the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 31 Jul 2024
Selecting allometric equations to estimate forest biomass from plot- rather than individual-level predictive performance
Abstract. In a context of global change, it is essential to quantify and monitor the carbon stored in forests. Allometric equations are mathematical models that predict the biomass of a tree from dendrometrical characteristics that are easier to measure, such as tree diameter, height or wood density. Various model forms have been proposed for allometric equations. Moreover, the model choice has a critical influence on the estimate of the biomass of a forest. So far, model selection for allometric equations has been performed based on the tree-level predictive performance of the models. Yet, allometric equations are used to estimate the biomass of plots rather than individual trees. The distribution of trees sampled for establishing allometric equations often differs from the forest structure. Moreover, at the plot-level, the residual individual errors for different trees can cancel off. Therefore, we expect the plot-level predictive performance of a model to differ from its tree-level performance. Using a dataset giving the observed biomass of 844 trees in central Africa and a null model for the size distribution of trees in the forest, we simulated forest plots between 0.1 and 50 ha in area. Then, using a Monte Carlo approach, we calculated the mean sum of squares (MSS) of the differences between observed and predicted plot biomass. We showed that MSS could be well approximated by a three-term formula, where the first term corresponded to bias, the second one to the tree residual error, and the third one to the uncertainty on model coefficients. For small plots (≤ 0.1 ha), the plot-level predictive performance was dominated by the tree residual error term. Model selection based on plot-level predictive performance was then consistent with that based on tree-level performance. For large plots, this term vanished. Model selection based on plot-level performance could then differ from that based on tree-level performance. In the case of large plots, chains of models that combined a general equation to predict biomass and local equations to predicts some of the predictors of the biomass equation could provide a good trade-off between the bias and the uncertainty on model coefficients. We recommend using plot-level rather than tree-level predictive performance to select allometric equations. The three-term formula that we developed provides an easy way to assess the effect of plot size on model selection and to balance the respective contributions of bias, tree residual error, and the uncertainty on model coefficients.
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CC1: 'Comment on egusphere-2024-2302', Robson Borges de Lima, 26 Aug 2024
Review Egusphefe - Selecting allometric equations to estimate forest biomass from plot-rather than individual-level predictive performance
The paper, Selecting allometric equations to estimate forest biomass from plot-rather than individual-level predictive performance, makes significant and relevant contributions to forest biomass estimation, with outstanding strengths. For example, it proposes a robust and innovative method that focuses on the predictive performance of allometric models at the plot level rather than at the individual tree level. This is especially relevant because, in many cases, allometric models are primarily used to estimate biomass in forest plots rather than individual trees. The developed methodology considers that residual errors in individual trees can cancel each other out within a plot, which can affect the accuracy in selecting the most appropriate models. The study proposes a three-term formula that balances bias, residual error, and uncertainty in model coefficients, depending on the plot size. Overall, it is also observed that the novel results highlight that, for small plots, model selection based on tree-level and plot-level performance is consistent. However, for larger plots, this consistency disappears, suggesting that different selection criteria should be applied depending on the scale of the analysis. By offering a more precise approach to selecting allometric equations, the study contributes to improving forest biomass estimates, which is crucial for sustainable forest management and monitoring carbon stocks in the context of climate change. These strengths make the article relevant to the literature, offering practical and methodological solutions to improve the accuracy of biomass estimation in different forest contexts.
In summary, I have no comments that discredit the quality of this manuscript. However, I would like to read the authors' responses to the following questions:
Methodology:
1) Although the study focuses on the giant Congo rainforest, the study employs a detailed approach to estimate biomass in tropical forests using different plot size strategies. Is the methodology used to calibrate and validate the models robust enough for possible different types of tropical forests? How do these methodologies deal with the heterogeneity of tropical forests, which can vary significantly in terms of structure and species composition?
2) Considering that field data collection is essential for model calibration, how was the potential bias from limited or non-representative sampling of different forest areas addressed? Can this be addressed in the manuscript?
Results, broader implications, and limitations of the study:
1) How do the authors interpret the results found regarding spatial and temporal variability of biomass in the studied forests? Is there any indication of changes in biomass stock over time that could be correlated with environmental or anthropogenic factors?
2) Is biomass quantification in line with estimates from similar studies? Can you provide data showing or not showing discrepancies, and what might explain them?
3) The results indicate that tropical forests have a significant capacity to store biomass. What are the implications of these findings for conservation and climate change mitigation policies? How do these results contribute to the global understanding of the role of tropical forests as carbon sinks?
4) To what extent does this study advance knowledge on the quantification of biomass and carbon in tropical forests? How does it contribute to the development of new methodologies or the improvement of existing methodologies?
5) How can the results of this study influence future research on changes in carbon stocks in tropical forests? Are there gaps that still need to be addressed?
6) What is the impact of this study on understanding the role of tropical forests in carbon sequestration, especially in the context of global climate change?
7) What are the main limitations of the methods used in the study, especially in terms of spatial scale? How might these limitations affect the interpretation of the results?
8) What were the main challenges in quantifying uncertainty associated with the methods associated with different plot sizes and individual trees, and how might this influence the results?
9) Are there any limitations related to the representativeness of the field data about the diversity of tropical forests? How might the lack of representativeness have impacted the results?
Main Scientific Contributions
- The study offers significant contributions to the science of ecology and the understanding of tropical forests as carbon sinks. What are the main methodological innovations presented?
- How does the study advance knowledge about spatial variation of biomass in tropical forests? What new insights does it offer for these forests' conservation and sustainable management?
- How can the results of this study be applied to other tropical regions in addition to the areas studied? Is there potential for replicating the methodologies in other areas or biomes?
I believe that the authors' input on these questions is crucial and that it can significantly contribute to the ongoing discussion of the manuscript. Their responses can guide a critical evaluation of the article, highlighting both its contributions and the areas that can be improved or better explored in future research.
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AC3: 'Reply on CC1', Nicolas Picard, 22 Nov 2024
Thanks for these comments. There are a copy of the comments by Reviewer 1, so please see our response to Reviewer 1 at https://doi.org/10.5194/egusphere-2024-2302-AC2.
Citation: https://doi.org/10.5194/egusphere-2024-2302-AC3
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AC3: 'Reply on CC1', Nicolas Picard, 22 Nov 2024
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RC1: 'Comment on egusphere-2024-2302', Anonymous Referee #1, 27 Aug 2024
Review Egusphefe - Selecting allometric equations to estimate forest biomass from plot-rather than individual-level predictive performance
The paper, Selecting allometric equations to estimate forest biomass from plot-rather than individual-level predictive performance, makes significant and relevant contributions to forest biomass estimation, with outstanding strengths. For example, it proposes a robust and innovative method that focuses on the predictive performance of allometric models at the plot level rather than at the individual tree level. This is especially relevant because, in many cases, allometric models are primarily used to estimate biomass in forest plots rather than individual trees. The developed methodology considers that residual errors in individual trees can cancel each other out within a plot, which can affect the accuracy in selecting the most appropriate models. The study proposes a three-term formula that balances bias, residual error, and uncertainty in model coefficients, depending on the plot size. Overall, it is also observed that the novel results highlight that, for small plots, model selection based on tree-level and plot-level performance is consistent. However, for larger plots, this consistency disappears, suggesting that different selection criteria should be applied depending on the scale of the analysis. By offering a more precise approach to selecting allometric equations, the study contributes to improving forest biomass estimates, which is crucial for sustainable forest management and monitoring carbon stocks in the context of climate change. These strengths make the article relevant to the literature, offering practical and methodological solutions to improve the accuracy of biomass estimation in different forest contexts.
In summary, I have no comments that discredit the quality of this manuscript. However, I would like to read the authors' responses to the following questions:
Methodology:
1) Although the study focuses on the giant Congo rainforest, the study employs a detailed approach to estimate biomass in tropical forests using different plot size strategies. Is the methodology used to calibrate and validate the models robust enough for possible different types of tropical forests? How do these methodologies deal with the heterogeneity of tropical forests, which can vary significantly in terms of structure and species composition?
2) Considering that field data collection is essential for model calibration, how was the potential bias from limited or non-representative sampling of different forest areas addressed? Can this be addressed in the manuscript?
Results, broader implications, and limitations of the study:
1) How do the authors interpret the results found regarding spatial and temporal variability of biomass in the studied forests? Is there any indication of changes in biomass stock over time that could be correlated with environmental or anthropogenic factors?
2) Is biomass quantification in line with estimates from similar studies? Can you provide data showing or not showing discrepancies, and what might explain them?
3) The results indicate that tropical forests have a significant capacity to store biomass. What are the implications of these findings for conservation and climate change mitigation policies? How do these results contribute to the global understanding of the role of tropical forests as carbon sinks?
4) To what extent does this study advance knowledge on the quantification of biomass and carbon in tropical forests? How does it contribute to the development of new methodologies or the improvement of existing methodologies?
5) How can the results of this study influence future research on changes in carbon stocks in tropical forests? Are there gaps that still need to be addressed?
6) What is the impact of this study on understanding the role of tropical forests in carbon sequestration, especially in the context of global climate change?
7) What are the main limitations of the methods used in the study, especially in terms of spatial scale? How might these limitations affect the interpretation of the results?
8) What were the main challenges in quantifying uncertainty associated with the methods associated with different plot sizes and individual trees, and how might this influence the results?
9) Are there any limitations related to the representativeness of the field data about the diversity of tropical forests? How might the lack of representativeness have impacted the results?
Main Scientific Contributions
- The study offers significant contributions to the science of ecology and the understanding of tropical forests as carbon sinks. What are the main methodological innovations presented?
- How does the study advance knowledge about spatial variation of biomass in tropical forests? What new insights does it offer for these forests' conservation and sustainable management?
- How can the results of this study be applied to other tropical regions in addition to the areas studied? Is there potential for replicating the methodologies in other areas or biomes?
I believe that the authors' input on these questions is crucial and that it can significantly contribute to the ongoing discussion of the manuscript. Their responses can guide a critical evaluation of the article, highlighting both its contributions and the areas that can be improved or better explored in future research.
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AC2: 'Reply on RC1', Nicolas Picard, 22 Nov 2024
Methodology
Question 1. Because it partitions the prediction error between bias, plot variability and coefficient variability, we believe that the method we propose is particularly relevant to study how biomass allometry varies when scaling up across different forest types. If we fit an allometric equation to a local forest type and then applies it to another forest with a different structure and species composition, we expect the bias component of MSS to be important. However, when dealing with the heterogeneity of tropical forests, the central question remains to know whether it is worth to address it by introducing in allometric equations additional covariates that explain this heterogeneity, or whether it is enough to leave it as a random noise that will cancel off if the plot is large enough. This question is a question of compromise between bias and variance. Our dataset provides an example of such a compromise linked to species composition. When looking at the tree-level, the model with the best predictive performance is model (21) that fits a different allometry for each species genus. It confirms that different tree genera have different biomass allometries. However, at the scale of the forest where the species composition is not exactly the same as in the calibration dataset, model (21) is also the one that results in the highest bias and the weakest overall predictive performance. The conclusion for this example is that, even there are differences in allometry between tree genera, if our objective is to predict the biomass of large plots, it is statistically more efficient to leave the heterogeneity in species composition as a random noise. We cannot say that this conclusion is general because it is based on our particular dataset. Nevertheless, the methods we provide will allow other people to address such questions in other contexts.
Question 2. We can address the question of the bias arising from the non-representativeness of the sample of trees by using a different dataset. To be more precise, we can fit the allometric equations using a dataset and assess their predictive performance using another dataset. This computation corresponds to the validation case that we discussed in Section 4.2 of the manuscript.
To exemplify this bias, we can fit the allometric equation using the dataset of Fayolle et al. (2018) and assess its predictive performance using the subset of the dataset of Chave et al. (2014) corresponding to the Amazon (with trees coming from Brazil, Colombia, French Guiana and Peru). We may expect indeed central African forests not be representative of Amazonian forests. The following partition of MSS is then obtained for model (20):
This partition of MSS is to be compared to model (20) in Figure 3. The coefficient variability and the plot variability are of the same order for Amazonian forests as for central African forests. However, the bias component is about 30 times bigger for Amazonian forests than for central African forests. This is not a surprise since the allometric equations were fitted using central African trees. Therefore, assessing the predictive performance of the allometric equations on a dataset that is not representative of the forest where the equations were fitted will inflate the role of bias in the overall performance.
We will add these elements in Section 4.2 of the manuscript.
Results, broader implications, and limitations
Questions 1 to 3. These three questions are indeed very important, but we are afraid these questions make sense at geographical scales beyond the forest (landscape, region, country, continent…). Our study deals with the scales between the tree and the forest. The overall objective of our study is to improve the strategy in developing allometric equations, by changing its target. The target of this strategy used to be the minimization of the prediction error at the tree level. Our proposal is to set it as the minimization of the prediction at the plot level. We expect our results to contribute to a better efficiency in the estimation of biomass stocks, but we are not providing actual estimates of biomass stocks. This latter objective would require forest inventory data. Such forest inventory data do exist, but it is out of the scope of our study. We prefer to make it clear, so that there is no misunderstanding between the results we are providing in this manuscript and the results the Reviewer might want to see.
For instance, there is no temporal dimension in our study, for the mere reason that biomass allometry is assumed to be a timeless characteristic of trees, deriving from their biological characteristics only. Changes in forest biomass stocks over time basically result from (1) changes in forest areas, and (2) changes in biomass density. Based on the FAO definition of forests that mainly refer to land use, the former changes (the so-called “activity data” in IPCC’s terminology) are driven by human factors. The latter changes may result from changes in forest structure and composition over time. To address this component of change, we would need forest inventory data at different dates.
This being said, we acknowledge that the objective of our study was not clearly stated in the introduction. We will modify the introduction to better explain it.
Question 4. Our study shows that minimizing the prediction error at the tree level may no not be the most efficient strategy to develop allometric equations when the objective is to assess forest biomass stocks at a large scale (at the forest scale and beyond). As a consequence, introducing additional covariates in the models, with additional measurements costs incurred, may not be needed. Our results may thus contribute to save efforts in measuring tree biomass for the future development of allometric equations. However, the development of allometric equations may be motivated by other objectives than the estimation of forest biomass stocks at large scales. For instance, there may be a theoretical interest in understanding the biological basis of biomass allometry. In that case, the focus will remain on the tree level.
We realize that our manuscript focused too much on the technical aspects of the question and did not explain the more general implication of our results. We will add a sentence in the introduction (line 32) to clarify that the development of new tree biomass allometric equations is still mobilizing a great deal of scientific efforts around the world. We will also add a few sentences in the conclusion to clarify that our results may contribute to be more efficient in these efforts.
Question 5. The question of research gaps on changes in carbon stocks in tropical forests is a very broad question. We here restrict it to the sub-question of the development of allometric equations. The determinants of tree biomass allometry are still not well understood. There is considerable effort in developing new allometric equations around the world (for more species, for more locations). However, with a few exceptions (like the metabolic scaling theory), there is no general theory underlying tree biomass allometry. As a consequence, the various efforts are difficult to aggregate under a common framework.
We will add some sentences in the discussion (after line 285) to clarify that this is a research gap that undermines our understanding of forest biomass stocks.
Question 6. Tropical forests are an important carbon pool at the global level. There are still uncertainties on the quantification of this pool. For instance, there are still major divergent estimates among large-scale biomass maps obtained through remote sensing and field data (Rodda et al., 2024). There are many factors contributing to these uncertainties. At the plot level, the uncertainty on the choice of the allometric equation used to convert inventory data into biomass estimates is one of the greatest sources of error (Picard et al., 2016). Our study contributes to making more informed choices among models.
Question 7. Additional sources of errors could be included in the MSS partition, such as measurement errors. However, previous studies have shown that measurement errors have a minor contribution to the overall biomass prediction error at the plot level (Picard et al., 2015). Therefore, we also expect measurement errors to have a minor influence on our results.
Another limitation of our method is the use of a simulated forest to generate plot data instead of actual forest inventory data. We are not aware of any field data giving the measured biomass of every tree in a forest. Such a dataset probably does not exist given the tremendous cost it would incur, even if LiDAR may change the game in a near future. Therefore, some minimal assumptions are needed to generate large-scale plot biomass data (where biomass is measured, not estimated by a model). At least, a starting point to generate such data could be to use forest inventory data. We could imagine for instance that every tree in the forest inventory data would be assigned the observed biomass of the individual that is closest in size to this tree. Even if tree biomass would not be actual measurements, this process would preserve the shifts in forest structure and species composition that are observed in real forests.
In our study, the bias contribution to MSS is almost independent of plot size (see Figure 2c). We expect this result to change if forest inventory data was used in place of the simulated forest. We would then expect the bias to increase with plot size. Therefore, the relative importance of bias in model selection for large plots would be even greater than it is at present. We thus expect our results to be conservative with respect to the role of bias in model selection.
Question 8. As already said, we are not aware of any dataset giving the measured biomass of every tree in a large plot, not to say a forest. Terrestrial LiDAR may change the game in a near future by providing non-destructive measurement of tree volume for all trees in a plot. We circumvented this issue by resampling measured trees. The bias contribution to MSS may thus have been underestimated in large plots.
Question 9. The method we propose to assess the predictive performance of allometric equations is general and can be applied to any forest. At explained in lines 256-257, the specific ranking of allometric equations is then dependent on the specific forest under study. We could investigate the influence of the forest structure on the model ranking by varying the parameter μ of the simulated forest.
The calibration dataset X has a greater proportion of large trees than the simulated forests F. Therefore, by comparing the bias statistics bX and the bias statistics bF given in Table 1, we can already predict how the model ranking would change if the forest had many large trees. Because the model performance for large plots is driven by the bias component, we expect the model ranking to shift from the ranking of bF to the ranking of bX as the proportion of large trees in the forest increases.
Main scientific contributions
Question 1. The main methodological innovation lies in the strategy to rank and select allometric equations. When the objective is to estimate plot-level biomass, allometric equations should be selected on their bias performance at the forest level rather than on their residual error at the tree level.
Question 2. Our study could contribute to reduce the uncertainty on the model choice that represents an important part of the uncertainty of biomass estimates in tropical forests. The drivers of spatial variation of biomass in tropical forests could then be more easily identified and understood.
Question 3. There is no restriction to apply the method we propose to other tropical regions. On the contrary, we encourage this method to be replicated in other tropical areas and other biomes. We expect the relative importance of bias, plot variability and coefficient variability in model selection to change from one place to another. However, the decreasing importance of plot variability with plot size should be a constant feature.
Additional references
- Picard, F. Boyemba Bosela, and V. Rossi, “Reducing the error in biomass estimates strongly depends on model selection,” Annals of Forest Science, vol. 72, no. 6, pp. 811–823, 2015, doi: 10.1007/s13595-014-0434-9.
- Picard et al., “Error in the estimation of emission factors for forest degradation in central Africa,” Journal of Forest Researc, vol. 21, no. 1, pp. 23–30, 2016, doi: 10.1007/s10310-015-0510-5.
- R. Rodda et al., “LiDAR-based reference aboveground biomass maps for tropical forests of South Asia and Central Africa,” Scientific Data, vol. 11, no. 1, p. 334, 2024, doi: 10.1038/s41597-024-03162-x.
Citation: https://doi.org/10.5194/egusphere-2024-2302-AC2
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AC2: 'Reply on RC1', Nicolas Picard, 22 Nov 2024
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RC2: 'Comment on egusphere-2024-2302', Anonymous Referee #2, 20 Oct 2024
The authors simulated forest plots using a null model based on the field data from central Africa, to test the plot-level predictive performance of a model. This is a valuable study, which statistically proves that the plot level models are applicable to biomass estimation of large plots. However, I believe that three issues need to be addressed before publication.
1. The authors repeatedly assert: "So far, model selection for allometric equations has been performed based on the tree-level predictive performance of the models." This is not entirely true. It suggests that the authors' understanding of the overall situation regarding the application and development of plot level models worldwide is incomplete. In other words, they seem to focus only on the application of the model in developed countries such as Europe and North America, which ignoring its application in the broader context of developing countries. Let me give you an example. In China, both plot level model and the tree level model are used. Plot level models have been used to estimate and predict forest biomass for decades. There is a substantial body of literature on this topic. I only list some papers as follows:
Fang J, Chen A, Peng C, Zhao S, Ci L (2001) Changes in forest biomass carbon storage in China between 1949 and 1998. Science 292:2320–2322
Pan Y, Luo T, Birdsey R, Hom J, Melillo J (2004) New estimates of carbon storage and sequestration in China’s forests: effects of age- class and method on inventory-based carbon estimation. Clim Chang 67:211–236
Fang J, Guo Z, Piao S, Chen A, (2007) Terrestrial vegetation carbon sinks in China, 1981–2000. Science in China Series D: Earth Sciences 50(9):1341–1350
Guo Z, Fang J, Pan Y, Birdsey R (2010) Inventory-based estimates of forest biomass carbon stocks in China: a comparison of three methods. Forest Ecol Manag 259(7):1225–1231
Fang J, Guo Z, Hu H, Kato T, Muraoka H, Son Y, (2014) Forest biomass carbon sinks in East Asia, with special reference to the relative contributions of forest expansion and forest growth. Global Change Biology 20(6):2019–2030.
Fang J, Yu G, Liu L, Hu S, Chapin FS (2018) Climate change, human impacts, and carbon sequestration in China. PNAS 115:4015–4020
The model they used is biomass/volume = BEF = a+b/volime, which is (biomass per hectare) = b +a*(volume per hectare). This is a typical plot-evel model. Beside this kind of linear model, there are also some models using power and polynomial functions, which contain variable DBH and tree height. The reason for using the plot-level model is straightforward. In China, only provincial forest inventory data (forest area and volume for each age group) are released to the public, excluding DBH and tree height data. Consequently, the researchers have to use various plot level models (volume-to-biomass model) to convert from volume to biomass per unit. This data issue is universal, as DBH and tree height data are not released in forest inventory reports in many developing countries. In this manuscript, the application and development of the plot levle model do not align with what the authors describe. I therefore suggest that the authors enhance the review in their manuscript to be comprehensive and avoid the straw man fallacy.
2. Mathematical content takes up too much space. Since this journal is not highly technical, and the potential readers have a broad knowledge background, I recommend including only the most necessary mathematical derivations, expressions, and explanations in the text. The rest can be put into supplementary information. This will improve the readability of the article.
3. Overall, the introduction is lengthy, and the discussion is inadequate. Some descriptions in the Introduction could be moved into the Methods section. In the Discussion, I believe two points need to be mentioned and analyzed.
The first is model structure. From Equation 20 to 24, despite these are certainly sound in their application, Sileshi (A critical review of forest biomass estimation models, common mistakes and corrective measures. For. Ecol. Manag. 329, 237–254. 2014) has pointed out that these equations are problematic in their expression of physiological characteristics of trees. I strongly suggest that the authors touch upon this problem. Although I note that the first author has analyzed this in a previous article, this should not be a reason to avoid the issue in this article.
The second point is about model performance. Judging by the performance of the models, their R^2s are all greater than 0.97 (Table 2). This suggests that there is no significant difference in the application effect of these models. However, if the range of independent variables expands to a certain extent (which is certain in rainforests), the performance of the model may deteriorate, necessitating a different set of parameters. My question is, is the error of predicting small trees with the plot level model and tree level model greater than that of predicting large trees? I suggest that the author increase the discussion of this issue.
Citation: https://doi.org/10.5194/egusphere-2024-2302-RC2 -
AC1: 'Reply on RC2', Nicolas Picard, 22 Nov 2024
Issue 1. We acknowledge that we overlooked BEF methods and other plot-level models in the introduction. We acknowledge too that we overlooked biomass studies from Asia. BEF and other plot-level models necessarily rely on plot-level biomass data for their calibration. Not all studies on BEF and plot-level models clearly indicate how they obtained these biomasses at plot-level. In many cases, plot-level biomass was actually obtained from tree-level measurements and tree-level allometric equations to convert these measurements into biomass. Pan et al. (2004), cited by the Reviewer, proceeded in this way. So did Brown et al. (1989), which is also an often-cited reference on BEF methods. Using allometric equations to derive plot-level biomass is precisely the point we are addressing in our manuscript. If the tree-level allometric equation is biased, so will be the plot-level biomass data obtained from it, and so will be the BEF and plot-level model fitted to these data.
In other words, BEF and plot-level models are not really an alternative to tree-level allometric equation. They are rather an intermediary step to scale up biomass estimates from the tree level to higher levels (plot, forest, region, country, continent…).
We will change the introduction to clarify that in the chain of measurements that starts from the tree and end with remote sensing techniques, there is an additional intermediary step that consists in BEF and plot-level methods. Lines 29 & sqq. will be changed as follows: “Plot-level biomass can be used to fit plot-level models that predict plot biomass from plot volume and other plot characteristics, using biomass expansion factors or related approaches (Pan et al., 2004; Fang et al., 2007; Guo et al., 2010). These plot-level models can then be used to estimate forest biomass at the country (Fang et al., 2007) and continental (Fang et al., 2014) scales. Plot-level biomass can be used too to calibrate remote sensing indices to predict the biomass of pixels in satellite images […]”.
Issue 2. For smoother reading, we will compile the mathematical expressions of the predictive performance statistics in a table that will be merged with Table 1. The new Table 1 will have three columns: statistics; mathematical expression; level (tree, plot or forest). All the equations related to the decomposition of the sum of squared errors (viz. equations (5) to (19)) will be collated and put into supplementary material.
Issue 3. We will streamline the introduction by moving some technical parts (lines 46-48, lines 54-57, and lines 68-72) to the methods section.
As regards the model form, the models we propose are all rooted in the concept of allometry as defined by Huxley & Teissier (1936). It assumes that the relative growth rates of two parts of an individual correlate (Gould, 1966). Models (20) to (23) correspond to simple allometry, where the ratio between relative growth rates is fixed. As discussed by White & Gould (1965), the biologically meaningful parameters are the coefficients associated to covariates. Model (24) correspond to complex allometry, where the relative growth rate of biomass is an increasing function of the relative growth rate of diameter. After back-transformation from the log-transform, model (24) also correspond to a log-normal model. Its parameters correspond to maximal biomass, the diameter where biomass reaches its maximum, and a shape parameter. These parameters also have a biological meaning. As a tree grow, it accumulates biomass as its diameter increases, until it reaches senescence. When senescent, it may lose biomass (because of dead branches, holes in the trunk, etc.) while its diameter still increases.
Apart from allometry, we could have indeed included other families of models that predict tree-level biomass. Geometric models are rooted in the tree taper concept. They predict biomass as wood density times volume, where volume is integrated from a taper equation (Manso et al., 2024). Another family of models emerges from the carbon allocation strategy of trees (Wolf et al., 2011; Yang et al., 2023).
While we agree that biomass models should aim at providing a biological interpretation and relate to theories, we disagree that model fitting should be restricted to those models with a theoretical basis. Theories need to be tested against observations and data, not the other way around.
We will add wording in the Methods section (§2.4) to clarify the biological concepts underlying the model studied. We will also add a paragraph in the discussion (after line 285) to clarify that other families of models could be used, thus contributing to the debate on the biological basis of biomass allometry.
As regards model performance, one way to assess the prediction error when covariates extend beyond the calibration range is to partition the dataset in two subsets depending on tree size, calibrate the allometric equation using one subset, and assess the prediction error using the other dataset. This approach is very similar to what we did in Section 4.2 based on tree height. For instance, we may partition the dataset into the subset X1 of trees with diameter < 48.9 cm and the subset X2 of trees with diameter ≥ 48.9 cm, where 48.9 cm is the median diameter of the dataset. If we use X2 to calibrate the allometric equations and predict the biomass of trees in X1, the following partition of MSS is obtained:
The other way around, if we use X1 to calibrate the allometric equations and predict the biomass of trees in X2, the following partition of MSS is obtained:
Therefore, the error of predicting the biomass of large trees with an allometric equation fitted to small trees is much greater than the error of predicting the biomass of small trees with an allometric equation fitted to large trees. Moreover, the bias is comparatively greater in the former case than in the latter case. There is nothing really new in these results. Due to heteroscedasticity, there is much more variability in tree biomass in large trees than in small trees. Including large trees in biomass datasets is a recommendation that is known for long (Chave et al., 2005). We may include these additional elements in the discussion (Section 4.2) even if, in our view, there is limited interest in doing so.
References (in addition to those cited by the Reviewer)
- Brown, A. J. R. Gillespie, and A. E. Lugo, “Biomass estimation methods for tropical forests with applications to forest inventory data,” Forest Science, vol. 35, no. 4, pp. 881–902, 1989, doi: 10.1093/forestscience/35.4.881.
- Chave et al., “Tree allometry and improved estimation of carbon stocks and balance in tropical forests,” Oecologia, vol. 145, no. 1, pp. 87–99, 2005, doi: 10.1007/s00442-005-0100-x.
- J. Gould, “Allometry and size in ontogeny and phylogeny,” Biological Reviews, vol. 41, no. 4, pp. 587–638, 1966, doi: 10.1111/j.1469-185X.1966.tb01624.x.
- S. Huxley and G. Teissier, “Terminology of relative growth,” Nature, vol. 137, pp. 780–781, 1936, doi: 10.1038/137780b0.
- Manso, A. Price, A. Ash, E. Macdonald, “Volume prediction of young improved Sitka spruce trees in Great Britain through Bayesian model averaging,” Forestry: An International Journal of Forest Research, cpae010, doi: 10.1093/forestry/cpae010
- F. White and S. J. Gould, “Interpretation of the coefficient in the allometric equation,” American Naturalist, vol. 99, no. 904, pp. 5–18, 1965, http://www.jstor.org/stable/2459251
- Wolf, C. B. Field, and J. A. Berry, “Allometric growth and allocation in forests: a perspective from FLUXNET,” Ecological Applications, vol. 21, no. 5, pp. 1546–1556, 2011, doi: 10.1890/10-1201.1.
- Yang et al., “Dynamic carbon allocation trade-off: A robust approach to model tree biomass allometry,” Methods in Ecology and Evolution, vol. 15, no. 5, pp. 886–899, 2024, doi: 10.1111/2041-210X.14315.
Citation: https://doi.org/10.5194/egusphere-2024-2302-AC1
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AC1: 'Reply on RC2', Nicolas Picard, 22 Nov 2024
Interactive discussion
Status: closed
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CC1: 'Comment on egusphere-2024-2302', Robson Borges de Lima, 26 Aug 2024
Review Egusphefe - Selecting allometric equations to estimate forest biomass from plot-rather than individual-level predictive performance
The paper, Selecting allometric equations to estimate forest biomass from plot-rather than individual-level predictive performance, makes significant and relevant contributions to forest biomass estimation, with outstanding strengths. For example, it proposes a robust and innovative method that focuses on the predictive performance of allometric models at the plot level rather than at the individual tree level. This is especially relevant because, in many cases, allometric models are primarily used to estimate biomass in forest plots rather than individual trees. The developed methodology considers that residual errors in individual trees can cancel each other out within a plot, which can affect the accuracy in selecting the most appropriate models. The study proposes a three-term formula that balances bias, residual error, and uncertainty in model coefficients, depending on the plot size. Overall, it is also observed that the novel results highlight that, for small plots, model selection based on tree-level and plot-level performance is consistent. However, for larger plots, this consistency disappears, suggesting that different selection criteria should be applied depending on the scale of the analysis. By offering a more precise approach to selecting allometric equations, the study contributes to improving forest biomass estimates, which is crucial for sustainable forest management and monitoring carbon stocks in the context of climate change. These strengths make the article relevant to the literature, offering practical and methodological solutions to improve the accuracy of biomass estimation in different forest contexts.
In summary, I have no comments that discredit the quality of this manuscript. However, I would like to read the authors' responses to the following questions:
Methodology:
1) Although the study focuses on the giant Congo rainforest, the study employs a detailed approach to estimate biomass in tropical forests using different plot size strategies. Is the methodology used to calibrate and validate the models robust enough for possible different types of tropical forests? How do these methodologies deal with the heterogeneity of tropical forests, which can vary significantly in terms of structure and species composition?
2) Considering that field data collection is essential for model calibration, how was the potential bias from limited or non-representative sampling of different forest areas addressed? Can this be addressed in the manuscript?
Results, broader implications, and limitations of the study:
1) How do the authors interpret the results found regarding spatial and temporal variability of biomass in the studied forests? Is there any indication of changes in biomass stock over time that could be correlated with environmental or anthropogenic factors?
2) Is biomass quantification in line with estimates from similar studies? Can you provide data showing or not showing discrepancies, and what might explain them?
3) The results indicate that tropical forests have a significant capacity to store biomass. What are the implications of these findings for conservation and climate change mitigation policies? How do these results contribute to the global understanding of the role of tropical forests as carbon sinks?
4) To what extent does this study advance knowledge on the quantification of biomass and carbon in tropical forests? How does it contribute to the development of new methodologies or the improvement of existing methodologies?
5) How can the results of this study influence future research on changes in carbon stocks in tropical forests? Are there gaps that still need to be addressed?
6) What is the impact of this study on understanding the role of tropical forests in carbon sequestration, especially in the context of global climate change?
7) What are the main limitations of the methods used in the study, especially in terms of spatial scale? How might these limitations affect the interpretation of the results?
8) What were the main challenges in quantifying uncertainty associated with the methods associated with different plot sizes and individual trees, and how might this influence the results?
9) Are there any limitations related to the representativeness of the field data about the diversity of tropical forests? How might the lack of representativeness have impacted the results?
Main Scientific Contributions
- The study offers significant contributions to the science of ecology and the understanding of tropical forests as carbon sinks. What are the main methodological innovations presented?
- How does the study advance knowledge about spatial variation of biomass in tropical forests? What new insights does it offer for these forests' conservation and sustainable management?
- How can the results of this study be applied to other tropical regions in addition to the areas studied? Is there potential for replicating the methodologies in other areas or biomes?
I believe that the authors' input on these questions is crucial and that it can significantly contribute to the ongoing discussion of the manuscript. Their responses can guide a critical evaluation of the article, highlighting both its contributions and the areas that can be improved or better explored in future research.
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AC3: 'Reply on CC1', Nicolas Picard, 22 Nov 2024
Thanks for these comments. There are a copy of the comments by Reviewer 1, so please see our response to Reviewer 1 at https://doi.org/10.5194/egusphere-2024-2302-AC2.
Citation: https://doi.org/10.5194/egusphere-2024-2302-AC3
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AC3: 'Reply on CC1', Nicolas Picard, 22 Nov 2024
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RC1: 'Comment on egusphere-2024-2302', Anonymous Referee #1, 27 Aug 2024
Review Egusphefe - Selecting allometric equations to estimate forest biomass from plot-rather than individual-level predictive performance
The paper, Selecting allometric equations to estimate forest biomass from plot-rather than individual-level predictive performance, makes significant and relevant contributions to forest biomass estimation, with outstanding strengths. For example, it proposes a robust and innovative method that focuses on the predictive performance of allometric models at the plot level rather than at the individual tree level. This is especially relevant because, in many cases, allometric models are primarily used to estimate biomass in forest plots rather than individual trees. The developed methodology considers that residual errors in individual trees can cancel each other out within a plot, which can affect the accuracy in selecting the most appropriate models. The study proposes a three-term formula that balances bias, residual error, and uncertainty in model coefficients, depending on the plot size. Overall, it is also observed that the novel results highlight that, for small plots, model selection based on tree-level and plot-level performance is consistent. However, for larger plots, this consistency disappears, suggesting that different selection criteria should be applied depending on the scale of the analysis. By offering a more precise approach to selecting allometric equations, the study contributes to improving forest biomass estimates, which is crucial for sustainable forest management and monitoring carbon stocks in the context of climate change. These strengths make the article relevant to the literature, offering practical and methodological solutions to improve the accuracy of biomass estimation in different forest contexts.
In summary, I have no comments that discredit the quality of this manuscript. However, I would like to read the authors' responses to the following questions:
Methodology:
1) Although the study focuses on the giant Congo rainforest, the study employs a detailed approach to estimate biomass in tropical forests using different plot size strategies. Is the methodology used to calibrate and validate the models robust enough for possible different types of tropical forests? How do these methodologies deal with the heterogeneity of tropical forests, which can vary significantly in terms of structure and species composition?
2) Considering that field data collection is essential for model calibration, how was the potential bias from limited or non-representative sampling of different forest areas addressed? Can this be addressed in the manuscript?
Results, broader implications, and limitations of the study:
1) How do the authors interpret the results found regarding spatial and temporal variability of biomass in the studied forests? Is there any indication of changes in biomass stock over time that could be correlated with environmental or anthropogenic factors?
2) Is biomass quantification in line with estimates from similar studies? Can you provide data showing or not showing discrepancies, and what might explain them?
3) The results indicate that tropical forests have a significant capacity to store biomass. What are the implications of these findings for conservation and climate change mitigation policies? How do these results contribute to the global understanding of the role of tropical forests as carbon sinks?
4) To what extent does this study advance knowledge on the quantification of biomass and carbon in tropical forests? How does it contribute to the development of new methodologies or the improvement of existing methodologies?
5) How can the results of this study influence future research on changes in carbon stocks in tropical forests? Are there gaps that still need to be addressed?
6) What is the impact of this study on understanding the role of tropical forests in carbon sequestration, especially in the context of global climate change?
7) What are the main limitations of the methods used in the study, especially in terms of spatial scale? How might these limitations affect the interpretation of the results?
8) What were the main challenges in quantifying uncertainty associated with the methods associated with different plot sizes and individual trees, and how might this influence the results?
9) Are there any limitations related to the representativeness of the field data about the diversity of tropical forests? How might the lack of representativeness have impacted the results?
Main Scientific Contributions
- The study offers significant contributions to the science of ecology and the understanding of tropical forests as carbon sinks. What are the main methodological innovations presented?
- How does the study advance knowledge about spatial variation of biomass in tropical forests? What new insights does it offer for these forests' conservation and sustainable management?
- How can the results of this study be applied to other tropical regions in addition to the areas studied? Is there potential for replicating the methodologies in other areas or biomes?
I believe that the authors' input on these questions is crucial and that it can significantly contribute to the ongoing discussion of the manuscript. Their responses can guide a critical evaluation of the article, highlighting both its contributions and the areas that can be improved or better explored in future research.
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AC2: 'Reply on RC1', Nicolas Picard, 22 Nov 2024
Methodology
Question 1. Because it partitions the prediction error between bias, plot variability and coefficient variability, we believe that the method we propose is particularly relevant to study how biomass allometry varies when scaling up across different forest types. If we fit an allometric equation to a local forest type and then applies it to another forest with a different structure and species composition, we expect the bias component of MSS to be important. However, when dealing with the heterogeneity of tropical forests, the central question remains to know whether it is worth to address it by introducing in allometric equations additional covariates that explain this heterogeneity, or whether it is enough to leave it as a random noise that will cancel off if the plot is large enough. This question is a question of compromise between bias and variance. Our dataset provides an example of such a compromise linked to species composition. When looking at the tree-level, the model with the best predictive performance is model (21) that fits a different allometry for each species genus. It confirms that different tree genera have different biomass allometries. However, at the scale of the forest where the species composition is not exactly the same as in the calibration dataset, model (21) is also the one that results in the highest bias and the weakest overall predictive performance. The conclusion for this example is that, even there are differences in allometry between tree genera, if our objective is to predict the biomass of large plots, it is statistically more efficient to leave the heterogeneity in species composition as a random noise. We cannot say that this conclusion is general because it is based on our particular dataset. Nevertheless, the methods we provide will allow other people to address such questions in other contexts.
Question 2. We can address the question of the bias arising from the non-representativeness of the sample of trees by using a different dataset. To be more precise, we can fit the allometric equations using a dataset and assess their predictive performance using another dataset. This computation corresponds to the validation case that we discussed in Section 4.2 of the manuscript.
To exemplify this bias, we can fit the allometric equation using the dataset of Fayolle et al. (2018) and assess its predictive performance using the subset of the dataset of Chave et al. (2014) corresponding to the Amazon (with trees coming from Brazil, Colombia, French Guiana and Peru). We may expect indeed central African forests not be representative of Amazonian forests. The following partition of MSS is then obtained for model (20):
This partition of MSS is to be compared to model (20) in Figure 3. The coefficient variability and the plot variability are of the same order for Amazonian forests as for central African forests. However, the bias component is about 30 times bigger for Amazonian forests than for central African forests. This is not a surprise since the allometric equations were fitted using central African trees. Therefore, assessing the predictive performance of the allometric equations on a dataset that is not representative of the forest where the equations were fitted will inflate the role of bias in the overall performance.
We will add these elements in Section 4.2 of the manuscript.
Results, broader implications, and limitations
Questions 1 to 3. These three questions are indeed very important, but we are afraid these questions make sense at geographical scales beyond the forest (landscape, region, country, continent…). Our study deals with the scales between the tree and the forest. The overall objective of our study is to improve the strategy in developing allometric equations, by changing its target. The target of this strategy used to be the minimization of the prediction error at the tree level. Our proposal is to set it as the minimization of the prediction at the plot level. We expect our results to contribute to a better efficiency in the estimation of biomass stocks, but we are not providing actual estimates of biomass stocks. This latter objective would require forest inventory data. Such forest inventory data do exist, but it is out of the scope of our study. We prefer to make it clear, so that there is no misunderstanding between the results we are providing in this manuscript and the results the Reviewer might want to see.
For instance, there is no temporal dimension in our study, for the mere reason that biomass allometry is assumed to be a timeless characteristic of trees, deriving from their biological characteristics only. Changes in forest biomass stocks over time basically result from (1) changes in forest areas, and (2) changes in biomass density. Based on the FAO definition of forests that mainly refer to land use, the former changes (the so-called “activity data” in IPCC’s terminology) are driven by human factors. The latter changes may result from changes in forest structure and composition over time. To address this component of change, we would need forest inventory data at different dates.
This being said, we acknowledge that the objective of our study was not clearly stated in the introduction. We will modify the introduction to better explain it.
Question 4. Our study shows that minimizing the prediction error at the tree level may no not be the most efficient strategy to develop allometric equations when the objective is to assess forest biomass stocks at a large scale (at the forest scale and beyond). As a consequence, introducing additional covariates in the models, with additional measurements costs incurred, may not be needed. Our results may thus contribute to save efforts in measuring tree biomass for the future development of allometric equations. However, the development of allometric equations may be motivated by other objectives than the estimation of forest biomass stocks at large scales. For instance, there may be a theoretical interest in understanding the biological basis of biomass allometry. In that case, the focus will remain on the tree level.
We realize that our manuscript focused too much on the technical aspects of the question and did not explain the more general implication of our results. We will add a sentence in the introduction (line 32) to clarify that the development of new tree biomass allometric equations is still mobilizing a great deal of scientific efforts around the world. We will also add a few sentences in the conclusion to clarify that our results may contribute to be more efficient in these efforts.
Question 5. The question of research gaps on changes in carbon stocks in tropical forests is a very broad question. We here restrict it to the sub-question of the development of allometric equations. The determinants of tree biomass allometry are still not well understood. There is considerable effort in developing new allometric equations around the world (for more species, for more locations). However, with a few exceptions (like the metabolic scaling theory), there is no general theory underlying tree biomass allometry. As a consequence, the various efforts are difficult to aggregate under a common framework.
We will add some sentences in the discussion (after line 285) to clarify that this is a research gap that undermines our understanding of forest biomass stocks.
Question 6. Tropical forests are an important carbon pool at the global level. There are still uncertainties on the quantification of this pool. For instance, there are still major divergent estimates among large-scale biomass maps obtained through remote sensing and field data (Rodda et al., 2024). There are many factors contributing to these uncertainties. At the plot level, the uncertainty on the choice of the allometric equation used to convert inventory data into biomass estimates is one of the greatest sources of error (Picard et al., 2016). Our study contributes to making more informed choices among models.
Question 7. Additional sources of errors could be included in the MSS partition, such as measurement errors. However, previous studies have shown that measurement errors have a minor contribution to the overall biomass prediction error at the plot level (Picard et al., 2015). Therefore, we also expect measurement errors to have a minor influence on our results.
Another limitation of our method is the use of a simulated forest to generate plot data instead of actual forest inventory data. We are not aware of any field data giving the measured biomass of every tree in a forest. Such a dataset probably does not exist given the tremendous cost it would incur, even if LiDAR may change the game in a near future. Therefore, some minimal assumptions are needed to generate large-scale plot biomass data (where biomass is measured, not estimated by a model). At least, a starting point to generate such data could be to use forest inventory data. We could imagine for instance that every tree in the forest inventory data would be assigned the observed biomass of the individual that is closest in size to this tree. Even if tree biomass would not be actual measurements, this process would preserve the shifts in forest structure and species composition that are observed in real forests.
In our study, the bias contribution to MSS is almost independent of plot size (see Figure 2c). We expect this result to change if forest inventory data was used in place of the simulated forest. We would then expect the bias to increase with plot size. Therefore, the relative importance of bias in model selection for large plots would be even greater than it is at present. We thus expect our results to be conservative with respect to the role of bias in model selection.
Question 8. As already said, we are not aware of any dataset giving the measured biomass of every tree in a large plot, not to say a forest. Terrestrial LiDAR may change the game in a near future by providing non-destructive measurement of tree volume for all trees in a plot. We circumvented this issue by resampling measured trees. The bias contribution to MSS may thus have been underestimated in large plots.
Question 9. The method we propose to assess the predictive performance of allometric equations is general and can be applied to any forest. At explained in lines 256-257, the specific ranking of allometric equations is then dependent on the specific forest under study. We could investigate the influence of the forest structure on the model ranking by varying the parameter μ of the simulated forest.
The calibration dataset X has a greater proportion of large trees than the simulated forests F. Therefore, by comparing the bias statistics bX and the bias statistics bF given in Table 1, we can already predict how the model ranking would change if the forest had many large trees. Because the model performance for large plots is driven by the bias component, we expect the model ranking to shift from the ranking of bF to the ranking of bX as the proportion of large trees in the forest increases.
Main scientific contributions
Question 1. The main methodological innovation lies in the strategy to rank and select allometric equations. When the objective is to estimate plot-level biomass, allometric equations should be selected on their bias performance at the forest level rather than on their residual error at the tree level.
Question 2. Our study could contribute to reduce the uncertainty on the model choice that represents an important part of the uncertainty of biomass estimates in tropical forests. The drivers of spatial variation of biomass in tropical forests could then be more easily identified and understood.
Question 3. There is no restriction to apply the method we propose to other tropical regions. On the contrary, we encourage this method to be replicated in other tropical areas and other biomes. We expect the relative importance of bias, plot variability and coefficient variability in model selection to change from one place to another. However, the decreasing importance of plot variability with plot size should be a constant feature.
Additional references
- Picard, F. Boyemba Bosela, and V. Rossi, “Reducing the error in biomass estimates strongly depends on model selection,” Annals of Forest Science, vol. 72, no. 6, pp. 811–823, 2015, doi: 10.1007/s13595-014-0434-9.
- Picard et al., “Error in the estimation of emission factors for forest degradation in central Africa,” Journal of Forest Researc, vol. 21, no. 1, pp. 23–30, 2016, doi: 10.1007/s10310-015-0510-5.
- R. Rodda et al., “LiDAR-based reference aboveground biomass maps for tropical forests of South Asia and Central Africa,” Scientific Data, vol. 11, no. 1, p. 334, 2024, doi: 10.1038/s41597-024-03162-x.
Citation: https://doi.org/10.5194/egusphere-2024-2302-AC2
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AC2: 'Reply on RC1', Nicolas Picard, 22 Nov 2024
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RC2: 'Comment on egusphere-2024-2302', Anonymous Referee #2, 20 Oct 2024
The authors simulated forest plots using a null model based on the field data from central Africa, to test the plot-level predictive performance of a model. This is a valuable study, which statistically proves that the plot level models are applicable to biomass estimation of large plots. However, I believe that three issues need to be addressed before publication.
1. The authors repeatedly assert: "So far, model selection for allometric equations has been performed based on the tree-level predictive performance of the models." This is not entirely true. It suggests that the authors' understanding of the overall situation regarding the application and development of plot level models worldwide is incomplete. In other words, they seem to focus only on the application of the model in developed countries such as Europe and North America, which ignoring its application in the broader context of developing countries. Let me give you an example. In China, both plot level model and the tree level model are used. Plot level models have been used to estimate and predict forest biomass for decades. There is a substantial body of literature on this topic. I only list some papers as follows:
Fang J, Chen A, Peng C, Zhao S, Ci L (2001) Changes in forest biomass carbon storage in China between 1949 and 1998. Science 292:2320–2322
Pan Y, Luo T, Birdsey R, Hom J, Melillo J (2004) New estimates of carbon storage and sequestration in China’s forests: effects of age- class and method on inventory-based carbon estimation. Clim Chang 67:211–236
Fang J, Guo Z, Piao S, Chen A, (2007) Terrestrial vegetation carbon sinks in China, 1981–2000. Science in China Series D: Earth Sciences 50(9):1341–1350
Guo Z, Fang J, Pan Y, Birdsey R (2010) Inventory-based estimates of forest biomass carbon stocks in China: a comparison of three methods. Forest Ecol Manag 259(7):1225–1231
Fang J, Guo Z, Hu H, Kato T, Muraoka H, Son Y, (2014) Forest biomass carbon sinks in East Asia, with special reference to the relative contributions of forest expansion and forest growth. Global Change Biology 20(6):2019–2030.
Fang J, Yu G, Liu L, Hu S, Chapin FS (2018) Climate change, human impacts, and carbon sequestration in China. PNAS 115:4015–4020
The model they used is biomass/volume = BEF = a+b/volime, which is (biomass per hectare) = b +a*(volume per hectare). This is a typical plot-evel model. Beside this kind of linear model, there are also some models using power and polynomial functions, which contain variable DBH and tree height. The reason for using the plot-level model is straightforward. In China, only provincial forest inventory data (forest area and volume for each age group) are released to the public, excluding DBH and tree height data. Consequently, the researchers have to use various plot level models (volume-to-biomass model) to convert from volume to biomass per unit. This data issue is universal, as DBH and tree height data are not released in forest inventory reports in many developing countries. In this manuscript, the application and development of the plot levle model do not align with what the authors describe. I therefore suggest that the authors enhance the review in their manuscript to be comprehensive and avoid the straw man fallacy.
2. Mathematical content takes up too much space. Since this journal is not highly technical, and the potential readers have a broad knowledge background, I recommend including only the most necessary mathematical derivations, expressions, and explanations in the text. The rest can be put into supplementary information. This will improve the readability of the article.
3. Overall, the introduction is lengthy, and the discussion is inadequate. Some descriptions in the Introduction could be moved into the Methods section. In the Discussion, I believe two points need to be mentioned and analyzed.
The first is model structure. From Equation 20 to 24, despite these are certainly sound in their application, Sileshi (A critical review of forest biomass estimation models, common mistakes and corrective measures. For. Ecol. Manag. 329, 237–254. 2014) has pointed out that these equations are problematic in their expression of physiological characteristics of trees. I strongly suggest that the authors touch upon this problem. Although I note that the first author has analyzed this in a previous article, this should not be a reason to avoid the issue in this article.
The second point is about model performance. Judging by the performance of the models, their R^2s are all greater than 0.97 (Table 2). This suggests that there is no significant difference in the application effect of these models. However, if the range of independent variables expands to a certain extent (which is certain in rainforests), the performance of the model may deteriorate, necessitating a different set of parameters. My question is, is the error of predicting small trees with the plot level model and tree level model greater than that of predicting large trees? I suggest that the author increase the discussion of this issue.
Citation: https://doi.org/10.5194/egusphere-2024-2302-RC2 -
AC1: 'Reply on RC2', Nicolas Picard, 22 Nov 2024
Issue 1. We acknowledge that we overlooked BEF methods and other plot-level models in the introduction. We acknowledge too that we overlooked biomass studies from Asia. BEF and other plot-level models necessarily rely on plot-level biomass data for their calibration. Not all studies on BEF and plot-level models clearly indicate how they obtained these biomasses at plot-level. In many cases, plot-level biomass was actually obtained from tree-level measurements and tree-level allometric equations to convert these measurements into biomass. Pan et al. (2004), cited by the Reviewer, proceeded in this way. So did Brown et al. (1989), which is also an often-cited reference on BEF methods. Using allometric equations to derive plot-level biomass is precisely the point we are addressing in our manuscript. If the tree-level allometric equation is biased, so will be the plot-level biomass data obtained from it, and so will be the BEF and plot-level model fitted to these data.
In other words, BEF and plot-level models are not really an alternative to tree-level allometric equation. They are rather an intermediary step to scale up biomass estimates from the tree level to higher levels (plot, forest, region, country, continent…).
We will change the introduction to clarify that in the chain of measurements that starts from the tree and end with remote sensing techniques, there is an additional intermediary step that consists in BEF and plot-level methods. Lines 29 & sqq. will be changed as follows: “Plot-level biomass can be used to fit plot-level models that predict plot biomass from plot volume and other plot characteristics, using biomass expansion factors or related approaches (Pan et al., 2004; Fang et al., 2007; Guo et al., 2010). These plot-level models can then be used to estimate forest biomass at the country (Fang et al., 2007) and continental (Fang et al., 2014) scales. Plot-level biomass can be used too to calibrate remote sensing indices to predict the biomass of pixels in satellite images […]”.
Issue 2. For smoother reading, we will compile the mathematical expressions of the predictive performance statistics in a table that will be merged with Table 1. The new Table 1 will have three columns: statistics; mathematical expression; level (tree, plot or forest). All the equations related to the decomposition of the sum of squared errors (viz. equations (5) to (19)) will be collated and put into supplementary material.
Issue 3. We will streamline the introduction by moving some technical parts (lines 46-48, lines 54-57, and lines 68-72) to the methods section.
As regards the model form, the models we propose are all rooted in the concept of allometry as defined by Huxley & Teissier (1936). It assumes that the relative growth rates of two parts of an individual correlate (Gould, 1966). Models (20) to (23) correspond to simple allometry, where the ratio between relative growth rates is fixed. As discussed by White & Gould (1965), the biologically meaningful parameters are the coefficients associated to covariates. Model (24) correspond to complex allometry, where the relative growth rate of biomass is an increasing function of the relative growth rate of diameter. After back-transformation from the log-transform, model (24) also correspond to a log-normal model. Its parameters correspond to maximal biomass, the diameter where biomass reaches its maximum, and a shape parameter. These parameters also have a biological meaning. As a tree grow, it accumulates biomass as its diameter increases, until it reaches senescence. When senescent, it may lose biomass (because of dead branches, holes in the trunk, etc.) while its diameter still increases.
Apart from allometry, we could have indeed included other families of models that predict tree-level biomass. Geometric models are rooted in the tree taper concept. They predict biomass as wood density times volume, where volume is integrated from a taper equation (Manso et al., 2024). Another family of models emerges from the carbon allocation strategy of trees (Wolf et al., 2011; Yang et al., 2023).
While we agree that biomass models should aim at providing a biological interpretation and relate to theories, we disagree that model fitting should be restricted to those models with a theoretical basis. Theories need to be tested against observations and data, not the other way around.
We will add wording in the Methods section (§2.4) to clarify the biological concepts underlying the model studied. We will also add a paragraph in the discussion (after line 285) to clarify that other families of models could be used, thus contributing to the debate on the biological basis of biomass allometry.
As regards model performance, one way to assess the prediction error when covariates extend beyond the calibration range is to partition the dataset in two subsets depending on tree size, calibrate the allometric equation using one subset, and assess the prediction error using the other dataset. This approach is very similar to what we did in Section 4.2 based on tree height. For instance, we may partition the dataset into the subset X1 of trees with diameter < 48.9 cm and the subset X2 of trees with diameter ≥ 48.9 cm, where 48.9 cm is the median diameter of the dataset. If we use X2 to calibrate the allometric equations and predict the biomass of trees in X1, the following partition of MSS is obtained:
The other way around, if we use X1 to calibrate the allometric equations and predict the biomass of trees in X2, the following partition of MSS is obtained:
Therefore, the error of predicting the biomass of large trees with an allometric equation fitted to small trees is much greater than the error of predicting the biomass of small trees with an allometric equation fitted to large trees. Moreover, the bias is comparatively greater in the former case than in the latter case. There is nothing really new in these results. Due to heteroscedasticity, there is much more variability in tree biomass in large trees than in small trees. Including large trees in biomass datasets is a recommendation that is known for long (Chave et al., 2005). We may include these additional elements in the discussion (Section 4.2) even if, in our view, there is limited interest in doing so.
References (in addition to those cited by the Reviewer)
- Brown, A. J. R. Gillespie, and A. E. Lugo, “Biomass estimation methods for tropical forests with applications to forest inventory data,” Forest Science, vol. 35, no. 4, pp. 881–902, 1989, doi: 10.1093/forestscience/35.4.881.
- Chave et al., “Tree allometry and improved estimation of carbon stocks and balance in tropical forests,” Oecologia, vol. 145, no. 1, pp. 87–99, 2005, doi: 10.1007/s00442-005-0100-x.
- J. Gould, “Allometry and size in ontogeny and phylogeny,” Biological Reviews, vol. 41, no. 4, pp. 587–638, 1966, doi: 10.1111/j.1469-185X.1966.tb01624.x.
- S. Huxley and G. Teissier, “Terminology of relative growth,” Nature, vol. 137, pp. 780–781, 1936, doi: 10.1038/137780b0.
- Manso, A. Price, A. Ash, E. Macdonald, “Volume prediction of young improved Sitka spruce trees in Great Britain through Bayesian model averaging,” Forestry: An International Journal of Forest Research, cpae010, doi: 10.1093/forestry/cpae010
- F. White and S. J. Gould, “Interpretation of the coefficient in the allometric equation,” American Naturalist, vol. 99, no. 904, pp. 5–18, 1965, http://www.jstor.org/stable/2459251
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Citation: https://doi.org/10.5194/egusphere-2024-2302-AC1
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AC1: 'Reply on RC2', Nicolas Picard, 22 Nov 2024
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Nicolas Picard
Noël Fonton
Faustin Boyemba Bosela
Adeline Fayolle
Joël Loumeto
Gabriel Ngua Ayecaba
Bonaventure Sonké
Olga Diane Yongo Bombo
Hervé Martial Maïdou
Alfred Ngomanda
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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