Entropy Applications to Water Monitoring Network Design: A Review
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paper_title: Water quality monitoring strategies - A review and future perspectives.

paper_content:

The reliable assessment of water quality through water quality monitoring programs (WQMPs) is crucial in order for decision-makers to understand, interpret and use this information in support of their management activities aiming at protecting the resource. The challenge of water quality monitoring has been widely addressed in the literature since the 1940s. However, there is still no generally accepted, holistic and practical strategy to support all phases of WQMPs. The purpose of this paper is to report on the use cases a watershed manager has to address to plan or optimize a WQMP from the challenge of identifying monitoring objectives; selecting sampling sites and water quality parameters; identifying sampling frequencies; considering logistics and resources to the implementation of actions based on information acquired through the WQMP. An inventory and critique of the information, approaches and tools placed at the disposal of watershed managers was proposed to evaluate how the existing information could be integrated in a holistic, user-friendly and evolvable solution. Given the differences in regulatory requirements, water quality standards, geographical and geological differences, land-use variations, and other site specificities, a one-in-all solution is not possible. However, we advance that an intelligent decision support system (IDSS) based on expert knowledge that integrates existing approaches and past research can guide a watershed manager through the process according to his/her site-specific requirements. It is also necessary to tap into local knowledge and to identify the knowledge needs of all the stakeholders through participative approaches based on geographical information systems and adaptive survey-based questionnaires. We believe that future research should focus on developing such participative approaches and further investigate the benefits of IDSS's that can be updated quickly and make it possible for a watershed manager to obtain a timely, holistic view and support for every aspect of planning and optimizing a WQMP.
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paper_title: Rainfall and streamflow sensor network design: a review of applications, classification, and a proposed framework

paper_content:

Sensors and sensor networks play an important role in decision-making related to water quality, operational streamflow forecasting, flood early warning systems, and other areas. In this paper we review a number of existing applications and analyse a variety of evaluation and design procedures for sensor networks with respect to various criteria. Most of the existing approaches focus on maximising the observability and information content of a variable of interest. From the context of hydrological modelling only a few studies use the performance of the hydrological simulation in terms of output discharge as a design criterion. In addition to the review, we propose a framework for classifying the existing design methods, and a generalised procedure for an optimal network design in the context of rainfall-runoff hydrological modelling.
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paper_title: The worth of hydrologic data for nonoptimal decision making

paper_content:

Data are of value in the design and operation of water resource projects because they provide information about uncertain states of nature. This information can in turn be used to reduce the risks inherent in the project. In this paper, risk calculations from the preposterior analysis of statistical decision theory are extended to cover nonoptimal decisions. Risk is measured in terms of the project objectives by embedding the data network into an information-response (IR) system. The value of addition or improvement to the data base is measured by the change in the risk. Measures of the performance of the IR system are developed. From these measures, the efficiency of the information subsystem, the response subsystem, and the overall IR system are defined. These concepts are illustrated by a simple example in which the additional data sample for estimating the 6¼-year flow is shown to have different values (negative in one case), depending on the estimation method or decision rule used. Five anomalies and paradoxes in the literature concerning the worth of data are explained.
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paper_title: Overview of conference on hydrologic data networks

paper_content:

This conference is the latest involving conferences whose research includes work in what is called the design of data networks. The broader scope of this conference reflects, in my view, movement toward greater sophistication in research and in subject matter, and it is good that these kinds of critical inquiry are going on. The rough estimates mentioned at the conference show data collection to be big business, even though data storage and retrieval tend to attract most public attention. The design of data systems, that is, the efficiency and effectiveness, must also be concerned with the manner of collection, the places and numbers of observations, their costs, and their utility. These matters constitute the fundamentals. Yet in the face of the wide range of present and prospective uses, the complex range of objectives, and the diversity of variables the products of research and critical inquiry appear to find few applications. That subject as well as the needs and opportunities were examined at this conference.
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paper_title: Developments in hydrometric network design: A review

paper_content:

[1] Hydrometric network design for surface water monitoring is employed to address a wide range of environmental and water resources problems. Historical overview of hydrometric network design is provided along with a discussion on new developments and challenges in the design of optimal hydrometric networks. This review starts with precise examples of decline in hydrometric network density, then highlights the increasing requirement of optimal network design in a context of climate and land use changes. An extensive survey of methodological development in hydrometric network design is provided along with discussion on the issue of uncertainty in hydrometric network design and the evolution in data collection techniques and technology. Finally, some conclusions are drawn on the future of hydrometric network design.
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paper_title: Entropy Theory in Hydrologic Science and Engineering

paper_content:

1. Entropy Theory 2. Morphological Analysis 3. Evaluation and Design of Sampling and Measurement Networks 4. Precipitation Variability 5. Rainfall Frequency Distributions 6. Assessment of Potential Water Resources Availability 7. Evaluation of Precipitation Forecasting Schemes 8. Infiltration 9. Soil Moisture 10. Groundwater Flow 11. Rainfall-Runoff Modeling 12. Hydrologic Frequency Analysis 13. Steamflow Simulation 14. Long-Term Streamflow Forecasting 15. Flood Forecasting: Bivariate Analysis 16. River Regime Classification 17. Sediment Yield Eco Index
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paper_title: Evaluation of rainfall networks using entropy: I. Theoretical development

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This paper, the first in a series of two, develops an entropy-based approach for evaluating rainfall networks. Space and time dependencies between raingages are examined by autocovariance and cross-covariance matrices. Multivariate distributions, associated with different dependencies, are obtained using the principle of maximum entropy (POME). Formulas for entropy (uncertainty in data of one raingage), joint entropy (uncertainty in data of two or more raingages) and transinformation (common information content among two or more raingages) are derived for each distribution, based on normal data. The decision whether to keep or eliminate a raingage depends entirely on reduction or gain of information at that raingage. The lines of equal information (isoinformation contours) are defined by considering two raingages (bivariate case) and many raingages (multivariate case).
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paper_title: Information Theoretical Analysis of Multivariate Correlation

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A set λ of stochastic variables, y1, y2,..., yn, is grouped into subsets, µ1, µ2,..., µk. The correlation existing in λ with respect to the µ's is adequately expressed by C= Σi=1k S(µi)-S(λ)≥0, where S(v) is the entropy function defined with reference to the variables y in subset v. For a given λ, C becomes maximum when each µi consists of only one variable, (n=k). The value Cis then called fhe total correlation in λ, Ctot(λ). The present paper gives various theorems, according to which Ctot(λ) can be decomposed in terms of the partial correlations existing in subsets of λ, and of quantities derivable therefrom. The information-theoretical meaning of each decomposition is carefully explained. As illustrations, two problems are discussed at the end of the paper: (1) redundancy in geometrical figures in pattern recognition, and (2) randomization effect of shuffling cards marked "zero' or "one."
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paper_title: Multivariate information transmission

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A multivariate analysis based on transmitted information is presented. It is shown that sample transmitted information provides a simple method for measuring and testing association in multi-dimensional contingency tables. Relations with analysis of variance are pointed out, and statistical tests are described.
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paper_title: Developments in hydrometric network design: A review

paper_content:

[1] Hydrometric network design for surface water monitoring is employed to address a wide range of environmental and water resources problems. Historical overview of hydrometric network design is provided along with a discussion on new developments and challenges in the design of optimal hydrometric networks. This review starts with precise examples of decline in hydrometric network density, then highlights the increasing requirement of optimal network design in a context of climate and land use changes. An extensive survey of methodological development in hydrometric network design is provided along with discussion on the issue of uncertainty in hydrometric network design and the evolution in data collection techniques and technology. Finally, some conclusions are drawn on the future of hydrometric network design.
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paper_title: Information theory-based decision support system for integrated design of multivariable hydrometric networks

paper_content:

Adequate and accurate hydrologic information from optimal hydrometric networks is an essential part of effective water resources management. Although the key hydrologic processes in the water cycle are interconnected, hydrometric networks (e.g., streamflow, precipitation, groundwater level) have been routinely designed individually. A decision support framework is proposed for integrated design of multivariable hydrometric networks. The proposed method is applied to design optimal precipitation and streamflow networks simultaneously. The epsilon-dominance hierarchical Bayesian optimization algorithm was combined with Shannon entropy of information theory to design and evaluate hydrometric networks. Specifically, the joint entropy from the combined networks was maximized to provide the most information, and the total correlation was minimized to reduce redundant information. To further optimize the efficiency between the networks, they were designed by maximizing the conditional entropy of the streamflow network given the information of the precipitation network. Compared to the traditional individual variable design approach, the integrated multivariable design method was able to determine more efficient optimal networks by avoiding the redundant stations. Additionally, four quantization cases were compared to evaluate their effects on the entropy calculations and the determination of the optimal networks. The evaluation results indicate that the quantization methods should be selected after careful consideration for each design problem since the station rankings and the optimal networks can change accordingly.
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paper_title: Entropy theory for analysing water resources in northeastern region of Brazil

paper_content:

ABSTRACT Using the Shannon entropy, the space–time variability of rainfall and streamflow was assessed for daily rainfall and streamflow data for a 10-year period from 189 stations in the northeastern region of Brazil. Mean values of marginal entropy were computed for all observation stations and entropy maps were then constructed for delineating annual and seasonal characteristics of rainfall and streamflow. The Mann-Kendall test was used to evaluate the long-term trend in marginal entropy as well as relative entropy for two sample stations. The marginal entropy values of rainfall and streamflow were higher for locations and periods with the highest amounts of rainfall. The entropy values were higher where rainfall was higher. This was because the probability distributions of rainfall and the resulting streamflow were more uniform and less skewed. The Shannon entropy produced spatial patterns which led to a better understanding of rainfall and streamflow characteristics throughout the northeastern region of Brazil. The total relative entropy indicated that rainfall and streamflow carried the same information content at annual and rainy season time scales.
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paper_title: The Xinanjiang model applied in China

paper_content:

Abstract The Xinanjiang model is a rainfall-runoff, distributed, basin model for use in humid and semi-humid regions. The evapotranspiration component is represented by a model of three soil layers. Runoff production occurs on repletion of storage to capacity values which are assumed to be distributed throughout the basin. Prior to 1980, runoff was separated into surface and groundwater components using Horton's concept of infiltration. Subsequently, the concept of hillslope hydrology was introduced with an additional component, interflow, being identified. Runoff concentration to the outflow of each sub-basin is represented by a unit hydrograph or by a lag and route technique. The damping or routing effects of the channel system connecting the sub-basins are represented by Muskingum routing. There are fifteen parameters in all, of which the model is particularly sensitive to six. Optimization of the parameters is achieved with different objective functions according to the nature of each parameter. The model has been widely used in China since 1980, mainly for flood forecasting, though more recently it is also being used for other purposes.
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paper_title: An algorithm for optimisation of a rain gauge network based on geostatistics and entropy concepts using GIS

paper_content:

There is a high level of spatio-temporal variability in rainfall events over a region. Rain gauges provide point measurements that are interpolated to estimate the rainfall in other points of a region or in order to estimate the regional depth of rainfall. Due to limited numbers of rain gauges that can be deployed, it is important to plan for the optimal number and locations of rain gauges in a region. Because of several factors that can affect the optimal number of stations as well as their locations, development of optimisation models for determining the number of rain gauges and their locations within a region is necessary. In this study, an optimisation model for determining the number and location of the rain gauges is proposed. The objectives of the model are maximising the minimum transformation entropy and minimising the rainfall estimation error. To determine the optimal number of new rain gauges, the candidate points, which are those with the maximum variance of Kriging error and the minimum inf...
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paper_title: LARGE AREA HYDROLOGIC MODELING AND ASSESSMENT PART I: MODEL DEVELOPMENT

paper_content:

A conceptual, continuous time model called SWAT (Soil and Water Assessment Tool) was developed to assist water resource managers in assessing the impact of management on water supplies and nonpoint source pollution in watersheds and large river basins. The model is currently being utilized in several large area projects by EPA, NOAA, NRCS and others to estimate the off-site impacts of climate and management on water use, nonpoint source loadings, and pesticide contamination. Model development, operation, limitations, and assumptions are discussed and components of the model are described. In Part II, a GIS input/output interface is presented along with model validation on three basins within the Upper Trinity basin in Texas.
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paper_title: Estimating information entropy for hydrological data: One‐dimensional case

paper_content:

There has been a recent resurgence of interest in the application of Information Theory to problems of system identification in the Earth and Environmental Sciences. While the concept of entropy has found increased application, little attention has yet been given to the practical problems of estimating entropy when dealing with the unique characteristics of two commonly used kinds of hydrologic data: rainfall and runoff. In this paper, we discuss four important issues of practical relevance that can bias the computation of entropy if not properly handled. The first (zero effect) arises when precipitation and ephemeral streamflow data must be viewed as arising from a discrete-continuous hybrid distribution due to the occurrence of many zero values (e.g., days with no rain/no runoff). Second, in the widely used bin-counting method for estimation of PDF's, significant error can be introduced if the bin width is not carefully selected. The third (measurement effect) arises due to the fact that continuously varying hydrologic variables can typically only be observed discretely to some degree of precision. The Fourth (skewness effect) arises when the distribution of a variable is significantly skewed. Here we present an approach that can deal with all four of these issues, and test them with artificially generated and real hydrological data. The results indicate that the method is accurate and robust.
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paper_title: An entropy-based investigation into the variability of precipitation

paper_content:

Summary Employing the entropy concept spatial and temporal variability of precipitation time series were investigated for the State of Texas, USA. Marginal entropy was used to investigate the variability associated with monthly, seasonal and annual time series. Also, apportionment entropy and intensity entropy were used for investigating the intra-annual and decadal distributions of monthly and annual precipitation amounts and numbers of rainy days within a year and decade respectively. Finally, the Hurst exponent and the Mann–Kendall test were used to evaluate the long-term persistence and trend in the variability of precipitation. Distinct spatial patterns in annual series and different seasons were observed. The variability of precipitation amount as well as number of rainy days within a year increased from east to west of Texas. The results also indicated that highly disorderliness in the amount of precipitation and number of rainy days caused severe droughts during the 1950’s in whole of Texas.
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paper_title: Spatiotemporal Scaling Effect on Rainfall Network Design Using Entropy

paper_content:

Because of high variation in mountainous areas, rainfall data at different spatiotemporal scales may yield potential uncertainty for network design. However, few studies focus on the scaling effect on both the spatial and the temporal scale. By calculating the maximum joint entropy of hourly typhoon events, monthly, six dry and wet months and annual rainfall between 1992 and 2012 for 1-, 3-, and 5-km grids, the relocated candidate rain gauges in the National Taiwan University Experimental Forest of Central Taiwan are prioritized. The results show: (1) the network exhibits different locations for first prioritized candidate rain gauges for different spatiotemporal scales; (2) the effect of spatial scales is insignificant compared to temporal scales; and (3) a smaller number and a lower percentage of required stations (PRS) reach stable joint entropy for a long duration at finer spatial scale. Prioritized candidate rain gauges provide key reference points for adjusting the network to capture more accurate information and minimize redundancy.
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paper_title: Developing an entropy-based model of spatial information estimation and its application in the design of precipitation gauge networks

paper_content:

Summary This study proposed a spatial information estimation model for the analysis of precipitation gauge networks, to improve on previous methods based on information theory. The proposed model employs a two-dimensional transinformation–distance ( T – D ) relationship in conjunction with multivariate information approximation to estimate transinformation to ungauged locations from existing stations, while taking into consideration the influence of multiple stations and anisotropy. The proposed model is used to evaluate the spatial distribution of precipitation data and the characteristics of information transfer, which are then applied in a spatial optimization algorithm for the selection of additional station locations. This framework was implemented to investigate temporal and spatial patterns in information content in the Shihmen Reservoir watershed. The results demonstrate obvious anisotropy associated with the delivery of information. By comparing different cases, it was determined that the efficiency of information delivery dominates the spatial distribution of the information content, such that eccentricity is merely supplemental. Efficiency in information delivery is also heavily influenced by temporal scale. For data covering long intervals (monthly and annual), efficiency in the delivery of information is relatively high, while the uncertainty or heterogeneity of hourly or daily time series produces low spatial correlations due to the inefficient delivery of information. The proposed spatial optimization algorithm confirmed that the optimal location for new stations lies close to the center of low information zones. Additional stations could improve information content considerably; however, the margin of improvement decreases with the number of stations.
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paper_title: Entropy theory based multi-criteria resampling of rain gauge networks for hydrological modelling – A case study of humid area in southern China

paper_content:

Summary Rain gauge networks are used to provide estimates of area average, spatial variability and point rainfalls at catchment scale and provide the most important input for hydrological models. Therefore, it is desired to design the optimal rain gauge networks with a minimal number of rain gauges to provide reliable data with both areal mean values and spatial–temporal variability. Based on a dense rain gauge network of 185 rain gauges in Xiangjiang River Basin, southern China, this study used an entropy theory based multi-criteria method which simultaneously considers the information derived from rainfall series, minimize the bias of areal mean rainfall as well as minimize the information overlapped by different gauges to resample the rain gauge networks with different gauge densities. The optimal networks were examined using two hydrological models: The lumped Xinanjiang Model and the distributed SWAT Model. The results indicate that the performances of the lumped model using different optimal networks are stable while the performances of the distributed model keep on improving as the number of rain gauges increases. The results reveal that the entropy theory based multi-criteria strategy provides an optimal design of rain gauge network which is of vital importance in regional hydrological study and water resources management.
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paper_title: Dimensionality reduction in drought modelling

paper_content:

For monitoring hydrological events characterized by high spatial and temporal variability, the number and location of recording stations must be carefully selected to ensure that the necessary information is collected. Depending on the characteristics of each natural process, certain stations may be spurious or redundant, whereas others may provide most of the relevant data. With the objective of reducing the costs of the monitoring system and, at the same time, improving its operational effectiveness, three procedures were applied to identify the minimum network of rain gauge stations able to capture the characteristics of droughts in mainland Portugal. Drought severity is characterized by the standardized precipitation index applied to the timescales of 1, 3, 6 and 12 consecutive months. The three techniques used to reduce the dimensionality of the network of rain gauges were as follows: (i) artificial neural networks with sensitivity analysis, (ii) application of the mutual information criterion and (iii) K-means cluster analysis using Euclidean distances. The results demonstrated that the best dimensionality reduction method was case dependent in the three regions of Portugal (northern, central and southern) previously identified by cluster analysis. All the reduction techniques lead to the selection of a subset of rain gauges capable of reproducing the original temporal patterns of drought. For specific severe drought events in Portugal in the past, the comparison between drought spatial patterns obtained with the original stations and the selected subset indicated that the subset produced statistically satisfactory results (correlation coefficients higher than 0.6 and efficiency coefficients higher than 0.5). Copyright © 2012 John Wiley & Sons, Ltd.
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paper_title: An entropy approach for evaluating the maximum information content achievable by an urban rainfall network

paper_content:

Abstract. Hydrological models are the basis of operational flood-forecasting systems. The accuracy of these models is strongly dependent on the quality and quantity of the input information represented by rainfall height. Finer space-time rainfall resolution results in more accurate hazard forecasting. In this framework, an optimum raingauge network is essential in predicting flood events. This paper develops an entropy-based approach to evaluate the maximum information content achievable by a rainfall network for different sampling time intervals. The procedure is based on the determination of the coefficients of transferred and nontransferred information and on the relative isoinformation contours. The nontransferred information value achieved by the whole network is strictly dependent on the sampling time intervals considered. An empirical curve is defined, to assess the objective of the research: the nontransferred information value is plotted versus the associated sampling time on a semi-log scale. The curve has a linear trend. In this paper, the methodology is applied to the high-density raingauge network of the urban area of Rome.
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paper_title: A multiscale information theory approach to assess spatial-temporal variability of daily precipitation.

paper_content:

Summary Information theory metrics are applied to ascertain the spatial and temporal variability of daily precipitation over the continental United States. Entropy is computed of the daily precipitation records and of the precipitation event size distribution. In addition, relative entropy is also computed between the two records and the Hurst exponent is calculated for comparison purposes. These values show little correlation with mean annual precipitation, number of rain days or station elevation. However, there is a clear spatial pattern in the precipitation and relative entropy fields corresponding to a breakpoint at approximately −95° longitude, which the Hurst exponent is not capable of resolving. Using wavelet multiresolution analysis and relative entropy, this breakpoint is shown to correspond to higher temporal variability (sub-monthly) in the western United States. In addition, scalewise mutual information content illustrates the general feature of three distinct scaling regions for precipitation: (1) synoptic (2–10 days), (2) monthly to annual times and (3) interannual variability. This analysis demonstrates the usefulness of an information theory approach to assessing the dynamics of precipitation.
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paper_title: Entropy expressions and their estimators for multivariate distributions

paper_content:

Entropy expressions for several continuous multivariate distributions are derived. Point estimation of entropy for the multinormal distribution and for the distribution of order statistics from D.G. Weinman's (Ph.D dissertation, Ariz. State Univ., Tempe, AZ, 1966) exponential distribution is considered. The asymptotic distribution of the uniformly minimum variance unbiased estimator for multinormal entropy is obtained. Simulation results on convergence of the means and variances of these estimators are provided. >
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paper_title: Hydrometric network design using dual entropy multi-objective optimization in the Ottawa River Basin

paper_content:

Water resources managers commonly rely on information collected by hydrometric networks without clear knowledge of their efficiency. Optimal water monitoring networks are still scarce especially in the Canadian context. Herein, a dual entropy multi-objective optimization (DEMO) method uses information theory to identify locations where the addition of a hydrometric station would optimally complement the information content of an existing network. This research explores the utility of transinformation (TI) analysis, which can quantitatively measure the contribution of unique information from a hydrometric station. When used in conjunction, these methods provide an objective measure of network efficiency, and allow the user to make recommendations to improve existing hydrometric networks. A technique for identifying and dealing with regulated basins and their related bias on streamflow regionalization is also examined. The Ottawa River Basin, a large Canadian watershed with a number of regulated hydroelectric dams, was selected for the experiment. The TI analysis approach provides preliminary information which is supported by DEMO results. Regionalization was shown to be more accurate when the regulated basin stations were omitted using leave one out cross validation. DEMO analysis was performed with these improvements and successfully identified optimal locations for new hydrometric stations in the Ottawa River Basin.
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paper_title: Entropy as a measure of hydrologic data uncertainty and model performance

paper_content:

Abstract This paper extends the original use of entropy by Amorocho and Espildora as a measure of uncertainty in hydrologic data and the reduction in that uncertainty due to application of a model. In many situations calculations of entropy are better based on a proportional rather than a fixed class interval. General equations are given for the proportional class interval, are solved for assumed log-normal and gamma distributions, and extended to data series with zero values. The solutions are shown to be independent of the units of measurement of the original data. The results are applied to comparative evaluation of hydrologic models using the same and different data sets, and a new criterion of model performance is suggested for the latter case.
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paper_title: Regionalization of constraints on expected watershed response behavior for improved predictions in ungauged basins

paper_content:

Approaches to modeling the continuous hydrologic response of ungauged basins use observable physical characteristics of watersheds to either directly infer values for the parameters of hydrologic models, or to establish regression relationships between watershed structure and model parameters. Both these approaches still have widely discussed limitations, including impacts of model structural uncertainty. In this paper we introduce an alternative, model independent, approach to streamflow prediction in ungauged basins based on empirical evidence of relationships between watershed structure, climate and watershed response behavior. Instead of directly estimating values for model parameters, different hydrologic response behaviors of the watershed, quantified through model independent streamflow indices, are estimated and subsequently regionalized in an uncertainty framework. This results in expected ranges of streamflow indices in ungauged watersheds. A pilot study using 30 UK watersheds shows how this regionalized information can be used to constrain ensemble predictions of any model at ungauged sites. Dominant controlling characteristics were found to be climate (wetness index), watershed topography (slope), and hydrogeology. Main streamflow indices were high pulse count, runoff ratio, and the slope of the flow duration curve. This new approach provided sharp and reliable predictions of continuous streamflow at the ungauged sites tested.
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paper_title: Information theory applied to evaluate the discharge monitoring network of the Magdalena River

paper_content:

The acquisition of good hydrologic information is an important issue in water management since it is the basis of decisions concerning the allocation of water resources to different users. However, sufficient data are often not available to describe the behaviour of such systems, especially in developing countries, where monitoring networks are inappropriately designed, poorly operated or are inadequate. Therefore, it is of interest to design and evaluate efficient monitoring networks. This paper presents two methodologies to design discharge monitoring networks in rivers using the concepts of Information Theory. The first methodology considers the optimization of Information Theory quantities and the second considers a new method that is based on ranking Information Theory quantities with different possible monitor combinations. The methodologies are tested for the Magdalena River in Colombia, in which the existing monitoring network is also assessed. In addition, the use of monitors at tributaries is explored. It is demonstrated that the ranking method is a promising way of finding the extremes of Pareto fronts generated during multi-objective optimization processes and that better (more informative and less redundant) monitoring network configurations can be found for the Magdalena River.
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paper_title: Hydrometric network evaluation for Canadian watersheds

paper_content:

In recent years, climate change impacts on water resources sectors have been extensively documented. Anticipated changes range from more severe storms to more frequent floods and drought at regional scale. Pressure on water resources and hence on the environment will probably increase with the need of quality data for sustainable design of water resources projects. Therefore, for an optimal network design, hydrometric networks are to be reviewed periodically based on the information needs of the various end users and the perspective for future water resources development. This paper evaluates hydrometric networks to identify essential streamflow stations and critical areas (highly poor network density) within major watersheds across the different provinces of Canada using entropy theory. The method is applied to daily streamflow data and information coefficients such as marginal entropy, joint entropy and transinformation index are used for the identification of important stations as well as critical areas in the basin. The analysis results show that almost all Canadian main watersheds contain deficient hydrometric networks. The most deficient streamflow networks are identified in Alberta (North Saskatchewan, Oldman, and Red Deer basins), Northern Ontario (Hudson Bay basin), and the Northwest Territories. The information might prove to be helpful for decision makers to undertake cost-benefit analyses for hydrometric network updating in each region.
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paper_title: Information theory-based decision support system for integrated design of multivariable hydrometric networks

paper_content:

Adequate and accurate hydrologic information from optimal hydrometric networks is an essential part of effective water resources management. Although the key hydrologic processes in the water cycle are interconnected, hydrometric networks (e.g., streamflow, precipitation, groundwater level) have been routinely designed individually. A decision support framework is proposed for integrated design of multivariable hydrometric networks. The proposed method is applied to design optimal precipitation and streamflow networks simultaneously. The epsilon-dominance hierarchical Bayesian optimization algorithm was combined with Shannon entropy of information theory to design and evaluate hydrometric networks. Specifically, the joint entropy from the combined networks was maximized to provide the most information, and the total correlation was minimized to reduce redundant information. To further optimize the efficiency between the networks, they were designed by maximizing the conditional entropy of the streamflow network given the information of the precipitation network. Compared to the traditional individual variable design approach, the integrated multivariable design method was able to determine more efficient optimal networks by avoiding the redundant stations. Additionally, four quantization cases were compared to evaluate their effects on the entropy calculations and the determination of the optimal networks. The evaluation results indicate that the quantization methods should be selected after careful consideration for each design problem since the station rankings and the optimal networks can change accordingly.
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paper_title: Quantifying trends in indicator hydroecological variables for regime-based groups of Canadian rivers

paper_content:

As a key contribution to Canada's Ecosystem Status and Trends (ESTR) national assessment, the goal of our study was to utilize available flow data as a surrogate of habitat suitability for aquatic ecological communities, and examine temporal trends in hydroecological variables over the 1970–2005 period. Daily flow data were extracted from the Reference Hydrological Basin Network, and an agglomerative hierarchical classification method was used to identify homogenous regions with similar seasonality of the flow regime. Six regime regions were identified reflecting the timing of the annual peaks and low flows in addition to the patterns in the rising and falling limbs. For each of the gauging station sites, the magnitude, duration, timing, frequency, and rate of change of annual hydrological events were quantified through 32 ecologically important hydrological variables. Long-term patterns in the hydroecological variables were quantified using the nonparametric Mann-Kendall trend statistic. The results revealed more trends than would be expected to occur by chance for most variables. Clear regional trend patterns were observed within individual regime groups demonstrating the often differing response to environmental variability within the different regions. Results at the national scale were highly variable, but trends towards increased variability in river flows were observed with a predominant increasing trend in the number of flow reversals over the water year and decreasing trend in the annual low-flow indices. The identified river regime regions offer an initial framework for scientific investigation of hydroecological patterns and an opportunity to move towards a more predictive approach to environmental flows assessment in sustainable resource management and planning. Copyright © 2011 John Wiley & Sons, Ltd.
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paper_title: Estimating information entropy for hydrological data: One‐dimensional case

paper_content:

There has been a recent resurgence of interest in the application of Information Theory to problems of system identification in the Earth and Environmental Sciences. While the concept of entropy has found increased application, little attention has yet been given to the practical problems of estimating entropy when dealing with the unique characteristics of two commonly used kinds of hydrologic data: rainfall and runoff. In this paper, we discuss four important issues of practical relevance that can bias the computation of entropy if not properly handled. The first (zero effect) arises when precipitation and ephemeral streamflow data must be viewed as arising from a discrete-continuous hybrid distribution due to the occurrence of many zero values (e.g., days with no rain/no runoff). Second, in the widely used bin-counting method for estimation of PDF's, significant error can be introduced if the bin width is not carefully selected. The third (measurement effect) arises due to the fact that continuously varying hydrologic variables can typically only be observed discretely to some degree of precision. The Fourth (skewness effect) arises when the distribution of a variable is significantly skewed. Here we present an approach that can deal with all four of these issues, and test them with artificially generated and real hydrological data. The results indicate that the method is accurate and robust.
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paper_title: Information theory-based approach for location of monitoring water level gauges in polders: INFORMATION THEORY FOR LOCATION OF MONITORING

paper_content:

[1] Data collection is a critical activity in the management of water systems because it supports informed decision making. Data are collected by means of monitoring networks in which water level gauges are of particular interest because of their implications for flood management. This paper introduces a number of modifications to previously published methods that use information theory to design hydrological monitoring networks in order to make the methods applicable to the design of water level monitors for highly controlled polder systems. The new contributions include the use of a hydrodynamic model for entropy analysis, the introduction of the quantization concept to filter out noisy time series, and the use of total correlation to evaluate the performance of three different pairwise dependence criteria. The resulting approach, water level monitoring design in polders (WMP), is applied to a polder in the Pijnacker region, Netherlands. Results show that relatively few monitors are adequate to collect the information of a polder area in spite of its large number of target water levels. It is found, in addition, that the directional information transfer DITYX is more effective in finding independent monitors, whereas DITXY is better for locating sets of monitors with high joint information content. WMP proves to be a suitable and simple method as part of the design of monitoring networks for polder systems.
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paper_title: Temporal variability of the optimal monitoring setup assessed using information theory

paper_content:

Hydrology is rich in methods that use information theory to evaluate monitoring networks. Yet in most existing studies, only the available data set as a whole is used, which neglects the intraannual variability of the hydrological system. In this paper, we demonstrate how this variability can be considered by extending monitoring evaluation to subsets of the available data. Therefore, we separately evaluated time windows of fixed length, which were shifted through the data set, and successively extended time windows. We used basic information theory measures and a greedy ranking algorithm based on the criterion of maximum information/minimum redundancy. The network investigated monitored surface and groundwater levels at quarter-hourly intervals and was located at an artificially drained lowland site in the Spreewald region in north-east Germany. The results revealed that some of the monitoring stations were of value permanently while others were needed only temporally. The prevailing meteorological conditions, particularly the amount of precipitation, affected the degree of similarity between the water levels measured. The hydrological system tended to act more individually during periods of no or little rainfall. The optimal monitoring setup, its stability, and the monitoring effort necessary were influenced by the meteorological forcing. Altogether, the methodology presented can help achieve a monitoring network design that has a more even performance or covers the conditions of interest (e.g., floods or droughts) best.
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paper_title: Entropy theory-based criterion for hydrometric network evaluation and design: Maximum information minimum redundancy: HYDROMETRIC NETWORK EVALUATION AND DESIGN

paper_content:

[1] Hydrometric information constitutes the fundamental input for planning, design, operation, and management of water resources systems. How to optimally site monitoring gauges such that they are effective and efficient in gathering the hydrometric information or data has received considerable attention. This paper presents a generic approach for the design (or evaluation) of hydrometric networks. First, an entropy theory-based criterion, named as maximum information minimum redundancy (MIMR), is proposed. The MIMR criterion maximizes the joint entropy of stations within the optimal set, and the transinformation between stations within and outside of the optimal set. Meanwhile, it insures that the optimal set contains minimum duplicated information. An easy-to-implement greedy ranking algorithm is developed to accomplish the MIMR selection. Two case studies are presented to illustrate the applicability of MIMR in hydrometric network evaluation and design. We also compare the MIMR selection with another entropy-based approach. Results illustrate that MIMR is apt at finding stations with high information content, and locating independent stations. The proposed approach is suitable for design (or evaluation) of any type of hydrometric network.
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paper_title: Variability in Canadian Seasonal Streamflow Information and Its Implication for Hydrometric Network Design

paper_content:

AbstractHydrologic extremes such as severe storms, floods, and droughts are inherently seasonal in nature and remain the main concern in designing hydrometric networks. In general, hydrometric networks have been designed without paying particular attention to the effect of seasonal streamflow information (SSI) at gauging stations on the efficiency of the hydrometric networks. This paper evaluates the effect of SSI on streamflow networks based on nonparametric implementation of entropy theory using the kernel density approach for estimating the mutual information between gauging stations on a seasonal basis. Overall, it is shown that the SSI of individual stations is season dependent and the efficiency of the streamflow network is also season dependent, therefore the effect of seasonality should be incorporated in future hydrometric network design. This methodology was applied at five river basins in Canada and its role for network design is discussed.
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paper_title: Catchment classification: empirical analysis of hydrologic similarity based on catchment function in the eastern USA

paper_content:

Hydrologic similarity between catchments, derived from similarity in how catchments respond to precipitation input, is the basis for catchment classification, for transferability of information, for generalization of our hydrologic understanding and also for understanding the potential impacts of environmental change. An important question in this context is, how far can widely available hydrologic information (precipitation-temperature-streamflow data and generally available physical descriptors) be used to create a first order grouping of hydrologically similar catchments? We utilize a heterogeneous dataset of 280 catchments located in the Eastern US to understand hydrologic similarity in a 6-dimensional signature space across a region with strong environmental gradients. Signatures are defined as hydrologic response characteristics that provide insight into the hydrologic function of catchments. A Bayesian clustering scheme is used to separate the catchments into 9 homogeneous classes, which enable us to interpret hydrologic similarity with respect to similarity in climatic and landscape attributes across this region. We finally derive several hypotheses regarding controls on individual signatures from the analysis performed here.
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paper_title: Optimizing streamflow monitoring networks using joint permutation entropy

paper_content:

Abstract Using joint permutation entropy we address the issue of minimizing the cost of monitoring, while minimizing redundancy of the information content, of daily streamflow data recorded during the period 1989–2016 at twelve gauging stations on Brazos River, Texas, USA. While the conventional entropy measures take into account only the probability of occurrence of a given set of events, permutation entropy also takes into account local ordering of the sequential values, thus enriching the analysis. We find that the best cost efficiency is achieved by performing weekly measurements, in comparison with which daily measurements exhibit information redundancy, and monthly measurements imply information loss. We also find that the cumulative information redundancy of the twelve considered stations is over 10% for the observed period, and that the number of monitoring stations can be reduced by half bringing the cumulative redundancy level to less than 1%.
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paper_title: CRDEMO: Combined regionalization and dual entropy-multiobjective optimization for hydrometric network design: Crdemo for Hydrometric Network Design

paper_content:

[1] Establishing an adequate hydrometric network to provide accurate and reliable continuous flow information for various users remains a major challenge. This includes the design of new networks or the evaluation of existing networks. This study proposes a combined regionalization and dual entropy-multiobjective optimization (CRDEMO) method for determining minimum network that meets the World Meteorology Organization (WMO) standards, which is considered herein an optimal minimum network. A regionalization approach is used to estimate flows in potential locations for new additional stations, and a dual entropy-multiobjective optimization approach is used to identify optimal trade-offs between the maximum possible information content and the minimum shared information among the stations. The method was examined in two Canadian River basins, namely, the St. John River and St. Lawrence River basins. The St. John River basin has a higher network density compared to the St. Lawrence River basin. Results of the analysis indicate that the St. Lawrence River basin requires a high number of new additional stations to meet the WMO minimum network density. It was also determined that existing stations do not have a significant influence in determining the locations of new stations in the St. Lawrence River basin. Conversely, however, in the St. John River basin, existing stations have significant influence on the determination of locations of new stations due to the higher number of existing stations. Overall, the CRDEMO technique is shown to be robust for designing optimal minimum hydrometric networks and can be a useful tool for evaluating current and proposed networks.
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paper_title: Hydrometric network design using streamflow signatures and indicators of hydrologic alteration

paper_content:

Summary This study highlights the impacts that the selected hydrologic characteristics of a basin have on the spatial variability of hydrometric networks. The study was conducted using streamflow monitoring networks in two Canadian basins, specifically in the Hamilton, Halton, Credit Valley basins of Ontario and the Columbia River basin of British Columbia. The Dual Entropy-Multiobjective Optimization (DEMO) model which has been demonstrated to be sufficiently robust for designing optimum networks in a large basin was used in these analyses. In addition to the entropy functions, the spatial variability of flow networks was examined by either excluding or including hydrologic signatures and indicators of hydrologic alteration (IHA) of a basin. The entropy functions are used to identify optimal trade-offs between the maximum possible information content and the minimum shared information among stations. The hydrologic signatures are used to quantify hydrological response characteristics among sub-basins, and the IHAs, which are normally used to determine how a hydrologic regime has been altered by an impact, are instead used to quantify differences between sub-basins. It was found that the optimal locations for the new stations were well captured by the objective functions. Also, new stations covered a wider area when hydrological signatures and IHAs were considered, enhancing the objective functions. The inclusion of streamflow signatures increased emphasis on the headwaters whereas the inclusion of IHAs increased emphasis on the downstream and disturbed regions. Accounting for such spatial variability in designing hydrometric networks is crucial in obtaining an optimal network.
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paper_title: A GIS-based multi-criteria decision-making approach for establishing a regional-scale groundwater monitoring

paper_content:

A weighted multi-criteria decision-making framework was designed to identify and prioritize areas for monitoring aquifer hydraulic heads within the Victoria County Groundwater Conservation District. The criteria address salient hydrogeological aspects including groundwater variability, recharge, surface water–groundwater interactions, and groundwater fluxes across district boundaries. Texas water statutes require groundwater conservation districts to quantify these factors and utilize them to manage aquifers. A stakeholder survey instrument was used to prioritize these criteria. A monitoring priority index (MPI), whose value theoretically ranges between 0 and 1 was computed as a weighted average of six mutually exclusive criteria. The MPI value was seen to range between 0.2 and 0.6 within the study area. Lower values of MPI indicate areas where the current level of monitoring is adequate and areas with a higher MPI point to locations where additional monitoring is necessary. In particular, monitoring along district boundaries, particularly along the western and southern sections, is recommended. The developed methodology was seen to provide a transparent and simple-to-use approach to identify and prioritize areas within the district for the purposes of groundwater monitoring. The proposed framework demonstrates the utility of GIS in facilitating a scientifically credible and stakeholder-driven approach for establishing groundwater monitoring networks and can be adapted in other similar applications.
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paper_title: A data fusion-based methodology for optimal redesign of groundwater monitoring networks

paper_content:

Abstract In this paper, a new data fusion-based methodology is presented for spatio-temporal (S-T) redesigning of Groundwater Level Monitoring Networks (GLMNs). The kriged maps of three different criteria (i.e. marginal entropy of water table levels, estimation error variances of mean values of water table levels, and estimation values of long-term changes in water level) are combined for determining monitoring sub-areas of high and low priorities in order to consider different spatial patterns for each sub-area. The best spatial sampling scheme is selected by applying a new method, in which a regular hexagonal gridding pattern and the Thiessen polygon approach are respectively utilized in sub-areas of high and low monitoring priorities. An Artificial Neural Network (ANN) and a S-T kriging models are used to simulate water level fluctuations. To improve the accuracy of the predictions, results of the ANN and S-T kriging models are combined using a data fusion technique. The concept of Value of Information (VOI) is utilized to determine two stations with maximum information values in both sub-areas with high and low monitoring priorities. The observed groundwater level data of these two stations are considered for the power of trend detection, estimating periodic fluctuations and mean values of the stationary components, which are used for determining non-uniform sampling frequencies for sub-areas. The proposed methodology is applied to the Dehgolan plain in northwestern Iran. The results show that a new sampling configuration with 35 and 7 monitoring stations and sampling intervals of 20 and 32 days, respectively in sub-areas with high and low monitoring priorities, leads to a more efficient monitoring network than the existing one containing 52 monitoring stations and monthly temporal sampling.
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paper_title: Evaluation of groundwater monitoring network of Kodaganar River basin from Southern India using entropy

paper_content:

A discrete entropy-based approach is used to assess the groundwater monitoring network that exists in Kodaganar River basin of Southern India. Since any monitoring system is essentially an information collection system, its technical design and evaluation require a quantifiable measure of information and this measure can be derived using entropy. The use of information-based measures of groundwater table shows that the existing monitoring network contains a sufficient number of wells but is not well designed for the measurement of groundwater level. Entropy-based results show that 15 wells are vital to measure regional groundwater level, not 28 wells which are being monitored effectively in this basin.
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paper_title: Augmentation of groundwater monitoring networks using information theory and ensemble modeling with pedotransfer functions

paper_content:

Summary Improving understanding of chemical transport in the subsurface commonly employs evolving groundwater monitoring networks. The objective of this work was to apply the information theory to propose an objective algorithm for augmenting a subsurface monitoring network (SMN) with the purpose of discrimination of conceptually different subsurface flow and transport models. This method determines new monitoring locations where the Kullback–Leibler total information gain is maximized. The latter is computed based on estimates of the uncertainty in modeling results and uncertainty in observations. The method was applied to discriminate models in (1) a synthetic case of groundwater contamination from a point source; (2) the tracer experiment conducted at the USDA-ARS OPE3 research site where a pulse of KCL solution was applied with irrigation water and CL − concentrations were subsequently monitored. Models were compared that included or ignored the effect of subsurface soil lenses on chemical transport. Pedotransfer functions were used to develop the ensemble of models for estimating the uncertainty in modeling results obtained with the numerical 3D flow and transport model. Peak tracer breakthrough concentrations were used to define the information gains. The determination of the new locations to augment existing ones was conducted on a 2-D grid. The information gain peaked in small area, and additional observation locations were very well spatially defined. Well-calibrated models provided a single optimal location, whereas, if models were not calibrated well, the Bayesian estimates of the new observation location depended on the activation sequence assumed for existing locations. The information gain maximization can suggest data collection locations to reduce uncertainties in the conceptual models of subsurface flow and transport.
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paper_title: Optimal redesign of groundwater quality monitoring networks: a case study.

paper_content:

Assessment and redesign of water quality monitoring networks is an important task in water quality management. This paper presents a new methodology for optimal redesign of groundwater quality monitoring networks. The measure of transinformation in discrete entropy theory and the transinformation-distance (T-D) curves are used to quantify the efficiency of sampling locations and sampling frequencies in a monitoring network. The existing uncertainties in the T-D curves are taken in to account using the fuzzy set theory. The C-means clustering method is also used to classify the study area to some homogenous zones. The fuzzy T-D curve of the zones is then used in a multi-objective hybrid genetic algorithm-based optimization model. The proposed methodology is utilized for optimal redesign of monitoring network of the Tehran aquifer in the Tehran metropolitan area, Iran.
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paper_title: Entropy based groundwater monitoring network design considering spatial distribution of annual recharge

paper_content:

Abstract This study explores the inclusion of a groundwater recharge based design objective and the impact it has on the design of optimum groundwater monitoring networks. The study was conducted in the Hamilton, Halton, and Credit Valley regions of Ontario, Canada, in which the existing Ontario Provincial Groundwater Monitoring Network was augmented with additional monitoring wells. The Dual Entropy-Multiobjective Optimization (DEMO) model was used in these analyses. The value of using this design objective is rooted in the information contained within the estimated recharge. Recharge requires knowledge of climate, geomorphology, and geology of the area, thus using this objective function can help account for these physical characteristics. Two sources of groundwater recharge data were examined and compared, the first was calculated using the Precipitation-Runoff Modeling System (PRMS), and the second was an aggregation of recharge found using both the PRMS and Hydrological Simulation Program-Fortran (HSP-F). The entropy functions are used to identify optimal trade-offs between the maximum information content and the minimum shared information between the monitoring wells. The recharge objective will help to quantify hydrological characteristics of the vadose zone, and thus provide more information to the optimization algorithm. Results show that by including recharge as a design objective, the spatial coverage of the monitoring network can be improved. The study also highlights the flexibility of DEMO and its ability to incorporate additional design objectives such as the groundwater recharge.
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paper_title: Temporal variability of the optimal monitoring setup assessed using information theory

paper_content:

Hydrology is rich in methods that use information theory to evaluate monitoring networks. Yet in most existing studies, only the available data set as a whole is used, which neglects the intraannual variability of the hydrological system. In this paper, we demonstrate how this variability can be considered by extending monitoring evaluation to subsets of the available data. Therefore, we separately evaluated time windows of fixed length, which were shifted through the data set, and successively extended time windows. We used basic information theory measures and a greedy ranking algorithm based on the criterion of maximum information/minimum redundancy. The network investigated monitored surface and groundwater levels at quarter-hourly intervals and was located at an artificially drained lowland site in the Spreewald region in north-east Germany. The results revealed that some of the monitoring stations were of value permanently while others were needed only temporally. The prevailing meteorological conditions, particularly the amount of precipitation, affected the degree of similarity between the water levels measured. The hydrological system tended to act more individually during periods of no or little rainfall. The optimal monitoring setup, its stability, and the monitoring effort necessary were influenced by the meteorological forcing. Altogether, the methodology presented can help achieve a monitoring network design that has a more even performance or covers the conditions of interest (e.g., floods or droughts) best.
---
paper_title: A Bayesian maximum entropy-based methodology for optimal spatiotemporal design of groundwater monitoring networks

paper_content:

This paper presents a new methodology for analyzing the spatiotemporal variability of water table levels and redesigning a groundwater level monitoring network (GLMN) using the Bayesian Maximum Entropy (BME) technique and a multi-criteria decision-making approach based on ordered weighted averaging (OWA). The spatial sampling is determined using a hexagonal gridding pattern and a new method, which is proposed to assign a removal priority number to each pre-existing station. To design temporal sampling, a new approach is also applied to consider uncertainty caused by lack of information. In this approach, different time lag values are tested by regarding another source of information, which is simulation result of a numerical groundwater flow model. Furthermore, to incorporate the existing uncertainties in available monitoring data, the flexibility of the BME interpolation technique is taken into account in applying soft data and improving the accuracy of the calculations. To examine the methodology, it is applied to the Dehgolan plain in northwestern Iran. Based on the results, a configuration of 33 monitoring stations for a regular hexagonal grid of side length 3600 m is proposed, in which the time lag between samples is equal to 5 weeks. Since the variance estimation errors of the BME method are almost identical for redesigned and existing networks, the redesigned monitoring network is more cost-effective and efficient than the existing monitoring network with 52 stations and monthly sampling frequency.
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paper_title: Spatial-temporal assessment and redesign of groundwater quality monitoring network: a case study.

paper_content:

Assessment of groundwater quality monitoring networks requires methods to determine the potential efficiency and cost-effectiveness of the current monitoring programs. To this end, the concept of entropy has been considered as a promising method in previous studies since it quantitatively measures the information produced by a network. In this study, the measure of transinformation in the discrete entropy theory and the transinformation-distance (T-D) curves, which are used frequently by other researchers, are used to quantify the efficiency of a monitoring network. This paper introduces a new approach to decrease dispersion in results by performing cluster analysis that uses fuzzy equivalence relations. As a result, the sampling (temporal) frequency determination method also recommends the future sampling frequencies for each location based on certain criteria such as direction, magnitude, correlation with neighboring stations, and uncertainty of the concentration trend derived from representative historical concentration data. The proposed methodology is applied to groundwater resources in the Tehran-Karadj aquifer, Tehran, Iran.
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paper_title: Design of an Optimal Soil Moisture Monitoring Network Using SMOS Retrieved Soil Moisture

paper_content:

Many methods have been proposed to select sites for grid-scale soil moisture monitoring networks; however, calibration/validation activities also require information about where to place grid representative monitoring sites. In order to design a soil moisture network for this task in the Great Lakes Basin (522 000 km2), the dual-entropy multiobjective optimization algorithm was used to maximize the information content and minimize the redundancy of information in a potential soil moisture monitoring network. Soil moisture retrieved from the Soil Moisture and Ocean Salinity (SMOS) mission during the frost-free periods of 2010–2013 were filtered for data quality and then used in a multiobjective search to find Pareto optimum network designs based on the joint entropy and total correlation measures of information content and information redundancy, respectively. Differences in the information content of SMOS ascending and descending overpasses resulted in distinctly different network designs. Entropy from the SMOS ascending overpass was found to be spatially consistent, whereas descending overpass entropy had many peaks that coincided with areas of high subgrid heterogeneity. A combination of both ascending and descending overpasses produced network designs that incorporated aspects of information from each overpass. Initial networks were designed to include 15 monitoring sites, but the addition of network cost as an objective demonstrated that a network with similar information content could be achieved with fewer monitoring stations.
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paper_title: CRDEMO: Combined regionalization and dual entropy-multiobjective optimization for hydrometric network design: Crdemo for Hydrometric Network Design

paper_content:

[1] Establishing an adequate hydrometric network to provide accurate and reliable continuous flow information for various users remains a major challenge. This includes the design of new networks or the evaluation of existing networks. This study proposes a combined regionalization and dual entropy-multiobjective optimization (CRDEMO) method for determining minimum network that meets the World Meteorology Organization (WMO) standards, which is considered herein an optimal minimum network. A regionalization approach is used to estimate flows in potential locations for new additional stations, and a dual entropy-multiobjective optimization approach is used to identify optimal trade-offs between the maximum possible information content and the minimum shared information among the stations. The method was examined in two Canadian River basins, namely, the St. John River and St. Lawrence River basins. The St. John River basin has a higher network density compared to the St. Lawrence River basin. Results of the analysis indicate that the St. Lawrence River basin requires a high number of new additional stations to meet the WMO minimum network density. It was also determined that existing stations do not have a significant influence in determining the locations of new stations in the St. Lawrence River basin. Conversely, however, in the St. John River basin, existing stations have significant influence on the determination of locations of new stations due to the higher number of existing stations. Overall, the CRDEMO technique is shown to be robust for designing optimal minimum hydrometric networks and can be a useful tool for evaluating current and proposed networks.
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paper_title: Evaluating sampling locations in river water quality monitoring networks: application of dynamic factor analysis and discrete entropy theory

paper_content:

In this paper, a methodology is proposed for evaluating sampling locations in an existing river water quality monitoring network. The dynamic factor analysis is utilized to extract the independent dynamic factors from time series of water quality variables. Then, the entropy theory is applied to the independent dynamic factors to construct transinformation–distance (T–D) curves. The computation time in the case of using dynamic factors is significantly less than when the raw data is used because the number of independent dynamic factors is usually much less than the number of monitored water quality variables. In this paper, it is also shown that by clustering the study area to some homogenous zones and developing T–D curves for each zone, the accuracy of the results is significantly increased. To evaluate the applicability and efficiency of the proposed methodology, it is applied to the Karoon River which is the most important river system in Iran.
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paper_title: Water quality monitoring strategies - A review and future perspectives.

paper_content:

The reliable assessment of water quality through water quality monitoring programs (WQMPs) is crucial in order for decision-makers to understand, interpret and use this information in support of their management activities aiming at protecting the resource. The challenge of water quality monitoring has been widely addressed in the literature since the 1940s. However, there is still no generally accepted, holistic and practical strategy to support all phases of WQMPs. The purpose of this paper is to report on the use cases a watershed manager has to address to plan or optimize a WQMP from the challenge of identifying monitoring objectives; selecting sampling sites and water quality parameters; identifying sampling frequencies; considering logistics and resources to the implementation of actions based on information acquired through the WQMP. An inventory and critique of the information, approaches and tools placed at the disposal of watershed managers was proposed to evaluate how the existing information could be integrated in a holistic, user-friendly and evolvable solution. Given the differences in regulatory requirements, water quality standards, geographical and geological differences, land-use variations, and other site specificities, a one-in-all solution is not possible. However, we advance that an intelligent decision support system (IDSS) based on expert knowledge that integrates existing approaches and past research can guide a watershed manager through the process according to his/her site-specific requirements. It is also necessary to tap into local knowledge and to identify the knowledge needs of all the stakeholders through participative approaches based on geographical information systems and adaptive survey-based questionnaires. We believe that future research should focus on developing such participative approaches and further investigate the benefits of IDSS's that can be updated quickly and make it possible for a watershed manager to obtain a timely, holistic view and support for every aspect of planning and optimizing a WQMP.
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paper_title: Optimizing an estuarine water quality monitoring program through an entropy-based hierarchical spatiotemporal Bayesian framework

paper_content:

[1] The total maximum daily load program aims to monitor more than 40,000 standard violations in around 20,000 impaired water bodies across the United States. Given resource limitations, future monitoring efforts have to be hedged against the uncertainties in the monitored system, while taking into account existing knowledge. In that respect, we have developed a hierarchical spatiotemporal Bayesian model that can be used to optimize an existing monitoring network by retaining stations that provide the maximum amount of information, while identifying locations that would benefit from the addition of new stations. The model assumes the water quality parameters are adequately described by a joint matrix normal distribution. The adopted approach allows for a reduction in redundancies, while emphasizing information richness rather than data richness. The developed approach incorporates the concept of entropy to account for the associated uncertainties. Three different entropy-based criteria are adopted: total system entropy, chlorophyll-a standard violation entropy, and dissolved oxygen standard violation entropy. A multiple attribute decision making framework is adopted to integrate the competing design criteria and to generate a single optimal design. The approach is implemented on the water quality monitoring system of the Neuse River Estuary in North Carolina, USA. The model results indicate that the high priority monitoring areas identified by the total system entropy and the dissolved oxygen violation entropy criteria are largely coincident. The monitoring design based on the chlorophyll-a standard violation entropy proved to be less informative, given the low probabilities of violating the water quality standard in the estuary.
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paper_title: Revising river water quality monitoring networks using discrete entropy theory: the Jajrood River experience.

paper_content:

This paper aims at evaluating and revising the spatial and temporal sampling frequencies of the water quality monitoring system of the Jajrood River in the Northern part of Tehran, Iran. This important river system supplies 23% of domestic water demand of the Tehran metropolitan area with population of more than 10 million people. In the proposed methodology, by developing a model for calculating a discrete version of pair-wise spatial information transfer indices (SITIs) for each pair of potential monitoring stations, the pair-wise SITI matrices for all water quality variables are formed. Also, using a similar model, the discrete temporal information transfer indices (TITIs) using the data of the existing monitoring stations are calculated. Then, the curves of the pair-wise SITI versus distance between monitoring stations and TITI versus time lags for all water quality variables are derived. Then, using a group pair-wise comparison matrix, the relative weights of the water quality variables are calculated. In this paper, a micro-genetic-algorithm-based optimization model with the objective of minimizing a weighted average spatial and temporal ITI is developed and for a pre-defined total number of stations, the best combination of monitoring stations is selected. The results show that the existing monitoring system of the Jajrood River should be partially strengthened and in some cases the sampling frequencies should be increased. Based on the results, the proposed approach can be used as an effective tool for evaluating, revising, or redesigning the existing river water quality monitoring systems.
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paper_title: Discrete entropy theory for optimal redesigning of salinity monitoring network in San Francisco bay

paper_content:

The paper presents an entropy-based method for designing an optimum bay water salinity monitoring network in San Francisco bay (S.F. bay) considering maximum-monitoring-information and minimum-data-lost criteria. Due to cost concerns, it is necessary to design the optimal salinity monitoring network with a minimal number of sampling stations to provide reliable data. The monthly data recorded from January 1995 to December 2014 were obtained over 37 active stations located in S.F. bay and is applied in the research. Transinformation entropy in discrete mode is used to calculate the stations9 optimum distance. The discrete approach uses the frequency table to calculate transinformation measures. After calculating these measures, a transinformation–distance (T-D) curve is developed. Then, the optimum distance between salinity monitoring stations is elicited from the curve. The study shows that the S.F. bay salinity monitoring stations provide redundant information and the existing stations can be reduced to 21 with an approximate distance of 7.5 km. The coverage of the proposed monitoring network by using the optimum distance is complete and the system does not generate redundant data. The results of this research indicate that transinformation entropy is a promising method for the design of monitoring networks in bays such as those found in San Francisco bay.
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paper_title: Efficient method for optimal placing of water quality monitoring stations for an ungauged basin

paper_content:

Abstract A core problem in monitoring water quality of a river basin is identifying an optimal positioning of a limited number of water-sampling sites. Various optimality criteria have been suggested for this selection process in earlier studies. However, the search for sets of sampling sites that satisfy such criteria poses a challenging optimization problem, especially for a large basin. Here, we show that for particular types of objective functions, the optimization procedure can be dramatically simplified via an analogy with the formulation of Shannon entropy. On this basis, we propose an efficient algorithm that can easily determine the optimal location of water quality sampling sites in a river network. The proposed algorithm can be used standalone or in conjunction with a heuristic optimization algorithm such as a genetic algorithm. For the latter, the proposed algorithm filters only competitive candidates and makes a contribution to reducing the problem size significantly. The superior performance of the proposed method is demonstrated via its application to actual river networks examined in earlier studies, in which the proposed method determines more optimal solutions in a shorter computation time. The idea presented in this study can also be applied to other problems in which the objective function can be formulated in a similar functional form.
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paper_title: Information theory-based decision support system for integrated design of multivariable hydrometric networks

paper_content:

Adequate and accurate hydrologic information from optimal hydrometric networks is an essential part of effective water resources management. Although the key hydrologic processes in the water cycle are interconnected, hydrometric networks (e.g., streamflow, precipitation, groundwater level) have been routinely designed individually. A decision support framework is proposed for integrated design of multivariable hydrometric networks. The proposed method is applied to design optimal precipitation and streamflow networks simultaneously. The epsilon-dominance hierarchical Bayesian optimization algorithm was combined with Shannon entropy of information theory to design and evaluate hydrometric networks. Specifically, the joint entropy from the combined networks was maximized to provide the most information, and the total correlation was minimized to reduce redundant information. To further optimize the efficiency between the networks, they were designed by maximizing the conditional entropy of the streamflow network given the information of the precipitation network. Compared to the traditional individual variable design approach, the integrated multivariable design method was able to determine more efficient optimal networks by avoiding the redundant stations. Additionally, four quantization cases were compared to evaluate their effects on the entropy calculations and the determination of the optimal networks. The evaluation results indicate that the quantization methods should be selected after careful consideration for each design problem since the station rankings and the optimal networks can change accordingly.
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paper_title: Information theory-based decision support system for integrated design of multivariable hydrometric networks

paper_content:

Adequate and accurate hydrologic information from optimal hydrometric networks is an essential part of effective water resources management. Although the key hydrologic processes in the water cycle are interconnected, hydrometric networks (e.g., streamflow, precipitation, groundwater level) have been routinely designed individually. A decision support framework is proposed for integrated design of multivariable hydrometric networks. The proposed method is applied to design optimal precipitation and streamflow networks simultaneously. The epsilon-dominance hierarchical Bayesian optimization algorithm was combined with Shannon entropy of information theory to design and evaluate hydrometric networks. Specifically, the joint entropy from the combined networks was maximized to provide the most information, and the total correlation was minimized to reduce redundant information. To further optimize the efficiency between the networks, they were designed by maximizing the conditional entropy of the streamflow network given the information of the precipitation network. Compared to the traditional individual variable design approach, the integrated multivariable design method was able to determine more efficient optimal networks by avoiding the redundant stations. Additionally, four quantization cases were compared to evaluate their effects on the entropy calculations and the determination of the optimal networks. The evaluation results indicate that the quantization methods should be selected after careful consideration for each design problem since the station rankings and the optimal networks can change accordingly.
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paper_title: Rainfall and streamflow sensor network design: a review of applications, classification, and a proposed framework

paper_content:

Sensors and sensor networks play an important role in decision-making related to water quality, operational streamflow forecasting, flood early warning systems, and other areas. In this paper we review a number of existing applications and analyse a variety of evaluation and design procedures for sensor networks with respect to various criteria. Most of the existing approaches focus on maximising the observability and information content of a variable of interest. From the context of hydrological modelling only a few studies use the performance of the hydrological simulation in terms of output discharge as a design criterion. In addition to the review, we propose a framework for classifying the existing design methods, and a generalised procedure for an optimal network design in the context of rainfall-runoff hydrological modelling.
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paper_title: Estimating information entropy for hydrological data: One‐dimensional case

paper_content:

There has been a recent resurgence of interest in the application of Information Theory to problems of system identification in the Earth and Environmental Sciences. While the concept of entropy has found increased application, little attention has yet been given to the practical problems of estimating entropy when dealing with the unique characteristics of two commonly used kinds of hydrologic data: rainfall and runoff. In this paper, we discuss four important issues of practical relevance that can bias the computation of entropy if not properly handled. The first (zero effect) arises when precipitation and ephemeral streamflow data must be viewed as arising from a discrete-continuous hybrid distribution due to the occurrence of many zero values (e.g., days with no rain/no runoff). Second, in the widely used bin-counting method for estimation of PDF's, significant error can be introduced if the bin width is not carefully selected. The third (measurement effect) arises due to the fact that continuously varying hydrologic variables can typically only be observed discretely to some degree of precision. The Fourth (skewness effect) arises when the distribution of a variable is significantly skewed. Here we present an approach that can deal with all four of these issues, and test them with artificially generated and real hydrological data. The results indicate that the method is accurate and robust.
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paper_title: Ecohydrologic process networks: 1. Identification: ECOHYDROLOGIC PROCESS NETWORKS, 1

paper_content:

[1] Ecohydrological systems may be characterized as nonlinear, complex, open dissipative systems. Such systems consist of many coupled processes, and the couplings change depending on the system state or scale in space and time at which the system is analyzed. The arrangement of couplings in a complex system may be represented as a network of information flow and feedback between variables that measure system processes. The occurrence of feedback on such a network provides sufficient conditions for self-organized and nonlinear behaviors to emerge. We adapt an information-theoretic statistical method called transfer entropy for the purposes of robustly measuring the directionality, relative strength, statistical significance, and time scale of information flow between pairs of ecohydrological variables using time series data. A process network may be delineated where variables are cast as nodes and information flows as weighted directional links between them. The process network captures key couplings and time scales and represents the state of the complex system as a whole, including functional groups of variables (subsystems) and synchronization resulting from feedbacks. It is therefore able to identify interactions which are not detectable using methods which examine the system using one relationship at a time. We assemble an information flow process network using July 2003 FLUXNET data for a Midwestern corn-soybean ecohydrological system in a healthy, peak growing season state and compare the results with those using July 2005 data for the same site during a severe drought. We find that the process network during drought is substantially decoupled, and regional-scale information feedback is reduced during the drought. We conclude that the proposed process network methodology is able to identify the differences between two states of an ecohydrological system on the basis of variations in the pattern of feedback coupling on the network.
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paper_title: Temporal variability of the optimal monitoring setup assessed using information theory

paper_content:

Hydrology is rich in methods that use information theory to evaluate monitoring networks. Yet in most existing studies, only the available data set as a whole is used, which neglects the intraannual variability of the hydrological system. In this paper, we demonstrate how this variability can be considered by extending monitoring evaluation to subsets of the available data. Therefore, we separately evaluated time windows of fixed length, which were shifted through the data set, and successively extended time windows. We used basic information theory measures and a greedy ranking algorithm based on the criterion of maximum information/minimum redundancy. The network investigated monitored surface and groundwater levels at quarter-hourly intervals and was located at an artificially drained lowland site in the Spreewald region in north-east Germany. The results revealed that some of the monitoring stations were of value permanently while others were needed only temporally. The prevailing meteorological conditions, particularly the amount of precipitation, affected the degree of similarity between the water levels measured. The hydrological system tended to act more individually during periods of no or little rainfall. The optimal monitoring setup, its stability, and the monitoring effort necessary were influenced by the meteorological forcing. Altogether, the methodology presented can help achieve a monitoring network design that has a more even performance or covers the conditions of interest (e.g., floods or droughts) best.
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paper_title: Spatiotemporal Scaling Effect on Rainfall Network Design Using Entropy

paper_content:

Because of high variation in mountainous areas, rainfall data at different spatiotemporal scales may yield potential uncertainty for network design. However, few studies focus on the scaling effect on both the spatial and the temporal scale. By calculating the maximum joint entropy of hourly typhoon events, monthly, six dry and wet months and annual rainfall between 1992 and 2012 for 1-, 3-, and 5-km grids, the relocated candidate rain gauges in the National Taiwan University Experimental Forest of Central Taiwan are prioritized. The results show: (1) the network exhibits different locations for first prioritized candidate rain gauges for different spatiotemporal scales; (2) the effect of spatial scales is insignificant compared to temporal scales; and (3) a smaller number and a lower percentage of required stations (PRS) reach stable joint entropy for a long duration at finer spatial scale. Prioritized candidate rain gauges provide key reference points for adjusting the network to capture more accurate information and minimize redundancy.
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paper_title: Developments in hydrometric network design: A review

paper_content:

[1] Hydrometric network design for surface water monitoring is employed to address a wide range of environmental and water resources problems. Historical overview of hydrometric network design is provided along with a discussion on new developments and challenges in the design of optimal hydrometric networks. This review starts with precise examples of decline in hydrometric network density, then highlights the increasing requirement of optimal network design in a context of climate and land use changes. An extensive survey of methodological development in hydrometric network design is provided along with discussion on the issue of uncertainty in hydrometric network design and the evolution in data collection techniques and technology. Finally, some conclusions are drawn on the future of hydrometric network design.
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paper_title: Entropy theory based multi-criteria resampling of rain gauge networks for hydrological modelling – A case study of humid area in southern China

paper_content:

Summary Rain gauge networks are used to provide estimates of area average, spatial variability and point rainfalls at catchment scale and provide the most important input for hydrological models. Therefore, it is desired to design the optimal rain gauge networks with a minimal number of rain gauges to provide reliable data with both areal mean values and spatial–temporal variability. Based on a dense rain gauge network of 185 rain gauges in Xiangjiang River Basin, southern China, this study used an entropy theory based multi-criteria method which simultaneously considers the information derived from rainfall series, minimize the bias of areal mean rainfall as well as minimize the information overlapped by different gauges to resample the rain gauge networks with different gauge densities. The optimal networks were examined using two hydrological models: The lumped Xinanjiang Model and the distributed SWAT Model. The results indicate that the performances of the lumped model using different optimal networks are stable while the performances of the distributed model keep on improving as the number of rain gauges increases. The results reveal that the entropy theory based multi-criteria strategy provides an optimal design of rain gauge network which is of vital importance in regional hydrological study and water resources management.
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paper_title: Optimizing streamflow monitoring networks using joint permutation entropy

paper_content:

Abstract Using joint permutation entropy we address the issue of minimizing the cost of monitoring, while minimizing redundancy of the information content, of daily streamflow data recorded during the period 1989–2016 at twelve gauging stations on Brazos River, Texas, USA. While the conventional entropy measures take into account only the probability of occurrence of a given set of events, permutation entropy also takes into account local ordering of the sequential values, thus enriching the analysis. We find that the best cost efficiency is achieved by performing weekly measurements, in comparison with which daily measurements exhibit information redundancy, and monthly measurements imply information loss. We also find that the cumulative information redundancy of the twelve considered stations is over 10% for the observed period, and that the number of monitoring stations can be reduced by half bringing the cumulative redundancy level to less than 1%.
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paper_title: A multiscale information theory approach to assess spatial-temporal variability of daily precipitation.

paper_content:

Summary Information theory metrics are applied to ascertain the spatial and temporal variability of daily precipitation over the continental United States. Entropy is computed of the daily precipitation records and of the precipitation event size distribution. In addition, relative entropy is also computed between the two records and the Hurst exponent is calculated for comparison purposes. These values show little correlation with mean annual precipitation, number of rain days or station elevation. However, there is a clear spatial pattern in the precipitation and relative entropy fields corresponding to a breakpoint at approximately −95° longitude, which the Hurst exponent is not capable of resolving. Using wavelet multiresolution analysis and relative entropy, this breakpoint is shown to correspond to higher temporal variability (sub-monthly) in the western United States. In addition, scalewise mutual information content illustrates the general feature of three distinct scaling regions for precipitation: (1) synoptic (2–10 days), (2) monthly to annual times and (3) interannual variability. This analysis demonstrates the usefulness of an information theory approach to assessing the dynamics of precipitation.
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paper_title: Ecohydrologic process networks: 2. Analysis and characterization

paper_content:

[1] Ecohydrological systems are complex, open dissipative systems characterized by couplings and feedback between subsystems at many scales of space and time. The information flow process network approach is developed to analyze such systems, using time series data to delineate the feedback, time scales, and subsystems that define the complex system's organization. Network statistics are used to measure the statistical feedback, entropy, and net and gross information production of subsystems on the network to study monthly process networks for a Midwestern corn-soybean ecosystem for the years 1998–2006. Several distinct system states are identified and characterized. Particularly interesting is the midsummer state that is dominated by regional-scale information feedback and by information flow originating from the ecosystem's photosynthetic activity. In this state, information flows both “top-down” from synoptic weather systems and “bottom-up” from the plant photosynthetic activity. A threshold in air temperature separates this summer state where increased organization appears from other system states. The relationship between Shannon entropy and information flow is investigated. It is found that information generally flows from high-entropy variables to low-entropy variables, and moderate-entropy variables participate in feedback.
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Title: Entropy Applications to Water Monitoring Network Design: A Review

Section 1: Introduction
Description 1: This section introduces the topic of water monitoring networks, their importance in water resource management, and the basics of entropy theory as related to water monitoring network design.

Section 2: Entropy Concept
Description 2: This section describes the fundamental concept of entropy in thermodynamics and information theory, including Shannon entropy and its significance.

Section 3: Marginal Entropy
Description 3: This section explains the concept of marginal entropy, its calculation, and its relevance to water monitoring network design.

Section 4: Multivariate Joint Entropy
Description 4: This section outlines the calculation of joint entropy for multiple variables and its importance in the context of water monitoring networks.

Section 5: Conditional Entropy
Description 5: This section discusses conditional entropy and its application in determining the contribution of individual variables to the overall uncertainty.

Section 6: Transinformation
Description 6: This section introduces the concept of transinformation, also known as mutual information, and its role in indicating how much information is shared between variables.

Section 7: Total Correlation
Description 7: This section differentiates between transinformation/mutual information and total correlation, which measures the amount of shared information among multiple variables.

Section 8: Other Entropy Terms
Description 8: This section briefly introduces additional entropy-related terms and measures that have been used in specific case studies.

Section 9: Applications of Entropy to Water Monitoring Network Design
Description 9: This section summarizes the recent applications of entropy theory in designing different types of water monitoring networks such as precipitation, streamflow, soil moisture, groundwater, and water quality networks.

Section 10: Precipitation Networks
Description 10: This section details methods and findings related to the design of precipitation monitoring networks using entropy-based approaches.

Section 11: Streamflow and Water Level Networks
Description 11: This section describes the application of entropy theory to the design of streamflow and water level monitoring networks, and discusses methodological considerations.

Section 12: Soil Moisture and Groundwater Networks
Description 12: This section reviews studies on designing soil moisture and groundwater monitoring networks using entropy measures and considerations for these types of networks.

Section 13: Water Quality Networks
Description 13: This section addresses the design of water quality monitoring networks and the use of entropy methods to optimize these networks.

Section 14: Integrated Network Design
Description 14: This section discusses the integrated design of water monitoring networks that consider multiple types of hydrologic variables simultaneously.

Section 15: Conclusions and Recommendations
Description 15: This section provides a summary of findings, draws conclusions on the use of entropy in water monitoring network design, and makes recommendations for future research and practice.