Intro to Spatial Analysis Most GIS support simple spatial analysis tasks such as selecting,...

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.