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

• Published in: Advances in water resources Vol. 32; no. 6; pp. 851 - 872
• Main Authors: Hendricks Franssen, H.J., Alcolea, A., Riva, M., Bakr, M., van der Wiel, N., Stauffer, F., Guadagnini, A.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.06.2009; Elsevier
• Subjects: Aquifer characterisation; aquifers; Comparison study; Conditional estimation; Earth sciences; Earth, ocean, space; Exact sciences and technology; flow to wells; groundwater flow; Hydrogeology; hydrologic models; Hydrology. Hydrogeology; inverse modeling; Inverse modelling; mathematical models; mathematics and statistics; simulation models; stochastic processes; Stochastic simulations; Well catchments; wells; Conditional estimation; Well catchments; Aquifer characterisation; Stochastic simulations; Inverse modelling; Comparison study; risk assessment; Monte Carlo analysis; ground water; inverse modeling; digital simulation; drainage basins; hydraulics; water resources; modern; aquifers; stochastic models; zoning; calibration; performances; flow; models; inverse problem; probability; hydrodynamics; heterogeneity; pumping; transmissivity
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2009.02.011

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 log-transmissivity 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.