Surrogate-based sensitivity analysis and calibration for the hydro-sedimentary modeling of an elementary agricultural catchment

Landscape evolution models typically solve three main processes: the conversion of rainfall to runoff, flow routing, erosion, and sediment transport, for a given precipitation time series, and a topographic surface. They can help to predict watershed dynamics in response to potential extreme events and anticipate potential damages. To that purpose, models must accurately represent the studied catchment and reproduce available observations, such as water discharge and sediment flux. This requires adjusting the model parameters representing the catchment characteristics, which can be challenging due to long simulation times, many uncertain characteristics and modeling errors.  

This study focuses on modeling the Pommeroye catchment — a 0.54 km² elementary watershed in the Canche River basin in northern France. The objective is to identify models able to reproduce the twenty extreme events identified in the data collected during the 2016-2017 hydrological year for discharge and suspended sediment at the catchment outlet. Topography is derived from a high-resolution (1m) LiDAR-derived digital elevation model. CAESAR-Lisflood is considered for dynamic simulation. The rainfall-to-runoff is modeled with a local storage term that has an exponential recession and is controlled by the water storage depth parameter “m”. From the generated surface runoff, the model continuously computes the flux of water and sediment across cells. Flow routing is solved via a reduced solution to the shallow water equations, where the friction term is computed via the Manning-Strickler model and hence controlled by the Manning’s roughness. Sediment transport follows the Wilcock and Crowe parameterization, with multiple controlling parameters. For the Pommeroye catchment, model run times are long, e.g. up to 24 hours on 36 CPUs, limiting the number of simulations that can be performed in practice. To overcome this, we developed a workflow combining machine learning-based surrogate models with sensitivity analysis and calibration. Gaussian processes are considered to mimic CAESAR-Lisflood from a limited training set and provide fast estimations of the simulator outputs for any input parameter values within given ranges. Instead of CAESAR-Lisflood, these predictions are used for variance-based sensitivity analysis (Sobol’ indices) and optimization (Efficient Global Optimization), drastically reducing the computation times.

A first sensitivity analysis highlighted that the m parameter mainly affects water discharge. However, no single m parameter value enables the model to correctly reproduce all data: the best fit is obtained with increasing values throughout the year, starting with low values in winter. In a second study, we thus added flexibility with time-dependent monthly values for m, leading to an improved match with water discharge data. Finally, the EGO approach - with fixed monthly m values - was considered to better reproduce suspended sediment data, identifying settling velocity and Manning’s roughness as key factors.