Spatial Analysis Part 2

Types of Spatial Analysis• We will consider six categories of

spatial analyses:

1. Queries (last lecture)2. Measurements (last lecture)3. Transformations (last lecture)4. Descriptive summaries (today)5. Optimization (today)6. Hypothesis testing (today)

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)http://www.csiss.org/learning_resources/content/good_sa/

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, inter-specific 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

•To the left are three images of part of the state of Rondonia in the Brazilian Amazon basin, collected in 1975, 1986, and 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.

Another Example:Deforestation in the Amazon

1975

1986

1992

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.

•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

Optimum Paths Example: Least-Cost Path

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?