Abstract

This study discussed water storage in aquifers of hillslopes under temporally varied rainfall recharge by employing a hillslope-storage equation to simulate groundwater flow. The hillslope width was assumed to vary exponentially to denote the following complex hillslope types: uniform, convergent, and divergent. Both analytical and numerical solutions were acquired for the storage equation with a recharge source. The analytical solution was obtained using an integral transform technique. The numerical solution was obtained using a finite difference method in which the upwind scheme was used for space derivatives and the third-order Runge–Kutta scheme was used for time discretization. The results revealed that hillslope type significantly influences the drains of hillslope storage. Drainage was the fastest for divergent hillslopes and the slowest for convergent hillslopes. The results obtained from analytical solutions require the tuning of a fitting parameter to better describe the groundwater flow. However, a gap existed between the analytical and numerical solutions under the same scenario owing to the different versions of the hillslope-storage equation. The study findings implied that numerical solutions are superior to analytical solutions for the nonlinear hillslope-storage equation, whereas the analytical solutions are better for the linearized hillslope-storage equation. The findings thus can benefit research on and have application in soil and water conservation.

Highlights

  • Mountains in Taiwan are considerably high and steep, and the flow velocity of surface water and subsurface water is so high that it can cause severe soil erosion on hillslopes

  • Mosley (1979) measured overland flow and subsurface flow in a forest watershed and found that the flow discharge in a river is greatly influenced by overland flow and subsurface flow and that the subsurface flow is considerably decreased on mild slopes

  • Both figures reveal that our results using the generalized integral transform technique agree well with the Laplace transform method by Troch et al (2004), validating our analytical solutions

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Summary

Introduction

Mountains in Taiwan are considerably high and steep, and the flow velocity of surface water and subsurface water is so high that it can cause severe soil erosion on hillslopes. Brutsaert (1994) linearized the Boussinesq equation and analytically solved it to describe groundwater level This solution provides a crucial framework to study slope features and their hydrological response. On the basis of Evans (1979), Troch et al (2002) presented nine hillslopes to represent the conventional hillslope types in hydrology and used the method of characteristics to analytically solve the hillslope-storage kinematic wave equation for subsurface flow. Employed an exponential form to describe the variation of hillslope width and substituted it into the linearized Boussinesq equation; they analytically solved the equation by using the Laplace transform and compared the results with numerical solutions for the nonlinear hill-storage equation with uniform rainfall recharge. The aquifer was assumed to be saturated, homogeneous, and isotropic, with a constant thickness and variable width

Governing equation
Boundary conditions
Analytical solution
Numerical method
Verification of the analytical solution
Verification of the numerical solution
Comparison between analytical solutions and numerical solutions
Variation of the remaining hill storage
Temporally varied recharge rates effect
Concluding remarks
Full Text
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