58 Inventory Field data were collected during a 100% tree inventory of the AU campus in 2009–2010 (Martin 2011) follow- ing i-Tree Eco protocol (i-Tree 2010b; i-Tree 2010c). Six- teen attributes were measured for each tree, including tree species, diameter at breast height (dbh) (1.37 m above the ground), tree height, average crown width, dieback, and missing crown. Data collection was completed in May 2010 and all field data were analyzed by the USDA Forest Ser- vice which generated information on the ecosystem servic- es provided by the AU urban forest. Information regarding these services included air pollution removal value (USD $), carbon storage (kilograms), and carbon sequestration (kilograms/year) for each tree. Air pollution removal was considered as a whole instead of evaluating the reported air pollutants individually for the plot number analysis be- cause air pollution was considered as one ecosystem service. Sampling Design 9 ArcMap™ All spatial analyses and operations were conducted using the ESRI ArcGIS® Martin et al.: Evaluation of Sampling Protocol for i-Tree Eco desired allowable error divided by the proportion of the area with trees. For example, if 200 plots with trees are required to meet a desired allowable error of ±10%, and 50% of the area had no trees, then a total of 400 plots would be needed since 50% of them would have no trees on them. Likewise any esti- mate of the ecosystem services would be estimated from only those plots with trees and the total value for the campus would use an estimate of the hectares with trees (120 hectares for the AU campus). Therefore, only the 1,500 plots with at least one tree were used to estimate the average value per hectare for air pollution removal, carbon storage, carbon sequestration, and number of trees. These plots also provided estimates of vari- ance between plots for each factor. The coefficient of vari- ance was then determined for each factor as the square root of the variance over the average. The number of plots needed to meet a range of allowable errors was then determined using a standard equation for sample size for a finite population of plots, which includes the correction factor for a finite popula- tion (Shiver and Borders, 1996). Equations were of the form: v.9.3 geographic information system (GIS) computer software. First, an aerial photograph of the AU campus was used to create a new shapefile of the boundaries of the study site. No infrastructure (buildings, parking lots, sidewalks) were excluded from the shapefile to provide an accurate picture of the urban environment. All field data and tree locations collected dur- ing the initial inventory (Martin 2011) were then used to create a new tree point shapefile with the collected tree data in an associated attribute table. Ecosystem services data for each tree were then ap- pended to the tree attribute table created in the tree point shapefile. Three thousand random points, created as plot centers, were then generated inside the study area with at least 22.54 m between the points to ensure that no plots would overlap to meet standard assumptions of random sampling and avoid the complications of trees belonging to more than one plot. The 3,000 plot centers were produced to provide a large enough sample so that the variance between plots could be calculated and produce a sufficient estimate of the proportion of area with trees on the AU campus. A plot covering 0.04 ha was created around each point (plot center). All 0.04 ha plots were then spatially joined with the tree point shapefile created from the inventory field data to select the trees that fell within each plot. Plot Number Analyses For each plot with at least one tree present, air pollution remov- al, carbon storage, carbon sequestration, and total tree popula- tion were determined on a per hectare basis. As with any urban environment, a large proportion of the Auburn campus consists of buildings, roads, and other open areas without trees (about 50%). Since plots located in these areas would have plot val- ues of zero for all the factors, this large proportion of zeroes would violate the normality assumption of the random sampling procedure. Therefore, the sample sizes used are for only those areas with trees, excluding those on campus without trees. It is reasonable to assume that areas at least 22.54 m from the closest tree could be removed from the sampling area by use of the aerial photograph in the GIS map of campus. If not, then the number of plots required to be located randomly across the area would be the number of plots with trees needed to meet the ©2013 International Society of Arboriculture [1] sample size = [4A(CV2)] / [A(E2 ) + 4P(CV2 )] where 4 represents the t-value squared at α = 0.05, A is the total hectares with trees determined by the total hectares on campus multiplied by the proportion of plots with trees, CV is the coefficient of variance, E is the allowable error, and P is the plot size used for this study, which was a 0.04 ha plot. The range of allowable errors was from ±1% to ±25%. RESULTS Of the 3,000 plots created, approximately 50% had at least one tree present. Figure 2 displays how many plots (with at least one tree present) would be necessary (y axis) to achieve an estimate with the desired allowable error of the total campus value (x axis) for each factor. Based on the principle of diminishing returns it was decided to use an allowable error of ±10% because any decrease in the allowable error would require a relatively large increase in the required sample size. To achieve an estimate with a ±10% allowable error of the total air pollution removal value of the 243 ha AU campus, researchers would require a sample size of 622 plots (0.04 ha each) that have at least one tree present. For car- bon storage, carbon sequestration, and number of trees it would require: sample sizes of 870, 483, and 258 plots, respectively. Due to the proportion of campus without trees, these sample sizes would be doubled (1,244; 1,740; 966; and 516, respectively) to incorporate the total number of sample plots needed to be created. It should be noted that the 200 plots recommended in the protocol (i-Tree 2010c) would produce allowable errors of ±19%, ±24%, ±16%, and ±11% for total air pollution removal value, carbon storage, carbon sequestration, and number of trees, respectively. DISCUSSION Ecosystem services were used as the basis for a sampling protocol because i-Tree Eco inventories are conducted to quantify the ecosystem services provided by the urban for- est to meet specific management objectives. Therefore, sam- pling should ideally follow a protocol in which the num- ber of plots sampled is based on the ecosystem service(s) of interest so that the inventory is providing accurate results.
March 2013
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