Instructions for use

The Ordinary Kriging method is the most common and widely used Krugin method. This method assumes that the expectation (average) of the field values used for interpolation is unknown and constant.

• The data used in the Ordinary Kriging method should conform to the assumption that the data changes are normally distributed.
• The most important feature of Ordinary Kriging interpolation is not only to provide a predicted value with minimum estimation error, but also to clearly indicate the size of the error value.
• The Ordinary Kriging method uses two ways to obtain the sampling points involved in the interpolation, and then obtain the predicted value of the corresponding position point: one is to obtain all the sampling points within a certain range around the position point of the predicted value to be calculated, and obtain the predicted value of the position point through a specific interpolation formula; The other is to obtain a certain number of sampling points around the position point of the predicted value to be calculated, and obtain the predicted value of the position point through a specific interpolation calculation formula.

Open the "Precipitation" Datasource "under the" Exercise Data/RasterAnalysis "folder, where there is precipitation data of meteorological monitoring stations in some regions. We use this data as an example.

Function Entry

• Spatial Analysis tab-> Raster Analysis group-> Interpolation Analysis-> Ordinary Kriging.
• Toolbox-> Raster Analysis-> Interpolation Analysis-> Ordinary Kriging. (iDesktopX)

Parameter Description

• Set public parameters for Interpolation Analysis, including Source Data, Bounds, Result Data, and Environment Settings. For the settings of public parameters such as source data, Bounds, and Result Data, please refer to Public Parameter Description .
• Set the sample point search mode: Fixed Count, Fixed Radius and block search are supported. For a detailed description of these three lookup methods, see: About interpolation .

Fixed Count: indicates to interpolate by using a fixed number of sample values within the maximum radius.

• Max Radius: Enter the size of the radius to use for Fixed Count. The default value is 0, which means to use the maximum radius to find.
• Find Points: Enter the number of points to use for Fixed Count. The default point is 12.

Fixed Radius: All points within the search radius are involved in the interpolation operation.

• Search radius: Enter the size of the set search radius. The default lookup radius is 1/5 of the larger value of the length or width of the range of the Dataset participating in the Interpolation Analysis. All the sampling points within the radius range shall participate in the interpolation operation.
• Minimum number of points: Enter the minimum number of points to be used for Fixed Count. The default is 5 points. When the number of points in the neighborhood is less than specified minimum, the lookup radius increases until it can contain the minimum number of points entered. The maximum value is 12.

Block Search: The Dataset is divided into blocks according to the set "Maximum number of points in a block", and then the points in the block are used for interpolation.

• Max Participation Points: Enter the Max Participation Interpolation Points. The default maximum number of participating interpolation points is 200. In order to avoid the appearance of cracks in the interpolation, the interpolation block used in the actual calculation will expand outward evenly on the basis of each block area, and the "maximum number of participating points" determines the size of the block area's outward expansion. Generally, this value should be greater than "maximum number of points in a block" set.
• Maximum number of points in a block: Enter the maximum number of points in each block. The default maximum number of points within a block is 50. If the number of points in the block is more than this value, the block division is continued; otherwise, the block division is stopped.

The setting of the Max Participation Points and Max Points in Block parameters directly affects the performance of fast lookups. The larger these two values are set, the longer the search will take, so it is recommended that users set more reasonable parameters when setting the parameters for fast search.

• Other Parameters: including semivariogram, Rotation angle, average value, sill value, autocorrelation threshold, nugget effect value, etc.

Semivariogram: Support spherical function, Exponential and Gaussian semivariogram. Which model to use depends on the Spatial Autocorrelation of the data and the prior knowledge of the data phenomena. Spherical functions are used by default.

Rotate: The angle by which each lookup neighborhood is rotated counterclockwise relative to the horizontal. The default is 0 degrees. Block lookup does not support Rotation Settings.

Abutment value: The vertex value reached by the semivariogram, that is, the value at which the semivariogram intersects the Y axis at a distance (X axis) of 0. The default is 0.

Autocorrelation threshold: The distance at which the semivariogram reaches the sill value, that is, the corresponding value of the X axis. The default value is 0.

Nugget Effect Value: The value at which the semivariance function intersects the Y axis at H = 0 (X axis). The default is 0.

See Kr Krügin interpolation for the relationship between the sill value, the autocorrelation threshold, and the nugget effect.

Figure: Ordinary Kriging interpolation result