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.

Bayesian Simultaneous Estimation of Unsaturated Flow and Solute Transport Parameters from a Laboratory Infiltration Experiment

“…Temporal discretization is performed with a variable order ODE (ordinary differential equation) solver via the method of lines (MOL), as in Fahs et al [33,34]. MOL has been successfully used for solving flow and/or solute transport in unsaturated porous media in many studies e.g., [10,12,21,35,36]. The ODE solver used in this work (DLSODIS: Double-precision Livermore Solver for ordinary differential equations-implicit form and sparse matrix) allows variable time-step and variable order integration with time error control [37,38].…”

Use of Global Sensitivity and Data-Worth Analysis for an Efficient Estimation of Soil Hydraulic Properties

“…Bayesian DWA, performed a priori, allows to quantify the improvement of the posterior uncertainty of the estimated parameters when adding a type of measurement. The results reveal that an accurate estimation of the soil properties can be obtained if the target parameter values are located in the regions of high influence in the parameter space.Water 2020, 12, 736 2 of 15 and evaporation experiments [13], unsaturated transport experiments [14][15][16][17], and hydrogeophysical experiments [18,19].Laboratory experiments are often time consuming, expensive, and tricky because of the risk of non-identifiability of the accepted parameters which depends on the measured data. Global sensitivity analysis (GSA) has been employed by Younes et al, [7] to help assess unsaturated soil hydraulic parameters.…”

“…Brunetti et al [21] used GSA to investigate the influence of soil hydraulic parameters on the behavior of a permeable pavement. Younes et al [19] used GSA to investigate the influence of hydraulic and geophysical parameters on the streaming potential signals. In van Griensven et al [22], GSA has been used to reduce the number of parameters and thus reduce over-parametrization of the numerical model.GSA allows to quantify the impact changes of parameters have on the model output.…”

“…The MCMC sampler randomly generates values of parameters from the joint probability density functions, using the Metropolis-Hastings algorithm [31,32]. The MCMC method is preferred over the gradient-based local optimization algorithms, which may fail to provide reliable confidence intervals [19,[33][34][35].…”

“…Water 2020, 12, 736 2 of 15 and evaporation experiments [13], unsaturated transport experiments [14][15][16][17], and hydrogeophysical experiments [18,19].…”