基于坡度的黑土区切沟密度协同克里格插值方法研究

切沟侵蚀已成为东北黑土区土壤侵蚀的重要组成部分。结合野外样区实地调查切沟分布数据与空间插值方法是快速获取大面积切沟密度值的有效手段。流域的平均坡度值是切沟形成的影响因素之一，为提高切沟密度值空间分布的插值精度，在黑龙江省海伦市内，利用网格法均匀选取40个1 km²左右的小流域，在实地测量区域内切沟密度数据的基础上，应用距离权重反比法、普通克立格和以小流域的平均坡度作为协同变量的协同克立格对其做空间插值。结果表明:切沟密度与协同区域化变量受结构性因素的影响远大于随机性因素，均为强空间自相关性；距离权重反比法与普通克里格法的预测精度相近；协同区域化变量的空间结构性优于单一变量，协同克立格法生成的空间分布图精细度明显提高，均方根误差降低20%以上，预测值与实测值的相关系数提高89%以上，协同克里格可有效提高区域切沟插值精度。

Interpolation of Permanent Gully Density Based on Slope Steepness in Black Soil Area

Gully erosion is serious in northeast China. Combining field-measured gully length density and spatial interpolation is an efficient method to identify gully erosion wizard in large area. Steepness is an important factor affecting gully development. As an auxiliary variable whether it could improve the spatial interpolation performance of gully length density was investigated in this research. The spatial variability of permanent gully density was interpolated by Inverse Distance Weighting, Ordinary Kriging and CoKriging with mean slope steepness of the field sample area from the 40 field-measured sampling data in Hailun county, Heilongjiang Province, located in the black soil area, northeastern of China, and their prediction accuracies were compared. The results indicated that the permanent gully density was strong spatial autocorrelation. The permanent gully density and its coregionalized variables were much more affected by structure factors than stochastic factors. Inverse Distance Weighting got similar prediction accuracy with Ordinary Kriging. Compared with Inverse Distance Weighting and Ordinary Kriging, the accuracy of permanent gully density interpolated by CoKriging was much improved, the root-mean-square error decreased more than 20%, and the determination coefficient between the observed and the predicted values increased more than 89%. Hence, CoKriging is a high accuracy method for the permanent gully density interpolation in northeastern China.