Correlogram

The Grids | Calculate | Calculus Fourier and spectral analysis, Grid Correlogram, assesses spatial patterns and spatial correlation of a grid. Correlograms indicate how well grid values correlate across the grid. They indicate underlying trends in the grid and give a measure of the anisotropy of the grid.

Correlograms are symmetric; Z(x,

A contour map of a DEM is shown on the left and the grid correlogram is shown on the right. The heavy line illustrates the approximate directions of anistropy on both maps.

Given gridded data z(u,v), where {u = 0, ..., NX-1} and {v = 0, ..., NY-1} the grid auto-covariance,

$image\img00184.png$

where the summation is over u and v such that

$image\img00185.png$

and $image\img00186.png$ is the arithmetic average of the grid values:

$image\img00187.png$

Note that the grid auto-covariance function is itself a grid.

The grid auto-covariance is the two-dimensional lattice equivalent of the time series auto-covariance function. It is comparable to the two-dimensional variogram; under the appropriate assumptions of statistical stationarity, there is a one-to-one relationship between the grid auto-covariance function and the variogram. (Beware, however, that the variogram of a raw data set - prior to gridding - is not the same as the variogram of the resulting grid.)

The grid correlogram, corr(r,s), is a scaled version of the grid auto-covariance function:

$image\img00188.png$

C(0,0) is the variance of the data in the grid.

The functions C(r,s) and

$image\img00189.png$

but,

$image\img00190.png$

in general. As such, the grids generated by the grid correlogram option of the Grids | Calculate | Calculus sub-system show this symmetry.

Correlogram

See Also