Lecture 17: Spatial Autocorrelation IV Topics: 2.3 Measures based on absolute adjacency 2.4 Measures based on distance between objects Semivariogram References: - Isaaks, E. H., and R. M. Srivastava, 1989. Applied Geostatistics, Oxford University Press, New York, 561 pp. Chapter 7. - Burrough, P.A. and R.A. McDonnell, 1998. Principles of Geographical Information Systems, Oxford University Press, New York, Chapter 6, pp. 132-137.

Outlines 2.4 Measures based on distance between objects 2.4.1 Semivariogram: 1) Calculation of semi-variance: where (h): semi-variance in data values for points of h distance apart N(h): number of pairs of points with h distance apart Zi: the data value at point i (i,j)|dij= h: all pairs of points which are separated by h distance

2) Example of calculating semi-variance 3) Construction of semivariogram (Figure 7.3 in Isaaks) 4) Description of semivariogram (Description of Semivariogram) The ratio of C1/C0 is an important measure of degree spatial autocorrelation 5) Modeling semivariogram a) Purpose of modeling: b) Modeling is a generalization c) Selective models of semivariogram (The five model diagram)

6) Complication of spatial continuity a) Stationarity assumption (i) spatial continuity is omnidirectional (ii) spatial continuity is the same over space b) Complication 2.4.2 Covariance: 2.4.3 Correlation functions:

Questions 1. How is semi-variance defined? Is there a difference between the semi-variance for a pair of points and that for the lag distance the pair of points separated by? 2. Why do people say that the semi-variance for a lag is a generalization? 3. What are the parameters for describing a semivariogram? What does each of them mean? What does it mean when C0 is much greater than C1? 4. When modeling a semivariogram, which part of the semivariogram one should pay special attention? Why do people say that modeling semivariogram adds another level of generalization? 5. What is stationarity assumption? Will it always be true?