Geographic Info Systms
Geographic Info Systms GEOG 350
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This 6 page Class Notes was uploaded by Cortney Leuschke on Saturday September 12, 2015. The Class Notes belongs to GEOG 350 at West Virginia University taught by Staff in Fall. Since its upload, it has received 24 views. For similar materials see /class/202690/geog-350-west-virginia-university in Geography at West Virginia University.
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Date Created: 09/12/15
Spatial Analysis Longley et al Ch 1415 Transformations Buffering Point Line Area Pointinpolygon Polygon Overlay Spatial Interpolation Theissen polygons Inversedistance weighting Kriging Density estimation Basic Approach Map Newmap Transluvmatiun Pointinpolygon Seieel pumt knuwn m be outside Seieel pumttu be leslee Create ime segment intersect With all boundary segments Count intersectiuns EVENOUTS DE ODD NS DE Create a buffer Raster MK Create a Buffer vector Combining maps RASTER As long as maps have same extent resolution etc overlay is direct pixelto pixel Otherwise needs interpolation Use map algebra Tomlin Tomlin s operators Focal Local Zonal Combining Maps VECTOR A problem Max Egenhofer Topological Overlay Relations C12 Creating new zones Rivevhimev Other spatial analysis methods Centrographic analysis mean center Dispersion measures stand Dist Point clustering measures NNS Moran39s I Spatial autocorrelation Clustering of neighboring values Fragmentation and fractional dimension Spatial optimization 7 F39Elirit 7 Ruute Spatial interpolation Moran s mv msasquotmmanngwmmapmmmmm Spatial autooorrelation Correlation ofa eld with itself ngh Maumum Spatial optimization Spatial interpolation Hallwavtmm AtnEl Value ls A a l 2 Nonlinear Interpolation When things aren39t or shouldn t be so simple Values computed by piecewise moving window asic types 1 Trend surface analysis I Polynomial 2 Minimum Curvature Spline 3 Inverse Distance Weighted 4 Kriging 1 Trend SurfacePolynomial o poin tbased Fits a polynomial to input points When calculating function that will describe surface uses leastsquare regression fit 0 approximate interpolator r Resulting surface doesn t pass through all data polnts a global trend ln data varying slowly overlain by local but raold fluctwtlons 1 Trend Surface cont flat but TLTED plane to fit data surface is approximated by linear equation polynomial degree 1 z a bx cy tilted but WARPED plane to fit data surface is approximated by quadratic equation polynomial degree 2 zabxcydx2exyfy2 Trend Surfaces 4 2nd dzgvee new mac 2 Minimum Curvature Splines Fits a minimumcurvature surface through input points Like bending a sheet of rubber to pass through points While minimizing curvature of that sheet repeatedly applies a smoothing equation piecewise polynomial to the surface Resulting surface passes through all points best for gently varying surfaces not for rugged ones can overshoot data values 3 Distance Weighted Methods 7 unknown elevation 4 known elevations 3 Inverse Distance Weighted Each input point has local in uence that diminishes with distance estimates are averages of values at n known points within window R r i V i u Z ZI UJquot iL 1 where w is some function of distance eg w 1ldk 20039 so as M 250 150 50 Distance 4 55039 7 300 IDW IDW is popular easy but problematic Interpolated values limited by the range of the data No interpolated value will be outside the observed range of 2 values How many points should be included in the averaging What about irregularly distributed points What about the map edges IDW Example ozone concentrations at CA measurement stations 1 estimate a complete eld make a map 2 estimate ozone concentrations at speci c locations eg Los Angeles Ozone in S Cal Text Example measuring stations am concentrations pmm shape iEJ CA outline Palvgan an ipe iei DEM vasevi IDW V zard in Geostatistical Analyst 7 de ne data source Mm maaammwwmmm Ihvlvmlwmhpw uwn nmhA I hiuaivul ww mmmnwi m ma u a39quot 39 39 quot lr39 l quot Further define interpolation method Power of mm Cross validation Result puinlslu mam nsvaiue En bsevved r mama 21 4 Kriging Assumes distance or direction betw sample points shows a spatial correlation that help describe the surface Fits function to Specified number of points OR All points within a window of specified radius Based on an analysis of the data then an application of the results of this analysis to interpolation Most appropriate when you already know about spatially correlated distance or directional bias in data Involves several steps Exploratory statistical analysis of data Variogram modeling Creating the surface based on variogram Kriging o Breaks up topography into 3 elements Drift general trend small deviations from the drift and random noise Random my spalially summed ulevzlinnul uctuations Ranmm nmse boulders To he stepped av Dnl lguneral elevalienal trend Kriging Result similar pattern to IDW less detail in remote areas smooth IDW vs Kriging Kriging appears to give a more smooth look to the a data Kriging avoids the bulls eye effect Kriging gives us a standard error