Similarity analysis of subsurface flow response of hillslopes with complex geometry

The matter of the efficient and parsimonious parameterization of hillslope subsurface flow remains an important issue in catchment hydrological studies (Brutsaert, 1995). Insights into the influence of the shape and hydraulic characteristics of hillslopes is required to further our understanding and our ability to model catchment hydrological processes. Recently, Troch et al. (2003) introduced the hillslope-storage Boussinesq (HSB) equation to describe subsurface flow and saturation along geometrically complex hillslopes. The HSB equation can be linearized and further reduced to an advection-diffusion equation for subsurface flow in hillslopes with constant bedrock slopes and exponential width functions. This paper presents a dimensional analysis of the latter equation in order to study the moments of the characteristic response function (CRF), corresponding to the free drainage of this type of hillslope. These moments, in a dimensionless form, can be expressed as functions of a similarity parameter, hereafter called the hillslope Peclet number, and a group of dimensionless numbers accounting for the effects of the boundary and initial conditions. The analytical expressions for the first four central CRF moments are derived for two types of initial conditions. The analysis of their respective influences shows that the hillslope Peclet number is an efficient similarity parameter to describe the hillslope subsurface flow response. Moreover, comparison between the CRF moments predicted by means of our similarity analysis and empirical moments derived from outflow measurements for different types of laboratory hillslopes shows good agreement.