Stochastic model of the width function

A new class of probabilistic models of the width function, based on so-call ed iterated random pulse (IRP) processes, is proposed. IRP processes reprod uce the main characteristics of empirical width functions (nonnegativity, n onstationarity, and power law decay of the spectrum) and require few and ea sily accessible parameters. IRP models are based on a simple conceptualizat ion of the geometrical structure of river basins and exploit in a natural w ay the self-similarity of natural channel networks. A result that is derive d from the IRP representation is that the exponent alpha of Hack's law, L s imilar to A(alpha), and the exponent beta of the power spectral density of the width function, S(omega) similar to \omega\(-beta), are related as alph a = 1/beta. Empirical values of beta are typically in the range 1.8-2.0 and are consistent with this theoretical result and the usual range of alpha.