Transit Times and StorAge Selection Functions in Idealized Hillslopes With Steady Infiltration

Abstract

Spatially integrated transport models have been applied widely to model hydrologic transport. However, we lack simple and process-based theoretical tools to predict the transport closures—transit time distributions (TTDs) and StorAge Selection (SAS) functions. This limits our ability to infer characteristics of hydrologic systems from tracer observations and to make first-order estimates of SAS functions in catchments where no tracer data is available. Here we present a theoretical framework linking TTDs and SAS functions to hydraulic groundwater theory at the hillslope scale. For hillslopes where the saturated hydraulic conductivity declines exponentially with depth, analytical solutions for the closures are derived that can be used as hypotheses to test against data. In the simplest form, the hillslope SAS function resembles a uniform or exponential distribution (corresponding to flow pathways in the saturated zone) offset from zero by the storage in the unsaturated zone that does not contribute to discharge. The framework is validated against nine idealized virtual hillslopes constructed using a 2-D Richards equation-based model, and against data from tracer experiments in two artificial hillslopes. Modeled internal age, life expectancy, and transit time structures reproduce theoretical predictions. The experimental data also support the theory, though further work is needed to account for the effects of time-variability. The shape and tailing of TTDs and their power spectra are discussed. The theoretical framework yields several dimensionless numbers that can be used to classify hillslope scale flow and transport dynamics and suggests distinct water age structures for high or low Hillslope number.