Global sensitivity analysis of a hydrogeophysical model coupling groundwater infiltration process and Surface Nuclear Magnetic Resonance

1: Introduction Water resources in mountainous areas are of major importance for local ecosystems as well as for human activities. Therefore, it is crucial to monitor the availability of these resources and to be able to predict their evolution accurately in the context of climate change. Hydrologic modeling is a useful tool to achieve this goal. To do so, the models need to be properly parameterized. Geophysical sounding techniques are very useful tools to provide information for the model calibration process. This work focuses on the Surface Nuclear Magnetic Resonance (SNMR) sounding technique. This geophysical method is based on nuclear magnetic resonance and has the advantages of being non-destructive and directly sensitive to the groundwater content (Legchenko and Valla 2002). A time-lapse SNMR survey was conducted in the Strengbach headwater catchment in the Vosges Mountains (France) during the winter 2021 with the aim of following an infiltration event. Before using this data set for hydrologic model calibration, we used Global Sensitivity Analysis (GSA) tools in order to determine which hydrologic parameters were most influential on the geophysical sounding outputs. This first step is useful for estimating parameters' identifiability. 2: Study site The study site of interest for this time-lapse SNMR experiment is the Strengbach experimental catchment. It is a small forested water catchment located in the Vosges Mountains (Northeast of France, Fig. 1). This catchment hosts the Observatoire Hydro-Géochimique de l'Environnement (OHGE): a long-term observatory where meteorological, hydrological and geochemical data have been measured since 1986. The OHGE is part of the French critical zone observatories network OZCAR. The main purpose of this observatory is to study long-term modifications of ecosystems under natural and anthropogenic pressures (Pierret et al. 2018). 3: SNMR method and hydrogeophysical model SNMR is a geophysical sounding technique based on nuclear magnetic resonance: an energizing electric pulse is generated in a wire loop at the ground surface. This pulse induces an electromagnetic field that triggers the protons from the hydrogen atoms in the groundwater molecules. After the perturbing electromagnetic field is shut down, one can observe a relaxation electromagnetic field as the protons shift back to their equilibrium state. The initial amplitude of the voltage induced in this loop by this relaxation electromagnetic field is directly proportional to the groundwater content. The groundwater flow is modelled by numerically solving Richards' 1D equation with time-variable boundary conditions. The upper (flux) boundary condition is computed from raw precipitations measured at the summit meteorological station, taking into account the presence of a snow layer and the effects of interception and evapotranspiration. The lower (pressure) boundary condition is derived from the water table level measured at the piezometer close to the SNMR station. Given a set of hydrologic parameters, one can compute the water content distributions at the time steps corresponding to SNMR data acquisition and use these water content distributions to compute the SNMR signals, Fig. 2. 4: Global sensitivity analysis In order to quantify the sensitivity of the SNMR signals to variations in the hydrological parameters, we used a tool called variance-based sensitivity analysis. The principle of variance-based sensitivity analysis is to consider a model's input parameters as random variables following given distributions. Then, a computational framework developed by Sobol (Sobol′ 2001) allows for the quantification of the impact of each model input parameter variance on the model output variance through sensitivity indices called Sobol indices. We were able to distinguish the most influential parameters from those that have a negligible impact on the SNMR signal variance.