Several GIS spatial interpolation methods

GIS spatial interpolation method is as follows:

1、IDW

IDW is a common and simple spatial interpolation method, which takes the distance between the interpolation point and the sampling point as the weight to average. The closer the sampling point is, the greater the weight is given. Suppose a series of discrete points are distributed on a plane, and their coordinates and values are known as Yi, Zi (i = 1, 2, ..., n). Find the value of z point by distance weighting.

IDW obtains the interpolation unit by averaging the values of each sampling point in adjacent areas. This method requires that the discrete points are evenly distributed and the density is enough to reflect the change of local surface in the analysis.

2. Kriging interpolation

Kriging method is a regression algorithm for spatial modeling and prediction (interpolation) of random process/random field according to covariance function.

Kriging method can give the best linear unbiased prediction (? BLUP), so it is also called spatial optimal unbiased estimator in geostatistics.

The research on kriging can be traced back to 1960s, and its algorithm prototype is called ordinary kriging (OK). Common improved algorithms include pan-kriging (UK), co-kriging (CK) and disjunctive kriging (DK). Kriging method can be combined with other models to form a hybrid algorithm.

3. Natural proximity method

The principle is to construct voronoi polygons, that is, Tai Sen polygons. Firstly, all spatial points are constructed into voronoi polygons, and then the points to be solved are also constructed into a voronoi polygon, which has many intersections with circular polygons. According to the area of each block, the values of the points to be solved can be obtained by setting the weights in proportion. Personally, I feel that this spatial interpolation method has no practical significance to support.

4. Spline interpolation of spline function

In the numerical analysis of mathematics, spline is a special function, which is defined by polynomial segments. Spline, English for Spline, comes from deformable spline tool, which is used to draw smooth shapes in shipbuilding and engineering drawing. In Chinese mainland, it was called "tooth function" in the early days. Later it was named after the word "lofting" in engineering terminology.

In interpolation problems, spline interpolation is usually better than polynomial interpolation. Using low-order spline interpolation can produce similar effects as high-order polynomial interpolation, and numerical instability called Runge phenomenon can be avoided. Low-order spline interpolation also has the important property of "convexity preservation"

5, terrain to grid

This method is suitable for all kinds of vector data, especially for contour data.

6. Trends

According to the known values of X series and Y series, a linear regression linear equation is constructed, and then the Y series corresponding to X series is calculated according to the constructed linear equation. The results calculated by the trend function and the prediction function are the same, but the calculation process is completely different.