the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Contextualizing Pan-Tropical Allometric Models for Biomass Estimation
Abstract. Allometric Models (AMs) play a central role in monitoring and mitigating climate change as they provide accurate estimation of biomass and carbon sequestered by trees from non-destructive, easy to obtain physical measurements. Unfortunately, practitioners spend considerable effort in researching, qualifying and choosing AMs for specific growth conditions. To overcome this situation Chave et al. (2014) developed a pan-tropical AM with equivalent accuracy to local, site-specific AMs. We ameliorate this result by incorporating contextual information pertaining to growth conditions in a Machine Learning (ML) model, eventually achieving a reduction in Mean Average Error (MAE) of -17 % as measured on hold-out data. This breakthrough shall have important impact in applications such as national forest inventories, carbon certifications and calibration of satellite based biomass maps to field data. To complete, we propose a principled method to estimate how much additional error one can expect when applying a given AM to shifting conditions and provide a data-driven safety check to practitioners.
Status: open (until 28 Mar 2026)
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RC1: 'Comment on egusphere-2025-6341', Anonymous Referee #1, 22 Feb 2026
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AC1: 'Reply on RC1', Eustache Diemert, 18 Mar 2026
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We thank Anonymous Referee 1 for their review RC1 and answer remarks and concerns on the following topics: contribution areas, intended readership, and significance of the work.
NB: [x] designates additional references in this answer whereas (author, year) refers to manuscript references.
Contribution Areas
We’d like to recall that - as described in the abstract - this paper proposes 2 main contributions:
- #1: a more precise pan-tropical allometric model
- #2: a method to predict the suitability of a given allometric model to new application conditions.
First of all, we remark that the five potential contribution types listed by RC1 only apply to contribution #1. Out of these 5 areas, our work targets (2) better representation of growth conditions, (3) correct evaluation of new models and (4) precision improvements over previous generation of models. We disagree with RC1 that only assumes our contribution to target (4). On (2), as described in Section 2.2 we recall that our proposed model does incorporate better representation of 5 important ecological factors: continent, primary vs secondary forest, forest type, altitude, rainfall and dry months. These factors are all missing in the baseline model from Chave and it is thus biologically plausible that incorporating them would increase precision of predictions. On (3), as described in Section 2.2.2 we perform a 30 random splits cross-validation and report 3 error metrics on both training and testing parts. This method is standard for evaluation Machine Learning (ML) models and produces valid confidence intervals that capture randomness of the data and of model coefficients. The work from (Sileshi 2014), while important in classical forestry modelling is not applicable to ML models directly as they are over-parametrized and thus traditional goodness of fit statistics are too easy to overfit. We would be curious to understand how our procedure can be criticized or improved when assessing ML based allometric models. As an example, [2] uses the same metrics and a near identical experimental procedure to assess ML models prediction quality on a related AGB estimation problem.
Finally, we assume that a valid contribution may only tackle some (in our case 3) of the 5 areas pointed by RC1. In our view interesting research may contribute to only some of these goals and still be scientifically sound and worth disseminating in the community.
On our contribution #2 (method for assessing suitability of an allometric model to new conditions), we agree with RC1 that our contribution #2 tackles “an important problem”. We would have hoped that this contribution would be more discussed in this review as it has important methodological implications for the community. Contrarily to what RC1 reports this contribution is announced in the last part of the abstract and highlighted clearly in the Introduction p.2 l.30.
Intended Readership
We selected BGU BioGeosciences (BG) journal because of the declared focus on “cutting across the boundaries of established sciences and achieve an interdisciplinary view of the interactions [between the biological, chemical, and physical processes …]”. In that respect we expect the readership of this journal to be far more extensive than the Forestry practitioners community that RC1 assumes to be the only potential target. We note that methodologically heavy papers tackling a problem close to our contribution #2 seem to have found their audience in this journal [1].
Our intention at the onset has been to introduce recent statistical learning techniques to the established field of allometry research. In that respect we expect our work to be of interest firstly to forward looking scientists and researchers aiming to modernize the field and apply novel ideas and techniques to important, established problems (especially contribution #2). Forestry practitioners with “no prior knowledge in statistical learning methods” (quoting RC1) is not our primary target as we agree that such readers would value less theoretical developments and more practical examples based on established theory. We note though that a quick search returns 496 papers using ML techniques in EGU and BG journals indicating an interested readership exists in this venue. More broadly we noted in the Introduction of the paper recent development of ML based allometric models, see (Dutta Roy and Debbarma, 2024; Wongchai et al., 2022) for instance.
We are also not at ease with the comment of RC1 that we wrote this paper “presumably motivated by the fact to reach out […] to clients, also, given the competing interests”. We declared our potential conflicts of interest in good faith and we assume that relevant, solid scientific work can (and arguably should, in a number of cases) be funded by private organizations. In any case this assertion is not falsifiable and should thus not appear in a scientific debate over the merits of a given piece of research work. To complete, we noted p.8 l.28 that our work - when applied to carbon sequestration projects - would imply to emit less carbon credits than the baseline from Chave (see also Figure 4). We don’t see how this could be of mercantile benefit to our employer or to its clients either. Nor do we see how RC1 comment could shed light on the soundness and relevance of our contributions.
Moreover, another assertion of RC1 seems overly antagonistic: “the whole text is full of technicalities that serve no other apparent purpose than making an impression on the non-specialized reader”. Again, this assertion is not falsifiable and should not be brought in scientific debate. In the contrary, we make a point of giving enough details so that readers with good enough knowledge of statistical learning can assess our methods and reproduce our experiments. Technically heavy sections such as 2.3.1 and 2.3.2 are necessary to explain the mathematical foundations of the work, in particular when it comes to transfer learning theory that underpins the development of the model that predicts suitability of an allometric equation to new conditions. Likewise in Section 2.2.1, for the sake of reproducible science we are bound to give enough details so that a trained practitioner can reproduce our experimental results in whatever programming language or computing environment that she chooses to use. We believe that RC1 has his/her own readership in mind but that appears to give a somewhat particular angle on the contributions of the papers, ignoring methodological contributions that would appeal to a larger, more fundamentally inclined or technically savvy audience.
Significance - Contribution #1: a more precise pan-tropical allometric model
We disagree with RC1 on the notion that “none of these complex models perform so well in a cross-validation test relative to the baseline”. In fact, Table 3 shows that the proposed COFARM-NN model improves upon the Chave baseline on all 3 metrics (R2, RMSE, MAE) with improvements in MAE of 17% and 14% in RMSE. Moreover, the calibration curve on Figure 4 explicitly demonstrates that the proposed model consistently makes less errors than the baseline on all tree sizes. We could debate endlessly about how much error reduction would be necessary to make a “substantial improvement”, yet the reported experiments show i) statistical significance ii) consistency over AGB ranges iii) double digit relative magnitude of the improvement with the proposed model. We also note that, indeed, some complex models such as HGBRT perform just on par with the Chave baseline, indicating that more complex models are not sufficient per se but rather that incorporation of relevant ecological information should be designed carefully to provide precision benefits. Simpler power models with access to the same information such as ContextualChave improve MAE by 7% only, confirming that the proposed COFARM-NN model more than doubles the benefits of incorporating additional ecological information compared to traditional approaches. In our view these two examples provide a sharp contrast and help to grasp the significance of the proposed model.
An interesting discussion related to RC1 comment and that we could emphasize more pertains to the tradeoff between model complexity and improved precision. ContextualChave has 7 parameters (Equation 3) and improves MAE by 7%, COFARM model has 28 parameters and improves MAE by 14%, COFARM-NN model has 132 parameters (Figure 3) and improves MAE by 17% whereas. All models may be seen as frugal by modern standards and are tractable to learn and use even on a low-end laptop computer. Ultimately we believe users may prefer different options based on non quantitative aspects such as explainability. In any case this work offers a number of options to practitioners and researchers that improve over existing baselines.
Significance - Contribution #2: a method to predict the suitability of a given allometric model to new application conditions
Again, we would have hoped a more thorough review of this contribution. We believe RC1 misses the significance of our results. The remark that “In practice, Table 2 only demonstrates that some covariates are significant predictors in the regression exercise” is misleading: Table 2 describes the experimental setup and not the results of the experiments. In that respect the relevant information from Table 2 is that different kind of shifts in growth conditions (such as eg when applying an allometric equation developed for a Dry Forest to a Moist Forest) produce different magnitudes of shift in the data distribution. To the best of our knowledge the fact that shifts in the data distribution (i.e. tree measurements) are informative of the additional biomass prediction error when applying an allometric equation to a new site is a novel result never heard of in the allometry literature. Moreover, the success of the additional prediction error model can be observed in Figure 5 where predicted additional errors and observed additional errors are compared for a variety of shifts in altitude, continent, dry months, forest type, rainfall and random controls. The fact that we can achieve a R2 of 0.832 when predicting this additional error is in our view a major feat and non trivial finding. What it means is that for the first time in our knowledge practitioners have a reliable, data driven procedure to quantify the suitability of a given allometric model to new sites. This is illustrated in a graphical manner in Figure 6 and discussed in Section 4.3.1.
Additional References
[1] Picard et al. 2025 “Selecting allometric equations to estimate forest biomass from plot rather than individual-level predictive performance”, in BG, 22, 1413–1426, 2025
[2] Contreras et al. 2025 “Multi-source remote sensing for large-scale biomass estimation in Mediterranean olive orchards using GEDI LiDAR and machine learning”, in BG, 22, 7625–7646, 2025
Citation: https://doi.org/10.5194/egusphere-2025-6341-AC1
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AC1: 'Reply on RC1', Eustache Diemert, 18 Mar 2026
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AC2: 'Proposed Manuscript Update', Eustache Diemert, 18 Mar 2026
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After reviewing Anonymous Referee 1 comments we propose to improve the following:
- add a discussion on model complexity vs improved precision in Section 3.1
- add a link to the open source code of the experiments at the start of Section 3 -> https://github.com/PUR-Projet/contextual_allometric_models
Citation: https://doi.org/10.5194/egusphere-2025-6341-AC2
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Biomass estimation models are used to estimate tree biomass from simple physical measurements, but choosing the right model for specific conditions is difficult. This paper reanalyzes a global dataset by developing a machine learning model. The resulting model is claimed to be much improved as it reduces prediction error by 17%. Improved biomass estimation models should be based on (1) larger sample sizes, (2) a better representation of a wider range of real-life conditions. Also, developers should ensure that (3) the resulting models are correctly evaluated using the proper goodness of fit methods (Sileshi 2014), and (4) minimize the goodness of fit and show significant improvements over the previous generation of models. Finally they should ensure that (5) they are easy to implement for a wide range of practitioners (including private owners, forestry consultants, academics, and businesses), and the conditions of their use is clearly stated.
This paper address one of the five goals, namely goal 4. It does nothing to address the crucial aspects (1) and (2), and the practical implementation of the method (condition 5) is likely to be more complex rather than simpler. Code availability in Python but also R is not reported, and the fact that the authors have competing interest in this development may explain this situation. Unfortunately, it is unlikely that this manuscript will make a valuable addition in the academic literature. Below are major issues with this study, none of which, unfortunately, is fixable with a minor revision of the text.
First, the argument that including more predictors in a statistical model generally improves its fit to observed data is as old as regression theory. Because the problem at hand is simple (non-linear regression of a single predicted variable), it makes it clear that adding environmental variables as predictors improves the fit. That model (3), vastly more complex that model (1), leads to a reduction of only 17% of the MAE should raise the question of whether this tremendous increase in complexity is worth the effort. There is no clear answer to this question in this manuscript because it is predicated on the assumption that the 4004-tree dataset encapsulates the full universe of possibles. This is a serious shortcoming. In fact, looking at the main result, the 17% reduction in MAE, this result is reported in Table 3. It is shown that none of these complex models perform so well in a cross-validation test relative to the baseline reported in the first column. Gains in RMSE and MAE are at best modest, so this method is better seem as a proof of concept rather than a breakthrough result for biomass regression models.
Second, the text is written for an audience of data scientists, and it misses its potential audience. For a readership with a training in data science, this study is an application of established methods. It may be of interest for the data science community precisely because it is so simple, and which case the manuscript should be submitted to a journal of statistical learning. The intention to submit to Biogeosciences is presumably motivated by the fact to reach out to the user community (and to clients, also, given the competing interests). Users (foresters, or private actors) will however likely find this text totally opaque. Section 2.2.1 is a case in point ("context-agnostic baselines", "we adjunct a L2 regularization", "hyper-parameter optimization", "target encoding") but the whole text is full of technicalities that serve no other apparent purpose than making an impression on the non-specialized reader. If the goal is to reach out to the user community, the recommendation is to take a radically different approach and explain each and every step, assuming no prior knowledge in statistical learning methods. This would imply to drastically cut down the material presented, to provide worked-out examples of applications, and most importantly to make fully open access all the methods and scripts (both in Python and R, the latter being a more go-to language in the foresty community).
Third and last, section 2.3 is seeks to explore situations where a biomass regression model may be applied outside of condition where it was calibrated. In principle this is an important problem. In practice, Table 2 only demonstrates that some covariates are significant predictors in the regression exercise, which was the assumption at the outset. Notably, none of this is reported in this abstract. It would take more practical case studies for this theoretical section to be a convincing addition to the literature on biomass estimation models.