Probabilistic numerical assessment of seawater intrusion overshoot in heterogeneous coastal aquifers

Seawater intrusion is considered as one of the main hazards to coastal aquifers. In coastal aquifers, an overshoot occurs when the freshwater–saltwater interface exceeds the steady state position due to sea level rise (SLR). Hence, it is considered a more critical state than the terminal state. In the present study, overshoot is characterized in an unconfined, heterogeneous two-dimensional aquifer. For a more accurate evaluation, overshoot is investigated using three indicators, seawater toe, salinized volume, and effective dispersivity. In combination with the associated land surface inundation (LSI) impact, two types of SLR are assumed, gradual SLR (GSLR) and instantaneous SLR (ISLR). For addressing the heterogeneity of the aquifer, 50 sets of log-normally-distributed conductivity fields using a spherical correlation function are generated for each of the scenarios. Heterogeneity of the aquifer is modeled using the variance of conductivity field (σlnk2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma_{{{ \ln }k}}^{2}$$\end{document}) and the longitudinal correlation length (λx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda_{x}$$\end{document}). Three different values of 0.5, 1, and 2 are assumed for σlnk2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma_{{{ \ln }k}}^{2}$$\end{document} where two values of 20 m and 40 m are assigned to λx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda_{x}$$\end{document}. Using Monte-Carlo simulations, it is shown that (1) in both GSLR and ISLR scenarios, the overshoot is observed for both the seawater toe and the salinized volume where LSI is not assumed; (2) the SLR impact is overshadowed by the significance of conductivity field properties in heterogeneous scenarios; (3) σlnk2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma_{{{ \ln }k}}^{2}$$\end{document} plays a more discernible role in the overshoot characteristics compared to λx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda_{x}$$\end{document}; (4) a realistic assumption of GSLR results in lower overshoot occurrence probability. These observations are interpreted using the associated behavior of the flow field in the aquifer and the time needed for hydraulic pressures in this field to re-equilibrate after SLR.