Cartographic modelling

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

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

6. 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.

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. COSTPATH example Overlay and distance

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

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

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

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

18. Neighbourhood filters Local, focal, zonal and global • 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. 1 2 1 3 4 1 1 2 3 1 2 4 5 1 2 2 1 2 4 1 1 2 4 5 2 Old class New class Supervised classification Local, focal, zonal and global

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

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

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

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

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