Tree-level Data Research Articles

High-Resolution Yield Mapping for Eucalyptus grandis—A Case Study

Yield data represent a valuable layer for supporting decision-making as they reflect crop management results. Forestry decision-makers often rely on coarse spatial resolution data (e.g., forest inventory plots) despite the availability of modern harvesters that can provide high-resolution forestry yield data. The objectives of this study were to present a method for generating high-resolution Eucalyptus grandis yield data (individual tree-level) and explore their applications, such as correlation analysis with soil attributes to aid nutrient recommendations. Two evaluations were conducted at two sites in Brazil: (a) assessing the positioning accuracy of the global navigation satellite system (GNSS) receiver positioning, and (b) analyzing the yield data and their correlation with the soil attributes. The results indicated that positioning the GNSS receiver at the harvesting head provided higher accuracy than placement at the top of the harvester cabin for individual tree-level data. Reliable yield data were generated despite the GNSS receiver’s increased susceptibility to damage when mounted on a harvest head. The linear correlation analysis between the Eucalyptus grandis yield data and soil attributes showed both negative (Clay, B, S, coarse sand, and potential acidity − H + Al) and positive correlations (K, Mg, pH-SMP, Ca, sum of bases, pH, base saturation, fine sand, total sand, and silt content). This study demonstrates the feasibility of obtaining high-resolution yield data at the individual tree-level and their correlation with soil attributes, providing valuable insights for improving forestry decision-making.

Long-term growth data of plantation-grown Eucalyptus established in south-eastern Uruguay

Behind beef production, Eucalyptus logs oriented to kraft pulp production represent Uruguay's second-largest export product. In this context, the analysis of long-term growth data of plantation-grown Eucalyptus forests acquires a material relevance. A total of 2208 permanent plots representing longitudinal growth data of Eucalyptus globulus, Eucalyptus maidenii, Eucalyptus dunnii, and Eucalyptus smithii trees were analyzed and modeled. The plots are part of a more extensive set established since 2012 on a forest state of over 22,000 ha planted. The selected plots were of variable shape, varying in size between 200 and 1000 m2. Both planted and coppiced areas were included. Tree-level data (diameter at the beast height and height) was measured on each plot over a different number of years. Plantation ages, at the time of measurement, ranged from 1 to 18 years. The forests were all planted for the first time under the context of degraded grasslands, where there was no other better alternative use for the land. Soils are not very deep, of medium-to-coarse texture, and have low natural fertility. The dominant land cover was grasslands. The results highlight the variability in site quality. Stand density varied between 100 and 2500 trees per ha (TPH), with a site index (SI) at base age 11 ranging between 12 and 38 m. A strong relationship between dominant height (DH) and standing volume (TV) is evident, reinforcing that SI is still a valuable quantity to represent site quality. A set of anamorphic SI curves fitted to the DH data showed that E. dunnii and E. smithii height far exceeds that of E. globulus and E. maidenii at the same age, with an average SI of 28 and 31 m, respectively. Similarly, a family of TV curves fitted to each species as a function of DH, TPH, basal area, and age showed that the implicit current annual growth (CAI), given the model form used, peaked between 7 and 9 years. Depending on the stocking and site index considered, the CAI varied; but, in all cases, the CAI of E. dunnii was the highest, followed by E. smithii, and then E. maidenii and E. globulus in descending order. As an example, for a fixed density of 1100 TPH, the peak CAI was almost 48.6 m3|ha|yr for E. dunnii (SI28), approximately 42.1 m3|ha|y for E. smithii (SI31), and 17.8-21.3 m3|ha|yr for E. maidenii and E. globulus (SI23).

Forest disturbance and recovery in Peruvian Amazonia.

Amazonian forests function as biomass and biodiversity reservoirs, contributing to climate change mitigation. While they continuously experience disturbance, the effect that disturbances have on biomass and biodiversity over time has not yet been assessed at a large scale. Here, we evaluate the degree of recent forest disturbance in Peruvian Amazonia and the effects that disturbance, environmental conditions and human use have on biomass and biodiversity in disturbed forests. We integrate tree-level data on aboveground biomass (AGB) and species richness from 1,840 forest plots from Peru's National Forest Inventory (NFI) with remotely-sensed monitoring of forest change dynamics, based on disturbances detected from Landsat-derived Normalized Difference Moisture Index (NDMI) time series. Our results show a clear negative effect of disturbance intensity tree species richness. This effect was also observed on AGB and species richness recovery values towards undisturbed levels, as well as on the recovery of species composition towards undisturbed levels. Time since disturbance had a larger effect on AGB than on species richness. While time since disturbance has a positive effect on AGB, unexpectedly we found a small negative effect of time since disturbance on species richness. We estimate that roughly 15% of Peruvian Amazonian forests have experienced disturbance at least once since 1984, and that, following disturbance, have been increasing in AGB at a rate of 4.7 Mg ha-1 year-1 during the first 20 years. Furthermore, the positive effect of surrounding forest cover was evident for both AGB and its recovery towards undisturbed levels, as well as for species richness. There was a negative effect of forest accessibility on the recovery of species composition towards undisturbed levels. Moving forward, we recommend that forest-based climate change mitigation endeavours consider forest disturbance through the integration of forest inventory data with remote sensing methods.

One-loop string amplitudes in AdS5×S5: Mellin space and sphere splitting

We study string corrections to one-loop amplitudes of single-particle operators mathcal{O} p in AdS5×S5. The tree-level correlators in supergravity enjoy an accidental 10d conformal symmetry. Consequently, one observes a partial degeneracy in the spectrum of anomalous dimensions of double-trace operators and at the same time equality of many different correlators for different external charges pi=1,2,3,4. The one-loop contribution is expected to lift such bonus properties, and its precise form can be predicted from tree-level data and consistency with the operator product expansion.Here we present a closed-form Mellin space formula for leftlangle {mathcal{O}}_{p1}{mathcal{O}}_{p2}{mathcal{O}}_{p3}{mathcal{O}}_{p4}rightrangle at order (α′)3, valid for arbitrary external charges pi. Our formula makes explicit the lifting of the bonus degeneracy among different correlators through a feature we refer to as ‘sphere splitting’. While tree-level Mellin amplitudes come with a single crossing symmetric kernel, which defines the pole structure of the AdS5× S5 amplitude, our one-loop amplitude naturally splits the S5 part into two separate contributions. The amplitude also exhibits a remarkable consistency with the corresponding flat space IIB amplitude through the large p limit.

Harvesting wind damaged trees: a study of prediction of windthrow damage in mixed-broadleaf stands via a machine learning model

ABSTRACT Due to climate change, windstorms are becoming increasingly common resulting in the destruction not only of extensive forest areas but, quite often, of small-sized and scattered forest lands, thereby adversely affecting both the productivity and the safety of workers employed in the harvest of windblown trees. In the present study, an attempt is made to identify and record areas in the northeastern forests of Greece covered by mixed stands of conifers and broadleaves that experienced massive windthrow following local storms. Our results reveal that where Pinus sylvestris was mixed either with Quercus sp. or with Fagus sylvatica, it had been substantially protected, while in plots where it stood on its own it had been extensively uprooted. On the other hand, Picea abies, even if it was mixed with Fagus sylvatica and Pinus sylvestris, had been blown down to a large extent. Based on tree-level data, local topographic features, forest characteristics, and the mechanical properties of green wood, a reliable model, to be used for the prediction of similar disturbances in the future, has been selected after a thorough comparative study of the most well-known intelligent Machine Learning (ML) algorithms. Specifically, Random Forest Classifier, k-Neighbors Classifier, Decision Tree Classifier, Light Gradient Boosting Machine, Gradient Boosting Classifier, Ada Boost Classifier, Ridge Classifier, Linear Discriminant Analysis, Logistic Regression, Naive Bayes, SVM – Linear Kernel, and Quadratic Discriminant Analysis were evaluated and compared using six performance measures (confusion matrix, accuracy, precision, recall, F1-score, and ROC).

Using multi-temporal tree inventory data in eucalypt forestry to benchmark global high-resolution canopy height models. A showcase in Mato Grosso, Brazil

The global monitoring of forest structure worldwide is increasingly being supported by refined and enhanced satellite mission datasets. Forest canopy height is a global metric to characterise and monitor dynamics in forest ecosystems worldwide. Satellite mapping missions as NASA's Global Ecosystem Dynamics Investigation (GEDI) are creating opportunities to refine global forest canopy height models adding forest structural information to time-series satellite imagery. A recent global canopy height model presented by Lang et al., (2022) using GEDI and 10-m Sentinel-2 and the map from Potapov et al., (2020) using GEDI and Landsat are both tested in this study using multi-temporal tree-level data collected over eucalypt plantations in Brazil. Our results at plot-level showed Lang et al., (2022)’s estimates of canopy height came short compared to 2020 maximum and mean tree height records in the plots, 7.6 and 3.6 m, respectively, but adding CHM standard deviation improves the agreement of ground records for maximum tree height. Higher errors were computed for the plots in 2019 using the Potapov's 30-m CHM: 14.2 and 9.5 m, respectively. Averaged stand values were more similar between the three sources tested. We report improvement from the 30-m CHM to the 10-m, but still height saturation problems were observed when accounting for height differences in tall eucalypt trees. As more global products for forest height and biomass are becoming available to users, more validation exercises as presented in this study are needed to assess the suitability of CHM products to forestry needs, and facilitate the uptake and actionability of the next generation of global height and biomass products. We provide recommendations and insights on the use of GEDI laser data for global mapping and on the potential of commercial forestry areas to benchmark the accuracy of satellite mapping missions focusing on tree height estimation in the tropics.

Void-Volume-Based Stem Geometric Modeling and Branch-Knot Localization in Terrestrial Laser Scanning Data

A comprehensive 3-D structural mapping of stem is essential for an accurate 3-D crown modeling and tree parameter estimation. Terrestrial laser scanning (TLS) is an effective technology for a comprehensive collection of individual tree level data, compared to destructive and costly field measurements. The performance of 3-D stem modeling techniques is adversely affected by laser shadowing and point-density variations in TLS data. In addition, most of the state-of-the-art techniques perform stem modeling using regular geometric shapes, such as circle, ellipse, and cylinder, which cannot accurately capture the complex 3-D stem geometric shapes. This results in stem modeling errors. In this article, we propose a 3-D stem modeling approach for both single- and multiscan TLS data that: 1) does not make any prior assumption on the stem geometry and 2) is minimally affected by undesirable stem shadowing and point-density variations. The proposed approach accurately models 3-D stem and localizes branch-knots for both coniferous and deciduous trees by mapping the void volume formed within the stem due to the opaqueness of tree stem to laser. The modeling performance was evaluated on both single- and multiscan data obtained for pine, spruce, and birch species. The low estimation errors associated with the stem diameter at breast height and branch-knot location, compared to the reference methods, prove the ability of the proposed method to both accurately model 3-D stem and localize branch-knots.

Estimation of Fruit Load in Australian Mango Orchards Using Machine Vision

The performance of a multi-view machine vision method was documented at an orchard level, relative to packhouse count. High repeatability was achieved in night-time imaging, with an absolute percentage error of 2% or less. Canopy architecture impacted performance, with reasonable estimates achieved on hedge, single leader and conventional systems (3.4, 5.0, and 8.2 average percentage error, respectively) while fruit load of trellised orchards was over-estimated (at 25.2 average percentage error). Yield estimations were made for multiple orchards via: (i) human count of fruit load on ~5% of trees (FARM), (ii) human count of 18 trees randomly selected within three NDVI stratifications (CAL), (iii) multi-view counts (MV-Raw) and (iv) multi-view corrected for occluded fruit using manual counts of CAL trees (MV-CAL). Across the nine orchards for which results for all methods were available, the FARM, CAL, MV-Raw and MV-CAL methods achieved an average percentage error on packhouse counts of 26, 13, 11 and 17%, with SD of 11, 8, 11 and 9%, respectively, in the 2019–2020 season. The absolute percentage error of the MV-Raw estimates was 10% or less in 15 of the 20 orchards assessed. Greater error in load estimation occurred in the 2020–2021 season due to the time-spread of flowering. Use cases for the tree level data on fruit load was explored in context of fruit load density maps to inform early harvesting and to interpret crop damage, and tree frequency distributions based on fruit load per tree.

Multi-objective forest planning at tree-level combining mixed integer programming and airborne laser scanning

The development of forest planning at tree-level is nowadays feasible due to the advances in laser scanning. Tree-level data remains still not fully utilized in the context of tree selection mechanisms and harvest-scheduling models. Using spatial optimization with tree-level data can shift the situation. The research presented a decision-support model set based on mixed integer programming (MIP) to select trees based on economical and spatial goals. Trees were represented as polygons to conduct spatial optimization and account for perimeter boundary minimization while establishing adjacency constraints. The proposed model framework method was tested in a Stone pine (Pinus pinea L.) stand of almost 4400 trees in Spain where individual tree detection with airborne laser scanning data was conducted. The MIP-based tree selections were presented using different priorities for single and multi-objective optimizations to demonstrate the potential of spatial goals to make forest management planning more efficient when controlling the spatial arrangement of solutions. The results showed the general MIP formulation is feasible and all presented combinatorial problems reached global optimality fast. The use of MIP formulations to schedule tree-level decisions has positive cascading effects towards operational forest planning while expanding the current frontiers of tree-level forest planning based on heuristic optimization.

Simplicity of AdS supergravity at one loop

We demonstrate the simplicity of AdS5× S5 IIB supergravity at one loop level, by studying non-planar holographic four-point correlators in Mellin space. We develop a systematic algorithm for constructing one-loop Mellin amplitudes from the tree-level data, and obtain a simple closed form answer for the leftlangle {mathcal{O}}_2^{SG}{mathcal{O}}_2^{SG}{mathcal{O}}_p^{SG}{mathcal{O}}_p^{SG}rightrangle correlators. The structure of this expression is remarkably simple, containing only simultaneous poles in the Mellin variables. We also study the flat space limit of the Mellin amplitudes, which reproduces precisely the IIB supergravity one-loop amplitude in ten dimensions. Our results provide nontrivial evidence for the persistence of the hidden conformal symmetry at one loop.

Combining spatial and economic criteria in tree-level harvest planning

BackgroundModern remote sensing methods enable the prediction of tree-level forest resource data. However, the benefits of using tree-level data in forest or harvest planning is not clear given a relative paucity of research. In particular, there is a need for tree-level methods that simultaneously account for the spatial distribution of trees and other objectives. In this study, we developed a spatial tree selection method that considers tree-level (relative value increment), neighborhood related (proximity of cut trees) and global objectives (total harvest).MethodsWe partitioned the whole surface area of the stand to trees, with the assumption that a large tree occupies a larger area than a small tree. This was implemented using a power diagram. We also utilized spatially explicit tree-level growth models that accounted for competition by neighboring trees. Optimization was conducted with a variant of cellular automata. The proposed method was tested in stone pine (Pinus pinea L.) stands in Spain where we implemented basic individual tree detection with airborne laser scanning data.ResultsWe showed how to mimic four different spatial distributions of cut trees using alternative weightings of objective variables. The Non-spatial selection did not aim at a particular spatial layout, the Single-tree selection dispersed the trees to be cut, and the Tree group and Clearcut selections clustered harvested trees at different magnitudes.ConclusionsThe proposed method can be used to control the spatial layout of trees while extracting trees that are the most economically mature.

Growing extra dimensions in AdS/CFT

What is the dimension of spacetime? We address this question in the context of the AdS/CFT Correspondence. We give a prescription for computing the number of large bulk dimensions, D, from strongly-coupled CFTd data, where “large” means parametrically of order the AdS scale. The idea is that unitarity of 1-loop AdS amplitudes, dual to non-planar CFT correlators, fixes D in terms of tree-level data. We make this observation rigorous by deriving a positive-definite sum rule for the 1-loop double-discontinuity in the flat space/bulk-point limit. This enables us to prove an array of AdS/CFT folklore, and to infer new properties of large N CFTs at strong coupling that ensure consistency of emergent large extra dimensions with string/M-theory. We discover an OPE universality at the string scale: to leading order in large N, heavy-heavy-light three-point functions, with heavy operators that are parametrically lighter than a power of N, are linear in the heavy conformal dimension. We explore its consequences for supersymmetric CFTs and explain how emergent large extra dimensions relate to a Sublattice Weak Gravity Conjecture for CFTs. Lastly, we conjecture, building on a claim of [1], that any CFT with large higher-spin gap and no global symmetries has a holographic hierarchy: D = d + 1.

A plot-level exploratory analysis of European forest based on the results from the BioSoil Forest Biodiversity project

The lack of multi-dimensional data is one of the major gaps which limit the knowledge and the assessment possibilities of European forests. Nowadays, the most extensive and complete data on the European forest statuses are given by National Forest Inventories (NFIs) which provide information about the extent of forest’s resources and their composition and structure. Traditionally, NFIs collect data related to trees, with a limited consideration of other habitat components, such as ground vegetation. This information which goes beyond the mere arboreal component is instead essential for a more complete forest biodiversity assessment. This paper is aimed at introducing the ICP Forests LI-BioDiv database which resulted from BioSoil Forest Biodiversity, a large collaborative European project. This database is organized as a multi-dimensional forest geodatabase that contains forest structure and vegetation records collected in 19 European countries in the period of 2005–2008. The data were acquired from 3311 geocoded plots where several different types of data were gathered: stand-level general information, tree-level data, deadwood, canopy closure and floristic composition. This paper is structured in order to: (1) give a clear overview of the raw data available in the database and to (2) present an elaboration of raw data to calculate simple plot-level forest variables (biomass, deadwood volume, alpha diversity). On the basis of the results we achieved, the LI-BioDiv database appears useful mainly for research purposes aimed at studying cross-relationships between multiple forest variables and not for an operative use for monitoring and assessing European forest. In particular, we hope that this contribution can stimulate scientists to carry out cross-analysis of the database for defining future forest biodiversity indicators that could be introduced into the field protocols of the NFIs in Europe.

Generating Tree-Level Harvest Predictions from Forest Inventories with Random Forests

Wood supply predictions from forest inventories involve two steps. First, it is predicted whether harvests occur on a plot in a given time period. Second, for plots on which harvests are predicted to occur, the harvested volume is predicted. This research addresses this second step. For forests with more than one species and/or forests with trees of varying dimensions, overall harvested volume predictions are not satisfactory and more detailed predictions are required. The study focuses on southwest Germany where diverse forest types are found. Predictions are conducted for plots on which harvests occurred in the 2002–2012 period. For each plot, harvest probabilities of sample trees are predicted and used to derive the harvested volume (m³ over bark in 10 years) per hectare. Random forests (RFs) have become popular prediction models as they define the interactions and relationships of variables in an automatized way. However, their suitability for predicting harvest probabilities for inventory sample trees is questionable and has not yet been examined. Generalized linear mixed models (GLMMs) are suitable in this context as they can account for the nested structure of tree-level data sets (trees nested in plots). It is unclear if RFs can cope with this data structure. This research aims to clarify this question by comparing two RFs—an RF based on conditional inference trees (CTree-RF), and an RF based on classification and regression trees (CART-RF)—with a GLMM. For this purpose, the models were fitted on training data and evaluated on an independent test set. Both RFs achieved better prediction results than the GLMM. Regarding plot-level harvested volumes per ha, they achieved higher variances explained (VEs) and significantly (p < 0.05) lower mean absolute residuals when compared to the GLMM. VEs were 0.38 (CTree-RF), 0.37 (CART-RF), and 0.31 (GLMM). Root means squared errors were 138.3, 139.9 and 145.5, respectively. The research demonstrates the suitability and advantages of RFs for predicting harvest decisions on the level of inventory sample trees. RFs can become important components within the generation of business-as-usual wood supply scenarios worldwide as they are able to learn and predict harvest decisions from NFIs in an automatized and self-adapting way. The applied approach is not restricted to specific forests or harvest regimes and delivers detailed species and dimension information for the harvested volumes.

An approach to estimating forest biomass change over a coniferous forest landscape based on tree-level analysis from repeated lidar surveys

ABSTRACTForests represent a significant opportunity for carbon sequestration, but quantifying biomass change at the landscape scale and larger remains a challenge. Here we develop an approach based on repeated tree-level analysis using high-resolution airborne lidar (around 8 pulses/m2). The study area was 53 km2 of actively managed coniferous forestland in the Coast Range Mountains in western Oregon. The study interval was 2006–2012. Tree heights and crown areas were determined from the lidar data using point cloud clustering. Biomass per tree was estimated with allometry. Tree-level data (N = 14,709) from local USDA Forest Service Forest Inventory and Analysis plots provided the basis for the allometry. Estimated biomass change over the 6-year interval averaged −1.3 kg m−2 year−1, with the average gain in undisturbed areas of 1.0 kg m−2 year−1. Full harvest occurred on 3% of the area per year. For surviving trees, the mean change in height was 0.5 m year−1 (SD = 0.3) and the mean change in biomass was 45.3 kg year−1 (SD = 6.7). The maximum bin-average increase in biomass per tree (57.3 kg year−1) was observed in trees of intermediate height (35–40 m). In addition to high spatially resolved tracking of forest biomass change, potential applications of repeated tree-level surveys include analysis of mortality. In this relatively productive forest landscape, an interval of 6 years between lidar acquisitions was adequate to resolve significant changes in tree height and area-wide biomass.

Quantifying aboveground components of Picea sitchensis for allometric comparisons among tall conifers in North American rainforests

Tree biomass is one of the most important variables for studying and managing forest ecosystems. With emphasis shifting from young forests grown for timber production to forests with old-growth characteristics, the need to quantify various components of individual trees in natural settings is increasing. Destructive methods are inherently limited by what is feasible to cut down, dissect, and measure. In contrast, crown mapping is a minimally invasive technique for quantifying aboveground tree components such as wood, cambium, bark, and leaves. Despite being applied mostly to large trees, it is generalizable to any woody plant and can be adapted to answer diverse questions about biology, ecology, and ecosystem functions. We present a generalized approach for non-destructively quantifying the three-dimensional structure and aboveground components of whole trees along with a new programmatic tool for error-checking, visualizing, and interacting with tree-level data. Crown-mapping data from 60 lowland rainforest Picea sitchensis trees are presented to demonstrate the utility of this method for deriving allometric equations of tree components based on ground measurements. The 60 trees range from 14 to 495 cm trunk diameter at breast height, 10 to 94 m tall, and include simple to structurally complex individuals in dominant to suppressed positions within forests varying widely in density. Final allometric equations explain > 90% of the variability in volumes and masses of bark, wood, and leaves; are applicable to P. sitchensis throughout much of its geographic range; and are conservative relative to equations based on smaller dissected trees. Dendrochronology and allometric equations demonstrate that Picea sitchensis radically out-paces both Pseudotsuga menziesii and Sequoia sempervirens in accumulation of aboveground biomass and leaves, becoming heavier (155 ± 9 Mg) than any living P. menziesii and almost half as heavy as any living S. sempervirens in <500 years.

Windthrow Dynamics in Boreal Ontario: A Simulation of the Vulnerability of Several Stand Types across a Range of Wind Speeds

In Boreal North America, management approaches inspired by the variability in natural disturbances are expected to produce more resilient forests. Wind storms are recurrent within Boreal Ontario. The objective of this study was to simulate wind damage for common Boreal forest types for regular as well as extreme wind speeds. The ForestGALES_BC windthrow prediction model was used for these simulations. Input tree-level data were derived from permanent sample plot (PSP) data provided by the Ontario Ministry of Natural Resources. PSPs were assigned to one of nine stand types: Balsam fir-, Jack pine-, Black spruce-, and hardwood-dominated stands, and, Jack pine-, spruce-, conifer-, hardwood-, and Red and White pine-mixed species stands. Morphological and biomechanical parameters for the major tree species were obtained from the literature. At 5 m/s, predicted windthrow ranged from 0 to 20%, with damage increasing to 2 to 90% for winds of 20 m/s and to 10 to 100% for winds of 40 m/s. Windthrow varied by forest stand type, with lower vulnerability within hardwoods. This is the first study to provide such broad simulations of windthrow vulnerability data for Boreal North America, and we believe this will benefit policy decisions regarding risk management and forest planning.

Implementation of Ranko Tracker Data Collection for Oil Palm Productivity Census

Current data collection for census in oil palm plantation produces only plantation data and block data. Lower level data, tree level data is not available. Tree level data needed for particularistic purpose, such as deep observation on a low yield block for production intensification purpose and higher accuracy in production projection. This research aim to produce digital spatial data to enable efficient productivity analysis by collecting a full population production census using Ranko Tracker method of data collection. Sets of color coding map successfully produced with this method, accurately locating specific area requires immediate action plan within efficient and effective manner.

Hybrid estimators for mean aboveground carbon per unit area

Carbon accounting is at the heart of efforts to mitigate the effects of climate change. One approach for estimating population parameters for live tree stem carbon entails three primary steps: (1) construction of an individual tree, allometric carbon model, (2) application of the model to tree-level data for a probability sample of plots, and (3) use of a probability-based (design-based) estimator of mean carbon per unit area for a population of interest. Compliance with the IPCC good practice guidance requires satisfaction of two criteria, one related to minimizing bias and one related to minimizing uncertainty. For this carbon estimation procedure, the portion of uncertainty attributed to the variance of the probability-based estimator of the population mean using the plot-level predictions is usually correctly estimated, but the portion attributed to the variance of the allometric model estimator is usually ignored. The result is that the total variance of the population mean estimator cannot be asserted to comply with the IPCC good practice criteria because not only is it not minimized, it is not even correctly estimated.Within the framework of what is coming to be characterized as hybrid inference, model-based inferential methods were used to estimate the variance of the tree-level allometric model estimator which was then propagated through to the variance of the probability-based estimator of mean carbon per unit area. This combined estimator, consisting of a model-based estimator used to predict a variable for a probability sample of a population followed by a probability-estimator of the population total or mean using the sample predictions, is characterized as a hybrid estimator. For this study, two probability-based estimators of the mean were considered, simple random sampling estimators and model-assisted regression estimators that used airborne laser scanning (ALS) data as auxiliary information. The variance of the allometric model estimator incorporated variances of distributions of diameter and height measurement errors, covariances of model parameter estimators, model residual variance, and variances of distributions of wood densities and carbon content proportions.The novel features of the study included the hybrid inferential framework, consideration of six sources of uncertainty including the variances of distributions of wood densities and carbon content proportions, use of ALS data with model-assisted regression estimators of the population mean, and use of confidence intervals for the population mean as the basis for comparisons rather than intermediate products such as model prediction accuracy. The primary conclusions were that the variance of the allometric model estimator was negligible or marginally negligible relative to the variance of the probability estimator when using species-specific allometric models and simple random sampling estimators, but non-negligible when using species-specific models and model-assisted regression estimators and when using a non-specific model with either estimator.

The effect of the interaction of tree slenderness and relative height with ring width on wood density in Abies balsamea and Picea glauca

Wood density affects the strength of lumber and paper products. Despite considerable research, however, the key factors influencing wood density are still not fully understood. The aim of this study was to analyze the effects of variables within and among trees on the density of current wood growth along the stem in order to further understanding and prediction of wood quality. Correlation analyses together with linear mixed effects and randomForest modelling were carried out using stem analysis and tree-level data from long-term balsam fir and white spruce stand density experiments in Eastern Canada. Wood density showed highly structured patterns of variation among trees. Mixed effects and randomForest models, which incorporated tree-level effects accounted for much of the wood density variation. The three most influential variables identified by randomForest analysis for both species were tree slenderness, relative height and ring width. Wood density increased with slenderness and relative height, and these variables affected relationships of wood density to ring width. Wood density is associated with interacting variables within and among trees including tree slenderness and relative height. Wood density is related to ring width, but this relationship is modulated by tree-level influences which likely reflect mechanical stability requirements.