PARALLEL IMPLEMENTATION OF A UNIT CONTRIBUTING AREA ALGORITHM THAT MINIMIZES GRID-RESOLUTION EFFECTS

Unit contributing area is a geomorphic quantity easily derived from pre-processed digital elevation models (DEM). It is therefore commonly used as a proxy for channel bed shear stress in stream-power-type landscape evolution models. However, if grid-resolution effects are not accounted for, then the numerical solutions of such models depend on the spacing of grid nodes. Solutions to this grid-resolution dependence have been developed for models run in serial. As parallel processing becomes ubiquitous in geomorphic applications, the need for parallelizable algorithms has arisen.

In this research, the unit contributing area algorithm developed by Pelletier (2010) on a regular grid is implemented in parallel using OpenMPI. The method minimizes the dependence of landscape evolution model solutions on grid resolution by computing drainage area on a higher-resolution interpolated DEM and then using the results in an error-corrector step. A node’s flow width is determined from this step to be either the width of the pixel (for non-convergent flow), or a power-law function of drainage area. Drainage area is solved on each grid following the implicit formulation of Richardson et al. (2014) and with the hypre suite of multigrid solvers for sparse linear systems. Square decomposition of the global domain assigns a portion of the grid to each processor. This implementation is compatible with any of the familiar flow-routing routines (e.g. D₄, D₈, D_inf, and MFD). While intended for use in a landscape evolution model, this formulation easily generalizes to any parallel application that requires estimates of unit contributing area.