一种以等差分级的DEM填洼算法

DEM的填洼是水系提取中最耗时的过程。真实的地表低高程点通常在空间上相邻,在对低高程栅格进行填洼时,少数栅格的高程值更新会导致级内大量栅格的循环迭代,从而消耗大量运算时间。为了提高DEM的填洼效率,在分级填洼的基础上,提出一种等差分级填洼算法,该算法顾及DEM各级填洼时间呈幂函数逐级递减这一地形规律。算法首先创建一系列数组,数组大小随等差数列递增;然后依次将排序后的DEM数据存放至数组中,由于定义的数组大小逐渐增大,因此,低高程区域被“分割”得很细;最后,当填洼运算从级内转至数组内时,低高程区域细致的划分极大缩短了栅格循环迭代时间,从而使得算法获得了较高的效率。新算法既能有效缩短填洼过程中的迭代时间,又能保证所提取水系的完整性与连贯性。为验证算法的有效性,选用四川省不同地区的SRTM 90 m分辨率DEM作为实验数据,并与已有的DEM分级填洼算法进行对比分析。实验结果显示：当研究区域栅格总数达到两千万个时,本文算法填洼效率提升了50%左右,且随着DEM数据量的增大,算法效率的提升更为明显,与此同时,利用新方法进行填洼后,DEM水文线连续性较强,表明了新方法的有效性。

A New Algorithm to Fill Depressions in Digital Elevation Model Based on Arithmetic Arrays

Depressions cause errors or breaks when extracting rivers from DEM. Filling the depressions in the initial DEM is important. Low elevated surface areas in space are usually adjacent, and high elevated surface areas in space are always discrete. Therefore, when the grids of low elevated areas are filled, a large number of grids in low elevated areas will have to be recalculated, which makes the process of depression filling more complex. This paper investigates a new ranking algorithm for improving the efficiency of filling the depressions of DEM. First, considering the fact that the depression filling time in different pieces decreases in the form of power function, the algorithm creates a list of variable arrays. Then the data of DEM, which has been ranked using quicksort algorithm, is put into the arrays successively. Finally, grids are filled within the variable arrays, whose lengths are increased with respect to arithmetic sequence. As the lengths of the arrays are increased, the low elevated areas are divided finely. With the increase of elevation, the arrays will contain more numbers of grids, which will reduce the depth of seeking path in iterations for the unfilled grids. The new algorithm keeps the integrity and continuity of the drainage networks extracted by the pits-removed DEM and well reduces the depth of seeking path in iterations to accelerate pits-removing process. To illustrate this approach, the algorithm has been employed in the SRTM DEM at a 90-meter resolution of Chengdu City. The results show a considerable efficiency. The efficiency of the algorithm outperforms the traditional algorithm, as it will improve 50% efficiency compared with previous algorithm when the number of grids of DEM reaches 20 million. And the improvement will be more evident when the amount of DEM data increases.