Arboriculture & Urban Forestry 41(4): July 2015 and four intercardinal). The simulated values for all TPC variables used in this study were based upon data from previous studies, typifying many urban landscape trees found in the U.S. (Simpson and McPherson 1998; Simpson 2002; Troxel et al. 2013). Shade Simulation Framework Tree shade simulations were processed with a com- puter program called Shadow Pattern Simulator (SPS, Windows Version 2.0), which was developed by scientists with the U.S. Forest Service (Simpson and McPherson 1998). Based on specifications for both a tree and a structure, the SPS program precisely estimated hourly shaded areas on each building surface as a percent of total exposed area [accuracy has been reported at 95%; see McPherson et al. (1985) for more details about the SPS pro- gram]. The SPS program had several limitations: it could only simulate basic geometric crown shapes, a static crown opacity factor, and a rectangular- shaped building. Nonetheless, it has tremendous computational capability for understanding daily and seasonal trends in shade provision and has been used in previous studies to quantify shaded areas on building surfaces as an intermediate step for energy consumption simulations (Simpson and McPherson 1998; Simpson 2002; Sawka et al. 2013). Tree Shade Simulations Each simulation using the SPS program calculated tree shade coverage on building surfaces using the following inputs: a TPC permutation, building spec- ifications, study area, and simulation time frame. Simulations were run at diurnal half-hour inter- vals (beginning of hour, middle of hour, and end of hour), and then the three half-hour shade coverage estimates were averaged for each hourly estimate. Monthly simulations were run one day per month (each at the middle of the month) over a year and then quantified as daily shade surface area (hereaſter referred to as shade provision), which represented the accumulated daily value of shade coverage on building surfaces from sunrise to sunset: [1] Shade Provisions (S) = Σ Ksunrise + … + Ksunset where K is an hourly shade estimate. Two measures of shade provision are reported here based on the simulations: average shade provision and maxi- 213 mum shade provision. Average shade provision is the value calculated by summing shade provisions divided by the number of months during either the cooling or heating season. Maximum shade provi- sion constitutes the greatest value (of single-day shade provision) over the duration of each season. Across the four study areas, a total of 6,912 shade provision estimates were acquired through a total of 576 tree shade simulations (144 TPC permutations × 4 study areas × 12 months). Average and maxi- mum shade provision values were then evaluated in the context of annual cooling and heating degree- days data for each of the four study areas (Table 2). RESULTS AND DISCUSSION Overall Trends in Shade Provision Within the calendar-year simulation time frame, maximum daily shade cast upon the exterior sur- face area of the prototypical residential structure ranged from 0 m2 tree) or 706 m2 (no shade) to 580 m2 (deciduous (coniferous tree), depending on the particular study area and simulated TPC. Figure 4 shows data for the large, nearby trees at the latitu- dinal extremes (Minneapolis and Orlando), which best exemplify the differential influence of TPC and latitude. In all simulations, compared to a deciduous tree, a coniferous tree provided more shade because of its higher crown opacity and year-round foliation. In addition, the larger the tree placed adjacent to the structure, the greater the shade provided. In con- trast, smaller trees placed at distances farther from the structure provided low levels of shade. Small trees placed ≥10 m away or medium trees ≥15 m away typically produced shade coverage less than 112 m2 , the 75th percentile of all shade estimates over the entire year (Figure 5). Among small and medium trees, only a few trees on the east or west aspect of the building provided shade greater than 112 m2 , during the yearlong simulation time frame. Differences in shading amongst study areas were due to latitudinal differences in sun angle above the horizons during the course of the day and year. In the same TPC permutation, trees placed on the south- ern aspects of the structure in northern cities cast more shade than those in southern cities (Figure 4). Because the sun was relatively lower above the hori- zon throughout the day and year in northern cities, the tree crowns intercepted more sunlight. Shade pro- ©2015 International Society of Arboriculture
July 2015
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