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Raster processing


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Introduction to map algebra

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Raster processing

  1. 1. Raster processing Dr. Hans van der Kwast OpenCourseWare
  2. 2. Learning objectives • After this course you will be able to • Understand different raster data types • Use map algebra for geoprocessing 2
  3. 3. Map algebra • Algebra for manipulating geographic data, developed in the 1980s by Dr. Dana Tomlin • Set of primitive operations in a GIS allowing for 2 or more raster layers of similar dimensions to produce a new raster layer using algebraic operations • Typically executed through a Raster Calculator, Command Line or script. 3
  4. 4. Syntax for operators • Syntax when using mathematical operators (+,-,*,/, etc.): • Result = expression1 operator expression2 −operator: name of the operator −expression1, expression2 are the arguments (i.e. inputs), these can be: −Maps −Expressions resulting in a map (i.e. nesting of expressions is possible) −Result is the return value (i.e. what is created): −One map 4
  5. 5. Syntax for operators • Example 1: multiply two maps (for each cell), arguments are maps: • MapA = MapB * MapC • Example 2: multiply two maps (for each cell), second argument is another expression: • MapA = MapB * (MapC + MapD) 5
  6. 6. Syntax for functions • Syntax when using GIS functions: • Result = function(expression1, expression2, …, expressionn) −function: name of the function −expression1, expression2, …, expressionn are the arguments (i.e. inputs), these can be: −Maps −Expressions resulting in a map −Result is the return value (i.e. what is created): −One map (sometimes more) 6
  7. 7. Syntax for functions • Example 1: calculate the slope of a Digital Elevation Model (DEM): • SlopeMap = slope(DEM) 7
  8. 8. Types of operations • Local or point operations • Focal or neighbourhood operations • Zonal or area operations • Global or map operations 8
  9. 9. Local operations • Independent of the property of neighbouring cells (i.e. no relations in lateral direction) • A new map is generated on a cell-by-cell basis 9
  10. 10. Local operations • Examples: 10 Newmap = MapA + MapB DepthToGroundwater = Elevation – GWLevel PrecTot = 12 * (Precip_jan + Precip_jul) / 2
  11. 11. Focal operations • Relates cells to its neighbours • Different types: 1. Window operations 2. Flow direction operations 3. Friction path operations 4. Transport of material over flow direction map 5. Visibility analysis 11
  12. 12. Focal operations • Examples: 12 AverageElevation = windowaverage(Elevation,3000) Diversity = windowdiversity(Habitats,5000) Slopemap = slope(DEM) RunoffMap = accuflux(LddMap,1000 * RainMm)
  13. 13. Zonal operations • cell value is determined on basis of values of cells which are in the same area as the cell under consideration. • aggregation of cell values over units of cartographic space (areas) 13
  14. 14. Zonal operations • Examples: 14 ClassAverage = areaaverage(temperature,landuse) AverageKsat = areaaverage(ksat,soilmap)
  15. 15. Global operations • computes one non-spatial value as a function of existing cell values of cells associated with a map • value is determined on basis of all cells in a map 15
  16. 16. Global operations • Examples: 16 totalPopulation = maptotal(populationmap) averagePrecipitation = mapaverage(precipitation)
  17. 17. Boolean operations • Boolean maps contain 1 (TRUE) and 0 (FALSE): • Yes/No • Suitable/Unsuitable • Visible/Not visible • Boolean operators result in a boolean map: • AND • NOT • OR • XOR 17 and expression1 Result expression2 True True True expression2 True False False expression2 False True False expression2 False False False or expression1 Result expression2 True True True expression2 True False True expression2 False True True expression2 False False False xor expression1 Result expression2 True True False expression2 True False True expression2 False True True expression2 False False False
  18. 18. Raster calculations and NODATA • For some functions boolean with TRUE and FALSE has a different meaning than a map with TRUE and NODATA • Example: distance calculations calculate the distance from NODATA cells to the cells with a value. So if there are zeros, the resulting map contains only NODATA • Every map algebra operation with NODATA in one input map results in NODATA in the output map. 18
  19. 19. Acknowledgments • The map algebra illustrations were taken from the PCRaster documentation: with permission from the Department of Physical Geography, Faculty of Geosciences, Utrecht University, the Netherlands 19