Lab: geostatistics Peter Fox GIS for Science ERTH 4750 (98271) Week 11, Friday, April 13, 2012

Statistics http://escience.rpi.edu/gis/data/radon2.xls The uncertainty in a value estimated by weighted averages is one over the square root of the sum of the weights. Use IDW to estimate the uncertainties in estimated values at (73.58W, 42.69N), at (73.45W, 42.83N), and at (73.46W, 42.51N) Hint: week5b slides and Excel for the calculations

Statistics http://escience.rpi.edu/gis/data/radon3.xlsx (originally from http://www.health.state.ny.us/nysdoh/radon/tables/county/rensselaer.htm ) Geocode the table by place names using Rens2000 and common sense. [You might add the lon/lat to your table…]

Statistics The uncertainty in a value estimated by weighted averages is one over the square root of the sum of the weights. Use IDW to estimate the uncertainties in estimated values at three different locations of your choosing, e.g. could be a place, street address or just a lon/lat

Statistics http://escience.rpi.edu/gis/data/radon3.xlsx Perform a weighted regression to fit basement radon based on living room radon Hint: http://escience.rpi.edu/gis/data/wtd_regression.xls contains all the Excel formulae Extra: Perform a weighted regression to fit living room radon based on basement radon

Recall Letting x represent the position vector (x, y) and assuming the variances in the differences between any 2 measurements depends only on the distance between them: E [ { z(x) – z(x+h) }2] = E [ { F'(x) – F'(x+h) }2] = 2 G(h). G(h) is known as the semivariance G(h) = (2n)-1 SUM i=1,n { z(xi) – z(xi + h) }2

Semivariance This represents a sum of the differences squared for all pairs of points that are a distance h apart. Typically one calculated G (h) for a range of distances and plots G (h) vs. h.

Semi-variance http://escience.rpi.edu/gis/data/radon2.xls Calculate the semi-variance and plot it In Excel (not the best way to do it but it will give you the idea) Calculate Hij=sqrt((Xi-Xj)^2+(Yi-Yj)^2) Zij=(Z(Xi,Yi)-Z(Xj,Yj))^2 Determine what the range of ‘h’ is and determine a reasonable number of ‘bins’ Then, over all i,j put Zij into one of those bins (to produce the smoothed (or not) curve Hint, do this for a sub-sample of radon2 to start

See the MapBasic program http://escience.rpi.edu/gis/mbprogs/semi-variance.mb As an example of what a simpler and basic piece of code looks like. NB. This has to be compiled to run, it will not work at the MapBasic window command line