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Topic 4 – Geographical Data Analysis

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Topic 4 – Geographical Data Analysis

A – The Nature of Spatial Analysis

B – Basic Spatial Analysis

A

- 1. Spatial Analysis and its Purpose
- 2. Spatial Location and Reference
- 3. Spatial Patterns
- 4. Topological Relationships

1

- Conceptual framework
- Search of order amid disorder.
- Organize information in categories.

- Method
- Inducting or deducting conclusions from spatially related information.
- Deduction: Deriving from a model or a rule a conclusion.
- Induction: Learning new concepts from examples.

- Spatial analysis as a decision-making tool.
- Help the user make better decisions.
- Often involve the allocation of resources.

- Inducting or deducting conclusions from spatially related information.

1

- Requirements
- 1) Information to be analyzed must be encoded in some way.
- 2) Encoding implicitly requires a spatial language.
- 3) Some media to support the encoded information.
- 4) Qualitative and/or quantitative methods to perform operations over encoded information.
- 5) Ways to present to results in an explicit message.

Information

Encoding

Media

Methods

Message

Remote sensing

Geomorphology

Climatology

Quantitative

methods

Physical Geography

Geographic Techniques

Biogeography

Cartography

Soils

GIS

Human Geography

Historical

Political

Economic

Behavioral

Population

1

Spatial

Analysis

1

1

- Data Retrieval
- Browsing; windowing (zoom-in & zoom-out).
- Query window generation (retrieval of selected features).
- Multiple map sheets observation.
- Boolean logic functions (meeting specific rules).

- Map Generalization
- Line coordinate thinning of nodes.
- Polygon coordinate thinning of nodes.
- Edge-matching.

DB

HD

SHP

1

- Map Abstraction
- Calculation of centroids.
- Visual editing & checking.
- Automatic contouring from randomly spaced points.
- Generation of Thiessen / proximity polygons.
- Reclassification of polygons.
- Raster to vector/vector to raster conversion.

- Map Sheet Manipulation
- Changing scales.
- Distortion removal/rectification.
- Changing projections.
- Rotation of coordinates.

6

5

4.5

7.5

1

- Buffer Generation
- Generation of zones around certain objects.

- Geoprocessing
- Polygon overlay.
- Polygon dissolve.
- “Cookie cutting”.

- Measurements
- Points - total number or number within an area.
- Lines - distance along a straight or curvilinear line.
- Polygons - area or perimeter.

1

- Raster / Grid Analysis
- Grid cell overlay.
- Area calculation.
- Search radius.
- Distance calculations.

- Digital Terrain Analysis
- Visibility analysis of viewing points.
- Insolation intensity.
- Grid interpolation.
- Cross-sectional viewing.
- Slope/aspect analysis.
- Watershed calculation.
- Contour generation.

15

3

- Relativity of objects
- Definition of an object in view of another.
- Create spatial patterns.

- Main patterns
- Size.
- Distribution/spacing : Uniform, random and clustered.
- Proximity.
- Density: Dense and dispersed.
- Shape.
- Orientation.
- Scale.

Size

Form

Orientation

Scale

Proximity

Uniform

Clustered

Positive autocorrelation

Random

3

- Spatial autocorrelation
- Set of objects that are spatially associated.
- Relationship in the process affecting the object.
- Negative autocorrelation.
- Positive autocorrelation.

4

- Proximity
- Qualitative expression of distance.
- Link spatial objects by their mutual locations.
- Nearest neighbors.
- Buffer around a point or a line.

- Directionality

4

- Adjacency
- Link contiguous entities.
- Share at least one common boundary.

- Intersection
- Containment
- Link entities to a higher order set.

City B

City A

1

2

3

4

5

6

4

- Connectivity
- Adjacency applied to a network.
- Must follow a path, which is a set of linked nodes.
- Shortest path.
- All possible paths.

4

Arable land

- Intersection
- What two geographical objects have in common.

- Union
- Summation of two geographical objects.

- Complementarity
- What is outside of the geographical object.

Flat land

Suitable for agriculture

Land

Non arable land

B

- 1. Statistical Generalization
- 2. Data Distribution
- 3. Spatial Inference

1

- Maps and statistical information
- Important to display accurately the underlying distribution of data.
- Data is generalized to search for a spatial pattern.
- If the data is not properly generalized, the message may be obscured.
- Balance between remaining true to the data and a generalization enabling to identify spatial patterns.
- Thematic maps are a good example of the issue of statistical generalization.

15

25

88

0-30

34

56

7

31-65

92

61

45

65-

77

39

21

1

Spatial Pattern

Data

Classification

1

- Number of classes
- Too few classes: contours of data distribution is obscured.
- Too many classes: confusion will be created.
- Most thematic maps have between 3 and 7 classes.
- 8 shades of gray are generally the maximum possible to tell apart.

1

- Classification methods
- Thematic maps developed from the same data and with the same number of classes, will convey a different message if the ranging method is different.
- Each ranging method is particular to a data distribution.

Frequency

Value

2

- Histogram
- The first step in producing a thematic map.
- See how data is distributed.
- Use of basic statistics such as mean and standard deviation.
- An histogram plots the value against the frequency.

Uniform

Normal

Exponential

C1

C2

C3

C4

L

H

2

- Equal interval
- Each class has an equal range of values.
- Difference between the lowest and the highest value divided by the number of categories.
- (H-L)/C

- Easy to interpret.
- Good for uniform distributions and continuous data.
- Inappropriate if data is clustered around a few values.

Frequency

Value

C1

C2

C3

C4

n(C4)

n(C1)

n(C2)

n(C3)

2

- Quantiles
- Equal number of observations in each category.
- n(C1) = n(C2) = n(C3) = n(C4).
- Relevant for evenly distributed data.
- Features with similar values may end up in different categories.

- Equal area
- Classes divided to have a similar area per class.
- Similar to quantiles if size of units is the same.

Frequency

Value

C1

C2

C3

C4

X

-1STD

+1STD

2

- Standard deviation
- The mean (X) and standard deviation (STD) are used to set cutpoints.
- Good when the distribution is normal.
- Display features that are above and below average.
- Very different (abnormal) elements are shown.
- Does not show the values of the features, only their distance from the average.

Frequency

Value

C1

C2

C3

C4

2

- Arithmetic and geometric progressions
- Width of the class intervals are increased in a non linear rate.
- Good for J shaped distributions.

Frequency

Value

C1

C2

C3

C4

2

- Natural breaks
- Complex optimization method.
- Minimize the sum of the variance in each class.
- Good for data that is not evenly distributed.
- Statistically sound.
- Difficult to compare with other classifications.
- Difficult to choose the appropriate number of classes.

Frequency

Value

2

- User defined
- The user is free to select class intervals that fit the best the data distribution.
- Last resort method, because it is conceptually difficult to explain its choice.
- Analysts with experience are able to make a good choice.
- Also used to get round numbers after using another type of classification method.
- $5,000 - $10,000 instead of $4,982 - $10,123.

- Using classification
- Classification can be used to deliberately confuse or hide a message.

2

“no problems” - Equal steps

“there is a problem” - Quantiles

2

“everything is within standards” - standard deviation

3

- Filling the gaps
- Sampling shortens the time necessary to collect data.
- Requires methods to “fill the gaps”.

- Interpolation and extrapolation
- Data at non-sampled locations can be predicted from sampled locations.
- Interpolation:
- Predict missing values when bounding values are known.

- Extrapolation:
- Predict missing values outside the bounding area.
- Only one side is known.

Interpolation line

Height

Sample

Location

Extrapolation line

Delay at the traffic light

Sample

Interpolation line

Number of vehicles

3

3

112

110

y = 0.1408x + 116.69

108

2

R

= 0.6779

106

Sex Ratio

104

102

100

98

96

-130

-120

-110

-100

-90

-80

-70

-60

Longitude

3

- Aggregation
- Data within a boundary can be aggregated.
- Often to form a new class.

- Data within a boundary can be aggregated.
- Conversion
- Data from a sample set can be converted for a different sample set.
- Changing the scale of the geographical unit.
- Switching from a set of geographical units to another.

- Data from a sample set can be converted for a different sample set.

Boreal Forest

District B1

District B2

3

Pine Trees

Poplar Trees

District A

District B