General Objective

The general objective of my PhD is to propose a methodology for estimating the parameters of a distributed spatio-temporal model for water and pesticide transfers (the PESHMELBA model) in the presence of external uncertainties (e.g., rainfall, evapotranspiration, pesticide application dates, etc.).

In Figure 1, the goal is to find x^∗ that minimizes the discrepancy between the simulation M and the observation yobs​, represented by the cost function f(x,Z(ω)). The cost function also depends on zzz (external forcing, such as rainfall), which leads to different results x^∗₁ ≠ x^∗₂​ depending on the realization of the external uncertainty (here z_1​ and z_2​). The aim of robust calibration is to reduce the dependency of the minimizer on the realization of Z(ω).

Context

Issues related to the use of pesticides represent a major challenge for sustainable and high-quality agriculture. It is therefore essential to have knowledge and tools to quantify pesticide transfers to surface waters and their environmental impact, in order to limit them. In this context, the PESHMELBA model (PESticides et Hydrologie: Modélisation à l’EcheLle du Bassin versant, Rouzies et al., 2019) proposes an original combination of conceptual modelling and physical laws to represent dominant transfers within a small agricultural watershed.
Considering that landscape elements (fields, hedgerows, grass strips, rivers, ditches, etc.) and their connections greatly influence pesticide fate, this tool requires specification of a large number of parameters (soil characteristics, vegetation, applied molecules) and dynamic inputs (climate, agricultural practices, etc.) that are sometimes difficult to measure or poorly known. However, in order to eventually use PESHMELBA as a decision-support tool for managing agricultural watersheds, it is necessary to reduce and/or quantify the uncertainties associated with the variables it simulates.
Inputs of a hydrological model can be classified into two types:

    - (i) Parameters to be estimated (x): their values can be adjusted to improve agreement between model outputs and observations (e.g., hydrodynamic properties).
   - (ii) External forcings (z): terms imposed on the model, such as rainfall, pesticide application dates, boundary conditions, discretization, etc.forçages externes (z) : termes que l’on impose au modèle, tels que les précipitations, lesdates d’application de pesticides, les conditions aux limites, la discrétisation, etc.

Model outputs suffer from uncertainties in both types of inputs, but their nature differs: the uncertainty in xxx arises from poor specification of parameters and can be reduced by acquiring more observations (calibration). Uncertainty in zzz, however, cannot be reduced during calibration since it is not explicitly part of it (it is "suffered").
Ignoring the uncertainties in z means that the estimated parameters xxx are only optimal locally for the given values of z (see Figure 1). Therefore, the calibrated model may not perform well when different values are assigned to z, such as in another time period or under future scenarios.

Proposed Approach

Robust control approaches aim to find a set of parameters that satisfy certain robustness criteria, such as minimizing the variance or expected value of a cost function, or any other robustness metric, while accounting for external uncertainties. This approach is computationally demanding, and applying it to PESHMELBA, which couples numerous processes and is relatively costly, is a real challenge. It requires the use of design of experiments to reduce the number of simulations and reduced-order models (metamodels) to lower computational costs.

Progress

A first step in calibration is sensitivity analysis, aiming to identify the most influential parameters on the output. In Radišić et al. (2024), we ranked the influence of input parameters using Sobol indices in a classical setting and then showed how different forcings—such as rainfall events or pesticide application dates—impacted the sensitivity analysis results. This second study highlighted the need to account for uncertainties in these forcings (Radišić et al., 2024).

Finally, a robust calibration of the PESHMELBA model has been implemented. The computational cost is reduced through stochastic metamodels (Lüthen et al., 2023). This approach is first applied to soil moisture profiles at the plot scale, then extended to pesticide transfers in a small virtual watershed representative of part of the Morcille catchment. Figure 2 illustrates the benefit of robust calibration, showing simulated concentrations that are closer to observations than those obtained through a classical approach.

In Figure 2, colors correspond to different calibrations. The sets of the same color represent the propagation of uncertainty on pesticide application dates. The black line corresponds to simulations with the actual (but unknown) parameter values.

Cite the thesis

Katarina Radišić. Consideration of external uncertainties in the estimation of parameters of a water and pesticide transfer model at the catchment scale. Mathematics [math]. Université Grenoble Alpes, 2025. English. ⟨NNT : ⟩. ⟨tel-05178484⟩

Access manuscript on HAL thèses

Funding

• Salary: funded 100% by INRAE (MathNum Department, under the INRAE–Inria co-supervised PhD program)
  Working environment: ECOPHYTO SPIRIT project and LEFE-MANU MARQUISE project

Références

• N. Lüthen, S. Marelli, and B. Sudret. A spectral surrogate model for stochastic simulators computed from trajectory samples. Computer Methods in Applied Mechanics and Engineering, 406:115875, Mar. 2023. ISSN 00457825. doi: 10.1016/j.cma.2022.115875. URL https://linkinghub.elsevier.com/retrieve/pii/S0045782522008313.
• K. Radišić, C. Lauvernet, and A. Vidard. Impact of input forcings variability on the global sensitivity analysis of a hydrological model. preprint, under review in Environmental Software Environment, Dec. 2024. URL https://hal.inrae.fr/hal-04849856.
• K. Radišić, E. Rouzies, C. Lauvernet, and A. Vidard. Global sensitivity analysis of the dynamics of a distributed hydrological model at the catchment scale. Socio-Environmental Systems Modelling, 5:18570, Jan. 2024. ISSN 2663-3027. doi: 10.18174/sesmo.18570. URL https://sesmo.org/article/view/18570.
• E. Rouzies, C. Lauvernet, C. Barachet, T. Morel, F. Branger, I. Braud, and N. Carluer. From agricultural catchment to management scenarios: A modular tool to assess effects of landscape features on water and pesticide behavior. Science of The Total Environment, 671:1144–1160, 2019. ISSN 0048-9697. doi: https://doi.org/10.1016/j.scitotenv.2019.03.060.