Global sensitivity analysis of Magnetic Resonance Sounding data to hydraulic parameters of a hydrogeological model applied at a catchment scale
Résumé
Combining hydrogeological models with hydrological and geophysical measurements helps constraining the geometry of aquifers and estimating the hydraulic parameters. We propose to explore here how the parameters of a hydrological model, coupling surface and underground water flows can impact Magnetic Resonance Sounding (MRS) data. MRS is a geophysical method that is directly sensitive to the water content below the recording station in both the saturated and non-saturated media. Thus, MRS data complement piezometric datasets that render the temporal variations of the water table position but do not offer any insight on the water content quantity in the porous media. The hydrological model is applied to the Strengbach headwater catchment, with meteorological forcing measured on the field. The hydrological model provides daily maps of the underground water content as output. From such maps, MRS data can directly be estimated at specific stations distributed over the catchment using petrophysical laws to evaluate the relaxation time. The hydraulic parameters of the model such as the aquifer
thickness, porosity or hydraulic conductivity at saturation (Ks) can then be explored to infer how the MRS data are sensitive to those parameters. The aquifer is divided in vertical layers: the soil and the saprolite, which thickness variation over the catchment is defined by generating geostatistical fields from the analysis of seismic refraction data. The thickness of each element of the hydrological model follows roughly a normal distribution. The porosity and Ks are considered as homogeneous over the catchment for each layer. The porosity parameter follows a uniform distribution, while Ks is distributed with a log-uniform law. The underground medium is defined with a porosity and Ks that both increase from depth to surface in order to mimic the scheme of the underground critical zone alteration degree. A global sensitivity analysis (GSA) approach is used in order to distinguish the respective contribution of the different parameters on the MRS signal variability. The objective is also to identify the temporal fluctuation of the MRS signal sensitivity to the different hydraulic parameters. Indeed, some parameters can be
more or less influent on the MRS signal depending on the meteorological forcing. In that goal, we use polynomial chaos expansion (PCE) as surrogate models trained from the analysis of MRS signal estimated after running the hydrological model with several hundreds of parameters sets. The contribution of each parameter variability on the MRS signal variance is then quantified directly by Sobol indices from the PCE coefficients. PCE allows also to quantify the variance related to the interactions between parameters. We highlight here the complementarity between MRS and piezometric data by applying the GSA on both data types. Results show that in the context of a small headwater catchment with a small inertia, MRS data are particularly sensitive to the medium porosity and Ks, while piezometric data are mainly controlled by Ks.