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CLOSING A GAP IN TROPICAL FOREST BIOMASS ESTIMATION: ACCOUNTING FOR CROWN MASS VARIATION IN PANTROPICAL ALLOMETRIES
Abstract
Accurately monitoring tropical forest carbon stocks is an outstanding challenge. Allometric models that consider tree diameter, height and wood density as predictors are currently used in most tropical forest carbon studies. In particular, a pantropical biomass model has been widely used for approximately a decade, and its most recent version will certainly constitute a reference in the coming years. However, this reference model shows a systematic bias for the largest trees. Because large trees are key drivers of forest carbon stocks and dynamics, understanding the origin and the consequences of this bias is of utmost concern. In this study, we compiled a unique tree mass dataset on 673 trees measured in five tropical countries (101 trees > 100 cm in diameter) and an original dataset of 130 forest plots (1 ha) from central Africa to quantify the error of biomass allometric models at the individual and plot levels when explicitly accounting or not accounting for crown mass variations. We first showed that the proportion of crown to total tree aboveground biomass is highly variable among trees, ranging from 3 to 88 %. This proportion was constant on average for trees < 10 Mg (mean of 34 %) but, above this threshold, increased sharply with tree mass and exceeded 50 % on average for trees ≥ 45 Mg. This increase coincided with a progressive deviation between the pantropical biomass model estimations and actual tree mass. Accounting for a crown mass proxy in a newly developed model consistently removed the bias observed for large trees (> 1 Mg) and reduced the range of plot-level error from -23–16 % to 0–10 %. The disproportionally higher allocation of large trees to crown mass may thus explain the bias observed recently in the reference pantropical model. This bias leads to far-from-negligible, but often overlooked, systematic errors at the plot level and may be easily corrected by accounting for a crown mass proxy for the largest trees in a stand, thus suggesting that the accuracy of forest carbon estimates can be significantly improved at a minimal cost.
Introduction
Monitoring forest carbon variation in space and time is both a sociopolitical challenge for climate change mitigation and a scientific challenge, especially in tropical forests, which play a major role in the world carbon balance (Hansen et al., 2013; Harris et al., 2012; Saatchi et al., 2011). Significant milestones have been reached in the last decade thanks to the development of broad-scale remote sensing approaches (Baccini et al., 2012; Malhi et al., 2006; Mitchard et al., 2013; Saatchi et al., 2011). However, local forest biomass estimations are still the bedrock of most (if not all) of these approaches for the calibration and validation of remote sensing models. As a consequence, uncertainties and errors in local biomass estimations may propagate dramatically to broad-scale forest carbon stock assessment (Avitabile et al., 2011; Pelletier et al., 2011; Réjou-Méchain et al., 2014). Aboveground biomass (AGB) is the major pool of biomass in tropical forests (Eggleston et al., 2006). The AGB of a tree (or TAGB) is generally predicted by empirically derived allometric equations that use measurements of the size of an individual tree as predictors of its mass (Clark and Kellner, 2012). Among these predictors, diameter at breast height (D) and total tree height (H) are often used to capture volume variations between trees, whereas wood density (ρ) is used to convert volume to dry mass (Brown et al., 1989). The most currently used allometric equations for tropical forests (Chave et al., 2005, 2014) have the following form: /'() = 01 » 3!²0# r 45, where diameter, height and wood density are combined into a single compound variable related to dry mass through a power law of parameters a and b. This model form, referred to hereafter as our reference allometric model form, performs well when b = 1 or close to 1 (Chave et al., 2005, 2014), meaning that trees can roughly be viewed as a standard geometric solid for which the parameter a determines the shape (or form factor) of the geometric approximation. However, the uncertainty associated with this model is still very high, with an average error of 50 % at the tree level, illustrating the high natural variability of mass between trees with similar D, H and ρ values. More importantly, this reference allometric model shows a systematic underestimation of TAGB of approximately 20 % in average for the heaviest trees (> 30 Mg) (Fig. 2 in Chave et al. 2014), which may contribute strongly to uncertainty in biomass estimates at the plot level. It is often argued that, by definition, the least-squares regression model implies that tree-level errors are globally centered on 0, thus limiting the plot-level prediction error to approximately 5-10 % for a standard 1-ha forest plot (Chave et al., 2014; Moundounga Mavouroulou et al., 2014). However, systematic errors associated with large trees are expected to disproportionally propagate to plot-level predictions because of their prominent contribution to plot AGB (Bastin et al., 2015; Clark and Clark, 1996; Sist et al., 2014; Slik et al., 2013; Stephenson et al., 2014). Thus, identifying the origin of systematic errors in such biomass allometric models is a prerequisite for improving local biomass estimations and thus limiting the risk of uncontrolled error propagation to broad-scale extrapolations.
As foresters have known for decades, it is reasonable to approximate stem volume using a geometric shape. Such an approximation, however, is questionable for assessing the total tree volume, including the crown. Because b is generally close to 1 in the reference allometric model, the relative proportion of crown to total tree mass (or crown mass ratio) directly affects the adjustment of the tree form factor a (e.g., Cannell 1984). Moreover, the crown mass ratio is known to vary greatly between species, reflecting different strategies of carbon allocation. For instance, Cannell (1984) observed that coniferous species have a lower proportion of crown mass (10-20 %) than tropical broadleaved species (over 35 %), whereas temperate softwood species were found to have a lower and less variable crown mass ratio (20-30 %) than temperate hardwood species (20-70 %; Freedman et al., 1982; Jenkins et al., 2003). In the tropics, distinct crown size allometries have been documented among species functional groups (Poorter et.al. 2003; Poorter, Bongers, et Bongers 2006; Van Gelder, Poorter, et Sterck 2006). For instance, at comparable stem diameters, pioneer species tend to be taller and to have shorter and narrower crowns than understory species (Poorter et al., 2006). These differences reflect strategies of energy investment (tree height vs. crown development) that are likely to result in different crown mass ratios among trees with similar0D² » H » $ values. Indeed, Goodman et al. (2014) obtained a substantially improved biomass allometric model when crown diameter was incorporated into the equation to account for individual variation in crown size.
Destructive data on tropical trees featuring information on both crown mass and classical biometric measurements (D, H, ρ) are scarce and theoretical work on crown properties largely remains to be validated with field data. In most empirical studies published to date, crown mass models use trunk diameter as a single predictor (e.g., Nogueira et al. 2008; Chambers et al. 2001). Such models often provide good results (R² ≥ 0.9), which reflect the strong biophysical constraints exerted by the diameter of the first pipe (the trunk) on the volume of the branching network (Shinozaki et al., 1964). However, theoretical results suggest that several crown metrics would scale with crown mass. For instance, Mäkelä et Valentine (2006) modified the allometric scaling theory (Enquist, 2002; West et al., 1999) by incorporating self-pruning processes into the crown. The authors showed that crown mass is expected to be a power function of the total length of the branching network, which they approximated by crown depth (i.e., total tree height minus trunk height). The construction of the crown and its structural properties have also largely been studied in the light of the mechanical stresses faced by trees (such as gravity and wind; e.g., McMahon et Kronauer 1976; Eloy 2011). Within this theoretical frame, crown mass can also be expressed as a power function of crown diameter (King and Loucks, 1978).
In the present study, we used a unique tree mass dataset containing crown mass information on 673 trees from five tropical countries and a network of forest plots covering 130 ha in central Africa to (i) quantify the variation in crown mass ratio in tropical trees; (ii) assess the contribution of crown mass variation to the reference pantropical model error, either at the tree level or when propagated at the plot level; and (iii) propose a new operational strategy to explicitly account for crown mass variation in biomass allometric equations. We hypothesize that the variation in crown mass ratio in tropical trees is a major source of error in current biomass allometric models and that accounting for this variation would significantly reduce uncertainty associated with plot-level biomass predictions.
Materials and Methods
Biomass data
We compiled tree AGB data from published and unpublished sources providing information on crown mass for 673 tropical trees belonging to 132 genera (144 identified species), with a wide tree size range (i.e., diameter at breast height, D: 10-212 cm) and aboveground tree masses of up to 76 Mg. An unpublished dataset for 77 large trees (with D ≥ 67 cm) was obtained from the fieldwork of PP, NB and SM in semi-deciduous forests of Eastern Cameroon (site characteristics and field protocol in Supplement S1.1 and S1.2.1). The remaining datasets were gathered from relevant published studies: 29 trees from Ghana (Henry et al., 2010), 285 trees from Madagascar (Vieilledent et al., 2011), and 51 trees from Peru (Goodman et al., 2014, 2013, Fayolle et al., 2013, and Ngomanda et al., 2014). The whole dataset is available from the Dryad Data Repository (http://dx.doi.org/10.5061/dryad.f2b52), with details about the protocol used to integrate data from published studies presented in the Supplementary Information (2.8.2.2). For the purpose of some analyses, we extracted from this crown mass database (hereafter referred to as DataCM1) a subset of 541 trees for which total tree height was available (DataCM2; all but Fayolle et al. 2013) and another subset of 119 trees for which crown diameter was also available (DataCD; all but Vieilledent et.al. 2011, Fayolle et.al. 2013, Ngomanda et.al. 2014 and 38 trees from our unpublished dataset). Finally, we used as a reference the data from Chave et al. (2014) on the total mass (but not crown mass) of 4,004 destructively sampled trees of many different species from all around the tropical world (DataREF).
Forest inventory data
We used a set of 81 large forest plots (> 1 ha), covering a total area of 130 ha, to propagate TAGB estimation errors to plot-level predictions. The forest inventory data contained the taxonomic identification of all trees with a diameter at breast height (D) ≥ 10 cm, as well as total tree height measurements (H) for a subset of trees, from which we established plot-level H vs. D relationships to predict the tree height of the remaining trees. Details about the inventory protocol along with statistical procedures used to compute plot AGB (or PAGB) from field measurements are provided in the Supplementary Information (2.8.3). Among these plots, 80 were from a network of 1 ha plots established in humid evergreen to semi-deciduous forests belonging to 13 sites in Cameroon, Gabon and the Democratic Republic of Congo (unpublished data1). In addition, we included a 50 ha permanent plot from Korup National Park, in the evergreen Atlantic forest of western Cameroon (Chuyong et al., 2004), which we subdivided into 1 ha subplots. Overall, the inventory data encompassed a high diversity of stand structural profiles ranging from open-canopy Marantaceae forests to old-growth monodominant Gilbertiodendron dewevrei stands and including mixed terra firme forests with various levels of degradation.
Allometric model fitting
We fitted the pantropical allometric model of Chave et al. (2014) to log-transformed data using ordinary least-squares regression: with TAGB (in kg) representing the aboveground tree mass, D (in cm) the tree stem diameter, H (in m) the total tree height, ρ (in g.cm-3) the wood density and e the error term, which is assumed to follow a normal distribution N ~ (0, RSE²), where RSE is the residual standard error of the model. This model, denoted m0, was considered as the reference model.
To assess the sensitivity of m0 to crown mass variations, we built a model (m1) that restricted the volume approximation to the trunk compartment and included actual crown mass as an additional covariate:
ln*TAGB, = % 6 &9 ln*D+9Ht9., 6 0:9 ln*Cm, 6 ; (eq. 2)
with Cm representing the crown mass (in kg) and Ht the trunk height (i.e., height to the first living branch, in m). Note that model m1 cannot be operationally implemented (which would require destructive measurements of crowns) but quantifies the maximal improvement that can be made through the inclusion of crown mass proxies in a biomass allometric model.
Development of crown mass proxies
We further developed crown mass proxies to be incorporated in place of the real crown mass (Cm) in the allometric model m1. From preliminary tests of various model forms (see Appendix A), we selected a crown mass sub-model based on a volume approximation similar to that made for the trunk component (sm1):
ln*Cm, = a 6 b9 ln*D+9Hc9., 6 ; (eq. 3)
where D is the trunk diameter at breast height (in cm) and Hc the crown depth (that is H – Ht, in m), available in our dataset DataCM2 (n=541).
In this sub-model, tree crowns of short stature but large width are assigned a small Hc, thus a small mass, whereas the volume they occupy is more horizontal than vertical. We thus tested in sub-model sm2 (eq. 4) whether using the mean crown size (eq. 5), which accounts for whether Hc and Cd (the crown diameter in m available in our dataset DataCD (n=119)) reduces the error associated with sm1:
Results
Contribution of crown to tree mass
Our crown mass database (DataCM1; 673 trees, including 128 trees > 10 Mg) revealed a huge variation in the contribution of crown to total tree mass, ranging from 2.5 to 87.5 % of total aboveground biomass, with a mean of 35.6 % (± 16.2 %). Despite this variation, a linear regression (model II) revealed a significant increase in the crown mass ratio with tree mass of approximately 3.7 % per 10 Mg (Figure 2-1 A). A similar trend was observed at every site, except for the Ghana dataset (Henry et al. 2010), for which the largest sampled tree (72 Mg) had a rather low crown mass ratio (46 %). Overall, this trend appeared to have been driven by the largest trees in the database (Figure 2-1 B). Indeed, the crown mass ratio appeared to be nearly constant for trees ≤ 10 Mg with an average of 34.0 % (± 16.9 %), and then to increase progressively with tree mass, exceeding 50 % on average for trees ≥ 45 Mg.
Table of contents :
1 GENERAL INTRODUCTION
1.1 Context and challenges
1.1.1 Tropical forests and climate change
1.1.2 REDD monitoring frame of tropical forest biomass: basics and challenges
1.1.3 Remote sensing-based modelling of tropical forest biomass
1.2 Research objectives
1.3 A pantropical approach
1.3.1 Study areas and datasets
1.3.2 Sampling strategy and data description
1.4 Thesis outline
1.5 List of (co-)publications
1.6 References
2 CLOSING A GAP IN TROPICAL FOREST BIOMASS ESTIMATION: ACCOUNTING FOR CROWN MASS VARIATION IN PANTROPICAL ALLOMETRIES
2.1 Introduction
2.2 Materials and Methods
2.2.1 Biomass data
2.2.2 Forest inventory data
2.2.3 Allometric model fitting
2.2.4 Development of crown mass proxies
2.2.5 Model error evaluation
2.3 Results
2.3.1 Contribution of crown to tree mass
2.3.2 Crown mass sub-models
2.3.3 Accounting for crown mass in biomass allometric models
2.4 Discussion
2.4.1 Crown mass ratio and the reference biomass model error
2.4.2 Model error propagation depends on targeted plot structure
2.4.3 Accounting for crown mass variation in allometric models
2.5 Appendix A: Crown mass sub-models
2.5.1 Method
2.5.2 Results & Discussion
2.6 Appendix B: Plot-level error propagation
2.7 References
2.8 Supplement: Field data protocols
2.8.1 Unpublished dataset: site characteristics
2.8.2 Biomass data
2.8.3 Inventory data
3 ASSESSING DA VINCI’S RULE ON LARGE TROPICAL TREE CROWNS OF CONTRASTED ARCHITECTURES: EVIDENCE FOR AREA-INCREASING BRANCHING
3.1 Introduction
3.2 Methods
3.2.1 Sampled trees and field protocol
3.2.2 MTE model assumptions and predictions of branch scaling exponents
3.2.3 Assessing the effect of asymmetry and node morphology on species area ratio
3.3 Results
3.3.1 Does the average tree conform to branch scaling exponents and area ratio predictions?
3.3.2 Is the average tree self-similar?
3.3.3 What is the effect of species asymmetry on branch scaling exponents and area ratio? .
3.3.4 Does node morphology induce systematic differences of area ratio at the species level?
3.4 Discussion
3.4.1 Evidence of area increasing branching (R > 1)
3.4.2 Sources of variation of the node area ratio
3.4.3 Optimal tree of the MTE model vs average real trees
3.4.4 Implications of the results
3.5. Reference
3.6. Supplementary figure
4 CANOPY TEXTURE ANALYSIS FOR LARGE-SCALE ASSESSMENTS OF TROPICAL FOREST STAND STRUCTURE AND BIOMASS
4.1 Introduction
4.2 Methodological background and rationale
4.3 Results from some case studies
4.4 Limits and perspectives
4.5 Reference
5 TOWARD A GENERAL TROPICAL FOREST BIOMASS PREDICTION MODEL FROM VERY HIGH RESOLUTION OPTICAL SATELLITE IMAGES
Abstract
5.1 Introduction
5.2 Material and Methods
5.2.1 Forest inventory data
5.2.2 Generation of 3D forest mockups
5.2.3 Simulation of canopy images
5.2.4 Real satellite images
5.2.5 Canopy texture analysis
5.2.6 Statistical analyses
5.3 Results
5.3.1 Texture analysis of virtual canopy images
5.3.2 Canopy texture – AGB models
5.3.3 Application to real satellite images
5.4 Discussion
5.4.1 Contrasted canopy texture – stand AGB relationships among sites
5.4.2 On 3D stand mockups and virtual canopy images for model calibration
5.5 Reference
5.6 Appendix
6 GENERAL DISCUSSION
6.1 Estimation of forest AGB from field data
6.1.1 Driver(s) of pantropical model bias on large trees
6.1.2 The influence of forest structure on plot-level AGB modelling error
6.2 The influence of forest structure on the canopy texture – AGB relationship
6.3 Key thesis findings
6.4 Reference
