Hillslope subsurface flow similarity: Real-world tests of the hillslope Péclet number

Similarity analysis offers the ability to model hydrological response using quantifiable landscape descriptors. It is possible to develop similarity indices based on analytical solutions to the governing dynamic equations (Brutsaert, 2005). Berne et al. (2005) provide derivation of such a similarity index (the hillslope Péclet number) of subsurface flow and saturation for hillslopes with exponential width functions. They showed that the hillslope Péclet number depends only on geometric properties of the hillslope. Their work was validated using laboratory experiments conducted on constructed hillslopes with homogeneous soil structure and varying bedrock slope angle. This study applies the similarity analysis of Berne et al. (2005) to two data sets: (1) the trench hillslope study at the Maimai research catchment conducted by Woods and Rowe (1996) and (2) the isolated hillslope study near Troy, Idaho, United States, conducted by Brooks et al. (2004). The Maimai trench study was selected because it provides subsurface flow data from hillslopes with different planform geometries. The Troy hillslope study was selected because the experimental results of Brooks et al. (2004) provide an estimate of hydraulic conductivity consistent with the support scale of the hillslope. We estimated the hillslope Péclet number of the hillslopes on the basis of elevation data and reported values of average soil depth. This hillslope Péclet number quantifies the geomorphological control on how water moves through these hillslopes and creates a basis for comparison independent of hydraulic properties. We then estimated the first and second moments of the characteristic subsurface response function of each hillslope on the basis of subsurface flow data. To compare the empirical and theoretical moments, the hydraulic properties (saturated hydraulic conductivity and drainable porosity) of the hillslopes were related using a base flow recession analysis. Then we were able to derive the dimensionless moments of the hillslopes' observed characteristic response function using hydraulic conductivities reported in the literature. The agreement between the observed and theoretical moments shows the promise of implementing the hillslope Péclet number as a similarity parameter to describe first-order hydrological response in humid environments.