Ordinary Kriging Interpolation

Feature Description

The Ordinary Kriging method is the most commonly used and widely applicable form of Kriging. This method assumes that the expectation (mean) of the interpolated field values is unknown and constant.

  • Data used for Ordinary Kriging should conform to the assumption of normal distribution.
  • The key feature of Ordinary Kriging interpolation is not only providing prediction values with minimal estimation errors, but also explicitly indicating the magnitude of error values.
  • Ordinary Kriging uses two approaches to select sample points for interpolation prediction:
    1. Collect all sample points within a specified radius around the prediction location.
    2. Select a fixed number of nearest sample points around the prediction location.
    Both approaches use specific interpolation formulas to calculate predicted values.

Open the "Precipitation" datasource in the "ExerciseData/RasterAnalysis" folder, which contains precipitation data from weather monitoring stations. We'll use this data for demonstration.

Feature Entry

  • Spatial Analysis Tab->Raster Analysis group->Interpolation Analysis->Ordinary Kriging.
  • Toolbox->Raster Analysis->Interpolation Analysis->Ordinary Kriging.

Parameter Description

Fixed Count: Uses a fixed number of sample points within maximum radius for interpolation.

Fixed Radius: All points within specified radius participate in interpolation.

Block: Divides dataset into blocks based on "Maximum Points per Block".

Semivariogram: Supports Spherical, Exponential, and Gaussian models. Selection depends on spatial autocorrelation and prior knowledge. Default: Spherical.

Rotation: Counter-clockwise rotation angle of search neighborhood. Default 0°. Not applicable for Block mode.

Sill: Semivariogram's plateau value where it stabilizes. Default 0.

Range: Distance where semivariogram reaches sill. Default 0.

Nugget: Semivariogram's intercept at zero distance. Default 0.

For parameter relationships, see: Kriging Interpolation.

Figure: Ordinary Kriging Interpolation Result
  • Set common parameters for interpolation analysis including source data, bounds, result data and environment settings. For parameter details see: Common Parameter Description.
  • Search Mode: Supports three approaches - Fixed Count, Fixed Radius, and Block. Detailed explanations: About Interpolation.
    • Maximum Radius: Defines search radius for fixed count. Default 0 indicates maximum radius search.
    • Point Count: Specifies number of sample points to use. Default is 12.
    • Search Radius: Defines search area. Default is 1/5 of dataset's longer dimension.
    • Minimum Points: Minimum required points (default 5). Search radius expands until reaching this threshold. Maximum 12.

    These parameters directly affect block search performance. Larger values increase computation time. Set reasonable values accordingly.

    • Maximum Points: Total points used per interpolation (default 200). Should be greater than "Maximum Points per Block".
    • Maximum Points per Block: Maximum points within each block (default 50). Blocks exceeding this will subdivide further.
  • Other Parameters: Includes semivariogram, rotation angle, mean value, sill, range, and nugget effect.