In press: Persistent drainage migration in a numerical landscape evolution model, Geophysical Research Letters.

Abstract: Numerical landscape evolution models driven by uniform vertical uplift often develop a static drainage network and a precise balance between uplift and erosion. Small-scale physical models of uplifting drainage basins, however, continually reorganize by ridge migration and do not reach an ideal steady state. Here I show that the presence or absence of persistent drainage migration in a bedrock numerical landform evolution model depends on the flow-routing algorithm used to determine upstream contributing area. The model version that uses steepest-descent routing achieves an ideal steady state, while the model
version that uses bifurcation routing results in continually-evolving drainage basins, even under conditions of uniform vertical uplift, bedrock erodibility, precipitation, and landsliding threshold. This result suggests that persistent drainage migration can occur by erosional processes alone. This result has important implications for numerical-modeling methodology, our understanding of the natural variability of landform evolution, and the interpretation of thermochronological data.

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Pelletier, J.D. The influence of piedmont deposition on the time scale of mountain-belt denudation, Geophysical Research Letters. v. 31, 10.1029/2004GL020052, 2004.

Abstract: The linear correlation between modern sediment yields and mean basin elevation suggests that mountain-belt topography is denuded exponentially with a time scale of approximately 50 Myr following the cessation of active uplift. However, some Paleozoic orogens still exist as high-elevation terrain. Here I explore this paradox within the broader question of what variables control the denudational time scales of mountain belts. Using a two-dimensional model that couples the stream-power law for bedrock channel erosion with the diffusion equation for alluvial piedmonts, I determined the time scale of mountain-belt denudation using numerical and analytic techniques. The piedmont plays an important role in mountain-belt denudation because it sets the base level for bedrock erosion, substantially reducing bedrock relief in mountain belts with broad or steep piedmonts. The persistence of the Appalachian and Ural Mountains may be understood within the model framework as the result of resistant bedrock and a broad piedmont, respectively.

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Pelletier, J.D., Self-organization and scaling relations of evolving river networks, J. Geophys. Res., 104, 7359-7375, 1999.

Abstract: The power spectrum S of linear transects of the earth's topography is often observed to be a power-law function of wave number k with exponent close to -2. In addition, river networks are fractal trees that satisfy several power-law relationships between their morphologic components. A model equation for the evolution of the earth's topography by erosional processes which produces fractal topography and fractal river networks is presented and its solutions compared in detail to real topography. The model is the diffusion equation for sediment transport on hillslopes and channels with the diffusivity constant on hillslopes and proportional to the square root of discharge in channels. The dependence of diffusivity on discharge follows from fundamental equations of sediment transport. We study the model in two ways. In the first analysis the diffusivity is parameterized as a function of elevation and a Taylor expansion procedure is carried out to obtain a differential equation for the landform elevation which includes the spatially-variable diffusivity to first order in the elevation. The solution to this equation is a self-affine or fractal surface with linear transects that have power spectra S(k) proportional to k^-1.8, independent of the age of the topography, consistent with observations of real topography. The hypsometry produced by the model equation is skewed such that lowlands make up a larger fraction of the total area than highlands as observed in real topography. In the second analysis we include river networks explicitly in a numerical simulation by calculating the discharge at every point. We characterize the morphology of real river basins with five independent scaling relations between six morphometric variables. Scaling exponents are calculated for seven river networks from a variety of tectonic environments using high-quality digital elevation models. River networks formed in the model match the observed scaling laws and satisfy Tokunaga side-branching statistics.

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