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Three-dimensional semi-analytical solution of variably saturated flow due to recharge from ephemeral streams in arid regions

Year: 2026
Type: article
Abstract: Study Region Arid regions of Iran and other Middle East countries. Study Focus Ephemeral stream infiltration constitutes the principal process of aquifer recharge in arid regions, particularly in the Middle East. Despite recent advances in mathematical modeling, no analytical solutions exist for three-dimensional saturated-unsaturated flow in unconfined aquifers recharged by ephemeral streams of arbitrary geometry. This paper presents a new semi-analytical solution that couples the Richards equation with the saturated groundwater flow equation, considering the continuity of pressure and vertical flux at the water table. The solution for a point-source recharge was derived using Laplace and Fourier transforms, and then stream recharge was simulated by integrating the solution along the stream path and combining the results via the principle of superposition. New Hydrological Insights The proposed model showed that the thickness and constitutive exponent of the unsaturated zone significantly control the spatiotemporal evolution of groundwater recharge mounds. Increasing the thickness of the unsaturated zone reduces groundwater mounding and delays the mound peak, particularly when saturated vertical hydraulic conductivity is low. The complex effects of variations in the constitutive exponent of the unsaturated zone, along with the influence of saturated zone parameters on the development of groundwater recharge mounds, were also examined. Validation of the result against a previous solution confirmed the accuracy of the proposed approach. This research offers a robust tool for the sustainable management of groundwater resources in arid and semi-arid regions.
DOI: 10.1016/j.ejrh.2026.104036
Language: English
Open Access status: gold
Estimated APC paid: $2,600
OpenAlex ID: W7214948314
FWCI:
Cites: 45
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Related to: 10