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Geographic Information Systems

Geographic Information Systems. GIS Analysis and Modeling. 5. (6) Spatial Interpolation. Predict the unknown value at a location using the known values at surrounding area Linear interpolation Thiessen polygon Inverse distance weighted Trend surface Fourier series Kriging.

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Geographic Information Systems

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  1. Geographic Information Systems GIS Analysis and Modeling

  2. 5. (6) Spatial Interpolation • Predict the unknown value at a location using the known values at surrounding area • Linear interpolation • Thiessen polygon • Inverse distance weighted • Trend surface • Fourier series • Kriging

  3. 5. (6) Spatial Interpolation • Linear interpolation Known and predicted values after interpolation Known values

  4. 5. (6) Spatial Interpolation • Thiessen polygon - Defines area of influence around a point in a way that polygon boundaries are equidistant to neighboring points

  5. Obstetrical Delivery Hospital Regions(Constructed Using Thiessen Polygons): North Carolina, 1989 This map uses Thiessen polygons to construct regions: in this case, obstetrical delivery hospital regions. This technique can be utilized with little technology, using nodal points to construct polygons and, ultimately, regions. Source: “Using Geographic Methods to Understand Health Issues,” U.S. Department of Health and Human Services http://geography.sdsu.edu/People/Pages/jankowski/public_html/Lect811.ppt#276,2,What is Spatial Interpolation?

  6. 5. (6) Spatial Interpolation • Inverse Distance weighted - IDW works by using a weight based on the distances from an unknown value to known values © Paul Bolstad, GIS Fundamentals Arthur Lambor, Cornel University

  7. 5. (6) Spatial Interpolation • Trend surface - Polynomial regression to fit a least-square surface to the input points First-order (linear) trend surface Second-order (quadratic) trend surface http://geography.sdsu.edu/People/Pages/jankowski/public_html/Lect811.ppt#276,2,What is Spatial Interpolation?

  8. Trends of one, two, and three independent variables for polynomial equations of the first, second, and third orders (after Harbaugh, 1964).

  9. 5. (6) Spatial Interpolation • Fourier series Single harmonic in X1 direction Two harmonics in X1 direction Single harmonic in both X1 and X2directions Two harmonics in both directions

  10. 5. (6) Spatial Interpolation • Kriging - It takes one step further from inverse distance weighted interpolation because it accounts for not only the distances between a location with unknown value to the locations with known values, but also distances between the location with known values Arthur Lambor, Cornel University

  11. Theissen Arthur Lambor, Cornel University

  12. Inverse Distance Weighting Arthur Lambor, Cornel University

  13. Kriging Arthur Lambor, Cornel University

  14. 5. (7) Proximity Analysis (Buffering) • The identification of a zone of interest around an entity or a set of entities

  15. Buffering http://www.sdsmt.edu/online-courses/geology/mprice/geo416/lecture9.ppt

  16. Buffering A multi-distance buffer (each ring is 150 m) A single distance buffer (250 m) http://geology.wlu.edu/harbor/geol260/lecture_notes/notes_location1.html

  17. 5. (8) Network Analysis • A network is a set of interconnected lines making up a set of features through which resources can flow • The shortest path problem • The traveling salesperson problem • Location-allocation

  18. The Shortest Path Problem • An evaluation of links and turns required to traverse a network between required stops • It can be the shortest, fastest, or least-costly route between any number of origins and destinations, with any number of intermediate points

  19. The Shortest Path Problem • Shortest and fastest routes http://www.caliper.com/TransCAD/ApplicationModules.htm

  20. The Shortest Path Problem • Traffic assignment http://www.caliper.com/TransCAD/ApplicationModules.htm

  21. The Traveling Salesperson Problem • An evaluation of best sequence to visit each of a set of stops and the best route between the stops http://www.caliper.com/TransCAD/ApplicationModules.htm

  22. Vehicle Routing/Dispatching • Pickup and delivery routing http://www.caliper.com/TransCAD/ApplicationModules.htm

  23. Location-Allocation • A match between supply and demand involving the movement of people, goods, information, and services Determining what areas are within 10 minutes of a fire station Locating schools within 30 min walking distance for children http://www.sdsmt.edu/online-courses/geology/mprice/geo416/lecture9.ppt

  24. Location Allocation • Delineate service areas http://www.caliper.com/TransCAD/ApplicationModules.htm

  25. Location Allocation • Evaluate possible facility locations http://www.caliper.com/TransCAD/ApplicationModules.htm

  26. Trip Generation/Production • Estimate the number of trips, by purpose, that are produced or originate in each zone of a study area http://www.caliper.com/TransCAD/ApplicationModules.htm

  27. Readings • Chapter 5,6,9,10

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