Understanding landscape evolution parameters using global 10Be erosion rates

Abstract

<p>Landscape evolution models simulate erosional and depositional changes in terrain surface over time and have proven useful for studying surface processes at a variety of scales. These models rely on several input parameters such as a coefficient of hillslope diffusion (D), as well as stream power exponents of drainage basin area (m) and slope (n), a value of minimum drainage area (Ac) below which advective fluvial processes dominate over diffusive hillslope processes, and an effective stream power/advection coefficient of rock ‘erodibility’ (k). In spite of the widespread application of landscape evolution models, values of these input parameters and their variation through space and time are generally poorly constrained in large part due to the large number of processes and physical properties which are amalgamated into the advection-based SP equation. Several recent studies have looked at global controls on erosion rates using stream power parameters and other river metrics by making use of sophisticated stream profile analysis tools, and we aim to build on these past studies by using a landscape evolution modelling framework.  Here, we make use of a global catalog of basin-averaged cosmogenic 10Be-derived apparent erosion rates to tune several landscape evolution model parameters. We employ an Approximate Bayesian Computation (ABC) approach which is based on the performance of many combinations of randomly selected parameters with respect to a likelihood function that measures how well a model fits a sample of observations for a given set of parameter values. Prescribing the commonly observed stream concavity ratio (m/n) of 0.5, maximum agreement between LEM-predicted and 10Be apparent erosion rates is obtained when the free parameters of stream power slope coefficient (n) is approximately 2, the ratio of hillslope diffusivity (D) to effective stream power coefficient (K) is between 103 and 104 mn-1 yr-1 and when critical drainage area (Ac) is ~0.1 km2<strong>. </strong>Additionally, we find that models can be optimized to a greater degree when the diffusive component of the LEMs is squared, in line with recent studies. Finally, we perform a search for optimal parameters in the face of variable stream concavity, climate, and geology which are encompassed in k, D, m, and n,  all of which show considerable variability over different climatic, lithologic, and ecologic regimes. Ultimately, this demonstrates that globally optimal parameters may not be applicable at the local to regional scale, but continent to global scale analyses could benefit from understanding these optimal parameters.</p>