1. SPATIAL ANALYSIS WHAT IS IT?
SUMBER:

2. Spatial Analysis What is it?
“…the purpose of geographic inquiry is to examine relationships between geographic features collectively and to use the relationships to describe the real-world phenomena that map features represent.” (Clarke 2001, 182).
One Definition: the quantitative procedures employed in the study of the spatial arrangement of features (points, lines, polygons and surfaces)

3. Geographic Information Analysis
“Geographic information analysis is…concerned with investigating the patterns that arise as a result of processes that may be operating in space” (p. 3).
“Techniques [that] enable the representation, description, measurement, comparison, and generation of spatial patterns…”

4. How Do We Represent the World (in Map or Digital Form?)
Raster – Vector
A Higher Level of Abstraction? (p. 5)
Objects and Fields
The key distinction (according to your authors)
A slightly different conceptualization
How do we choose the “best” representation(s)?

5. Spatial Analysis: What is it?
What types of relationships exist between geographic features, and how do we express them?
Properties of spatial features and/or relationships between them: size, distribution, pattern, contiguity, neighborhood, shape, scale, orientation

6. 3 Fundamental Questions Regarding Spatial Relationships
How can two (or more) spatial distributions be compared with each other?
How can variations in geographic properties over a single area or data set be described and/or analyzed?
How can we use what we have learned from an analysis(es) to predict future spatial distributions?
Spatial Analysis can cover the spectrum implied by these questions!

7. What role does GIS play in Spatial Analysis?
GIS is a tool with unique capabilities:
Can handle geographically-referenced data
Spatial/attribute data entry/update capabilities
Data conversion functions
Storage and organization of a variety of spatial and attribute data
Manipulation of spatial and attribute data (encompasses many different operations)
Presentation/display capabilities
Spatial analysis tools (many tools may be used in combination)

8. Do you remember the 5 functional elements of a GIS?
Data acquisition
Preprocessing
Database Management
Manipulation/Analysis
Final product output
These elements are all part of the spatial analysis “equation” (and a GIS professional’s knowledge base).

9. Our framework this semester for discussing GIS operations/procedures that are useful for spatial analysis…
The Pitfalls and Potential of Spatial Data
Maps as Outcomes of Processes
Point Pattern Analysis
Describing and Analyzing Fields
Statistical Analysis of Fields/Spatial Interpolation
Map Overlay Concepts and Procedures
Spatial Modeling
Network Analysis

10. How can we characterize Spatial Analysis (what skills does it require)?
Spatial analysis is an artistic and a scientific endeavor (what does this mean?)
It requires knowledge of the problem and/or question to be answered
It requires knowledge about the data (how it was collected, organized, coded, etc.)
It requires knowledge of GIS capabilities
It may require knowledge of statistical techniques
It requires envisioning the results of any operation…and the combination of any operations
It is not completely objective, in fact some argue that it is completely subjective
Many times there is more than one way to derive information that answers a question

11. Are Spatial Data “Special,” and if They Are, Why?
Spatial Data are Special…
Why?
How?
What are the implications?
Pitfalls
Potential
Why “They” Need “Us”

12. The “Pitfalls” of Spatial Data
Most spatial samples are not random!!
This situation/problem is known as spatial autocorrelation
The earth’s surface is not an isotropic plane
Positive autocorrelation, negative auto correlation, zero autocorrelation
“…Describing the autocorrelation structure, is of primary importance in spatial analysis.” (p. 29)
First order, and second order spatial variation

13. The “Pitfalls” of Spatial Data
The Modifiable Areal Unit Problem
“…aggregation units used are arbitrary with respect to the phenomena under investigation”
“If spatial units…were specified differently, we might observe very different patterns…” (p. 30)
The Ecological Fallacy
Rampant in media reporting

14. The “Pitfalls” of Spatial Data
Scale Issues
Examples
Nonuniformity of Space and Edge Effects
Space is not uniform
Edge Effects?

15. The Potential of Spatial Data
Quantification of Spatial Relationships
How? What kind of relationships matter?
Summarizing spatial relationships
How?

16. Spatial data are the building blocks of any spatial analysis
Spatial data structures:
Raster: geographically-referenced matrix of uniform size cells…advantages and disadvantages
Vector: features on the earth’s surface are represented as geographically-referenced vector objects (points, lines, polygons)…advantages and disadvantages

17. Representation of vector spatial objects
Hierarchical nature of objects (points, lines, polygons)
Points: different types
Entity, label, area, node
Lines:
Line, arc, link, etc.
Polygons:
Area, polygon, complex polygon

18. Basic elements of spatial information required to undertake spatial analysis
Location
X,Y coordinate or locational reference
Attribute data
Describing the (aspatial) characteristics of locations
Topology
Describing the spatial relationships between spatial features

19. Measurement of Location: GIS Issues
A GIS suitable for spatial analysis must have the necessary functions dealing with coordinate systems
What are these functions?
What coordinate systems do we normally see or work with in a GIS…and what are their characteristics?

20. Measurement of Location: GIS Issues
Basic measurement of spatial features:
Points are defined by x,y coordinates
Lines are represented by an ordered sequence of points…they can be “decomposed” into sections of straight line segments
The distance between two points on a Cartesian plane is derived through Euclidean distance…the length of a line segment is the sum total of the Euclidean distances of all segments that compose it (p. 105 Chou)
The area of any feature represented as a polygon an be computed by constructing a trapezoid from every line segment delineating the polygon…then systematically aggregating the trapezoid areas (both positive and negative) (p. 106 Chou)

21. Attribute Data Measurement
Categories: Nominal and Ordinal data
Numeric: Interval and ratio data
Measures of Central Tendency (mode, median, mean) and Dispersion (variance, standard deviation)
Must be cognizant of spatial units and geographic sampling techniques

22. Topology: What kinds of spatial relationships between spatial features?
Adjacency: Which polygons are adjacent to which? Often used in the spatial analysis of areal data.
Containment: Which spatial features are contained within which? Can be used for selection or perhaps geocoding.
Connectivity: Which line segments are connected? Often used for network analysis.

23. The Arc-node Data Model: a method of expressing vector topology
Used for ARC/INFO coverages (we will use this as our example)…a proprietary ESRI vector spatial data structure
Topological data is stored in “attribute tables”: point attribute tables (PATs), arc attribute tables (AATs), polygon attribute tables (PATs)…what is contained in these tables?

24. Sample Attribute Tables
Arc Attribute Tables (AATs) - contain the following data fields: arc-ID, Length, F-node, T-node, L-poly, R-poly
Polygon Attribute Tables (PATs) – contain the following data fields: poly-ID, perimeter, area
Point Attribute Tables (PATs) – the same fields as above, but zero perimeter and area
** These tables store the topological data needed to quantify the spatial relationships between features

25. Spatial Data Formats
Spatial data formats are the product of the private sector working to create data files that allow users to:
Create maps
Manipulate spatial data
Perform spatial analysis
Example ESRI spatial data formats (files): shapefiles, coverages, GRIDs, geodatabases, TINs, Routes

26. 3 Major vector-based datasets used in ArcGIS: Shapefiles, Coverages, Geodatabases
ESRI Shapefiles:
Spatial data is stored in binary files
Attribute data is stored in dBase tables
Contain one simple feature class
No topology is developed for spatial features
Types of shapefiles: point, line, polygon and multi-point

27. 3 Major vector-based datasets used in ArcGIS: Shapefiles, Coverages, Geodatabases
ESRI ARC/INFO Coverages:
Spatial data is stored in binary files
Topological and attribute tables are stored in INFO tables
Contain topological features classes that define line or polygon topology
Topology is “built” for lines and polygons - lines: arcs, nodes and routes; polygons: arcs, label points, polygons, regions
Primary coverage feature classes are: point, arc, polygon, and node; secondary: tic, link, annotation; compound: region, route

28. ARC/INFO Coverages
ARC coverage files: defined by header files, index files, ARC, PAL, LAB, CNT, PRJ, LOG, TOL
ARC: arc definitions and vertices; PAL: contains polygon definitions; LAB: contains label point records; CNT: contains polygon centroid information; PRJ: contains projection information; TOL: contains the tolerance values to use when processing a polygon coverage

29. ESRI GRID file ESRI’s proprietary raster file structure
Readable in ArcGIS without any extensions
The Spatial Analyst extension needed to perform analysis on these files
Follow conventions we have learned about:
Uniform raster cell size
Single value per cell
Continuous data (including null values)

30. “Special” Spatial Data Structures: TINs and Routes
Triangulated Irregular Networks (TINs): sample points are connected to form triangles, with the relief inside each represented as a plane or facet
VIPs (Very Important Points)
Delaunay Triangulation
3-dimensional surface description
ArcGIS can generate these through the 3-D Analyst extension

31. “Special” Spatial Data Structures: TINs and Routes
Routes are spatial data structures generated to represent linear features
Used when the definition of linear features does not meet the needs of a network-based application
Dynamic segmentation procedure
New line segments are defined…
Based on the location of “events”
Measurements of offsets on segments
Network Analyst and ARC/INFO

32. 3 Major vector-based datasets used in ArcGIS: Shapefiles, Coverages, Geodatabases
ESRI Geodatabase
All spatial, topological, and attribute data is stored in tables in a relational database
A feature dataset in a geodatabase can contain simple or topological feature classes
Many feature classes can be associated with a topological role within the geodatabase
User-defined associations can be created between features in different feature classes
Types of feature classes: point, line, polygon, annotation, simple junction, complex junction, simple edge, complex edge

33. The Geodatabase Data Model: “…a better way to associate behavior with [spatial] features was needed”
An object-oriented data model: data “objects” can have rules, relationships, topology
Facilitates the creation of “smart features” that are more complex than generic points, lines, or polygons
All data is stored in a relational database ( as opposed to separate spatial and attribute data)

34. Centralized management of data
Geodatabases organize data into a hierarchy of data objects: object classes, feature classes, feature datasets
Object class: a table in a geodatabase that stores non-spatial data
Feature class: a collection of features with the same type of geometry and the same attributes
Feature dataset: a collection of feature classes that have the same spatial reference system
“Simple” feature classes can exist either within or outside a feature dataset; topological feature classes must be contained within a feature dataset

35. Maps as Outcomes of Processes
[Spatial] patterns provide clues to a possible causal [spatial] process(es)
“…Usefulness of maps…remains in their inherent ability to suggest patterns in the phenomena they represent.” p. 52
Conceptualizing spatial analysis as processes and patterns

36. Types of Processes: Spatial Processes and their Possible Realizations
Could the pattern we observe have been generated by this particular process?
Deterministic processes:
Processes whose outcome can be predicted exactly from knowledge of initial conditions
Many times can be mathematically described
Outcome always the same
Stochastic processes:
Processes whose outcome is subject to variation that cannot be given precisely by a mathematical formula
Introduction of a random (stochastic) element to model the range of potential solutions
“Chance process with well-defined mechanisms” p. 58

37. Predicting Patterns: Expected Results
Assumptions
Example: independent random process (IRP) (or complete spatial randomness (CSR))
Math used to predict frequency distribution under assumed randomness
Observed vs. expected
What is this assumption called in the scientific method?
Real World – usually not characterized by spatial randomness
First-order effects: the earth is not an isotropic plane, and therefore some areas will be more attractive of phenomena than others
Second-order effects: the assumption that events are independent of each other is not realistic…i.e. the location of events will influence the location of other events

38. Point Pattern Analysis
The spatial properties of the entire set of points is analyzed (rather than individual points)
Requirements/Assumptions according to O’Sullivan and Unwin (pp.78-79)?
Descriptive statistics for point distributions
Frequency; density; geometric center; spatial dispersion; spatial arrangement

39. Point Pattern Analysis
Thinking about point patterns…
How can we describe and analyze them
The geographical properties of a point pattern are characterized (described) by geometric center and dispersion
Geometric (mean) center = mean x,y coordinates; dispersion = standard distance of x and y distribution
Geometric (mean) center is not a reliable measure of central tendency when either the x or y standard distance is large
What are these measures useful for?

40. Point Pattern Analysis
Density-based and distance-based measures
i.e. Point Density and Point Separation
Density: ratio of frequency to area…intensity of a pattern
depending on distribution within a defined study area may be misleading (pp )
Quadrat Count Methods
Census or random methods
Issues?

41. Density-based measures
Quadrat Analysis – based on the frequency of occurrence of points within quadrat units
Requires overlaying quadrats onto a layer of point features
Once quadrats are overlayed onto the point layer, frequencies of points per quadrat can be counted
All quadrats are classified according to observed frequency of points
Null hypothesis: point features are randomly distributed

42. Density-based Measures
Kernel Density Estimation
A pattern has a density at any location…
Continous densities for defined “kernels” to create a continous surface

43. Distance-based Point Pattern Measures
The Logic of Distance Measures
Can be described using types (categories):
Clustered – points are concentrated in one or more groups/areas
Uniform – points are regularly spaced with relatively large interpoint distance
Random – Neither the clustered or uniform pattern is prevalent

44. Measuring Spatial Arrangement
Nearest Neighbor Analysis (Index)
Measures the degree of spatial dispersion in a point distribution based on minimizing interpoint distances
Logic: in general the average distance between points in a clustered pattern is less than in a uniform pattern\
Logic: a random pattern is associated with an avg. interpoint distance larger than a clustered pattern but smaller than a uniform pattern
The “nearest neighbor” for each point feature must be determined, and the interpoint distance is computed

45. Measuring Spatial Arrangement
Nearest Neighbor Analysis (Index) con’t
Observed average nearest neighbor distances compared to expected average nearest distances assuming complete spatial randomness [CSR] (1/2 sq.rt. A/n)
NNI = Ad/Ed p.100
NNI range: 0 to …where 0 indicates perfectly clustered and indicates perfectly uniform (values close to 1 indicate a random pattern)
To test the statistical significance of an NNI value, a computed z value can be compared to a critical value (1.96)

46. Measuring Spatial Arrangement
Nearest Neighbor Analysis: Pros and Cons
Pros: relatively simple; easy to compute; straightforward logic
Cons: is not sensitive to complex patterns unless extended to include more than just nearest neighbors

47. The Concept of Spatial Autocorrelation
Spatial Autocorrelation: measures the extent to which the occurrence of one feature is influenced by the distribution of similar features in the adjacent area Why is this idea important in the context of “classical” statistical analysis?
Captures some aspects of point spatial distribution not reported by NNI or quadrat analysis
Spatial auto correlation is characterized as positive (the existence of one feature tends to attract similar features) or negative (the existence of one feature tends to deter the location of similar features)

48. Types of Area Objects Natural Areas vs. Command Regions
Who cares?
Issues with Command Regions?
Raster
Pros and Cons?
Planar-enforced areas…
GIS-context?

49. Geometric Properties of Areas
How is it calculated?
Shape
Comparison of a polygon to a known shape
Spatial pattern
Contact numbers
Fragmentation (FRAGSTATS)

50. Spatial Autocorrelation
Most common spatial autocorrelation statistic is Moran’s I coefficient
Similar to a traditional correlation coefficient
The I coefficient for the most part ranges between –1 and +1; larger negative values indicate a scattered pattern…positive values indicate a clustered pattern
Also Geary’s C (Geary’s Ratio)
The C coefficient tends to range between 0 and 2; values approaching 0 imply similar values of a variable tend to cluster (positive spatial autocorrelation)…values approaching 2 indicate that dissimilar values tend to cluster

51. Spatial Autocorrelation
Joins Count approach
Logic?