On the potential of variational calibration for a fully distributed hydrological model: application on a Mediterranean catchment

Abstract

Abstract. Calibration of a conceptual distributed model is challenging due to a number of reasons, which include fundamental (model adequacy and identifiability) and algorithmic (e.g., local search vs. global search) issues. The aim of the presented study is to investigate the potential of the variational approach for calibrating a simple continuous hydrological model (GRD; Génie Rural distributed involved in several flash flood modeling applications. This model is defined on a rectangular 1 km2 resolution grid, with three parameters being associated with each cell. The Gardon d'Anduze watershed (543 km2) is chosen as the study benchmark. For this watershed, the discharge observations at five gauging stations, gridded rainfall and potential-evapotranspiration estimates are continuously available for the 2007–2018 period at an hourly time step. In the variational approach one looks for the optimal solution by minimizing the standard quadratic cost function, which penalizes the misfit between the observed and predicted values, under some additional a priori constraints. The cost function gradient is efficiently computed using the adjoint model. In numerical experiments, the benefits of using the distributed against the uniform calibration are measured in terms of the model predictive performance, in temporal, spatial and spatiotemporal validation, both globally and for particular flood events. Overall, distributed calibration shows encouraging results, providing better model predictions and relevant spatial distribution of some parameters. The numerical stability analysis has been performed to understand the impact of different factors on the calibration quality. This analysis indicates the possible directions for future developments, which may include considering a non-Gaussian likelihood and upgrading the model structure.

Signature and sensitivity-based comparison of conceptual and process oriented models, GR4H, MARINE and SMASH, on French Mediterranean flash floods

“…The variational algorithm presented in Jay-Allemand et al ( 2020) and enabling the calibration of spatially distributed model parameters, that is high dimensional optimization problems, under various constrains is performed. This variational calibration algorithm starts from a spatially uniform prior guess on the sought parameters (Jay-Allemand et al, 2020). This prior guess is obtained with a simple global calibration algorithm as in Jay-Allemand et al (2020).…”

“…This variational calibration algorithm starts from a spatially uniform prior guess on the sought parameters (Jay-Allemand et al, 2020). This prior guess is obtained with a simple global calibration algorithm as in Jay-Allemand et al (2020). The minimization of the cost function is then done using the LBFGS-B (Limited memory Broyden-Fletcher-Goldfarb-Shanno Bound-constrained) descent algorithm (Zhu et al, 1994) making use of the gradient of the cost function that is obtained from the adjoint model thanks to the Tapenade automatic differentiation engine (Hascoet and Pascual, 2013).…”

“…discharge) it has been trained for, it can fail in reproducing meaningful system-internal dynamics and patterns (Hrachowitz and Clark, 2017), thus providing right answers for wrong reasons (Kirchner, 2006). Then arises the problem of better calibrating/validating hydrological models, and in particular distributed models, which makes it possible to take into account the spatial variabilities in the properties of the basins and atmospheric signals, to simulate spatialized hydrological quantities, but are confronted to the problem of equifinality and over-parameterizations (see discussion in Jay-Allemand et al (2020) in a flash flood context with spatially distributed calibration of SMASH model).…”

“…To address these questions a methodology is designed based on global parametric sensitivity analysis, calibration-validation, analysis of response surfaces, performances and simulated signatures. We consider two flash flood prone catchments in the South of France and three models of increasing complexity for hydrological modeling analysis: lumped conceptual model GR4H (Génie Rural) (Mathevet, 2005), spatially distributed conceptual models SMASH (Spatially-distributed Modeling and ASsimilation for Hydrology) (Jay-Allemand et al, 2020) with a Green and Ampt infiltration component, process oriented distributed model MARINE (Modélisation de l'Anticipation du Ruissellement et des Inondations pour des évéNements Extremes) (Roux et al, 2011). The parameters sensitivity and identifiability is investigated for each model followed by a split sample calibration-validation with global performance analysis in time.…”

“…-distributed Modeling and ASsimilation for Hydrology) is a computational software framework dedicated to spatially distributed continuous hydrological modeling including variational data assimilation(Jay-Allemand et al, 2020). We use the 3 components model (production, transfer, routing) from Jay-Allemand et al (2020).…”