Sensitivity and identifiability of hydraulic and geophysical parameters from streaming potential signals in unsaturated porous media

Abstract

Abstract. Fluid flow in a charged porous medium generates electric potentials called streaming potential (SP). The SP signal is related to both hydraulic and electrical properties of the soil. In this work, global sensitivity analysis (GSA) and parameter estimation procedures are performed to assess the influence of hydraulic and geophysical parameters on the SP signals and to investigate the identifiability of these parameters from SP measurements. Both procedures are applied to a synthetic column experiment involving a falling head infiltration phase followed by a drainage phase. GSA is used through variance-based sensitivity indices, calculated using sparse polynomial chaos expansion (PCE). To allow high PCE orders, we use an efficient sparse PCE algorithm which selects the best sparse PCE from a given data set using the Kashyap information criterion (KIC). Parameter identifiability is performed using two approaches: the Bayesian approach based on the Markov chain Monte Carlo (MCMC) method and the first-order approximation (FOA) approach based on the Levenberg–Marquardt algorithm. The comparison between both approaches allows us to check whether FOA can provide a reliable estimation of parameters and associated uncertainties for the highly nonlinear hydrogeophysical problem investigated. GSA results show that in short time periods, the saturated hydraulic conductivity (Ks) and the voltage coupling coefficient at saturation (Csat) are the most influential parameters, whereas in long time periods, the residual water content (θs), the Mualem–van Genuchten parameter (n) and the Archie saturation exponent (na) become influential, with strong interactions between them. The Mualem–van Genuchten parameter (α) has a very weak influence on the SP signals during the whole experiment. Results of parameter estimation show that although the studied problem is highly nonlinear, when several SP data collected at different altitudes inside the column are used to calibrate the model, all hydraulic (Ks,θs,α,n) and geophysical parameters (na,Csat) can be reasonably estimated from the SP measurements. Further, in this case, the FOA approach provides accurate estimations of both mean parameter values and uncertainty regions. Conversely, when the number of SP measurements used for the calibration is strongly reduced, the FOA approach yields accurate mean parameter values (in agreement with MCMC results) but inaccurate and even unphysical confidence intervals for parameters with large uncertainty regions.