Coupled numerical-analytical approach to landscape evolution modeling

The Earth's topography is shaped by surface processes that operate on various scales. In particular, river processes control landscape dynamics over large length scales, whereas hillslope processes control the dynamics over smaller length scales. This scale separation challenges numerical treatments of landscape evolution that use space discretization. Large grid spacing cannot account for the dynamics of water divides that control drainage area competition, and erosion rate and slope distribution. Small grid spacing that properly accounts for divide dynamics is computationally inefficient when studying large domains. Here we propose a new approach for landscape evolution modeling that couples irregular grid-based numerical solutions for the large-scale fluvial dynamics and continuum-based analytical solutions for the small-scale fluvial and hillslope dynamics. The new approach is implemented in the landscape evolution model DAC (divide and capture). The geometrical and topological characteristics of DAC's landscapes show compatibility with those of natural landscapes. A comparative study shows that, even with large grid spacing, DAC predictions fit well an analytical solution for divide migration in the presence of horizontal advection of topography. In addition, DAC is used to study some outstanding problems in landscape evolution. (i) The time to steady-state is investigated and simulations show that steady-state requires much more time to achieve than predicted by fixed area calculations, due to divides migration and persistent reorganization of low-order streams. (ii) Large-scale stream captures in a strike-slip environment are studied and show a distinct pattern of erosion rates that can be used to identify recent capture events. (iii) Three tectono-climatic mechanisms that can lead to asymmetric mountains are studied. Each of the mechanisms produces a distinct morphology and erosion rate distribution. Application to the Southern Alps of New Zealand suggests that tectonic advection, precipitation gradients and non-uniform tectonic uplift act together to shape the first-order topography of this mountain range. Copyright (c) 2014 John Wiley & Sons, Ltd.