Lecture 15 Principles of Gridbased modelling

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Lecture 15Principles of Grid-based modelling

• Outline
• introduction
• linking models to GIS
• basics of cartographic modelling
• modelling in Arc/Info GRID

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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

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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)

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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

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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!

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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

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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

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A simple example
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Input 1
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Input 2
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Output
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Question

• How determine topological relationships?
• i.e. Boolean AND, NOT, OR, XOR
• What is the arithmetic equivalent?

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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

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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

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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)

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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

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Local functions
input
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output sqr(input)
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Some examples
input
output reclass(input)
output log2(input)
output tan(input)
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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.

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Focal functions
input
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output focalsum(input)
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Some examples
input
output focalstd(input)
output focalvariety(input)
output focalmean(input, 20)
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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.)

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Supervised classification
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Unsupervised classification
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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.

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Zonal functions
input
Zone 2
zone
Zone 1
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output zonalsum(zone, input)
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Some examples
input
Input_zone
535.54
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6280
766.62
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10800
output zonalthickness(input_zone)
output zonalmax(input_zone, input)
output zonalperimeter(input_zone)
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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.

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Global functions
input
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output trend(input)
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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

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Some examples
input
source
output eucdistance(source)
output eucdirection(source)
output costdistance(source, input)
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COSTPATH example
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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

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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 (150,000 OS Panorama data)
• 10m interval contour data (150,000 OS Panorama
  data)
• 25m resolution land cover data (ITE LCM90 data)
• soil map (1250,000 Soil Survey England and
  Wales)

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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)
  14.5C)
• 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

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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

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Useful web links

• Lecture on alternative representations of space
• http//www.ncgia.ucsb.edu/giscc/units/u054/u054.ht
  ml
• PCRaster an alternative to GRID
• http//www.geog.uu.nl/pcraster/pcraster.html

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Next week

• Terrain modelling the basics
• DEMs and DTMs
• derived variables
• example applications
• Practical Using DEMs for hillslope geomorphology