A comparison of seven methods for the inverse modelling of groundwater flow. Application to the characterisation of well catchments

Inverse modelling is a key step in groundwater-related hydrological studies. Several inversion techniques were developed during the last decades, but hardly any comparison between them was presented. We compare seven modern inverse methods for groundwater flow: the Regularised Pilot Points Method (both the estimation, RPPM-CE, and the Monte Carlo (MC) simulation variants, RPPM-CS), the MC variant of the Representer Method (RM), the Sequential Self-Calibration Method (SSC), the Moment Equations Method (MEM), the Zonation Method (ZM) and a non-iterative Semi-Analytical Method (SAM). These methods are applied to a two-dimensional synthetic example, depicting steady-state groundwater flow around a pumping well. Their relative performance is assessed in terms of their ability to characterise the logtransmissivity and hydraulic head fields and to predict the extent of the well catchment, both for a mildly and a strongly heterogeneous transmissivity field. The main conclusions drawn from the comparison are: (1) MC-based methods (RPPM-CS, SSC and RM) yield very similar results, regardless the degree of heterogeneity and despite they use different parameterisation schemes and objective functions; (2) statistical moments of the target quantities provided by MEM and RPPM-CE are similar to those of MC-based methods; (3) ZM and SAM are negatively affected by strong heterogeneity; and (4) in general, observed differences between the performances of all methods are not very large. MC-based inverse methods need considerably more CPU time than the other tested approaches. An advantage of MC-based methods is that they allow computing the posterior probability distribution of the target quantities, which can be directly fed to probabilistic risk-assessment procedures.