Determination of probability distributions for Strahler stream lengths based on Poisson process and DEM

One of the basic tasks in geomorphologic analysis is to know the probabilit y distributions of the stream lengths of different orders. In practical app lications, this information is useful for basin rainfall-runoff modelling. The objective of this study is to determine the length distributions of the Strahler streams. A Poisson process was used to derive the theoretical dis tributions. The result showed that the length distribution of the first-ord er stream is an exponential distribution and the second-order or higher ord er stream length is a gamma distribution. In order to verify the theoretica l distributions, a digital elevation model (DEM) was adopted to calculate t he stream lengths of four basins in Taiwan. Kolmogorov-Smirnov and chi-squa re tests were used to test the goodness-of-fit of the data. Results showed that the length distributions of the first- and second-order streams analys ed by using DEM correspond with those from the derived distribution method.