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

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.