Extension of Boussinesq equation to investigate water storage in complex hillslopes

Hillslopes can be considered as the basic landscape elements of many catchments. A proper understanding of the interaction and feelbacks between hillslope forms and the processes responsible for hillslope hydrology are of great importance for catchment scale land management. The hydrologic response of a hillslope to rainfall involves a complex, transient saturated-unsaturated interaction that usually leads to a water table rise. Since the dynamic response of hillslopes is strongly dependent on plan shape, slop curvature and slope angle; a three dimensional model of dynamic hillslope hydrology is needed for studying the hydrological processes of complex hillslopes. The mathematical description of these flow processes results in the formulation of the 3D Richards equation, which is difficult to solve numerically. To overcome difficulties associated with three-dimensional models, low-dimensional hillslope models have been developed by Troch and co-workers. These models are able to treat geometric complexity in a simple way, resulting in a significant reduction in model complexity. This reduction of the dimensionality is achieved by introducing the subsurface storage capacity function. This defines the thickness of the pore space along the hillslope and accounts for plan shape, through the width function, and bedrock profile curvature, through the soil depth function. Because of the strong relation between hydrological processes, hillslope shape and slope curvature, efficient tools are needed to investigate the effect of complex topography on slope hydrology at the landscape scale. Existing tools either neglect topographic curvature or model it in a very complex computationally inefficient manner. The main purpose of this study is therefore to present a dynamic low dimensional but physically-based model that includes both hydrological processes (saturated and unsaturated zone storage) for hillslopes with different topographic characteristics. To develop the HSB Equation and keep the model low-dimensional, the average soil moisture in the unsaturated zone has been calculated according to Campbell’s method, using Darcy’s law with the unit-gradient assumption. Hence, in this paper we present a methodology to investigate the effect of rainfall and water table variations on hydrological processes (subsurface flow) in complex hillslopes. Our results show that after a certain period of rainfall, the convergent hillslopes with concave and straight profiles have higher storage and drain slower than others.

کلیدواژه ها:

Boussinesq equation ، water resources ، storage ، complex hillslope