# Introduction to ArcGIS - Get as PowerPoint by hcj

VIEWS: 12 PAGES: 26

• pg 1
```									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:
• 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
• 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