The Mixed Gamma Model for channel link lengths

An investigation of the lengths of exterior and interior links in 12 disparate areas suggests that link length distributions for most, if not all, natural landscapes represent a mixture of link length populations from different parts of the landscape characterized by different ground slope and/or environmental conditions. The mixed gamma density is derived for link lengths by assuming that both the component link length distribution for each relatively homogeneous part of the landscape and the mixing distribution of weights assigned to the various component distributions can be represented by gamma distributions. The mixed gamma density satisfactorily fits 84% of the 70 link length distributions examined, compared with 67% fitted by the log normal and 59% fitted by the gamma density. Deviations from the mixed gamma density are largely ascribed to spatial distributions of slope and environmental conditions which give rise to nongamma‐mixing distributions.