The Interpolation Window provides access to Kriging, Cokriging, Conditional Simulation, and Inverse Distance Weighting techniques for estimating values for points not sampled. Interpolation produces an output file that is used by GS+ for mapping. The output file can also be read by other mapping programs.
Defines where to place interpolation estimates – in a regularly spaced grid across a rectangular area or at user-specified locations, in either case with or without masks that can define areas to include or exclude.
• Regular x-y grid (specified intervals)
A grid is defined by a rectangle that has an X-direction length, a Y-direction length, and for each direction, intervals between the grid intersections. Interpolation locations are at every grid intersection.
The default range is defined by the minimum and maximum X-coordinate and Y-coordinate values, and an interval based on a certain number of points in each direction. For 1-dimensional data sets, there is no y direction.
The grid can be changed with the Define command, which will display an Interpolation Grid dialog window.
• Irregular x-y grid (specified points)
A nonuniform grid is composed solely of interpolation locations specified by the user. Press Define to bring up an Interpolate Worksheet within which locations can be defined or imported from an external text file.
• Include irregular shapes (polygons)
An irregular grid is composed solely of interpolation locations specified by the user. Press Define to bring up a Polygon Outlines Worksheet within which to define polygons.
• In inclusive polygons, the area within the polygon is interpolated.
• In exclusive polygons, the area within the polygon is not interpolated.
• Constrain Z estimates
The estimated Z values (interpolates) can be constrained to a specific range. For example, if values less than zero are inappropriate you can specify that Z estimates less than zero be reported as zero. Press Define to bring up a worksheet to specify Z Estimate Boundaries.
Press Select to select an existing or new file to which kriging interpolation estimates will be written. For existing files, you may examine the contents of the file by pressing View.
The format with which GS+ will write estimates to the file can be one of several types:
• GS+ Krig format (.krg) – in this format a header area defines the interpolation grid, variate names, and other information about the file needed to initiate mapping later, and the data records include for each X and Y Coordinate location that is kriged the interpolation or Z-estimate, the standard deviation of the Z-estimate, and the number of neighbors that were used to make the estimate.
• Surfer Grid format (.grd) – in this format a short header area defines information needed for mapping, and the data is written as a continuous stream of Z-estimates beginning from a specific corner of the interpolation grid. The standard deviation of the estimate and the number of neighbors used for interpolation are NOT included in this format. This format is compatible with Golden SoftwareSurfer mapping program. Note that this format is not the same as the Surfer XYZ Input file format.
• ArcView Format (.asc) – this is similar to the Surfer format but the header area is formatted differently and the Z-estimates are written in a pattern that begins from a different corner of the interpolation grid. The standard deviation of the estimate and the number of neighbors used for interpolation are NOT included in this format. Also for this format, the x and y interpolation intervals must be the same (you can set them to be the same from the Interpolation Grid dialog window). This format is compatible with ESRIArc-Info Geographic Information System.
• GSLib Format (.out) – this format is similar to the GeoEas input format. A long first record contains coordinate interval information that is read by GS+ when mapping GSLib files. The second record of the file specifies three header records named “estimate,” “estimation variance” (or “standard deviation”), and “neighbors.” Records that follow are in the same order as for Surfer® , but there are three fields per record (estimate, estimation error, and number of neighbors) rather than just one field (the Z-estimate).
You may choose to report estimation error as estimation variance or as estimation standard deviation.
GS+ interpolates values for a specific location using nearest neighbor values weighted by distance. Only a certain number of near neighbors are used to calculate the interpolation estimate, and neighbors can be required to be within a particular geographic area around the location being estimated.
The default value of 16 nearest neighbors is usually sufficient, and also by default no restrictions are placed on the neighborhood radius (in Kriging, neighbors outside of the variogram range are weighted identically and, if significant structural dependence is present, weighted minimally). Specifying more than 16 neighbors can slow interpolation substantially, although up to 64 neighbors are allowed. The geographic area to be searched can be either round or elliptical; if elliptical, the angle of the ellipsoid in addition to its width and length must be specified – the default angle is the same as the anisotropic axis orientation used for semivariance analysis.
Additionally, you may specify an octant search, in which the geographic neighborhood is divided into 8ths, and only a limited number of neighbors within the octant are used for interpolation. This is useful when there are many more neighbors on one side of an estimation location than on another, and there is a danger of using a disproportionate number of neighbors from that side. An octant search limits the number of neighbors that can be used from any given octant.
When cokriging, you may specify a separate set of search criteria for the covariate (Z2). These criteria are set on the Covariate tab of the Search box.
You may choose to interpolate using either Kriging, Cokriging, Conditional Simulation, or IDW (Inverse Distance Weighting) by choosing one or the other tabs on the right hand side of the window; click Kriging, Cokriging, IDW, or Simulate for a description of options on each tab:
Perform interpolation analysis. During analysis values are written to the output file in the specified format. You can stop analysis by pressing the <Escape> key or the Cancel button on the progress bar.
Validation
Two types of validation are provided by GS+: Cross-validation and Jackknife analysis. In cross-validation analysis each measured point in the spatial domain is individually removed from the domain and its value estimated as though it were never there. Then the point is replaced and the next point is removed and estimated, and so on. In this way a graph can be constructed of estimated vs. actual values for each sample location in the domain.
In Jackknife analysis, estimates are compared against measured values for a set of locations different from those used as input data. The jackknife data are specified in a worksheet that appears when the “Define” command is pressed.