A Linking Test to reduce the number of hydraulic parameters necessary to simulate groundwater recharge in unsaturated soils

In environmental studies, numerical simulation models are valuable tools for testing hypothesis about systems functioning and to perform sensitivity studies under scenarios of land use or climate changes. The simulations depend upon parameters which are not always measurable quantities and must be calibrated against observations, using for instance inverse modelling. Due to the scarcity of these observations, it has been found that parameter sets allowing a good matching between simulated and measured quantities are often non-unique, leading to the problem of equifinality. This can lead to non-physical values, erroneous fluxes and misleading sensitivity analysis. Therefore, a simple but robust inverse method coined the Linking Test is presented to determine if the parameters are linked. Linked parameters are then sub-divided into classes according to their impact on water fluxes. The Linking Test establishes the causes of non-uniqueness of parameter sets and the feasibility of the inverse modelling. The Linking Test is applied to a one-dimensional soil-vegetation water flow model to predict groundwater recharge from the Richards' equation. Under the tested climates and by assuming the vegetation parameters constant, the Linking Test showed that only 2 parameters out of 6 Mualem-van Genuchten parameters are required to determine an accurate recharge for soils not reaching saturation. For a reference soil, the Linking Test enables to determine, all the different combinations of the parameters that give similar recharge. The parameter sets are obtained by optimising the parameters against time series of soil moisture profiles. The Linking Equations established for the reference soil have important implications for sensitivity analysis, upscaling and infiltration tests.