1. Cartographic modelling

2. Day 1: cartographic modelling
Principles
Mathematical and logical functions
Overlay and distance functions
Local, focal, zonal and global functions
Spatial Analyst and ArcGrid
* All of these are encapsulated in tools and various selection processes

3. 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

4. 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”

5. Principles A simple example... 5 4 7 6 3 2 1 13 10 8 Input 1 + Input 2=
Output

6. Maths and logic Mathematical operators Logical 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.

7. Overlay and distance Overlay is achieved mathematically
e.g. in raster calculator

8. Overlay and distance 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

9. Some examples Overlay and distance input source
output = eucdistance(source)
output = eucdirection(source)
output = costdistance(source, input)

10. Overlay and distance
COSTPATH example

11. 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)

12. Local, focal, zonal and global
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

13. Local, focal, zonal and global
Local functions 25 16 5 4 7 49
input
output = sqr(input)

14. output = reclass(input)
Local, focal, zonal and global
Some examples
input
output = tan(input)
output = reclass(input)
output = log2(input)

15. Local, focal, zonal and global
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.

16. output = focalsum(input)
Local, focal, zonal and global
Focal functions 5 4 7 16 11
input
output = focalsum(input)

17. output = focalstd(input) output = focalvariety(input)
Local, focal, zonal and global
Some examples
input
output = focalstd(input)
output = focalvariety(input)
output = focalmean(input, 20)

18. Neighbourhood filters
Local, focal, zonal and global
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.)

19. Supervised classification
Local, focal, zonal and global
Supervised classification 1 2 3 4 5
Old class
New class

20. Unsupervised classification
Local, focal, zonal and global
Unsupervised classification 1 3 4 2 5
diversity
modal
minimum
maximum
mean

21. Local, focal, zonal and global
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.

22. output = zonalsum(zone, input)
Local, focal, zonal and global
Zonal functions 5 4 7
input
output = zonalsum(zone, input)
zone
Zone 1
Zone 2 9

23. Local, focal, zonal and global
Some examples
input
Input_zone
535.54
766.62
127
160
output = zonalmax(input_zone, input)
output = zonalperimeter(input_zone)
6280
10800
output = zonalthickness(input_zone)

24. Local, focal, zonal and global
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.

25. Local, focal, zonal and global
Global functions 5 4 7
input
output = trend(input) 9 8 6

26. Cartographic modelling in ArcMap
Practical exercise
Hands-on Exercise #3
Cartographic modelling in ArcMap
Demo