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Figure 13.5 Spatial autocorrelation analysis of artificial spatial structures shown on the left: (a) nine bumps;

(b) waves; (c) a single bump. Centre and right: all-directional correlograms. Dark squares: autocorrelation statistics that remain significant after progressive Bonferroni correction (a = 0.05); white squares: non-significant values.

study area. The correlogram is said to be all-directional or omnidirectional. Directional correlograms, which are computed for a single direction of space, are discussed together with anisotropy and directional variograms in Subsection 3.

Correlograms are analysed mostly by looking at their shapes. Examples will help clarify the relationship between spatial structures and all-directional correlograms. The important message is that, although correlograms may give clues as to the underlying spatial structure, the information they provide is not specific; a blind interpretation may often be misleading and should always be supported by maps (Section 13.2).

Numerical example. Artificial data were generated that correspond to a number of spatial patterns. The data and resulting correlograms are presented in Fig. 13.5.

• Nine bumps — The surface in Fig. 13.5a is made of nine bi-normal curves. 225 points were sampled across the surface using a regular 15 x 15 grid (Fig. 13.5f). The "height" was noted at each sampling point. The 25 200 distances among points found in the upper-triangular portion of the distance matrix were divided into 16 distance classes, using Sturge's rule (eq. 13.3), and

(d) Gradient

Moran's correlograms

Geary's correlograms

(d) Gradient

Moran's correlograms

Geary's correlograms

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