1. Raster Analysis and Terrain Analysis
Chapter 10 Part 2 & 11
Raster Analysis
Lecture 11

2. Scope: Neighborhood operations
Vector neighborhoods are not well-defined and depends upon the size and shape of the feature and neighboring feature, Raster neighborhood is better defined.
Lecture 11

3. Neighborhood Operations
Moving Windows
(Windows can be any size; often odd to provide a center)
Lecture 11

4. Kernels vs. Moving Window
Lecture 11

5. Neighborhood Operations:
Separate edge kernals can be used

6. Neighborhood Operations
Lecture 11

7. Example:Identifying spatial differences in a raster layer
This is an edge detection operation – The first kernel amplifies differences in the x direction the second amplifies differences in the y direction.

8. Raster Analysis
Moving windows and kernals can be used with a mean kernal to reduce the difference between a cell and surrounding cells. (done by average across a group of cells)
Raster data may also contain “noise”; values that are large or small relative to their spatial context.
(Noise often requiring correction or smooth(ing))
Know as “high-pass” filters
The identified spikes or pits can then be corrected or removed by editing
Lecture 11

9. Zonal Functions
Zonal operations apply functions based on defined regions or zones.

10. Scope: Global operation
Global operations can be useful for continuous data like temperature and rainfall. You want to find global maximums.
Lecture 11

11. ArcMap’s Raster Calculator
                                                                          
Raster Calculator tool dialog box example
Xor is an exclusive OR – exactly one of the operands is true
"ceil" returns the smallest integer (represented as a double precision number) that is greater than or equal to "x".
In mathematics and computer science, the floor and ceiling functions map a real number to the next smallest or next largest integer. More precisely, floor(x) = ⌊x⌋ is the largest integer not greater than x and ceiling(x) = ⌈x⌉ is the smallest integer not less than x.[1]
From ArcGIS Help Files
Lecture 11

12. Cost Surface
The minimum cost of reaching cells in a layer from one or more sources cells
“travel costs”
Time to school; hospital;
Chance of noxious foreign weed spreading out from an introduction point
Units can be money, time, etc.
Distance measure is combined with a fixed cost per unit distance to calculate travel cost
If multiple source cells, the lowest cost is typically placed in the output cell
Lecture 11

13. A cost surface is based on a fixed cost such as miles per gallon.
Lecture 11

14. Friction Surface (version of a Cost Surface)
The cell values of a friction surface represent the cost per unit travel distance for crossing each cell – varies from cell to cell
Used to represent areas with variable travel cost.
Notes:
Barriers can be added.
Multiple paths are often not allowed
Cost and Friction Surfaces are always related to a source cell(s); “from something”
The center of a cell is always used the distance calculations
Lecture 11

15. Friction Surface Lecture 11 Variable cost
Total distance is 22.4/ 4 segments = 5.6
Lecture 11

16. Chapter 10 Assignment Read Ch. 10
Problems: 2, 4, 6, 8, 12, 14, 16,19, 22, 23
Lecture 11

17. Terrain Analysis
Lecture 11

18. Digital Elevation Models (DEM)/Terrain Analysis
Terrain determines the natural availability and location of surface water, and hence soil moisture and drainage.
Water quality through control of sediment entrainment and transport, slope steepness and direction defines flood zones, watershed boundaries and hydrologic networks.
Terrain also strongly influences location and nature of transportation networks or the cost and methods of house and road construction.
Lecture 11

19. Lecture 11

20. Digital Elevation Models Terrain Analysis Slope and Aspect
Used for: hydrology, conservation, site planning, other infrastructure development.
Watershed boundaries, flowpaths and direction, erosion modeling, and viewshed determination all use slope and/or aspect data as input.
Slope is defined as the change is elevation (a rise) with a change in horizontal position (a run).
Slope is often reported in degrees (0° is flat, 90° is vertical)
Lecture 11

21. Slope (continued)

22. Measured in the steepest direction of elevation change
Slope (continued)
Measured in the steepest direction of elevation change
Often does not fall parallel to the raster rows or columns
Which cells to use?
Several different methods:
Four nearest cells
3rd Order Finite Difference
Lecture 11

23. Slope (continued) Elevation is Z
Using a 3 by 3 (or 5 by 5) moving window
Each cell is assigned a subscript and the elevation value at that location is referred to by a subscripted Z value
The most common formula:
Lecture 11

24. Slope (continued) for Zo ΔZ/Δx = (49 – 40)/20 = 0.45
ΔZ/Δy = (45 – 48)/20 = -0.15
Lecture 11

25. Slope (continued) Generalized formula for ΔZ/Δx and ΔZ/Δy
ΔZ/Δx = (Z5 – Z4)2*
ΔZ/Δy = (Z2 – Z7)2*
Using the four nearest cells
for Zo
ΔZ/Δx = (49 – 40)/20 = 0.45
ΔZ/Δy = (45 – 48)/20 = -0.15
* = times cell width
Slope calculation base on cells adjacent to the center cell
The distance is from cell center to cell center
Lecture 11

26. Slope (continued) Multiply (kernal, cell by cell) Add (results)
Divide by #cells x cell width
Use slope formula
Kernal for ΔZ/Δx
Kernal for ΔZ/Δy
ΔZ/Δx = (49 – 40)/20 = 0.45
ΔZ/Δy = (45 – 48)/20 = -0.15
Lecture 11

27. Multiply (kernal, cell by cell)
Add (results)
Divide by #cells x cell width
Use slope formula
Lecture 11

28. Slope in ArcGIS 10
From ArcGIS 10 Help
Lecture 11

29. Aspect
Lecture 11

30. Aspect The orientation (in compass angles) of a slope Calculation:
Aspect = tan-1[ -(ΔZ/Δy)/(ΔZ/Δx)]
As with slope, estimated aspect varies with the methods used to determine ΔZ/Δx and ΔZ/Δy
Aspect calculations also use the four nearest cell or the 3rd-order finite difference methods
Lecture 11

31. Aspect in ArcGIS 10
From ArcGIS 10 Help
Lecture 11

32. Curvature
Lecture 11

33. Viewshed The viewshed for a point is the collection
of areas visible from that point.
Views from any non-flat location are blocked by
terrain.
Elevations will hide a point if they are higher than the viewing point, or higher than the line of site between the viewing point and target point
Lecture 11

34. Lecture 11

35. Lecture 11

36. Shaded Relief Surfaces
Lecture 11

37. Flow Direction
From ArcGIS 10 Desktop Help
Lecture 11

38. Raster Analysis High pass filters Return:
Small values when smoothly changing values.
Large positive values when centered on a spike
Large negative values when centered on a pit
Lecture 11

39. High Pass Filter
Raster data may also contain “noise”; values that are large or small relative to their spatial context.
A mean kernal is used to reduce the difference between a cell and surrounding cells. (done by average across a group of cells)
The identified spikes or pits can then be corrected or removed by editing
Lecture 11

40. 35.7

42. Watershed Drainage network
An area that contributes flow to a point on the landscape
Water falling anywhere in the upstream area of a watershed will pass through that point.
Many be small or large
Identified from a flow direction surface
Drainage network
A set of cells through which surface water flows
Based on the flow direction surface
Lecture 11

43. Lecture 11

44. Routing and Allocation
Finding the shortest path between any nodes in a network
Optimal path 
Each link in the net can also be assigned an impedance value 
Using an accumulated distance and the impedance factor
Most efficient route can be found, rather than just the shortest
Nodes can also be coded with stops and barriers
Preventing movement and forcing traffic along another path
Although routing can be done in raster, it is much easier if performed in a vector system

45. Routing and Allocation
Process used to define the areal extent of services areas
Service areas are defined around a site
Region is formed that includes a defined area
Location/allocation model (optimizes network efficiency)
Technique for the evaluation of multiple facility locations
Determining the configuration of facilities (location)
Assigning demand for the facilities (allocation)
Lecture 11

46. Assignments for Chapter 11
Read chapter 11.
Problems: 3, 4, 6, 8, 22
Lecture 11