Probabilistic assessment of seawater intrusion under multiple sources of uncertainty

• We investigate the impact of uncertain system properties on sea water intrusion.
• We employ and test generalized Polynomial Chaos Expansion techniques (gPCE).
• gPCE allows to compute joint, marginal and conditional pdf of target descriptors.
• The gravity number greatly influences the median toe penetration.
• Transverse Péclet number chiefly affects the variance of the width of the mixing zone.

Coastal aquifers are affected by seawater intrusion (SWI) on a worldwide scale. The Henry’s problem has been often used as a benchmark to analyze this phenomenon. Here, we investigate the way an incomplete knowledge of the system properties impacts the assessment of global quantities (GQs) describing key characteristics of the saltwater wedge in the dispersive Henry’s problem. We recast the problem in dimensionless form and consider four dimensionless quantities characterizing the SWI process, i.e., the gravity number, the permeability anisotropy ratio, and the transverse and longitudinal Péclet numbers. These quantities are affected by uncertainty due to the lack of exhaustive characterization of the subsurface. We rely on the Sobol indices to quantify the relative contribution of each of these uncertain terms to the total variance of each of the global descriptors considered. Such indices are evaluated upon representing the target GQs through a generalized Polynomial Chaos Expansion (gPCE) approximation. The latter also serves as a surrogate model of the global system behavior. It allows (a) computing and analyzing the joint and marginal probability density function (pdf) of each GQ in a Monte Carlo framework at an affordable computational cost, and (b) exploring the way the uncertainty associated with the prediction of these global descriptors can be reduced by conditioning of the joint pdf on available information. Corresponding analytical expressions of the marginal pdfs of the variables of interest are derived and analyzed.