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GIS - consists of:
Components People, organizational setting Procedures, rules, quality control Tools, hardware & software Data, information
Functions Data gathering Data distribution
Geographic Data ( i.e. not spatial information)
Spatial Data location shape relationship among
features
Descriptive Data attributes, or characteristics of
the features
Spatial Data: the spatial attribute is explicitly stated and linked to the thematic attribute for each data item.
Spatial Information
Three Attributes of Geographic Data that constitutes Information Thematic (Value Variable)
Nominal, … name, label Ordinal, … rank ordered Interval / Ratio, … measurement on a scale
Spatial (location) Temporal
After Sinton, 1978:Components of spatial information: time, space, theme (attribute)
Sounds obvious. One must be fixed, one controlled, one measured.
Spatial - thematic value types
Sta. 94, DOC 4.9
WELL200’
100’
100’
200’
Former Land Fill
URBANDuvall, pop 1170
FOREST
FOREST
AGRICULTURE
Snoqualmie River, 1
BrushCreek, 2
Stream,3
GeographiesLayers, Coverages, Themes
Land useSoils
Streets
Hydrology
Parcels
Concept of Spatial Objects POINTS
LINES
AREA
Spatial Encoding - RASTER
0 00
00 0 0
01
POINT
1
0
1
11
0 0
00
0
5 5 3
3311 2
LINE
AREA
Spatial Encoding - VECTORPOINT - x, y
LINE - x1, y1- x2, y2..- xN, yN
Area (Polygons)
- x1, y1- x2, y2..- xN, yN (closure Point)
* a single node with NO area
* a connection of nodes (vertices) beginning with a “to” and ending with a “from”
(Arcs)
* a series of arc(s) that close around a “label” point
Vector - TopologyObject Spatial Descriptive
12 3
45
15
1211
10
123
x1,y1x2,y2x3,y3
123
12
12
12
12
VAR1 VAR2
VAR1 VAR2
VAR1 VAR2
Fnode Tnode x1y1, x2y21 2 xxyy, xxyy2 3 xxyy,xxyy
10, 11, 12, 1510, …….
12 3
1
2
Raster Data Model
Set Selections
Reduce Select - RESEL GT 5 = [6 7 8 9 10]
Add Select - ASEL EQ 5 = [5 6 7 8 9 10]
Unselect - UNSEL GE 9 = [5 6 7 8 ]
Null Select - NSEL = [1 2 3 4 9 10 ]
[ 1 2 3 4 5 6 7 8 9 10 ]
AND, OR, XOR
1 2 32
AND = 2
OR
XOR
= 1,2,3
= 1
Spatial Overlay - UNION
1
2 3
4 5
1
2
3
1 23
4 5
6
7 8
9 10
11 12
13 14
1516 17
12345
# attribute
123
# attribute
12345
# IN attribut OUT attribute
ABCD
102103
102 A A 102 B 102
Spatial Overlay - INTERSECT
1
2 3
4 5
1
2
3
1
12345
# attribute
123
# attribute
12345
# IN attribut OUT attribute
ABCD
102103
A 102 B 102 A 103 B 103
2 3
4 5
6 7
8 9
Spatial Overlay - IDENTITY
1
2 3
4 5
1
2
3
1
12345
# attribute
123
# attribute
12345
# IN attribut OUT attribute
ABCD
102103
A A 102 B 103 B
2
3 4
5
6 7
8 9
10 1112 13
Spatial Poximity - BUFFER
Constant Width
Variable Width
Spatial Poximity - NEAR
Assign a point to the nearest arc
Spatial Proximity - Pointdistance
123
123
2,0451,8991,743
DISTANCE
Spatial Proximity - Thiessen Polygons
Map AlgebraIn a raster GIS, cartographic modeling is also named Map Algebra.
Mathematical combinations of raster layers several types of functions: • Local functions • Focal functions • Zonal functions • Global functions
Functions can be applied to one or multiple layers
Local FunctionSometimes called layer functions -
Work on every single cell in a raster layer
•Cells are processed without reference to surrounding cells
•Operations can be arithmetic, trigonometric, exponential, logical or logarithmic functions
Local Functions: Example•Multiply by constant value
X 3 =
•Multiply by a grid
X =
2 0 1 1 2 3 0 4 1 1 2
3 2
2 0 1 1 2 3 0 4 1 1 2
3 2
6 0 3 3 6 9 0 12 3 3 6
9 6
2 0 2 2 3 3 3 3 2 2 2
1 1
4 0 2 2 6 9 0 12 2 2 4
3 2
Focal FunctionFocal functions process cell data depending on the values of neighbouring cells
We define a ‘kernel’ to use as the neighbourhood •for example, 2x2, 3x3, 4x4 cells
Types of focal functions might be: •focal sum, •focal mean, •focal max, •focal min, •focal range
Focal Function: Examples
2 0 1 1 2 3 0 4 2 1 1 2
2 3 3 2
2 0 1 1 2 3 0 4 4 2 2 3
1 1 3 2
•Focal Sum (sum all values in a neighborhood)
=
=
•Focal Mean (moving average all values in a neighborhood)
1.8 1.3 1.5 1.5 2.2 2.0 1.8 1.8 2.2 2.0 2.2 2.3
2.0 2.2 2.3 2.5
(3x3)
(3x3) 12 13
17 19
Zonal FunctionProcess and analyze cells on the basis of ‘zones’
Zones define cells that share a common characteristic Cells in the same zone don’t have to be contiguous
A typical zonal function requites two grids •a zone grid which defines the size, shape and location of each zone •a value grid which is processed
Typical zonal functions •zonal mean, •zonal max, •zonal sum, •zonal variety
Zonal FunctionAn Example
•Zonal maximum – Identify the maximum in each zone
Useful when we have different regions “classified” and wish to treat all grid cells of each type as a single “zone” (ie. Forests, urban, water, etc.)
2 2 1 1 2 3 3 1 3 2
1 1 2 2
1 2 3 4 5 6 7 8 1 2 3 4
5 6 7 8
5 5 8 8 5 7 7 8 7 8
8 8 8 8
=
Global functionIn global functions -
•The output value of each cell is a function of the entire grid
•Typical global functions are distance measures, flow directions, or weighting measures.
•Useful when we want to work out how cells ‘relate’ to each other
Golbal FunctionAn Example
•Distance Measures – Euclidean distance based upon cell size
Or – some function which must consider all cells before determining the value of any cell – (“cost” associated with a path across the surface)
1 1 1 2
2 1 0 01.4 1 1 0 1 0 1 1
1.4 1 1.4 2
=
Examples
outgrid = zonalsum(zonegrid, valuegrid)
outgrid = focalsum(ingrid1, rectangle, 3, 3)
outgrid = (ingrid1 div ingrid2) * ingrid3
Spatial ModelingSpatial modeling is analytical procedures applied with a GIS. Spatial modeling uses geographic data to attempt to describe, simulate or predict a real-world problem or system.
There are three categories of spatial modeling functions that can be applied to geographic features within a GIS: •geometric models, such as calculating the Euclidean distance between features, •coincidence models, such as topological overlay; •adjacency models (pathfinding, redistricting, and allocation)
All three model categories support operations on spatial data such as points, lines, polygons, tins, and grids. Functions are organized in a sequence of steps to derive the desired information for analysis.
The following references are excellent introductions to modeling in GIS:Goodchild, Parks, and Stegaert. Environmental Modeling with GIS. Oxford University Press, 1993.Tomlin, Dana C. Geographic Information Systems and Catograhic Modeling. Prentice Hall, 1990.
