF to three-dimensional problems and to examine the model predictability after dynamic data assimilation. It is found from these examples that EnKF provides an efficient approach for obtaining satisfactory estimation of the hydraulic conductivity field with dynamic measurements. After data assimilation the conductivity field matches the reference field very well, and different kinds of incorrect prior knowledge of the formation properties may also be rectified to a certain extent.
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paper_title: Groundwater parameter estimation using the ensemble Kalman filter with localization

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The ensemble Kalman filter (EnKF), an efficient data assimilation method showing advantages in many numerical experiments, is deficient when used in approximating covariance from an ensemble of small size. Implicit localization is used to add distance-related weight to covariance and filter spurious correlations which weaken the EnKF’s capability to estimate uncertainty correctly. The effect of this kind of localization is studied in two-dimensional (2D) and three-dimensional (3D) synthetic cases. It is found that EnKF with localization can capture reliably both the mean and variance of the hydraulic conductivity field with higher efficiency; it can also greatly stabilize the assimilation process as a small-size ensemble is used. Sensitivity experiments are conducted to explore the effect of localization function format and filter lengths. It is suggested that too long or too short filter lengths will prevent implicit localization from modifying the covariance appropriately. Steep localization functions will greatly disturb local dynamics like the 0-1 function even if the function is continuous; four relatively gentle localization functions succeed in avoiding obvious disturbance to the system and improve estimation. As the degree of localization of the L function increases, the parameter sensitivity becomes weak, making parameter selection easier, but more information may be lost in the assimilation process.
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paper_title: Investigation of flow and transport processes at the MADE site using ensemble Kalman filter

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In this work the ensemble Kalman filter (EnKF) is applied to investigate the flow and transport processes at the macro-dispersion experiment (MADE) site in Columbus, MS. The EnKF is a sequential data assimilation approach that adjusts the unknown model parameter values based on the observed data with time. The classic advection–dispersion (AD) and the dual-domain mass transfer (DDMT) models are employed to analyze the tritium plume during the second MADE tracer experiment. The hydraulic conductivity (K), longitudinal dispersivity in the AD model, and mass transfer rate coefficient and mobile porosity ratio in the DDMT model, are estimated in this investigation. Because of its sequential feature, the EnKF allows for the temporal scaling of transport parameters during the tritium concentration analysis. Inverse simulation results indicate that for the AD model to reproduce the extensive spatial spreading of the tritium observed in the field, the K in the downgradient area needs to be increased significantly. The estimated K in the AD model becomes an order of magnitude higher than the in situ flowmeter measurements over a large portion of media. On the other hand, the DDMT model gives an estimation of K that is much more comparable with the flowmeter values. In addition, the simulated concentrations by the DDMT model show a better agreement with the observed values. The root mean square (RMS) between the observed and simulated tritium plumes is 0.77 for the AD model and 0.45 for the DDMT model at 328 days. Unlike the AD model, which gives inconsistent K estimates at different times, the DDMT model is able to invert the K values that consistently reproduce the observed tritium concentrations through all times.
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paper_title: Jointly Mapping Hydraulic Conductivity and Porosity by Assimilating Concentration Data via Ensemble Kalman Filter

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Summary Real-time data from on-line sensors offer the possibility to update environmental simulation models in real-time. Information from on-line sensors concerning contaminant concentrations in groundwater allow for the real-time characterization and control of a contaminant plume. In this paper it is proposed to use the CPU-efficient Ensemble Kalman Filter (EnKF) method, a data assimilation algorithm, for jointly updating the flow and transport parameters (hydraulic conductivity and porosity) and state variables (piezometric head and concentration) of a groundwater flow and contaminant transport problem. A synthetic experiment is used to demonstrate the capability of the EnKF to estimate hydraulic conductivity and porosity by assimilating dynamic head and multiple concentration data in a transient flow and transport model. In this work the worth of hydraulic conductivity, porosity, piezometric head, and concentration data is analyzed in the context of aquifer characterization and prediction uncertainty reduction. The results indicate that the characterization of the hydraulic conductivity and porosity fields is continuously improved as more data are assimilated. Also, groundwater flow and mass transport predictions are improved as more and different types of data are assimilated. The beneficial impact of accounting for multiple concentration data is patent.
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paper_title: Best unbiased ensemble linearization and the quasi-linear Kalman ensemble generator: QUASI-LINEAR KALMAN ENSEMBLE GENERATOR

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[1] Linearized representations of the stochastic groundwater flow and transport equations have been heavily used in hydrogeology, e.g., for geostatistical inversion or generating conditional realizations. The respective linearizations are commonly defined via Jacobians (numerical sensitivity matrices). This study will show that Jacobian-based linearizations are biased with nonminimal error variance in the ensemble sense. An alternative linearization approach will be derived from the principles of unbiasedness and minimum error variance. The resulting paradigm prefers empirical cross covariances from Monte Carlo analyses over those from linearized error propagation and points toward methods like ensemble Kalman filters (EnKFs). Unlike conditional simulation in geostatistical applications, EnKFs condition transient state variables rather than geostatistical parameter fields. Recently, modifications toward geostatistical applications have been tested and used. This study completes the transformation of EnKFs to geostatistical conditioning tools on the basis of best unbiased ensemble linearization. To distinguish it from the original EnKF, the new method is called the Kalman ensemble generator (KEG). The new context of best unbiased ensemble linearization provides an additional theoretical foundation to EnKF-like methods (such as the KEG). Like EnKFs and derivates, the KEG is optimal for Gaussian variables. Toward increased robustness and accuracy in non-Gaussian and nonlinear cases, sequential updating, acceptance/rejection sampling, successive linearization, and a Levenberg-Marquardt formalism are added. State variables are updated through simulation with updated parameters, always guaranteeing the physicalness of all state variables. The KEG combines the computational efficiency of linearized methods with the robustness of EnKFs and accuracy of expensive realization-based methods while drawing on the advantages of conditional simulation over conditional estimation (such as adequate representation of solute dispersion). As proof of concept, a large-scale numerical test case with 200 synthetic sets of flow and tracer data is conducted and analyzed.
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paper_title: An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering

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Abstract The ensemble Kalman filter (EnKF) is a commonly used real-time data assimilation algorithm in various disciplines. Here, the EnKF is applied, in a hydrogeological context, to condition log-conductivity realizations on log-conductivity and transient piezometric head data. In this case, the state vector is made up of log-conductivities and piezometric heads over a discretized aquifer domain, the forecast model is a groundwater flow numerical model, and the transient piezometric head data are sequentially assimilated to update the state vector. It is well known that all Kalman filters perform optimally for linear forecast models and a multiGaussian-distributed state vector. Of the different Kalman filters, the EnKF provides a robust solution to address non–linearities; however, it does not handle well non-Gaussian state-vector distributions. In the standard EnKF, as time passes and more state observations are assimilated, the distributions become closer to Gaussian, even if the initial ones are clearly non-Gaussian. A new method is proposed that transforms the original state vector into a new vector that is univariate Gaussian at all times. Back transforming the vector after the filtering ensures that the initial non-Gaussian univariate distributions of the state-vector components are preserved throughout. The proposed method is based in normal-score transforming each variable for all locations and all time steps. This new method, termed the normal-score ensemble Kalman filter (NS-EnKF), is demonstrated in a synthetic bimodal aquifer resembling a fluvial deposit, and it is compared to the standard EnKF. The proposed method performs better than the standard EnKF in all aspects analyzed (log-conductivity characterization and flow and transport predictions).
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paper_title: Diffusion wave modeling of distributed catchment dynamics

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A diffusion wave model of distributed catchment dynamics is presented. The effects of catchment topography and river network structure on storm-flow response are incorporated by routing surface runoff in cascade throughout a digital elevation model (DEM) based conceptual transport network, where the Muskingum-Cunge scheme with variable parameters is used to describe surface runoff dynamics. Dynamic scaling of hydraulic geometry is also incorporated in the model by using the 1953 “at-a-station” and “downstream” relationships by \ILeopold and Maddock\N. Numerical experiments indicate that the model is more than 98% mass conservative for possible slope and roughness configurations, which may occur for hillslopes in a natural catchment. Fluctuations in the simulated discharge may occur in response to discontinuities in rainfall excess representation if Courant number \ICu\N during the simulation exceeds a threshold of about 3. Catchment scale simulations with different temporal resolution show that the model response is independent of structural parameters (model consistency). Also, the overall accuracy is preserved for computationally inexpensive space-time discretizations (for which \ICu\N > 3) because fluctuations that may occur at the local scale are dampened when propagating downstream. Comparison of model results with observed outlet hydrographs of the Rio Missiaga experimental catchment (Eastern Italian Alps) show this approach to be capable of describing both overland and channel phases of surface runoff in mountainous catchments.
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paper_title: A detailed model for simulation of catchment scale subsurface hydrologic processes

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A catchment scale numerical model is developed based on the three-dimensional transient Richards equation describing fluid flow in variably saturated porous media. The model is designed to take advantage of digital elevation data bases and of information extracted from these data bases by topographic analysis. The practical application of the model is demonstrated in simulations of a small subcatchment of the Konza Prairie reserve near Manhattan, Kansas. In a preliminary investigation of computational issues related to model resolution, we obtain satisfactory numerical results using large aspect ratios, suggesting that horizontal grid dimensions may not be unreasonably constrained by the typically much smaller vertical length scale of a catchment and by vertical discretization requirements. Additional tests are needed to examine the effects of numerical constraints and parameter heterogeneity in determining acceptable grid aspect ratios. In other simulations we attempt to match the observed streamflow response of the catchment, and we point out the small contribution of the streamflow component to the overall water balance of the catchment.
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paper_title: Estimating geostatistical parameters and spatially-variable hydraulic conductivity within a catchment system using an ensemble smoother

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Groundwater flow models are important tools in assessing baseline conditions and investigating management alternatives in groundwater systems. The usefulness of these models, however, is often hindered by insufficient knowledge regarding the magnitude and spatial distribution of the spatially-distributed parameters, such as hydraulic conductivity ( K ), that govern the response of these models. Proposed parameter estimation methods frequently are demonstrated using simplified aquifer representations, when in reality the groundwater regime in a given watershed is influenced by strongly-coupled surface-subsurface processes. Furthermore, parameter estimation methodologies that rely on a geostatistical structure of K often assume the parameter values of the geostatistical model as known or estimate these values from limited data. In this study, we investigate the use of a data assimilation algorithm, the Ensemble Smoother, to provide enhanced estimates of K within a catchment system using the fully-coupled, surface-subsurface flow model CATHY. Both water table elevation and streamflow data are assimilated to condition the spatial distribution of K . An iterative procedure using the ES update routine, in which geostatistical parameter values defining the true spatial structure of K are identified, is also presented. In this procedure, parameter values are inferred from the updated ensemble of K fields and used in the subsequent iteration to generate the K ensemble, with the process proceeding until parameter values are converged upon. The parameter estimation scheme is demonstrated via a synthetic three-dimensional tilted v-shaped catchment system incorporating stream flow and variably-saturated subsurface flow, with spatio-temporal variability in forcing terms. Results indicate that the method is successful in providing improved estimates of the K field, and that the iterative scheme can be used to identify the geostatistical parameter values of the aquifer system. In general, water table data have a much greater ability than streamflow data to condition K . Future research includes applying the methodology to an actual regional study site.
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paper_title: Parameterization of stream channel geometry in the distributed modeling of catchment dynamics

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A simple and efficient procedure for incorporating the effects of stream channel geometry in the distributed modeling of catchment dynamics is developed. At-a- station and downstream fluvial relationships are combined and the obtained laws of variability in space and time for water-surface width and wetted perimeter are incorporated into a diffusion wave routing model based on the Muskingum-Cunge method with variable parameters. The parameterization obtained is applied to the approximately 840-km 2 Sieve catchment (Central Italian Apennines) to test the possibility of estimating channel geometry parameters from cross-section surveys and to assess the impact of dynamic variations in the channel geometry on catchment dynamics. The use of the estimated channel geometry in surface runoff routing produces a significant improvement in the flood hydrograph description at the catchment outlet with respect to less detailed network parameterizations. In addition, the results obtained from a "downstream" analysis of the velocity field indicate that the stream characteristics related to the locally varying cross-section shape may have a strong control on flow velocities, and thus they should be monitored and synthesized for a comprehensive description of the distributed catchment dynamics.
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paper_title: Ensemble smoother assimilation of hydraulic head and return flow data to estimate hydraulic conductivity distribution

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[1] Numerical groundwater models, frequently used to enhance understanding of the hydrologic and chemical processes in local or regional aquifers, are often hindered by an incomplete representation of the parameters which characterize these processes. In this study, we present the use of a data assimilation algorithm that incorporates all past model results and data measurements, an ensemble smoother (ES) to provide enhanced estimates of aquifer hydraulic conductivity (K) through assimilation of hydraulic head (H) and groundwater return flow volume (RFV) measurements into groundwater model simulation results. On the basis of the Kalman filter methodology, residuals between forecasted model results and measurements, together with covariances between model results at measurement locations and nonmeasurement locations, are used to correct model results. Parameter estimation is achieved by incorporating model parameters into the algorithm, thus allowing the correlation between H, RFV, and K to correct the K fields. The applicability of the ES is demonstrated using a synthetic two-dimensional transient groundwater modeling simulation. Sensitivity analyses are carried out to show the performance of the ES in regard to measurement error, number of measurements, number of assimilation times, correlation length of the K fields, and the number of stream gage locations. Results show that the departure of the K fields from a reference K field is greatly reduced through data assimilation and demonstrate that the ES scheme is a promising alternative to other inverse modeling techniques because of low computational burden and the ability to run the algorithm entirely independent of the groundwater model simulation.
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paper_title: A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems

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Picard iteration is a widely used procedure for solving the nonlinear equation governing flow in variably saturated porous media. The method is simple to code and computationally cheap, but has been known to fail or converge slowly. The Newton method is more complex and expensive (on a per-iteration basis) than Picard, and as such has not received very much attention. Its robustness and higher rate of convergence, however, make it an attractive alternative to the Picard method, particularly for strongly nonlinear problems. In this paper the Picard and Newton schemes are implemented and compared in one-, two-, and three-dimensional finite element simulations involving both steady state and transient flow. The eight test cases presented highlight different aspects of the performance of the two iterative methods and the different factors that can affect their convergence and efficiency, including problem size, spatial and temporal discretization, initial solution estimates, convergence error norm, mass lumping, time weighting, conductivity and moisture content characteristics, boundary conditions, seepage faces, and the extent of fully saturated zones in the soil. Previous strategies for enhancing the performance of the Picard and Newton schemes are revisited, and new ones are suggested. The strategies include chord slope approximations for the derivatives of the characteristic equations, relaxing convergence requirements along seepage faces, dynamic time step control, nonlinear relaxation, and a mixed Picard-Newton approach. The tests show that the Picard or relaxed Picard schemes are often adequate for solving Richards' equation, but that in cases where these fail to converge or converge slowly, the Newton method should be used. The mixed Picard-Newton approach can effectively overcome the Newton scheme's sensitivity to initial solution estimates, while comparatively poor performance is reported for the various chord slope approximations. Finally, given the reliability and efficiency of current conjugate gradient-like methods for solving linear nonsymmetric systems, the only real drawback of using Newton rather than Picard iteration is the algebraic complexity and computational cost of assembling the derivative terms of the Jacobian matrix, and it is suggested that both methods can be effectively implemented and used in numerical models of Richards' equation.
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paper_title: Ensemble Kalman filter data assimilation for a process-based catchment scale model of surface and subsurface flow: EnKF FOR A MODEL OF SURFACE AND SUBSURFACE FLOW

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[1] A sequential data assimilation procedure based on the ensemble Kalman filter (EnKF) is introduced and tested for a process-based numerical model of coupled surface and subsurface flow. The model is based on the three-dimensional Richards equation for variably saturated porous media and a diffusion wave approximation for overland and channel flow. A one-dimensional soil column experiment and a three-dimensional tilted v-catchment test case are presented. A preliminary analysis of the assimilation scheme is undertaken for the one-dimensional test case in order to validate the implementation by comparison with published results and to assess the influence of various factors on the filter's performance. The numerical results suggest robustness with respect to the ensemble size and provide useful information for the more complex tilted v-catchment test case. The assimilation frequency and the effects induced by data assimilation on the surface and/or subsurface system states are then evaluated for the v-catchment experiment using synthetic observations of pressure head and streamflow. The results suggest that streamflow prediction can be improved by assimilation of pressure head and streamflow, either individually or in tandem, whereas assimilation of streamflow data alone does not improve the subsurface system state. In terms of the global system state, i.e., surface and subsurface variables, frequent updates are especially beneficial when assimilating both pressure head and streamflow. Furthermore, it is shown that better evaluation of the subsurface volume resulting from assimilation of head data is crucial for improving subsequent surface response.
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paper_title: Assimilation of streamflow and in situ soil moisture data into operational distributed hydrologic models: Effects of uncertainties in the data and initial model soil moisture states

paper_content:

Abstract We assess the potential of updating soil moisture states of a distributed hydrologic model by assimilating streamflow and in situ soil moisture data for high-resolution analysis and prediction of streamflow and soil moisture. The model used is the gridded Sacramento (SAC) and kinematic-wave routing models of the National Weather Service (NWS) Hydrology Laboratory’s Research Distributed Hydrologic Model (HL-RDHM) operating at an hourly time step. The data assimilation (DA) technique used is variational assimilation (VAR). Assimilating streamflow and soil moisture data into distributed hydrologic models is new and particularly challenging due to the large degrees of freedom associated with the inverse problem. This paper reports findings from the first phase of the research in which we assume, among others, perfectly known hydrometeorological forcing. The motivation for the simplification is to reduce the complexity of the problem in favour of improved understanding and easier interpretation even if it may compromise the goodness of the results. To assess the potential, two types of experiments, synthetic and real-world, were carried out for Eldon (ELDO2), a 795-km2 headwater catchment located near the Oklahoma (OK) and Arkansas (AR) border in the U.S. The synthetic experiment assesses the upper bound of the performance of the assimilation procedure under the idealized conditions of no structural or parametric errors in the models, a full dynamic range and no microscale variability in the in situ observations of soil moisture, and perfectly known univariate statistics of the observational errors. The results show that assimilating in situ soil moisture data in addition to streamflow data significantly improves analysis and prediction of soil moisture and streamflow, and that assimilating streamflow observations at interior locations in addition to those at the outlet improves analysis and prediction of soil moisture within the drainage areas of the interior stream gauges and of streamflow at downstream cells along the channel network. To assess performance under more realistic conditions, but still under the assumption of perfectly known hydrometeorological forcing to allow comparisons with the synthetic experiment, an exploratory real-world experiment was carried out in which all other assumptions were lifted. The results show that, expectedly, assimilating interior flows in addition to outlet flow improves analysis as well as prediction of streamflow at stream gauge locations, but that assimilating in situ soil moisture data in addition to streamflow data provides little improvement in streamflow analysis and prediction though it reduces systematic biases in soil moisture simulation.
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paper_title: Hydrology laboratory research modeling system (HL-RMS) of the US national weather service

paper_content:

This study investigates an approach that combines physically-based and conceptual model features in two stages of distributed modeling: model structure development and estimation of spatially variable parameters. The approach adds more practicality to the process of model parameterization, and facilitates an easier transition from current lumped model-based operational systems to more powerful distributed systems. This combination of physically-based and conceptual model features is implemented within the Hydrology Laboratory Research Modeling System (HL-RMS). HL-RMS consists of a well-tested conceptual water balance model applied on a regular spatial grid linked to physically-based kinematic hillslope and channel routing models. Parameter estimation procedures that combine spatially distributed and ‘integrated’ basin-outlet properties have been developed for the water balance and routing components. High-resolution radar-based precipitation data over a large region are used in testing HL-RMS. Initial tests show that HL-RMS yields results comparable to well-calibrated lumped model simulations in several headwater basins, and it outperforms a lumped model in basins where spatial rainfall variability effects are significant. It is important to note that simulations for two nested basins (not calibrated directly, but parameters from the calibration of the parent basin were applied instead) outperformed lumped simulations even more consistently, which means that HL-RMS has the potential to improve the accuracy and resolution of river runoff forecasts. Published by Elsevier B.V.
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paper_title: Real-Time Variational Assimilation of Hydrologic and Hydrometeorological Data into Operational Hydrologic Forecasting

paper_content:

Variational assimilation (VAR) of hydrologic and hydrometeorological data into operational hydrologic forecasting is explored. The data assimilated are the hourly real-time observations of streamflow and precipitation, and climatological estimates of potential evaporation (PE). The hydrologic system considered is a single headwater basin for which soil moisture accounting and routing are carried out in a lumped fashion via the Sacramento model (SAC) and the unit hydrograph (UH), respectively. The control variables in the VAR formulation are the fast-varying SAC soil moisture states at the beginning of the assimilation window and the multiplicative adjustment factors to the estimates of mean areal precipitation (MAP) and mean areal potential evaporation (MAPE) for each hour in the assimilation window. In a separate application of VAR as a parameter estimation tool, the estimation of empirical UH is also explored by treating its ordinates as the control variables. To evaluate the assimilation procedure thus developed, streamflow was forecast with and without the aid of VAR for three basins in the southern plains under the assumption of perfectly forecast future mean areal precipitation (FMAP). The streamflow forecasts were then compared with each other and with those based on persistence and the state space-based state-updating procedure, the state-space Sacramento model (SS-SAC). The results indicate that the VAR procedure significantly improves the accuracy of the basic forecast at short lead times and compares favorably with SS-SAC.
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paper_title: The soil and water assessment tool—Historical development applications, and future research directions

paper_content:

The Soil and Water Assessment Tool (SWAT) model is a continuation of nearly 30 years of modeling efforts conducted by the USDA Agricultural Research Service (ARS). SWAT has gained international acceptance as a robust interdisciplinary watershed modeling tool as evidenced by international SWAT conferences, hundreds of SWAT-related papers presented at numerous other scientific meetings, and dozens of articles published in peer-reviewed journals. The model has also been adopted as part of the U.S. Environmental Protection Agency (USEPA) Better Assessment Science Integrating Point and Nonpoint Sources (BASINS) software package and is being used by many U.S. federal and state agencies, including the USDA within the Conservation Effects Assessment Project (CEAP). At present, over 250 peer-reviewed published articles have been identified that report SWAT applications, reviews of SWAT components, or other research that includes SWAT. Many of these peer-reviewed articles are summarized here according to relevant application categories such as streamflow calibration and related hydrologic analyses, climate change impacts on hydrology, pollutant load assessments, comparisons with other models, and sensitivity analyses and calibration techniques. Strengths and weaknesses of the model are presented, and recommended research needs for SWAT are also provided.
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paper_title: Data assimilation for distributed hydrological catchment modeling via ensemble Kalman filter

paper_content:

Catchment scale hydrological models are critical decision support tools for water resources management and environment remediation. However, the reliability of hydrological models is inevitably affected by limited measurements and imperfect models. Data assimilation techniques combine complementary information from measurements and models to enhance the model reliability and reduce predictive uncertainties. As a sequential data assimilation technique, the ensemble Kalman filter (EnKF) has been extensively studied in the earth sciences for assimilating in-situ measurements and remote sensing data. Although the EnKF has been demonstrated in land surface data assimilations, there are no systematic studies to investigate its performance in distributed modeling with high dimensional states and parameters. In this paper, we present an assessment on the EnKF with state augmentation for combined state-parameter estimation on the basis of a physical-based hydrological model, Soil and Water Assessment Tool (SWAT). Through synthetic simulation experiments, the capability of the EnKF is demonstrated by assimilating the runoff and other measurements, and its sensitivities are analyzed with respect to the error specification, the initial realization and the ensemble size. It is found that the EnKF provides an efficient approach for obtaining a set of acceptable model parameters and satisfactory runoff, soil water content and evapotranspiration estimations. The EnKF performance could be improved after augmenting with other complementary data, such as soil water content and evapotranspiration from remote sensing retrieval. Sensitivity studies demonstrate the importance of consistent error specification and the potential with small ensemble size in the data assimilation system.
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paper_title: Ensemble Kalman filter data assimilation for a process-based catchment scale model of surface and subsurface flow: EnKF FOR A MODEL OF SURFACE AND SUBSURFACE FLOW

paper_content:

[1] A sequential data assimilation procedure based on the ensemble Kalman filter (EnKF) is introduced and tested for a process-based numerical model of coupled surface and subsurface flow. The model is based on the three-dimensional Richards equation for variably saturated porous media and a diffusion wave approximation for overland and channel flow. A one-dimensional soil column experiment and a three-dimensional tilted v-catchment test case are presented. A preliminary analysis of the assimilation scheme is undertaken for the one-dimensional test case in order to validate the implementation by comparison with published results and to assess the influence of various factors on the filter's performance. The numerical results suggest robustness with respect to the ensemble size and provide useful information for the more complex tilted v-catchment test case. The assimilation frequency and the effects induced by data assimilation on the surface and/or subsurface system states are then evaluated for the v-catchment experiment using synthetic observations of pressure head and streamflow. The results suggest that streamflow prediction can be improved by assimilation of pressure head and streamflow, either individually or in tandem, whereas assimilation of streamflow data alone does not improve the subsurface system state. In terms of the global system state, i.e., surface and subsurface variables, frequent updates are especially beneficial when assimilating both pressure head and streamflow. Furthermore, it is shown that better evaluation of the subsurface volume resulting from assimilation of head data is crucial for improving subsequent surface response.
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paper_title: Real-time forecasting of water table depth and soil moisture profiles

paper_content:

We present a method for real-time forecasting of water table depth and soil moisture profiles. The method combines a simple form of data-assimilation with a moving window calibration of a deterministic model describing flow in the unsaturated zone and local as well as regional drainage. The local drainage level is calibrated on-line using a moving window calibration. Assigning more weight to the last available measurements then yields a form of model adaptation that is in between on-line calibration and data-assimilation (i.e. a simplified form of Newtonian nudging). Five-day hydrological forecasts are performed based on 5-day weather forecasts, while on-line observations of phreatic level and soil moisture content are assimilated on a daily basis. Advantages of the proposed method are that it improves the real-time forecasts compared to off-line calibration and ordinary moving window calibration and that it yields physically consistent soil moisture profiles.
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paper_title: Modelling forest transpiration and CO2 fluxes: response to soil moisture stress

paper_content:

The effects of soil drought on the leaf gas exchange variables of a stomatal conductance model are assessed in the case of woody plants, based on a meta-analysis of data sets available from the literature. For the first stage, 32 data sets obtained in well-watered conditions are analysed. For the second stage, we analyse four data sets including a soil drying cycle under present and doubled atmospheric CO2 concentration (350 and 700mol mol −1 , respectively) for two tree species, maritime pine and sessile oak. Interesting relationships emerge, which suggest that woody plants may adopt one or two strategies when facing drought. A simple parameterisation of the effects of soil drought is proposed to account for the two types of drought responses which are: drought-avoiding (maritime pine) and drought-tolerant (sessile oak). © 2004 Elsevier B.V. All rights reserved.
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paper_title: Data Assimilation for Estimating the Terrestrial Water Budget Using a Constrained Ensemble Kalman Filter

paper_content:

Abstract A procedure is developed to incorporate equality constraints in Kalman filters, including the ensemble Kalman filter (EnKF), and is referred to as the constrained ensemble Kalman filter (CEnKF). The constraint is carried out as a two-step filtering approach, with the first step being the standard (ensemble) Kalman filter. The second step is the constraint step carried out by another Kalman filter that optimally redistributes any imbalance from the first step. The CEnKF is implemented over a 75 000 km2 domain in the southern Great Plains region of the United States, using the terrestrial water balance as the constraint. The observations, consisting of gridded fields of the upper two soil moisture layers from the Oklahoma Mesonet system, Atmospheric Radiation Measurement Program Cloud and Radiation Testbed (ARM-CART) energy balance Bowen ratio (EBBR) latent heat estimates, and U.S. Geological Survey (USGS) streamflow from unregulated basins, are assimilated into the Variable Infiltration Capacity (...
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paper_title: Joint assimilation of surface soil moisture and LAI observations into a land surface model

paper_content:

Land Surface Models (LSM) offer a description of land surface processes and set the lower boundary conditions for meteorological models. In particular, the accurate description of those surface variables which display a slow response in time, like root-zone soil moisture or vegetation biomass, is of great importance. Errors in their estimation yield significant inaccuracies in the estimation of heat and water fluxes in Numerical Weather Prediction (NWP) models. In the present study, the ISBA-A-gs LSM is used decoupled from the atmosphere. In this configuration, the model is able to simulate the vegetation growth, and consequently LAI. A simplified 1D-VAR assimilation method is applied to observed surface soil moisture and LAI observations of the SMOSREX site near Toulouse, in south-western France, from 2001 to 2004. This period includes severe droughts in 2003 and 2004. The data are jointly assimilated into ISBA-A-gs in order to analyse the root-zone soil moisture and the vegetation biomass. It is shown that the 1D-VAR improves the model results. The efficiency score of the model (Nash criterion) is increased from 0.79 to 0.86 for root-zone soil moisture and from 0.17 to 0.23 for vegetation biomass.
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paper_title: Modeling ground heat flux in land surface parameterization schemes

paper_content:

A new ground heat flux parameterization for land surface schemes, such as those used in climate and numerical weather prediction models, is described. Compared with other approaches that lump the canopy layer and ground surface, or empirically based approaches that consider the effect of radiation attenuation through the canopy layer, the new parameterization has several advantages. First, the reduction of radiation available for conducting soil surface exchange under vegetated areas is represented in a manner that assures that heat is conserved in the long term. Second, problems in representing properly the phase of the ground heat flux are alleviated. Finally, the approach is relatively simple and is computationally efficient, requiring only two soil thermal layers. Comparison of the method with analytical solutions for special cases shows that the new method approximates the analytical solution very well for different conditions, and that the new method is superior to the force-restore and the Crank-Nicholson method. Model-derived ground heat heat fluxes for the French HAPEX-MOBILHY (Hydrology-Atmosphere Pilot Experiment - Modelisation de Bilan Hydrique) site and the Brazilian ABRACOS (Anglo-Brazilian Amazonian Climate Observation Study) cleared ranch land site are shown to be in close agreement with observations. Sensitivity analyses show that if the attenuation of radiation under vegetation and soil heat storage are ignored, the daytime peak and nighttime minima of ground heat flux, latent and sensible heat fluxes, and surface temperature can be significantly in error. In particular, neglecting the radiation attenuation through the canopy layer can result in significant overestimation (underestimation) of daytime (nighttime) ground heat flux, while neglecting soil heat storage can result in significant phase errors.
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paper_title: One-dimensional statistical dynamic representation of subgrid spatial variability of precipitation in the two-layer variable infiltration capacity model

paper_content:

The two-layer variable infiltration capacity (VIC-2L) model is extended to incorporate a representation of subgrid variability in precipitation, using an analytical one-dimensional statistical dynamic representation for partial area coverage of precipitation. The analytical approach allows the effects of subgrid-scale spatial variability of precipitation on surface fluxes, runoff production, and soil moisture to be represented explicitly. With this method, spatially integrated representations of surface fluxes, runoff, and soil moisture due to subgrid-scale spatial variability in precipitation, infiltration, and vegetation cover are obtained. The results are compared with those obtained using an exhaustive pixel-based approach, and the results obtained by applying uniform precipitation over the precipitation-covered area. The precipitation coverage over a grid cell is shown to play a primary role in estimating the surface fluxes, runoff, and soil moisture. In general, the spatial distribution of precipitation within the precipitation-covered area plays a secondary role, in part because VIC-2L represents the subgrid spatial variability of soil properties. While the analytical approach gives good approximations to the pixel-based approach, and is superior to the uniform precipitation approach in general, the differences are not large.
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paper_title: Root zone soil moisture from the assimilation of screen‐level variables and remotely sensed soil moisture

paper_content:

[1] In most operational NWP models, root zone soil moisture is constrained using observations of screen-level temperature and relative humidity. While this generally improves low-level atmospheric forecasts, it often leads to unrealistic model soil moisture. Consequently, several NWP centers are moving toward also assimilating remotely sensed near-surface soil moisture observations. Within this context, an EKF is used to compare the assimilation of screen-level observations and near-surface soil moisture data from AMSR-E into the ISBA land surface model over July 2006. Several issues regarding the use of each data type are exposed, and the potential to use the AMSR-E data, either in place of or together with the screen-level data, is examined. When the two data types are assimilated separately, there is little agreement between the root zone soil moisture updates generated by each, indicating that for this experiment the AMSR-E data could not have replaced the screen-level data to obtain similar surface turbulent fluxes. For the screen-level variables, there is a persistent diurnal cycle in the model-observations bias, which is not related to soil moisture. The resulting diurnal cycle in the analysis increments demonstrates how assimilating screen-level observations can lead to unrealistic soil moisture updates, reinforcing the need to assimilate alternative data sets. However, when the two data types are assimilated together, the near-surface soil moisture provides a much weaker constraint of the root zone soil moisture than the screen-level observations do, and the inclusion of the AMSR-E data does not substantially change the results compared to the assimilation of screen-level variables alone.
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paper_title: On the Efficacy of Combining Thermal and Microwave Satellite Data as Observational Constraints for Root-Zone Soil Moisture Estimation

paper_content:

Abstract Data assimilation applications require the development of appropriate mathematical operators to relate model states to satellite observations. Two such “observation” operators were developed and used to examine the conditions under which satellite microwave and thermal observations provide effective constraints on estimated soil moisture. The first operator uses a two-layer surface energy balance (SEB) model to relate root-zone moisture with top-of-canopy temperature. The second couples SEB and microwave radiative transfer models to yield top-of-atmosphere brightness temperature from surface layer moisture content. Tangent linear models for these operators were developed to examine the sensitivity of modeled observations to variations in soil moisture. Assuming a standard deviation in the observed surface temperature of 0.5 K and maximal model sensitivity, the error in the analysis moisture content decreased by 11% for a background error of 0.025 m3 m−3 and by 29% for a background error of 0.05 m...
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paper_title: Multiscale modeling of spatially variable water and energy balance processes

paper_content:

This paper presents the model development component of a body of research which addresses aggregation and scaling in multiscale hydrological modeling. Water and energy balance models are developed at the local and catchment scales and at the macroscale by aggregating a simple soil-vegetation-atmosphere transfer scheme (SVATS) across scales in a topographic framework. A spatially distributed approach is followed to aggregate the SVATS to the catchment scale. A statistical-dynamical approach is utilized to simplify the large-scale modeling problem and to aggregate the SVATS to the macroscale. The resulting macroscale hydrological model is proposed for use as a land surface parameterization in atmospheric models. It differs greatly from the current generation of land surface parameterizations owing to its simplified representation of vertical process physics and its statistical representation of horizontally heterogeneous runoff and energy balance processes. The spatially distributed model formulation is explored to understand the role of spatial variability in determining areal-average fluxes and the dynamics of hydrological processes. The simpler macroscale formulation is analyzed to determine how it represents these important dynamics, with implications for the parameterization of runoff and energy balance processes in atmospheric models.
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paper_title: Joint Assimilation of Surface Temperature and L-Band Microwave Brightness Temperature in Land Data Assimilation

paper_content:

Soil moisture and soil temperature are tightly coupled variables in land surface models. The objective of this study was to evaluate the impact of the joint assimilation of soil moisture and land surface temperature data in a land surface model on soil moisture and soil temperature characterization. Three synthetic tests evaluated the joint assimilation of surface temperature (measured by MODIS) and brightness temperature (from L-band) into the Community Land Model using the local ensemble transform Kalman filter (LETKF). The following three tests were performed for dry and wet conditions: (i) assimilating surface temperature observations only
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paper_title: An interactive vegetation SVAT model tested against data from six contrasting sites

paper_content:

The interactions between soil, biosphere, and atmosphere scheme (ISBA) is modified in order to account for the atmospheric carbon dioxide concentration on the stomatal aperture. The physiological stomatal resistance scheme proposed by Jacobs (1994) is employed to describe photosynthesis and its coupling with stomatal resistance at leaf level. In addition, the plant response to soil water stress is driven by a normalized soil moisture factor applied to the mesophyll conductance. The computed vegetation net assimilation can be used to feed a simple growth submodel, and to predict the density of vegetation cover. Only two parameters are needed to calibrate the growth model: the leaf life expectancy and the effective biomass per unit leaf area. The new soil–vegetation–atmosphere transfer (SVAT) scheme, called ISBA–A–gs, is tested against data from six micrometeorological databases for vegetation ranging from temperate grassland to tropical forest. It is shown that ISBA–A–gs is able to simulate the water budget and the CO2 flux correctly. Also, the leaf area index predicted by the calibrated model agrees well with observations over canopy types ranging from shortcycled crops to evergreen grasslands or forests. Once calibrated, the model is able to adapt the vegetation density in response to changes in the precipitation distribution.
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paper_title: A simple hydrologically based model of land surface water and energy fluxes for general circulation models

paper_content:

A generalization of the single soil layer variable infiltration capacity (VIC) land surface hydrological model previously implemented in the Geophysical Fluid Dynamics Laboratory (GFDL) general circulation model (GCM) is described. The new model is comprised of a two-layer characterization of the soil column, and uses an aerodynamic representation of the latent and sensible heat fluxes at the land surface. The infiltration algorithm for the upper layer is essentially the same as for the single layer VIC model, while the lower layer drainage formulation is of the form previously implemented in the Max-Planck-Institut GCM. The model partitions the area of interest (e.g., grid cell) into multiple land surface cover types; for each land cover type the fraction of roots in the upper and lower zone is specified. Evapotranspiration consists of three components: canopy evaporation, evaporation from bare soils, and transpiration, which is represented using a canopy and architectural resistance formulation. Once the latent heat flux has been computed, the surface energy balance is iterated to solve for the land surface temperature at each time step. The model was tested using long-term hydrologic and climatological data for Kings Creek, Kansas to estimate and validate the hydrological parameters, and surface flux data frommore » three First International Satellite Land Surface Climatology Project Field Experiment (FIFE) intensive field campaigns in the summer-fall of 1987 to validate the surface energy fluxes.« less
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paper_title: Ability of the land surface model ISBA-A-gs to simulate leaf area index at the global scale: Comparison with satellites products

paper_content:

[1] The land surface model (LSM) ISBA-A-gs (Interactions between Soil, Biosphere and Atmosphere, CO2-reactive) is specifically designed to simulate leaf stomatal conductance and leaf area index (LAI) in response to climate, soil properties, and atmospheric carbon dioxide concentration. The model is run at the global scale, forced by the GSWP-2 meteorological data at a resolution of 1° for the period of 1986–1995. We test the model by comparing the simulated LAI values against three satellite-derived data sets (ISLSCP Initiative II data, MODIS data and ECOCLIMAP data) and find that the model reproduces the major patterns of spatial and temporal variability in global vegetation. As a result, the mean of the maximum annual LAI estimates of the model falls within the range of the various satellite data sets. Despite no explicit representation of phenology, the model captures the seasonal cycle in LAI well and shows realistic variations in start of the growing season as a function of latitude. The interannual variability is also well reported for numerous regions of the world, particularly where precipitation controls photosynthesis. The comparison also reveals that some processes need to be improved or introduced in the model, in particular the snow dynamics and the treatment of vegetation in cultivated areas, respectively. The overall comparisons demonstrate the potential of ISBA-A-gs model to simulate LAI in a realistic fashion at the global scale.
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paper_title: A Bayesian spatial assimilation scheme for snow coverage observations in a gridded snow model

paper_content:

A method for assimilating remotely sensed snow covered area (SCA) into the snow subroutine of a grid dis- tributed precipitation-runoff model (PRM) is presented. The PRM is assumed to simulate the snow state in each grid cell by a snow depletion curve (SDC), which relates that cell's SCA to its snow cover mass balance. The assimilation is based on Bayes' theorem, which requires a joint prior dis- tribution of the SDC variables in all the grid cells. In this paper we propose a spatial model for this prior distribution, and include similarities and dependencies among the grid cells. Used to represent the PRM simulated snow cover state, our joint prior model regards two elevation gradients and a degree-day factor as global variables, rather than describing their effect separately for each cell. This transformation re- sults in smooth normalised surfaces for the two related mass balance variables, supporting a strong inter-cell dependency in their joint prior model. The global features and spatial interdependency in the prior model cause each SCA obser- vation to provide information for many grid cells. The spa- tial approach similarly facilitates the utilisation of observed discharge. Assimilation of SCA data using the proposed spatial model is evaluated in a 2400 km 2 mountainous region in cen- tral Norway (61 N, 9 E), based on two Landsat 7 ETM+ images generalized to 1 km 2 resolution. An image acquired on 11 May, a week before the peak flood, removes 78% of the variance in the remaining snow storage. Even an image from 4 May, less than a week after the melt onset, reduces this variance by 53%. These results are largely improved compared to a cell-by-cell independent assimilation routine previously reported. Including observed discharge in the up- dating information improves the 4 May results, but has weak
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paper_title: Feasibility Test of Multifrequency Radiometric Data Assimilation to Estimate Snow Water Equivalent

paper_content:

Abstract A season-long, point-scale radiometric data assimilation experiment is performed in order to test the feasibility of snow water equivalent (SWE) estimation. Synthetic passive microwave observations at Special Sensor Microwave Imager (SSM/I) and Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR-E) frequencies and synthetic broadband albedo observations are assimilated simultaneously in order to update snowpack states in a land surface model using the ensemble Kalman filter (EnKF). The effects of vegetation and atmosphere are included in the radiative transfer model (RTM). The land surface model (LSM) was given biased precipitation to represent typical errors introduced in modeling, yet was still able to recover the true value of SWE with a seasonally integrated rmse of only 2.95 cm, despite a snow depth of around 3 m and the presence of liquid water in the snowpack. This ensemble approach is ideal for investigating the complex theoretical relationships between the snowpack proper...
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paper_title: Mapping of snow water equivalent and snow depth in boreal and sub-arctic zones by assimilating space-borne microwave radiometer data and ground-based observations

paper_content:

Abstract The monitoring of snow water equivalent (SWE) and snow depth (SD) in boreal forests is investigated by applying space-borne microwave radiometer data and synoptic snow depth observations. A novel assimilation technique based on (forward) modelling of observed brightness temperatures as a function of snow pack characteristics is introduced. The assimilation technique is a Bayesian approach that weighs the space-borne data and the reference field on SD interpolated from discrete synoptic observations with their estimated statistical accuracy. The results obtained using SSM/I and AMSR-E data for northern Eurasia and Finland indicate that the employment of space-borne data using the assimilation technique improves the SD and SWE retrieval accuracy when compared with the use of values interpolated from synoptic observations. Moreover, the assimilation technique is shown to reduce systematic SWE/SD estimation errors evident in the inversion of space-borne radiometer data.
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paper_title: Impact of Accuracy, Spatial Availability, and Revisit Time of Satellite-Derived Surface Soil Moisture in a Multiscale Ensemble Data Assimilation System

paper_content:

This study evaluates the sensitivity of a multiscale ensemble assimilation system to different configurations of satellite soil moisture observations, namely the retrieval accuracy, spatial availability, and revisit time. We perform horizontally coupled assimilation experiments where pixels are updated not only by observations at the same location but also all in the study domain. Carrying out sensitivity studies within a multiscale assimilation system is a significant advancement over previous studies that used a 1-D assimilation framework where all horizontal grids are uncoupled. Twin experiments are performed with synthetic soil moisture retrievals. The hydrologic modeling system is forced with satellite estimated rainfall, and the assimilation performance is evaluated against model simulations using in-situ measured rainfall. The study shows that the assimilation performance is most sensitive to the spatial availability of soil moisture observations, then to revisit time and least sensitive to retrieval accuracy. The horizontally coupled assimilation system performs reasonably well even with large observation errors, and it is less sensitive to retrieval accuracy than the uncoupled system, as reported by previous studies. This suggests that more information may be extracted from satellite soil moisture observations using multiscale assimilation systems resulting in a potentially higher value of such satellite products.
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paper_title: Comparison of Data Assimilation Techniques for a Coupled Model of Surface and Subsurface Flow

paper_content:

Data assimilation in the geophysical sciences refers to methodologies to optimally merge model predictions and observations. The ensemble Kalman filter (EnKF) is a statistical sequential data assimilation technique explicitly developed for nonlinear filtering problems. It is based on a Monte Carlo approach that approximates the conditional probability densities of the variables of interest by a finite number of randomly generated model trajectories. In Newtonian relaxation or nudging (NN), which can be viewed as a special case of the classic Kalman filter, model variables are driven toward observations by adding to the model equations a forcing term, or relaxation component, that is proportional to the difference between simulation and observation. The forcing term contains four-dimensional weighting functions that can, ideally, incorporate prior knowledge about the characteristic scales of spatial and temporal variability of the state variable(s) being assimilated. In this study, we examined the EnKF and NN algorithms as implemented for a complex hydrologic model that simulates catchment dynamics, coupling a three-dimensional finite element Richards9 equation solver for variably saturated porous media and a finite difference diffusion wave approximation for surface water flow. We report on the retrieval performance of the two assimilation schemes for a small catchment in Belgium. The results of the comparison show that nudging, while more straightforward and less expensive computationally, is not as effective as the ensemble Kalman filter in retrieving the true system state. We discuss some of the strengths and weaknesses, both physical and numerical, of the NN and EnKF schemes.
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Title: Multivariate and Multiscale Data Assimilation in Terrestrial Systems: A Review

Section 1: Introduction
Description 1: Introduces the concept of data assimilation (DA) in terrestrial systems, highlights the importance of combining measurements and models, and outlines the objectives of the review.

Section 2: Data Assimilation Theory
Description 2: Discusses the theoretical background of various data assimilation techniques, including the Ensemble Kalman Filter (EnKF), Particle Filter (PF), and variational methods (VAR).

Section 3: Ensemble Kalman Filter (EnKF)
Description 3: Provides an in-depth examination of the Ensemble Kalman Filter methodology, its application, and its variants such as the Ensemble Kalman Smoother (EnKS).

Section 4: Particle Filter (PF)
Description 4: Reviews the Particle Filter method, detailing its procedure, advantages, drawbacks, and specific applications in hydrological modeling.

Section 5: Variational Assimilation (VAR)
Description 5: Explains the variational assimilation technique, focusing on its cost function minimization approach and applications in numerical weather prediction and terrestrial systems.

Section 6: Data Assimilation across States and Scales
Description 6: Analyzes different approaches to DA based on the number of states and scales, detailing univariate single-scale, univariate multiscale, multivariate single-scale, and multivariate multiscale data assimilation.

Section 7: Univariate Single-Scale Data Assimilation (UVSS)
Description 7: Discusses DA methods that assimilate a single type of data without scale mismatch considerations, providing specific examples and applications.

Section 8: Multivariate Single-Scale Data Assimilation (MVSS)
Description 8: Reviews the techniques and benefits of assimilating multiple types of observation data on the same spatial scale into simulation models.

Section 9: Univariate Multiscale Data Assimilation (UVMS)
Description 9: Focuses on DA methods that handle data obtained at different resolutions than the model resolution, employing scaling techniques for proper assimilation.

Section 10: Multivariate Multiscale Data Assimilation (MVMS)
Description 10: Covers the complex integration of various types and scales of data, detailing studies and methods for efficiently combining and assimilating these data sets.

Section 11: Multisource DA
Description 11: Defines the scenario where a single state variable is updated by multiple data sources at the same scale, highlighting its distinct advantages and applications.

Section 12: Methodology
Description 12: Compares different strategies for assimilating data obtained at varying resolutions, including observation operators and prior downscaling techniques.

Section 13: Applications
Description 13: Provides examples of diverse applications of univariate and multivariate data assimilation across different terrestrial systems.

Section 14: Advantages and Disadvantages of Multivariate and Multiscale Data Assimilation
Description 14: Summarizes the benefits and challenges of using multivariate and multiscale DA methods versus univariate single-scale approaches.

Section 15: Other Aspects
Description 15: Discusses additional considerations in DA, such as parameter estimation verification and the computational demands of high-resolution models.

Section 16: Conclusions
Description 16: Summarizes the current state and future potential of DA in terrestrial systems, emphasizing the need for further research and application to fully leverage available environmental data.