高程梯度性质和算法不确定性的初步分析

高程梯度指高程在平面坐标中x和y两个方向上的变化率。在坡度算法θ=（p²+q²）/2中分别用p和q表示，因为高程梯度p和q算法的不同而衍生出多种坡度算法，因此对p，q算法性质和精度的研究是坡度算法精度评价的基础。选取陕西省绥德县、秦岭、黑龙江省拜泉县的三个样区，基于7种不同算法计算了高程梯度（p和q），并对其统计分布特征、空间结构特征、p和q相互关系、算法稳定性与不确定性等进行了分析。结果表明:（1）p和q均值为零，相互独立，方差相等，呈正态分布；（2）各种算法均能表现局地结构和样区之间的差异；（3）从算法稳定性、精度等方面看，Evans-Young算法，特别是经过Shary改进的Evans-Young算法的效果最佳。

Preliminary Properties and Precision Analysis of Elevation Gradient Algorithm

Elevation gradient is the ratio of the elevation in x & y direction of Cartesian coordinate system,usually they are denoted as p and q in the general algorithm of slope steepness,i.e.θ =(p2+q2)/2.The differences of varied slope algorithms are mainly due to the different algorithms of p and q,and therefore,the accuracy of slope steepness depends on the precision of p and q algorithms,p and q have been calculated and analyzed in seven p/q algorithms in three sample sites,including Suide and Qinling of loess hills in Shaanxi Province,Baiquan of undulate hill in Heilongjiang Province.The analysis includes statistical distribution and spatial pattern (or structure) of p and q,the interrelation of p and q,the stability and uncertainty of algorithms.The results show that:(1) the mean values of p and q are almost zero,p and q are independent from each other,the variance of p and q are equal,and they follow the pattern of normal distribution;(2) all algorithms can represent the local structure and the differences among the sample sites;(3) with respect to the algorithm stability and uncertainty,Evans-Young algorithm,especially the improved EvansYoung algorithm by Shary is the best.