Abstract
Abstract. We hypothesize that total hillslope water loss for a rainfall–runoff event is inversely related to a function of a lognormal random variable, based on basin- and point-scale observations taken from the 21 km2 Goodwin Creek Experimental Watershed (GCEW) in Mississippi, USA. A top-down approach is used to develop a new runoff generation model both to test our physical-statistical hypothesis and to provide a method of generating ensembles of runoff from a large number of hillslopes in a basin. The model is based on the assumption that the probability distributions of a runoff/loss ratio have a space–time rescaling property. We test this assumption using streamflow and rainfall data from GCEW. For over 100 rainfall–runoff events, we find that the spatial probability distributions of a runoff/loss ratio can be rescaled to a new distribution that is common to all events. We interpret random within-event differences in runoff/loss ratios in the model to arise from soil moisture spatial variability. Observations of water loss during events in GCEW support this interpretation. Our model preserves water balance in a mean statistical sense and supports our hypothesis. As an example, we use the model to generate ensembles of runoff at a large number of hillslopes for a rainfall–runoff event in GCEW.
Highlights
Runoff generation is the net result of separating rainfall into a surface runoff component and a “loss” component that includes infiltration, interception, and evapotranspiration
We introduce a physical-statistical hypothesis, developed from basin-scale and point-scale observations, that total hillslope water loss for a rainfall-runoff event is inversely related to a function of a lognormal random variable
Our objective is to develop an expression for the runoff/loss ratio at the hillslope scale that provides a method of simulating event-based total runoff volume for each hillslope draining an unnested basin
Summary
Runoff generation is the net result of separating rainfall into a surface runoff component and a “loss” component that includes infiltration, interception, and evapotranspiration. The following overarching question captures these issues and serves as the focus of our paper: how can space–time variable runoff generation in a river basin be modeled at a large number of hillslopes when the finest scale of observed runoff is substantially larger, and the scale of existing infiltration equations and related measurements is much smaller?. The hillslope scale represents an important transition in land surface form and process. At this scale, surface runoff from a hillslope enters a channel link in a river network. Surface runoff from a hillslope enters a channel link in a river network This scale, runoff occurs in multiple links draining a sub-basin. Scale problems have been recognized in hydrology literature for quite some time (Amerman and McGuinness, 1967; Pilgrim, 1983)
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