Final ReviewLecture 18Lecture 19Lecture 20The Nominal Data CaseBiasFuzzy Approaches to UncertaintyLecture 21TopologyQueriesMeasurement of LengthVariable Distance BufferingRaster BufferingPoint Frequency/Density AnalysisLine in Polygon AnalysisLecture 22Boolean Operations with Raster LayersSimple Arithmetic OperationsSpatial InterpolationSpatial Interpolation: Inverse Distance Weighting (IDW)Lecture 23Neighborhood OperationsSlide 23Neighborhood Operation: Majority FilterEdge EnhancementThe CentroidUSA Population CentroidLecture 24Landcover Pattern MetricsLocation-Allocation ProblemsLecture 25Population EnvironmentFinal Review•Final will cover all lectures, book, and class assignments.•New lectures since last test are 18 – 26, summarized here. Over half the test will come from this last portion of the course.Lecture 18•Review the following satellite products:•Landsat MSS•Landsat TM•SPOT•IKONOS•QUICKBIRD•Terra•MODIS•GOES•For each: know basic applications, spatial resolution, approximate temporal resolution.Lecture 19•How does Differential Correction aid in GPS accuracy?Lecture 20Error: Difference between the real world and the geographic data representation of it.• Location errors• Attribute errorsAccuracy: (another way of describing error)Extent to which map data values match true valuesforest fields urban waterTotalforest 80 4 0 15 7 106fields 2 17 0 9 2 30urban 12 5 9 4 8 38water 7 8 0 65 0 80Wetlands3 2 1 6 38 50Total 104 36 10 99 55 304ClassificationReferenceThe Nominal Data Case•An example is when you determine the accuracy of a landcover classification.•We can build something called a confusionmatrix:–This compares your classification with your ground-truth sample (the very accurate sample data, as mentioned)wetlandsBias•Error is unbiased when the error is in ‘random’ directions.–GPS data–Human error in surveying points•Error is biased when there is systematic variation in accuracy within a geographic data set–Example: GIS tech mistypes coordinate values when entering control points to register map to digitizing tabletall coordinate data from this map is systematically offset (biased)•Example: the wrong datum is being usedFuzzy Approaches to Uncertainty•Consider a landcover classification with these classes:–Forest–Field–Urban–water•We don’t assign a single class to each landcover pixel. •Instead,wecreateaprobabilityofmembershiptoeachclass.•We create 4 layers: •Layer 1:•The attribute data for each pixel is the probability that pixel is in forest.•Layer 2:•The attribute data for each pixel is the probability that pixel is a field.•Layer 3:•The attribute data for each pixel is the probability that pixel is urban.•Layer 4:•The attribute data for each pixel is the probability that pixel is water.Lecture 21•Spatial analysis: analysis is considered spatial if the results depend on the locations of the objects being analyzed.Topology•Most spatial analyses are based on topological questions:–Hownear is Feature A to Feature B–What features contain other features?–What features are adjacent to other features?–What features are connected to other features?Queries•Queries –Attribute based•Example: show me all pixels in a raster image with BV > 80.–Location based•Find all block groups in Orange County with an average of > 1 child per householdMeasurement of Length•Types of length measurements–Euclideandistance: straight-line distance between two points on a flat plane (as the crow flies)–ManhattanDistance limits movement to orthogonal directions–GreatCircle distance: the shortest distance between two points on the globe–NetworkDistance:•Along roads •Along pipe network•Along electric grid•Along phone grid•By river channels•The buffer zone constructed around each feature can be based on a variable distance according to some feature attribute(s)•Suppose we have a point pollution source, such as a power plant. We want to zone residential areas some distance away from each plant, based on the amount of pollution that power plant producesFor smaller power plants, the distance might be shorter. For larger power plants that generate a lot of pollutant, we choose longer distancesVariable Distance BufferingRaster Buffering•Buffering operations also can be performed using the rasterdatamodel•In the raster model, we can perform a simple distance buffer, or in this case, a distance buffered according to values in a friction layer (e.g. travel time for a bear through different landcover):lakeAreas reachable in 5 minutesAreas reachable in 10 minutesOther areas•We can use point in polygon results to calculate frequencies or densities of points per area•For example, given a point layer of bird’s nests and polygon layer of habitats, we can calculate densities:Habitat Area(km2) Frequency Density . A 150 4 0.027 nests/km2 B 320 6 0.019 nests/km2 C 350 3 0.009 nests/km2 D 180 3 0.017 nests/km2Bird’s NestsA BDCHabitat TypesA BDCAnalysis ResultsPoint Frequency/Density Analysis•Overlay line layer (A) with polygon layer (B)–In which B polygons are A lines located?» Assign polygon attributes from B to lines in AABExample: Assign land use attributes (polygons) to streams (lines):Line in Polygon AnalysisDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Lecture 22•Questions from this section are likely to be ‘problems’ – I may show you a small raster image (with numbers in each cell), and have you calculate the intersection/‘and’ or the union/‘or’ image.0 1 10 0 11 0 10 0 01 1 10 0 1AND=Boolean Operations with Raster Layers0 1 10 0 11 0 10 0 01 1 10 0 1OR=•The AND operation requires that the value of cells in both input layers be equal to 1 for the output to have a value of 1:•The OR operation requires that the value of a cells in either input layer be equal to 1 for the output to have a value of 1:101100110100111000+=201211110Summation101100110100111000=100100000Multiplication101100110100111000+=301322110100111000+Summation of more than two layersSimple Arithmetic OperationsNear the mall Near friend’s houseNear workGood place to live?Spatial Interpolation•You have point data (temp or air pollution levels).•You want