1. Spatial Models and Modeling
June 7, 2013
Institute of Space Technology, Karachi

2. Chapter 13: Spatial Models and Modeling

3. Model Description of reality For this class
Static reproduction that represents basic shape and form of an object
A conceptual description of key elements and processes in a system
Sophisticated replica of objects, events, or processes
For this class
Restricted to computer-based models of spatial features
It may be…..
Spatial models

4. Computer Based Spatial Models
Combination of
GIS
Computer programming languages
Spatial and non-spatial analytical tools

5. Two Broad Classes Spatio-temporal Models Cartographic Models
Dynamic in both space and time
Example: analysis of oil after spill
Cartographic Models
Static models
Involve application of spatial operations
Example: buffer, interpolation, reclassification, overly
Combine data from multiple data layers
Analysis of oil after spill: current, winds, wave action, and physics of oil separation and evaporation on exposure to air might be combined in a model to predict the changing location of an oil slick. The actions of objects as they move across an environment may also be represented in a spatio-temporal model.

6. Cartographic Models
Represent spatial features at a fixed point or points of time
Most GIS models are cartographic models that are temporally static
Provides information through a combination of spatial data sets, functions and operations
Reclassification
Overlay
Interpolation
Terrain analysis
Buffering,
Map algebra, etc.
Temporally static: Although we may use them to analyze a change over a period of time e.g. vegetation change over a 10-year period. Each data layer represents the vegetation boundaries at a fixed point in time. Polygon boundaries for a given layer do not change.
Data in base layers are mapped for a given period. These data are the basic for spatial operations that may create new data layers.

7. Example: Suitability Analysis
Suitable park sites based on the proximity to Roads and Lakes and the absence of Wetlands
Most common type of ~models

8. Flow Chart
A graphic representation of the spatial data, operations and their sequence of use in a cartographic model
Cartographic models may be represented by Flowcharts:
Near road, near lake, not wetland.
Data layers represented by rectangles, operations by ellipses, and sequences by arrow.

9. Application Land use planning
Transportation route and corridor studies
Design and development of water distribution systems
Human disease spread
Site selection
Pollution response planning
Endangered species preservation
Useful to managers, public and policy makers.

10. Designing a Cartographic Model
Spatial functions and operations are mixed and matched in cartographic models
Variation in sequence of same operations will result in entirely different outputs
With a small set of data layers and tools, a huge number of models can be created
Usually produces a large number of ‘intermediate’ or temporary data layers that are not needed in final output or decision making

11. Designing the BEST Cartographic Model
Selection of appropriate spatial tools and specification of their sequence
Most important and often the most difficult process in ~.

12. Conti.. Designing a Cartographic Model
Based on a set of criteria
These criteria are usually defined in qualitative terms
The slope must not be too steep
Interpretation /translation of criteria into selection and sequence of spatial operations
What is meant by “too steep”
Need to be converted to specific, quantitative measures
Sometime conversion from qualitative to quantitative criteria involves iterative process with repeated interaction between the analyst and manager/decision maker.

13. Example: Home Site Selection
Problem: Ranking sites by suitability for home construction
Criteria:
Slopes should not be too steep
Southern aspect is preferred to enhance solar warming
Soils suitable for on-site septic systems
Sites should be far enough from a main road to offer some privacy but not so far as to be isolated
The area to be analyzed has steep terrain and is in a seasonally cold climate.
Steep slopes may substantially increase costs
There is a range of soil types in the study area, with a range of suitabilities for septic system installation.
These criteria must be converted to more specific restrictions prior to the development and application in a cartographic model.
Discussion between the analyst and decision maker: what type of classification required, what range of classes, what type of ranking, ordinal, ratio/interval? Measurement scale of results?
Slope threshold beyond which construction is infeasible can be defined by studying how slopes affect construction costs.

14. First convert these criteria into more specific quantitative terms
Check availability and quality of data
Do the required data layers exist for the study area?
Are spatial accuracies, spatial resolution and attributes appropriate for analysis
What level of map generalization?
If required data is not available
Obtain or develop the required data OR
Modify the goals
Explicit ranking of the relative importance of different classes or types of criteria
Map generalization: will inclusion of different soil types in a soil polygon lead to inappropriate results? Is the minimum mapping unit appropriate?

15. General Criteria Refined Criteria
Slopes Not Too Steep
Slope < 30 degrees
Southern Aspect Preferred
90 < aspect < 270
Soils Suitable for Septic System
Specified list of septic-suitable soil units
Far enough from Road to Provide Privacy, But Not Isolated
300 meters < distance to road < 2000 meters

16. Ranking and Weighting
Ranking: Assignment of relative values within the same layer
How we rank a sandy soil vs. a silty soil in a soil layer
‘Weighting’ – assigning the relative values of different layers
How we weight the values in an elevation layer vs. the values in a land use layer

17. Ranking Within Criteria
Each Criterion in cartographic model is usually expressed by a data layer or ‘criterion layer’
Each criterion layer is a spatial representation of some constraint or selection condition
Select site outside floodplain: Floodplain sites = 0, Upland sites = 1
select site outside floodplain may consist of a set of numbers in a layer identifying flood plain locations.
Obtain floodplain maps
Interpret codes in the map to delineate the most flood-prone areas.
Rank areas based on the likelihood of flooding.

18. Discrete vs. Continuous Ranking
Discrete: when input data are interpreted such that criterion data layer is a map of discrete value
Soil = Good, Bad
Slope = steep or acceptable
Continuous: ranks vary along a scale
Soils: Rated from 1 to 100 for construction suitability
When there are clear discrete classes to be represented in criteria.
Continuous: ranks or scores range over real or large integer interval e.g. 1 to 100 or 1 to Not necessarily a linear relationship but may be complex relationship between an input value and output ranking scores.

19. Discrete and Continuous ranking

20. Non-linear relationship. Mercury concentration in drinking water

21. At 1150 meters = rank 1
Criterion: desirable sites are greater than 300 but less than 2000 meters from road

23. Weighting Among Criteria
Criteria combined in spatial analysis – in overlay or addition process
How to weigh one layer over another?
How important is slope relative to aspect?
Will an optimum aspect offset a moderately steep site?
The relative weightings given to each criterion will influence the result
Different weights are likely to result in different suitability rankings
Easy to define when importance of the various criteria expressed on a common scale – money
Reducing all criteria to a common scale removes differential weighting among criteria
Continuous ranking may be combined, often through a weighted addition process to generate a combined suitability score.
Assign slopes a monetary values as it affects construction cost.
Costs can be calculated
Nuisance cost for noise and distance cost in lost time or travel might be quantifiable

24. Assigning Weights based on Importance Ranking

25. In our example all criteria are equally weighted and all criteria are binary. 3 base layers are needed Elevation, Soils and Roads. 3 branches in the flowchart.
Reclassify: areas that do and don't meet the respective criteria.

26. Left most branch of the flowchart.
Low elevation = black
Low slopes = light shades
Aspect= light to dark from 0 – 360
Reclassify based on the threshold values.
Two main river systems in the study area:
Running from west to east
Running from south to north

29. Major roads: all divided and multilane roads.

31. Spatio-temporal Models
Includes time driven processes within the framework of model
Feature boundaries, point feature locations, and attribute variables may change within model run
Complicated models
Involves lots of computer coding.