school of geography faculty of environment cartographic modelling

School of GeographyFACULTY OF ENVIRONMENT

Cartographic modelling

Day 1: cartographic modelling

• Principles

• Mathematical and logical functions

• Overlay and distance functions

• Local, focal, zonal and global functions

• Spatial Analyst and ArcGrid

Principles

• Mathematics applied to raster maps

• Map algebra or ‘mapematics’

• e.g. combination of maps by:

• Addition

• Subtraction

• Multiplication

• division, etc.

• operations on single layers

• operations on multiple layers

Principles

“A generic means of expressing and organising the methods by which spatial variables and spatial operations are

selected and used to develop a GIS model”

Principles

• A simple example...

Input 15

476

4

4

6

66

6

44

4

4

3

3

33

3 3

23

22

2

2

2

2

1

1

1

1

25

7 7 6 6

7 7 13 56 10 8

5 5 10

Input 2

Output

+

=

Maths and logic

• Mathematical operators

• Addition, subtraction, multiplication, division

• Square, squareroot, logarithms, exponents, etc.

• Trigonometry, etc.

• Logical operators

• Boolean (AND, OR, NOT, XOR)

• Relative (maximum, minimum, etc.)

• Combinatory

• Etc.

Overlay and distance

• Overlay is achieved mathematically

• e.g. in raster calculator

• Distance functions• calculate the linear distance of a cell from a target cell(s) such as

point, line or area

• use different distance decay functions

• linear

• non-linear (curvilinear, stepped, exponential, root, etc.)

• use target weighted functions

• use cost surfaces


Some examples

input source

output = eucdistance(source)

output = eucdirection(source)

output = costdistance(source, input)


COSTPATH example


Local, focal, zonal and global

• Four basic categories of functions in map algebra:• local

• focal

• zonal

• global

• Operate on user specified input grid(s) to produce an output grid, the cell values in which are a function of a value or values in the input grid(s)

Local functions

Output value of each cell is a function of the corresponding input value at each location

• value NOT location determines result

• e.g. arithmetic operations and reclassification

• full list of local functions in GRID is enormous• Trigonometric, exponential and logarithmic

• Reclassification and selection

• Logical expressions in GRID

• Operands and logical operators

• Connectors, statistical, and other local functions


Local functions

2516

54

7

49

input

output = sqr(input)


Some examples

input

output = tan(input)

output = reclass(input)

output = log2(input)


Focal functions

Output value of each cell location is a function of the value of the input cells in the specified neighbourhood of each location

Type of neighbourhood function• various types of neighbourhood:

• 3 x 3 cell or other

• calculate mean, SD, sum, range, max, min, etc.


Focal functions

54

7

1611

input

output = focalsum(input)


Some examples

output = focalmean(input, 20)

input

output = focalstd(input)

output = focalvariety(input)


Neighbourhood filters

Type of focal function

• used for processing of remotely sensed image data

• change value of target cell based on values of a set of neighbouring pixels within the filter

• size, shape and characteristics of filter?

• filtering of raster data• supervised using established classes

• unsupervised based on values of other pixels within specified filter and using certain rules (diversity, frequency, average, minimum, maximum, etc.)


Supervised classification

123

45

1

2

Old class New class

1 3 42 4 51 2 4

1 1 21 2 21 1 2


Unsupervised classification

1 3 42 4 51 2 4

diversity

modal

minimum

maximum

mean

5

4

1

5

3


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 neighbourhood function

• use complex neighbourhoods or zones

• calculate mean, SD, sum, range, max, min, etc.


Zonal functions

54

7

input

output = zonalsum(zone, input)

zoneZone 1

Zone 2

99

99

99

99

7 7 77 7 7

77


Some examples

output = zonalthickness(input_zone)

input Input_zone

535.54

766.62

127

160

output = zonalmax(input_zone,

input)

output = zonalperimeter(input_zone

)

6280

10800


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.

• Again, full list of global functions in GRID is enormous

• euclidean distance functions

• weighted distance functions

• surface functions

• hydrologic and groundwater functions

• multivariate.


Global functions

54

7input

output = trend(input)

9

87

6

8

76

6

7

65

544

5

6


Practical exercise

Hands-on Exercise #3Cartographic modelling in ArcMap

school of geography faculty of environment cartographic modelling

Documents