单位汇水面积（Specific Catchment Area，SCA）是描述表面水流分布的定量化指标，可用于许多复合地形属性的计算（如地形湿度指数TWI）、地学建模的输入（如分布式水文模型）等。传统基于栅格流向的SCA计算方法由于单独计算汇水面积和水流宽度而分别引入误差，且计算精度受到分辨率的明显影响。Gallant和Hutchinson（2011，WRR）提出了一种基于差分方程的SCA数值解算方法，精度较高，但由于计算复杂度高，目前串行的计算方式满足该算法实用中的计算效率需求。

我们根据该计算方法的特点，设计了基于共享内存的openMP并行算法，大幅提高计算效率，增强了该方法的实用性，并对该计算方法进行了参数敏感性分析。

Qin C-Z, Ai B-B, Zhu A-X,Liu J-Z. An efficient method for applying a differential equation to deriving the spatial distribution of specific catchment area from gridded digital elevation models. Computers & Geosciences, 2016, 10.1016/j.cageo.2016.12.009.

Abstract

Deriving the spatial distribution of specific catchment area (SCA) from a gridded digital elevation model (DEM) is one of the most important issues in digital terrain analysis. Conventional methods usually estimate SCA for each cell using a flow direction algorithm, but the results obtained are often unsatisfactory. Recently, Gallant and Hutchinson (2011, Water Resources Research, 47(5), W05535) proposed a differential equation which quantifies the change of SCA along a slope line, and thus the numerical solution of SCA at any point on a surface can be calculated accurately by integrating the differential equation. However, obtaining the numerical SCA solution based on this differential equation is so computationally intensive that it is too time-consuming to use it to derive the overall SCA spatial distribution from a gridded DEM. In this study, we developed a parallel algorithm based on OpenMP to make the numerical SCA solution based on Gallant and Hutchinson (2011)’s differential equation practical to derive the spatial distribution of SCA from a gridded DEM. Experiments based on two artificial surfaces with theoretical SCA and a more complex real terrain surface demonstrated that the proposed parallel algorithm obtained satisfactory acceleration performance and a much lower error than the MFD-md algorithm, which is a representative of conventional grid-based flow direction algorithms. Due to the speedup effects of the proposed parallel algorithm, we analyzed the effects of the DEM grid size and integration step length on the numerical SCA solution in detailed experiments. The experimental results suggested that the proposed algorithm performed best normally at the resolution of 5 m. A step ratio of 0.5 is suitable in applications of the proposed parallel algorithm.