Variational data assimilation to improve subsurface drainage model parameters

Abstract

• Identification of the most influential model parameters using the global adjoint SA. • Variational data assimilation significantly reduces the water volume discrepancy. • The gradient-based stochastic procedure performs without the need for the prior. • A new hybrid BV method offers an automatic tool to select a robust parameter set. Variational data assimilation (VDA) has been implemented to enhance the estimation of the unknown input parameters of a new agricultural subsurface drainage model (SIDRA-RU) through assimilating drainage discharge observations. The adjoint model of SIDRA-RU has been successfully generated through the generic automatic differentiation tool (TAPENADE). First, the adjoint model is used to explore the local and global adjoint sensitivities of the valuable function defined over the drainage discharge simulations with respect to model input parameters. Next, the most influential parameters are estimated by applying the Variational DA approach. The performed sensitivity analysis shows that the most influential parameters on drainage discharge are those controlling the dynamics of the water table; the second most influential parameters manage the drainflow start of each drainage season. Compared to an alternative gradient-free calibration performance, the estimation of these governing parameters by the variational method improves the overall quality of the drainage discharge prediction, in particular in terms of the cumulative water volume. Improved parameters generate less than 5 mm (1%) of the discrepancy between simulated and observed water volumes, based on the five years of daily discharge observations on the Chantemerle agricultural parcels (36 ha). Preliminary numerical tests have shown the potential presence of multiple local minima, thus pointing out the equifinality issues. The latter can be highlighted by the self-compensation of both the physical soil parameters and the main conceptual parameters. For improving the robustness of the parameter estimates, a novel hybrid “Bayesian Variational” method is suggested. This method is based on the Bayesian averaging of an ensemble of optimal estimates.