基于Kriging的地形高程插值

将地形高程作为区域化变量,根据普通Kriging法由散乱的高程点进行地形高程插值,并采用Matlab软件开发专门的程序,实现研究区高程插值计算与结果可视化分析。以广州市南沙区10 km2范围内的200个高程点数据为例,分别运用球面模型、指数模型和高斯理论变差函数模型进行10 m×10 m格网插值,借助Matlab可视化分析插值结果及其精度,表明采用指数模型效果最好。

Terrain Interpolation Based on Kriging Method

Kriging arithmetic is an optimum,linear,unbiased method for estimative value interpolation,which is suitable for terrain interpolation.In order to get accurate digital elevation model by scattered sample points,this paper applies ordinary Kriging arithmetic to elevation interpolation,and designs complete procedure and special programs for terrain interpolating and analyzing based on Matlab software.The research originated from terrain 3D modeling in Nansha district of Guangzhou,and sample data are 200 altimetric points covering 10 km2.As local variable,the correlation of terrain elevation decreases with the increasing of distance,and sample points are divided into groups by difference distance.According to formula of experiment variation and elevation variations,each group can be calculated and approached theory semivariogram of the sphere model,index model and Gauss model.After contrasting deviations of three models,the index model was chosen to compute semivariogram matrix of all sample points.Kriging vector is made by distance between sample points with a grid to be evaluated.Then,lagrange modulus for the grid is calculated.So,the z value and deviation variance of the grid are computed.Perhaps most importantly,the error variances of Kriging estimates are the minimum possible of any linear estimation method,and they can be estimated at every location where a Kriging estimate is made.It is concluded that ordinary Kriging is right for terrain interpolation of the study area and the result by index model is the best.