Spatial Analysis Part 2
Types of Spatial Analysis
• We will consider six categories of spatial
analyses:
1.
2.
3.
4.
5.
6.
Queries
Measurements
Transformations
Descriptive summaries
Optimization
Hypothesis testing
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4. Descriptive Summaries
• As the name implies, this branch of spatial
analysis is concerned with describing and
summarizing spatial data
• Characteristics of spatial objects that may be
of interest
– The center of an object or a set of objects?
– The size & shape of objects
– The arrangement of objects
Centroids
• A centroid is the arithmetic mean (a.k.a. the
“center of mass”) of a spatial data object or set
of objects, which is calculated mathematically
• In the simplest case the centroid is the
geographic mean of a single object
• I.e., imagine taking all the points making up the outer edge of
of a polygon, adding up all the X values and all the Y values,
and dividing each sum by the number of points. The
resulting mean X and Y coordinate pair is the centroid.
• For example: the center of a circle or square
Centroids
• A more complicated case is when a centroid is
the geographic mean of many spatial objects
• This type of centroid would be calculated using
the geographic mean of all the objects in one or
more GIS layer
• I.e., the coordinates of each point and/or of each individual
polygon centroid are used to calculate an overall mean
• For example: the center of a population
Centroids in Irregular Polygons
• Confusing point #1
• Where is the centroid for the following shapes?
• In these cases the true centroid is outside of the
polygons
• If we don’t want this for our analysis we’d have to
calculate other types of “center” points
Similar to centroids…. but not centroids
• Confusing point #2
• The bivariate median is the point for which half of the
distribution is to the left, half to the right, half above and
half below
• The point of minimum aggregate travel (MAT) is the
point that minimizes aggregate distance (if the objects
were people and they all traveled to the centroid, the
total distance traveled would be minimum)
• For your purposes just remember that the centroid is the
mean (a.k.a. the average location)
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Spatial Patterns
• Pattern analysis is an important way to
understand spatial relationships between objects
• Why do we care?
– Processes (e.g., ecological, economic, social, cultural,
etc.) create patterns visible in space
– Therefore, patterns can be indicative of processes
and allow us to ask questions like:
• What happened in the past that led to the current pattern?
• What processes were most responsible for producing what
we now see?
• What is the landscape likely to look like in the future?
Describing Spatial Patterns
• Elements of spatial pattern that we commonly
study include:
– The size and shape of objects
• These measures are derived from characteristics like the
length, area, and perimeter of objects (and relationships
between these characteristics)
– The arrangement of spatial objects (i.e., topological
relationships)
• Proximity – how close or far are objects to each other (i.e.,
clustering)?
• Adjacency – what objects (or types of objects) are next to
each other?
• Continuity – are the objects continuous or are there gaps
between them (i.e., fragmentation)?
• Orientation – how are objects arranged relative to each other?
• Diffusion – how does the arrangement of objects change
through time?
Spatial Pattern Example 1
• Think about how cities & towns look from an airplane or tall
building
– Pattern might indicate age
• Older cities tend to have narrow streets, dense housing, tall buildings, etc.
• New suburbs have wide roads, sparse housing, low (yet still large) buildings,
etc.
– Pattern might indicate socio-economic conditions
• Slums with “chaotic” organization
• Planned communities with well designed infrastructure
• These differences in pattern result from different processes of
development
– For example:
• Transportation differences (i.e., before and after cars)
• Economic changes (e.g., factories & farms vs. information technology)
• Landscape characteristics (e.g., amount of available land)
Spatial Pattern Example 2
• Think about forests in around Chapel Hill
– FYI, the “climax” (i.e., late successional) community in the NC
Piedmont is an oak-hickory forest
– Forest pattern might suggest past land use
• Interspersed stands of loblolly pine might suggest past logging,
agriculture, etc.
– Forest pattern might suggest landscape disturbance
• Canopy gaps, areas with different species, etc. associated with
weather related tree falls, fire scars, insect damage, etc.
– Forest pattern might suggest environmental controls (biotic and
abiotic)
• Patches of uniform species may indicate dispersal patterns, interspecific competition, landscape variability, etc.
Pattern Analysis
• Point distribution patterns include:
– Regular - Uniform
– Clustered - In spatially separated groups
– Random - No apparent organization
Clustered
Regular
Random
http://en.wikipedia.org/wiki/Image:Snow-cholera-map.jpg
Landscape Pattern Analysis
• Landscape Ecology is the field devoted to
quantifying and explaining the pattern of patches
(e.g., landcover polygons) in a landscape
• According to the International Association for
Landscape Ecology:
– Landscape Ecology is the study of spatial variation in
landscapes at a variety of scales. It includes the
biophysical and societal causes and consequences of
landscape heterogeneity.
Landscape Ecology
• Landscape Ecology is concerned with such questions as:
– How have humans changed the landscape?
• How has landcover composition changed?
• How has landcover pattern changed?
– How fragmented has the landscape become?
– Are large tracts of forest left? And in what spatial pattern?
– Are there connecting corridors of natural areas between large patches?
– What are the relationships between landscape patterns and
species & ecological communities?
• How have changes in landcover composition and pattern affected
biodiversity?
• What species compositional changes are likely to occur if/when
landscape patterns change due to climate change?
Pattern Metrics
• Pattern metrics are one method used to describe the
pattern of features in a landscape
• Pattern metrics are equations that quantify patterns on
the landscape, the class, and the patch levels
• Examples
– Fragmentation
• Average patch size
• Distance between patches of the same type
– Patch shape
• Long and thin vs. round or square
• Jagged edges vs. clean edges
Pattern Metrics
• Pattern metric results can be derived in a software
package called FragStats
• The typical input data type for pattern metric analysis is
landcover data, often derived from classified satellite
imagery
• Example: The alpine treeline ecotone
–
–
–
–
Closed canopy forests below
Tundra, rock, snow, and ice above
Patchy forest in the middle
The pattern of that patchy forest is ecologically important &
indicative of the processes taking place
1975
Another Example:
Deforestation in the Amazon
•To the left are three images of part of the
state of Rondonia in the Brazilian Amazon
basin, collected in 1975, 1986, and 1992
1986
1992
•Note the increasing fragmentation of the
natural habitat as a result of settlement (forest
canopy appears deep red, locations of
development appear cyan blue)
•Such fragmentation can adversely affect
the success of wildlife populations
•Fragmentation statistics (a subset of pattern
metrics) quantify the amount and pattern of
fragmentation in a landscape.
Issues With Pattern Metrics
• Pattern metrics are useful for describing a landscape, but what
can we do with that information?
• For single species we can ask and answer some interesting
questions
– E.g., some birds need large, contiguous blocks of forest to nest while
other like edges. Pattern metrics provide a means of mapping “likely
habitat”.
• For larger questions the answers aren’t as clear
– E.g. which landscape pattern is the “best” for preserving biodiversity or
for carbon sequestration?
• Another issue is redundancy
– There are literally hundreds of pattern metrics available and many of
them tell basically the same story
– They are built on the same basic elements (i.e., the size, shape, and
arrangement of patches)
5. Optimization
• Spatial analysis can be used to solve many problems of
design, such as “where is the best place to build a new x”
• The decision of where to build a new facility is often
approached by minimizing travel time from a certain
catchment or service area
• For example:
– We may want to locate a hospital in an area where the nearest
hospital is an unacceptably long drive away.
– Where should we put it to best serve the residents in the area and
minimize overall travel time for the area?
– We can do this using Euclidean distance.
– Better to use travel time.
Location-Allocation
• One class of optimization problems is known as
location-allocation
• Solving them usually involves choosing locations for
services, and allocating demand to them to achieve
specified goals
• Those goals might include:
–
–
–
–
–
minimizing competition
minimizing the largest distance traveled by any customer
maximizing profits
maximizing visibility
minimizing opening costs
• The result of location allocation analyses are “best”
points or areas that solve our problem
Optimum Paths
• Another sort of optimization problem is encountered
when we have a known origin and destination,
and we need to find the best route between the two,
given data that describes the ‘cost’ of taking various
paths
• Optimum paths are calculated for a continuous
cost surface (i.e., raster representation)
– The goal is to minimize total cost
– The total cost usually combines many separate layers
(e.g., slope, vegetation density, & streams that all
contribute to ease of movement in the mountains)
– A route is generated from point A to B using the cost
surface
– This approach can be used to locate highways, power
lines, etc.
Optimum Paths Example: Least-Cost Path
•The figure to the left shows the
solution of a least-cost path problem
•The white line represents the
optimum solution, or path of least
total cost, across a friction surface
represented as a raster layer
•The area is dominated by a mountain
range, and cost in this example is
determined by elevation and slope
•The best route uses a narrow pass
through the range. The blue line results
from solving the same problem using a
coarser raster
Routing
• Routing is like optimum path selection, but for vector data
• Example 1:
– Finding the optimal route between two locations on a vector road
network utilizing road attributes (e.g., speed limit, congestion, # of
lanes)
• Routing often involves multiple paths – so it can
incorporates both the paths and the order of stops
• Example 2: The ‘traveling salesman problem’
– Suppose we have a set of locations we need to visit, and we want
to minimize travel time.
– Our route must find the shortest path from the origin, through a set
of destinations, and back to the origin.
Example Routing Problem:
Routing Service Technicians for an Elevator Co.
• Every day this
company’s service
crews must visit a
different set of
locations in Los
Angeles.
• GIS is used to partition
the day’s workload
among the crews and
trucks (color coding)
and to optimize the
route to minimize time
and cost.
6. Hypothesis Testing
• We collect or acquire data and use statistics to test
hypothesized relationships between variables from
spatial data, such as:
– Respiratory disease and distance from polluting factories.
– Distance from power lines and brain cancer incidence.
– Do more wildlife survive when greater than a mile from
regular human activity?
– Do the restaurants of a chain located in higher income areas
bring in more revenue?
– What combination of soil type, climatic conditions, and
fertilizer use generally produce the highest crop yield?