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. GSA results show that at short times, the saturated hydraulic conductivity (KS) and the voltage coupling coefficient at saturation (Csat) are the most influential parameters, whereas, at long times, the residual water content (σr), the Mualem-van Genuchten parameter (n) and the Archies’s 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, σr, and n) and geophysical (na and Csat) parameters 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.

Coupled inversion of hydraulic and self‐potential data from transient outflow experiments to estimate soil petrophysical properties

“…This is consistent with the results shown in Younes et al. (2018). The relatively high uncertainty of m is understandable because, in such an outflow experiment (Figure 2), the effective electrical conductivity of the soil is not directly measured.…”

“…Inserting Equations and into Equation yields the relationship between the streaming current density and Darcy velocity, which is expressed as (Linde et al., 2007 ; Revil et al., 2007; Younes et al., 2018) …”

“…In general conditions, numerical methods are required to solve Equations and to determine the spatial and temporal distributions of h and ϕ in the soil. In this study, we use the finite volume method (Caviedes‐Voullième et al., 2013; Eymard et al., 1999) to solve the governing equations, and many similar applications can be found in the literature (Manzini & Ferraris, 2004; Namin & Boroomand, 2012; Pei et al., 2006; Younes et al., 2018).…”

Groundwater Modelling Quality in the Cold Region of the Athabasca River Basin

“…Groundwater assessment is complex, involving identification of surface and groundwater quality and quantity drivers and the occurrence, interaction and determination of the probability of the occurrence of such problems [17,18]. In order to simulate both saturated and unsaturated water flow from the porous media, many widely used physical models of recharge equations has been used by [19,20]. This approach is could capture the groundwater dynamics [20] but lacks representation of land surface information like vegetation cover.…”

“…In order to simulate both saturated and unsaturated water flow from the porous media, many widely used physical models of recharge equations has been used by [19,20]. This approach is could capture the groundwater dynamics [20] but lacks representation of land surface information like vegetation cover. In order to address this limitation, scientists have developed various hydrological models to simulate interactions among water, soil, and vegetation.…”