Gradient-based estimation of spatially distributed parameters of a shallow water 2D rainfall-runoff model

This contribution presents a gradient-based inverse modeling approach for the inference of distributed infiltration parameters in a 2D shallow water hydraulic model. It describes the implementation of rain and infiltration mass source terms in the DassFlow direct-inverse modeling platform and their validation against experimental data. Synthetic experiments are used to showcase the complexity of the inverse problems posed by the inference of infiltration parameters through hydraulic signature analysis, stochastic parameter space exploration and inverse modeling with distributed or multi-variate controls. To address spatial uncertainty in the context of sparse observations, spatial constraints are imposed to sought infiltration parameters in the form of homogeneous areas, or patches, sharing the resolution of available soil maps. They are also introduced in the form of a parameter model based on pedotransfer functions, which are used to reduce the dimensionality of the inverse problem and impose spatial coherence to the inferred distributed parameters. This upgrade of the direct model enables integrating a priori knowledge of parameter distribution carried by physical descriptor maps into the assimilation process, hence providing a spatially regularizing effect. Inference results for a fully distributed parametrization without regularization, which is achieved by solving of a high-dimensional inverse problem, are also presented. The methodology is applied to real catchments within the Réal Collobrier hydrological observatory in southeastern France, monitored by INRAE. In a model containing high-resolution topography and rain data, real downstream discharge observations are assimilated to infer distributed infiltration parameters maps, including through regionalized pedotransfer functions. This leads to the inference of effective infiltration model parameters that provide a better fit to real flow observations.