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In this research I explored the use of the statistical characteristics of the distribution of elevation points within a basin for predicting the rate at which at peak in rainfall at some point within the basin becomes at peak in runoff at the outlet of that basin. My research was stimulated by the desire to improve flood forecasting in ungauged basins and based on the pioneering hydrology research of Langbein, Horton and Strahler as updated by Harlin and Luo. I developed a simplified model of a basin with stream development and showed how basin factors known to affect runoff – area, slope, stream network development, and basin shape – could be represented by the statistical characteristics N (count), standard deviation, median less minimum, skewness, and kurtosis. Linear regression of average runoff accumulation rate on the statistical characteristics showed N, median less minimum, and skewness to have a significant effect with an R-squared of 83%, a residual standard error of 0.25 on 28 degrees of freedom, and an overall p-value of 2.4e-11. A model skill assessment through cross-validation yielded a mean square error of 11%.
