GIS Operations and Spatial Analysis Turns raw data into useful information by adding greater...

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

• 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 AlgebraMap 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 FunctionsLocal 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 12 4 03 1

* 3 = 6 0 36 12 09 3

2 0 12 4 03 1

1 5 34 4 32 5 6

2 0 38 16 06 6

* =

Polygon Overlay, Discrete Object Case

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.

A B

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 FunctionsFocal 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

41

43 6

1

43 6

41

43 65 2

3 441

43 65 2

3 4

Kinds of NeighborhoodsKinds 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 OperationsNeighborhood Operations

41

43 6 X

some function

Functions:Total: X = 18 Variety: X = 4Average: X = 4 Median: X = 4Minimum: X = 1 Deviation: X = 0Maximum: X = 6 Std. dev.: X = 2Minority: X = 1 (or 3, or 6) Proportion: X = 40Majority: X = 4 . . .

Neighborhood StatisticsNeighborhood 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 NeighborhoodBuffer: 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

Point

Polyline

Polygon

Applications of BuffersApplications 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 FunctionsZonal Functions

• assign values to all cells in a zone, based on values from another map

zonal grid + values grid => output grid

2 0 02 4 03 4

1 2 34 5 67 8 9

4 6 64 9 67 9

max

again, many types of functions are available

Global (incremental) FunctionsGlobal (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 CombinationRules 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. ScreeningDominance 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)

1 1 0 00 0 1 00 1 1 11 1 1 0

and

0 1 0 00 1 0 10 1 0 10 0 1 0

0 1 0 00 0 0 00 1 0 10 0 1 0

==>

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

Dominance Rules: Excl. RankingDominance 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)

1 2 1 23 3 1 31 3 1 21 1 1 2

and

3 1 1 12 1 3 31 1 2 11 1 1 3

3 2 1 23 3 3 31 3 2 21 1 1 3

==>

Dominance: Highest Bid/BidderDominance: Highest Bid/Bidder

• apply to ratio data • examples:

• max profit for a site => highest bid• activity/developer providing the maximum profit

=> highest bidder

5.3 6.2 6.7 8.11.1 1.4 5.6 6.66.5 7.4 8.2 9.13.3 5.5 7.7 6.2

6.1 7.5 6.2 7.13.1 2.4 7.6 5.66.3 7.5 8.0 5.12.3 6.5 5.7 5.2

Factor 1 Factor 2

6.1 7.5 6.7 8.13.1 2.4 7.6 6.66.5 7.5 8.2 9.13.3 6.5 7.7 6.2

2 2 1 1 2 2 2 1 1 2 1 1 1 2 1 1

and

highestbid

highestbidder

Contributory: Voting TabulationContributory: Voting Tabulation

• how many positive (or negative) factors occur at a location (number of votes cast)

• applies to nominal categories

1 1 0 00 0 1 00 1 1 11 1 1 0

+

0 1 0 00 1 0 10 1 0 10 0 1 0

1 2 0 00 1 1 10 2 1 21 1 2 0

==>

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 VotingContributory: Weighted Voting

• weights express relative importance of each factor, factors are still 0 and 1

1 1 0 00 0 1 00 1 1 11 1 1 0

+

0 1 0 00 1 0 10 1 0 10 0 1 0

3 8 0 00 5 3 50 8 3 83 3 8 0

==>3 x 5 x

weights of factors

Contributory: Linear CombinationContributory: Linear Combination

• each factor map is expressed as a set of site rankings

• these rankings are added up for each cell

1 2 1 23 3 1 31 3 1 21 1 1 2

+

3 1 1 12 1 3 31 1 2 11 1 1 3

4 3 2 35 4 4 62 4 3 32 2 2 5

==>

consider this:2 = 1 + 13 = 1 + 2 = 2 + 14 = 1 + 3 = 2 + 2 = 3 + 15 = 2 + 3 = 3 + 26 = 3 + 3

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

Contributory: Weighting and RatingContributory: Weighting and Rating

• factor maps composed of rankings, weights externally assigned

• a rather problematic, though very popular method

Also, there is Non-linear combination (like USLE) -particularly sensitive to errors, zero values...

1 2 1 23 3 1 31 3 1 21 1 1 2

+

3 1 1 12 1 3 31 1 2 11 1 1 3

18 11 8 1119 14 18 24 8 14 13 11 8 8 8 21

==>3 x 5 x

weights of factors

How to Assign WeightsHow 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 1Interaction 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 2 1 23 3 1 31 3 1 21 1 1 2

and

3 1 1 12 1 3 31 1 2 11 1 1 3

3 4 1 48 7 3 91 7 2 41 1 1 6

==>

1 : 1 & 12 : 1 & 23 : 1 & 34 : 2 & 15 : 2 & 26 : 2 & 37 : 3 & 18 : 3 & 29 : 3 & 3

legend

number of potential categories rises quickly,but fortunately just a small fraction survive

Interaction Rules 2Interaction 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, NEIGHBORHOODOPERAITONS, ZONAL OPERATIONS, etc. - everywhere where you need to combine values