A Method for Developing Probability Distributions for Rill Flow and Density

Abstract

Procedures are presented and evaluated for developing probability distribution functions for rill numbers (density) and rill flow rates that can be used to represent the stochasticity of rill networks in recent erosion models such as PRORIL. Subsoil and topsoil data sets, including photographs, collected at the University of Kentucky were used in the evaluation. Photographic images were corrected for optical distortion and visually analyzed to develop the rill networks. A digital terrain model (DTM) that allowed combining of channels, but not flow splitting, was also utilized to develop a flow network and compared to the photographically determined network. The DTM generated network did not provide a good fit to the photographically determined network, likely because of problems with interpolation and with the inability to predict rill splitting. The DTM generated networks were utilized to develop probability density functions (PDFs) for rill numbers and conditional PDFs for rill flow rates given a number of rills. The binomial distribution provided a good fit to rill number distributions as defined by the Kolmogorov-Smirnov test. The Weibull distribution provided the best fit to the conditional PDF for flow rates, but the goodness of fit was poor. This lack of fit, likely due to inadequacies of the DTM, should improve with improved DTMs.