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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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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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
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