Efficient numerical solution of the basic equations governing landscape evolution

Abstract:

We have developed a new algorithm (Braun and Willett, 2013) to solve the two-dimensional stream power law that is both implicit in time and O(n), i.e. the number of operations required to solve the equation is directly proportional to the number of nodes, n, in the numerical grid. I have recently generalized the algorithm to take into account sediment transport and deposition in the channels, sediment production and slope-dependent transport along the valley sides and by including a maximum slope angle. The algorithm remains O(n) and implicit in time with respect to slope. I will demonstrate through a few examples the efficiency of this algorithm and how it can be used to study landscape evolution across a broad range of temporal and spatial scales. In particular I will consider the time evolution of the predicted distribution of slopes during an orogenic cycle and compare it to a few natural systems, using high resolution SRTM-derived DEMs.