Integrated individual tree biomass simultaneous equations for two larch species in northeastern and northern China

Forest biomass estimation at large scale has become an important topic in the background of facing global climate change, and it is fundamental to develop individual tree biomass equations suitable for large-scale estimation. Based on the measured data of biomass components and stem volume from 100 sample trees of two larch species (Larix gmelinii and L. principis-rupprechtii) in northeastern and northern China, an integrated equation system including individual tree biomass equations, stem volume equation and height–diameter regression model were constructed using the dummy variable model and error-in-variable simultaneous equations. In the system, all the parameters of equations were estimated simultaneously, so that the aboveground biomass equation was compatible to stem volume equation and biomass conversion factor (B_CF) function; the belowground biomass equation was compatible to root-to-shoot ratio (R_SR) function; and stem wood, stem bark, branch and foliage biomass equations were additive to aboveground biomass equation. In addition, the system also ensured the compatibility between one- and two-variable models. The results showed that: (1) whether aboveground biomass equations or belowground biomass equations and stem volume equations, the estimates for larch in northeastern China were greater than those in northern China; (2) B_CF of a larch tree decreased with the growing diameter while R_SR increased with the growing diameter; (3) the proportion of stem wood biomass to aboveground biomass increased with the growing diameter while those of stem bark, branch, and foliage biomass decreased.     

Individual tree biomass equations and growth models sensitive to climate variables for <Emphasis Type="Italic">Larix</Emphasis> spp. in China

Climate change has increased the need of information on amount of forest biomass. The biomass and carbon storage for larch (Larix spp.) in large geographic regions in China were failed to be accurately estimated from current biomass equations, because they were usually based on a few sample trees on local sites, generally incompatible to volume estimation, and not additive between components and total biomass. China needs reliable biomass estimation of the important species in the whole country. This study was based on the mensuration data of above- and belowground biomass from 600 and 198 destructive sample trees of larch from four regions in China, respectively. The main purpose was to develop compatible individual tree equations on both national and regional levels for above- and belowground biomass, biomass conversion factor and root-to-shoot ratio, using the nonlinear error-in-variable simultaneous equation approach. In addition, diameter at breast height (D) and tree height (H) growth models were also developed, and effects of key climate variables on biomass variation and growth process were analyzed. The results showed that mean prediction errors (MPEs) of regional aboveground biomass models were from 3.86 to 7.52%, and total relative errors (TREs) are within ±3%; and for regional belowground biomass equations, the MPEs are from 9.91 to 28.85%, and the TREs are within ±4%. The above- and belowground biomass and D- and H-growth were significantly related to mean annual temperature and mean annual precipitation. The biomass equations and growth models developed in this paper will provide good basis for estimating and predicting biomass of larch forests in China.     

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。     

用分段建模方法建立东北落叶松立木材积和生物量方程

以东北落叶松(Larix spp.)立木材积和地上生物量数据为例,通过采用误差变量联立方程组和分段建模方法,研究建立了相容的立木材积方程、地上生物量方程及生物量转换函数.结果表明:采用误差变量联立方程组能确保立木材积与地上生物量之间估计结果的相容性,而分段建模方法能有效解决常用模型在小径阶存在的系统偏估问题;本文所建立的分段一元模型,地上生物量和立木材积的总体预估误差均不超过5％;分段二元模型,地上生物量的预估误差基本在4％以内,立木材积的预估误差则小于3％.     

Developing individual tree-based models for estimating aboveground biomass of five key coniferous species in China

Estimating individual tree biomass is critical to forest carbon accounting and ecosystem service modeling. In this study, we developed one- (tree diameter only) and two-variable (tree diameter and height) biomass equations, biomass conversion factor (BCF) models, and an integrated simultaneous equation system (ISES) to estimate the aboveground biomass for five conifer species in China, i.e., Cunninghamia lanceolata (Lamb.) Hook., Pinus massoniana Lamb., P. yunnanensis Faranch, P. tabulaeformis Carr. and P. elliottii Engelm., based on the field measurement data of aboveground biomass and stem volumes from 1055 destructive sample trees across the country. We found that all three methods, including the one- and two-variable equations, could adequately estimate aboveground biomass with a mean prediction error less than 5%, except for Pinus yunnanensis which yielded an error of about 6%. The BCF method was slightly poorer than the biomass equation and the ISES methods. The average coefficients of determination (R ²) were 0.944, 0.938 and 0.943 and the mean prediction errors were 4.26, 4.49 and 4.29% for the biomass equation method, the BCF method and the ISES method, respectively. The ISES method was the best approach for estimating aboveground biomass, which not only had high accuracy but also could estimate stocking volumes simultaneously that was compatible with aboveground biomass. In addition, we found that it is possible to develop a species-invariant one-variable allometric model for estimating aboveground biomass of all the five coniferous species. The model had an exponent parameter of 7/3 and the intercept parameter a ₀ could be estimated indirectly from stem basic density (a ₀ = 0.294 ρ).     

Development of equations for predicting Puerto Rican subtropical dry forest biomass and volume

Carbon accounting, forest health monitoring and sustainable management of the subtropical dry forests of Puerto Rico and other Caribbean Islands require an accurate assessment of forest aboveground biomass (AGB) and stem volume. One means of improving assessment accuracy is the development of predictive equations derived from locally collected data. Forest inventory and analysis (FIA) measured tree diameter and height, and then destructively sampled 30 trees from 6 species at an upland deciduous dry forest site near Ponce, Puerto Rico. This data was used to develop best parsimonious equations fit with ordinary least squares procedures and additive models fit with nonlinear seemingly unrelated regressions that estimate subtropical dry forest leaf, woody, and total AGB for Bucida buceras and mixed dry forest species. We also fit equations for estimating inside and outside bark total and merchantable stem volume using both diameter at breast height (d.b.h.) and total height, and diameter at breast height alone for B. buceras and Bursera simaruba. Model fits for total and woody biomass were generally good, while leaf biomass showed more variation, possibly due to seasonal leaf loss at the time of sampling. While the distribution of total AGB into components appeared to remain relatively constant across diameter classes, AGB variability increased and B. simaruba and B. buceras allocated more carbon into branch biomass than the other species. When comparing our observed and predicted values to other published dry forest AGB equations, the equation developed in Mexico and recommended for areas with rainfall >900 mm/year gave estimates substantially lower than our observed values, while equations developed using dry forest data from forest in Australia, India and Mexico were lower than our observed values for trees with d.b.h. <25 cm and slightly higher for trees with d.b.h. >30 cm. Although our ability to accurately estimate merchantable stem volume and live tree AGB for subtropical dry forests in Puerto Rico and other Caribbean islands has been improved, much work remains to be done to sample a wider range of species and tree sizes.     

Total aboveground biomass and net dry matter accumulation by plant component in young Eucalyptus globulus in response to irrigation

A system of equations describing total aboveground biomass, the proportion of total aboveground biomass accumulated by different plant components, and instantaneous net dry matter accumulation fraction is developed as a function of tree diameter, height, and the growth rates of diameter and height. This system is utilized in the analysis of a Eucalyptus globulus fertilization/irrigation experiment in central Portugal. The data were from the period prior to competition-induced mortality in the stands, but previous analyses had reported apparent changes in tree growth rates due to intraspecific competition in the experimental stands. The irrigation treatments affected the relationship between tree dimensions and total aboveground biomass as well as the accumulation of biomass by different aboveground plant components (p≤0.05). There were no differences in these relationships due to fertilization (p=0.05), in spite of previously reported increases in biomass production in response to fertilization. Even though irrigation affects dimensional biomass relationships in E. globulus, analyses demonstrate that previously reported differences in biomass production and accumulation by the various aboveground plant components are, to a much greater extent, due to changes in the growth rates of diameter and height among the treatments rather than to the changes in structural relationships due to the experimental treatments.     

Allometric equations from a non-destructive approach for biomass prediction in natural forest and plantation in West Africa

Allometric equations are required for a rapid estimation of commercial timber volume and forest biomass stocks. In order to preserve the forest ecosystem, this study applied a non-destructive sampling approach to measure biophysical properties of living trees. From these measurements, volume and biomass models were developed for 11 dominant tree species in a semi-deciduous natural forest and for Acacia auriculiformis in a plantation located in southern Benin. The observations were combined to develop also generic models applicable to non-dominant tree species. Wood samples of the tree species were collected with an increment borer and analysed in the laboratory to determine species-specific wood densities. The sample size was composed of 243 trees in natural forest and 21 trees in plantation. The measurements were conducted in 30 plots of 50 m × 50 m. The graphical assessment of correlation between model outputs (biomass and volume) and variables (diameter and height) and the statistical analysis confirmed that the logarithmic model with two variables had the best predictions. The assessment also confirmed that the model using diameter only as a variable had good predictions when observations on height were unavailable. The comparative analysis of model predictions showed that the generic model in this study over-estimated biomass by up to 74.80% for certain species and under-estimated biomass by 21.18% for other species. The study shows that there are no statistically significant differences between the wood densities in this research and that published in previous studies.     

中国西南地区栎类和桦木立木地上及地下生物量模型研建

依据中国西南地区栎类和桦木的立木材积及生物量实测数据,采用度量误差模型的方法,建立栎类和桦木材积相容的地上生物量及地下生物量模型。结果表明,在地上生物量模型中,增加树高因子,立木材积模型的相关统计指标有较大幅度的改进,栎类和桦木二元材积模型的平均预估精度分别达到了97.86%和97.08%,而二元地上生物量模型的相关统计指标并没明显的改进;两树种一元与二元地下生物量模型的相关统计指标差异并不明显,平均预估精度均达到了90%以上。     

东北落叶松相容性立木材积和地上生物量方程研建

以东北落叶松立木材积和地上生物量数据为例,通过改进模型的结构形式,采用误差变量联立方程组的方法,研究建立了相容的立木材积方程、地上生物量方程及生物量转换函数。结果表明:与常用的非线性模型相比,在材积方程和生物量方程中增加截距常数,能显著改进模型的拟合效果;建立的一元相容性方程,地上生物量和立木材积的预估误差均不超过5%;二元相容性方程,地上生物量的预估误差约为4%,立木材积的预估误差则小于3%。     

Aboveground biomass estimation of small diameter woody species of tropical dry forest

Estimation of accurate biomass of different forest components is important to estimate their contribution to total carbon stock. There is lack of allometric equations for biomass estimation of woody species at sapling stage in tropical dry forest (TDF), and therefore, the carbon stored in this forest component is ignored. We harvested 46 woody species at sapling stage in a TDF and developed regression models for the biomass estimation of foliage, branch, bole and the total aboveground part. For foliage and branch biomass, the models with only stem diameter as estimator showed greater R ². For bole and aboveground biomass, the models including wood specific gravity or wood density exhibited higher R ² than those without wood density. Also, the model consisting of wood density, stem diameter and height had the lowest standard error of estimate for bole and aboveground biomass. Moreover, the R ² values are very similar among models for each component. The measurement error of height and the use of a standard value of wood density together may introduce more than 2 % error into the models. Therefore, we suggest using diameter-only model, which may be more practical and equally accurate when applied to stands outside our study area.     

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.     

Volume equations and biomass estimates for three species in tropicalmoist forest in the Orientale province,Democratic Republic of Congo

Volume equations predict the volume of the stem of a tree from dendrometrical characteristics that are easy to measure, such as diameter and/or height. These equations can serve as a surrogate for biomass equations, by converting the stem volume to stem biomass, and then expanding it to the total aboveground biomass. This is especially important for Central Africa where biomass equations are scarce, whereas volume equations are common. We measured the stem volume of 459 trees in the Yoko forest, Orientale province, Democratic Republic of Congo. These trees belonged to three species: Gilbertiodendron dewevrei (limbali), Guarea thompsonii (bossé foncé) and Scorodophloeus zenkeri (divida). Species-specific volume equations were fitted using these data, and biomass estimates were derived from these volume equations. The fitted volume equations were consistent with other location-specific volume equations for the same species. The biomass estimates derived from the fitted volume equations were also found to be consistent with multispecies pantropical biomass equations.     

Equations for estimating aboveground biomass of cadaghi (Corymbia torelliana) trees in farm windbreaks

Agroforestry systems have received global attention lately as a strategy for carbon mitigation but still are one of the least studied systems. This study was conducted in south Florida to develop biomass equations for windbreak grown cadaghi (Corymbia torelliana) trees and to estimate biomass in various aged windbreaks. Trees were selected for destructive sampling based on diameter at breast height (DBH) distribution from five windbreaks. Crown biomass was estimated using randomized branch sampling (RBS) and trunk biomass by taking disks every 1.5?m along the stem. Separate nonlinear equations were developed for crown, trunk and whole tree biomass estimation using DBH and height as predictors. Results indicated that DBH alone was sufficient to predict aboveground biomass, but including height in the models gave better results. Average oven-dry whole tree biomass ranged between 6 and 935?kg for 2- and 20-year-old windbreaks. Oven-dry whole tree biomass per100?m windbreak length in the same windbreaks ranged between 166 and 26,605?kg. Because fast-growing cadaghi is efficient and can produce significantly more biomass in a short period versus other windbreak species, landowners can expect higher returns from biomass or carbon trade over a shorter period, where available, to offset the cost of land occupied by the windbreaks.     

林分径阶蓄积量与材种出材量测算的研究

研究了林分径阶蓄积量与材种出材量的估测模型,其基本原理是应用相对树高曲线法测定林分径阶蓄积量,应用一致性削度方程法计算径阶单木材种出材率;相对树高曲线法与一致性削度方程法是基于胸径和树高两个测树因子的二元立木材积测定系统,通过建立较完善的数学模型改进计算方法,提高估测效果.     

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。     

Improvement in accuracy of aboveground biomass estimation in Eucalyptus nitens plantations: Effect of bole sampling intensity and explanatory variables

Two sets of aboveground biomass equations were fitted for stem only and stem plus crown predictive variables in Eucalyptus nitens plantations in Northern Spain. A sample of 40 trees was chosen after a complete study of variation in tree height and diameter in the region. The trees were felled and the biomass was divided into the following components: wood, bark, thick branches, thin branches, twigs, leaves and dead branches along the stem. Bole biomass was estimated by systematic subsampling of one 5 cm-thick disk every 0.5 m. Such intensive subsampling enabled determination of the effect of subsampling intensity on accuracy and bias of wood estimation, considering two ratio-type estimators: stem weight to dry matter, determined by the complete weighing (CW) method (i.e. of the fresh weight of the entire stem) and volume to dry matter, determined by the partial weighing (PW) method. The changes in moisture content and basic density along the stem explained the serious risk of dry mass or weight overestimation when a systematic subsample is considered. The average basic density was usually found at a relative height of 30-35% along the stem. The default choice of the bottom disk or log as the first section resulted in overestimations for the CW method and underestimations for the PW one. The biomass equations were fitted by seemingly unrelated regression, with corrections for heteroscedasticity carried out by weighted fitting. Diameter at breast height was the best explanatory variable, and the inclusion of height did not improve the accuracy, except for wood. The inclusion of crown variables improved the predictive ability for crown fractions, increasing the accuracy for estimating thick branches (by 10.8%), twigs (by 19.1%) and leaves (by 17.3%). The biomass of each fraction decreased in the following order: wood > bark > thick branches > dead branches along the stem > leaves > thin branches > twigs. The changes in these percentages with diameter class and the predictive ability of the fitted equations were also studied.     

利用度量误差模型和分段建模方法建立云南云杉相容性立木材积和地上生物量模型

以云南云杉实测立木材积和地上生物量数据为例,利用度量误差模型方法和分段建模方法建立相容性的一元和二元立木材积和地上生物量模型。结果表明,无论常规模型还是分段模型二元立木材积模型的相关统计指标得到了大幅度的改进,而二元地上生物量模型的相关指标与一元模型相比差异不大;常规二元立木材积模型在小径阶下存在明显的偏差,分段模型从整体上能够有效地解决系统偏差问题;所建的分段一元立木材积模型和地上生物量模型的平均预估精度分别到了90％和95％,同时分段二元立木材积模型和地上生物量模型的平均预估精度均到了97％。     

Construction of tree volume equations for Chinese fir plantations in Guizhou Province, southwestern China

Forest volume, the major component of forest biomass, is an important issue in forest resource monitoring.It is estimated from tree volume tables or equations. Based on tree volume data of 1840 sample trees from Chinese fir （Cunninghamia lanceolata） plantations in Guizhou Province in southwestern China, parallel one- and two-variable tree volume tables and tree height curves for central and other areas were constructed using an error-in-variable modeling method. The results show that, although the one-variable tree volume equations and height curves between the central and other areas were significantly different, the two-variable volume equations were sufficiently close, so that a generalized two-variable tree volume equation could be established for the entire province.     

新疆云杉一体化立木生物量模型系统研建

[目的]研究建立地上生物量与地下生物量、立木材积之间相容,以及地上生物量与各分量之间可加的一体化生物量模型系统,为准确估计森林生物量提供定量依据。[方法]以新疆自治区的云杉(Picea spp.)为研究对象,基于230株和78株样木的实测地上生物量、树干材积和地下生物量数据,综合利用误差变量联立方程组方法和哑变量建模方法,研究建立集地上生物量、树干材积和地下生物量为一体,兼具相容性和可加性的二元和一元生物量模型系统,并分析一元模型是否受地域的影响。[结果]所建云杉一元和二元一体化生物量模型系统,地上生物量方程的平均预估误差在7%以下,干、皮、枝、叶各分项生物量方程的平均预估误差在10%左右,地下生物量方程的平均预估误差在15%以下,均达到了相关技术规定的预估精度要求。除了干材和树皮生物量的估计效果不如二元模型外,一元模型对其它各项生物量的估计均要优于二元模型。比例控制法和代数控制法均能解决地上生物量与干、皮、枝、叶各分项生物量之间的可加性问题,且两种方法得出的模型预估结果无显著差异。[结论]将哑变量引入误差变量联立方程组,不仅能解决地上生物量和地下生物量样本单元数不相等时如何联合建模的问题,还能同时解决地上生物量与地下生物量和立木材积之间的相容性问题及地上生物量与各分量之间的可加性问题,方法切实可行;对地上生物量、地下生物量及立木材积的估计,含区域因子的哑变量模型均要优于总体平均模型。