Hydrologists usually gain insights into topographic variability by using a high-performance algorithm to estimate the catchment area from a digital elevation model (DEM) image. In the literature, the grid-based algori...
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Hydrologists usually gain insights into topographic variability by using a high-performance algorithm to estimate the catchment area from a digital elevation model (DEM) image. In the literature, the grid-basedalgorithms are more popular than the contour-basedalgorithms;however, the existing ones cannot reduce the error when higher resolution DEM is available. This paper introduces a new contour-based algorithm, formulated with the physically-based concept, to estimate catchment from contour-based DEM data. The formulation was derived from the semi-analytical solution of Laplace's partial differential equation based on the boundary element method (BEM). With this approach, the algorithm can estimate the catchment area along the smooth surface water paths (SWPs), which are delineated from the physically-based algorithm. The proposed algorithm was validated with the standard synthetic surfaces, where the theoretical specific catchment areas (SCAs) for error assessment are exactly known. When estimating the SCAs with ordinary resolution, the average error of the estimated SCAs is between 14.19 and 2.32%, but the average error from the popular grid-basedalgorithms is between 77.8 and 17.0 %. With higher resolutions, between 12.5 and 0.88 meters, the proposed algorithm significantly reduces the average error from 15 to 0.8%.
Hydrologists delineate surface water path (SWP) from digital elevation model (DEM) images to gain insights into catchment characteristics. Currently, high-resolution DEM can be obtained to improve the SWP delineation ...
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Hydrologists delineate surface water path (SWP) from digital elevation model (DEM) images to gain insights into catchment characteristics. Currently, high-resolution DEM can be obtained to improve the SWP delineation accuracy. It was found that accuracy is still the same for the popular existing grid-basedalgorithms, but is much higher for the physically-based and contour-basedalgorithms. Unfortunately, the contour-basedalgorithms suffer complexity at high resolution. Accordingly, we develop the algorithm to decrease the error with high-resolution DEMs by enhancing an existing contour-based algorithm, constructed with a physically-based concept, derived from the semi-analytical solution of Laplace's partial differential equation through the boundary element method (BEM). To reduce the complexity, we propose the framework integrating the enhanced algorithm with pre-processing that reduces the input data size from very long contours by transforming those contours into the closed paths, exploited by the enhanced algorithm to delineate SWPs with the numerical BEM-based solution. The results show the framework's ability to successfully delineate the forward SWPs from hilltops to reservoirs over a real-world large-terrain DEM image and to depict the drainage networks flowing into real rivers. Analyzing the catchment boundary at the outlet along the real river, the framework successfully delineates the reverse SWPs from the outlet to hilltops and accurately demarcates the catchment boundary, consistent with the results from a popular GIS software. These findings indicate that the framework, which leverages the BEM-based numerical solution, reduces the complexity of the physically-based and contour-based algorithm in delineating the SWPs over a real-world large-terrain DEM image while maintaining robustness in problematic regions.
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