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Measurement

Measurement. GEOG 370 Instructor: Christine Erlien. Outline. Why do we care? Quantifiable attributes allow comparisons Measurements Lines: Length, sinuosity Polygons: Length, perimeter, area, shape Distance: simple distance, functional distance (shortest path, least cost). A. A. B.

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Measurement

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  1. Measurement GEOG 370 Instructor: Christine Erlien

  2. Outline • Why do we care? • Quantifiable attributes allow comparisons • Measurements • Lines: Length, sinuosity • Polygons: Length, perimeter, area, shape • Distance: simple distance, functional distance (shortest path, least cost)

  3. A A B B Measuring Linear Objects • 1D: Length Vector • Distance measurements affected by elevation changes • Easily calculated with computer

  4. Measuring Linear Objects Raster • Add up # grid cells, multiply by resolution • But what about diagonal or highly sinuous lines? • Length possibly underrepresented Take home: Vector best for length calculations!

  5. Measuring Polygons • 2D: Length, width • More dimensionality, more measurements! • Orientation, elongation, perimeter, area, shape

  6. Measuring Polygons: Length Vector • Calculate lengths of all opposing polygon vertices • Compare to see which is longest • Ratio of major to minor axes  elongation • Easiest for convex polygons

  7. Measuring Polygons: Perimeter Vector • Calculate & sum the distance of each line segment making up polygon Raster • Identify perimeter cells, sum & multiply by cell resolution • Less accurate for complex polygons • Take home: Vector best for perimeter calculations!

  8. Vector Simple polygons (e.g., rectangle, triangle, circle)easy calculation Complex polygonsdivide polygon into shapes easily measured with available formulas Often calculated during the digitizing process Perimeter/area ratio: Measure of polygon complexity Measuring Polygons: Areas

  9. Measuring Polygons: Areas Raster • Regions • Assign a unique value to each region (recode/reclassify), then count the number of cells for each region & multiply by area • Tabulate data to find # grid cells for each attribute • Provides measure of proportion of different attribute types

  10. Measuring Shape: Sinuosity • Relating objects to their environment • Sinuosity • Closer to 1, less sinuous • Sometimes want to know about curvature http://forest.mtu.edu/staff/mdhyslop/gis/sinuosity.html

  11. Measuring Shape: Polygons • Spatial integrity: Measure of the amount of perforation in a perforated region • Euler function • Measures fragmentation & perforation • Euler number = (# holes) – (#fragments –1)

  12. Measuring Shape: Polygons • Boundary configuration • Convexity index: Compares polygon shape to that of a circle (most compact shape) CI=kP/A k=constant, P=perimeter, A=area Perfect circle will have a value of 100 Can also be calculated for raster

  13. Measuring Shape: Polygons • Boundary configuration • Edginess: Measure of amount of edge for a polygon • Filters (roving windows) applied to remote sensing data result in edge enhancement or smoothing • Edge enhancement  edges become more prominent • Smoothing  averaging of values

  14. Measuring shape: Polygons From Demers (2005) Fundamentals of Geographic Information Systems

  15. Measuring Distance Euclidean distance: Calculation of simple distance Isotropic surface: Measures distance outward from a single point throughout a coverage; no obstructions or frictional changes exist After Demers (2005) Fundamentals of Geographic Information Systems

  16. Measuring Distance • Surface distance • Can be calculated by vector data model (TIN)  computationally expensive • Best to defer to raster for surface calculations

  17. Measuring Distance • Functional Distance: Measurement of non-Euclidean distance as a function of a variable such as time, energy, expense • Friction surface: Movement across non-isotropic surfaces incurs a cost • Example: Topography, a continuous variable, may impose a friction value based both on surface roughness and/or vegetation variables

  18. Measuring Distance • Barriers: Objects whose attributes stop or impede movement through the rest of the coverage • Absolute barriers (cliff, fenced areas, lakes, etc.) prevent or deflect movement. • Impermeable • Permeable: Has points of access through which travel is permitted (e.g., bridge)

  19. Measuring Distance Direction of Movement Absolute Barrier (impermeable) Absolute Barrier (permeable) After Demers (2005) Fundamentals of Geographic Information Systems

  20. Shallow Stream Measuring Distance Relative barriers: Barriers thatincur a cost for movement; result in slower movement or expenditure of additional energy Examples – narrow ridges of hilly terrain, shallow streams that are passable for off-road vehicles.

  21. Measuring distance Raster modeling of barriers/friction surfaces From Demers (2005) Fundamentals of Geographic Information Systems

  22. Measuring Distance Raster • Incremental distance: Measurement of each increment traveled • Used to calculate • Shortest path • Least cost path (for frictional surfaces)

  23. MeasuringDistance

  24. Measuring Distance • Accumulated distance  produces least cost surface

  25. Measuring distance Vector measures: Euclidean Non-Euclidean • Manhattan • Other modifications of the Pythagorean theorem

  26. Wrapping up Lots of measurements we can make These measurements allow for richer analyses Measurements • Lineslength, sinuosity • Polygonslength, area, perimeter, sinuosity, spatial integrity, convexity, edge • Distance  Euclidean, Functional (shortest & least cost)

  27. Applications: Sinuosity http://pubs.usgs.gov/tm/2005/tm6c01/

  28. Applications: Elongation Measuring the rain shield of a hurricane, researchers found that storms with elongated polygons at landfall were more intense http://ams.confex.com/ams/pdfpapers/108831.pdf

  29. Applications: Friction Surface Vulnerability of landscape to oil spills: Landcover and planimetric information was used to generate a friction or impedance surface that adjusts the cost of migration of oil through the landscape. For example, swamp forest and dredged spoils were given higher friction values (shown in deep reds above), while water, sand and cut banks are given a lower friction value (illustrated in white and light red tones). http://gis.esri.com/library/userconf/proc99/proceed/papers/pap460/p460.htm

  30. Application: Least Cost Surface Least cost surface developed to describe how focal species (bobcat, mountain lion, gray fox) move between habitat areas. Costs based on: Habitat Suitability Road Density Slope http://www.bren.ucsb.edu/research/2003Group_Projects/links/Final/links_brief.pdf

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