Arboriculture & Urban Forestry 36(5): September 2010 Annual precipitation for reference cities is defined as the total amount of precipitation used in the i-Tree Streets program’s calcu- lations of tree interception (Table 2). The year selected for calcu- lating interception had a full complement of hourly meteorological data, and total precipitation was relatively similar to the 30-year average. While many sources exist, average annual precipitation data for most cities can be obtained online at World Weather (2009). Analysis To determine which reference city (RC) best matches the sub- ject city (SC) the analyst calculates the root mean squared er- ror (RMSE) for each reference city. The city with the low- est RMSE is the best match. The RMSE is calculated as: RMSE = SQRT [a * (HDDSC – HDDRCi + c * (APSC – APRCi and reference city i APSC is the percentage of tree species/genera that match for reference city i (whole number) reference city i TMRCi and APRCi a, b, c, and d are nonnegative coefficients that add to 1.0 and express the relative importance of each criterion. This approach requires two-steps. First, raw and differ- ence values for each criterion are normalized so that they range from 0 to 10. Lower values indicate a better match with the reference city than higher values. The second step weights each of the four criteria based on its relative impor- tance. It is recognized that the Tree Match criterion is fun- damentally different than the others because the raw value remains the value of interest. For the other criteria, the value of interest is a difference value obtained by subtracting refer- ence city raw values from subject city raw values. Because the Tree Match values are unique, the types of statistical analyses that can be conducted to identify the best match are limited. First, to normalize data the ranges of raw val- ues are identified for each criterion and 10 equal inter- vals are calculated. Each of the raw and difference val- ues are normalized and given a value between 0 and 10. Linear interpolation is used to calculate the normalized values. The second step is to assign a weight value to each coef- ficient that reflects its relative importance. For example, if the criteria are equally important, 0.25 is assigned to each of the four coefficients. The coefficient values must sum to 1.0. Factors influencing the relative importance of each criterion include extent of annual tree growth, severity of the climate, seasonality of rainfall, and total amount of annual rainfall. For example, in a northern latitude city with cold, snowy city and reference city i CDDSC where, HDDSC and HDDRCi and CDDRCi )2 + d * TMRCi 2 ] )2 + b * (CDDSC – CDDRCi )2 233 winters and cool, dry summers, it is more important to match HDDs than CDDs or annual precipitation. In a coastal re- gion with mild temperatures and much rainfall, it is more im- portant to match annual precipitation than HDDs and CDDs. Table 2. Annual precipitation and location for sixteen U.S. reference cities. Reference City Charleston, SC Charlotte, NC Claremont, CA Indianapolis, IN are Heating Degree Days for the subject are Cooling Degree Days for the subject city LISBON, PORTUGAL EXAMPLE are annual precipitation for the subject city and Lisbon, Portugal serves to demonstrate application of the ap- proach to select the best matching reference city. Also, it pro- vides opportunity to discuss how the relative importance of each criterion is assessed and values assigned to its coefficient. Lisbon, the capital city of Portugal, has approximately 2.6 million inhabitants and a Mediterranean climate that al- lows a large number of tree species to thrive. Lisbon (lati- tude 38.7071631, longitude -9.135517) is located along the Tagus River, and its climate is influenced by the nearby At- lantic Ocean. The annual temperature cycle is relatively mild, with cool winters and warm summers. During summer, tem- peratures frequently reach 30°C or above. Winters are wet and windy, temperatures averaging around 10°C. Annual precipi- tation throughout the region ranges from 500 to 760 mm an- nually, with most precipitation from October through April. Comparable Reference Cities Initially, the number of candidate reference cities is pared down from sixteen by excluding cities that are obvious mismatches and cities with similar values for the selection criteria. Comparing ref- erence city data (Appendix; Tables 1–2) with values for Lisbon, Portugal (Table 3) indicate annual rainfall (622 and 702 mm, re- spectively) and CDDs (383 and 474, respectively), in Minneapo- lis, MN, are good matches with Lisbon. CDDs and the tree species composition in Fort Collins, CO, also have much in common with Lisbon (Table 3). Claremont, Santa Monica, and Modesto, CA, share Lisbon’s Mediterranean climate. HDDs in Charleston, SC, closely match HDDs in Lisbon (1,171 and 1,084, respectively). Six reference cities passed this initial screening. Fort Collins, Colorado, rests at the foot of the Rocky Mountains (elevation 1,500 m) and has a semi-arid climate. Winters are cold, with snow staying on the ground for days or weeks. The growing sea- son ranges from 75 to 150 days (Brenzel 1997). The area receives approximately 457 mm of rain and 1,397 mm of snow per year. ©2010 International Society of Arboriculture Precip. (mm) Latitude Albuquerque, NM 250 Berkeley, CA Boise, ID 564 417 1,555 1,426 523 Fort Collins, CO 452 Glendale, AZ Honolulu, HI 174 392 Minneapolis, MN 622 Modesto, CA Queens, NY 1,110 315 1,041 Santa Monica, CA 570 Longview, WA 1,059 Orlando, FL 1,367 35.0844909 37.8715926 43.612631 32.7765656 35.2270869 34.0966764 40.5852602 33.5386523 21.3069444 39.767016 44.9799654 37.6390972 40.7498243 34.0194543 45.6387281 28.5383355 Longitude -106.6511367 -122.272747 -116.211076 -79.9309216 -80.8431267 -117.7197785 -105.084423 -112.1859866 -157.8583333 -86.156255 -93.2638361 -120.9968782 -73.7976337 -118.4911912 -122.6614861 -81.3792365
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