An evaluation of flow-routing algorithms for calculating contributing area on regular grids

IF 2.8 2区 地球科学 Q2 GEOGRAPHY, PHYSICAL Earth Surface Dynamics Pub Date : 2024-04-22 DOI:10.5194/egusphere-2024-1138
Alexander B. Prescott, Jon D. Pelletier, Satya Chataut, Sriram Ananthanarayan
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Abstract

Abstract. Calculating contributing area (often used as a proxy for surface water discharge) within a Digital Elevation Model (DEM) or Landscape Evolution Model (LEM) is a fundamental operation in geomorphology. Here we document that a commonly used multiple-flow-direction algorithm for calculating contributing area, i.e., D∞ of Tarboton (1997), is sufficiently biased along the cardinal and ordinal directions that it is unsuitable for some standard applications of flow-routing algorithms. We revisit the purported excess dispersion of the MFD algorithm of Freeman (1991) that motivated the development of D∞ and demonstrate that MFD is superior to D∞ when tested against analytic solutions for the contributing areas of idealized landforms and the predictions of the shallow-water-equation solver FLO-2D for more complex landforms in which the water-surface slope is closely approximated by the bed slope. We also introduce a new flow-routing algorithm entitled IDS (in reference to the iterative depth-and-slope-dependent nature of the algorithm) that is more suitable than MFD for applications in which the bed and water-surface slopes differ substantially. IDS solves for water flow depths under steady hydrologic conditions by distributing the discharge delivered to each grid point from upslope to its downslope neighbors in rank order of elevation (highest to lowest) and in proportion to a power-law function of the square root of the water-surface slope and the five-thirds power of the water depth, mimicking the relationships among water discharge, depth, and surface slope in Manning’s equation. IDS is iterative in two ways: 1) water depths are added in small increments so that the water-surface slope can gradually differ from the bed slope, facilitating the spreading of water in areas of laterally unconfined flow, and 2) the partitioning of discharge from high to low elevations can be repeated, improving the accuracy of the solution as the water depths of downslope grid points become more well approximated with each successive iteration. We assess the performance of IDS by comparing its results to those of FLO-2D for a variety of real and idealized landforms and to an analytic solution of the shallow-water equations. We also demonstrate how IDS can be modified to solve other fluid-dynamical nonlinear partial differential equations arising in Earth-surface processes, such as the Boussinesq equation for the height of the water table in an unconfined aquifer.
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对用于计算规则网格面积的流路算法进行评估
摘要在数字高程模型(DEM)或地貌演化模型(LEM)中计算汇水面积(通常用作地表水排放量的代用指标)是地貌学中的一项基本操作。在此,我们记录了一种常用的计算汇水面积的多流向算法,即 Tarboton(1997 年)的 D∞,该算法在心向和序向有足够的偏差,因此不适合某些标准流向算法的应用。我们重新审视了弗里曼(1991 年)的 MFD 算法所谓的过度分散问题(这也是开发 D∞ 算法的动因),并证明了 MFD 算法在与理想化地貌汇水面积的分析解法以及浅水方程求解器 FLO-2D 对更复杂地貌(其中水面坡度与床面坡度非常接近)的预测结果进行比较时优于 D∞。我们还介绍了一种名为 IDS 的新水流路径算法(指该算法与深度和坡度相关的迭代性质),它比 MFD 更适用于河床坡度和水面坡度相差很大的应用。IDS 在稳定的水文条件下求解水流深度,方法是将每个网格点的排水量按高程顺序(从高到低)从上坡分配到下坡相邻网格点,并与水面坡度的平方根和水深的三分之二幂的幂律函数成比例,模拟曼宁方程中排水量、水深和水面坡度之间的关系。IDS 有两种迭代方式:1)水深以较小的增量增加,使水面坡度逐渐不同于河床坡度,从而促进水流在横向无约束水流区域的扩散;2)可重复将排水量从高海拔向低海拔划分,随着每次连续迭代,下坡网格点的水深变得更加接近,从而提高了求解的准确性。我们将 IDS 的结果与 FLO-2D 对各种真实和理想地貌的结果以及浅水方程的解析解进行了比较,从而评估了 IDS 的性能。我们还演示了如何修改 IDS 以求解地球表面过程中出现的其他流体动力非线性偏微分方程,如无约束含水层中地下水位高度的布森斯克方程。
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来源期刊
Earth Surface Dynamics
Earth Surface Dynamics GEOGRAPHY, PHYSICALGEOSCIENCES, MULTIDISCI-GEOSCIENCES, MULTIDISCIPLINARY
CiteScore
5.40
自引率
5.90%
发文量
56
审稿时长
20 weeks
期刊介绍: Earth Surface Dynamics (ESurf) is an international scientific journal dedicated to the publication and discussion of high-quality research on the physical, chemical, and biological processes shaping Earth''s surface and their interactions on all scales.
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