Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment1 Lecture 15 Principles of Grid-based modelling Outline – introduction – linking models to GIS – basics of cartographic modelling – modelling in Arc/Info GRID

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment2 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

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment3 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)

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment4 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

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment5 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!

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment6 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

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment7 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”

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment8 A simple example… Input Input 2 Output + =

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment9 Question… How determine topological relationships? i.e. Boolean: AND, NOT, OR, XOR What is the arithmetic equivalent?

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment10 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

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment11 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

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment12 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)

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment13 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

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment14 Local functions input output = sqr(input)

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment15 Some examples input output = tan(input) output = reclass(input)output = log2(input)

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment16 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.

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment17 Focal functions input output = focalsum(input)

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment18 Some examples input output = focalmean(input, 20) output = focalstd(input)output = focalvariety(input)

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment19 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.)

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment20 Supervised classification Old classNew class

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment diversity modal minimum maximum mean Unsupervised classification

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment22 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.

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment23 Zonal functions input output = zonalsum(zone, input) zone Zone 1 Zone

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment24 Some examples input output = zonalthickness(input_zone) Input_zone output = zonalmax(input_zone, input) output = zonalperimeter(input_zone)

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment25 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.

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment26 Global functions input output = trend(input)

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment27 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

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment28 Some examples inputsource output = eucdistance(source)output = eucdirection(source)output = costdistance(source, input)

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment29 COSTPATH example

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment30 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

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment31 Practical Land capability mapping Task: Map land capability classes for Long Preston area, RibblesdaleRibblesdale 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)

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment32 Practical Steps: 1.Calculate slope from DEM and use reclass to divide into slope classes(g) 2.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 3.Calculate climatic limitations(c) using rainfall model from last week (assume PT = 50mm and T(x) = 14.5°C) 4.Use GRID to overlay g,w,s,e,c input layers using MAX function to identify capability class. 5.Display land capability classes with the ITE LCM90 data in ArcMap to compare actual with potential land use

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment33 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

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment34 Useful web links Lecture on alternative representations of space – PCRaster – an alternative to GRID –

Week 18GEOG2750 – Earth Observation and GIS of the Physical Environment35 Next week… Terrain modelling: the basics –DEMs and DTMs – derived variables – example applications Practical: Using DEMs for hillslope geomorphology