基于不同方向参考系DEM提取坡度的差异性分析

Analysis of the Diversity of Slope Gradients Derived from DEM based on Spatial Reference Systems with Varied Orientations

坡度指标通常基于DEM数据以固定算法直接提取。坡度误差主要来源于算法模型误差和数据误差等,很少顾及在建立DEM时空间参考系方向的变化引起的坡度差异。本文以数学高斯曲面为基准,通过改变参考系X、Y轴方向,对不同参考系下的DEM数据以三阶反距离平方权差分坡度算法提取坡度并分析其差异,结果表明:1.空间参考系方向变化对坡度差异的影响与地表剖面曲率有关,在山顶、谷底以及鞍部等坡度变化较为明显的地形区域,较为显著,两者成一定的正相关,而且与坡向变化率也存在相关关系。2.坡度、坡向差异随着空间参考系方向变化呈现周期性,周期为90°,近似按正弦(y=a·sin(1/2kπ+φ)φ∈[0,π/2])规律变化,在45°处达到峰值,而在0°与90°附近,6°范围内平均差异变化较为平缓,但与正弦曲线偏离较大,且随着空间分辨率的降低,参考系方向引起的坡度、坡向差异有增加的趋势。实验表明在研究区建立独立参考系时应顺应平均坡向原则,以减小参考系方向对坡度、坡向的影响。

Slope metrics are usually based on DEM data and are extracted directly using a fixed algorithm. Slope errors mainly are attributed to algorithm model errors and data errors,with little regard for the differences in slopes generated by changes in the directions of a spatial references when building DEM. In this paper,based on the mathematical Gaussian surface and by changing the direction of a reference frame X and Y,the derived slope gradients from DEM data were analyzed by the third-order reverse distance squared weight differential slope algorithm under different reference frames. Results showed that： 1. the influence of the change in the direction of spatial reference systems on slope difference was related to the curvature of a surface profile. In the terrain areas where the slope changes are more obvious,such as the top of a mountain,valley bottom,and saddle,they were positively related to each other. There was also a correlation with the rates of changes in aspect. 2. The difference between slope and slope direction was periodic with the change of the direction of a spatial reference system. The period was 90°,which shifted approximately according to the sine（y = a·sin（1/2 kπ ＋φ） φ∈[0,π/2]″） law,reaching the peak at 45°. Around 0° and 90°,the average variation in the 6° range was relatively flat,but it deviated greatly from the sinusoid,and as the spatial resolution decreased,the slope and slope direction caused by the reference system direction increased. The experiment suggested that the principle of average slope direction should be complied with in the establishment of independent reference system in a study area,so as to reduce the influence of reference system on slope and slope direction.