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Lecture-8b_Bb_3SlidesPerPage - Spatial Analysis II Sp...

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Unformatted text preview: Spatial Analysis II Sp Transformations (2 of 2) Overlay Maps Represented As Raster Raster overlay can implement the equivalent operation of polygon overlay But raster overlay brings a lot of flexibility due to its capacity to represent a continuous surface. It can deal with overlays between nominal/ categorical data, and numerical data (ordinal, interval, ratio) Categorical data is represented by index, (e.g. use 1 to represent forest, 2 to represent grass) Raster overlay is relatively easy to implement through Map Algebra Map Algebra Map algebra is a data manipulation language designed specifically for raster based GIS. Map Map algebra is similar to arithmetic algebra but in map algebra algebra, but in map algebra expressions: expressions: The objects are grids or values; Use not only arithmetic but also other statistical operators, such as maximum; • Include many special functions working on an individual cell, or a set of a cell’s neighbors, or the whole grid • Other more complex operations Map Map Algebra Operators can be placed between two input raster two layers (grids), or one raster layer and a number: Addition: [inlayer1] + [inlayer2] OR [inlayer1] + 2 operation: adding the values on a cell-by-cell basis and result written to a new grid. 1 23 1 32 1 11 + 222 222 222 = 345 354 333 Other arithmetic operator (-, *, /, ) has similar operation process Many Many functions (Abs, Int/Float, Sin, Exp, Sqr …) can Int/Float, be applied to ONE grid on a cell-by-cell basis ONE cell-by- ArcMap, Spatial Analyst, Raster Calculator Arithmetic operators: Two grids, cell-by-cell The functions all apply to a raster layer, cell-by-cell Weighted Overlay ArcMap, Spatial Analyst, Raster Calculator Weighted overlay is possible by using Map Algebra: simply multiply each input grid layer with a weight number before addition Complex Complex Statistics Of Two Or More Grids The cell value for output grid can be the statistics of the values of the same cell in all the input grids Complex Statistics Of Two Or More Grids ArcMap, Spatial Analyst, Cell Statistics Supported statistics For categorical data Spatial Interpolation Values of a field are often measured at sample points; always need to estimate values at other points Spatial interpolation is based on Tobler’s first law of geography: Everything is related to everything else, but near things are more related than distant things. If such an assumption doesn’t hold, spatial interpolation will fail Local interpolation The value of a predicted point is estimated based on sample points within a chosen neighborhood Many local interpolation methods. They differ in: • The sample points used • The relative importance of sample points to interpolation Spatial Spatial Interpolation The sample points can be specified in several ways Number of nearest points • But points may be too far away to be of use Points within a neighborwithin neighbor hood search shape • A circle with a fixed radius r. – r should be determined by the phenomena • An ellipse may be used if directional difference is known • To avoid bias in a particular direction, the circle or ellipse can be divided into sectors from which an equal number of points are selected. Thiessen Polygons (Proximity Polygons, For Coverage) Assign un-sampled point with the value at its nearest unsample point Each proximity polygon contains only one sample point, and any location within a polygon is closer to its control point than to the other control points All points within the proximity polygon are assumed to share the same value as the sample point. A B Thiessen Polygons Thiessen Thiessen Polygons Result in a blocky discontinuous surface with abrupt jumps across the boundaries of polygons. Applicability depending on underlying phenomena and the assumption of phenomena, and the assumption of abrupt abrupt change For nominal data, e.g. soil, vegetation types, this approach is often reasonable and useful, although not usually called interpolation Inverse Distance Weighting (IDW) The unknown value of a field at a point is estimated by taking an average over the known values But weighing each known value by its distance from the point, giving greatest weight to the nearest points Point si known value Z(si) distance di0 The estimate is a weighted average unknown value (to be interpolated) At location s0 Weights decline with distance, Issues Issues With IDW The range of interpolated values cannot exceed the range of observed values: Not bigger than the max, Nor smaller than the min in the data It is important to position sample points to It include the extremes of the field This can be very difficult This set of six data points may interpolate into a surface (solid line) different than the real hill profile (dashed line). ...
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