# Parsimonious machine learning for the global mapping of aboveground biomass potential

Diego Bengochea Paz, Alba Marquez-Torres, João Pompeu, Olivier

Martin-Ducup, Ferdinando Villa, Carmen Köhler, Stefano Balbi

► To cite this version:

Diego Bengochea Paz, Alba Marquez-Torres, João Pompeu, Olivier Martin-Ducup, Ferdinando Villa, et al.. Parsimonious machine learning for the global mapping of aboveground biomass potential. Ecography, 2025, 2025 (7), pp.e07587. 10.1111/ecog.07587. hal-05017757

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ECOGRAPHY

Research article

Parsimonious machine learning for the global mapping of
aboveground biomass potential

Diego Bengochea Paz<fnref n="1" />,<fnref n="2" />, Alba Marquez-Torres<fnref n="1" />,<fnref n="3" />,<fnref n="4" />, João Pompeu<fnref n="1" />,<fnref n="5" />,<fnref n="6" />, Olivier Martin-Ducup<fnref n="7" />,<fnref n="8" />,
Ferdinando Villa<fnref n="1" />, Carmen Köhler<fnref n="1" /> and Stefano Balbi<fnref n="1" />

**Correspondence:** Diego Bengochea Paz (diego.bengoche@mncn.csic.es)

Ecography

2025: e07587

doi: 10.1111/ecog.07587

Subject Editor: Kenneth Feeley

Editor-in-Chief:
Christine N. Meynard

Accepted 05 February 2025

<figure><img src="image_3.png" /></figure>

Advances in computational power and methods, and the widespread availability of remote sensing data have driven the development of machine learning models for estimating global carbon storage. Current models often rely on dozens of predictor variables to estimate aboveground biomass density (AGBD), resulting in accurate but complex models that are challenging to interpret from a biological and ecological standpoint. Yet, it remains unclear whether such model complexity is essential to achieving accurate predictions. This manuscript investigates the potential to create a simpler, yet accurate, global AGBD model. Our approach leverages only climate-based predictors, using a systematic predictor selection process to determine the optimal subset of variables that maximize model accuracy. Surprisingly, we found that a minimal model trained with only four bioclimatic variables outperformed more complex models. When compared to a state-of-the-art complex model and ground-based data, our model achieved comparable accuracy using only four predictors, far fewer than the 186 predictors used in the complex model. In conclusion, we present a lightweight, interpretable climate-based model for AGBD estimation, with the additional advantage of being adaptable for projecting AGBD under future climate scenarios.

Keywords: Aboveground biomass, carbon cycle, carbon stocks, climate change, ecological modelling, machine learning

<figure><img src="image_4.png" /></figure>

<footnote n="1">¹Basque Center for Climate Change (BC3), Science Park UPV-EHU, Leioa, Spain</footnote>

<footnote n="2">²Department of Biogeography and Global Change, National Museum of Natural Sciences (MNCN), CSIC, Madrid, Spain</footnote>

<footnote n="3">³Department of Agricultural and Forest Sciences and Engineering, University of Lleida, Lleida, Spain</footnote>

<footnote n="4">⁴Forest Science and Technology Centre of Catalonia (CTFC), Solsona, Spain</footnote>

<footnote n="5">⁵Center for Nuclear Energy in Agriculture (CENA), University of São Paulo (USP), Piracicaba, Brazil</footnote>

<footnote n="6">⁶National Institute for Space Research (INPE), São José dos Campos, Brazil</footnote>

<footnote n="7">⁷CIRAD, UMR AMAP, Montpellier, France</footnote>

<footnote n="8">⁸AMAP, CIRAD, CNRS, INRAE, IRD, Université de Montpellier, Montpellier, France</footnote>
Introduction

Forests and woodlands hold a significant portion of the Earth's terrestrial carbon, making them essential to regulating the global carbon cycle and climate system. However, shifts in climate and land use are altering the carbon storage capacity of woody vegetation, impacting forest ecosystem functions and intensifying atmospheric greenhouse gas concentrations (Mitchard 2018, Friedlingstein et al. 2024). Accurate global mapping of carbon storage in woody vegetation is crucial for assessing current baselines and identifying key carbon sequestration hotspots. Additionally, estimating the global carbon storage potential is vital for identifying gaps and guiding restoration and conservation priorities, thereby supporting more effective climate mitigation strategies (Chiti et al. 2024).

Advances in machine learning (ML) and the widespread availability of open-access remote-sensing data have catalyzed the development of data-driven models for estimating aboveground biomass density (AGBD), a key observable for calculating carbon storage (Saatchi et al. 2011, Baccini et al. 2012, Harris et al. 2021, Walker et al. 2022, Mo et al. 2023). By capturing empirical relationships between AGBD and environmental factors or satellite imagery, ML models present a computationally efficient alternative to complex mechanistic models, which traditionally simulate detailed ecological, physiological and phenological processes for AGBD estimation (Schaphoff et al. 2006, Zaehle et al. 2007, Gustafson et al. 2018, Miquelajauregui et al. 2019, Zhao et al. 2020, Wang et al. 2022, Wu et al. 2023). By reducing computational demands, ML models streamline and accelerate the creation of high-resolution, global AGBD maps, making it more feasible to monitor carbon storage dynamics across Earth's ecosystems.

Data-driven modeling of AGBD requires first compiling AGBD data to serve as training instances, followed by selecting predictor variables as the basis for model learning. Most training instances are derived from allometric relationships that link canopy height, estimated through geospatial LiDAR, with the AGBD of the measured forest stand (Saatchi et al. 2011, Baccini et al. 2012, Harris et al. 2021, Duncanson et al. 2022, Walker et al. 2022). More recent studies have also incorporated ground-based data from exhaustive forest inventories to build the training dataset (Mo et al. 2023). In terms of predictor selection, early models relied on satellite imagery (Saatchi et al. 2011, Baccini et al. 2012), while recent studies have included a broader set of variables, such as climate, soil, topography and human-related factors (Harris et al. 2021, Walker et al. 2022, Mo et al. 2023). The inclusion of satellite imagery as covariates has been particularly beneficial in improving prediction accuracy (Baccini et al. 2012). Moreover, satellite-based models facilitate near-real-time monitoring of AGBD across large spatial areas with high spatio-temporal resolution. However, these models have notable caveats: they do not offer insights into the biological factors driving AGBD, nor can they project changes in AGBD in response to global environmental shifts. This restricts their utility in formulating long-term climate change mitigation strategies.

Effective climate change mitigation planning requires mapping both existing and potential AGBD storage to identify unrealized hot spots. Recent studies have addressed this by developing data-driven models for potential AGBD (Walker et al. 2022, Mo et al. 2023). Here, potential AGBD refers to the biomass density that would exist in the absence of significant human disturbances. By comparing current and potential AGBD, these models estimate the carbon sequestration potential achievable through nature-based solutions, such as forest restoration and conservation, for climate mitigation. These models, based on climate, soil and topographic predictors, aim to reduce prediction biases caused by human disturbance effects embedded in the training data. Two main approaches have been adopted: Walker et al. (2022) filtered the training dataset to exclude data from young or disturbed forests, while Mo et al. (2023) included human footprint predictors in model training but controlled for these effects during prediction. Despite this methodological variation, both studies share a reliance on dozens of predictors – 186 in Walker et al. (2022) and 49 in Mo et al. (2023) – which results in complex yet accurate models. The explainability of such models is limited, and the necessity of including so many variables for similar predictive quality remains untested. Recent methodological advances have enabled better interpretation of ML models’ results by providing tools to quantify the effects of individual predictors and their interactions on model outcomes (Barredo Arrieta et al. 2020, Linardatos et al. 2021). However, the usefulness of explainability metrics is hindered by a sheer number of predictors, as the possible interactions between predictors that need to be grasped by the human mind grow exponentially – a phenomenon known as the curse of dimensionality (Altman and Krzywinski 2018). Although this complexity does not necessarily impair prediction accuracy, it poses a significant barrier to model understanding and interpreting results from ML models.

In this manuscript, we adhere to the principle of parsimony to develop a simple yet accurate model for estimating global potential AGBD using only climate predictors. Like Walker et al. (2022) and Mo et al. (2023), by potential AGBD we refer to the biomass density predicted in the absence of significant human disturbances, such as land-use. To construct our AGBD training dataset, we leveraged non-exhaustive forest inventory data from the unique, open-access global database of tree-size measurements (Jucker et al. 2022), setting our work apart from previous studies (Walker et al. 2022, Mo et al. 2023). We employed a gradient-boosting machine learning model (XGBR; Chen and Guestrin 2016) and calibrated it using a systematic predictor-selection process based on evolutionary algorithms (NSGA-II; Deb et al. 2002). From an initial set of 20 bioclimatic variables (Brun et al. 2022), we identified an optimal subset of only four, which yielded the most accurate predictions. To validate our approach, we assessed our model's performance by comparing its ability to reproduce ground-based AGBD data from biomass reference measurement sites (GEOTREES; Shchepashchenko et al. 2019) against
a state-of-the-art, complex model (Walker et al. 2022). Our results showed no statistically significant difference in accuracy between our parsimonious model, trained with only five predictors – four climatic variables and a human footprint variable – and the complex model, which utilized 186 predictors. This work serves as a proof of concept, demonstrating that simpler models can achieve similar predictive accuracy to complex models, challenging the notion that higher complexity necessarily improves the performance of ecological models. Ultimately, we provide a lightweight, interpretable model capable of projecting AGBD changes in response to future climate scenarios, offering a valuable tool for climate impact analysis and conservation planning.

# Methods

## Method overview

Our method is based on tree size measurements published in the Tallo database (Jucker et al. 2022) that compiles data from publicly available forest inventories worldwide that include a total of 498 838 measured trees. We calculated the above-ground biomass (AGB) of trees using region and species-specific allometries based on stem diameter for extra-tropical trees (collected in Gonzalez-Akre et al. 2022) and a pan-tropical allometry based on height and stem diameter for tropical trees (Chave et al. 2014). We scaled from the AGB of trees to AGBD of forest stands by clustering trees based on geographic proximity using a hierarchical density-based clustering algorithm (HDBSCAN; McInnes et al. 2017). For each cluster, we estimated the AGB distribution of the trees and utilized data from a global, machine learning-based map of tree density (Crowther et al. 2015a, 2015b) to sample the AGB distribution according to the number of trees per hectare at each location. Finally, we summed the sampled values and produced an estimate of AGBD at each location to obtain a global AGBD database. We used the database to train a gradient-boosting machine learning algorithm (XGBoost; Chen and Guestrin 2016) using exclusively bioclimatic observables as predictors (CHELSA-BIOCLIM+; Brun et al. 2022). The central part of the training consisted of a predictor selection process that used an evolutionary algorithm (NSGA-II; Deb et al. 2002) to identify the optimal combination of climatic variables that leads to the most accurate predictions of AGBD in unseen data. Finally, we included information regarding human footprint to control for the effect of human pressure in potential AGBD. We performed a global estimate of potential AGBD at a resolution of 1 km². A graphical representation of the modeling workflow is depicted in Fig. 1. In summary, our methodology consists of two steps and seven sub-steps that are more thoroughly described in the following subsections:

AGBD estimation from non-exhaustive forest inventories

1. Clustering of trees.

2. Estimation of AGB of trees in each cluster.

3. Estimation of the AGB distribution of trees within clusters.

4. Estimation of AGBD in each cluster.

Calibration and training of a machine learning model.

1. Inclusion of 0 AGBD instances.

2. Training and predictor selection process.

3. Controlling for the human footprint bias.

## Clustering of trees

We based our work on the Tallo tree size database (Jucker et al. 2022) which is, to our knowledge, the only completely open and publicly available global database on tree-size measurements. The database compiles measurements from multiple studies published, for the most part, within the years 2000 and 2020 and hosts data on 498 838 trees from 61 856 experimental plots. In plots with exhaustive tree inventories, estimating the AGBD of the forest stand boils down to summing the AGB of every tree in the plot and dividing the result by the area of the plot. This operation becomes more complex when tree measurements do not come from exhaustive inventories, or when plot area is not reported. Unfortunately, the Tallo database contains data from non-exhaustive inventories and does not report the area of the experimental plots.

We palliated this limitation by estimating AGB distributions within plots and calculating AGBD by sampling the AGB distribution according to external tree density data from a machine learning-based global map (Crowther et al. 2015a, 2015b). However, numerous plots contain measurements on very few trees (e.g. less than 10), which leads to two problems. On the one hand, estimating AGB distributions with such a low number of samples is error prone. On the other hand, in non-exhaustive inventories, there is no guarantee that the sampled trees are an adequate representation of the forest stand and consequently, AGB distributions could be biased. We overcame this limitation by merging plots that are close to each other using a clustering algorithm. Our hypothesis is that trees from two nearby plots that share similar bioclimatic conditions could be interchanged between plots and could thus be part of a unique larger plot. In summary, we hypothesize that nearby plots are representations of the same forest type. Under the above-mentioned hypothesis, creating clusters of trees from different plots allows us to obtain larger meta-plots with more robust tree-level statistics, and thus more robust estimations of AGBD.

We clustered trees from the Tallo database based on geographical location using a hierarchical density based clustering algorithm (HDBSCAN; McInnes et al. 2017) implemented in *Scikit-Learn* Python library (Pedregosa et al. 2011). Unlike similar algorithms, HDBSCAN is designed to detect clusters of dissimilar densities, and is thus well suited for our database where the spatial distribution of data is far from uniform, with alternating regions of high and low concentrations of sampled trees. We set the minimum cluster size to 25 samples, meaning that clusters with less than 25 trees were discarded as outliers. We chose this value heuristically under the
<figure><img src="image_5.png" /><figcaption>(b) Prediction of Aboveground Biomass Density with ML model</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 1. Schematic representation of the AGBD estimation method. The steps to obtain a global database of AGBD starting from tree inventories data are presented in (a). Individual trees are clustered to estimate the AGB distribution within the cluster. Next, the distribution is sampled according to data on tree density at the location to make an estimation of AGBD. In (b) we describe the steps that we followed to develop a machine learning model to make a global estimation of AGBD based on bioclimatic observables. We evaluated the error and calibrated the model over spatial cross-validation folds that were defined according to the autocorrelation distance of the AGBD data to avoid autocorrelation between different folds. Model calibration was performed using evolutionary algorithms to select the best hyperparameters and environmental predictors. We used the gradient-boosting algorithm XGBoost.</figcaption></figure>

assumption that 25 is a sufficient number of samples to make
an empirical estimate of close-to-normal distributions. This
is relevant because later steps of our methodology are based
on the empirical estimation of the AGB distributions of trees
in every cluster, which are close to normal in the logarith-
mic space (Supporting information). Additionally, we set the
clustering distance threshold to 25 meters, which implies that
every pair of clusters at a distance lower than 25 meters are
merged together. This resulted in the avoidance of large num-
bers of micro-clusters in regions with a high concentration of
sampled trees in favor of a lesser number of larger clusters.
Finally, we let the minimum number of samples parameter
to its default value, i.e. the same as the minimum cluster size
(25). Increasing the value of this parameter results in more
conservative clustering and thus in fewer clusters and more

outliers. We did not investigate the effect of this parameter on
the clustering output. As a result of the clustering procedure,
we obtained 3456 clusters, and discarded 39 980 outlier trees
from the initial 498 838 (Fig. 2a). The average intracluster
coefficient of variation across climatic variables was 0.5%, the
tree density coefficient of variation was 10% and the average
intra-cluster distance between trees was 2.23 km (Supporting
information). Finally, clustering homogeneity with respect to
ecoregion class was 0.94. Ecoregions were determined accord-
ing to the classification provided in Dinerstein et al. (2017).
Cluster homogeneity ranges between 0 and 1, where a score
of 1 would indicate that all trees in every cluster belong to
the same ecoregion (Rosenberg and Hirschberg 2007). This
supports the validity of the tree clustering procedure, since,
in general, all trees grouped within the same cluster belong
<figure><img src="image_7.png" /><figcaption>(b) Dataset's climatic space
(AGBD>0)</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(c) Biome-level dataset's AGBD distribution
(AGBD>0)</figcaption></figure>

<figure><img src="image_9.png" /></figure>

Figure 2. Characterization of the AGBD training data set. (a) Global coverage of the AGDB data set. The map regions and training instances are colored according to the biome class. We adopted the biome classification proposed in Dinerstein et al. (2017). The disks correspond to positive AGBD instances estimated from tree-size data. The inverted triangles correspond to 0 AGBD instances that were drawn randomly from locations with 0 tree density and climatic conditions outside of the positive AGBD data set (depicted in (b)). There is a significant number of 0 AGBD points in African tropical savannas which could be inaccurate. Vast regions of the world are not represented in the training dataset. Although for most biomes training instances span a diversity of regions, samples in tropical dry forests are highly localized, with most instances located in narrow areas of the Yucatan Peninsula and Mexico's Pacific coast, leading to a poor diversity in the biome's representation. (b) Depiction of the dataset's climatic space in terms of annual precipitation and mean annual temperature. Only positive AGBD instances are shown. The disks' colors correspond to point density. (c) Distribution of AGBD by biome class for positive AGBD instances represented with a Boxen plot (Hofmann et al. 2017). The number of instances in each biome is reported in the Supporting information. The large AGBD estimates in montane grasslands are likely caused by slight geolocation errors in the tree-size data set. The vast majority of these instances are located on the Tibetan plateau of northern Pakistan, at a short distance from the subalpine conifer forests to which they are likely to belong.
to the same ecoregion, experience very similar climatic conditions and are at close geographical distance. Thus, trees within the same cluster might belong to the same forest stand even if they are not in reality. This procedure certainly averages potential fine-grained differences across nearby sites but our analysis shows that it is a reasonable approximation.

## Estimation of trees' AGB

We estimated the AGB of trees in each cluster using allometric size-biomass relationships. Specifically, we used the equations implemented in two peer-reviewed R packages: 'allodb' (www.r-project.org, Gonzalez-Akre et al. 2022) for extratropical regions and 'BIOMASS' (Réjou-Méchain et al. 2017) for tropical regions. allodb contains a compilation of 570 allometric equations calibrated using 701 woody species in 24 temperate and boreal forest plots representing major extratropical forest types. Given the coordinates, wood density, species, and stem diameter of a tree, allodb identifies the most suitable allometry or combination of allometries, to estimate AGB. On the other hand, the 'BIOMASS' package features the pantropical allometry from Chave et al. (2014) based on stem diameter, tree height and wood density. When tree height data where absent, we used the diameter-height allometries featured in the package that were locally calibrated with size data from trees in the same cluster. Due to the lack of specific allometries in the subtropical region (within 23°26′12.2″ and 35°) we employed a simple rule of thumb to estimate the AGB in these ecosystems taking the average of tropical and extratropical estimates.

## Estimation of the AGB distribution of trees within clusters

Assuming that there was no tree-size bias during data collection in the primary data sets that form the global tree-size database, the AGB distribution within each cluster is a good approximation of the realized AGB distribution at that location. We estimated the AGB distribution for each cluster using a kernel density estimation algorithm (Scikit-learn implementation; Pedregosa et al. 2011) on log-transformed AGB values. This contributes to obtaining better fits because AGB distributions are heavy-tailed, and the log-transformation yields distributions that are close to normal (Supporting information). For each cluster, we calibrated the kernel density estimation by optimizing the bandwidth parameter using uniform sampling in the [0.1–2.0] interval and a nested cross-validation scheme with 10 outer folds, 5 inner folds and 10 repetitions.

## Estimation of AGBD in every cluster

For each cluster, we sampled the estimated AGB distribution according to the average tree density at the location of each tree that belongs to that cluster (Fig. 1a). We drew tree density values from the global map developed by Crowther et al. (2015a, 2015b) using a machine learning approach. The sum

of every value sampled from the distribution is therefore an estimate of the AGB stored in one unit area of the forest at the cluster location and thus of the AGBD at that location. For robustness, the final AGBD value retained for each cluster was the median of 100 independent samplings. The variation between samplings was remarkably low, with a coefficient of variation of 1.2%.

The resulting data set is characterized in Fig. 2, where Fig. 2a depicts the geographical coverage (disks in the map), Fig. 2b the climatic space in terms of annual precipitation and temperature and Fig. 2c the AGBD distributions per biome. Predominant forested biomes are well represented in the data set (Supporting information). However, in the case of tropical dry forests, most of the instances are located within small areas in the Yucatán peninsula and Mexico's Pacific coast, which leads to a limited representation of the ecosystem. Additionally, most of the instances located in montane grasslands are concentrated in the mountain plateaus of northern Pakistan and are probably the result of incorrect classification due to geolocation errors. Most of these instances are very likely located in subalpine temperate conifer forests very close to the plateaus but at a lower elevation. This explains the large AGBD estimated in montane grasslands (Fig. 2c last column). Significant data gaps remain in certain regions of the world that lack any sampling coverage. This limitation can introduce biases and reduce prediction accuracy in data-poor areas, impacting the model's reliability across these underrepresented regions.

## Inclusion of 0 AGBD instances

We built a global AGBD data set from globally available tree-size measurements. By construction our data set only contains information on locations where woody vegetation occurred, ignoring regions where woody vegetation is absent due to harsh environmental conditions. Training a machine learning algorithm on this data set would make it impossible to predict the occurrence of regions where AGBD is null. Additionally, by ignoring a significant fraction of the potential climatic space of the Earth, it would force error prone predictions outside of the data set's climatic range. This constitutes a considerable limitation for the projection of AGBD in the future because the increase of temperatures and changes in precipitation is expected to cause desertification in many regions. We overcome this limitation by including instances of 0 AGBD in the training data set. 0 AGBD instances were selected by uniform sampling among locations with null tree density according to the map published by Crowther et al. (2015a). We further constrained the potential locations to regions whose climatic conditions fall outside of the climatic space of the tree database. For each of the 20 bioclimatic predictors, we calculated their min-max ranges and selected only samples where at least one climatic variable fell outside these ranges. In this way, we ensured that most 0 AGBD instances are related to harsh climatic conditions rather than to human pressures. The number of 0 AGBD instances was set so that it represents 39% of the total data set. This matches the fraction
of land area with null tree density according to Crowther et al. (2015a) estimation. Specifically, instances were located in the northernmost latitudes of Canada, Russia and Greenland, desertic regions in the south-west USA, Mexico, the Pacific coastline in Perú and northern Chile, the Andean Altiplano, the Argentinean Pampa and Patagonia, Namibia, the Sahara desert, African savannas, the Arabian peninsula, central Asia, central Australia and various mountain ranges (Fig. 2a, inverted triangles). A large number of 0 AGBD instances are located in African savannas in the Sahel and the horn of Africa. While these ecosystems host very low tree densities, a value of 0 AGBD might represent an underestimate.

## Training and predictor selection process

We used the AGBD data set to train a gradient-boosting model XGBoost (Chen and Guestrin 2016) using as predictors 20 bioclimatic variables (Supporting information) from the CHELSA-BIOCLIM+ database (Brun et al. 2022) at a resolution of 30 arc seconds (i.e. 1 km²). We carried out a predictor selection process to identify the most meaningful environmental determinants of AGBD on a global scale and reduce model complexity by discarding irrelevant predictors that can be sources of noise. We treated predictors as model parameters and performed a calibration experiment using the OpenMole (Reuillon et al. 2013) implementation of the NSGA-II evolutionary algorithm (Deb et al. 2002) to find the set of predictors and hyperparameters that minimize the root mean squared error of predictions.

We estimated model error using a nested cross-validation scheme over 100 spatial cross-validation folds (Ploton et al. 2020). Using spatial folds avoids information leakage between training and testing data sets, and thus results in trustworthy error estimates and optimal model calibration for prediction in unseen data. The spatial cross-validation folds were generated by clustering instances based on geographical proximity. We parameterized a hierarchical clustering algorithm (Scikit-Learn AgglomerativeClustering) according to the AGBD autocorrelation length in our data set, which was estimated at 1000 km based on variogram plots (Supporting information). We obtained the 100 spatial folds as a result of the clustering procedure. After estimating model error using the nested cross-validation scheme, we performed a second calibration experiment over 54 000 generations using the same spatial cross-validation folds and the entire data set. The result of this calibration yielded the set of predictors and hyper-parameters that minimize root mean squared error when predicting in unseen data.

## Controlling for the human footprint bias

A key limitation of potential AGBD models is that training instances represent realized, rather than potential, AGBD values. This means that some training instances may reflect reduced AGBD due to human disturbances, potentially causing the model to predict lower values than would be possible in undisturbed conditions. To assess human impact in our

training data, we used a spatially explicit dataset from 2009 that aggregates multiple human-related variables into a single index representing human pressure, ranging from pristine areas (values near 0) to highly degraded areas (values near 50) (Venter et al. 2016). We normalized the original dataset's range of [0, 50] to [0, 1]. Although most of our training instances fall within areas of low or very low human footprint, with a median footprint of 0.1 and 95% of instances below 0.4 (Supporting information), this residual influence of human disturbance can introduce bias into potential AGBD predictions.

This bias can be mitigated by either filtering out training instances with high human footprints (Walker et al. 2022) or by incorporating human footprint effects into the model, accounting for them during prediction (Mo et al. 2023). We adopted the latter approach, integrating human footprint data into our training process after calibration. This enabled the model to learn the relationship between human footprint and AGBD. During prediction, we set the human footprint variable to zero across all locations, simulating a pristine environment in which potential AGBD could be fully realized. This approach effectively removes human disturbance bias from our potential AGBD predictions.

## Model validation

We validated our model by comparing its predictions against those from a state-of-the-art, more complex model of potential AGBD by Walker et al. (2022) (baseline potential model). Since Walker et al. (2022) provided maps of aboveground carbon density, we converted these predictions to AGBD using biome-specific carbon-to-biomass conversion rates (Martin et al. 2018). We conducted a pixel-wise comparison of the global AGBD maps produced by both models, analyzed the predicted AGBD distribution across biomes, and compared median AGBD predictions at the ecoregion level. Additionally, we evaluated total AGB stocks predicted by each model at global, latitudinal, biome, and ecoregion scales, including relative stock contributions across biomes.

Beyond inter-model consistency, we validated model predictions using field data from GEOTREES biomass reference sites (Shchepashchenko et al. 2019). Specifically, we compared overall and biome-level distributions of absolute percentage errors (APE) and calculated median APE at the ecoregion level. To test for statistically significant differences in error distributions, we used the Mann-Whitney U-test (Mann and Whitney 1947), allowing us to determine if one model significantly outperformed the other in specific cases. To supplement quantitative results, we visualized APE distributions with Q-Q plots for a direct, graphical comparison.

The GEOTREES database includes measurements of current, realized AGBD, rather than potential AGBD. To ensure an accurate comparison between model predictions and field data, we excluded all forest plots categorized as burnt, recently burnt, or young forests from our analysis. This allowed us to compare the potential AGBD values predicted by the models with AGBD measurements taken from sites with minimal
human disturbance. By doing so, we ensured that our validation dataset closely aligns with potential AGBD, resulting in a more meaningful comparison.

# Results

## Model performance and selected predictors

The nested cross-validation experiment yielded a median of mean absolute errors across inner spatial cross-validation folds of 42 Mg ha⁻¹ (Supporting information). The predictor selection procedure showed that the optimal subset of predictors was composed by only four out of the 20 bioclimatic variables initially considered (Fig. 3a). On average prediction errors were found to increase when training on more than five predictors (Fig. 3b). After 50 000 generations, the evolutionary algorithm converged into a unique combination of predictors composed of 1) mean annual air temperature, 2) maximum air temperature of the warmest month, 3) annual precipitation amount, and 4) annual range of air temperature (Fig. 3c).

We evaluated the impact of these four predictors using Shapley values, which quantify both individual and interactive effects on model predictions (Lundberg 2017). The resulting explainability plots (Supporting information) demonstrate how non-linear interactions between predictors shape the model's output. While these plots reveal the model's decision-making process, the relationships they uncover should not be interpreted as causal.

## Comparison with predictions from a state-of-the-art complex model

Hereafter, we refer to our model as the ‘simple model’ and to the potential model developed by Walker et al. (2022) (‘baseline potential’ model) as the ‘complex model’. The simple model’s global estimate of current potential AGBD aligns well with established large-scale biomass patterns (Fig. 4a). However, at the pixel level, the models show notable differences in tropical regions, with discrepancies exceeding 200 Mg ha⁻¹ in some areas. Specifically, the simple model predicts higher potential AGBD in the tropical moist forests of the

<figure><img src="image_10.png" /><figcaption>Figure 3. Results from the predictor selection process during calibration. (a) Number of predictors as a function of the evolutionary algorithm generations. The optimization algorithm converges to four predictors (out of 20 potentially) in the long term. (b) Cross-validation error during the calibration for varying number of predictors. On average, including more predictors yields larger model errors (10% more). The error is normalized by the maximum error obtained during the calibration. The actual error value is not important, as the estimation of the model error is not done during the final model calibration but separately with a nested cross-validation scheme to avoid information leakage between training and testing folds. (c) The plot shows the fraction of times that each predictor was selected in a given generation. Each line corresponds to a different predictor. In the long run the optimization algorithm converges to a unique set of four predictors. In the final generations, this does not mean that a single model was selected. There are multiple configurations with the same set of predictors but different hyper-parameter values.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>(b) Difference between models' predictions</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>(c) AGB Latitude profiles</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>(d) Ecoregion-scale AGB stocks</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>(e) Large-scale AGB stocks</figcaption></figure>

<figure><img src="image_15.png" /></figure>

Figure 4. (a) Global estimation of potential AGBD under current climatic conditions. Darker shades of green represent larger AGBD values. The color scale is truncated at 300 Mg ha⁻¹ for visualization purposes and AGBD values predicted by the simple model attain 1200 Mg ha⁻¹. However, AGBD in 95% of the world is smaller than 280 Mg ha⁻¹, with the remaining 5% located in tropical moist forests. Therefore, truncation of color scale only affects the visualization of AGBD variability in these regions. (b) Global map depicting differences in potential AGBD predicted by the simple and complex model. The simple model predicts larger and lower values than the complex model in regions colored in blue and red, respectively. The color scale is truncated in both ends for visualization purposes. However, differences in 95% of the world are smaller than 120 Mg ha⁻¹. (c) Latitudinal distribution of AGB stocks for the simple and complex models, in blue and orange, respectively. (d) Scatter-plot of AGB stocks at the ecoregion-level for the simple and complex models, in the y-axis and x-axis, respectively. The r² value corresponds to the square of the Pearson correlation coefficient between model predictions. (e) AGB distribution at broad climatic scales in absolute and relative values at the top and bottom panels, respectively.
Americas and Africa, while estimating lower values in African savannas and in the tropical forests of south and southeast Asia (Fig. 4b). For a set of representative regions, the median and 95th percentile AGBD values predicted by both models are summarized in Table 1.

When examining latitudinal profiles of total AGB stocks, the complex model predicts higher stocks in northern high- latitude regions and tropical-subtropical areas in the Northern Hemisphere. In contrast, the simple model estimates greater AGB stocks near the equator and at high southern latitudes (Fig. 4c). Overall, these latitudinal patterns show strong agreement between the models.

At the ecoregion level, both models demonstrate a high correlation in predicted AGB stocks, indicating consistent spatial patterns across the globe (Fig. 4d, Supporting information). When analyzed at broader spatial scales, the two models yield nearly identical distributions of AGB stocks across tropical, temperate, boreal, and dryland regions (Fig. 4e, bottom panel, Supporting information). In terms of absolute values, however, the differences are greater and concentrated in tropical regions. Globally, the complex model predicts a total AGB stock of 1346 Gt, whereas the simple model predicts 1009 Gt – a 29% difference in overall AGB stock (Supporting information).

## Validation against field data from worldwide biomass reference measurement sites

We found no statistically significant difference between the distributions of absolute percentage errors (APE) for both models when compared to field data, with a p-value of 0.79 (Fig. 5a and b). Both models exhibited nearly identical

median APE values of 37% for the simple model and 36% for the complex model. However, at the biome level, we observed larger differences in APE distributions (Fig. 5c; see also the Supporting information). Statistically significant differences were present in only half of these cases (Fig. 5c, d, e, and f, with statistical significance indicated by stars).

Specifically, the simple model outperformed the complex model in Afrotropical mangroves and Neotropical moist forests and savannas (Fig. 5c, d, and e), while the complex model demonstrated superior performance in Palearctic temperate and Mediterranean forests, as well as in Afrotropical moist and Neotropical dry forests (p-values reported in the Supporting information). Although we did not include comparisons at the ecoregion level in the main manuscript due to their statistical limitations – stemming from a lower number of samples – these results are presented in the Supporting information.

## Discussion

Our study presents a simple climate-based model for estimating potential AGBD globally, leveraging climatic data and worldwide tree-size measurements derived from non-exhaustive forest inventories. We calibrated the model through a systematic predictor selection process aimed at identifying the subset of bioclimatic predictors that minimized model error. Our analysis revealed that the optimal set of predictors comprises only four variables: 1) mean annual temperature, 2) maximum temperature of the warmest month, 3) annual precipitation amount, and 4) annual temperature range.

We validated our model by comparing its predictions with results from a highly complex state-of-the-art model and with

<table><caption>Table 1. Median and 95th percentile AGBD values predicted by the simple and complex models across a series of large-scale regions from most relevant biomes with respect to carbon storage.</caption><thead><tr><th rowspan="2">Biome</th><th rowspan="2">Region</th><th colspan="2">Median AGBD</th><th colspan="2">95th percentile AGBD</th></tr><tr><th>Simple model</th><th>Complex model</th><th>Simple model</th><th>Complex model</th></tr></thead><tbody><tr><td rowspan="5">Tropical moist</td><td>Amazon</td><td>429</td><td>326</td><td>656</td><td>419</td></tr><tr><td>Central Africa</td><td>290</td><td>323</td><td>837</td><td>444</td></tr><tr><td>Asia-Pacific</td><td>106</td><td>294</td><td>489</td><td>429</td></tr><tr><td>Continental Asia-Pacific</td><td>83</td><td>231</td><td>260</td><td>382</td></tr><tr><td>Insular Asia-Pacific</td><td>237</td><td>380</td><td>590</td><td>445</td></tr><tr><td rowspan="5">Tropical dry</td><td>Yucatan</td><td>22</td><td>172</td><td>59</td><td>219</td></tr><tr><td>Northeast Brazil</td><td>17</td><td>70</td><td>159</td><td>180</td></tr><tr><td>Chiquitano</td><td>66</td><td>198</td><td>108</td><td>265</td></tr><tr><td>Dry India</td><td>3</td><td>61</td><td>61</td><td>176</td></tr><tr><td>Indochina/Vietnam</td><td>61</td><td>196</td><td>159</td><td>352</td></tr><tr><td rowspan="3">Grasslands/savannas</td><td>Northern Amazonia</td><td>245</td><td>124</td><td>652</td><td>265</td></tr><tr><td>Dry Chaco</td><td>33</td><td>69</td><td>95</td><td>170</td></tr><tr><td>Uruguay/Argentina savanna</td><td>107</td><td>18</td><td>151</td><td>76</td></tr><tr><td rowspan="3">Mediterranean forests</td><td>Mediterranean Europe</td><td>89</td><td>127</td><td>147</td><td>208</td></tr><tr><td>Northern Africa</td><td>1</td><td>13</td><td>89</td><td>135</td></tr><tr><td>Southwest Australia</td><td>3</td><td>13</td><td>110</td><td>68</td></tr><tr><td rowspan="4">Temperate</td><td>Western Europe</td><td>198</td><td>162</td><td>370</td><td>223</td></tr><tr><td>Central/East Europe</td><td>119</td><td>127</td><td>196</td><td>194</td></tr><tr><td>East Australia</td><td>101</td><td>116</td><td>202</td><td>213</td></tr><tr><td>Northamerican Pacific</td><td>127</td><td>208</td><td>431</td><td>613</td></tr><tr><td rowspan="2">Boreal forests</td><td>Northern Nearctic</td><td>45</td><td>47</td><td>146</td><td>101</td></tr><tr><td>Northern Palearctic</td><td>42</td><td>77</td><td>129</td><td>161</td></tr></tbody></table>
<figure><img src="image_16.png" /><figcaption>Figure 5. Comparison of the predictions from the simple and complex models with field data from worldwide biomass reference measurement sites. (a) Histogram depicting the overall APE distribution for the simple and complex models, in blue and orange, respectively. (b) Q–Q plot of the APE distributions of the simple model (y-axis) and complex model (x-axis). The location of each disk is given by the APE value at identical quantiles, therefore all disks fall in the 1:1 line for two identical distributions (represented in black in the plot). (c) Boxplot representing the biome-level APE distributions for the simple and complex models, in blue and orange, respectively. Black stars represent statistically significant differences estimated with a Mann–Whitney U-test (Mann and Whitney 1947) and choosing a threshold of 0.05 for p-values. (d, e, f) Stratification of the APE distributions across biogeographical realms for moist tropical forests, tropical savannas and temperate broadleaf forests, respectively. Across the remaining biomes, only one realm is represented in field data, therefore the APE distributions cannot be examined in greater detail than already presented in (c).</figcaption></figure>
field data from biomass reference measurement sites world-
wide (Shchepashchenko et al. 2019). Overall, we found that
both models reproduced ground measurements equally well.
In contrast to the complex model, which uses 186 predic-
tors and is difficult to interpret from a biological and ecologi-
cal standpoint, our simple model's predictions can be easily
explained through the analysis of the interaction of just four
bioclimatic variables and a human footprint variable that
controls the effect of human disturbances at the prediction
stage (Supporting information).

Our model has two main advantages over existing global
models of potential AGBD. First, its reduced number of pre-
dictors enhances the biological interpretation of its predic-
tions. Second, its exclusive dependency on climatic predictors
makes it well-suited for projecting future AGBD changes
under different climate scenarios. Moreover, we make our
trained model freely available, providing researchers and
practitioners with an human-understandable and computa-
tionally efficient tool to investigate how climate change may
reshape global patterns of tree carbon storage in the future.

Global patterns of potential AGBD

At the pixel-level, our results show substantial variability
between models' predictions in tropical areas, and mod-
erate to low variability in temperate and boreal latitudes.
However, these discrepancies decrease when predictions are
compared at broader spatial scales. At the levels of ecoregions
and biomes, both our simple model and the complex model
by (Walker et al. 2022) predict very similar spatial patterns
of AGBD and total AGB stocks(Fig. 4d and e, Supporting
information). At the global scale, our estimate of overall AGB
stocks falls within the range predicted by recent state-of-the-
art models (974–1424 Gt), as synthesized in the meta-analy-
sis by Mo et al. (2023).

Key discrepancies with Walker et al. (2022) are most evi-
dent in African savannas and tropical dry forests globally,
where relative inter-model differences reach 70% and 80%,
respectively (Fig. 4b, Table 1, Supporting information). In
both regions, our simpler model predicts lower biomass
stocks and exhibits larger deviations from field data, although
differences are not statistically significant in African savannas.
This suggests that the complex model's predictions are likely
more reliable for these areas.

We attribute the lower performance of our model in these
regions to three factors. First, tropical dry forests are under-
represented in our training dataset, with instances limited to
a few specific areas, resulting in lower diversity in the biome's
representation. Second, the pan-tropical allometries for tree
size and biomass used in our model are not well-calibrated for
tropical dry ecosystems (Hernández-Stefanoni et al. 2020),
which may introduce biases in AGBD estimates. Third, many
zero AGBD instances in our training dataset are situated in
African savannas (Fig. 2a), which have similar climatic char-
acteristics to tropical dry forests. These instances likely exert
a downward bias on AGBD estimates in regions with com-
parable climates. Our predictions in tropical savannas are

consistently lower than the AGBD values in our training
dataset (Supporting information and Fig. 2c), supporting this
hypothesis of downward bias.

We estimate higher potential AGBD values than those
reported by Walker et al. (2022) in tropical and temperate
savannas of South America, particularly in the Atlantic coast
Campos of Argentina and Uruguay, as well as the Amazonian
savannas across northern Brazil, Guiana, and Venezuela
(Fig. 4b, Table 1). In these areas, the growth of native tree
species is predominantly constrained by soil conditions and
livestock pressures (Medina and Silva 1990, Lloyd et al. 2013,
Bernardi et al. 2019), resulting in landscapes with notably
low tree densities (Crowther et al. 2015a). However, the
growth of the forestry sector highlights the potential for rapid
forest expansion in these regions, with eucalyptus and acacia
plantations increasingly established for paper production and
timber extraction (Aguiar Jr et al. 2014, Pozo and Säumel
2018, Bernardi et al. 2019, FAO 2020). In this case, the
discrepancy between models likely stems from Walker et al.
(2022) incorporation of soil variables.

These extensive commercial monoculture plantations,
however, pose significant risks to natural grassland ecosys-
tems, often degrading ecological integrity by simplifying
community structures and altering soil properties (Bremer
and Farley 2010, Six et al. 2014, Aguiar Jr et al. 2014, Pozo
and Säumel 2018, Cerullo et al. 2024, Salazar et al. 2024).
While plantations can contribute to carbon storage, their
life-cycle contributions to long-term carbon sequestration are
variable and uncertain.

In Europe, where we predict a broad coverage of high
potential AGBD spanning Germany, the United Kingdom,
Ireland, France and northern Iberia, our results align closely
with those of Walker et al. (2022) (Fig. 4a and b, Table 1),
further supporting the reliability of both models for estimat-
ing potential biomass. The history of human settlement and
intensive land use has extensively degraded Europe's forests,
which today exist primarily as fragmented patches cover-
ing only 30% of land in France and Germany (Lang et al.
2023). In Ireland, forest cover plummeted from 80% to just
1% in the early 20th century, though it has since rebounded
to approximately 10% (O'Carroll and OCarroll 2004,
Lang et al. 2023).

Parsimonious machine learning for ecological big
data

The widespread availability of vast datasets, coupled with
advances in computational frameworks, has driven rapid
growth in ML modeling across scientific fields (Jordan
and Mitchell 2015). Ecology is no exception (Peters et al.
2014, Farley et al. 2018, Liu et al. 2018, Christin et al.
2019, Scowen et al. 2021, Nathan et al. 2022, Tuia et al.
2022), with the recent development of global carbon stor-
age models serving as a prime example (Saatchi et al. 2011,
Baccini et al. 2012, Harris et al. 2021, Duncanson et al.
2022, Walker et al. 2022, Mo et al. 2023, Roebroek et al.
2023). In carbon modeling, Earth observation data has
exponentially increased training sample sizes, enabling ML models to achieve unprecedented accuracy. Moreover, this influx of data has expanded the range of potential observables that can be used as model predictors, opening new avenues for predictive power.

While larger training datasets typically lead to better model accuracy, the assumption that more predictors always yield better models has introduced a critical, often-overlooked issue. Current models frequently rely on dozens of predictors, driven by the belief that additional predictors inherently improve performance (Mo et al. 2023). This assumption stems from the correct observation that the accuracy of non-parametric models like Random Forest or MaxEnt is not heavily impacted by predictor correlation (Strobl et al. 2008). However, this has led to the erroneous conclusion that reducing the predictor set – either by selecting a subset or using dimensionality reduction techniques like principal component analysis – is unnecessary.

In reality, high-dimensional predictor spaces bring a host of challenges collectively referred to as the ‘curse of dimensionality’ (Altman and Krzywinski 2018). Addressing these challenges through more parsimonious ML models may not only improve model explainability and interpretability but also enhance model performance in ecological and environmental research.

Using an excessive number of predictors can paradoxically reduce model accuracy, as demonstrated by our findings. As the number of predictors increases, the density of training instances across the predictor space decreases, leading to data sparsity. This sparsity, in turn, reduces the representativeness of training samples and heightens the risk of overfitting, limiting the model’s ability to generalize to new data (Altman and Krzywinski 2018). To mitigate these issues, the inclusion of additional predictors should ideally be matched by an increase in the number of training instances.

In the context of global carbon storage models, it might be argued that the vast sample sizes – often in the range of millions to tens of millions of instances – can help offset data sparsity. However, even with such large datasets, the ‘data sparsity’ effect imposes a fundamental constraint on how many predictors can be effectively used. Crucially, existing global carbon models have not rigorously evaluated whether their predictor sets truly optimize model accuracy, raising the possibility that they include an unnecessarily high number of predictors (Harris et al. 2021; Walker et al. 2022; Mo et al. 2023). This highlights a pressing need for model refinement and predictor selection in big data-driven ecological modeling.

The complexity of ML models is closely tied to their explainability, i.e. the extent to which humans can understand how predictors influence model outcomes. Model complexity arises largely from the choice of training algorithms and the dimensionality of the predictor space. Increasingly complex algorithms, such as tree ensembles and especially neural networks, have spurred advances in explainable artificial intelligence (XAI) to make these models more interpretable (Barredo Arrieta et al. 2020). Recent methodological

breakthroughs have made it possible to mitigate the black-box nature of such models, providing insights into their inner workings (Barredo Arrieta et al. 2020; Linardatos et al. 2021).

The most common XAI methods seek to rank or quantify the influence of each predictor on model outcomes (Cortez and Embrechts 2011; Lundberg 2017). Beyond assessing the importance of individual predictors, these methods also shed light on complex interactions between predictors. However, high-dimensional predictor spaces severely limit the practicality of these approaches. As the number of predictors increases, the potential interactions to evaluate grow exponentially, quickly surpassing human capacity for interpretation and, paradoxically, rendering even the results of explainability analyses opaque (Supporting information). This underscores the need for parsimonious approaches to maintain both model accuracy and interpretability.

The rationale for using large sets of predictors often stems from the expectation that more predictors yield higher prediction accuracy. This reflects an implicit epistemological choice that favors predictive performance over understanding. However, our findings suggest that the tradeoff between model simplicity and performance is not as rigid as often assumed. While big data and artificial intelligence offer powerful tools to advance ecological science, we argue that this progress should not come at the expense of fully sacrificing explainability, as understanding lies at the heart of scientific inquiry. We advocate for a widespread application of Occam’s razor in data-driven ecological modeling, aiming to leverage big data to build models that can capture complex phenomena with the greatest possible simplicity.

## Conclusions

Estimating potential AGBD is essential for designing effective climate adaptation and mitigation policies. By identifying gaps between realized and potential AGBD, ML models provide valuable information to guide the prioritization of conservation and restoration efforts. Importantly, understanding not only the current, but also the future potential of AGBD under changing climate conditions is crucial for long-term planning. Our simple model, which relies on only four bioclimatic variables to make inference, offers a lightweight and interpretable tool for this purpose. In addition to its utility for the estimation of potential carbon storage, our work demonstrates, particularly in the era of big data, that increasing model complexity through additional predictors does not necessarily improve performance.

*Funding* – DB’s work is funded by the IKUR programme (https://www.science.eus/en/ikur). This research is supported by María de Maeztu Excellence Unit 2023-2027 Ref. CEX2021-001201-M, funded by MCIN/AEI /10.13039/501100011033; and by the Basque Government through the BERC 2022-2025 programme. Computational analysis was carried on in the infrastructure of the DIPC Supercomputer Center (https://dipc.ehu.eus/en/supercomputing-center)
## Author contributions

**Diego Bengochea Paz:** Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Software (lead); Visualization (lead); Writing - original draft (lead); Writing - review and editing (lead). **Alba Marquez-Torres:** Investigation (supporting); Methodology (supporting); Writing - review and editing (supporting). **João Pompeu:** Investigation (supporting); Methodology (supporting); Writing - original draft (supporting); Writing - review and editing (supporting). **Olivier Martin-Ducup:** Writing - review and editing (supporting). **Ferdinando Villa:** Funding acquisition (lead); Resources (lead); Writing - review and editing (supporting). **Carmen Köhler:** Project administration (lead); Writing - review and editing (supporting). **Stefano Balbi:** Funding acquisition (lead); Resources (lead); Writing - review and editing (supporting).

## Transparent peer review

The peer review history for this article is available at https://www.webofscience.com/api/gateway/wos/peer-review/eco.g.07587.

## Data availability statement

All the code needed to reproduce the analysis and relevant data produced during the execution of the method (e.g. final maps, model calibration results), as well as the final trained model, are made publicly available in the Zenodo repository https://zenodo.org/records/14792615 (Paz et al. 2025).

## Supporting information

The Supporting information associated with this article is available with the online version.

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