Lecture 15 Principles of Grid-based modelling

1. Lecture 15Principles ofGrid-based modelling Outline introduction linking models to GIS basics of cartographic modelling modelling in Arc/Info GRID GEOG2750 – Earth Observation and GIS of the Physical Environment

2. Introduction • GIS provides: • comprehensive set of tools for environmental data management • limited spatial analysis functionality • but does provides framework of application • limited spatial analysis functionality may be addressed by linking models into GIS GEOG2750 – Earth Observation and GIS of the Physical Environment

3. 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) GEOG2750 – Earth Observation and GIS of the Physical Environment

4. GIS-able models • Types of models applicable to integration with GIS include: • certain aspatial models • black box models • lumped models • all spatial models • distributed models • temporal models GEOG2750 – Earth Observation and GIS of the Physical Environment

5. 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! GEOG2750 – Earth Observation and GIS of the Physical Environment

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 GEOG2750 – Earth Observation and GIS of the Physical Environment

7. 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” GEOG2750 – Earth Observation and GIS of the Physical Environment

8. 5 7 4 A simple example… 4 1 3 2 3 6 Input 1 4 2 2 6 1 2 3 + 6 3 3 4 2 1 6 2 Input 2 4 6 4 3 1 3 2 4 = 7 7 6 6 13 5 7 7 Output 6 10 8 5 2 10 5 5 GEOG2750 – Earth Observation and GIS of the Physical Environment

9. Question… • How determine topological relationships? i.e. Boolean: AND, NOT, OR, XOR • What is the arithmetic equivalent? GEOG2750 – Earth Observation and GIS of the Physical Environment

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 GEOG2750 – Earth Observation and GIS of the Physical Environment

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 GEOG2750 – Earth Observation and GIS of the Physical Environment

12. Modelling in ArcGRID • 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) GEOG2750 – Earth Observation and GIS of the Physical Environment

13. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

14. 5 7 4 Local functions input 25 49 16 output = sqr(input) GEOG2750 – Earth Observation and GIS of the Physical Environment

15. Some examples input output = reclass(input) output = log2(input) output = tan(input) GEOG2750 – Earth Observation and GIS of the Physical Environment

16. 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. GEOG2750 – Earth Observation and GIS of the Physical Environment

17. 5 7 4 Focal functions input 11 16 output = focalsum(input) GEOG2750 – Earth Observation and GIS of the Physical Environment

18. Some examples input output = focalstd(input) output = focalvariety(input) output = focalmean(input, 20) GEOG2750 – Earth Observation and GIS of the Physical Environment

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.) GEOG2750 – Earth Observation and GIS of the Physical Environment

20. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

21. diversity 1 3 4 modal 2 4 5 1 2 4 minimum maximum mean Unsupervised classification 5 4 1 5 3 GEOG2750 – Earth Observation and GIS of the Physical Environment

22. 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. GEOG2750 – Earth Observation and GIS of the Physical Environment

23. 5 7 4 Zonal functions 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

24. Some examples input Input_zone 535.54 127 6280 766.62 160 10800 output = zonalthickness(input_zone) output = zonalmax(input_zone, input) output = zonalperimeter(input_zone) GEOG2750 – Earth Observation and GIS of the Physical Environment

25. 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. GEOG2750 – Earth Observation and GIS of the Physical Environment

26. 5 7 4 Global functions input 6 7 8 9 5 6 7 8 4 5 6 7 output = trend(input) 4 5 6 6 GEOG2750 – Earth Observation and GIS of the Physical Environment

27. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

28. Some examples input source output = eucdistance(source) output = eucdirection(source) output = costdistance(source, input) GEOG2750 – Earth Observation and GIS of the Physical Environment

29. COSTPATH example GEOG2750 – Earth Observation and GIS of the Physical Environment

30. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

31. Practical • Land capability mapping • Task: Map land capability classes for Long Preston area, Ribblesdale • Data: The following datasets are provided for the Long Preston area… • 50m resolution DEM (1:50,000 OS Panorama data) • 10m interval contour data (1:50,000 OS Panorama data) • 25m resolution land cover data (ITE LCM90 data) • soil map (1:250,000 Soil Survey England and Wales) GEOG2750 – Earth Observation and GIS of the Physical Environment

32. Practical • Steps: • Calculate slope from DEM and use reclass to divide into slope classes(g) • Use soil map to create GRID images of soil wetness class(w), soil limitations class(s) and erosivity class(e). Use Tables and dissolve in Arc before converting to GRID using polygrid • Calculate climatic limitations(c) using rainfall model from last week (assume PT = 50mm and T(x) = 14.5°C) • Use GRID to overlay g,w,s,e,c input layers using MAX function to identify capability class. • Display land capability classes with the ITE LCM90 data in ArcMap to compare actual with potential land use GEOG2750 – Earth Observation and GIS of the Physical Environment

33. Learning outcomes • Experience at simple cartographic model building • Experience with spatial modelling functions within Arc and GRID (reclass and overlay) • Familiarity with land resource assessment models GEOG2750 – Earth Observation and GIS of the Physical Environment

34. Useful web links • Lecture on alternative representations of space • http://www.ncgia.ucsb.edu/giscc/units/u054/u054.html • PCRaster – an alternative to GRID • http://www.geog.uu.nl/pcraster/pcraster.html GEOG2750 – Earth Observation and GIS of the Physical Environment

35. Next week… • Terrain modelling: the basics • DEMs and DTMs • derived variables • example applications • Practical: Using DEMs for hillslope geomorphology GEOG2750 – Earth Observation and GIS of the Physical Environment