Analytical Analysis of Groundwater Responses to Estuarine and Oceanic Water Stage Variations Using Superposition Principle

Abstract

Aquifers at the coasts are influenced by both oceanic and estuarine water stage variations, resulting in complex behavior of groundwater level fluctuation in coastal aquifers. The two-dimensional linear Boussinesq equation is invariably employed to understand the tidal dynamics of coastal aquifers. Previous studies emphasized L-shaped aquifer responses to sinusoidal tidal waves in an estuary and ocean, ignoring the groundwater-level fluctuation induced by arbitrary water stages variations in non-L-shaped aquifers. To resolve this problem, a universal analytical solution is derived according to the superposition principle. Groundwater level fluctuations induced by oceanic and estuarine water stage variations are translated into the sum of noninteracting cross shore and alongshore tidal wave propagations in the aquifers. Then the developed solution was applied to predict groundwater levels in an L-shaped aquifer in Kumamoto, Japan. The simulated results fitted favorably with the observed data. The developed solution was also applicable to simulate groundwater responses to anomalous oceanic and estuarine water stage variations. The dynamic change of groundwater level in both L-shaped and non-L-shaped aquifers during exponential oceanic storms and step rising estuarine water stage variations was evaluated using this approach. The proposed solution performs well in both L-shaped and non-L-shaped cases. The developed solution provides an effective method to describe the non-L-shaped aquifers responses to arbitrary oceanic and estuarine water stage variations.