Development and application of a catchment similarity index for subsurface flow

In this study, we develop a similarity parameter to describe shallow subsurface hydrological response of small catchments on the basis of the hillslope-Peclet number. This new similarity parameter, named the catchment-Peclet (caPe) number, provides a theoretical framework to compare the relative hydrologic response derived from shallow subsurface flow of small catchments on the basis of geomorphic properties. Using 400,000 synthetically derived catchments to model catchment-scale characteristic response functions (CRFs), we see good agreement between the synthetic and theoretical relationships relating the caPe number to the first two dimensionless moments of the CRF of small catchments. Working with real-world data, however, requires the estimation of hydrologic parameters and delineation of hillslopes to apply the caPe number. Allowing for uncertainty in the estimation of hydrologic parameters and in the definition of the extent of the channel network, the caPe number is able to recreate the observed moments of an approximate catchment-scale CRF for four small catchments ranging in size from 0.025 to 880 ha in two distinct climatic and geologic settings. By using physics to underpin the link between landscape and hydrological response, the caPe number creates a functional relationship between hydraulic theory and a catchment's pedogeomorphological structure. While this study is limited to small headwater catchments, it lays the groundwork for a catchment-scale similarity parameter that could be expanded to larger scales where channel network structure and storage become more important.