SPATIAL ANALYSIS
WHAT IS IT?
SUMBER:
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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)
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…”
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)?
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
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!
What role does GIS play in
Spatial Analysis?
• GIS is a tool with unique capabilities:
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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)
Do you remember the 5
functional elements of a GIS?
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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).
Our framework this semester for
discussing GIS operations/procedures
that are useful for spatial analysis…
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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
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
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”
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
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
The “Pitfalls” of Spatial Data
• Scale Issues
– Examples
• Nonuniformity of Space and Edge Effects
– Space is not uniform
– Edge Effects?
The Potential of Spatial Data
• Quantification of Spatial Relationships
– How? What kind of relationships matter?
• Summarizing spatial relationships
– How?
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
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
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
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?
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)
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
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.
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?
Sample Attribute Tables
• Arc Attribute Tables (AATs) - contain the
following data fields: arc-ID, Length, F-node, Tnode, 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
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
3 Major vector-based
datasets used in ArcGIS:
Shapefiles, Coverages, Geodatabases
• ESRI Shapefiles:
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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
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
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
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)
“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
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VIPs (Very Important Points)
Delaunay Triangulation
3-dimensional surface description
ArcGIS can generate these through the 3-D
Analyst extension
“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
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
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)
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 nonspatial 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
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
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
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
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
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?
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. 81-82)
• Quadrat Count Methods
– Census or random methods
– Issues?
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
Density-based Measures
• Kernel Density Estimation
– A pattern has a density at any location…
– Continous densities for defined “kernels” to
create a continous surface
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
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
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 2.1491…where 0 indicates perfectly
clustered and 2.1491 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)
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
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)
Types of Area Objects
• Natural Areas vs. Command Regions
– Who cares?
• Issues with Command Regions?
• Raster
– Pros and Cons?
• Planar-enforced areas…
– GIS-context?
Geometric Properties of Areas
• Area
– How is it calculated?
• Shape
– Comparison of a polygon to a known shape
• Spatial pattern
– Contact numbers
– Fragmentation (FRAGSTATS)
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
Spatial Autocorrelation
• Joins Count approach
– Logic?