Learning Regionalization within a Differentiable High-Resolution
  Hydrological Model using Accurate Spatial Cost Gradients
Ngo Nghi Truyen Huynh Pierre-André Garambois François Colleoni Benjamin Renard Hélène Roux Julie Demargne Pierre Javelle
Estimating spatially distributed hydrological parameters in ungauged
catchments poses a challenging regionalization problem and requires imposing
spatial constraints given the sparsity of discharge data. A possible approach
is to search for a transfer function that quantitatively relates physical
descriptors to conceptual model parameters. This paper introduces a Hybrid Data
Assimilation and Parameter Regionalization (HDA-PR) approach incorporating
learnable regionalization mappings, based on either multivariate regressions or
neural networks, into a differentiable hydrological model. It enables the
exploitation of heterogeneous datasets across extensive spatio-temporal
computational domains within a high-dimensional regionalization context, using
accurate adjoint-based gradients. The inverse problem is tackled with a
multi-gauge calibration cost function accounting for information from multiple
observation sites. HDA-PR was tested on high-resolution, hourly and kilometric
regional modeling of two flash-flood-prone areas located in the South of
France. In both study areas, the median Nash-Sutcliffe efficiency (NSE) scores
ranged from 0.52 to 0.78 at pseudo-ungauged sites over calibration and
validation periods. These results highlight a strong regionalization
performance of HDA-PR, improving NSE by up to 0.57 compared to the baseline
model calibrated with lumped parameters, and achieving a performance comparable
to the reference solution obtained with local uniform calibration (median NSE
from 0.59 to 0.79). Multiple evaluation metrics based on flood-oriented
hydrological signatures are also employed to assess the accuracy and robustness
of the approach. The regionalization method is amenable to state-parameter
correction from multi-source data over a range of time scales needed for
operational data assimilation, and it is adaptable to other differentiable
geophysical models.