Bridging process-based and empirical approaches to modeling tree growth

The gulf between process-based and empirical approaches to modeling tree growth may be bridged, in part, by the use of a common model. To this end, we have formulated a process-based model of tree growth that can be fitted and applied in an empirical mode. The growth model is grounded in pipe model theory and an optimal control model of crown development. Together, the pipe model and the optimal control model provide a framework for expressing the components of tree biomass in terms of three standard inventory variables: tree height, crown height and stem cross-sectional area. Growth rates of the inventory variables and the components of biomass are formulated from a carbon balance. Fundamentally, the parameters of the model comprise physiological rates and morphological ratios. In principle, the values of these parameters may be estimated by lower-level process models. Alternatively, the physiological and morphological parameters combine, under reasonable assumptions, into a set of aggregate parameters, whose values can be estimated from inventory data with a statistical fitting procedure.     

Stem biomass and volume models of selected tropical tree species in West Africa

Estimating tree volume and biomass constitutes an essential part of the forest resources assessment and the evaluation of the climate change mitigation potential of forests through biomass accumulation and carbon sequestration. This research article provides stem volume and biomass equations applicable to five tree species, namely Afzelia africana Sm. (Caesalpiniaceae), Anogeissus leiocarpa (DC.) Guill. and Perr. (Combretaceae), Ceiba pentandra (L.) Gaertn. (Bombacaceae), Dialium guineense Willd. (Caesalpiniaceae), Diospyros mespiliformis Hochst. ex A.DC. (Ebenaceae) in natural protected tropical forests and, in addition, Tectona grandis L.f. (Verbenaceae) in plantations. In addition to the tree species specific equations, basic wood density, as well as carbon, nitrogen, organic matter and ash content were determined for these tree species in tropical conditions in West Africa. One hundred and sixty-two sample trees were measured through non-destructive sampling and analysed for volume and biomass. Stem biomass and stem volume were modelled as a function of diameter (at breast height; Dbh) and stem height (height to the crown base). Logarithmic models are presented that utilise Dbh and height data to predict tree component biomass and stem volumes. Alternative models are given that afford prediction based on Dbh data alone, assuming height data to be unavailable. Models that include height are preferred, having better predictive capabilities. Ranges in carbon, nitrogen and ash contents are given as well. The successful development of predictive models through the use of non-destructive methods in this study provide valuable data and tools for use in determining the contribution of these major African rainforest tree species to global carbon stocks, while ensuring the preservation of this valued African resource. This study needs to be expanded to further regions and tree species to complete a full inventory of all tree species, emphasising the relevance of African trees to carbon stocks at a global scale.     

Dynamics of water storage in mature subalpine Picea abies: temporal and spatial patterns of change in stem radius

Internal water reserves in bark and foliage of trees contribute to transpiration (T) and play an essential role in optimizing water transport by buffering extreme peaks of water consumption. We examined patterns of stem shrinkage and their relationship to tree water dynamics. We measured fluctuations in root radius and stem radius at different stem heights, T of twigs at the top of the crown and sap flow velocities in stem sections of mature subalpine Norway spruce (Picea abies (L.) Karst.) trees over 2 years. The output of each sensor was coupled by physical functions to a mechanistic flow and storage model of tree water relations. The data verified the model-predicted lag in water storage depletion in response to the onset of transpiration and the lag increased with increasing distance from the crown periphery. Between the crown and stem base, the delay ranged from a few minutes to several hours, depending on microclimatic conditions and tree water status. Stem volume changes were proportional to the amount of water exchanged between the elastic tissues of the bark and the rigid xylem, indicating that the "peristaltic" wave of stem contraction along the flow path represented depletion of water stored in bark. On a daily basis, stems lost between 0.2 and 0.5% of their volume as a result of bark dehydration, corresponding to about 2 to 5 l of water. This water contributed directly to T. According to the model based on hydraulic principles, there are three main components underlying the dynamics of water storage depletion: flow resistance, storage capacities of needles and bark, and T of each tree section. The resistances and capacities were proportional to the response delay, whereas T in the lower parts of the tree was inversely proportional. The pattern of T within the crown depended on water intercepted by the branches. Because of these weather-dependent factors, there was no time constant for the response delay along the flow path. Nevertheless, the upper crown and the root section tended to have longer response delays per meter of flow path than the stem. The diurnal course of stem radius fluctuations represents the sum of all external and internal conditions affecting tree water relations; stem radius fluctuations, therefore, provide a sensitive measure of tree water status.     

Structural development of pinus sylvestris stands with varying initial density: A simulation model

The growth and structural development of Scots pine (Pinus sylvestris L.) trees growing at different spacing was simulated using a model based on the dry matter production per needle biomass unit and its allocation to needles, branches and stem. Special emphasis was given to the effect of stand density on the growth of the crown system and its implications on branchiness and timber quality. The simulations showed that the needle biomass culminates considerably earlier than the branch biomass with a time lag inversely related to the stand density. The lengths of living and dead crown were also inversely related to stand density. The resulting differences in branchiness were especially obvious in the early development of the tree stands. In the long run these differences tend to disappear, indicating equal external branchiness independently of the initial spacing for mature stands of Scots pine. The internal branchiness, however, was particularly sensitive to the initial spacing.     

辽东山区日本落叶松生物量相容性模型的研究

基于60株辽东山区日本落叶松样木生物量的实测数据,分析不同林龄条件下立木各部分生物量的变化情况,并应用度量误差方法建立立木相容性生物量模型。结果表明:树叶、树枝、树皮生物量占总生物量的比值随林龄增长呈下降趋势,干材占总生物量的比值随林龄增长呈上升趋势。在筛选出总生物量与各分量最优独立模型的基础上,应用三级控制的方法建立生物量相容性模型,并采用加权回归方法消除总量和各分量模型的异方差。建立的总量、地上部分、树干、干材、树皮生物量模型,其R2均大于0.9;树根、树冠、树叶和树枝生物量的R2略低,介于0.7 0.9之间。通过独立样本对模型的相容性和预测精度进行检验,各分量预测值所占总生物量的百分比之和为1,模型完全相容;根、冠、叶和枝的模型预测精度略低于90%,其他部位模型的预测精度都在95%以上,模型的预测精度较高。     

Biomass,stem basic density and expansion factor functions for five exotic conifers grown in Denmark

Adequate allometric equations are needed for estimating carbon pools of fast growing tree species in relation to international reporting of CO₂ emissions and for assessing their possible contribution to increasing forest biomass resources. We developed models for predicting biomass, stem basic density and expansion factors of stem to above-ground biomass for five fast growing conifers. Data included destructive measurements of 236 trees from 14 sites, covering a wide range of growth conditions. To ensure model efficiency, models for predicting stem, crown and total above-ground biomass for the five species were estimated simultaneously using a linear, mixed effects model that allowed contemporaneous correlations between the different tree components. Models differed among species and included dbh and tree height. The models explained more than 98% of the variation in above-ground biomass and reflected differences in the allometry between tree species. Stem density differed among species but generally declined with increasing site index and dbh. The overall model for predicting stem basic density included dbh, H₁₀₀ and site index and explained 66% of the total variation. Expansion factors decreased from 1.8–2.0 in small trees (dbh < 10 cm) to 1.1–1.2 for large trees (dbh > 25 cm), but differed among species. The overall model explained 86% of the variation and included quadratic mean diameter and dbh.     

Tree growth as indicator of tree vitality and of tree reaction to environmental stress: a review

The intensive monitoring plots (Level II) of ICP Forests serve to examine the effects of air pollution and other stress factors on forest condition, including tree vitality. However, tree vitality cannot be measured directly. Indicators, such as tree growth or crown transparency, may instead be used. Tree growth processes can be ranked by order of importance in foliage growth, root growth, bud growth, storage tissue growth, stem growth, growth of defence compounds and reproductive growth. Under stress photosynthesis is reduced and carbon allocation is altered. Stem growth may be reduced early on as it is not directly vital to the tree. Actual growth must be compared against a reference growth, such as the growth of trees without the presumed stress, the growth of presumed healthy trees, the growth in a presumed stress-free period or the expected growth derived from models. Several examples from intensive monitoring plots in Switzerland illustrate how tree-growth reactions to environmental stresses may serve as vitality indicator. Crown transparency and growth can complement each other. For example, defoliation by insects becomes first visible in crown transparency while stem growth reaction occurs with delay. On the other hand, extreme summer drought as observed in large parts of Europe in 2003 affects stem growth almost immediately, while foliage reduction becomes only visible months later. Residuals of tree growth models may also serve as indicators of changed environmental conditions. Certain stresses, such as drought or insect defoliation cause immediate reactions and are not detectable in five-year growth intervals. Therefore, annual or inter-annual stem growth should be assessed in long-term monitoring plots. An erratum to this article can be found at     

Pipe-model ratio distributions and branch foliage biomass: differences between two sympatric spruce species

The foliage biomass–sapwood relationship (the pipe model) is critical for tree growth and is used in tree growth models for understanding the implications of this structural relationship on the allocation of resources. In this research, we compared this relationship for two commercially important and sympatric species, black spruce (Picea mariana (Mill.) B.S.P.) and white spruce (Picea glauca (Moench) Voss). At locations in eastern Canada, 57 black and 50 white spruce trees were destructively sampled to obtain foliage biomass, crown structure, and tree stem measures. Using a model-based approach, we compared foliage biomass–branch basal area and foliage biomass–sapwood relationships at the tree and disk (i.e. along the tree stem) levels (i.e. pipe-model ratios) between these two species. We found that (i) branch foliage biomass–branch basal area was greater for black spruce than white spruce and (ii) pipe-model ratios along the tree stem given tree size were greater for black spruce than for white spruce. We attributed these differences to: (i) greater shade tolerance and leaf longevity of black spruce; (ii) slower growth rates of black spruce; and (iii) differing hydraulic strategies and mechanical requirements.     

Calibration and Uncertainty Analysis of a Carbon Accounting Model to Stem Wood Density and Partitioning of Biomass for Eucalyptus globulus and Pinus Radiata

There is a need to calibrate models for carbon accounting in forest systems if they are to be applied for carbon trading and off-set schemes. One such model, Full Carbon Accounting Model (FullCAM), calculates stem mass by taking annual inputs of tree growth in stem volume and multiplying these by basic stem wood density. Stem mass is then multiplied by user-entered coefficients to determine the mass of other tree components. Using datasets of Pinus radiata and Eucalyptus globulus that comprised of between 73 and 187 observations, we determined empirical relationships that can be used in FullCAM to relate basic stem wood density to stand age, and masses of bark, foliage or branches to mass of stem wood for these two species. All fitted relationships were highly significant (p < 0.001), explaining between 35 and 89% of the variance. These calibrations were then tested using three case studies where data on volume yield curves and repeated measures of biomass of stand components were available: one of P. radiata and two of E. globulus. Although accumulation of biomass in foliage and branches were not well predicted by the model, sensitivity analysis showed that this was relatively unimportant to total carbon storage because of the dominance of the stem, particularly once the stand is older than 5 years. Indeed, FullCAM accounted for 99% of the variance in measured above-ground biomass at all three sites because calibrations for the mass of stem was reasonably well constrained. Uncertainty analysis showed that despite the standard errors of parameters used in relationships for basic density and biomass partitioning, and for estimates of carbon contents of tree components, we can be 95% confident that sequestration of carbon in trees and debris of Pinus radiata and Eucalyptus globulus plantations are, on average, within 13% of that predicted by FullCAM. Ensis is a joint venture between CSIRO FFP P/L and Scion Australasia P/L     

林木竞争对臭冷杉生物量分配的影响

用不同高度树干直径建立并比较臭冷杉各器官生物量方程,分析林木竞争对臭冷杉地上、地下生物量分配的影响。结果表明:臭冷杉不同高度树干直径中,胸径是预测各器官生物量的最可靠变量;利用不同高度树干直径建立各器官生物量方程均会高估小个体样木(直径≤10cm)的生物量,并且随着直径增大,预测误差也随之增大;臭冷杉地上生物量与地下生物量的比值(T/R)与树木年龄、单株生物量、整株生物量年均生长率及树高年均生长率间均没有显著相关性(P>0.05);随着竞争增强,臭冷杉树干生物量占单株生物量的比例逐渐减小,枝叶生物量比例逐渐增大,而粗根生物量比例则基本保持不变;胸径年均生长率、树高年均生长率及单株生物量年均生长率均随着竞争强度增大逐渐减小,而T/R值并不受林木竞争的影响。     

Applicability of semi-destructive method to derive allometric model for estimating aboveground biomass and carbon stock in the Hill zone of Bangladesh

Biomass estimation using allometric models is a nondestructive and popular method.Selection of an allometric model can influence the accuracy of biomass estimation.Bangladesh Forest Department initiated a nationwide forest inventory to assess biomass and carbon stocks in trees and forests.The relationship between carbon storage and sequestration in a forest has implications for climate change mitigation in terms of the carbon sink in Bangladesh.As part of the national forest inventory,we aimed to derive multi-species biomass models for the hill zone of Bangladesh and to determine the carbon concentration in tree components(leaves,branches,bark and stem).In total,175 trees of 14 species were sampled and a semi-destructive method was used to develop a biomass model,which included development of smaller branch(base dia 7 cm) biomass allometry and volume estimation of bigger branches and stems.The best model of leaf,branches,and bark showed lower values for adjusted R2(0.3152-0.8043) and model efficiency(0.436-0.643),hence these models were not recommended to estimate biomass.The best fit model of stem and total aboveground biomass(TAGB) showed higher model efficiency 0.948 and 0.837,respectively,and this model was recommended for estimation of tree biomass for the hill zone of Bangladesh.The best fit allometric biomass model for stem was Ln(Stem)=-10.7248+1.6094*Ln(D)+1.323*Ln(H)+1.1469*Ln(W);the best fit model for TAGB was Ln(TAGB)=-6.6937+0.809*Ln(D^2*H*W),where DBH=Diameter at Breast Height,H=Total Height,W=Wood density.The two most frequently used pan-tropical biomass models showed lower model efficiency(0.667 to 0.697) compared to our derived TAGB model.The best fit TAGB model proved applicable for accurate estimation of TAGB for the hill zone of Bangladesh.Carbon concentration varied significantly(p 0.05) by species and tree components.Higher concentration(48-49%) of carbon was recorded in the tree stem.     

Growth of Young Sitka Spruce (Picea sitchensis (Bong.) Carr.) and the Effect of Simulated Browsing, Staking and Treeshelters

Sitka spruce (Picea sitchensis (Bong.) Carr.) 1 + 1 transplantswere grown at 1 x 1 m for 3 years with 100 per cent chemicalweed control on a very fertile site. Treatments were control,firm staking, staked with 15 cm diameter netting with simulatedbrowsing, staked with simulated browsing to 15 cm diameter crown,1.2 m treeshelter, 1.2 treeshelter with holes and no browsing.No leaders were browsed. Trees were assessed for annual heightgrowth, stem diameter at 0.5 m and 1.0 m, total above and belowground biomass, root:shoot ratio, root plate diameter, rootdepth and root volume. No 3-year heights were significantlydifferent but third-year increments were; the greatest finalheight was in the control at 200.7 cm. All other tree parametershad significant treatment differences demonstrating the needto select carefully the criteria of success in experiments.Treatments which restricted the horizontal development of thecanopy either physically or by simulated browsing seriouslyreduced stem diameter and root development. The controls hada root:shoot ratio of 0.418; treeshelter treatments had thesmallest root:shoot ratio of 0.238; staked trees were 0.379while staked browsed trees had the highest value at 0.447. Acceptanceof browsing or use of shelters or guards to protect trees frombrowsing may seriously reduce growth.     

Effect of complete competition control and annual fertilization on stem growth and canopy relations for a chronosequence of loblolly pine plantations in the lower coastal plain of Georgia

Stem growth, developmental patterns and canopy relations were measured in a chronosequence of intensively managed loblolly pine stands. The study was located on two distinct sites in the lower coastal plain of Georgia, USA and contained a factorial arrangement of complete control of interspecific competition (W) and annual nitrogen fertilization (F). The W treatment increased growth rate for several years, while the F treatments led to sustained growth increases. The combination of the W and F treatments resulted in more than 180 Mg ha⁻¹ stem biomass production at age 15 which is more than double the production of control treatment. Stem biomass production is continuing to increase through age 15 as indicated by the current annual increment in stem biomass continuing to exceed the mean annual increment in stem biomass. The F treatment decreased wood quality by decreasing whole tree latewood specific gravity from 0.565 to 0.535 and by lengthening the transition from juvenile to mature wood from 4 to 5 years. Increased rates of stem growth in response to cultural treatments were largely mediated by increased leaf area, with strong functional relationships between leaf area index and current annual increment. However, growth efficiency (stem production per unit of leaf area) decreased with stand age. These results indicate that nutrient amendments are necessary for sustaining high rates of stand development on relatively nutrient poor lower coastal plain soils.     

Species-specific biomass allometric models and expansion factors for indigenous and planted forests of the Mozambique highlands

Secondary Miombo woodlands and forest plantations occupy increasing areas in Mozambique, the former due to anthropogenic activities. Plantations, mainly species of Eucalyptus and Pinus, are being established on sites previously covered by secondary Miombo woodlands. This affects the evolution, cycle and spatiotemporal patterns of carbon(C) storage and stocks in forest ecosystems. The estimation of C storage, which is indispensable for formulating climate change policies on sequestrating CO_2, requires tools such as biomass models and biomass conversion and expansion factors(BCEF). In Mozambique, these tools are needed for both indigenous forests and plantations. The objective of this study is to fit species-specific allometric biomass models and BCEF for exotic and indigenous tree species. To incorporate efficient inter-species variability, biomass equations were fitted using nonlinear mixed-effects models. All tree component biomass models had good predictability; however, better predictive accuracy and ability was observed for the 2-predictors biomass model with tree height as a second predictor. The majority of the variability in BCEF was explained by the variation in tree species. Miombo species had larger crown biomass per unit of stem diameter and stored larger amounts of biomass per stem volume. However, due to relatively rapid growth, larger stem diameters, heights, and stand density, the plantations stored more biomass per tree and per unit area.     

Forest structure and carbon dynamics of an intact lowland mixed dipterocarp forest in Brunei Darussalam

Tropical forests play a critical role in mitigating climate change because they account for large amount o terrestrial carbon storage and productivity.However,there are many uncertainties associated with the estimation o carbon dynamics.We estimated forest structure and carbon dynamics along a slope(17.3°–42.8°)and to assess the relations between forest structures,carbon dynamics,and slopes in an intact lowland mixed dipterocarp forest,in Kuala Belalong,Brunei Darussalam.Living biomass,basa area,stand density,crown properties,and tree family composition were measured for forest structure.Growth rate,litter production,and litter decomposition rates were also measured for carbon dynamics.The crown form index and the crown position index were used to assess crown properties,which we categorized into five stages,from very poor to perfect.The living biomass,basal area and stand density were 261.5–940.7 Mg ha~(-1),43.6–63.6 m~2ha~(-1)and 6,675–8400 tree ha~(-1),respectively.The average crown form and position index were 4,which means that the crown are mostly symmetrical and sufficiently exposed for photosynthesis.The mean biomass growth rate,litter production,litter decomposition rate were estimated as11.9,11.6 Mg ha~(-1)a~(-1),and 7.2 g a~(-1),respectively.Biomass growth rate was significantly correlated with living biomass,basal area,and crown form.Crown form appeared to strongly influence living biomass,basal area and biomass growth rate in terms of light acquisition.However,basal area,stand density,crown properties,and biomass growth rate did not vary by slope or tree family composition.The results indicate that carbon accumulation by tree growth in an intact lowland mixed dipterocarp forest depends on crown properties.Absence of any effect of tree family composition on carbon accumulation suggests that the main driver of biomass accumulation in old-growth forests of Borneo is not species-specific characteristics of tree species.     

Generic biomass functions for Norway spruce in Central Europe--a meta-analysis approach toward prediction and uncertainty estimation

To facilitate future carbon and nutrient inventories, we used mixed-effect linear models to develop new generic biomass functions for Norway spruce (Picea abies (L.) Karst.) in Central Europe. We present both the functions and their respective variance-covariance matrices and illustrate their application for biomass prediction and uncertainty estimation for Norway spruce trees ranging widely in size, age, competitive status and site. We collected biomass data for 688 trees sampled in 102 stands by 19 authors. The total number of trees in the "base" model data sets containing the predictor variables diameter at breast height (D), height (H), age (A), site index (SI) and site elevation (HSL) varied according to compartment (roots: n = 114, stem: n = 235, dry branches: n = 207, live branches: n = 429 and needles: n = 551). "Core" data sets with about 40% fewer trees could be extracted containing the additional predictor variables crown length and social class. A set of 43 candidate models representing combinations of lnD, lnH, lnA, SI and HSL, including second-order polynomials and interactions, was established. The categorical variable "author" subsuming mainly methodological differences was included as a random effect in a mixed linear model. The Akaike Information Criterion was used for model selection. The best models for stem, root and branch biomass contained only combinations of D, H and A as predictors. More complex models that included site-related variables resulted for needle biomass. Adding crown length as a predictor for needles, branches and roots reduced both the bias and the confidence interval of predictions substantially. Applying the best models to a test data set of 17 stands ranging in age from 16 to 172 years produced realistic allocation patterns at the tree and stand levels. The 95% confidence intervals (% of mean prediction) were highest for crown compartments (approximately +/- 12%) and lowest for stem biomass (approximately +/- 5%), and within each compartment, they were highest for the youngest and oldest stands, respectively.     

桂西南米老排人工林单株生物量回归模型

通过对桂西南大青山林区28a生米老排(Mytilaria laosensis)人工林林分进行每木检尺和生物量的测定,建立了米老排各器官生物量与胸径、树高和胸径平方乘树高(D2 H)的相关关系;分别选用幂函数等5种模型,用回归分析方法对米老排人工林单株生物量模型进行了拟合。结果表明:树叶和树根生物量分别与胸径和树高的相关关系最显著,而树干、树枝、树皮和全株的生物量都与D2 H的相关关系最为显著。胸径、树高和D2 H与各器官生物量拟合的模型中,全株、树干和树皮的拟合效果最好,树叶和树根的拟合效果中等,树枝的拟合效果较差。除树皮外,各器官均以幂指数模型的拟合效果最好。     

基于树高和树冠因子的立木材积与地上生物量相容模型研究

【目的】无人机机载激光雷达能够准确地测定单木、林分乃至大尺度森林结构参数(树高和树冠因子)。为应用无人机激光雷达技术准确估测森林蓄积量、生物量和碳储量提供计量依据和技术支撑。【方法】以150株实测马尾松生物量样本数据为研究对象,采用非线性回归估计方法和度量误差联立方程组方法,分析立木材积和地上生物量与树高、树冠因子的相关性,并在此基础上研究建立基于树高和树冠因子的立木材积与地上生物量相容模型。【结果】单株材积和地上生物量与树高因子的相关性最为紧密,其次才是树冠因子;基于树高和冠幅因子的二元材积和地上生物量模型预估精度较高,达到92%以上,再考虑冠长因子的三元模型预估精度改进不大;基于树高和冠幅因子的二元立木材积与地上生物量相容模型估计效果更好,相对于一元相容模型系统而言,二元相容模型拟合效果有较大幅度提高,预估精度达到92%以上。【结论】采用度量误差联立方程组方法可以有效解决基于树高和树冠因子的立木材积与地上生物量相容问题,并且预估精度达到92%以上,所建二元立木材积与地上生物量相容模型可为应用激光雷达技术反演森林蓄积量和生物量提供计量依据。     

Stem growth and respiration in loblolly pine plantations differing in soil resource availability

Stem respiration and growth in 10-year-old loblolly pine (Pinus taeda L.) plantations were measured monthly during the third year of fertilization and irrigation treatments to determine whether soil resource availability differentially altered growth and respiration in stem tissue. Fertilized trees had significantly greater stem biomass, stem nitrogen concentration ([N]) and growth rate than unfertilized trees. Stem respiration (Rt) was significantly greater in fertilized trees when expressed on a per unit surface area (Rt,a, micromol CO2 m-2 s-1), sapwood volume (Rt,v, micromol CO2 m-3 s-1), or mass (Rt,w, nmol CO2 g-1 s-1) basis; however, there was no difference between treatments when expressed as a function of stem N content (Rt,n, micromol CO2 (mol N)-1 s-1). Irrigation had no significant effect on Rt or annual stem growth. Daily total respiration (Rd, mol CO2 m-2 day-1) and stem diameter growth both had a seasonal bimodal pattern with peaks in early spring and midsummer. Stem [N] declined significantly during the growing season. Stem growth rate and [N] explained 75% of the seasonal variation in temperature-normalized Rt,a. The mature tissue method was used to partition total stem respiration (Rt) into maintenance (Rm) and growth (Rg) components. There was a linear correlation between winter Rt,v, a measure of basal Rm, and sapwood N content; however, Rt,v per unit N was greater in January before diameter growth started than in the following December after growth ceased, indicating that Rt,v declined as stem diameter increased. Consequently, estimates of annual maintenance respiration (RM) based on January data were 44% higher than estimates based on December data. Growth respiration was correlated with stem growth rate (r2 = 0.55). The growth respiration coefficient (rg)-the slope of the relationship between Rg and stem growth rate-was 0.24. Respiration accounted for 37% of annual stem carbon budget. Stem carbon-use efficiency (CUE)-the ratio of stem growth to stem growth plus respiration-averaged 0.63 and was unaffected by fertilization.