Towards an Algebra for Terrain-Based Flow Analysis

David G. Tarboton, Utah State University
M. E. Baker


Topography is an important land surface attribute for hydrology that, in the form of Digital Elevation Models (DEMs), is widely used to derive information for the modeling of hydrologic processes. Much hydrologic terrain analysis is conditioned upon an information model for the topographic representation of downslope flow derived from a DEM, which enriches the information content of digital elevation data. This information model involves procedures for removing spurious sinks, deriving a structured flow field, and calculating derivative surfaces. We present a general method for recursive flow analysis that exploits this information model for calculation of a rich set of flow-based derivative surfaces beyond current weighted flow accumulation approaches commonly available in Geographic Information Systems, through the integration of multiple inputs and a broad class of algebraic rules into the calculation of flow related quantities. This flow algebra encompasses single and multi-directional flow fields, various topographic representations, weighted accumulation algorithms, and enables untapped potential for a host of application-specific functions. We illustrate the potential of flow algebra by presenting examples of new functions enabled by this perspective that are useful for hydrologic and environmental modeling. Future opportunities for advancing flow algebra functionality could include the development of a formulaic language that provides efficient implementation and greater access to these methods. There are also opportunities to take advantage of parallel computing for the solution of problems across very large input datasets.