资源环境科技发展态势分析平台

Total contributing area (TCA) has important hydrological, geological and geomorphological implications in digital terrain analysis. Currently, the validity of estimated TCA is challenged by the approximation error of digital elevation models (DEMs) to real‐world terrains, the choice of flow direction algorithms and the difficulty in a quantitative evaluation. To solve these problems, this work employs a range of synthetic surfaces for free from approximation errors. Theoretical TCA for any cell on synthetic surfaces is analytically solved by using subsection integral and L'Hospital's rule based on the topographical definition of TCA. The impacts of grid discretization on the spatial patterns of theoretical TCA are explained mathematically and geometrically. In case studies, the analytically solved theoretical TCA is treated as a benchmark to quantitatively evaluate the TCAs estimated by three SFD algorithms (i.e. D8, Rho8 and D8‐LTD) and three MFD algorithms (i.e. FDFM, MFD‐md and D∞). Results show that (1) SFD algorithms obtain unsmooth and discontinuous spatial patterns of estimated TCA, due to the existence of source cells caused by the basic hypothesis of allowing only one receiving cell; (2) Cross compensation induced by artificial dispersion in MFD algorithms leads to a less error in the quantity of estimated TCA but a larger error in the physical position of estimated TCA; (3) The addition of contour length errors does not promise larger specific contributing area (SCA) errors than TCA errors. To summarize, this work offers a theoretical and quantitative evaluation on the precision of the TCAs estimated by flow direction algorithms.

This article is protected by copyright. All rights reserved.