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A differential equation for specific catchment area
Author(s) -
Gallant John C.,
Hutchinson Michael F.
Publication year - 2011
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2009wr008540
Subject(s) - terrain , catchment area , digital elevation model , drainage basin , benchmark (surveying) , elevation (ballistics) , differential equation , ordinary differential equation , mathematics , grid , hydrology (agriculture) , mathematical optimization , computer science , geology , remote sensing , geometry , geodesy , mathematical analysis , geography , cartography , geotechnical engineering
Analysis of the behavior 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 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, digital elevation model networks (DEMON), and D∞ methods indicate that the D∞ method is the best of those methods for estimating specific catchment area, but all methods overestimate in divergent terrain.