1. Raster Analysis
Ming-Chun Lee

2. Raster Analysis Performed on cells and grids. Raster cells store data
Nominal – land use
Ordinal – street classification
Interval/Ratio – temperature, elevation
Perform analysis based on manipulations on cell values for a single raster layer or multiple layers.
Raster analysis is Performed on cells and grids.
Raster cells store data, a single cell contains a value which represents a measurement of a certain phenomenon..
Nominal – land use
Ordinal – street classification
Interval/Ratio – temperature, elevation
Perform analysis based on manipulations on cell values for a single raster layer or multiple layers.

3. Why use Raster GIS
Raster is better suited for spatially continuous data
Elevations, pH, air pressure, temperature, salinity
Raster is better for creating visualizations and modeling environmental phenomena
Raster data is a simplified realization of the world, and allows for fast and efficient processing
Why use Raster GIS
A quick recap on advantages of raster data model:
Raster is better suited for spatially continuous data
Elevations, pH, air pressure, temperature, salinity
Raster is better for creating visualizations and modeling environmental phenomena
Some natural phenomena are hard to visualize as a whole, raster helps us visualize those phenomena over a piece of land..
Raster data is a simplified realization of the world, and allows for fast and efficient processing

4. Map Algebra
Cell by Cell combination of raster data layers using mathematical operations
one layer
multiple layers
Each number represents a value at a raster cell location
Simple operations can be applied to each number
Raster layers may be combined through operations
Addition, subtraction and multiplication
Raster analysis is mainly based on so-called map algebra:
What is map algebra:
Combine raster data layers cell by cell using mathematical operations
one layer
multiple layers
Each number represents a value at a raster cell location
Simple operations can be applied to each number
Raster layers may be combined through operations
Addition, subtraction and multiplication

5. Map Algebra
Raster analysis creates a new layer, or new grid, you didn’t actually change the original layers, what you did is take out values from the original layers and do some kind of manipulation on them, and output a new layer..

6. Map Algebra 1 4 3 2 5 4 7 6 3
Input 1 2 4 2 1 2 3 6 + 6 3 3 4 2 1 6 2
Input 2 4 6 4 3 1 3 2 4 = 7 7 6 6 7 7 13 5
Output 6 10 8 5 2 5 5 10

7. Map Algebra
The computer will allow you to perform virtually any mathematical calculation
beware: some will make sense, others won’t.
For example, water = 0, land = 1. Then, you can multiply this grid with an elevation map. The output will include 0’s where water existed (x * 0 = 0), and the original elevation value where land existed (x * 1 = x)
Or, you can add the elevations and the grid with 0’s and 1’s together (but, it would be meaningless!)
The computer will allow you to perform virtually any mathematical calculation
beware: some will make sense, others won’t.
For example, water = 0, land = 1. Then, you can multiply this grid with an elevation map. The output will include 0’s where water existed (x * 0 = 0), and the original elevation value where land existed (x * 1 = x)
Or, you can add the elevations and the grid with 0’s and 1’s together (but, it would be meaningless!)

8. Map Algebra
Grid1 * Grid2 = Grid3
Grid1
Grid2 1 * =
Grid3

9. Map Algebra Multiple grid themes share the same X, Y coordinate space
A single output grid theme is the result of the multiple grids
Multiple grid themes share the same X, Y coordinate space
When you apply map algebra to multiple layers, those layers have to share the same coordinate system.
A single output grid theme is the result of the multiple grids

10. Map Algebra Mathematical Operators: Arithmetic Boolean Relational
+, -, *, /
Boolean
AND, OR, NOT, XOR
Relational
=, <, >, ≤, ≥, <>
Algebraic Functions
Powers & Roots, Trigonometry, Logarithm
Those mathematical operations that you can use for rater analysis, can be grouped into four categories:
Arithmetic Operators –
The Arithmetic operators (*, /, -, +)
allow for the addition, subtraction, multiplication, and
division of two grid themes.
Boolean Operators –
The Boolean operators (And, Not, Or,
and Xor) use Boolean logic (TRUE or FALSE) on the input
values. Output values of TRUE are written as 1 and FALSE
as 0.
Relational Operators –
The Relational operators (<, <=, <>,
=, >, and >=) evaluate specific relational conditions. If the
condition is TRUE, the output is assigned 1; if the condition
is FALSE, the output is assigned 0.
Algebraic Functions to a single layer…
Powers & Roots, Trigonometry, Logarithm

11. Mathematical Operator: Arithmetic

12. Mathematical Operator: Boolean

13. Mathematical Operator: Relational

14. Mathematical Operator: Algebraic Functions

15. Scope of Computations Local Functions Focal/Neighborhood Functions
Process cells on a cell-by-cell basis.
only use data in a single cell to calculate an output value
Focal/Neighborhood Functions
Process data for each pixel using the attribute values of the neighboring cells of that pixel.
Zonal Functions
Process cells on the basis of zones.
Global Functions
Process data at each pixel on the output grid using entire source grid.
Now, we have looked at map algebra, looked at some operations you can apply to raster layers.
Now let’s look at Scope of Computations
The scope of calculation or operation, can be different depend on your analysis purpose..
Local Functions
Process cells on a cell-by-cell basis.
only use data in a single cell to calculate an output value
Focal/Neighborhood Functions
Process data for each pixel using the attribute values of the neighboring cells of that pixel.
Zonal Functions
Process cells on the basis of zones.
Global Functions
Process data at each pixel on the output grid using entire source grid.

16. Local Functions 5 4 7 input 25 49 output = sqr(input) 16
(use only the data at one input data point to determine value at a corresponding output location)
Operations that modify a single cell
Data type changes
Arithmetic operations involving a constant
Converting one value to another according to a rule (Recode)
Local operations on multiple layers
Map algebra (Output = f(Input1, Input2,…)
Functions may be mathematical or logical
output = sqr(input) 16

17. Local Functions Operations that modify a cell on a single grid
Data type changes
Arithmetic operations
Converting one value to another according to a rule (Recode)
Local operations on multiple layers
Map algebra (Output = f(Input1, Input2,…)
Functions may be mathematical or logical
Operations that modify a cell on a single grid
Data type changes
Arithmetic operations
Converting one value to another according to a rule (Recode)
Local operations on multiple layers
Map algebra (Output = f(Input1, Input2,…)
Functions may be mathematical or logical

18. Local Functions
Single grid
Multiple grid
(addition)

19. Focal/Neighborhood Functions5 4 7
input 11
(data from both an input location plus nearby locations to determine the output value) 16
output = focalsum(input)

20. Focal/Neighborhood Functions
Moving window
Assigns the value of a neighborhood of grid cells to one particular grid cell (kernel)
Useful for calculating local statistical functions
Moving Windows
(Windows can be any size; often odd to provide a center)

21. Neighborhood Functions
You may want to study ecosystem, and want to figure out the variety of species for each neighborhoods, where is lacking a variety of animals.
Different land cover types,

22. Zonal Functions Zone Sum 1 9 2 7 5 4 7 input Zone 2 zone Zone 1
output = zonalsum(zone, input)
Similar to focal function, but which cells being taken into calculation not depend on neighborhood, but depend on zones, which are usually defined by another layer. 9 7 7 7
Zone
Sum 1 9 2 7 9 7 7 7 9 9 9 7 9 9 9 7

23. Zonal Functions
Output value at each location depends on the values of all the input cells in an input value grid that shares the same input value zone
Type of complex neighborhood function
use complex neighborhoods or zones
Output value at each location depends on the values of all the input cells in an input value grid that shares the same input value zone
Type of complex neighborhood function
use complex neighborhoods or zones

24. input
Input_zone
535.54
127
6280
766.62
160
10800

25. Global Functions 5 4 7 input 6 7 8 9 5 6 7 8 output = trend(input) 4 5

26. Global Functions
Output value of each location is potentially a function of all the cells in the input grid
e.g. distance functions, surfaces, interpolation, etc.
Output value of each location is potentially a function of all the cells in the input grid
e.g. distance functions, surfaces, interpolation, etc.

27. Distance to Features
Cell value is the Distance from the Cell Center to the Nearest Feature(s) in a Specified Layer
Physical distance– equivalent to buffers
Cost distance
Requires a cost grid as input
Cost grid contains costs for unit distance
Cost distance between two cells is the average of the two values multiplied by the distance between them
Total cost is calculated to source cells.
Cell value is the Distance from the Cell Center to the Nearest Feature(s) in a Specified Layer
Physical distance– equivalent to buffers
Cost distance
Requires a cost grid as input
Cost grid contains costs for unit distance
Cost distance between two cells is the average of the two values multiplied by the distance between them
Total cost is calculated to source cells.

28. Distance to Features

29. Interpolation Between Features
Interpolation predicts values for cells in a raster from a limited number of sample data points.
Elevation, rainfall, chemical concentration, noise level
Average of Nearby Features’ Values, Weighted by Distance, Regardless of Density
Example: Number of Bus Routes Serving a Neighborhood!
Average of Nearby Features’ Values, Weighted by Distance, Regardless of Density
Example: Number of Bus Routes Serving a Neighborhood!
Interpolation predicts values for cells in a raster from a limited number of sample data points..
Elevation, rainfall, chemical concentration, noise level,
Visiting every location in a study area to measure is expensive, and sometimes just impossible..
The assumption that makes interpolation a viable option is that spatially distributed objects are spatially correlated.
Things that are close together tend to have similar characteristics.

30. Interpolation Between Features

31. Density of Features
Value Assigned Based on the Neighborhood Density of a Feature
Can be Weighted on an Attribute Value
Example: Estimate a Population Density Surface Using Census Tract Population
Another Example – Bus Service Density
Value Assigned Based on the Neighborhood Density of a Feature
Can be Weighted on an Attribute Value
Example: Estimate a Population Density Surface Using Census Tract Population
Another Example – Bus Service Density

32. Density of Features

33. Spatial Analyst functions
Find Distance
Calculate Density
Interpolate Surface
Derive Slope, Aspect
Create Contour
Cell Statistics
Summarize Zones
Tabulate Areas
Map Query, Calculator
Neighborhood Statistics
Reclassify

34. Raster-based Analysis
Finding potential sites for a new school
(ESRI: Using ArcGIS Spatial Analyst)
Criteria:
On flat land
Near recreation sites
Away from existing schools
Land use in terms of cost
Agricultural – cheapest
Barren land
Brush/Transitional
Forest
Built up – most expensive
Finding potential sites for a new school
(ESRI: Using ArcGIS Spatial Analyst)
Criteria:
On flat land
Near recreation sites
Away from existing schools
Land use in terms of cost
Agricultural – cheapest
Barren land
Brush/Transitional
Forest
Built up – most expensive

35. Slope

36. Slope

37. Distance

38. Distance

39. Reclassify

40. Reclassify

41. Reclassify

42. Reclassify
Lecture 9

43. Weighting and Combining Datasets
Weights:
Dist to Rec_sites: 0.5
Dist to schools: 0.25
Landuse: 0.125
Slope: 0.125

44. Raster Calculation

45. Raster Calculation

46. Result

47. Finding an Access Road to New Sites

48. Cost Layer Slope: Land Use: High values (10) to steeper slopes
Agricultural: 4
Brush/Transitional: 5
Barren land: 6
Forest: 8
Built up: 9
Water: 10

49. Cost Layer

50. Cost Layer

51. Cost Weighted Distance

52. Cost Weighted Distance

53. Shortest Path

54. Shortest Path

55. Shortest Path