Spatial Interpolation

TO USE OR PRINT this presentation click : http://videosliders.com/r/311 ============================================================== Spatial Interpolation Inverse Distance Weighting The Variogram Kriging Much thanks to Bill Harper for his insights in Practical Geostatistics 2000 and personal conversation ,Objectives In this session we will evaluate a dataset and attempt to: Explore the theory and implementation of inverse distance weighting Evaluate issues with IDW interpolation Explore the theory and implementation of the semi-variogram and it’s applicability to interpolation Explore the theory and implementation of kriging and it’s applicability to interpolation ,Simulated Borehole data (PG 2000) Iron concentration Need to interpolate iron content for unsampled areas General Statistics 47 samples Mean value: 36.3 S.D.: 3.73 Data Set ,General Statistics Histogram shows the relative distribution of the data Generally follows a normal distribution Other observations Minor skew, no big deal ,The best unbiased estimate for the standard deviation is 3.726 (see right) Therefore, we are 90% confident that a point drawn at random would be: 30 < T < 42.6 This is based on consulting a students t distribution with 47 samples Data Set ,Subset of borehole data Upper left side General Statistics 7 samples Mean value: 40 S.D.: 2.82 Getting somewhat better Subset of Area (northwest area) ,The best unbiased estimate for the standard deviation is 3.05 (see right) Therefore, we are 90% confident that a point drawn at random would be: 34.2 < T < 45.7 This is based on consulting a students t distribution with 7 samples Now, the question is, do some of the points exhibit more influence than others? Probably, so lets evaluate the point taking nearness into account ,Inverse Distance Weighting IDW works by using an unbiased weight matrix based on the distances from an unknown value to known values. Weights may be defined a number of different ways ,IDW ArcGIS provides a nice interface to view points This example looks at 7 neighbors Now, lets look at it the “old fashioned way…” ,Using 7 neighboring points allows us to interpolate a value based on distances Interpolated value is 39.9 So, our calculation is the same as that in ArcGIS – its just math…. IDW ,We will compute it, without considering the autocorrelation in the data: Standard error 2.75 Therefore, we are 90% confident that a point drawn at random would be: 34.7 < T < 45.1 This is based on consulting a students t distribution with 7 samples IDW – standard Error Caveat: we are treating IDW like weighted mean, and the standard deviation like a weighted standard deviation. In reality, you shouldn’t develop confidence intervals for data that is autocorrelated ,IDW Methods Power = 2, search = 230 Power = 2, search = 600 So which is best??? Power = 2, search = 150 Power = 4, search = 600 ,10 Questions to Evaluate1 What function of distance should we use? H