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GIS Operations and Spatial Analysis. Turns raw data into useful information by adding greater informative content and value Reveals patterns, trends, and anomalies that might otherwise be missed Provides a check on human intuition by helping in situations where the eye might deceive

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gis operations and spatial analysis
GIS Operations and Spatial Analysis
  • Turns raw data into useful information
    • by adding greater informative content and value
  • Reveals patterns, trends, and anomalies that might otherwise be missed
  • Provides a check on human intuition
    • by helping in situations where the eye might deceive
  • Thousands of techniques exist…
map of cholera deaths by john snow
Map of Cholera Deaths by John Snow
  • Provides a classic example of the use of location to draw inferences
  • But the same pattern could arise from contagion
    • if the original carrier lived in the center of the outbreak
    • contagion was the hypothesis Snow was trying to refute
    • today, a GIS could be used to show a sequence of maps as the outbreak developed
    • contagion would produce a concentric sequence, drinking water a random sequence
map algebra
Map Algebra
  • C. Dana Tomlin (1983…)
  • implemented in many grid analysis packages, including ArcGrid, Idrisi, MapII, ArcView Spatial Analyst
  • Four classes of operations:
    • local
    • focal
    • zonal
    • incremental

DEMO

local functions
Local Functions
  • work on single cells, one after another, value assigned to a cell depends on this cell only
  • examples:
    • arithmetic operations with a constant, or with another grid:
    • also logical operations, comparisons (min, max, majority, minority, variety, etc.)

2 0 1

2 4 0

3 1

6 0 3

6 12 0

9 3

2 0 1

2 4 0

3 1

1 5 3

4 4 3

2 5 6

2 0 3

8 16 0

6 6

* 3 =

=

*

polygon overlay discrete object case
Polygon Overlay, Discrete Object Case

B

A

In this example, two polygons are intersected to form 9 new polygons. One is formed from both input polygons; four are formed by Polygon A and not Polygon B; and four are formed by Polygon B and not Polygon A.

spurious or sliver polygons
Spurious or Sliver Polygons
  • In any two such layers there will almost certainly be boundaries that are common to both layers
    • e.g. following rivers
  • The two versions of such boundaries will not be coincident
  • As a result large numbers of small sliver polygons will be created
    • these must somehow be removed
    • this is normally done using a user-defined tolerance
focal functions
Focal Functions
  • assign data value to a cell based on its neighborhood (variously defined)
  • uses:
    • smoothing - moving averaging
    • edge detection
    • assessing variety, etc.
  • examples:
    • focal sum - adds up values in cell neighborhood, and assigns this value to the focal cell
    • focal mean - averages values in neighborhood,and assigns the result to the focal cell
    • also: logical functions, other mathematical
shapes of neighborhoods
Shapes of Neighborhoods

1

1

3

4

6

3

6

4

4

5

1

2

5

1

2

3

4

6

3

4

6

3

4

4

3

4

4

kinds of neighborhoods
Kinds of Neighborhoods
  • Neighborhood: a set of locations each of which bears a specified distance and/or directional relationship to a particular location called the neighborhood focus (D. Tomlin)
    • distance and directional neighbors
    • immediate and extended neighbors
    • metric and topological neighbors
    • neighbors of points, lines, areas...
neighborhood operations
Neighborhood Operations

some function

1

3

4

6

X

4

Functions:

Total: X = 18 Variety: X = 4

Average: X = 4 Median: X = 4

Minimum: X = 1 Deviation: X = 0

Maximum: X = 6 Std. dev.: X = 2

Minority: X = 1 (or 3, or 6) Proportion: X = 40

Majority: X = 4 . . .

neighborhood statistics
Neighborhood Statistics
  • In Spatial Analyst you can specify:
    • shape of neighborhood: | Circle | Rectangle | Doughnut | Wedge
    • size of neighborhood: radius (circle), inner and outer radius (doughnut), radius, start and end angles (wedge), width and height (rectangle)
    • operation: | Minimum | Maximum | | Mean | Median | Sum | Range | Standard Dev. | Majority | Minority | Variety |
buffer a typical neighborhood
Buffer: a Typical Neighborhood
  • Buffers and offsets
  • Buffers in vector form
    • either a chain of “sausages”
    • or a Voronoi network
  • Buffers in raster form
    • a two-step operation: (1) create a map of distances from the object; (2) reclassify it into a binary map
buffering
Buffering

Polyline

Polygon

Point

applications of buffers
Applications of Buffers
  • Exclusionary screening / ranking - in site selection studies
  • Environmental regulations

Main question: how wide??

-depends on a variety of political / social / economic / cultural circumstances, often difficult to formalize... differs by states and counties

zonal functions
Zonal Functions
  • assign values to all cells in a zone, based on values from another map

zonal grid + values grid => output grid

2 0 0

2 4 0

3 4

1 2 3

4 5 6

7 8 9

4 6 6

4 9 6

7 9

max

again, many types of functions are available

global incremental functions
Global (incremental) Functions
  • cell value for each cell depends on processing the entire grid
  • examples:
    • computing distance from one cell (or group of cells) to all other cells
    • distance can be weighted by some impedance factor => cost-distance surfaces
  • uses:
    • diffusion modeling
    • shortest path modeling, distance-based site selection
    • visibility analysis
    • connectivity and fragmentation in habitat analysis, etc.
rules of map combination
Rules of Map Combination
  • Dominance
    • selects one value from those available, other values ignored; an external rule is used for selection
  • Contributory
    • values from each map contribute to the result, typically combined with some arithmetic operation, ignoring interdependence of factors (each value contributes without regard to others)
  • Interaction
    • interaction between factors is accounted for, more flexible design

+

dominance rules excl screening

1 1 0 0

0 0 1 0

0 1 1 1

1 1 1 0

0 1 0 0

0 1 0 1

0 1 0 1

0 0 1 0

0 1 0 0

0 0 0 0

0 1 0 1

0 0 1 0

Dominance Rules: Excl. Screening
  • Exclusionary screening
    • selects one value from the available set, ignoring others, usually by an externally specified rule
    • exclusionary screening(“one strike and you’re out”)
      • binary (yes/no)
      • typically an iterative process (two risks: either too much area left, or too much excluded)

and

==>

in map calculator, with 0/1 themes, can simply multiply them

dominance rules excl ranking

1 2 1 2

3 3 1 3

1 3 1 2

1 1 1 2

3 1 1 1

2 1 3 3

1 1 2 1

1 1 1 3

3 2 1 2

3 3 3 3

1 3 2 2

1 1 1 3

Dominance Rules: Excl. Ranking
  • for ordinal data => take min, or max
    • common for land resource assessment
    • for example: encode areas with most severe limitation by any of the factors (max)

and

==>

dominance highest bid bidder

6.1 7.5 6.7 8.1

3.1 2.4 7.6 6.6

6.5 7.5 8.2 9.1

3.3 6.5 7.7 6.2

5.3 6.2 6.7 8.1

1.1 1.4 5.6 6.6

6.5 7.4 8.2 9.1

3.3 5.5 7.7 6.2

6.1 7.5 6.2 7.1

3.1 2.4 7.6 5.6

6.3 7.5 8.0 5.1

2.3 6.5 5.7 5.2

2 2 1 1

2 2 2 1

1 2 1 1

1 2 1 1

Dominance: Highest Bid/Bidder
  • apply to ratio data
  • examples:
    • max profit for a site => highest bid
    • activity/developer providing the maximum profit => highest bidder

highest

bid

and

highest

bidder

Factor 1

Factor 2

contributory voting tabulation

1 1 0 0

0 0 1 0

0 1 1 1

1 1 1 0

0 1 0 0

0 1 0 1

0 1 0 1

0 0 1 0

1 2 0 0

0 1 1 1

0 2 1 2

1 1 2 0

Contributory: Voting Tabulation
  • how many positive (or negative) factors occur at a location (number of votes cast)
  • applies to nominal categories

+

==>

also, can produce the most frequent/least frequent value, etc.

… is an area excluded on two criteria twice as excluded as area excluded on one factor?...

contributory weighted voting

1 1 0 0

0 0 1 0

0 1 1 1

1 1 1 0

0 1 0 0

0 1 0 1

0 1 0 1

0 0 1 0

3 8 0 0

0 5 3 5

0 8 3 8

3 3 8 0

Contributory: Weighted Voting
  • weights express relative importance of each factor, factors are still 0 and 1

3 x

5 x

+

==>

weights of factors

contributory linear combination

1 2 1 2

3 3 1 3

1 3 1 2

1 1 1 2

3 1 1 1

2 1 3 3

1 1 2 1

1 1 1 3

4 3 2 3

5 4 4 6

2 4 3 3

2 2 2 5

Contributory: Linear Combination
  • each factor map is expressed as a set of site rankings
  • these rankings are added up for each cell

+

==>

consider this:

2 = 1 + 1

3 = 1 + 2 = 2 + 1

4 = 1 + 3 = 2 + 2 = 3 + 1

5 = 2 + 3 = 3 + 2

6 = 3 + 3

this is what happens when you add up ordinal data. Perhaps, convert them to ratio (dollars)?

contributory weighting and rating

1 2 1 2

3 3 1 3

1 3 1 2

1 1 1 2

3 1 1 1

2 1 3 3

1 1 2 1

1 1 1 3

Contributory: Weighting and Rating
  • factor maps composed of rankings, weights externally assigned
  • a rather problematic, though very popular method

18 11 8 11

19 14 18 24

8 14 13 11

8 8 8 21

3 x

5 x

+

==>

weights of factors

Also, there is Non-linear combination (like USLE) -

particularly sensitive to errors, zero values...

how to assign weights
How to Assign Weights
  • Delphi techniques
    • to aid decision-makers in making value judgments; elicit and refine group judgments where exact knowledge is unavailable
      • rounds of “blind’ individual ratings by professionals
      • rounds of open discussion of differences
      • re-evaluations
      • often: categories and their sets are redefined
      • task: to obtain a reliable consensus
  • Binary comparisons
interaction rules 1

1 2 1 2

3 3 1 3

1 3 1 2

1 1 1 2

3 1 1 1

2 1 3 3

1 1 2 1

1 1 1 3

3 4 1 4

8 7 3 9

1 7 2 4

1 1 1 6

Interaction Rules 1
  • “Gestalt”, or Integrated Survey
    • a field team is sent out to produce an integral map...
  • Factor combination
    • all possible combinations are considered and rated

1 : 1 & 1

2 : 1 & 2

3 : 1 & 3

4 : 2 & 1

5 : 2 & 2

6 : 2 & 3

7 : 3 & 1

8 : 3 & 2

9 : 3 & 3

and

==>

legend

number of potential categories rises quickly,

but fortunately just a small fraction survive

interaction rules 2
Interaction Rules 2
  • Interaction tables
    • values of one factor determine weights of other factors, then weighting/rating scheme is applied
  • Hierarchical rules of combination
  • Binary comparisons

NOTE THAT ALL THESE METHODS -

Dominance, Contributory, Interaction -

APPLY TO OVERLAY, NEIGHBORHOOD

OPERAITONS, ZONAL OPERATIONS, etc. -

everywhere where you need to combine values