Geographic Information Systems GIS Analysis and Modeling 11

Geographic Information Systems GIS Analysis and Modeling

11. 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 ►

11. Spatial Interpolation ► Linear interpolation Known values Known and predicted values after interpolation

11. Spatial Interpolation ► Thiessen polygon - Defines area of influence around a point in a way that polygon boundaries are equidistant to neighboring points

Construction of Polygon + 130 + 200 + 150 + 180 + 130 Polygon of influence for x=180

Construction of Polygon. . + 130 + 200 + 150 + 180 + 130 Draw line segments between x and other points

Construction of Polygon. . + 130 + 200 + 150 + 180 + 130 Find the midpoint and bisect the lines.

Construction of Polygon. . + 130 + 200 + 150 + 180 + 130 Extend the bisecting lines till adjacent ones meet.

Construction of Polygon. . + 130 + 200 + 150 + 180 + 130 Continue this process.

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/Lect 811. ppt#276, 2, What is Spatial Interpolation?

11. Interpolation – Proximal. . ► http: //gizmodo. com/5884464/

11. Spatial Interpolation. . ► Inverse Distance Weighted - IDW works by using a weight based on the distances from an unknown value to known values Arthur Lambor, Cornel University © Paul Bolstad, GIS Fundamentals

11. 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/Lect 811. ppt#276, 2, What is Spatial Interpolation?

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

11. Spatial Interpolation ► Fourier series Single harmonic in X 1 direction Two harmonics in X 1 direction Single harmonic in both X 1 and X 2 directions Two harmonics in both directions

11. 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

Theissen Arthur Lambor, Cornel University

Inverse Distance Weighting Arthur Lambor, Cornel University

Kriging Arthur Lambor, Cornel University

12. 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

12. 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

The Shortest Path Problem ► Shortest and fastest routes http: //www. caliper. com/Trans. CAD/Application. Modules. htm

The Shortest Path Problem ► Traffic assignment http: //www. caliper. com/Trans. CAD/Application. Modules. htm

12. 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/Trans. CAD/Application. Modules. htm

Vehicle Routing/Dispatching ► Pickup and delivery routing http: //www. caliper. com/Trans. CAD/Application. Modules. htm

12. Location-Allocation ► A match between supply and demand involving the movement of people, goods, information, and services Locating schools within 30 min walking distance for children Determining what areas are within 10 minutes of a fire station http: //www. sdsmt. edu/online-courses/geology/mprice/geo 416/lecture 9. ppt

Location Allocation ► Evaluate possible facility locations http: //www. caliper. com/Trans. CAD/Application. Modules. htm

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/Trans. CAD/Application. Modules. htm

Readings ► Chapter 5, 6, 9, 10