Copyright, 1998-2012 © Qiming Zhou

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TPU-based Population Density0 - 1200012000 - 3520035200 - 5920059200 - 102400102400 - 193700

Distance Zones to Hospital123

Population Density0 - 1270012700 - 3690036900 - 6870068700 - 110700110700 - 193700

# Surveyed Hospitals

6 0 6 12 18 24 Kilometers

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Hong Kong Hospital Coverage

GEOG3600. Geographical Information Systems

Spatial Analysis

Spatial Analysis 2

Spatial Analysis

Analysis or modelling? Vector GIS analysis capabilities Raster GIS analysis capabilities Geographical analysis procedure

Spatial Analysis 3

Map analysis and modelling

“What distinguishes a GIS from other types of information systems are its spatial analysis functions. These functions use the spatial and non-spatial attribute data in the GIS database to answer questions about the real world”.

Aronoff, 1989, pp 189.

Spatial Analysis 4

Analysis or modelling?

The advantage a GIS can provide is the capability for transforming the original spatial data to answer user’s questions.

Such transformations are often referred to as “data analysis” capabilities in GIS.

However, most so-called “analysis” capabilities of today’s GIS are in fact data manipulation and maintenance functions, very rare of them are actually tell us something by “analysing” spatial data.

Spatial Analysis 5

Definitions What is “analysis”?

Analysis specifies data transformations which are analytical.

“Analysis” is the process to resolve and separate the reference system into its parts to illuminate their nature and interrelationships, and to determine general principles of behaviour.

What is “modelling”? Modelling specifies data transformations which

involve the synthesis of information. The “synthesis” is the process to put together

expressions of general principles with representations of parts of the reference system so as to form a replica that exhibits behaviour similar to that of the reference system.

Spatial Analysis 6

Analysis versus modelling

A theory is the product of analysis.

A model is the product of syntheses, using theory.

Spatial Analysis 7

Spatial analysis and GIS

Geographical analysis allows the study of real-world processes by developing and applying models.

A GIS enhances this process by providing tools which can be combined in a meaningful sequences to develop new models. These models may reveal new or previously unidentified relationships thus increasing our understanding of the real world.

Results of geographical data analysis can be communicated with maps, reports, or both.

Spatial Analysis 8

Geographical model

A GIS database is a model of the real world that can be used to mimic certain aspects of reality.

A model must represent certain entities and relationship among them.

A model may be represented in words, in mathematical equations, or as a set of spatial relations presented by maps or GIS.

Spatial Analysis 9

The nature of models

Models are designed to mimic only selected aspects of reality.

A more complex model may or may not provide “better” answer.

A model can be tested and manipulated more conveniently at a faster (or slower) rate and less expensively than the condition it mimics.

Spatial Analysis 10

The use of models

Models are used when it is more convenient or it is not possible to collect the information directly. e.g. It is convenient to measure road distance on a

map. e.g. The height a forest will reach in 100 years time is

impossible to measure directly. A model is used to understand what happened

in the past and to present scenario on what consequence might be with the present conditions.

Spatial Analysis 11

Organising geographical data for analysis Data layers

A data layer consists of a set of logically related geographical features and their attributes

Representations of a data layer Raster grid, overlay (grid cells) Vector coverage (point, line, polygon)

Spatial Analysis 12

GIS analysis functions

A GIS provides analysis and modelling capability by means of its analysis functions.

GIS analysis functions are capable of processing spatial and attribute data together.

Based on GIS data model, GIS analysis functions can be categorised into vector and raster analysis functions.

Spatial Analysis 13

Vector analysis functions

Geographical query (introduced previously)

Data manipulation Topological overlay Buffering Terrain analysis (to be introduced later) Network Analysis (to be introduced later)

Spatial Analysis 14

Mostly for manipulate spatial data to fit into application specifications.

For example, in working with area objects to aggregate areas based on attributes:

Commonly a three-step procedure is used: Reclassify areas by a single attribute or some combination; Dissolve boundaries between areas of same type by delete

the arc between two polygons if the relevant attributes are the same in both polygons;

Merge polygons into large objects by recording the sequence of line segments that connect to form the boundary and assigning new ID numbers to each new object.

Data manipulation

Spatial Analysis 15

Reclassify, dissolve and merge

Soil types A, B and C with growth potentials d and f

Soil types A, B and C

Soil types A, B and C

Ad

Bd Cf

BfCd

Ad

A

B

B

C

CA

A

B

C

A

Reclassify

Dissolve & merge

Spatial Analysis 16

Topological overlay

Suppose individual layers have planar enforcement, when two layers are combined (overlaid or superimposed), the result must have planar enforcement as well.

New intersection must be calculated and created wherever two lines cross and a line across an area object will create two new area objects.

When topological overlay occurs, spatial relationships between objects area updated for the new, combined map.

Spatial Analysis 17

Point in polygon

ID Restaurant

1 McDonald

2 Pizza Hut

3 KFC

4 McDonald

5 Berger King

ID Town

A Shi Qi

B Gang Kou

C San Jiao

ID Town Restaurant

1 Shi Qi McDonald

2 Gang Kou Pizza Hut

3 Gang Kou KFC

4 San Jiao McDonald

5 San Jiao Berger King

Fast food restaurant

Towns

1 2

3

4 5

1 2

3

4 5

AB

C

Spatial Analysis 18

Line on polygon

ID Road No.

1 35

2 22

3 35

4 60

5 60

6 35

7 82

8 35

ID Geology

A Granite

B Sandstone

C Sand

ID Original Road No.

Geology

1 2 22 Granite

2 2 22 Sandstone

3 1 35 Sandstone

4 3 35 Sandstone

5 4 60 Granite

6 4 60 Sandstone

7 5 60 Sandstone

8 6 35 Sandstone

9 6 35 Sand

10 7 82 Sand

11 8 35 Sand

Roads Geology12

345

67

8

1 2 3

456

78

910

11

AB

C

Spatial Analysis 19

Polygon on polygon

ID Watershed

County

1 1 A

2 1 B

3 3 B

4 2 A

5 2 B

6 4 B

7 2 C

8 4 C

Watershed

County

1

2

3

4A

B

C

1 2 3

4

5 6

7 8

Spatial Analysis 20

Buffering A buffer can be constructed around a point, line or area. Buffering algorithm creates a new area enclosing the

buffered object. The application of this buffering algorithms

fundamentally addresses the creation of zones around the target. e.g. protected zone around lakes, reservoirs or

streams zone of noise pollution around highways or airports service zone around bus route groundwater pollution zone around waste site

Spatial Analysis 21

Buffering on point, line and area

d

d

d

Buffering a point

e.g. area within 1km to a hospital. Buffering a

line

e.g. area within 100m to a road.

Buffering an area

e.g. area within 100m to a building.

Spatial Analysis 22

Buffering example

Spatial Analysis 23

Raster analysis functions

Local functions (point functions) Zonal functions (regional functions) Focal functions (neighbourhood

functions) Global functions

Spatial Analysis 24

Local functions

Local functions operate on the values of all the attributes relating to each cell (location). The operations are independent of the effects of attribute values from neighbouring cells.

A local function results in a new grid as a function of one or more input grids.

Spatial Analysis 25

The generic form of local functions

U = f (X1, X2, …)

For example:

new_map = old_map_1 + old_map_2

Spatial Analysis 26

Spatial context of local functions

X

Y

Z

A

B

U

U = f (A, B)

Spatial Analysis 27

Average

3.0

3.0

2.5

2.0

3.0

2.5

3.0

3.0

2.5

3.0

2.5

3.0

1.5

2.0

2.5

2.0

1

2

1

1

1

2

2

1

1

3

3

2

2

3

3

2

5

4

4

3

5

3

4

5

4

3

2

4

1

1

2

2= mean ,

n

ii

n

iii

n

XXXXfU

1

121 ),...,,(

Eg. outgrid = mean(ingrid_1, 2 * ingrid_2, (ingrid_3 + ingrid_4))

Spatial Analysis 28

Merge

1

4

1

1

1

3

4

1

1

3

3

4

1

3

3

2

1

N

1

1

1

N

N

1

1

3

3

N

N

3

3

N

5

4

4

3

5

3

4

5

4

3

2

4

1

1

2

2= merge ,

Eg. outgrid = merge(ingrid_1, ingrid_2, …)

If X1 == NODATA then

U = X2

elseU = X1

Spatial Analysis 29

Maximising

5

4

4

3

5

3

4

5

4

3

3

4

2

3

3

2

1

2

1

1

1

2

2

1

1

3

3

2

2

3

3

2

5

4

4

3

5

3

4

5

4

3

2

4

1

1

2

2= max ,

Eg. outgrid = max (ingrid_1, ingrid_2)

U = max (X1, X2, …)

Spatial Analysis 30

Minimising

1

2

1

1

1

2

2

1

1

3

2

2

1

1

2

2

1

2

1

1

1

2

2

1

1

3

3

2

2

3

3

2

5

4

4

3

5

3

4

5

4

3

2

4

1

1

2

2= min ,

Eg. outgrid = min (ingrid_1, ingrid_2)

U = min (X1, X2, …)

Spatial Analysis 31

Reclassification – arbitrary1

2

1

1

1

2

2

1

1

3

3

2

2

3

3

2

5

4

5

5

5

4

4

5

5

2

2

4

4

2

2

4

Given a1, a2, …, an

and b1, b2, …, bn

if X == a1 thenU = b1

else if X == a2 thenU = b2

…else

U = X

X U

123

542

Lookup table

Eg. If (ingrid == 1)outgrid = 5

else if (ingrid == 2)outgrid = 4

else if (ingrid == 3)outgrid = 2

endif

or outgrid = con(ingrid == 1, 5, ~con(ingrid == 2, 4, 2))

Spatial Analysis 32

3

N

N

N

3

N

N

3

3

N

N

N

4

N

N

4

1

2

1

1

1

2

2

1

1

3

3

2

2

3

3

2

5

3

3

3

5

3

3

5

5

3

2

5

2

2

2

2

Given a1, a2, …, an; b1, b2, …, bn;c1, c2, …, cn

if X1 == a1 and X2 = b1 thenU = c1

else if X1 == a2 and X2 == b2 thenU = c2

…else

U = NODATA

Eg. If (ingrid1 == 1 & ingrid2 == 2)outgrid = 1

else if (ingrid1 == 2 & ingrid2 == 2)

outgrid = 4else if (ingrid1 == 1 & ingrid2 == 5)

outgrid = 3endif

Coding scheme

ingrid2

ingri

d1 123

2 3 5

1 - 34 - -- - -

Boolean

Reclassification – Boolean

Spatial Analysis 33

Zonal functions

Zonal functions operate on properties of the region (or zone) to which a given cell belongs.

These properties might be: length, area or shape number of locations having a certain

attribute value on one grid that occurs within the area defined by a region on another grid.

Spatial Analysis 34

Characteristics of zonal functions Do not change boundaries of regions Change attribute values for each region (or

zone) according to its statistics or user’s specification

Useful for understanding spatial distribution of objects, quantitative measurement of shapes, statistical properties of objects and spatial associations

Spatial Analysis 35

Outcome of zonal functions

StatisticTables

Reclassify

Summarising properties of regions Spatial correlation

Spatial Analysis 36

Reclassification – statistical

SliceDivide range values intoin either equal intervalsor equal areas

Slice in equal intervals

Slice in equal areas

Outgrid = slice(ingrid, ~EQAREA | EQINTERVAL, ~nzones, base_zone#, ~in_min, in_max)

Spatial Analysis 37

Zonal statistics

2.0

2.0

2.0

0.75

2.0

0.75

2.0

2.0

2.0

0.75

0.75

2.0

0.5

0.5

0.75

0.75

4

4

4

3

4

3

4

4

4

3

2

4

1

1

2

2= zonalarea

Database definition: 1 cell = 2,500 m2Unit: km2

Zonal AreaReassign the value to each region according to the area measurement

Outgrid = zonalarea (ingrid)(based on 50x50m grid cell size)

Spatial Analysis 38

The focal and global functions The focal functions relate a cell to its

neighbours. These are functions that explicitly make

use of some kind of spatial associations in order to determine the value for the locations on the new output grid.

Spatial Analysis 39

Focal function parameters

Every focal function requires at least three basic parameters: Target location(s) (neighbourhood focus) A specification of the neighbourhood

around each target A function to be performed on the

elements within the neighbourhood

Spatial Analysis 40

Problem addressed by focal functions

Fire station

Question: What is the number of residential buildings within 5km to the given fire station?

Target: fire station

Neighbourhood: the area within 5km radius

Function: count the number of residential buildings

Spatial Analysis 41

Spatial search

Compute an attribute value for each target cell as a function of attribute values of its neighbourhood in an existing grid.

Target: target cell(s) on focal grid Functions: sum, mean, standard deviation, etc. Neighbourhood: circular, square or “ring-shape”

Spatial Analysis 42

Focal statistics

1

4

3

5

6

3

2

2

1

5

1

1

2

1

2

6

2

3

1

7

5

5

4

7

5

6

2

2

4

5

6

8

2

8

6

4

3

1

7

8

3

2

3

5

1

1

4

3

1

2

2

4

3

2

1

2

5

2

2

6

5

7

3

2

3.5

3.8

1

4

3

5

6

3

2

2

1

5

1

1

2

1

2

6

2

3

1

7

5

5

4

7

5

6

2

2

4

5

6

8

2

8

6

4

3

1

7

8

3

2

3

5

1

1

4

3

1

2

2

4

3

2

1

2

5

2

2

6

5

7

3

2

Focal mean

Focal grid

Data grid

Result grid

Spatial Analysis 43

Contiguity

Uniquely identifying individual contiguous groups or “clumps” of cells on an existing grid

The output grid has every polygon (or group of cells) uniquely numbered ranging from 1 to n, where n is the total number of polygons found in the grid.

Spatial Analysis 44

Contiguity analysis outcome

1

1

5

5

1

2

2

2

1

5

5

1

1

1

2

4

1

3

3

1

1

5

4

5

2

2

2

2

4

5

5

5

2

2

2

4

3

1

4

5

3

2

3

3

1

1

4

4

3

2

3

1

4

1

1

2

3

2

3

4

4

4

1

2

1

1

4

4

7

11

11

11

1

4

4

7

7

7

11

13

1

5

5

7

7

12

13

12

2

2

2

2

8

12

12

12

2

2

2

8

6

9

14

12

3

2

6

6

9

9

14

14

3

2

6

9

10

9

9

15

3

2

6

10

10

10

9

15

Spatial Analysis 45

Proximity

Compute an attribute value for each cell according to the length of the shortest path between that cell and the target location or area.

The distance can be measured in Euclidean distance or “cost distance” (or “weighted distance”).

The least-cost path is the route between two targets where the cost distance is the minimum.

In many cases, the cost distance is different from the Euclidean distance.

Spatial Analysis 46

Proximity analysis variables

A

1 2 3 4 5

6

7

B

A

1 2 3 4 5

6

7B

Absolute Barrier

89

A

1 2 3 4 5

6

7B

89

Travel zones defined by Euclidean distance The effect of an

absolute barrier on travel zones

The effect of a partial barrier (friction) on travel zones

Spatial Analysis 47

Spatial analysis procedure

Establish the objectives and criteria for the analysis.

Prepare the data for spatial operations. Perform the spatial operations. Prepare the derived data for tabular

analysis. Perform the tabular analysis. Evaluate the interpret the results. Refine the analysis as needed.

Spatial Analysis 48

Summary

One most significant advantage for GIS is the capability for geographical analysis.

GIS analytical capabilities are closely related to its data model.

Vector data analysis functions include, e.g., geographical query, manipulation, topological overlay, buffering, terrain analysis and network analysis.

Raster data analysis functions include, e.g., local, zonal, focal and global functions.