A differential equation for specific catchment area

TitleA differential equation for specific catchment area
Publication TypeJournal Article
Year of Publication2011
AuthorsGallant, J.  C., and M.  F. Hutchinson
Refereed DesignationRefereed
JournalWater Resources Research

Analysis of the behaviour of specific catchment area in a stream tube leads to a simple nonlinear differential equation describing the rate of change of specific catchment area along a flow path. The differential equation can be integrated numerically along a flow path to calculate specific catchment area at any point on a digital elevation model (DEM) without requiring the usual estimates of catchment area and width. The method is more computationally intensive than most grid-based methods for calculating specific catchment area so its main application is as a reference against which conventional methods can be tested. This is the first method that provides a benchmark for more approximate methods in complex terrain with both convergent and divergent areas, not just on simple surfaces for which analytical solutions are known. Preliminary evaluation of the D8, M8, DEMON and Dinf methods indicate that the Dinf method is the best of those methods for estimating specific catchment area, but all methods over-estimate in divergent terrain.

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