Groundwater mounding due to recharge from ephemeral streams

Abstract

Recharge from ephemeral streams (called Masil in Farsi and Wadi in Arabic) is the main process of groundwater recharge in arid regions of the world where groundwater is the most important source of water supply. Despite advances in mathematical models of simulating infiltration from these streams, there is no versatile analytical model to simulate the groundwater mound due to recharge from an ephemeral stream. The goal of this paper is to present a semi-analytical model of the groundwater mound due to recharge from an ephemeral stream of an arbitrary geometric shape in aerial view. A three-dimensional anisotropic unconfined aquifer is considered, and a point recharge is imposed to the water table at first. The point- recharge solution is obtained via the Laplace and Fourier transforms. The image well method is employed to incorporate the lateral no-flow boundary that represents the margin of the unconfined aquifer. The point-recharge solution is then extended to simulate the groundwater mound due to recharge from the stream of an arbitrary shape by approximating the stream by multiple straight segments and integration of the point-recharge solution along the desired directions of those segments and the principle of superposition. A constant head variable discharge well is also placed near the stream to calculate the sustainable yield which is the average discharge of a constant-head well as compared to an equivalent constant-flux well. The results of this work are presented in the form of groundwater mound-time curve and groundwater mound spatial maps. The scaled sensitivity of groundwater head to recharge from the stream-time curves and depletion volume of the nearby well-time curve are also obtained. The influences of aquifer parameters on the groundwater mound and sustainable development of the aquifer near the ephemeral stream are analyzed. This study shows that: (1) Groundwater mound follows the shape of the stream and spreads spatially from the stream over time and the groundwater mound is higher inside the convex part of the stream due to interference from the neighboring stream segments; (2) The groundwater head collected from an observation well in a fine-grain aquifer is more valuable to estimate the recharge from the ephemeral stream than a coarse-grain aquifer; (3) The sustainable yield of a production well in an alluvial aquifer is maximum near the stream in a coarse-grain non-layered aquifer than the (coarse- or fine-grain) layered aquifer. The results of this work can be utilized as a valuable tool for managing the unconfined aquifers in the arid and semi-arid regions when ephemeral streams are the primary sources of recharge.