Introduction to ArcGIS - Get as PowerPoint by hcj

VIEWS: 12 PAGES: 26

									School of Geography
FACULTY OF ENVIRONMENT




 Cartographic modelling
Day 1: cartographic modelling

• Principles
• Mathematical and logical functions
• Overlay and distance functions
• Local, focal, zonal and global functions
• Spatial Analyst and ArcGrid
Principles

• Mathematics applied to raster maps
• Map algebra or ‘mapematics’
 • e.g. combination of maps by:
   • Addition
   • Subtraction
   • Multiplication
   • division, etc.
 • operations on single layers
 • operations on multiple layers
Principles

“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”
Principles

• A simple example...
                             1                        4               3               2
                         5                    6                   7               3
                     2                    4                   4               2           Input 1
             1                   2                        3               6
                                                                                            +
                         6                    3                   3               4
                     2                1                       6               2
                                                                                          Input 2
                 4               6                        4               3
         1                   3                    2                   4
                                                                                            =
                         7                7                    6                  6
                     7                7                       13              5
             6                   10                   8                   5               Output
         2                   5                    5                10
Maths and logic

• Mathematical operators
 • Addition, subtraction, multiplication, division
 • Square, squareroot, logarithms, exponents, etc.
 • Trigonometry, etc.
• Logical operators
 • Boolean (AND, OR, NOT, XOR)
 • Relative (maximum, minimum, etc.)
 • Combinatory
 • Etc.
Overlay and distance

• Overlay is achieved mathematically
 • e.g. in raster calculator
Overlay and distance

• 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
Overlay and distance

Some examples




                               input                      source




output = eucdistance(source)    output = eucdirection(source) output = costdistance(source, input)
Overlay and distance

COSTPATH example
Local, focal, zonal and global

•   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)
Local, focal, zonal and global

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, and other local functions
Local, focal, zonal and global

Local functions




        5            7
                                 input
             4




        25           49
             16                  output = sqr(input)
Local, focal, zonal and global

Some examples




                                   input




     output = tan(input)   output = reclass(input)   output = log2(input)
Local, focal, zonal and global

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.
Local, focal, zonal and global


Focal functions



       5           7
                                    input
            4




                   11
            16                   output = focalsum(input)
Local, focal, zonal and global

Some examples




                                         input




 output = focalmean(input, 20)   output = focalstd(input)   output = focalvariety(input)
Local, focal, zonal and global

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.)
Local, focal, zonal and global

Supervised classification


                   1
        1 3 4          2                   1 1 2
                           3     1
        2 4 5                              1 2 2
        1 2 4                              1 1 2
                   4
                       5         2

                Old class      New class
Local, focal, zonal and global

Unsupervised classification

                         5

                      diversity      4

          1 3 4                    modal
          2 4 5                               1
          1 2 4
                                            minimum
                                     5

                         3        maximum

                       mean
Local, focal, zonal and global

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.
Local, focal, zonal and global

Zonal functions

                 5                               7
                             4                                           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
Local, focal, zonal and global
Some examples




                          input                     Input_zone




         535.54                         127                        6280




             766.62                        160                        10800

          output =                  output =                       output =
 zonalthickness(input_zone) zonalmax(input_zone, input)   zonalperimeter(input_zone)
Local, focal, zonal and global

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.
Local, focal, zonal and global

Global functions




             5                               7
                                                                      input
                         4


                 6               7               8               9
             5               6               7               8
         4               5               6               7           output = trend(input)
     4               5               6               6
Practical exercise



     Hands-on Exercise #3
       Cartographic modelling in ArcMap

								
To top