Modelling of hillslope storage under temporally varied rainfall recharge

Abstract

Water storage inside hillslopes is a crucial issue of environment and water resources. This study separately built a numerical model and an analytical model employing a hillslope-storage equation to simulate the water storage in a sloping aquifer response to recharge. The variable width of hillslope was hypothetically represented by an exponential function to categorize the hillslope into three types: uniform, convergent, and divergent. An integral transform technique was introduced to derive the analytical solution whereas a finite difference method was employed for the numerical modelling. As a result, under the same scenario a gap existed between the two solutions to distinct forms of the water storage equation, and the gap decreases with a falling recharge rate for convergent hillslopes. Moreover, all outflows gradually approached one value based on different hillslopes under the same accumulative recharge amount for six typical rainfall recharge patterns. Particularly, while the recharge stops, the outflow decreases and then mildly rises for a long time for convergent hillslope because of the slow water release near the upstream boundary where the storage water is relatively abundant due to the widest width.