How is a global sensitivity analysis of a catchment-scale, distributed pesticide transfer model performed? Application to the PESHMELBA model

Abstract

Abstract. Pesticide transfers in agricultural catchments are responsible for diffuse but major risks to water quality. Spatialized pesticide transfer models are useful tools to assess the impact of the structure of the landscape on water quality. Before considering using these tools in operational contexts, quantifying their uncertainties is a preliminary necessary step. In this study, we explored how global sensitivity analysis could be applied to the recent PESHMELBA pesticide transfer model to quantify uncertainties on transfer simulations. We set up a virtual catchment based on a real one, and we compared different approaches for sensitivity analysis that could handle the specificities of the model: a high number of input parameters and a limited size of sample due to computational cost and spatialized output. After a preliminary screening step, we calculated Sobol' indices obtained from polynomial chaos expansion, Hilbert–Schmidt independence criterion (HSIC) dependence measures and feature importance measures obtained from random forest surrogate model. Results from the different methods were compared regarding both the information they provide and their computational cost. Sensitivity indices were first computed for each landscape element (site sensitivity indices). Second, we proposed to aggregate them at the hillslope and the catchment scale in order to get a summary of the model sensitivity and a valuable insight into the model hydrodynamic behaviour. Conclusions about the advantages and disadvantages of each method may help modellers to conduct global sensitivity analysis on other such modular and distributed hydrological models as there has been a growing interest in these approaches in recent years.

Global sensitivity analysis of the dynamics of a distributed hydrological model at the catchment scale

“…In the studied case, the virtual catchment is divided in 𝑀 = 14 plots, each belonging to one of three soil units (SU): SU1 (sandy soil), SU2 (sandy soil on clay) or SU3 (heterogeneous sandy soils), illustrated in Figure 1. The virtual catchment is presented with more details in Rouzies et al (2023). PESHMELBA is a three-dimensional model, where the heterogeneity of the soil layers along the vertical axis is also taken into account.…”

“…The marginal probability distributions of the 𝐾 = 52 input parameters represent the variability of the parameters across the Morcille catchment and are determined from previous studies and available data on the soil, vegetation and pesticide properties of the Morcille catchment, (Frésard, 2010;Peyrard et al, 2016). The distributions are listed in Table S1 in Supplementary Material and justified in details in Rouzies et al (2023). Furthermore, the hydrological input parameters are assumed independent (Song et al, 2015).…”

“…For instance, a sensitivity analysis on the spatialized maximum water depth of a coastal flooding risk model in Perrin et al (2021); both a temporal and a spatial sensitivity analysis of a model describing nitrogen transfers in Ferrer Savall et al (2019); and a comparison between various sensitivity indices on a spatio-temporal radionuclide atmospheric dispersion model in De Lozzo & Marrel (2017). A sensitivity analysis was also performed for spatially distributed PESHMELBA outputs in Rouzies et al (2023) by calculating site specific sensitivity indices, then aggregating them to blocks via the definition provided in Gamboa et al (2014), but without studying the sensitivity of the dynamics of PESHMELBA.…”

“…Furthermore, once the metamodel is built, the sensitivity index calculation is analytical (Sudret, 2008). Applications of PCE for Sobol' index calculation can be found in Fajraoui et al (2011) or in Rouzies et al (2023). For multidimensional outputs, principal component analysis (PCA) can be used prior to PCE to reduce the dimensionality, as done for an urban drainage model in Nagel et al (2020).…”

“…We are particularly interested in detecting different behaviors in the model dynamics, and analyzing which inputs drive their occurrence. Another objective is to deploy this type of method for spatio-temporal outputs, such as those of distributed hydrological models (whether physically-based or semi-conceptual), as this has never been done on spatio-temporal variables in hydrology, but essentially on integrated variables, mostly cumulative outputs or quality criteria such as Nash-Sutcliffe model efficiency coefficient (Saltelli et al, 2019;Rouzies et al, 2023). The outputs considered are the surface moisture outputs simulated over a two-month period on a catchment of assorted mesh elements (plots).…”