Stochastic Model of the Width Function

A new class of probabilistic models of the width function, based on so-called iterated random pulse (IRP) processes, is proposed. IRP processes reproduce the main characteristics of empirical width functions (nonnegativity, nonstationarity, and power law decay of the spectrum) and require few and easily accessible parameters. IRP models are based on a simple conceptualization of the geometrical structure of river basins and exploit in a natural way the self-similarity of natural channel networks. A result that is derived from the IRP representation is that the exponent alpha of Hack's law, L similar 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 alpha = 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.