1. Geographical Information Systems
Pavel Hrubeš

2. Department of Transport Telematics
Rehearsal
Model of the Earth
Sphere
Elipsoid/Spheroid
Geoid
Projections
Plane
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

3. Modelling - Introduction
GIS provides:
comprehensive set of tools for spatial data management
limited spatial analysis functionality
but does provides framework of application
limited spatial analysis functionality may be addressed by linking models into GIS
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

4. Spatial modelling issues
Model problems:
most models do not provide tools for data management and display, etc.
many models are aspatial
GIS provides:
framework of application
allows user to add spatial dimension (if not already built into the model)
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

5. Department of Transport Telematics
Modelling guidelines
In order to ensure that model results are as close to reality as possible the following guidelines apply:
ensure data quality
beware of making too many assumptions
match model complexity with process complexity
compare predicted results with empirical data where possible and adjust model parameters and constants to improve goodness of fit
use results with care!
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

6. Basics of cartographic modelling
Mathematics applied to raster maps
often referred to as map algebra or ‘mapematics’
e.g. combination of maps by:
addition
subtraction
multiplication
division, etc.
operations on single or multiple layers
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

7. Department of Transport Telematics
A definition
“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”
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

8. Department of Transport Telematics
A simple example… 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
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

9. Department of Transport Telematics
Question…
How determine topological relationships?
i.e. Boolean: AND, NOT, OR, XOR
What is the arithmetic equivalent?
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

10. Building spatial models
It is (in theory) surprisingly simple:
algebraic combination of:
OPERATORS and FUNCTIONS
rules and relationships
inputs (and outputs)
interfaces
run at the command line/menu interface
batch file
embedded in system macro/script
‘hard’ programmed into system
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

11. Problems in model building
Knowledge
systems and processes
relationships and rules
Compatability
input data available
outputs required
Quality issues
data quality (accuracy, appropriateness, etc.)
model assumptions and generalisation
confidence and communication
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

12. Department of Transport Telematics
Modelling
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)
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

13. Department of Transport Telematics
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
Other local functions
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

14. Department of Transport Telematics
Local functions 5 4 7
input 25 49 16
output = sqr(input)
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

15. output = reclass(input)
Some examples
input
output = tan(input)
output = reclass(input)
output = log2(input)
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

16. Department of Transport Telematics
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.
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

17. Department of Transport Telematics
Focal functions 5 4 7
input 11 16
output = focalsum(input)
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

18. Some examples input output = focalmean(input, 20)
output = focalstd(input)
output = focalvariety(input)
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

19. 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.)
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

20. Supervised classification1 2 3 4 5
Old class
New class
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

21. Unsupervised classification1 3 4 2 5
diversity
modal
minimum
maximum
mean 5 4 1 5 3
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

22. Department of Transport Telematics
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.
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

23. Department of Transport Telematics
Zonal functions 5 4 7
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
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

24. Some examples input Input_zone 535.54 127 6280 766.62 160 10800
output = zonalthickness(input_zone)
output = zonalperimeter(input_zone)
output = zonalmax(input_zone, input)
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

25. Department of Transport Telematics
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.
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

26. Department of Transport Telematics
Global functions 5 4 7
input 6 7 8 9 5 6 7 8 4 5 6 7
output = trend(input) 4 5 6 6
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

27. Department of Transport Telematics
Distance functions
Simple 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
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

28. Some examples input source output = eucdistance(source)
output = eucdirection(source)
output = costdistance(source, input)
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

29. Department of Transport Telematics
COSTPATH example
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics

30. Department of Transport Telematics
Conclusions
Linking/building models to GIS
Idea of maths with maps
surprisingly simple, flexible and powerful technique
basis of all raster GIS
Fundamental to spatial interpolation, distance and neighbourhood functions
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics