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UNC-Chapel Hill GEOG 370 - Spatial Analysis Part 1

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Spatial Analysis Part 1Spatial AnalysisSlide 3Steps in Spatial AnalysisSpatial Relationships are at the Core of Spatial AnalysisTypes of Spatial Analysis1. QueriesThe Map ViewThe Table View2. MeasurementsMeasurement of LengthEuclidean DistanceManhattan DistanceGreat Circle DistanceSlide 15Slide 16Slide 17Issues with Length MeasurementSlide 193. TransformationsBuffering (Proximity Analysis)Slide 22Variable Distance BufferingBuffering Points, Lines, and PolygonsLine and Polygon Buffer ExamplesRaster BufferingFeature in Feature TransformationsThe Point in Polygon AlgorithmPoint in Polygon AlgorithmPoint Frequency/Density AnalysisLine in Polygon AnalysisPolygon Overlay, Discrete Object CaseSlide 33Boolean OperationsPolygon CombinationBoolean Operations with Raster LayersProblems with Vector Overlay Analysis (esp. Polygon)Slide 38Slide 39Slide 40Algebraic Operations w/ Raster LayersSimple Arithmetic OperationsRaster Difference (Subtraction)Raster DivisionMore Complex OperationsApplying a Model to Our DataMaking Inferences from SamplesSpatial Interpolation: Inverse Distance Weighting (IDW)Slide 49Issues with IDWSlide 51Slide 52Spatial Analysis Part 1Spatial Analysis•What is spatial analysis?–It is the means by which we turn raw geographic data into useful information–It does so by adding greater informative content and value•Spatial analysis reveals patterns, trends, and anomalies that might otherwise be missed–It provides a check on human intuition–It allows for analysis of data that could never be done by humansSpatial Analysis•Analysis is considered spatial if the results depend on the locations of the objects being analyzed.–Thus if you move the objects, the results of spatial analyses will change.–Spatial analyses generally requires both attributes and locations of objects.Steps in Spatial Analysis1. Frame the question we wish to ask.2. Find appropriate data to answer the question.3. Choose an analytical method appropriate to answer question.4. Process the data using the chosen method.5. Interpret the results of the analysis.Spatial Relationships are at the Core of Spatial Analysis•Most spatial analyses are based on topological relationships:–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?•From these topological building blocks, we can develop all sorts of spatial analysis approaches to answer many complex questionsTypes of Spatial Analysis•We will consider six categories of spatial analyses:1. Queries (today)2. Measurements(today)3. Transformations (today)4. Descriptive summaries (next lecture)5. Optimization (next lecture)6. Hypothesis testing (next lecture)1. Queries•Queries –Attribute based•Example: show me all pixels in a raster image with BV > 80.–Location based•List all the block groups that fall within Orange County•A GIS can respond to queries by selecting the appropriate data in:–A map view–A table–BothThe Map View•Queries can be performed through interaction with a GIS on-screen map–Identify objects–Query data objects based on specific criteria of attributes –Find coordinates of objectsThe Table View•Queries can be performed through interaction with a table–Attribute based queries can be performed in the table.–When objects are selected in a table, a GIS can automatically highlight the selected data objects in the map view, and vice versa.2. Measurements•Measure:–Distance between two points•Distances can be summed–Example: a truck makes multiple stops on a route. What is the total distance traveled on the route?•Other mathematical operations can be applied to distances:–We can square a set of distances, add them up, divide by the amount of distances calculated in the set, and take the square root. What is an example of when this operation is used?–Area of a polygon–Example: What is the area of a preserved forest tract?Measurement 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 channelsEuclidean Distance•Distances can be calculated between points, along lines, or in a variety of fashions with areas•Euclidean Distance – is calculated in a Cartesian frame of reference:(x1 – x2)2 + (y1 – y2)2C=CP1 (x1,y1)P2 (x2,y2)• On what scales is this valid? • Can we use this with latitude and longitude?Manhattan Distance•Manhattan Distance is useful in some urban environments with orthogonal road networks. •Movement is limited to city streets:P1 (x1,y1)P2 (x2,y2)dm = | x1 – x2 | + | y1 – y2 |a reminder – the | symbols denote absolute valueGreat Circle Distance•The Great Circle distance is the shortest distance between two points on the globe. •The two points must be specified using geographic coordinates (i.e., latitude & longitude positions).Great Circle Distance•Calculating the great circle distance is actually pretty complicated–A = Latitude of point A–B = Latitude of point B–C = Difference in longitude between the points (i.e., Longitude of point A – Longitude of point B)–D = angular distance •Simple version (spherical distance)–cos(D) = sin(A) sin(B) + cos(A) cos(B) cos(C)Great Circle Distance•ONE more complicated version (also more accurate) To use these equations:1. Convert latitude and longitude (degree, minute, second) to decimal degrees (if necessary)2. Convert degrees to into radians3. Solve the equation for D4. Great Circle Distance = D * the radius of the earth (6372.795 km)OR1. Convert latitude and longitude (degree, minute, second) to decimal degrees (if necessary)2. Convert degrees to into radians3. Solve the equation for D4. Convert D into degrees5. Great Circle Distance = D * length of 1 degree at the equator (111.32 km)Starting from: Carrboro, NC 27510 Save AddressArriving at: Washington, DC Save Addressistance:272.5 miles Approximate Travel Time:5 hours 23 mins Network DistanceYahoo maps:Issues with Length Measurement•The length of a true curve is longer than the length of its polyline or polygon representation:Issues with Length Measurement•Length measurements in


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UNC-Chapel Hill GEOG 370 - Spatial Analysis Part 1

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