Mathematical Modeling of Subsurface Aquifer Dynamics: A Case Study
Authors
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Chloe Baker
Northern Institute of Technology
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Fiona Richardson
Starlight Academy
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Greg Cox
Global Dynamics Corp.
https://orcid.org/0009-0000-0000-0000
Abstract
The sustainable management of groundwater resources is a critical challenge for arid and semi-arid regions worldwide. This study presents a comprehensive mathematical model to simulate subsurface aquifer dynamics. We employ a finite element method (FEM) to solve the governing partial differential equations (PDEs) of porous media flow, incorporating factors such as hydraulic conductivity, anisotropic soil properties, and variable recharge rates from precipitation and irrigation. By assimilating satellite-derived data (e.g., GRACE) and in-situ well-level measurements, our model provides a high-resolution spatiotemporal forecast of aquifer depletion and land subsidence. The results offer a robust tool for policymakers to evaluate the long-term impacts of different water management strategies, such as managed aquifer recharge (MAR). This research underscores the essential role of applied mathematics in quantifying and preserving one of Earth's most vital, yet invisible, resources.
Copyright (c) 2026 Chloe Baker, Fiona Richardson, Greg Cox (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.