A stochastic approach to modeling the role of rainfall variability in drainage basin evolution

Abstract

Abstract. We develop a simple stochastic theory for erosion and sediment transport, based on the Poisson pulse rainfall model, in order to analyze how variability in rainfall and runoff influences drainage basin evolution. Two cases are considered: sediment transport by runoff in rills and channels and particle detachment from bedrock or cohesive soils. Analytical and numerical results show that under some circumstances, rainfall variability can have an impact equal to or greater than that of mean rainfall amount. The predicted sensitivity to rainfall variability is greatest when (1) thresholds for runoff generation and/or particle detachment are significant and/or (2) erosion and transport are strong nonlinear functions of discharge. In general, sediment transport capacity is predicted to increase with increasing rainfall variability. Depending on the degree of nonlinearity, particle detachment capacity may either increase or decrease with increasing rainfall variability. These findings underscore the critical importance of hydrogeomorphic thresholds and other sources of nonlinearity in process dynamics. The morphologic consequences of rainfall variability are illustrated by incorporating the pulse rainfall theory into a landscape simulation model. The simulation results imply that, all else being equal, catchments experiencing a shift toward greater climate variability will tend to have (1) higher erosion rates, (2) higher drainage density (because of increased runoff erosion efficiency), and ultimately (3) reduced relief. The stochastic approach provides a useful method for incorporating physically meaningful climate data within the current generation of landscape evolution models.

Creative computing with Landlab: an open-source toolkit for building, coupling, and exploring two-dimensional numerical models of Earth-surface dynamics

“…In this case, the model is driven by a stochastic storm generator (the PrecipitationDistribution class), based on that suggested by Eagleson (1978) and similar to the one underlying the CHILD landscape evolution model (Tucker and Bras, 2000;Tucker et al, 2001b). Unlike CHILD, but in keeping with Eagleson's original derivation, here an explicit inverse relationship between storm length and intensity is built into the distribution, by calculating storm water depth as a gamma-distributed random variable and then deriving storm intensity as the quotient of depth and (exponentially distributed) duration.…”

Describing the interannual variability of precipitation with the derived distribution approach: effects of record length and resolution

“…Under this derived distribution (DD) approach (Benjamin and Cornell, 1970, p. 100), only a few years of continuously gauged precipitation data, from which storm arrivals and depths can be extracted and their distributions estimated, are necessary to estimate the probability distribution of annual precipitation for a site. Even though Eagleson's (1978) original paper has a large number of citations, most of these relate to ecohydrological modeling of soil moisture and vegetation dynamics (e.g., Dufrêne et al, 2005;Ivanov et al, 2008), derived distributions of runoff and flood frequency (e.g., Freeze, 1980;Díaz-Granados et al, 1984), rainfall modeling (for example, Onof et al, 1998;Willems, 2001), or morphological evolution of drainage basins (Tucker and Bras, 2000). We are not aware of any previous attempt at applying Eagleson's DD approach to the study of the interannual variability of precipitation, even though the method seems particularly well suited to deal with locations with short records, as well as to account for nonstationarities introduced by a changing climate.…”

Developing and exploring a theory for the lateral erosion of bedrock channels for use in landscape evolution models

“…For example, bedrock incision models now include theories for the adjustment of channel width (e.g., Stark and Stark, 2001;Wobus et al, 2006;Turowski et al, 2009;Yanites and Tucker, 2010), the role of sediment size and bed cover (e.g., Whipple and Tucker, 2002;Sklar and Dietrich, 2004;Yanites et al, 2011), and thresholds for incision (e.g., Tucker and Bras, 2000;Snyder et al, 2003b). Rivers may respond to changing boundary conditions by adjusting both slope and channel width (Lavé and Avouac, 2001;Duvall et al, 2004;Snyder and Kammer, 2008, e.g.,) and landscape evolution models must be able to capture both of these responses if we are to fully describe the behavior and function of landscapes.…”