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Lab: geostatistics

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.

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Lab: geostatistics

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

  2. 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

  3. 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…]

  4. 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

  5. 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

  6. 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

  7. 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.

  8. 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

  9. 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

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