The KRIG2D function interpolates a regularly- or irregularly-gridded set of points z = f ( x, y ) using kriging. It returns a two dimensional floating-point array containing the interpolated surface, sampled at the grid points.
The parameters of the data model - the range, nugget, and sill - are highly dependent upon the degree and type of spatial variation of your data, and should be determined statistically. Experimentation, or preferably rigorous analysis, is required.
For n data points, a system of n +1 simultaneous equations are solved for the coefficients of the surface. For any interpolation point, the interpolated value is:
The following formulas are used to model the variogram functions:
d( i,j ) = the distance from point i to point j.
V = the variance of the samples.
C( i,j ) = the covariance of sample i with sample j.
C( x 0 , y 0 , x 1 , y 1 ) = the covariance of point ( x 0 , y 0 ) with point ( x 1 , y 1 ).
This routine is written in the IDL language. Its source code can be found in the file
subdirectory of the IDL distribution.
Arrays containing the Z , X , and Y coordinates of the data points on the surface. Points need not be regularly gridded. For regularly gridded input data, X and Y are not used: the grid spacing is specified via the XGRID and YGRID (or XVALUES and YVALUES) keywords, and Z must be a two dimensional array. For irregular grids, all three parameters must be present and have the same number of elements.
If specified, C1 is the covariance value for a zero distance, and the variance of the random sample z variable. If only a two element vector is supplied, C1 is set to the sample variance. (C0 + C1) = the sill , which is the variogram value for very large distances.
If set, the Z parameter is a two dimensional array of dimensions ( n,m ), containing measurements over a regular grid. If any of XGRID, YGRID, XVALUES, or YVALUES are specified, REGULAR is implied. REGULAR is also implied if there is only one parameter, Z . If REGULAR is set, and no grid specifications are present, the grid is set to (0, 1, 2, ...).
The output grid spacing. If present, GS must be a two-element vector [ xs, ys ], where xs is the horizontal spacing between grid points and ys is the vertical spacing. The default is based on the extents of x and y . If the grid starts at x value xmin and ends at xmax , then the default horizontal spacing is ( xmax - xmin )/(NX-1). ys is computed in the same way. The default grid size, if neither NX or NY are specified, is 26 by 26.
If present, BOUNDS must be a four-element array containing the grid limits in x and y of the output grid: [ xmin, ymin, xmax, ymax ]. If not specified, the grid limits are set to the extent of x and y .