1. Prof. Qiming Zhou
Spatial Analysis
Spatial Analysis

2. Spatial Analysis Analysis or modelling?
Prof. Qiming Zhou
Spatial Analysis
Analysis or modelling?
Vector GIS analysis capabilities
Raster GIS analysis capabilities
Geographical analysis procedure
Spatial Analysis
Spatial Analysis

3. Map analysis and modelling
Prof. Qiming Zhou
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
Spatial Analysis

4. Prof. Qiming Zhou
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
Spatial Analysis

5. Definitions What is “analysis”?
Prof. Qiming Zhou
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
Spatial Analysis

6. Analysis versus modelling
Prof. Qiming Zhou
Analysis versus modelling
A theory is the product of analysis.
A model is the product of syntheses, using theory.
Spatial Analysis
Spatial Analysis

7. Spatial analysis and GIS
Prof. Qiming Zhou
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
Spatial Analysis

8. Prof. Qiming Zhou
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
Spatial Analysis

9. Prof. Qiming Zhou
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
Spatial Analysis

10. Prof. Qiming Zhou
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
Spatial Analysis

11. Organising geographical data for analysis
Prof. Qiming Zhou
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
Spatial Analysis

12. GIS analysis functions
Prof. Qiming Zhou
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
Spatial Analysis

13. Vector analysis functions
Prof. Qiming Zhou
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
Spatial Analysis

14. Prof. Qiming Zhou
Data manipulation
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.
Spatial Analysis
Spatial Analysis

15. Reclassify, dissolve and merge
Prof. Qiming Zhou
Reclassify, dissolve and merge Ad Bd Cf Bf Cd
Reclassify
Dissolve & merge A B C A B C
Soil types A, B and C with growth potentials d and f
Soil types A, B and C
Soil types A, B and C
Spatial Analysis
Spatial Analysis

16. Prof. Qiming Zhou
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
Spatial Analysis

17. Point in polygon Fast food restaurant Towns ID Restaurant 1 McDonald 2
Prof. Qiming Zhou
Point in polygon
Fast food restaurant
Towns 1 2 3 4 5 ID
Restaurant 1
McDonald 2
Pizza Hut 3
KFC 4 5
Berger King A B C ID
Town A
Shi Qi B
Gang Kou C
San Jiao ID
Town
Restaurant 1
Shi Qi
McDonald 2
Gang Kou
Pizza Hut 3
KFC 4
San Jiao 5
Berger King 1 2 3 4 5
Spatial Analysis
Spatial Analysis

18. Line on polygon Roads Geology Spatial Analysis Prof. Qiming ZhouID
Road No. 1 35 2 22 3 4 60 5 6 7 82 8 1 2 3 4 5 6 7 8 A B C ID
Geology A
Granite B
Sandstone C
Sand ID
Original
Road No.
Geology 1 2 22
Granite
Sandstone 3 35 4 5 60 6 7 8 9
Sand 10 82 11 1 2 3 4 5 6 7 8 9 10 11
Spatial Analysis
Spatial Analysis

19. Polygon on polygon Watershed County Spatial Analysis Prof. Qiming Zhou1 2 3 4 A B C ID
Watershed
County 1 A 2 B 3 4 5 6 7 C 8 1 2 3 4 5 6 7 8
Spatial Analysis
Spatial Analysis

20. Buffering A buffer can be constructed around a point, line or area.
Prof. Qiming Zhou
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
Spatial Analysis

21. Buffering on point, line and area
Prof. Qiming Zhou
Buffering on point, line and area d
Buffering a point
e.g. area within 1km to a hospital. d
Buffering a line
e.g. area within 100m to a road. d
Buffering an area
e.g. area within 100m to a building.
Spatial Analysis
Spatial Analysis

22. Prof. Qiming Zhou
Buffering example
Spatial Analysis
Spatial Analysis

23. Raster analysis functions
Prof. Qiming Zhou
Raster analysis functions
Local functions (point functions)
Zonal functions (regional functions)
Focal functions (neighbourhood functions)
Global functions
Spatial Analysis
Spatial Analysis

24. Prof. Qiming Zhou
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
Spatial Analysis

25. The generic form of local functions
Prof. Qiming Zhou
The generic form of local functions
U = f (X1, X2, …)
For example:
new_map = old_map_1 + old_map_2
Spatial Analysis
Spatial Analysis

26. Spatial context of local functions
Prof. Qiming Zhou
Spatial context of local functions Z A B
U = f (A, B) Y U X
Spatial Analysis
Spatial Analysis

27. Prof. Qiming Zhou
Average
3.0
3.0
2.5
1.5 1 1 1 2 5 5 4 1
2.0
3.0
3.0
2.0 1 1 2 2 3 5 4 2
= mean ,
2.5
3.0
2.5
2.5 1 2 3 3 4 4 2 2
3.0
2.5
3.0
2.0 2 2 3 3 4 3 3 1
Eg. outgrid = mean(ingrid_1, 2 * ingrid_2, (ingrid_3 + ingrid_4))
Spatial Analysis
Spatial Analysis

28. Merge , = merge Eg. outgrid = merge(ingrid_1, ingrid_2, …)
Prof. Qiming Zhou
Merge 1 1 1 1 1 1 1 N 5 5 4 1 1 1 4 2 1 1 N N 3 5 4 2
= merge , 1 4 3 3 1 N 3 3 4 4 2 2 4 3 3 3 N N 3 3 4 3 3 1
If X1 == NODATA then U = X2 else U = X1
Eg. outgrid = merge(ingrid_1, ingrid_2, …)
Spatial Analysis
Spatial Analysis

29. Maximising = max , U = max (X1, X2, …)
Prof. Qiming Zhou
Maximising 5 5 4 2 1 1 1 2 5 5 4 1 3 5 4 2 1 1 2 2 3 5 4 2
= max , 4 4 3 3 1 2 3 3 4 4 2 2 4 3 3 3 2 2 3 3 4 3 3 1
U = max (X1, X2, …)
Eg. outgrid = max (ingrid_1, ingrid_2)
Spatial Analysis
Spatial Analysis

30. Minimising = min , U = min (X1, X2, …)
Prof. Qiming Zhou
Minimising 1 1 1 1 1 1 1 2 5 5 4 1 1 1 2 2 1 1 2 2 3 5 4 2
= min , 1 2 2 2 1 2 3 3 4 4 2 2 2 2 3 1 2 2 3 3 4 3 3 1
U = min (X1, X2, …)
Eg. outgrid = min (ingrid_1, ingrid_2)
Spatial Analysis
Spatial Analysis

31. Reclassification – arbitrary
Prof. Qiming Zhou
Reclassification – arbitrary X U 1 2 3 5 4
Lookup table 1 1 1 2 5 5 5 4 1 1 2 2 5 5 4 4 1 2 3 3 5 4 2 2 2 2 3 3 4 4 2 2
Given a1, a2, …, an and b1, b2, …, bn
if X == a1 then U = b1 else if X == a2 then U = b2 … else U = X
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
Spatial Analysis

32. Reclassification – Boolean
Prof. Qiming Zhou
Reclassification – Boolean 1 1 1 2 5 5 5 2
Given a1, a2, …, an; b1, b2, …, bn; c1, c2, …, cn
if X1 == a1 and X2 = b1 then U = c1 else if X1 == a2 and X2 == b2 then U = c2 … else U = NODATA 1 1 2 2 3 5 5 2 1 2 3 3 3 3 2 2 2 2 3 3 3 3 3 2
Boolean
Coding scheme
ingrid2
ingrid1 1 2 3
2 3 5
1 - 3
4 - -
- - - 3 3 3 4
Eg. If (ingrid1 == 1 & ingrid2 == 2) outgrid = 1 else if (ingrid1 == 2 & ingrid2 == 2) outgrid = 4 else if (ingrid1 == 1 & ingrid2 == 5) outgrid = 3 endif N 3 N 4 N N N N N N N N
Spatial Analysis
Spatial Analysis

33. Prof. Qiming Zhou
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
Spatial Analysis

34. Characteristics of zonal functions
Prof. Qiming Zhou
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
Spatial Analysis

35. Outcome of zonal functions
Prof. Qiming Zhou
Outcome of zonal functions
Reclassify
Statistic Tables
Summarising properties of regions
Spatial correlation
Spatial Analysis
Spatial Analysis

36. Reclassification – statistical
Prof. Qiming Zhou
Reclassification – statistical
Slice
Divide range values into in either equal intervals or equal areas
Slice in equal intervals
Slice in equal areas
Outgrid = slice(ingrid, ~ EQAREA | EQINTERVAL, ~ nzones, base_zone#, ~ in_min, in_max)
Spatial Analysis
Spatial Analysis

37. Zonal statistics Zonal Area = zonalarea
Prof. Qiming Zhou
Zonal statistics
Zonal Area
Reassign the value to each region according to the area measurement
2.0
2.0
2.0
0.5 4 4 4 1
0.75
2.0
2.0
0.75 3 4 4 2
= zonalarea
2.0
2.0
0.75
0.75 4 4 2 2
2.0
0.75
0.75
0.5 4 3 3 1
Unit: km2
Database definition: 1 cell = 2,500 m2
(based on 50x50m grid cell size)
Outgrid = zonalarea (ingrid)
Spatial Analysis
Spatial Analysis

38. The focal and global functions
Prof. Qiming Zhou
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
Spatial Analysis

39. Focal function parameters
Prof. Qiming Zhou
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
Spatial Analysis

40. Problem addressed by focal functions
Prof. Qiming Zhou
Problem addressed by focal functions
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
Fire station
Spatial Analysis
Spatial Analysis

41. Prof. Qiming Zhou
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
Spatial Analysis

42. Focal statistics Focal grid Focal mean Result grid Data grid
Prof. Qiming Zhou
Focal statistics
Focal grid
Focal mean
Result grid 1 1 2 5 2 3 1 5 4 5 3 6 8 2 2 2 3 1 1 2 6 3 2 2
3.5 5 1 7 2 4 5 4 6
Data grid 6 2 5 4 3 1 3 5 3 1 5 5 1 1 2 7
3.8 1 1 2 5 2 3 1 5 2 2 4 6 7 4 1 3 4 5 3 6 8 2 2 2 2 6 7 8 8 3 2 2 3 1 1 2 6 3 2 2 5 1 7 2 4 5 4 6 6 2 5 4 3 1 3 5 3 1 5 5 1 1 2 7 2 2 4 6 7 4 1 3 2 6 7 8 8 3 2 2
Spatial Analysis
Spatial Analysis

43. Prof. Qiming Zhou
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
Spatial Analysis

44. Contiguity analysis outcome
Prof. Qiming Zhou
Contiguity analysis outcome 1 1 1 2 2 3 3 3 1 1 1 2 2 3 3 3 1 5 3 2 2 2 2 2 1 4 5 2 2 2 2 2 5 5 3 2 2 3 3 3 4 4 5 2 2 6 6 6 5 1 1 2 4 3 1 4 4 7 7 2 8 6 9 10 1 1 1 4 3 1 4 4 7 7 7 8 6 9 10 10 2 1 5 5 1 1 1 4 11 7 12 12 9 9 9 10 2 2 4 5 4 4 1 1 11 11 13 12 14 14 9 9 2 4 5 5 5 4 2 2 11 13 12 12 12 14 15 15
Spatial Analysis
Spatial Analysis

45. Prof. Qiming Zhou
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
Spatial Analysis

46. Proximity analysis variables
Prof. Qiming Zhou
Proximity analysis variables A 1 2 3 4 5 6 7 B
The effect of a partial barrier (friction) on travel zones A 1 2 3 4 5 6 7 B
Absolute Barrier 8 9 A 1 2 3 4 5 6 7 B 8 9
Travel zones defined by Euclidean distance
The effect of an absolute barrier on travel zones
Spatial Analysis
Spatial Analysis

47. Spatial analysis procedure
Prof. Qiming Zhou
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
Spatial Analysis

48. Prof. Qiming Zhou
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.
Spatial Analysis
Spatial Analysis