Arboriculture & Urban Forestry 38(5): September 2012 analyses of biotic and abiotic factors were combined to “train” artificial neural networks to predict tree growth. The modeling method demonstrates robust predictive capability despite dif- ferences in morphological characteristics within study species. In research that could be adapted to urban settings, Salas et al. (2010) studied the use of airborne laser scanning, LIDAR and geographically weighted regressions to model DBH from LIDAR-based variables. LIDAR measurements in conjunc- tion with a linear mixed-effect model produced DBH esti- mates with a 4% error rate. Seidel and others (2011) have used terrestrial LIDAR, also called 3D laser scanning, to non- destructively monitor plant biomass and growth of juvenile trees, with good correlation between scan and destructive har- vest data for predicting leaf area and aboveground biomass. Additional studies conducted in the search for efficient tree growth measuring and monitoring include the develop- ment of Urban Crowns (Patterson et al. 2011), a software program developed by the USDA Forest Service South- ern Research Station that provides estimates of crown and tree height, diameter, ratio, volume, transparency, and den- sity using a digital photographs and basic field measurements. USDA FOREST SERVICE REFERENCE CITY RESEARCH The authors compiled a master database containing all field data collected in the 16 i-Tree Streets reference cities plus several additional cities where research was conducted (Pep- er and McPherson in preparation). This database consists of more than 17,000 trees representing 171 unique species in 16 U.S. climate regions. In addition to the tree size variables measured for each tree and listed previously, the tree records include location information, measured growing space, set- back distance, and orientation from tree to nearest conditioned space, land use, planting site description, wire and sidewalk conflicts, tree shape, and condition. The objective was to es- tablish an accessible international tree growth database that researchers can use for comparative analyses. Selected trees may be re-measured to study growth over time. Multivariate statistical analyses may be conducted to identify relationships between tree size, growth, and biotic and abiotic variables. The analytical approaches applied to the reference city data evolved over the ten-year period that research was conducted. During the first study in 1998, the study authors attempted to adapt the sigmoid-shaped model used by Frelich (1992) for Minneapo- lis, Minnesota, trees, but found that a loglog model fit better. The loglog model is typically used to fit tree growth data collected in forest stands. As the cross-country data collection continued, it became evident that no single model would fit all growth vari- ables for any one species, let alone all species. Eventually, de- pending upon the city and species, loglogs, simple polynomials tested at various weights, and exponential models were fitted. Analysis tools providing researchers with more accurate and efficient methods for comparing and selecting the best models have increased in number and capability since 1998. Thus, all of the data were recently re-analyzed using SAS 9.3 program- ming to test seven types of growth predictions for each species in each of the 16 climate regions. The objective was to select the best models and produce predictive equations for tree height, crown height, crown diameter, and leaf area from measures of DBH, as well as to predict DBH from age and crown diame- 175 ter. Seven models were tested (linear, quadratic, cubic, loglog, exponential, two-segment linear, three-segment linear) at four weights (equal weighted, sqrt(x), 1/x, and 1/x2 , where x = DBH or age). For a city where data were collected on 18 species, this method resulted in the testing of 3,528 models (18 sp × 7 pa- rameters × 7 models types × 4 weights) to determine the best fit. Models having the best fit were selected using second- rule of thumb, a Δi for the model. The Δi The limitation of AICc AICC order Akaike Information Criterion) testing (AICc) and the del- ta AICC (Δi ) to rank all models relative to the best model. As a less than two suggests substantial evidence for all selected models was less than one. is that if only poor models are tested, selects the best of the poor. Therefore, the adjusted R2 and mean squared error were examined and reported for each model as well. This analysis produced nearly 2,600 regionally specific equations predicting various tree dimensions. These, along with the database, will be published and placed online in a spreadsheet format for free public access and download. Comparing Growth and Services Produced by the Same Species Tree growth equations developed through the reference city work have been foundational for many tools used to calcu- late ecosystem services, including i-Tree Streets (i-Tree Team 2011), the National Tree Benefit Calculator (Casey Trees and Davey 2011), and Urban Forest Map (2011). They also provide opportunity for comparison with growth equations developed by other scientists and for like species growing in different regions. Many of the i-Tree reference cities share several of the same predominant species. For example, sweetgum (Liquidambar styraciflua) and honeylo- cust (Gleditsia triacanthos) are among the top 20 species in 10 cities, silver maple (Acer saccharinum) and callery pear (Pyrus calleryana) in nine cities, and green ash (Fraxinus pennsylvanica) in eight cities. As shown by the following examples, the predictive equations developed for these spe- cies allow professionals to examine trends and assess pos- sible reasons for growth differences. Additionally, the master database and predictive equations are producing the basic parameters required for improved tools such as the web- based Tree Carbon Calculator (USDA Forest Service 2008). Studies conducted in Westminster, Colorado, and Chey- enne, Wyoming, both in the U.S. North Climate Region, al- low comparison with growth models developed from data collected on predominant species in Fort Collins, Colorado (McPherson et al. 2003). The Westminster study permitted verification of Fort Collins growth models (predicting di- ameter at breast height from age) with an independent data set from a nearby city (81 km south of Fort Collins) hav- ing similar growing conditions (Wood 2010). The study re- ported growth for 16 years after initial planting for 10 of the species shared by both cities. With the exception of cot- tonwood (Populus sargentii) and Austrian/ponderosa pine (Pinus nigra/P. ponderosa) (2.0 and 0.5 cm DBH smaller in Fort Collins), the remaining Fort Collins species were pre- dicted to grow larger than Westminster’s (Figure 1). The difference ranged from about 2 cm DBH for blue spruce to 7 cm DBH for silver maple over the 16-year period. While relatively small, the differences probably reflect varia- ©2012 International Society of Arboriculture
September 2012
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