Lecture 15 Principles of Gridbased modelling Outline introduction

Lecture 15 Principles of Grid-based modelling • Outline – introduction – linking models to GIS – basics of cartographic modelling – modelling in Arc/Info GRID Week 18 GEOG 2750 – Earth Observation and GIS of the Physical 1

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 18 GEOG 2750 – Earth Observation and GIS of the Physical 2

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 18 GEOG 2750 – Earth Observation and GIS of the Physical 3

GIS-able models • Types of models applicable to integration with GIS include: – certain aspatial models Ø black box models Ø lumped models – all spatial models Ø distributed models – temporal models Week 18 GEOG 2750 – Earth Observation and GIS of the Physical 4

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 18 GEOG 2750 – Earth Observation and GIS of the Physical 5

Basics of cartographic modelling • Mathematics applied to raster maps – often referred to as map algebra or ‘mapematics’ – e. g. combination of maps by: Ø addition Ø subtraction Ø multiplication Ø division, etc. – operations on single or multiple layers Week 18 GEOG 2750 – Earth Observation and GIS of the Physical 6

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 18 GEOG 2750 – Earth Observation and GIS of the Physical 7

A simple example… 4 1 5 2 3 4 6 13 7 6 10 5 8 5 + Input 2 3 2 7 7 2 4 7 4 6 6 1 Week 18 3 1 Input 1 6 3 4 2 3 6 2 3 4 4 1 2 7 6 2 2 3 6 5 5 = Output 10 GEOG 2750 – Earth Observation and GIS of the Physical 8

Question… • How determine topological relationships? i. e. Boolean: AND, NOT, OR, XOR • What is the arithmetic equivalent? Week 18 GEOG 2750 – Earth Observation and GIS of the Physical 9

Building spatial models • It is (in theory) surprisingly simple: – algebraic combination of: OPERATORS and FUNCTIONS Ø rules and relationships Ø inputs (and outputs) Ø – interfaces run at the command line/menu interface Ø batch file Ø embedded in system macro/script Ø ‘hard’ programmed into system Ø Week 18 GEOG 2750 – Earth Observation and GIS of the Physical 10

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 18 GEOG 2750 – Earth Observation and GIS of the Physical 11

Modelling in Arc. GRID • 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 18 GEOG 2750 – Earth Observation and GIS of the Physical 12

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 Ø Ø Ø Ø Week 18 Trigonometric, exponential and logarithmic Reclassification and selection Logical expressions in GRID Operands and logical operators Connectors Statistical Other local functions GEOG 2750 – Earth Observation and GIS of the Physical 13

Local functions 5 7 4 25 49 16 Week 18 input output = sqr(input) GEOG 2750 – Earth Observation and GIS of the Physical 14

Some examples input output = tan(input) Week 18 output = reclass(input) output = log 2(input) GEOG 2750 – Earth Observation and GIS of the Physical 15

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: Ø 3 – Week 18 x 3 cell or other calculate mean, SD, sum, range, max, min, etc. GEOG 2750 – Earth Observation and GIS of the Physical 16

Focal functions 5 7 4 input 11 16 Week 18 output = focalsum(input) GEOG 2750 – Earth Observation and GIS of the Physical 17

Some examples input output = focalmean(input, 20) Week 18 output = focalstd(input) output = focalvariety(input) GEOG 2750 – Earth Observation and GIS of the Physical 18

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 Ø unsupervised based on values of other pixels within specified filter and using certain rules (diversity, frequency, average, minimum, maximum, etc. ) Ø Week 18 GEOG 2750 – Earth Observation and GIS of the Physical 19

Supervised classification 1 3 4 2 4 5 1 2 4 1 4 2 3 5 Old class Week 18 1 1 1 2 2 New class GEOG 2750 – Earth Observation and GIS of the Physical 20

Unsupervised classification 5 diversity 1 3 4 2 4 5 1 2 4 4 modal 1 minimum 5 3 maximum mean Week 18 GEOG 2750 – Earth Observation and GIS of the Physical 21

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 – – Week 18 use complex neighbourhoods or zones calculate mean, SD, sum, range, max, min, etc. GEOG 2750 – Earth Observation and GIS of the Physical 22

Zonal functions 5 7 4 input Zone 2 zone Zone 1 9 7 9 9 Week 18 7 7 9 9 7 output = zonalsum(zone, input) 7 GEOG 2750 – Earth Observation and GIS of the Physical 23

Some examples input 535. 54 766. 62 Input_zone 127 6280 160 output = zonalthickness(input_zone) zonalmax(input_zone, input) Week 18 10800 output = zonalperimeter(input_zone) GEOG 2750 – Earth Observation and GIS of the Physical 24

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 Ø weighted distance functions Ø surface functions Ø hydrologic and groundwater functions Ø multivariate. Ø Week 18 GEOG 2750 – Earth Observation and GIS of the Physical 25

Global functions 5 7 input 4 6 7 5 6 4 4 Week 18 8 7 5 5 9 8 6 6 7 output = trend(input) 6 GEOG 2750 – Earth Observation and GIS of the Physical 26

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 Ø linear Ø non-linear etc. ) – – Week 18 (curvilinear, stepped, exponential, root, use target weighted functions use cost surfaces GEOG 2750 – Earth Observation and GIS of the Physical 27

Some examples input source output = eucdistance(source) output = eucdirection(source) output = costdistance(source, input) Week 18 GEOG 2750 – Earth Observation and GIS of the Physical 28

COSTPATH example Week 18 GEOG 2750 – Earth Observation and GIS of the Physical 29

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 18 GEOG 2750 – Earth Observation and GIS of the Physical 30

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… – – Week 18 50 m resolution DEM (1: 50, 000 OS Panorama data) 10 m interval contour data (1: 50, 000 OS Panorama data) 25 m resolution land cover data (ITE LCM 90 data) soil map (1: 250, 000 Soil Survey England Wales) GEOG 2750 – Earth Observation and GIS of the Physical 31

Practical • 1. 2. 3. 4. 5. 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 = 50 mm 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 LCM 90 data in Arc. Map to compare actual with potential land use Week 18 GEOG 2750 – Earth Observation and GIS of the Physical 32

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 18 GEOG 2750 – Earth Observation and GIS of the Physical 33

Useful web links • Lecture on alternative representations of space – http: //www. ncgia. ucsb. edu/giscc/units/u 054. html • PCRaster – an alternative to GRID – http: //www. geog. uu. nl/pcraster. html Week 18 GEOG 2750 – Earth Observation and GIS of the Physical 34

Next week… • Terrain modelling: the basics – DEMs and DTMs – derived variables – example applications • Practical: Using DEMs for hillslope geomorphology Week 18 GEOG 2750 – Earth Observation and GIS of the Physical 35