River flow mass exponents with fractal channel networks and rainfall

An important problem in hydrologic science is understanding how river flow is influenced by rainfall properties and drainage basin characteristics. In this paper we consider one approach, the use of mass exponents, in examining the relation of river flow to rainfall and the channel network, which provides the primary conduit for transport of water to the outlet in a large basin. Mass exponents, which characterize the power-law behavior of moments as a function of scale, are ideally suited for defining scaling behavior of processes that exhibit a high degree of variability or intermittency. The main result in this paper is an expression relating the mass exponent of flow resulting from an instantaneous burst of rainfall to the mass exponents of spatial rainfall and that of the network width function. Spatial rainfall is modeled as a random multiplicative cascade and the channel network as a recursive replacement tree; these fractal models reproduce certain types of self-similar behavior seen in actual rainfall and networks. It is shown that under these modeling assumptions the scaling behavior of flow mirrors that of rainfall if rainfall is highly variable in space, and on the other hand flow mirrors the structure of the network if rainfall is not so highly variable.     

Scaling in river corridor widths depicts organization in valley morphology

Landscapes have been shown to exhibit numerous scaling laws from Horton's laws to more sophisticated scaling in topography heights, river network topology and power laws in several geomorphic attributes. In this paper, we propose a different way of examining landscape organization by introducing the “river corridor width” (lateral distance from the centerline of the river to the left and right valley walls at a fixed height above the water surface) as one moves downstream. We establish that the river corridor width series, extracted from 1 m LIDAR topography of a mountainous river, exhibit a rich multiscale statistical structure (anomalous scaling) which varies distinctly across physical boundaries, e.g., bedrock versus alluvial valleys. We postulate that such an analysis, in conjunction with field observations and physical modeling, has the potential to quantitatively relate mechanistic laws of valley formation to the statistical signature that underlying processes leave on the landscape. Such relations can be useful in guiding field work (by identifying physically distinct regimes from statistically distinct regimes) and advancing process understanding and hypothesis testing.     

Evidence for inherent nonlinearity in temporal rainfall

We examine the underlying structure of high resolution temporal rainfall by comparing the observed series with surrogate series generated by a invertible nonlinear transformation of a linear process. We document that the scaling properties and long range magnitude correlations of high resolution temporal rainfall series are inconsistent with an inherently linear model, but are consistent with the nonlinear structure of a multiplicative cascade model. This is in contrast to current studies that have reported for spatial rainfall a lack of evidence for a nonlinear underlying structure. The proposed analysis methodologies, which consider two-point correlation statistics and also do not rely on higher order statistical moments, are shown to provide increased discriminatory power as compared to standard moment-based analysis.