Intro to Spatial Analysis by jennyyingdi

VIEWS: 3 PAGES: 21

									       Intro to Spatial Analysis
• Most GIS support simple spatial analysis tasks
  such as selecting, counting, and generating
  descriptive statistics such as mean and standard
  deviation
• More sophisticated spatial analysis (e.g.
  regression, analysis of spatial relationships
  between objects, etc.) often necessitate linking to
  other software (e.g. a statistical package) and/or
  significant programming by the user
       Intro to Spatial Analysis
• Finding and returning information about an object

   – what objects have a certain attribute value?
   – what is the attribute value of a certain object?

   – What locations have a certain attribute value?
   – What is the attribute value at a certain location?
       Intro to Spatial Analysis
• Basic spatial properties of objects (besides location)
   – Point
   – Line
      • length
      • orientation
      • sinuosity
   – Polygon
      •   area
      •   perimeter
      •   shape
      •   eccentricity (elongation)
      •   orientation
                Measurement
• Vector Line Length
  – Length of straight line calculated by pythagorean
    theorem using beginning and ending point locations
  – length of a curvillinear line calculated by adding lengths
    of individual line segments
• Raster Line Length
  – Number of grid cells x length of grid cell
  – Can incorporate greater distance for diagonal orientation
               Measurement
• Sinuosity of a Line
                            Length of line A
                            -------------------
                            Length of line B

                        A




                            B
                Measurement
• Vector Polygon Area
  – Break complex polygon into simpler geometric shapes
    such as right triangles and rectangles whose area can be
    calculated
• Raster Region Area
  – Count number of grid cells with certain attribute value
  – May have to define a separate raster layer to find areas of
    contiguous regions of a certain attribute value
              Measurement
                                       Hole or
• Regions: Vector                      island




 Contiguous         Fragmented   Perforated
 region             region       region
                   Measurement
• Regions: Vector
Vector data layer that describes agricultural land cover

                   Polygons B and C           Poly ID      Crop
                   and not agricultural
           B       land but they are          A            corn
       A           polygons and still         B
   C               appear in the
                   relational table           C


   Perforated
   region
                   Measurement
• Regions: Vector
Vector data layer that describes countries

                  Polygons A, B, and         Poly ID   country
       A          C are islands that
                                             A         Fragmentland
                  compose one
C
           B      country, but in            B         Fragmentland
                  relational table each
                                             C         Fragmentland
                  polygon is a
 Fragmented       separate record
 region
                Measurement
• Regions: Raster


    0   0   0   1   1   No way to distinguish
                        between contiguous,
    0   0   0   1   1
                        fragmented, and
    1   1   0   0   0   perforated regions unless
    1   1   0   0   0   we explicitly attribute
    1   1   1   0   0   each grid cell as part of a
                        contiguous region
             Measurement
 0 - Meadow
 1 - Forest

 0   0   0   1   1
 0   0   0   1   1    • Raster Region Area
 1 1 0 0 0
 1 1 0 0 0
 1 1 1 0 0

How many grid cells
where value = 1
                Measurement
• Calculating Raster Region Area for each individual
  contiguous region
                                     0 - Meadow
  0 - Meadow                         1 - Forest stand 1
  1 - Forest                         2 - Forest stand 2

  0 0   0   1   1                    0   0   0   2   2
  0 0   0   1   1      reclassify    0   0   0   2   2
  1 1   0   0   0                    1   1   0   0   0
  1 1   0   0   0                    1   1   0   0   0
  1 1 1 0 0                          1 1 1 0 0
 How many grid cells                How many grid cells
 where value = 1                    where value = 2
                 Measurement
• Calculating Vector Polygon
  Perimeter
   – calculate lengths of all
     component lines


• Calculating Raster Region       0   0   0   0   0
  Perimeter                       0   1   1   1   0
   – find ‘boundary’ grid cells
                                  1   1   1   1   1
   – calculate lengths of all
                                  1   1   1   1   0
     component ‘lines’
                                  0   1   1   0   0
                 Measurement
• Calculating Polygon Eccentricity

      Length of A
      --------------
      Length of B




                       B       A
                Measurement
• Calculating Distance
   – Simple distance assumes an isotropic surface in
     Euclidean space
   – Functional distance incorporates ‘cost’
                 Measurement
• Calculating Simple Distance
   – Between 2 points
      • Pythagorean theorem
   – Between 2 polygons
      • measure distance between centroids using Pythagorean
        theorem
      • measure distance between polygons bounding box
                 Measurement
• Calculating Simple Distance in Raster
   – Raster ‘spread’ operation defines a raster of
     distance from a point or many points

                    2   2   2   2   2
                    2   1   1   1   2
                    2   1   0   1   2
                    2   1   1   1   2
                    2   2   2   2   2
                   Measurement
• Calculating Functional Distance in Raster
    – raster ‘friction’ surface defines impedance value at
      each grid cell
    – relative barriers
    – absolute barriers
                                           1   2   3   3     2
  Difficulty for tank travel               1   2   3   3     2
1 - open land (no impedance)               1   1   1   2     2
2 - small trees (relative barrier)         1   3   2   2     1
3 - large trees (absolute barrier)
                                           3   3   3   3     1
                   Measurement
• Calculating
  a Least Cost
  Path in
  Raster
   – choose a
     starting
     point and
     search
     nearest
     neighbors
     for easiest
     route
                     Measurement
• Calculating a Least Cost Path in Raster
   – accumulated cost from one point to each cell in the grid to
     find least cost path between two points


    Cost surface       Accumulated cost         From 4,4 to 2,2
    1 1 3 1              4.8 3.8 4.4 3
                                                0.5 (1.4 x 1) = 0.7
    1 3    1   1          3.8   4.2   2.4   2   0.5 (1.4 x 3) = 2.1
    3 1    1   1          4.4   2.4   1.4   1   + (prev val) 1.4
    1 1    1   1          3     2     1     0                  4.2
                    Measurement
• Least Cost Path Can be Applied to Vector Networks
  – each line has a cost associated with it
  – to find a least cost path between two points is exhaustive
    (must try all paths before determining the shortest) and
    therefore time consuming
  – costs on a street network include speed limit, traffic lights,
    stop signs, dead ends, cul de sacs, wait to make a left turn at
    a busy intersection, etc.

								
To top