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Lab 7: Gravity Models Geography 409/891AN Lab 7 Page 1 Lab 7: Gravity Models Due Date: March 29 Introduction Gravity models are among the most widely used types of spatial interaction models. Physicists define gravity as a force of attraction between two bodies that is directly proportional to their masses and inversely proportional to the square of the distance between them. Geographers have borrowed this concept and replaced "bodies" with "locations" and "masses" with other measurable attributes, such as population, retail space, or the number of hospital beds. Although the gravity model concept has had its greatest influence in economic geography, it has been widely applied to many different aspects of the discipline. Part A: Theory Questions (each question is worth 2 marks) 1. Describe how the gravity model concept is related to Christaller's central place theory. 2. What is Reilly's law of retail gravitation? Describe its basic ideas in words. 3. Reilly's law, and other gravity models, tend to square the distance between locations. In general, however, the squared distance can easily be replaced with any other exponent and is frequently represented in gravity models with the Greek letter beta, β. Why is beta (β) is called the friction of distance? What effect will larger and smaller values of β have on the spatial interaction of the locations in the model? 4. What is the Huff model? Describe its basic ideas in words. Part B: Proximal Areas and Huff Models Review Wang Case Study 4A: Defining Fan Bases of Chicago Cubs and White Sox. The data can be found on TerraServer\Data\CourseData\Geog409\Lab7. NOTES: Before you start Step 1, load the data files into ArcMap, ignoring any projection warnings. Step 1: Follow these instructions instead: o File Add Data Geocoding Geocode Addresses… o Choose the 10.0 US Streets Geocode Service (ArcGIS Online). o Pull down the menu beside the Address input field and select STREET. o Output shapefile or feature class: …\cubsox_geo o OK o Project cubsox_geo to cubsox_prj using the projection defined for the coverage chitrt. Choose the WGS_1984_(ITRF00)_To_NAD_1983 transformation. Step 4: The Thiessen Polygons can be created with: ArcToolbox Analysis Tools Proximity Create Thiessen Polygons J.M. Piwowar 2011.03.17 Geography 409/891AN Lab 7 Page 2 Problem Statement Perhaps not unlike the Chicago Cubs and White Sox fan base division, the Universities of Regina and Saskatchewan "compete" for students in this province. In order to help the marketing efforts by each institution, you need to define the student base for the universities by the proximal area and Huff model methods. You will make the naïve assumption that the primary attractor of each institution is its size, in terms of number of full-time students. For simplicity, you can measure proximity based on Euclidean distances and use β=2 as the distance friction coefficient. Data Provided Data for this part of the lab can be found in the Saskatchewan GIS Data\Saskatchewan Shapefiles folder on TerraServer: SKmun – municipalities You will need to: o Project it to UTM (NAD'83, zone 13) SKedu – educational institutions You will need to: o Extract the locations of the 2 universities – use their main campus locations only. o Add a field for the student enrollments and enter the values of 11,923 and 18,418 for the Universities of Regina and Saskatchewan, respectively.1 o Project it to UTM (NAD'83, zone 13) Procedure (each step is worth 2 marks) 1. Produce a choropleth map showing the Euclidean distance proximal areas for the whole study area (within Saskatchewan) for the Universities of Regina and Saskatchewan. 2. Produce a choropleth map showing the Thiessen polygon proximal areas (within Saskatchewan) for the Universities of Regina and Saskatchewan. 3. Produce a choropleth map showing the probabilities (within Saskatchewan) of choosing the University of Regina by the Huff model. 4. Complete this table: Student Bases of the Universities of Saskatchewan and Regina Euclidean Distance Proximal Areas Thiessen Huff Institution 100 km Saskatchewan Polygons Model U.Regina U.Saskatchewan 5. Why are the Saskatchewan-wide student bases the same for the Euclidean Distance and Thiessen Polygon methods? 6. Draw a flow chart of the procedures you used in your analysis. 1 2008-09 statistics. J.M. Piwowar 2011.03.17 .
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