Reduced-Complexity and Robust Surface Water Path Delineation for Large Real-World Terrain Using Boundary Element Method

Abstract

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-based algorithms, but is much higher for the physically-based and contour-based algorithms. Unfortunately, the contour-based algorithms 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.

Keywords

• Boundary element method (BEM)
• digital elevation model (DEM)
• flow direction algorithm
• physically-based algorithms
• real-world terrain