1. Geog. 579: GIS and Spatial Analysis - Lecture 21 Overheads 1 Point Estimation: 3. Methods: 3.3 Local sample mean (Moving average) 3.4 Inverse distance method Topics: Lecture 21: Spatial Interpolation IV References: - - Chapter 11, Isaaks, E. H., and R. M. Srivastava, 1989. Applied Geostatistics, Oxford University Press, New York - - Chapter 5, Burrough, P.A. and R.A. McDonnell, 1998. Principles of Geographical Information Systems, Oxford University Press, New York, pp. 113-117.

2. Geog. 579: GIS and Spatial Analysis - Lecture 21 Overheads 2 Outlines 3. Methods: 3.3 3.3 Local sample mean (Moving average) 3.3.1 The Idea: 3.3.1 The Idea: Use the average condition of the nearby neighborhood around Use the average condition of the nearby neighborhood around the site to estimate the value at the site the site to estimate the value at the site 3.3.2 Implementation: 3.3.2 Implementation: (1) Fixed window size implementation (1) Fixed window size implementation Use the sample points only in a specified window (radius) Use the sample points only in a specified window (radius) (Fixed Window Size Figure) (Fixed Window Size Figure)Fixed Window Size FigureFixed Window Size Figure The number sample points can vary from location to location The number sample points can vary from location to location There may be times that there are no samples in the window There may be times that there are no samples in the window (2) Fixed sample size implementation (2) Fixed sample size implementation Use selected number of sample points around the site Use selected number of sample points around the site (Fix Sample Size Figure) (Fix Sample Size Figure)Fix Sample Size FigureFix Sample Size Figure There may be times that distant (irrelevant) sample points are There may be times that distant (irrelevant) sample points are used to meet the number of sample point requirement used to meet the number of sample point requirement

3. Geog. 579: GIS and Spatial Analysis - Lecture 21 Overheads 3 3.3.3 The issues: 3.3.3 The issues: 1) Number of sample points: vary 1) Number of sample points: vary less sensitive to the accuracy of one point less sensitive to the accuracy of one point 2) Distribution of sample points: need quadrant search 2) Distribution of sample points: need quadrant search 3) Weight allocation: equally weighted (1/n) 3) Weight allocation: equally weighted (1/n) 4) Uncertainty information: variance can be used as uncertainty 4) Uncertainty information: variance can be used as uncertainty 3.4 Inverse Distance Method: 3.4.1 The Idea: 3.4.1 The Idea: Distance is inversely related to the weight assigned to each point Distance is inversely related to the weight assigned to each point (close things are more related than distant things) (close things are more related than distant things) w i =f(1/d i0 q ) w i =f(1/d i0 q ) where: where: w i is the weight assigned to the ith selected sample point w i is the weight assigned to the ith selected sample point d i0 is the distance between the site and the ith sample point d i0 is the distance between the site and the ith sample point q is a distance decay coefficient determining how fast weight q is a distance decay coefficient determining how fast weight will decrease as distance increases (The q Figure) will decrease as distance increases (The q Figure)The q FigureThe q Figure

4. Geog. 579: GIS and Spatial Analysis - Lecture 21 Overheads 4 3.4 Inverse Distance: (continued …) 3.4.2 Implementation: 3.4.2 Implementation: (1) Fixed window size implementation (1) Fixed window size implementation (Fixed window size Figure) (Fixed window size Figure)Fixed window size FigureFixed window size Figure (2) Fixed sample size implementation (2) Fixed sample size implementation (Fixed sample size Figure) (Fixed sample size Figure)Fixed sample size FigureFixed sample size Figure 3.4.3 The Issues: 3.4.3 The Issues: 1) Number of sample points: vary 1) Number of sample points: vary less sensitive to the accuracy of one point less sensitive to the accuracy of one point 2) Distribution of sample points: need quadrant search 2) Distribution of sample points: need quadrant search 3) Weight allocation: f(1/d i0 q ) 3) Weight allocation: f(1/d i0 q ) 4) Uncertainty information: none 4) Uncertainty information: none 5) How to determine the value of distance decay coefficient? 5) How to determine the value of distance decay coefficient? (Impact of Distance Decay Coefficient Figure) (Impact of Distance Decay Coefficient Figure)Impact of Distance Decay Coefficient FigureImpact of Distance Decay Coefficient Figure

5. Geog. 579: GIS and Spatial Analysis - Lecture 21 Overheads 5 1. What is the idea behind the local same mean (moving average)? How is information on spatial autocorrelation used in this approach? What are the major issues associated with this method? 2. What does the variation of sample values within a neighborhood say about the estimated value at the site in this neighborhood? 3. What is the idea behind the inverse distance approach? How is information on spatial autocorrelation used in this approach? What are the major issues associated with this method? 4. What does the distance decay coefficient measure do? What are the ways which can help us to choose a proper value for it? 5. What is the weight for a sample point in a pool of 4 sample points with distance to the estimation site to be (d 1, d 2, d 3, d 4 ) using a distance decay value of q? Questions