intro to spatial analysis most gis support simple spatial analysis tasks such as selecting,...
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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
A
B
Length of line A ------------------- Length of line 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• Regions: Vector
Contiguous region
Fragmented region
Perforated region
Hole or island
Measurement• Regions: Vector
Perforated region
A
Poly ID Crop
A corn
B
C
Vector data layer that describes agricultural land cover
B
C
Polygons B and C and not agricultural land but they are polygons and still appear in the relational table
Measurement• Regions: Vector
Poly ID country
A Fragmentland
B Fragmentland
C Fragmentland
Vector data layer that describes countries
Polygons A, B, and C are islands that compose one country, but in relational table each polygon is a separate recordFragmented
region
A
BC
Measurement• Regions: Raster
0
11
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
No way to distinguish between contiguous, fragmented, and perforated regions unless we explicitly attribute each grid cell as part of a contiguous region
Measurement
• Raster Region Area
0
11
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0 - Meadow 1 - Forest
How many grid cells where value = 1
Measurement• Calculating Raster Region Area for each individual
contiguous region
0
11
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0 - Meadow 1 - Forest
How many grid cells where value = 1
0
11
1
1
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0 - Meadow 1 - Forest stand 1 2 - Forest stand 2
How many grid cells where value = 2
reclassify
Measurement• Calculating Vector Polygon
Perimeter– calculate lengths of all component
lines
• Calculating Raster Region Perimeter– find ‘boundary’ grid cells
– calculate lengths of all component ‘lines’
0
11
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
Measurement• Calculating Polygon Eccentricity
AB
Length of A -------------- Length of B
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
12
2
2
2
1
1
2
2
2
0
1
2
1
2
2
2
2
2
1
2
1
1
2
Measurement
• Calculating Functional Distance in Raster– raster ‘friction’ surface defines impedance value at each grid cell– relative barriers– absolute barriers
1
11
1
3
2
2
3
3
1
3
1
2
3
3
2
2
2
1
1
2
3
3
2
3
1 - open land (no impedance) 2 - small trees (relative barrier) 3 - large trees (absolute barrier)
Difficulty for tank travel
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
1
1
3
1
3
1
1
1
1
1
1
1
1
3
1
1
3.8
4.8
4.4
3
4.2
2.4
2
3.8
2
3
1
0
2.4
4.4
1.4
1
From 4,4 to 2,2
0.5 (1.4 x 1) = 0.7 0.5 (1.4 x 3) = 2.1 + (prev val) 1.4
4.2
Cost surface Accumulated cost
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.