Signatures-and-sensitivity-based multi-criteria variational calibration for distributed hydrological modeling applied to Mediterranean floods

Multiscale Learnable Physical Modeling and Data Assimilation Framework: Application to High-Resolution Regionalized Hydrological Simulation of Flash Floods

“…with ρ = (ρ 1 , ρ 2 ) the vector of trainable parameters, invariant to the spatial coordinate x over Ω, of the pair of neural networks. In this study, we use two multilayer perceptrons, the first one ϕ 1 for spatiotemporal corrections of the model internal fluxes f q (x, t) and the second ϕ 2 for spatialized parameters θ(x) regionalization as used in Huynh, Garambois, Colleoni, Renard, et al (2023) (refer to SI, Text S2 for further details). Here, the fluxes correction f q = f q,i=1..Nq T predicted by ϕ 1 , are applied as multiplicative factors, for each pixel x and time t, to the N q = 4 internal fluxes of the GR hydrological operators to correct simultaneously the actual evapotranspiration and infiltration into the production reservoir, the net rainfall partitioning with a non-conservative exchange effect, and the non-conservative exchange flux.…”

“…Monnier (2021)). Regarding rivers networks, adjoint-based optimization has been applied to dynamic non-linear and highly parameterized spatially distributed models in 2D hydraulics (Honnorat et al, 2009), in spatially distributed hydrological VDA (Castaings et al, 2009;Jay-Allemand et al, 2020), and in ANN-based regionalization (Huynh, Garambois, Colleoni, Renard, et al, 2023). Nevertheless, incorporating neural networks into a differentiable spatialized hydrological model with a data assimilation framework, for learning physical processes parameterization from massive data, has never been performed and is a very challenging problem addressed here.…”

“…This article presents a novel framework for building Multiscale spatially distributed Learnable Physical Modeling (MLPM) with Learnable Parameter Regionalization (LPR). The approach builds on differentiable modeling and combines interpretable process-based modeling along with neural networks, including learnable regionalization of conceptual parameters with an ANN from Huynh, Garambois, Colleoni, Renard, et al (2023), and another ANN introduced for process parameterization learning applied here to correct internal fluxes within a spatially distributed hydrological model. The MLPM-PR framework is illustrated with a parsimonious conceptual grid-based GR-like model with kinematic wave routing scheme, implemented in the open-source SMASH software (Spatially distributed Modelling and ASsimilation for Hy-drology) that enables multiscale modeling, numerical adjoint model derivation via automatic differentiation and VDA.…”