Urban sprawl is a common problem for modern cities. It is caused by the materials that are commonly used in road construction, building materials and other non-naturally occuring items. These items absorb a high amount of solar radiation from the sun and then reradiates them into the immediate area. This results in above average temperatures in city areas which can result in higher heat related illnesses. The following are a couple methods of measuring urban sprawl using GIS tools such as ArcGIS.

*Confusion Matrix*

For each city of research, a confusion matrix was constructed based on land use change frequencies for time periods 1971-1985 and 1985-1999. Fundamentally, the structure of these frequency tables is relatively simple. The cells going diagonally across the table from the upper left to the lower right represent no change of land use between two specified years. Values on either side of this diagonal line show the land use change. Rows display previous uses while the columns present the current use of a polygon. These frequency tables were converted into probability tables using the following formula:

Pij = Cij / Ti

Each cell value (C) was divided by the row total (T) to determine the probability (P) of change. This provides a basic model to predict future land use changes. To test for dependence and randomness the Chi-Squared (Χ2) test is used:

eij = Ri Cj/T

Χ2 =Σi Σj (Oij – eij)2/eij

The observed value (O) are taken from the confusion matrix while the expected values (e) is calculated by the Row (R) and Column (C) totals which are then divided by the total number of polygons (T).

*Mean* *Center*

Mean center is a way of tracking changes in distribution by taking the average coordinates of a point distribution and calculating the center location. The formulas used to calculate mean center are as follows:

Xmean = Σi Xi/N

YMean =Σi Yi/n

What the formulas do is add up all the point’s x-coordinate (X) and y-coordinate (Y) values. Each sum is then divided by the total number of points (n) to create the mean values of all the points in the calculation. The mean center is the result of this mean x, y coordinate pair.

To apply this method to this project the data must first altered slightly. The land use layers provided by MassGIS don’t contain points but rather polygons, or areas. Also, there are classes contained within the set are far more detailed then is needed. In actuality, tracking urbanization distribution only requires two classes: urban and non-urban. Urbanized areas were then selected by querying the newly formed class and exported into a separate file. The Feature-to-Point function was next used to take the polygon features of this new map and convert them into point data. Lastly, the mean center was finally calculated using the points. This was done over all time periods for each city. Maps showing the results of the mean center analysis can be viewed here at the end of the report.