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Land surface topography is one of the most important terrain properties which impact hydrological, geomorphological, and ecological processes active on a landscape. In our previous efforts to develop a soil depth model based upon topographic and land cover variables, we derived a set of hydrological proximity measures (HPMs) from a Digital Elevation Model (DEM) as potential explanatory variables for soil depth. These HPMs are variations of the distance up to ridge points (cells with no incoming flow) and variations of the distance down to stream points (cells with a contributing area greater than a threshold), following the flow path. The HPMs were computed using the D-infinity flow model that apportions flow between adjacent neighbors based on the direction of steepest downward slope on the eight triangular facets constructed in a 3 × 3 grid cell window using the center cell and each pair of adjacent neighboring grid cells in turn. The D-infinity model typically results in multiple flow paths between 2 points on the topography, with the result that distances may be computed as the minimum, maximum or average of the individual flow paths. In addition, each of the HPMs, are calculated vertically, horizontally, and along the land surface. Previously, these HPMs were calculated using recursive serial algorithms which suffered from stack overflow problems when used to process large datasets, limiting the size of DEMs that could be analyzed. To overcome this limitation, we developed a message passing interface (MPI) parallel approach designed to both increase the size and speed with which these HPMs are computed. The parallel HPM algorithms spatially partition the input grid into stripes which are each assigned to separate processes for computation. Each of those processes then uses a queue data structure to order the processing of cells so that each cell is visited only once and the cross-process communications that are a standard part of MPI are handled in an efficient manner. This parallel approach allows efficient analysis of much larger DEMs than were possible using the serial recursive algorithms. The HPMs given here may also have other, more general modeling applicability in hydrology, geomorphology and ecology, and so are described here from a general perspective. In this paper, we present the definitions of the HPMs, the serial and parallel algorithms used in their computation and their potential applications.
