biometrics

Modeling Climatic Effects on Stand Height/SiteIndex of Plantation-Grown Jack Pine and BlackSpruce TreesMahadev Sharma, Nirmal Subedi, Micheal Ter-Mikaelian, and John Parton

Stand height/site index equations that incorporate climate variables were developed for plantation-grown jack pine (Pinus banksiana Lamb.) and black spruce (Piceamariana [Mill.] B.S.P.). Study data came from stem analysis of three dominant or codominant trees sampled from 73 plots for jack pine and 75 plots for black sprucewithin even-aged monospecific plantations located on 50 sites (25 sites per species) in the Canadian boreal forest region of Northern Ontario. A nonlinear mixed-effectsapproach was applied to fit the stand height equations. The climate variables that were significant in explaining the variation in heights of dominant and codominanttrees were growing season mean temperature and growing season total precipitation. Including climate variables significantly improved the fit statistics of the stand heightmodel for both species. For each species, stand heights were predicted for a randomly selected location for the growth period of 2011 to 2040 under A2 and B2 climatechange scenarios. At the end of the growth period, projected heights were reduced by 8 and 2% for jack pine and 28 and 16% for black spruce under A2 and B2climate change scenarios, respectively, compared with heights projected under a current climate scenario. The site index of a stand can be estimated using the standheight model by calculating height at a given base (index) age. In the absence of climate data, the model fitted to only the height-age pair data can be used as astand height/site index equation.

Keywords: biophysical effects, height growth, dynamic equations, hierarchical clustered data, climate change

Accurate measures of site productivity of forest stands is a keycomponent in predicting forest growth and yield, and suchmeasures are commonly assumed to remain constant over

time (Goelz and Burk 1992, Martín-Benito et al. 2008). However,site productivity depends on environmental factors that includebiotic, edaphic, and climatic conditions (Clutter et al. 1983, p. 31).Changes in climatic conditions have led to uncertainty in determin-ing site productivity because it is unclear how the climate changewill affect tree growth. Such changes may include the length of thegrowth season, ranges in temperature, and quantity and timing ofprecipitation. For example, Menzel and Fabian (1999) reported thatsince the 1960s, growing season length has increased by 11 daysacross Europe. Similarly, Zhou et al. (2001) reported a growingseason length increase in North America of 12 � 5 days between1981 and 1999. In addition, global average surface air temperatureis projected to warm between 1.4 and 5.8° C by 2100 relative to that

in 1990 (Intergovernmental Panel on Climate Change [IPCC]2000). For the province of Ontario, Canada, based on the A2 sce-nario (IPCC 2000), summer temperatures are expected to rise by 3to 6° C by the end of the 21st century, with more pronounceddifferences in the north (Colombo et al. 2007). Rising temperaturescould increase forest productivity by providing additional heat toincrease growth (Monserud et al. 2008). However, if temperatureincreases are not accompanied by associated increases in precipita-tion, forest productivity may be reduced (Hamann and Wang2006).

The most common and well-accepted method for assessing siteproductivity is to develop stand/top height-age relationships (Van-clay 1994, p. 31) and estimate the site index (SI), which is defined asthe average height of dominant and codominant trees (stand/topheight) at a specified (index) age (Sharma et al. 2002). To investigatethe biophysical effects on site productivity, Hunter and Gibson

Manuscript received December 2, 2013; accepted May 1, 2014; published online June 5, 2014.

Affiliations: Mahadev Sharma (mahadev.sharma@ontario.ca), Ontario Forest Research Institute, Ministry of Natural Resources, Sault Ste. Marie, ON, Canada.Nirmal Subedi (nirmal.subedi@gov.sk.ca), Ministry of Environment, Forest Service, Saskatchewan. Micheal Ter-Mikaelian (micheal.termikaelian@ontario.ca),Ontario Forest Research Institute. John Parton (john.parton@ontario.ca), Ministry of Natural Resources, South Porcupine.

Acknowledgments: This study was supported by the Ontario Ministry of Natural Resources (MNR) and its Climate Change Program. Support for data collection wasprovided by the Forestry Futures Trust Enhanced Forest Productivity Science Program. We thank Daniel McKenney and Pia Papadopol, Canadian Forest Service,for providing estimates of climate variables for study sites, to Peter Newton, Canadian Forest Service, for his assistance with the WinDendro program used for stemanalysis, and also Lisa Buse and Abby Obenchain, MNR’s Ontario Forest Research Institute, for editing and an anonymous associate editor and three reviewers fortheir help in improving a previous version of this article.

FUNDAMENTAL RESEARCH For. Sci. 61(1):25–34http://dx.doi.org/10.5849/forsci.13-190

Copyright © 2015 Society of American Foresters

Forest Science • February 2015 25

(1984) expressed SI in terms of environmental variables (averageannual temperature, annual rainfall, and the sum of the summermaximum temperatures minus the sum of the winter minima).However, results of a study by Ung et al. (2001) indicated thatcorrelations between the SI and biophysical variables were insuffi-cient for use in growth-and-yield models.

Beaumont et al. (1999) presented another approach for relatingSI to biophysical variables by defining the parameters of the SIequation as a function of selected variables (ecological regions anddrainage classes). Wang et al. (2007) extended this approach usingmean annual rainfall and average daily maximum temperature inJuly (winter) as parameters of a height growth model for Eucalyptusglobulus Labill. plantations in southeastern Australia. Similarly,Bravo-Oviedo et al. (2008) followed this approach by includingclimate variables (drought length, mean annual temperature, andtotal autumn and winter precipitation) in SI equations to improvemodel efficiency and reduce prediction bias.

Recently, Albert and Schmidt (2010) modeled SI in terms oflatitude, longitude, and nine soil and climate variables (soil nutrientclass, growing season precipitation sum, growing season potentialand centered potential evapotranspiration, soil moisture, growingseason mean temperature, mean annual and centered mean annualnitrogen depositions, and growing season water balance) for Nor-way spruce (Picea abies [L.] Karst.) and common beech (Fagus syl-vatica L.) trees in Lower Saxony, Germany. They found that bio-physical variables for these tree species explained �40% of SIvariability. Similarly, Weiskittel et al. (2011) reported that two vari-ables derived from three climate-related variables (growing seasonprecipitation, summer-winter temperature differential, and mini-mum growing degree-days � 0° C) explained 68% of SI variabilityacross western US forests.

Fritts (1958) reported that more than half the radial growth ratechanges due to concurrent environmental variation in Americanbeech (Fagus grandifolia [Ehrh.] Little) trees from a central Ohioforest could be attributed to maximum temperature and soil mois-ture. Further, he reported that during the early part of the growingseason, maximum temperature was more influential than soil mois-ture, but later in the season soil moisture became more important.Similarly, Pokharel and Froese (2009) found mean annual temper-ature to be important in describing basal area growth of four treespecies including jack pine (Pinus banksiana Lamb.) and blackspruce (Picea mariana [Mill.] B.S.P.) grown in natural stands ineastern Canada. Huang et al. (2010) also found that winter andspring as well as entire growing season temperatures were the majorfactors that explained the radial growth of jack pine and black sprucetrees grown in the eastern Canadian boreal forest. Similarly, Subediand Sharma (2013) reported that the mean growing season temper-ature, precipitation during the wettest quarter, and total precipita-tion during the growing season contributed significantly to explain-ing diameter growth of jack pine and black spruce plantations ineastern Canada. Overall, temperature and moisture seem to be thefactors most limiting for radial growth in the eastern boreal region ofNorth America.

However, there is no clearly defined single climate variable thatcan be used in modeling the SI for all tree species at all locations,because the climate and other biophysical variables used to model SIare not consistent from one study to another. Furthermore, work ondeveloping height growth models by including climate variables(e.g., Wang et al. 2007, Bravo-Oviedo et al. 2008) has not clarifiedwhether climate affects site productivity negatively or positively;

these studies merely show that including climate and other biophys-ical variables improved fit statistics. Other researchers (e.g., Albertand Schmidt 2010, Weiskittel et al. 2011) have looked at the cli-matic effect on SI without developing a height growth model byincorporating climatic variables. However, stand height growthmodels that include climate variables and can also be used to assessclimatic effect on site productivity would be very useful to forestmanagers.

Even though climate change with its effects on forest growth is anemergent issue in Canada, growth-and-yield models that incorpo-rate climate variables are not available for planted jack pine andblack spruce, which are the primary commercial timber species.Therefore, the two objectives of this study were to develop standheight/SI models for plantation-grown jack pine and black sprucethat directly incorporate climate variables using a mixed-effectsmodeling approach and to assess the effects of future climate scenar-ios on the stand height growth of these tree species.

Materials and MethodsHeight and Age Data

Data used in this study were collected from plantation-grownjack pine and black spruce trees. For each species, 25 even-agedmonospecific plantations were sampled from throughout the borealforest region (Rowe 1972) of Northern Ontario (Figure 1). Withineach plantation, three variable-size circular temporary sample plotswere established. Minimum plot size was set at 400 m2 but wasincreased as necessary to include a minimum of 80 trees of the targetspecies. For each target species, three planted dominant or codomi-nant trees that did not exhibit any visible deformities, such as forks,major stem injuries, dead or broken tops, were randomly selectedand sampled from each plot. From each sampled tree, disks were cutat 0.15, 0.5, 0.9, and 1.3 m from ground level. The remainingheight of the tree (between breast height and tip) was then dividedby 10, and disks were cut at the resulting interval to yield 13 disksper tree.

Each sampled tree and disk was assigned a unique code. All disksfrom a tree were placed in a large breathable bag, transported, andstored at �10° C until 24 hours before they were prepared foranalysis, which involved sanding the surface of the disk. At thetime of analysis, geometric mean radius (r) was calculated from thediameters obtained from the major (r1) and minor (r2) axes on eachdisk (i.e., r � (r1 � r2)0.5). On each section, two radii matching thisgeometric mean were located and marked. All measurements wereto the inner bark. The sanded sections were scanned, and the result-ing images were saved at a minimum resolution of 720 dpi.WINDENDRO software was used to analyze the images for diam-eter growth and ring number along the radii marked from the pith.

Height of the trees at a given age along the boles was determinedusing Graves’ (1906) method, which Subedi and Sharma (2010)reported as being more accurate than other available methods foridentifying where annual height growth ended for the species in thisstudy. Under this method, stems are generally assumed to be sec-tioned just above the year’s height growth (terminal bud) and aheight-age prediction algorithm is developed by interpolatingheight growth between two consecutive stem sections relative totime elapsed between sections. Annual height growth was then cal-culated for each tree for each species.

To determine whether height growth of the trees used in thisstudy was inconsistent in the early years, for all sample trees of bothspecies the total time required for each tree to reach breast height was

26 Forest Science • February 2015

determined. Because the time taken to reach breast height variedsignificantly (from 3 to 9 years for jack pine and from 3 to 18 yearsfor black spruce) height growth was considered erratic below breastheight. Therefore, in this study tree height refers to height abovebreast height and age as breast height age (BHA).

Observed heights and ages were plotted to form height-agecurves for each tree (Figure 2). These curves were visually inspectedfor indications of early suppression in height growth, top breakage,or dieback. Trees for which curves indicated possible injuries orearly height growth suppression were discarded. This process re-sulted in only two sample trees for some plots (13 and 4 plots for jackpine and black spruce, respectively) and no trees for 2 plots from onejack pine site. To obtain plot-level observations of stand height, thegrowth series from each plot were averaged to provide a mean plotgrowth curve. When ages of trees in a plot differed, the longer serieswere truncated to the age of the youngest tree. This resulted in 75(three from each of 25 sites) and 73 (three from each of 24 sites andone from the 25th site) total height-age series for black spruce andjack pine, respectively. The average 5-year height increment wascalculated for each series, so that the model prediction intervalwould match the interval at which the forest resource inventory andforest management plans are updated in Ontario. Summary statis-tics for tree and stand characteristics are presented in Table 1.

Climate DataThe climate of the region is continental with cold winters and

warm summers. Temperature decreases toward the east and north in

Ontario, but temperature differences are much smaller in summerthan in winter (Phillips 1990). Maximum precipitation in the re-gion occurs during summer, and the amount of precipitation isaffected by proximity to the Great Lakes, prevailing winds, and theaspect, elevation, and slope of the terrain (Phillips 1990). In On-tario, annual precipitation is relatively consistent from year to yearand periods of excessively dry or wet weather are infrequent, al-though periods of drought are more likely to occur in late summer(i.e., at the end of growing season) (Phillips 1990).

The Ontario climate model (Mackey et al. 1996) was used toestimate a suite of climate variables for each plot location. Estimatesof long-term average values of selected variables were calculatedbased on 1971–2000 climate records from 471 meteorological sta-tions located both within and geographically close to the provinceof Ontario. A continuous climate grid was generated usingANUSPLINE based on 1961–1990 climate data for Ontario. Atotal of 65 variables were calculated, including mean, minimum,and maximum air temperatures and total precipitation, estimatedfor each month of the year, for each quarter (consecutive 3-monthperiods), and for the whole year. In addition, estimates were pro-duced for start, end, and length of the growing season and the sumof growing degree-days using a base temperature of 5° C. Growingseason was defined as the length of time between the day after March1 when mean daily temperature is �5° C for 5 consecutive days andthe day after August 1 when minimum daily temperature is ��-2°C. More detailed information about the definition of climate

Figure 1. Distribution of jack pine and black spruce plantation sites sampled across Northern Ontario, Canada. Latitude and longituderanged from 47� N to 50� N and 80� W to 92� W, respectively.

Forest Science • February 2015 27

variables and their estimation is outlined by Mackey et al. (1996).Estimates of the above variables for all plot locations in this studywere produced by Daniel McKenney (McKenney et al. 2007).Monthly means of four soil moisture-related variables (potentialevapotranspiration, available soil moisture, soil moisture deficit, andsoil moisture deficit index) from May to October (active growingseason) were also calculated for each plot location and used in theanalysis. Similarly, latitude, longitude, and site elevation were in-cluded in the analysis.

Stand Height/SI EquationsHeight of a tree over time (height-age relationship) is generally

described using nonlinear mathematical models. These models areoften derived from simpler, single-curve base models, which can beexponential or fractional functions (Cieszewski 2003). The mostcommon exponential base model used to describe height develop-ment over time is Chapman-Richards (Richards 1959, Chapman1961, see also Burkhart and Tennent 1977, Carmean and Lenthall1988, Goelz and Burk 1992, Garcia 2005). Similarly, the fractionalfunction most suited to developing SI equations is Hossfeld IV(Cieszewski 2003). Therefore, Chapman-Richards and Hossfeld IVfunctions were considered as base models from which to derive SIequations. Several variants of these two functions were evaluatedusing the study data sets. For both species, the following variant ofthe Hossfeld IV function, also known as McDill-Amateis growthfunction (see Burkhart and Tome 2012, p. 126), resulted in the bestfit (in terms of R2 and mean square error) and the most consistentand biologically realistic height estimates across productivity classes

H ��0

1 � �1 ��0

H1��A1

A ��1(1)

where H and H1 are heights at ages A and A1, respectively, and �0

and �2 are model parameters. Therefore, this model form was cho-sen as the height development model for this study. To model theeffects of climate on height growth, the asymptote and rate param-eter (�0 and �1, respectively) in Equation 1 were expressed in termsof climate variables.

Reference Age for SIBecause the trees in this study had maximum BHAs of 60 and 46

years for jack pine and black spruce, respectively, a youngest possiblebase age that provided accurate estimates of heights at other ages wasinvestigated. Base ages of 15, 20, 25, and 30 years were evaluated forboth species by estimating tree heights at all other ages using theheights at these base ages in stand height/SI equations. For bothspecies, the smallest relative errors were obtained when A was set to25 years in Equation 1. Therefore, 25 years was selected as thereference age (base age). For each species, SI was then determined foreach site as the average height of dominant and codominant trees ata BHA of 25 (Table 1). Because the trees in some plots were youngerthan 25 years BHA, the total number of plots for which SI could becalculated was 70 for jack pine and 58 for black spruce.

Model Fitting and EvaluationThe data used in this study originated from stem analysis.

Height-age series for a plot were obtained by multiple measure-ments on individual trees sampled from the plot, resulting in hier-archical data sets (i.e., height-age series within plots). As a result, twosources of variation exist: among plots and within a plot. Observa-tions among plots are independent, but observations within a plot(height-age series) are dependent (correlated) because they originatefrom the same trees. The autocorrelation problem within a samplingunit can be addressed by using the mixed-effects modeling tech-nique (Meng et al. 2009, Subedi and Sharma 2011, 2013) or cor-relation structure (Dieguez-Aranda et al. 2006), or both (Trincadoand Burkhart 2006, Subedi and Sharma 2013).

Equation 1 was first fitted to the data set for each species using thegeneralized least squares method in R (R Development Core Team2011). As noted by Huang (1997), all possible 5-year multiplegrowth intervals of height and age were used to fit the models.Variables related to site (latitude, longitude, and elevation), climate(temperature and precipitation), and soil moisture and all their pos-sible two-way interactions were then introduced and evaluated fortheir contribution to improving the fit of the model. For both spe-cies, climate and soil moisture variables were selected that weresignificant (� � 0.05) and also improved model fit. This model wasthen fitted for both species using the mixed-effects modeling ap-proach, i.e., the nlme (Pinheiro et al. 2011) package in R. Random-effects parameters were added sequentially to the fixed-effects coef-ficients starting at one for each species. The model with randomeffects was evaluated based on goodness-of-fit criteria such as thelog-likelihood (twice the negative log-likelihood) ratio, assessmentof model residuals, and Akaike’s information criterion (AIC)(Akaike 1978). The model with the smallest goodness-of-fit value isconsidered best.

The residuals of the model with random group (i.e., plot) effects

Figure 2. Dominant and codominant tree height versus BHA forjack pine (A) and black spruce (B) trees sampled from NorthernOntario, Canada.

28 Forest Science • February 2015

were analyzed for possible temporal autocorrelations and heterosce-dasticity for each species. The residuals showed no signs of het-eroscedasticity for either species. However, for both species, tempo-ral autocorrelation was evident among residuals within plots. As aresult, the final model was fitted as a nonlinear mixed-effects model,and within-plot autocorrelation (Pinheiro and Bates 2000) wasmodeled directly. Two autocorrelation structures, first-order au-toregressive [AR(1)] and autoregressive moving average (ARMA),were evaluated and the one that gave the best fit (i.e., smaller AIC)and provided expected behavior of residuals was selected. The coef-ficients of the final models were determined using the reduced max-imum likelihood (REML) method.

Height-growth models were further evaluated using bootstrap-ping techniques. Height prediction residuals (observed � pre-dicted) were calculated for each species and were grouped across theheight and age classes. For each class, the mean residual (bias) and its95% confidence interval were calculated using a “bias corrected andaccelerated (BCa) percentile” (Efron and Tibshirani 1996, p. 178)bootstrapping technique using a built-in function bootci in Matlab(version 7.10.0499). Fifty thousand bootstrap samples were used tocalculate the bias and its confidence intervals for each height and ageclass for each species.

To examine future stand height growth under a changing cli-mate, temperature and precipitation for two scenarios (A2 and B2)(IPCC 2000) were estimated for one location (Timmins,47°28�12�N and 81°55�12�W) for the period 2011–2040. Theseestimates were made using the predicted values of future tempera-ture and precipitation that Colombo et al. (2007) summarized forOntario using Version 2 of the Canadian Coupled Global Circula-tion Model. Results were compared with those obtained using cur-rent climate conditions (no-change scenario). According to theIPCC (2000), the A2 scenario envisions population growth to 15billion by the year 2100 and rather slow economic and technologicaldevelopment, whereas the B2 scenario projects slower populationgrowth (10.4 billion by 2100) with a more rapidly evolving econ-omy and more emphasis on environmental protection.

ResultsThe climate variables that were significant (� � 0.05) in explain-

ing the variation in height growth of dominant and codominant jackpine and black spruce trees were growing season mean temperature(GSMT) and growing season total precipitation (GSTP). Both theasymptote and the rate parameter expressed as a linear function ofthese climate variables in Equation 1 resulted in the best model forboth species. The model form that included climate variables was

H ��0 � �1GSTP � �2GSMT

1 � �1 ��0 � �1GSTP � �2GSMT

H1��A1

A��3��4GSTP��5GSMT � (2)

where �0–�5 are parameters and other variables are as defined ear-lier. No site- or soil moisture-related variables or interactions weresignificant in the regression.

For both species, all fit statistics (root mean square error, log-like-lihood, and AIC) decreased (Table 2) when climate variables wereincluded in the model. Thus, Equation 2 not only incorporatedclimate variables but also improved the fit statistics. As a result,Equation 2 could be used to explain the effects of climate on standheight growth for jack pine and black spruce. As mentioned earlier,random-effects parameters were added to the fixed-effects coeffi-cients sequentially starting at 1. Only site- and plot-level (plotnested within site) random effects associated with �0 were signifi-cant for jack pine. However, no random effects associated with anyof the fixed effects (�0–�5) at any level were significant for black

Table 1. Summary statistics for SI, stand height (above breast height), and BHA for calibration and validation data sets for plantation-grown jack pine and black spruce stands from Northern Ontario, Canada, used in this study.

Species/variable

Jack pine Black spruce

n Mean SD Minimum Maximum n Mean SD Minimum Maximum

SI (m)* 70 11.52 1.19 9.01 14.07 58 8.71 1.34 5.8 11.25Stand height (m) 73 15.35 2.37 10.5 21.21 75 10.59 2.22 6.03 15.56BHA (yr) 73 38.26 9.91 24 59 75 31.39 6.93 20 46GSTP (mm)† 25 463.22 26.00 421.4 502.4 25 449.46 23.38 402.6 492.2GSMT (°C)‡ 25 12.90 0.49 11.97 13.54 25 12.70 0.33 12.19 13.39

n, number of samples; BHA, breast height age.* Index age for site index � 25 yr BHA.†GSTP values projected for the period 2011–2040 in Timmins under A2 and B2 scenarios were 456.65 and 456.50 mm, respectively.‡GSMT values projected for the period 2011–2040 in Timmins under A2 and B2 scenarios were 14.04 and 13.54° C respectively.

Table 2. Parameter estimates, their SEs, fit statistics, and df for themodel without climate variables (Equation 1) and with climatevariables (Equation 2) for jack pine and black spruce trees fromNorthern Ontario, Canada.

Parameters

Jack pine Black spruce

Estimate* SE Estimate SE

Model without climatevariables

�0 32.2567 0.2792 36.8046 0.7592�1 1.2156 0.0046 1.1638 0.0054e

2 0.5178 0.2796�2ln(L) 8,751.98 4,720.79AIC 8,757.98 4,726.79Total df 4,016 3,020Residual df 4,014 3,018

Model with climatevariables

�0 112.1626 7.4231 �284.6675 17.3662�1 0.0654 0.0148 0.3359 0.0182�2 �8.6023 0.9173 13.5367 1.2542�3 0.6130 0.1272 3.4545 0.1145�4 �0.0004 0.0001 �0.0022 0.0002�5 0.0625 0.0105 �0.1027 0.0095e

2 0.4877 0.2425�2ln(L) 8,508.02 4,285.61AIC 8,522.02 4,299.61Total df 4,016 3,020Residual df 4,010 3,014

e2, root mean square error; �2ln(L), twice the negative log-likelihood.

*All parameter estimates were statistically significant (P � 0.01).

Forest Science • February 2015 29

spruce. Thus, the final mixed-effects stand height growth model forjack pine was written as

Hijk

��0 � b0i � b0ij � �1GSTPi � �2GSMTi

1 � �1 ��0 � b0i � b0ij � �1GSTPi � �2GSMTi

Hijll�k��Aijll�k

Aijk��3��4GSTPi��5GSMTi

� ijk (3)

where Hijk is the stand height at age Aijk (kth observations atplot/series j and site i), Hijl is the stand height at age Aijl at the sameplot/series and site (lth observations at plot/series j and site i and l �k), b0i and b0ij are site- and plot-level random effects, respectively,and are independent of ijk. Random effects b0i and b0ij are normallydistributed with mean zero and variances s

2 and p2, respectively

[i.e., b0i �N(0, s2) and b0ij �N(0, p

2)]. Other variables are asdefined earlier. When autocorrelations occur among observationswithin a plot, ijk will have a multivariate normal distribution withmean zero and a variance-covariance matrix R [i.e., ijk �N(0, R)].Because the random effect was not significant for black spruce, thefinal stand height growth model for black spruce remains the same asEquation 2.

As mentioned earlier, heteroscedasticity was not apparent foreither species, but the residual plots showed some temporal autocor-relation among the residuals within plots for both species. To resolvethis problem, the final models were fitted with AR(1) and ARMA(ARMA1 and ARMA2) covariance structures. For both species,both structures resulted in smaller values of AICs than those withoutautocorrelation. However, the AIC value was smaller for AR(1) thanfor ARMA1 and ARMA2. For both species, estimates of studentizedresiduals (observed � predicted) from stand height growth werecalculated [with the AR(1) structure in the model] for all 5-yeargrowth periods for each tree and plotted against the predicted standheight growth (not shown here). Trends in error structure did notsuggest any signs of autocorrelation or heteroscedasticity.

Because the model for jack pine contained random-effects pa-rameters, the final model with the AR(1) covariance structure wasfitted using the REML method in R. For black spruce, for which arandom-effects parameter was not included, the model was fittedusing the generalized nonlinear least squares method in R (Table 3).For both species, all model coefficients were significant (� � 0.05).

Although the asymptotes and the rate parameters for jack pineand black spruce are functions of the same climate variables, i.e.,temperature (GSMT) and precipitation (GSTP), the signs and mag-nitudes of the coefficients in the expressions differed between spe-cies. As a result, the climatic effect on stand height growth alsodiffers between species. The intercept of the linear expression for theasymptote was positive for jack pine and negative for black spruce.However, the coefficient of GSTP for the asymptote was positive forboth species. In contrast, the coefficient of GSMT was negative forjack pine and positive for black spruce. This result indicates that anincrease in precipitation would positively affect the asymptote (themaximum potential height) for both species. However, a rise intemperature would negatively affect the asymptote for jack pine andpositively affect that for black spruce.

For both species, the intercept of the linear expression for the rateparameter was positive and the coefficient of the growing seasontotal precipitation was negative. The coefficient of temperature,however, was positive for jack pine and negative for black spruce.This finding implies that an increase in precipitation would increase

height growth of both species. On the other hand, a warmer growingseason would increase jack pine height growth but decrease that ofblack spruce. The first-order autoregressive autocorrelation struc-ture (�) indicated that for both species the model error terms werepositively correlated with the residual of prediction from the previ-ous period.

Equations 2 and 3 were further evaluated by bootstrapping theresiduals (observed � predicted) obtained in predicting the heightsfor each species. Bias (average residual) and its 95% confidenceintervals were calculated for each height and age class for both spe-cies (Table 4). The bias in estimating stand height across both classes(height and age) was very small for all height and age classes andspecies. Although the 95% confidence interval did not include zerofor all height and age classes, its range was small and closer to zero forboth species. The largest estimated 95% confidence interval for thebias was 0.098 to 0.229 m for jack pine for the age class 36–40years.

To predict future stand height growth under a changing climate,the stand heights of jack pine and black spruce were estimated at onelocation (Timmins) in northeastern Ontario under two (A2 and B2)climate change scenarios (Figure 3). These estimates were madeusing only fixed-effects coefficients in the models (Equation 3 forjack pine and Equation 2 for black spruce). For both species, theaverage height value at age 1 year (0.35 m) was used as the initialheight for generating height-age curves. For both climate scenarios,average values of GSTP and GSMT for the period 2011–2040 wereused to estimate future stand heights. For the same period, standheights were estimated for both species using current climate param-eters. As illustrated in Figure 4, for both the A2 and B2 climatescenarios, stand heights at age 30 are reduced for both species rela-tive to those for current climate.

Jack pine height growth was not significantly affected by climatechange until the age of 15. Thereafter, the heights under both the A2and B2 climate scenarios separated from those for the current cli-mate scenario, but the difference was less pronounced for the B2than the A2 scenario. At age 30, stand heights were shorter, reducedby 2 and 8% for the B2 and A2 scenarios, respectively, relative tothose for the current climate scenario. For black spruce, heightgrowth under both climate scenarios decreased from the outset. The

Table 3. Parameter estimates, their SEs, fit statistics, and AIC forstand height/SI Equations 3 for jack pine and 2 for black spruce inNorthern Ontario, Canada, fitted with climate variables.

Parameters

Jack pine Black spruce

Estimate* SE Estimate SE

�0 89.5840 24.95638 �289.91773 18.11761�1 0.11364 0.034845 0.28115 0.01956�2 �8.60793 2.09684 15.85996 1.41543�3 0.98026 0.123851 3.55130 0.12819�4 �0.00091 0.000186 �0.00172 0.00018�5 0.05248 0.010589 �0.12589 0.01129

e2 0.236682 0.24364

s2 2.798327

p2 37.12087

� 0.80540 0.79164�2ln(L) 1,296.273 1,324.069AIC 1,316.273 1,341.069

e2, root mean square error; s

2, variance of site-level random effects; p2, variance of

plot-level random effects; �, autocorrelation; �2ln(L), twice the negative log-like-lihood.*All parameter estimates were statistically significant (P � 0.01).

30 Forest Science • February 2015

decrease was more pronounced under the A2 than the B2 scenario.At age 30, stand heights were reduced by 16 and 28% under the B2and A2 scenarios, respectively, relative to those for the current cli-mate scenario.

Finally, height-age curves were produced for a scenario for whichclimate variables were assumed to be unavailable. This was accom-plished by using Equation 1 with the parameters estimated using thegeneralized least squares method in R (Table 2) and applying themodels to estimate heights at different ages. These curves were pro-duced for both species for sites with varying site productivity (Figure4). Stand heights at the index age of 25 years were used as siteindices. These curves were very consistent and realistic across allproductivity classes.

DiscussionAs Clutter et al. (1983) stated, the productivity of a site depends

on environmental conditions (biotic, edaphic, and climatic) existingat a particular location. Similarly, Latta et al. (2010) mentioned thatforest productivity is directly influenced by changes in temperatureand precipitation regimes. Our results indicated that climate vari-ables (temperature and precipitation) are important in determiningthe productivity of a site. These variables could be incorporated inexisting height growth models to make them climate-sensitive. Thiscan be accomplished, at least in the McDill-Amateis growth func-tion, by expressing the parameters (often referred to as the asymp-tote and rate parameter) in terms of climate variables.

We found that a combination of temperature- and precipitation-related variables (i.e., GSTP and GSMT) were significant in ex-plaining the variation in stand height growth of jack pine and blackspruce trees across plantations in the study area. Soil moisture-re-lated variables, however, were not significant in the regressions. Forboth species, the fit statistics of the stand height growth modelimproved significantly when climate variables were included. Theclimatic effect differed by species. Climate affected height growth ofjack pine less than that of black spruce under both climate scenarios.

These results are consistent with the findings of previous studies.Wang et al. (2007) and Bravo-Oviedo et al. (2008) reported that

Figure 3. Stand height profiles generated using average values ofall climate variables during the periods 1971–2000 and2011–2040 for plantation-grown jack pine (ignoring random ef-fects) (A) and black spruce (B) trees in Northern Ontario, Canada.Climate variables for the period 2011–2040 were projected usingCanadian A2 and B2 emissions scenarios (IPCC 2000) for a sitenear those from which the data were collected.

Table 4. Bias (observed � predicted) and its 95% upper and lower confidence intervals of the residuals resulted from fitting Equations 2for black spruce and 3 for jack pine trees in Northern Ontario, Canada.

Jack pine Black spruce

n Bias LCI UCI n Bias LCI UCI

Height class0–3.5 m 568 0.048 0.028 0.069 628 �0.002 �0.022 0.0183.6–6.5 m 638 �0.092 �0.118 �0.066 766 �0.081 �0.109 �0.0536.6–9.5 m 746 �0.137 �0.169 �0.106 756 0.006 �0.031 0.0439.6–12.5 m 804 �0.012 �0.048 0.023 650 0.049 0.002 0.09712.5–15.5 m 627 0.089 0.048 0.130 220 0.122 0.032 0.218 15.5 m 633 0.131 0.089 0.173

Age class0–5 yr 490 0.085 0.064 0.107 429 0.053 0.035 0.0746–10 yr 490 �0.082 �0.110 �0.055 429 �0.070 �0.097 �0.04211–15 yr 490 �0.134 �0.169 �0.100 429 �0.081 �0.116 �0.04315–20 yr 490 �0.115 �0.153 �0.078 429 �0.037 �0.083 0.00520–25 yr 484 �0.003 �0.050 0.044 417 0.017 �0.034 0.06826–30 yr 456 0.045 �0.002 0.092 369 0.036 �0.019 0.09131–35 yr 391 0.123 0.072 0.172 518 0.073 0.009 0.13536–40 yr 289 0.165 0.098 0.22940–45 yr 163 0.050 �0.039 0.134 45 yr 273 �0.026 �0.089 0.035

These numbers were obtained from 50,000 bootstrap samples for each height and age class for each species. n, number of bootstrapped values in the class; UCI, upperconfidence interval; LCI, lower confidence interval.

Forest Science • February 2015 31

including climate variables improved the fit and predictive accuracyof the model in their studies. However, it was not clear from theirstudies whether growth increased, decreased, or was unaffected bythe change in climate. Newton (2012) reported that jack pine yieldson low-to-medium quality sites would largely be unaffected by cli-mate change by the end of a 60-year growth period (2011–2070)but that the mean dominant height growth on good to excellentquality sites would be reduced by 6.6 and 12% under the B1 and A2scenarios, respectively. Because the trees used in our study occurredon good-quality sites, these results are consistent with our findings.The reduction in height growth in our study, however, is smallerthan the one found by Newton (2012), because we used a shortergrowth period than Newton did (30 versus 60 years).

Similarly, Way and Sage (2008) conducted an experiment in2004 and 2005 in which black spruce was grown at two differenttemperatures (low and high). They found that the dominant heightof black spruce grown under high temperature was reduced by 20%compared with that of dominant trees grown under low tempera-ture. Recently, more studies reporting the effects of changing cli-mate on the growth of jack pine and black spruce trees have beenpublished (e.g., Huang et al. 2010, Huang et al. 2013, Subedi andSharma 2013). However, these studies were focused on radial ratherthan height growth, so the results are not directly comparable withthose of this study.

With the models developed by expressing SI directly in terms ofclimate variables, Albert and Schmidt (2010) found that biophysical

variables (latitude, longitude, soil, and climate) explained 39 and34% of SI variability in Norway spruce and common beech, respec-tively. However, Weiskittel et al. (2011) reported that 68% of the SIvariability was accounted for by variations in climate-related vari-ables across western US forests.

To check whether SI modeled directly in terms of climate andother biophysical variables results in similar fits to the data used inthis study, we regressed SI using climate, soil moisture, and topo-graphic (longitude, latitude, and elevation) variables. The meantemperature and total growing season precipitation along with totalprecipitation of the wettest period and total precipitation of thedriest period explained 39% of SI variability for jack pine. Similarly,the mean temperature and total growing season precipitation, end ofgrowing season Julian day, and total precipitation of wettest periodexplained 48% of SI variability in black spruce. However, no soilmoisture-related variables were significant in explaining SI variabil-ity in both species. The coefficient of determination (R2) for themodels presented here (i.e., Equations 2 and 3) was 98% for bothspecies.

Obviously, total growing season precipitation is the clear winnerbecause it explained SI variability in all studies. The second mostimportant climate variable is GSMT, although it was not been useddirectly by Weiskittel et al. (2011). These two variables (growingseason mean temperature and growing season total precipitation)are the most obvious climate variables that can be easily interpretedin explaining the growth of any tree species. Not surprisingly, grow-ing season, mean temperature, and total growing season precipita-tion turned out to be important in modeling the stand heightgrowth in a changing climate for the tree species used in our study.

Process-based models have also been proposed for site produc-tivity because they integrate both soil and climate factors (Swensonet al. 2005). However, as Weiskittel et al. (2011) pointed out, thesemodels have drawbacks: they are often complex, are difficult toparameterize, and depend on information that is not readily ob-tained. Carbon use efficiency (CUE) could also be used to measuresite productivity, and Kwon and Larsen (2013) analyzed it for itsdependency on environmental conditions. They reported that CUEdecreased with increases in temperature and precipitation across theeastern United States. The information required to calculate CUE,however, cannot be easily obtained and is more suitable for ecosys-tem process models, such as CASA (Kwon and Larsen 2013).

The models presented here can be readily applied to statisticalgrowth-and-yield models to better represent site productivity undera changing climate. These models represent not only stand heightgrowth models that can be used under a changing climate but also ameans to assess the effect of climate on site productivity, dependingon the tree species. The climatic effect on site productivity for agiven tree species can be explained by interpreting the sign andmagnitude of the coefficients of the climate variables used in themodels.

ConclusionsStand height/SI equations that incorporate climate variables

were developed for jack pine and black spruce plantations. Climatevariables that were significant in explaining the variation in heightgrowth of dominant and codominant jack pine and black sprucetrees were GSMT and GSTP. For both species, the fit statistics ofthe stand height growth model were significantly improved by theaddition of climate variables.

For both species, stand heights were predicted for a randomly

Figure 4. Stand height/SI profiles generated using Equation 1 forplantation-grown jack pine (A) and black spruce (B) trees in North-ern Ontario for the range of site productivity.

32 Forest Science • February 2015

selected location for the period 2011–2040 under the A2 and B2climate scenarios. At the end of 2011–2040 growth period, pro-jected heights for both species were reduced under both scenarioscompared with those under a no-climate change scenario. For bothspecies, the decrease in height growth was more pronounced underthe A2 than the B2 scenario. Climate affected black spruce heightgrowth more than that of jack pine.

The models developed here can be used to estimate stand heightat any age, given the height at a point in time and the relevantclimate variables, thereby supporting more informed forest manage-ment decisions. That said, although the study sites were well distrib-uted across Northern Ontario (some sites were separated by morethan 1,000 km), the absolute range in most observed climate vari-ables was relatively narrow. Therefore, caution is warranted whenthe models are applied beyond the range of climate values reportedhere.

In addition, height estimated at the base age will provide the SIvalue. Therefore, the models can also serve as SI equations. Further-more, when climate variables are unavailable, the equation fitted toonly the height-age pair data can be used as a stand height/SI equa-tion for jack pine and black spruce plantations.

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