Spatial Analysis Part 2Types of Spatial Analysis4. Descriptive SummariesCentroidsSlide 5Slide 6Centroids in Irregular PolygonsSimilar to centroids…. but not centroidsSpatial PatternsDescribing Spatial PatternsSpatial Pattern Example 1Spatial Pattern Example 2Pattern AnalysisSlide 14Landscape Pattern AnalysisLandscape EcologyPattern MetricsSlide 18Slide 19Slide 20Slide 21Slide 22Another Example: Deforestation in the AmazonIssues With Pattern Metrics5. OptimizationLocation-AllocationOptimum PathsOptimum Paths Example: Least-Cost PathRoutingExample Routing Problem: Routing Service Technicians for an Elevator Co.6. Hypothesis TestingSpatial Analysis Part 2Types 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 objectsCentroids•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 squareCentroids•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 populationCentroids 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” pointsSimilar 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 organizationClusteredRegularRandomhttp://en.wikipedia.org/wiki/Image:Snow-cholera-map.jpgLandscape 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