EQUATIONS FOR PREDICTING DIAMETER, HEIGHT, CROWN WIDTH, AND LEAF AREA OF SAN JOAQUIN VALLEY STREET...

306 Peper et al.: Predicting Diameter, Height, Crown Width, and Leaf Area

EQUATIONS FOR PREDICTING DIAMETER,HEIGHT, CROWN WIDTH, AND LEAF AREAOF SAN JOAQUIN VALLEY STREET TREESby Paula J. Peper1, E. Gregory McPherson1, and Sylvia M. Mori2

Abstract. Although the modeling of energy-use re-duction, air pollution uptake, rainfall interception,and microclimate modification associated with urbantrees depends on data relating diameter at breastheight (dbh), crown height, crown diameter, and leafarea to tree age or dbh, scant information is availablefor common municipal tree species. In this study, treeheight, crown width, crown height, dbh, and leafarea were measured for 12 common street tree speciesin the San Joaquin Valley city of Modesto, California,U.S. The randomly sampled trees were planted from 2to 89 years ago. Using age or dbh as explanatory vari-ables, parameters such as dbh, tree height, crownwidth, crown height, and leaf area responses weremodeled using two equations. There was strong corre-lation (adjusted R2 > 0.70) for total height, crown di-ameter, and leaf area with dbh. Correlations for dbhwith age and crown height for several species wereweaker. The equations for predicting tree sizes and leafarea are presented and applied to compare size andgrowth for all species 15 and 30 years after planting.Tree height, crown diameter, and dbh growth ratestended to slow during the second 15 years, but the leafarea growth rate increased for most species. Compari-sons of predicted sizes for three species common toModesto and Santa Monica trees suggest that pruninghas a significant impact on tree size and leaf area, po-tentially more than climate and soil characteristics.

Key Words. Urban forest; tree growth; predic-tive equations; size relationships; leaf area.

In rural forest stands and plantations, growth andyield are modeled using diameter-at-breast-height (dbh) relationships with tree height,crown height, and crown diameter (Furnival

1961; Curtis 1967; Stage 1973). Shinozaki et al.(1964) presented a pipe model theory showing astrong relationship between conducting tissues(the "pipes" running from roots to branch tips)and the tissues that receive water and nutrientsin the crown. This theory provided the basis forequations predicting leaf area from dbh and sap-wood area. For urban forests, the development ofequations to predict dbh, height, crown diameter,crown height, and leaf area of dominant munici-pal tree species will enable arborists, researchers,and urban forest managers to model costs and ben-efits, analyze alternative management scenarios,and determine the best management practices forsustainable urban forests (McPherson et al. 2000).For instance, pollutant uptake by open-growntrees depends on the leaf area because leaves ab-sorb pollutants such as ozone and nitrogen oxidesthrough leaf stomata and intercept particulatematter (e.g., dust, ash, pollen, smoke) on leaf sur-faces (Scott et al. 1998). Shade simulators used todetermine energy savings associated with theshading of homes require estimates of treeheights and crown diameters (Simpson 1998).Similarly, the modeling of carbon sequestration,rainfall interception, and microclimate modifica-tion also depends on the availability of data relat-ing dbh, height, crown height, crown diameter,and leaf area to tree age or dbh (Huang et al.1987; Simpson 1998; Xiao et al. 1998). Unfortu-nately, equations developed for rural forests havenot been directly transferable to open-grown mu-nicipal trees (Nowak 1994; Peper and McPherson1998), and references currently available in the

Journal of Arboriculture 27(6): November 2001 307

United States for predicting size and leaf area ofcommon municipal tree species at particular agesare limited.

Nowak's (1996) allometric method for esti-mating leaf area is based on data collected on 54open-grown park trees in Chicago, Illinois, thatwere selected with full crowns in excellent con-dition and additional data on 34 smaller treesobtained from Gacka-Grzesikiewicz (1980) inWarsaw, Poland. Frelich (1992) measured onlyhealthy trees (221 trees representing 12 species)growing in Twin Cities, Minnesota, to predictsize relationships. Similarly, to develop linear re-lationships between dbh, height, crown spread,and age, Fleming (1988) measured trees in NewJersey having full healthy crowns. In each ofthese studies, sampling methods were neitherrandom nor designed to address the broad rangeof tree conditions and locations along citystreets. In addition, the data were collected fromUSDA climate zones 3 to 6 (USDA 1990) hav-ing 150 to 180 frost-free days, representing a sig-nificantly shorter growing season than those inmany southern and western states. They may notpredict tree size at a given age in warmer climatezones with longer growing seasons.

Equations to predict total height, crownheight, crown diameter, and leaf area from dbh,or to predict dbh from age after transplant, for 16common street tree species growing in thecoastal southern California city of Santa Monica(USDA climate zone 10) represent the only pre-dictive models for urban tree species growing inwarmer climate zones of the United States. Al-though Modesto and Santa Monica have similarrainfall [315 mm (12.4 in.) and 322 mm (12.7in.), respectively], Santa Monica has a year-roundgrowing season (Brenzel 1997). The Modestogrowing season extends from early Marchthrough mid-November, with 20-year averagelows ranging from -3°C to -9°C (26 °F to 16°F),compared to Santa Monica's average lows of 7°Cto -4°C (44°F to 24°F). Modesto is located inthe San Joaquin Valley, a northern California in-

land area that is one of the world's five Mediter-ranean climate regions (Dallman 1998).

The objective of this study was to developregression equations to predict dbh from treeage, and to predict total height, crown diameter,crown height, and leaf area from dbh for 12common street tree species growing in Modesto,California (USDA zone 9).

METHODSField Data Collection ProceduresModesto manages 75,649 street trees belongingto 184 species (McPherson et al. 1999). How-ever, the 12 species sampled in this study accountfor 41% of the entire street tree population.Computerized street tree inventories and hand-written documents containing planting recordsfor trees were utilized to randomly sample com-mon street tree species. Ginkgo (Ginkgo biloba)were 3 years old at planting, silver maple (Acersaccharinum), European ash (Fraxinus excelsior'Hessei'), crapemyrtle (Lagerstroemia indica), Lon-don plane (Platanus x acerifolia), Bradford pear(Pyrus calleryana 'Bradford'), and zelkova (Zelkovaserrata) were 1-year-old 'whips at planting, and allother species were 2-year-old whips at planting.To obtain size information spanning the lifecycle of each of the 12 species, stratified randomsampling was conducted in different-aged neigh-borhoods with trees of known planting age.Stratification consisted of two groups, a "youngtree" group (planted from 1970s through 1990s)and an "old tree" group (planted prior to 1970).Fifteen trees of known age were randomlydrawn for each group for each species. Five addi-tional trees were drawn as substitutes if originaltrees could not be located.

Data collected for each tree from Junethrough September 1998 included species, age,address, dbh [to nearest 0.1 cm (0.39 in.) bytape], and tree height [to nearest 0.5 m (1.64 ft)by clinometer or range pole], crown diameter intwo directions [maximum and minimum axis, tothe nearest 0.5 m (1.64 ft) by tape], height to the


base of crown (to nearest 0.5 m by clinometer orrange pole), and leaf area. Observational data in-cluded a visual estimate of crown shape, pruninglevel, tree condition code (explained in para-graph below), and planting location (i.e., frontlawn, planting strip, sidewalk cutout).

Condition code (to nearest 5%) was calcu-lated per the Guide for Plant Appraisal (Council ofTree and Landscape Appraisers 1992). Pruninglevel estimation, recorded on a scale of 0 to 3,where 0 = no pruning, 1= less than 10% ofcrown pruned, 2 = 10% to 39% pruned, and 3 =40% or more pruned, was based on total per-centage of crown removed due to crown raising,reduction, thinning, and heading during the last4-year pruning cycle. Modesto's municipal treeswere on a 4-year inspection and pruning cyclewith all work conducted by city crews. Youngtree pruning followed the American NationalStandard Institute A300-1995 guidelines for treemaintenance (National Arborist Association1995). As trees matured, pruning included crownraising. Mature tree maintenance typically con-sisted of crown cleaning and thinning.

Two digital photos of each tree crown, takenat perpendicular angles (chosen to provide themost unobstructed view of the crown), wereused to estimate leaf area using an image process-ing method (Peper and McPherson 1998; Peperand Mori, forthcoming). Focal length of thecamera (5 cm [1.97 in.]) and distance from cam-era to the tree were recorded to nearest 0.1 m(0.33 in.) using the Sonin® Combo Pro CSTdistance measuring device. Clinometer and sonardevice measurements were checked for accuracyseveral times per week by measuring heights anddistances with a tape or range pole.

Due to limited resources and the time re-quired for data collection and verification of treeages, we were unable to collect a sufficientamount of data for validation of the equations.Initially it was assumed that planting ages couldbe determined from the city tree inventory and

development ages. However, ages of trees forwhich age data were missing or entered incor-rectly in the database were verified throughsearching handwritten planting records, inter-viewing residents and city arborists, or incre-ment coring to count growth rings. Crownheight was calculated by subtracting the boleheight (distance to base of crown) from total treeheight.

Data AnalysisOf the original 360 trees selected for sampling,341 were used in the analyses. Trees were ex-cluded if they could not be located in the field(felled and removed), or if photos revealed that thetree was incorrectly identified or entered into thedatabase. Therefore, eight species have fewer thanthe 30 trees originally drawn for sampling.

Typically, street tree databases include dbhsize classes but rarely any age information foreach tree. Therefore, in this study only dbh isregressed on age; all other variables are regressedon dbh, enabling users to predict the other di-mensions using measures of dbh alone. Threecurve-fitting models were tested, including amodified Weibull model fitted by Frelich (1992)to a small sample of healthy trees. The logarith-mic regression model provided the best fit forpredicting all parameters except leaf area, forwhich the nonlinear exponential model •wasused (see appendix). Visual observation of thedata revealed increasing variability with age andsize of the trees; therefore, we assumed the errorto be multiplicative as is indicated by the confi-dence intervals shown in Figure 1. A brief de-scription of the models is in the appendix. Acomplete description of the analysis and models,including the necessary standard error of esti-mates, response sample mean, and correlationvalues needed for calculating confidence inter-vals is available on the Center for Urban ForestResearch web site at http://wcufre.ucdavis.edu/urbanforestinventoryandmonitoring.htm.


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Figure 1. Actual measurements (asterisks), predicted responses (solid line), and confidenceintervals (dotted lines) for zelkova growing in Modesto, California. Equation (2), E(leaf area.)= a*(^*m' - 1) where E = expected value and a and b are parameters to be estimated, was usedto model leaf area for 12 species. Equation (1), E(y) = a*[\og(x. + l)]b was used to predict allother dimensions.


RESULTS AND DISCUSSIONThe SampleThe majority (61%) of Modesto's street treeswere growing in front lawns within 3.5 m (11.5ft) of a sidewalk or street. Twenty-three percentwere in planting strips wider than 1.2 m (4 ft).Only 16% of the trees grew in restricted loca-tions, either in sidewalk cutouts measuring 1.2by 1.2 m or smaller or planting strips of less than1.2 m width. Trees planted in lawns usually re-ceived irrigation, and the amount varied widely,depending on the home owner (front yards) orbusiness owner (planting strips). Typically, irriga-tion was for the lawn rather than deep-wateringfor trees.Table 1 shows the age range sampled foreach species. Eighty-one percent of the treessampled were in good to excellent condition,17% fair, and 2% poor, dead, or dying.

Table 1. The range of years included insample for each species along with the mini-mum and maximum ages are shown.

Common nameMin.age

Max.age

No. ofyears

Silver maple 5 67 62Camphor tree 6 73 67European ash 2 48 46Ginkgo 8 35 27Goldenrain tree 3 37 34Crape myrtle 5 48 43Sweetgum 15 39 24Southern magnolia 8 49 41Chinese pistache 4 36 32London plane 4 89 85Bradford pear 8 48 40Zelkova 3 33 30

With the exception of crapemyrtle, sweetgum(Liquidambar styraciflua), and eight trees (repre-senting six species) growing beneath power lines,crown reduction and heading were rarely ob-served within the sample. Perhaps because of itsaccessibility, the small-statured crapemyrtle oftenwas shaped by home owners rather than city treecrews. Crown reduction to reduce weight onsweetgums having weak secondary branch at-

tachments was also observed within the sample.Otherwise, maintenance pruning appeared con-servative, conducted when necessary to maintainthe health and structure of the trees.

Dbh, Height, and Crown DiameterThe regression coefficients (A = y-intercept andb = slope) for predicting dbh from age, and heightand crown diameter from dbh are presented inTable 2 along with the mean standard error(MSE) and adjusted coefficients of determination(adjusted R2). All equations were significant (P <0.01). The dbh model displayed good fit (R2 =0.70) for seven species. The R2 values are a directmeasure of the strength of association betweenvariables such as dbh and height. The higher theR2 , the stronger the association. Tree height andcrown diameter displayed good fit for ten of the12 species (Table 2). The model explained themost variation in the data for silver maple, cam-phor tree (Cinnamomum camphom), ginkgo, gold-enrain tree (Koelreutaria paniculata), and zelkova.The age range for these species spanned a mini-mum of 30 years (Table 1). An example of thefitted models for zelkova is shown in Figure 1.Since the data were fitted with a statistical modelthat accounted for the increase of the variabilitywith the increase of the mean values, one noticesthe confidence bounds expand with increasingtree age and size. This trend represents a commoneffect and was evident for all species, expressingthe increasing variability within species due to thecumulative effects of differences in genotype, cul-ture, site condition, biotic, and abiotic factors thatinfluence tree health.

Species with the lowest R2 were sweetgumand southern magnolia (Magnolia grandiflora). Sev-eral factors contributed to this low R2. TheModesto municipal tree inventory did not differ-entiate among cultivars for either of these species,and their inclusion in the sample contributed togreater variation in dbh, height, and crown size.During our inventory, we noted several cultivars


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for each of these species. For example, thesweetgum sample included 'Palo Alto' and 'Bur-gundy' cultivars. There were three or four south-ern magnolia cultivars. Additionally, sweetgumhad not been planted in the past 15 years, and thesouthern magnolia sample contained only twotrees that were planted within the past 25 years.

The model fit crapemyrtle dimensions well,with the exception of dbh and age. The samplecontained both multi- and single-stemmed speci-mens. Stems in several multi-stemmed trees hadbeen removed. This reduced dbh and contributedto the variability in dbh—age relationships. How-ever, there was no obvious explanation for the evenhigher variability (low R2) between Bradford peardbh and tree age.

Generally, the relationship between crown di-ameter and dbh was stronger than the relationshipbetween height, crown height, and leaf area anddbh, most likely because the forms are more sub-ject to cultural practices. Municipal tree pruningaffects tree height and height to the base of thecrowns more than crown diameter due to crownraising for vehicular and pedestriantraffic and crown reduction aroundutilities and signs. The R2 for crowndiameter and dbh for ten of 12 spe-cies was greater than 0.80. For six spe-

surements were affected by both crown raising andcrown reduction. Many of the crowns had beenraised in previous pruning cycles, but we had dataonly for the past 4 years; therefore, we were unableto account for differences in crown height based onpruning history.

For leaf area, a nonlinear exponential modelshowed good fit (R2 > 0.70) for nine of the 12species, with R2 greater than 0.65 for two addi-tional species (Table 3). Sweetgum and southernmagnolia were planted over a shorter time spanrelative to other species and showed weaker cor-relations. Variability in leaf area for crapemyrtlewas probably higher due to the pruning ofcrowns by home owners.

Growth ComparisonFifteen years after planting, estimated dbh forModesto trees ranged from 10 to 38 cm (4.1 to15 in.), and tree height ranged from 5 to 14 m(15.7 to 45.8 ft) (Table 4). The fastest-growingtrees by dbh were London plane, zelkova,Bradford pear, and silver maple, while the slowest

Table 3. The coefficient and mean standard error values

(MSE) for predicting tree leaf area from dbh using Equa-

tion (2) for the modeling data set. Leaf area can be pre-

cies it was greater than 0.90. The best dieted by: LA = EXP(A\* EXp((bDBH\ - 1 j * EXP(MSE/2)correlations in the Santa Monica - - - - - - ~ - Lstudy were also between crown diam-eter and dbh.

Crown Height and LeafAreaThe predictive model for crownheight showed good fit (R2 = 0.70)for seven species (Table 2), and allequations were highly significant {P <0.01). The crown height adjusted R2

was generally lower for most speciesthan tree height and crown values forthe same species. This may be relatedto pruning since crown height mea-

where LA = estimated leaf area and EXP = the inverse

of the natural logarithm.

Common name

Silver mapleCamphorEuropean ashGinkgoGoldenrain treeCrape myrtleSweetgumSouthern magnoliaChinese pistacheLondon planeBradford pearZelkova

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Table 4. Predicted sizes for 12 species at 15 and 30 years after planting are shownsorted by fastest growth (dbh) in first 15 years after planting.

Common name

London planeZelkovaBradford pearSilver mapleChinese pistacheCamphor treeEuropean ashSweetgumGoldenrain treeSouthern magnoliaGinkgoCrapemyrtle

Dbh15

38.1137.8931.3027.4727.1526.6024.1923.7721.8718.9812.9410.44

(cm)30

48.1753.3840.9058.1238.1246.0539.1245.7737.1530.1938.7716.24

Height (m)15

13.9711.3610.4713.1110.709.129.1811.898.777.557.924.79

30

15.5112.8511.4818.6212.4112.2110.2715.9410.509.8011.745.50

Crown15

11.4812.649.279.2210.177.387.546.607.175.804.983.77

diameter (m)30

12.8914.9110.7013.6711.9610.909.899.719.047.388.504.68

Leaf area (m2)15

262.22297.44174.29151.03179.1886.6793.92152.2772.4365.8345.1523.41

30

353.87589.15240.18427.56358.48264.01220.47387.07175.21113.87235.2941.76

growing were crapemyrtle, ginkgo, southernmagnolia, and goldenrain trees. These findingsare compatible with the species descriptions inthe Sunset Western Garden Book (Brenzel 1997).

Dbh growth tended to slow during the second15 years for the species studied. The median rateof annual growth dropped from 1.67 cm (0.66in.) during the first 15 years to 1.06 cm (0.42 in.).Exceptions were ginkgo, with a growth rate thatdoubled during the second 15 years, and silvermaple with a growth rate about 11% higher thanin the first 15 years. Ginkgo went from the secondslowest- to the second fastest-growing species,supporting anecdotal accounts of it having alonger establishment period compared to othermedium- to large-growing trees.

Like dbh growth, tree height and crown di-ameter growth also slowed during the second 15years. The median annual rates of height growthdropped from 0.66 m (2.16 ft) to 0.16 (0.52 ft)between the first and second 15-year periods.Larger-growing species such as London plane,silver maple, zelkova, and sweetgum were amongthe tallest after 15 years. Sweetgum and silvermaple continued growing at relatively fast rates,but London plane and zelkova were replaced byginkgo and camphor tree as the fastest growersduring the second fifteen years. Zelkova and

camphor tree, listed in regional tree guides(Brenzel 1997; Reimer and Mark 2001) as largetrees, were medium-sized after 30 years inModesto, measuring 12.8 and 13.4 m (41.9 and43.9 ft), respectively.

Although crown diameters for two small- tomedium-sized trees, Bradford pear and Chinesepistache (Pistada chinensis), were among the fast-est growing in the first 15 years, they slowedsignificantly during the second. Average annualcrown diameter growth generally decreased dur-ing the second 15 years for all species.

The median annual estimated rate of leaf areagrowth increased from 8.2 m2 (88.3 ft2) for thefirst 15 years to 10.1 m2 (108.7 ft2) for the next15 years. Only four species exhibited a decreasedrate of leaf area growth during the second 15years (London plane, Bradford pear, southernmagnolia, and ginkgo). Silver maple is consid-ered a large tree in regional planting guides, andits height in Modesto classified it as large, butzelkova, a medium-sized tree in Modesto, hadmore leaf area. Although not as tall as silvermaple, zelkova's crown at 15 and 30 years waswider and more dense. Bradford pear and Chi-nese pistache, described by Benzel (1997) assmall-to-medium and medium trees, respectively,were among the four species adding the most

314 Peper et al: Predicting Diameter, Height, Crown Width, and Leaf Area

leaf area to their crowns during the first 15 years ofgrowth. Although Bradford pear rank changedfrom the top four in the first 15 years to the bot-tom three in the second 15 years, Chinese pistacheremained ranked in the top four species adding themost leaf area along with zelkova, silver maple, andsweetgum. Like zelkova, the higher leaf area forChinese pistache when compared with Bradfordpear was related to its wider crown diameter.

Customarily, regional planting guides use mea-surements of tree height alone to classify trees assmall, medium, or large. However, our findingsshow that the "medium-sized" zelkova is wider,with more leaf area than the "large" London planetree. Similarly the "medium-sized" Chinesepistache is wider, with more leaf area than the"large" camphor tree. This suggests that usingheight alone to indicate mature tree "size" pro-vides an inaccurate picture, particularly when themajority of benefits (hydrologic, air quality, energysavings) are usually linked to crown volume, leafarea and crown area, as well as tree height.

Modesto and Santa MonicaComparisonCamphor tree, sweetgum, and southern magnoliawere common to Modesto and Santa Monica, al-lowing comparison of predicted tree sizes in thetwo cities. Predicted tree sizes at years 15 and 30were compared using equations reported here andequations developed for Santa Monica species. Alldimensions and leaf area were larger for camphortree and sweetgum growing in Modesto than inSanta Monica. Camphor trees in Modesto were1.38 and 2.19 m (4.53 and 7.18 ft) taller than SantaMonica camphor trees at 15 and 30 years afterplanting. Crown diameters were closer in size, withModesto trees being 0.59 and 0.46 m (1.94 and1.51 ft) wider 15 and 30 years after planting. How-ever, at year 30, Modesto camphor trees had over100 m2 (1076 ft2) more leaf area than their SantaMonica counterparts. These differences were moredramatic for sweetgum. By year 30, Modestosweetgums were more than 4.5 m (14.76 ft) taller

and 3.2 m (10.5 ft) wider, with 181 m2 (1948 ft2)more leaf area, than Santa Monica sweetgums. Atmaturity, sweetgums in Modesto were large trees[>17 m (55 ft)], but Santa Monica sweetgums werepruned to a medium height [12 m (40 ft)] and leafarea. Santa Monica sweetgums were pruned heavilyin an effort to reduce root size and associated side-walk damage. Camphor trees were also pruned butnot to the extent of sweetgums. In contrast, southernmagnolias in Santa Monica were 0.16 m (0.52 ft)taller, 1.82 m (5.97 ft) wider, and had 17 m2 (183 ft2)more leaf area than Modesto southern magnolias.The majority of southern magnolias were planted infront lawns in Santa Monica and received little prun-ing beyond crown raising for vehicle and pedestriantraffic. Size differences were cultural.

The equations for modeling dbh as a function ofage, and tree height, crown diameter, and leaf area asfunctions of dbh, produced strong correlations, par-ticularly for those species planted over a longer pe-riod of time. Application of these equations shouldbe limited to populations of trees falling within thesame climate zone, maintenance category, and dbh(or planting age). However, the approach used todevelop the models is transferable, providing a basisfor city urban forest managers to better understandthe changing architecture of their street trees. Otherapplications include estimating pruning costs associ-ated with different pruning cycles or the productionof waste wood and leaf litter.

CONCLUSIONSThe application of the models to compare tree sizesat 15 and 30 years after planting showed that severalModesto species grow to different sizes than indi-cated in regional planting guides. The finding thatshorter trees with wide crowns had more surfaceleaf area than taller trees with narrow crowns indi-cates that classifying trees on the basis of one ortwo dimensions (e.g., dbh or height) is inadequate.The Modesto data suggest the need to develop afour-dimensional approach for classifying and visu-alizing tree growth, an approach that better de-scribes the three-dimensional tree and how those


dimensions change and grow over time. Predictiveequations provide the essential data required to de-velop computerized visualization programs capableof "growing" trees in a variety of urban locations.This information will assist arborists, landscape ar-chitects, and municipal tree managers to bettermatch trees to planting sites.

The continued collection of data and develop-ment of predictive equations for additional treespecies can provide a basis for comparing the effectsof climate and alternative management scenarioson like species of trees throughout different regionsof the world. However, comparisons of predictedsizes for Modesto and Santa Monica trees suggestthat cultural practices, especially pruning, have asignificant impact on tree size and leaf area, poten-tially more than climate and soil characteristics. Es-sentially, pruning is a highly variable social factorinvolving multiple managers and multiple pruningpractices. This makes the application of the predic-tive equations to other populations in similar cli-mate zones difficult unless a pruning index isdeveloped to adequately and consistently describereductions to crown dimensions and density.

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APPENDIXModels for Predicting Dbh, TreeHeight, and Crown DiameterUsing age (years after planting) or dbh as explana-tory (dependent) variables, mean values of dbh,tree height, and crown diameter responses weremodeled using the following regression equation:

where

wherey, = observed response i, i = 1, 2, ..., n;

n = number of observationsx — age or dbha, b = parameters to be estimatedE() = expected value.

The following regression model was used forthe transformed response:

log(y,.) = A + b log(log(x; +1)) + e. (l1)

This model can be rewritten as

zi = A + bv{ + 8.

whereA,b = parameters to be estimatedz, = log (y.)v. = log(log(*. + 1))8; = error term

The estimated j>arameters, A and b, are de-noted by A and 6.The Baskerville (1972) biascorrection, ^i&EI2^ w a s applied to the back-transformed fitted, ex' , ez' :

z{ = A + bvi and

MSE = mean sum of squares from leastsquares estimation (LSE) procedure. There-fore, the fitted value of y. is given by

where4 = gA+MSE/2

Estimates A and b , and MSE are used to predictdimensions for each species listed in Table 2.

Model for Predicting Leaf AreaThe expected value of leaf area was modeled asfollows:

E(leaf area.)= a*\e ' — 1) (2)

Again, we assumed the errors to be multipli-cative and log transformed the leaf area response:

z.= I og (leaf area.) =

e (2)

The A and b coefficients were estimated usinga nonlinear regression estimation (NLE) tech-nique. As before, the back-transformed estimatedez' was bias corrected with eMSB/2

; where MSE isthe mean sum of squares from NLE.

Acknowledgments.This study was made pos-sible by a grant from the City of Modesto, Parks andRecreation Department, and additional funds pro-vided by the International Society of ArboricultureResearch Trust (Duling Grant), and the Elvinia J.Slosson Fund. We are indebted to Chuck Gilstrap,Alan Lagarbo, and Derald Weaver from the City ofModesto.We especially thank our crew of data collec-tors and image processors: Giacomo Damonte, KlausScott, Rosalie Venterea, Stacy Kontrabecki, SabrinaMathis, and Todd Prager.


UUSDA Forest ServicePacific Southwest Research Station

c/o Department of Environmental HorticultureOne Shields AvenueUniversity of CaliforniaDavis, CA, U.S., 95616-8587

2USDA Forest ServicePacific Southwest Research StationBerkeley, CA, U.S.

^Corresponding author

Resume. Meme si la moderation de la reductiond'energie utilisee, du captage des polluants, de l'interception depluie et de la modification du microclimat associes aux arbresurbains depend des donnees reliant DHP (diametre a hauteurde poitrine), hauteur de cime, largeur de cime et surface foliairea celles de l'age de l'arbre ou du DHP, des informationspartielles sont disponibles pour les especes les plus communesd'arbres de villes. Dans cette etude, la hauteur de l'arbre, lalargeur de cime, la hauteur de cime, le DHP et la surface foliaireont ete mesures pour 12 especes communes d'arbres de ruesdans la vallee de San Joaquin de la ville de Modesto enCalifornie. Les arbres echantillonnes aleatoirement ont eteplantes de 2 a 89 ans auparavant. En utilisant l'age ou le DHPcomme variables explicatives, des parametres comme le DHP, lahauteur de l'arbre, la largeur de cime, la hauteur de cime et lasurface foliaire ont ete modelises au moyen de deux equations.II y avait une correlation forte (R2 > 0,70) pour la hauteurtotale, la largeur de cime et la surface foliaire avec le DHP. Lescorrelations du DHP avec l'age et la hauteur de cime etaientplus faibles pour plusieurs especes. Les equations pour predireles dimensions de l'arbre et la surface foliaire sont presentees etappliquees pour comparer la dimension et le taux de croissancede chaque espece 15 et 30 ans apres leur plantation. Les taux decroissance en hauteur de l'arbre, en largeur de cime et en DHPtendent a ralentir durant la seconde periode de 15 ans, mais letaux de croissance de la surface foliaire de la plupart des especess'accroit. Des comparaisons de prediction de dimensions pourtrois especes communes d'arbres a Modesto et Santa Monicasuggerent que l'elagage a un impact significatif sur la dimensiondes arbres et la surface foliaire, potentiellement plus que leclimat et les caracteristiques du sol.

Zusammenfassung. Obwohl die Simulation vonvermindertem Energieverbrauch, Luftverschmutzungszunah-me, Regenfallaufhahme und Modifikation vom Mikroklima inVerbindung mit Stadtbaumen auf den Daten beziiglichBrusthohendurchmesser (BHD), Kronenhohe, Kronendurch-messer und Blattflache zur Baumhohe und BHD basiert, ist nur

sparliche Information iiber offentlich verwendete Baumartenerhaltlich. In dieser Studie wurde die Hohe, Kronenhohe und —breite, BHD und Blattflache an 12 gewohnlichenStraBenbaumarten in San Joaquin Valley, City of Modesto, Cal.gemessen. Die zufallig ausgewahlten Baume wurden vor 2 bis89 Jahren gepflanzt. Unter Verwendung von zwei Gleichungenwurden die Antworten, bestehend aus Angaben iiber Alter oderBHD als BezugsgroBen, Parameter wie BHD, Hohe und Breiteder Krone und Blattflache, in ein Modell einbezogen. Es gabeine starke Korrelation (angepasst R2 > 0.70) fur die totaleKronenhohe, -durchmesser und Blattflache mit BHD. DieKorrelationen fur BHD mit Alter und Kronenhohe war fureinige Arten schwacher. Die Gleichungen zum Bestimmen vonBaumgroBe du Blattflache wurden dargestellt und angewendet,um die GroBe undWachstum aller Arten 15 und 30 Jahre nachdem Pflanzen zu vergleichen. Baumhohe, Kronendurchmesserund BHD Wachstumsraten tendierten wahrend der zweiten 15Jahre zum Verlangsamen, aber die Blattflachenwachstumsratestieg bei den meisten Baumarten. Vergleiche zwischen denvorhergesagten GroBen dreier Baumarten in Modesto undSanta Monica wiesen daraufhin, dass Riickschnitt einendeutlichen Einfluss auf die BaumgroBe und Blattflache hat,insbesondere mehr als klimatische oder Bodenfaktoren.

Resumen. A pesar de que el modelamiento de lareduction de energia, control de la contamination del aire,interception de la lluvia y modification microclimaticaasociada con los arboles urbanos depende de los datosrelacionados con el diametro a la altura del pecho (dap), alturade la copa, diametro de la copa y area foliar, la information noes suficiente para el comun de los arboles urbanos. En esteestudio, la altura del arbol, el diametro de la copa, la altura de lacopa, el dap y el area foliar fueron medidos para 12 especies dearboles comunes en la ciudad de Modesto en el Valle SanJoaquin, California. Los arboles muestreados al azar fueronplantados desde hace 2 a 89 afios. Con el uso de la edad odiametro como variables explicatorios se modelaron losparametros tales como dap, altura del arbol, anchura de la copa,altura de la copa y area foliar usando dos ecuaciones. Existe unafuerte correlation (R2 > 0.70) para altura total, diametro de lacopa y area foliar, con dap. Las correlaciones para dap con edady altura de la copa para varias especies fueron debiles. Lasecuaciones para predecir los tamanos de los arboles y area foliarson presentadas y aplicadas para comparar tamano ycrecimiento para todas las especies, 15 y 30 afios despues de laplantation. Las tasas de crecimiento en altura del arbol, diametrode la copa y dap tienden a bajar durante los segundos 15 afios,pero la tasa de crecimiento del area foliar increments para lamayoria de las especies. Las comparaciones de los tamanospredichos para tres especies comunes sugieren que las podastienen un impacto significativo sobre el tamafio de los arboles yel area foliar, potencialmente mas que el clima y lascaracteristicas del suelo.

EQUATIONS FOR PREDICTING DIAMETER, HEIGHT, CROWN WIDTH, AND LEAF AREA OF SAN JOAQUIN VALLEY STREET...

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