Structural diversity can be characterized in a variety of ways depending on the data from which it is calculated and the intended application. In this work we adopted the common definition where diversity is defined in the vertical dimension as heterogeneity of vegetation height and in the horizontal dimension as canopy heterogeneity (Hakkenberg and Goetz, 2021). We chose a set of metrics that would characterize the heterogeneity within and among structural features for a given area, reflecting both local (alpha) and regional (beta) measures of structural diversity. These complementary metrics have been demonstrated to be particularly crucial for predicting tree diversity and ecosystem functioning (Coverdale and Davies, 2023; Ma et al., 2022; Zhai et al., 2024). A summary of the metrics with the input data used is reported in Table 1. Several GEDI products, including Foliage Height Diversity (FHD from the GEDI L2B product) and the Waveform Structural Complexity Index (WSCI, from the GEDI L4C product), already capture important aspects of forest structural heterogeneity and have proven highly valuable for large-scale analyses. However, recent work has shown that these indices exhibit strong scaling relationships with top-of-canopy height (RH98) (de Conto et al., 2024).

In the context of this study, our objective was therefore not to directly use existing GEDI products as target variables, but to develop structural diversity metrics that explicitly quantify heterogeneity while minimising direct dependence on canopy height. This motivated the selection of eight complementary metrics based on the distributional properties of GEDI relative height profiles and canopy cover, ecologically interpretable, minimally redundant with each other and with height, and suitable for spatial aggregation and wall-to-wall mapping using multi-sensor satellite data.

The eight structural diversity metrics were designed to span three complementary dimensions of forest structural diversity (Table 1). Vertical heterogeneity within individual canopy profiles is characterised using distributional metrics derived from GEDI relative height profiles, namely the coefficient of variation, skewness, and kurtosis, which capture differences in vertical layering and profile shape. Horizontal heterogeneity is described by the variability among GEDI observations within a spatial unit, quantified through the standard deviation of canopy height (CH) and canopy cover (CC), reflecting spatial variation in canopy structure across the landscape. Finally, combined structural diversity is represented using multivariate metrics (Shannon index (SW), Rao's quadratic entropy (RAO), and convex hull volume (CVH)), which synthesize information from multiple GEDI measurements into a single integrated index per spatial unit. Together, these metrics provide an interpretable yet comprehensive characterisation of forest structural diversity while minimising redundancy among metrics and with top-of-canopy height.

The variables used as ML predictors were calculated from Sentinel-1, Sentinel-2, and ALOS-PALSAR-2 observed data, which provide complementary information on forest canopy structure derived from optical reflectance, C- and L-band SAR backscatter, and associated textural properties. The predictor calculation involved the following steps:

appropriate bands/indices ϕα were calculated from the remote sensing raster images;

We used a machine learning method – Random Forest (Breiman, 2001) – to quantify the relations between the remote sensing predictors and the eight metrics. Random Forest is an ensemble learning method based on decision trees that is widely employed for regression tasks. A key advantage of Random Forests is that model fitting is relatively fast and hyperparameter optimization requires only a moderate amount of tuning, compared to other machine learning methods. Optimization of the Random Forest model typically involves tuning a number of hyperparameters. These include the size of the forest (i.e. the number of decision trees), the method of bootstrapping samples, and the setting of the maximum depth for the trees. We specified a fixed number of trees, 600; bootstrapping, a technique that involves random sampling with replacement, which contributes to the diversity of the decision trees in the model and helps prevent overfitting; and we did not impose any limitations on the depth of the individual decision trees, allowing them to expand fully. To evaluate the performance of the Random Forest model, we used mean squared error (MSE) as the metric.

To mitigate the potential for overfitting, we used a backward stepwise selection process that begins with a full model including all available predictors. The algorithm then iteratively removes the least important feature, as determined by its contribution to model performance. The relative importance of predictors was assessed using a permutation procedure (Altmann et al., 2010). At each iteration, the model complexity is reduced by one predictor, and the resulting model is evaluated. We compared each newly simplified model to the immediate predecessor to determine whether there was an improvement in performance or a decrease that was less than 1 % worse. The elimination process is halted if the removal of additional predictors causes the model's performance to decrease by more than 1 % compared to the previous iteration. At each step, a spatial cross-validation procedure is used to assess the performance of the model. The metric we utilized to assess model performance throughout this process was the coefficient of determination (R2).

To validate the reduced models, we used two types of validation techniques to assess their predictive accuracy and robustness:

Random train-validation split: in this approach, the dataset was randomly split, allocating 33 % for model validation. Random validation is a common method that provides a quick and often effective means of evaluating model performance on unseen data. However, it has a notable drawback when dealing with spatial data: it disregards the spatial structure inherent in the dataset (i.e. points close to each other are, generally, more similar than points further away). By ignoring this spatial autocorrelation, random validation may inadvertently conceal overfitting issues, leading to an overly optimistic perception of the model's predictive capabilities.

Models were fitted to datasets created at different resolutions including data calculated at 10, 5 and 1 km. Prediction uncertainty was quantified by calculating the standard deviation of predictions across the ensembles of decision trees in the Random Forest models. This metric captures the variability in predictions among individual trees within each model, providing a measure of uncertainty associated with predictions for the different response variables.

The dataset includes spatial grids for eight structural diversity metrics at three different resolutions (10, 5 and 1 km).

These metrics show a significant variation in structural diversity across the European forests as shown in Fig. 2 (see also Figs. S3 and S4 in the Supplement for 5 and 1 km resolution datasets).

An examination of the variability in the 10 km resolution metrics in climate space revealed distinct patterns along temperature and precipitation gradients (Fig. 3). Patterns of variability in metrics describing vertical heterogeneity showed significant differences when comparing the coefficient of variation (τCV) and skewness (τSK) against kurtosis (τKU). The coefficient of variation and skewness primarily exhibited high values at the extremes of the climatic gradient. This is observed in warm and arid climates where total annual precipitation is below ∼ 500 mm and Annual Mean Temperature is above ∼ 10 °C, as well as in colder climates where Annual Mean Temperature is below ∼ 5 °C. Patterns of variability in the kurtosis were more nuanced, consistently showing negative values across the European domain, which suggests a tendency for a platykurtic distribution in the vertical profile of canopies under diverse environmental conditions. The most pronounced negative kurtosis values were observed for the northern part of the temperate climate zone (Fig. 3). By contrast, more heterogeneous patterns occurred in other areas such as those with a Mediterranean climate, showing high variability (Fig. 3). Diversity metrics describing structural heterogeneity in horizontal space, as well as combined metrics, (τCH ,τCC, τSW, τRAO, τCVH) also showed considerable variability along precipitation and temperature gradients. With the exception of the convex hull (τCVH), all metrics displayed low diversity values in hot and dry climates.

Specifically, a combination of precipitation levels below ∼ 500 mm and annual mean temperatures above ∼ 10 °C (Fig. 3) was associated with the lowest levels of diversity. By contrast, the highest levels of diversity generally occurred in areas with higher precipitation levels (> 500 mm). Patterns of variability in the metrics in climate space for 5 and 1 km resolution (see Figs. S5 and S6 in the Supplement) dataset were broadly concordant with the 10 km dataset, indicating that the results are insensitive to the grain size at which they were calculated.

An examination of the 10 km resolution structural diversity metrics along gradients of temperature and precipitation variability (Fig. 4) revealed distinct but less pronounced patterns compared to those observed in mean climate space (Fig. 3).

Several metrics showed contrasting responses to climate variability. The coefficient of variation of the vertical profile (τCV) exhibited an inverse pattern, with highest values occurring at low climate variability (low SD in both temperature and precipitation), suggesting that stable climates may promote more heterogeneous vertical canopy structures. In contrast, the standard deviation of canopy height (τCH) showed the most striking pattern, exhibiting high values when temperature variability exceeded 10 °C and precipitation variability fell below 25 mm. Kurtosis (τKU) showed relatively modest variation across climate variability space, with a weak tendency toward more negative values (more platykurtic distributions) at higher precipitation variability. The standard deviation of canopy cover (τCC) showed a clear vertical gradient, with values increasing primarily as a function of precipitation variability, relatively independent of temperature variability. Similarly, Shannon entropy (τSW) was highest at high levels of precipitation variability combined with low to moderate temperature variability. In contrast, Rao's quadratic entropy (τRAO) exhibited a bimodal pattern, reaching its highest values both at very low precipitation and low temperature and, to a lesser extent, at high precipitation variability. The convex hull volume (τCHV) showed the most uniform distribution across climate variability space, with generally low values and limited systematic variation. Overall, metrics displayed considerably more scatter along gradients of climatic variability than in mean climate space, suggesting that climate variability plays a more complex role in shaping forest structural diversity than mean climate conditions.

An examination of structural diversity patterns by biogeographic region largely reinforced the patterns revealed in the climate space plots (Fig. 5, see Figs. S7 and S8 in the Supplement for the 5 and 1 km datasets), while revealing additional topographic effects. Combined horizontal-vertical diversity metrics (Shannon, Rao) were lowest in the Mediterranean region, consistent with the low diversity observed in hot, arid climates, and highest in Continental, Atlantic, and Alpine regions. Conversely, vertical canopy heterogeneity (Skewness τSK) was highest in the Mediterranean region, reinforcing the pattern of elevated skewness at climatic extremes. Canopy height variability (τCH) was markedly elevated in the Alpine region (Med=8.11) compared to Mediterranean (Med=6.00), Continental (Med=6.26), and Atlantic (Med=7.09), regions likely reflecting greater topographic heterogeneity. CV of vertical profile remained consistent across all regions (∼ 0.65–0.70), while (τKU) and σ of canopy cover τCC, showed minimal biogeographic variation.

A Principal Component Analysis (PCA) biplot (Fig. 6d) was used to explore the degree of intercorrelation among the eight structural diversity metrics. The PCA shows that the metrics are distributed across the principal component space with generally wide angular separation among vectors, indicating low to modest correlations. These patterns are consistent across spatial resolutions (Figs. S9, S11d and S12d in the Supplement).

The final models, derived from the stepwise backward elimination procedure, retained between 7 and 23 predictors, representing the extremes observed across various resolutions of input data and output variable types. The number of selected predictors generally increased with the resolution of the input data (Fig. S10 in the Supplement). Models trained for standard deviation of canopy cover (τCC) and convex hull (τCVH) retained the highest number of predictors. In contrast, models for skewness (τSK) and Rao quadratic entropy (τRAO) retained the lowest number of predictors (Fig. S10 in the Supplement).

An examination of the type of predictors selected in the final models highlighted the importance of radar-related predictors, over optical ones as shown in Fig. 6a (see Figs. S11a and S12a in the Supplement for the 5 and 1 km datasets). The average proportion of radar-related variables selected across all diversity metrics and resolutions was 0.64, although there was considerable variability. In general, as the resolution of the input dataset increased, the proportion of radar-related variables selected through the feature elimination procedure also increased (Fig. 6a; for the 5 and 1 km datasets see Figs. S11a and S12a in the Supplement). The diversity variables for which the highest number of radar-related predictors were selected was the convex hull (τCVH). On the other hand, the one for which the highest number of optical-related predictors were selected, was canopy cover (τCC).

Among the predictors retained in the final models, texture-related types were the most commonly selected, followed by backscatter, spectral indices, and coherence (Fig. 6b; for the 5 and 1 km datasets see Figs. S11b and S12b in the Supplement). Notably, texture metrics constituted, on average, the largest proportion of selected variables at a 10 km resolution (Fig. 6b). Conversely, the proportion of backscatter-related variables and spectral indices increased in models using the finer resolution input data (Figs. S11b and S12b in the Supplement).

Model validation revealed that random cross-validation consistently outperformed spatial cross-validation across all resolutions. At 10 km resolution, the model for the Shannon the model for Shannon index τSW achieved the highest scores, with 0.73 in random validation and 0.64 in spatial validation (Fig. 6c and Tables B1 and B2). Conversely, the model with convex hull (τCVH) as a variable showed the lowest performance, scoring 0.29 in random cross-validation and 0.20 in spatial cross-validation. This difference likely reflects the contrasting statistical properties of the metrics: Shannon entropy integrates information across the full distribution of GEDI observations within a spatial unit and is therefore more robust to sampling variability, whereas convex hull–based metrics are more sensitive to outliers and local sampling density.The best-performing models at 5 and 1 km differed from those at 10 km, with skewness models (τSK) yielding the best results at both 5 and 1 km, while canopy cover variability (τCC) was the lowest-performing at 1 km and convex hull (τCVH) at 5 km (Tables B1 and B2; Figs. S11c and S12c in the Supplement).

Models estimating metrics describing horizontal variability, particularly the standard deviation of canopy cover (τCC) and convex hull volume (τCVH), showed lower predictive performance, especially at finer spatial resolutions (R2 < 0.30 at 1 km). These metrics rely more directly on variability among individual GEDI observations within a spatial unit, which is less consistently preserved when locally derived optical and SAR predictors are spatially aggregated to the grid-cell level. In contrast, models estimating metrics describing vertical heterogeneity and combined structural diversity (e.g. τSK, τCV, τSW), particularly at 10 km resolution, exhibited higher validation scores and greater stability across validation schemes.

An examination of the standard deviation of model outputs revealed generally increasing trend of prediction uncertainty across resolutions (Figs. S13, S14 and S15 in the Supplement), except in Rao (τRAO) and convex hull (τCVH). Overall, uncertainty was generally low across the spatial domain of interest, reflecting limited variability within the ensemble. Notable exceptions occur in the Mediterranean region for the convex hull, kurtosis, and standard deviation of canopy height metrics. Further variability is observed in Eastern Europe, particularly for the convex hull, skewness, kurtosis, Shannon index, and standard deviation of canopy height.

Our dataset provides eight metrics describing the structural heterogeneity of European forests. To our knowledge, this is the first attempt to comprehensively map forest structural diversity at a quasi-continental scale (because GEDI is unable to observe anything above 50° N). Datasets such as the one presented here contribute to an emerging landscape of data products based on spaceborne LiDAR data, ranging from regional to global scales (e.g. Lang et al., 2023; Shendryk, 2022; Sothe et al., 2022). However, while most efforts have primarily focused on mapping top canopy height, we aimed to create a set of complementary metrics describing the diversity of canopy structure, an ecologically important yet neglected aspect in research.

Some of the ecological indices employed in this study are routinely applied to optical data to quantify landscape-level heterogeneity using multispectral data (Tuanmu and Jetz, 2015). For instance, the Rao and Shannon diversity indices, which can be calculated from spectral indices, have been widely used to quantify the heterogeneity of vegetation and are often proposed as indicators of ecosystem heterogeneity (Rocchini et al., 2021). These heterogeneity indicators have proved to be useful in a variety of contexts, including biodiversity modelling and quantifying the vulnerability of forest ecosystems to disturbances (Forzieri et al., 2021; Taddeo et al., 2021). However, indices based solely on optical data fail to capture crucial aspects of structural heterogeneity, which are related to the three-dimensional arrangement of vegetative elements in the canopy (Fassnacht et al., 2022). Our study addresses a critical gap by introducing the first consistent dataset that maps structural diversity across the forested domain in Europe. This development will contribute to a more detailed and robust regional analysis on ecosystem dynamics, which critically depend on vegetation structure (Migliavacca et al., 2021) and structural diversity (LaRue et al., 2023), and other facets of biodiversity, which requires information on the vertical profile of plants (Fassnacht et al., 2022).

Our findings revealed that model performance differed according to the spatial resolutions and diversity metrics, with several models achieving R2 values indicative of moderate to strong predictive accuracy, particularly at coarser spatial resolutions (Appendix B, Tables B1 and B2). This variation highlights the critical role of resolution in model performance, indicating that, depending on the application of interest, coarser resolutions may optimize the utility of the models. As expected, spatial cross-validation consistently yielded lower R2 values than random train-validation random validation across most metrics and resolutions. This outcome reflects the challenges inherent on machine learning methods (Meyer and Pebesma, 2021) of predicting outcomes in areas geographically distinct from the training data. Neverthless, the decrease was generally modest, affirming the broad applicability of our models beyond the training domain.

The recursive feature elimination procedure highlighted the importance of textural variables (Fig. S10 in the Supplement) across diversity metrics and spatial resolutions. Entropy, derived from ALOS-PALSAR-2 data, stood out as the most influential variable, corroborating research that demonstrates textural metrics' effectiveness in capturing spatial heterogeneity in structural diversity (Bae et al., 2019). Additionally, the significant role of coherence, which aligns with evidence of its predictive power for forest structural features (Bruggisser et al., 2021; Cartus et al., 2022), suggests its potential in reflecting changes in forest structural density and composition. Collectively, our findings underscore the benefits of integrating various sensor data to enhance the prediction of structural diversity, as evidenced by the diverse contributions of optical and radar-based predictors.

We envisage that our structural diversity dataset will significantly advance future research and practical applications across several disciplines. We identify three key areas where the dataset could be utilised.

Firstly, the dataset could aid in the development of different biodiversity indicators. Ecosystem structure has been identified as an Essential Biodiversity Variable (EBV) (Valbuena et al., 2020), and a wide range of studies have shown a strong correlation between LiDAR-based metrics and ground-based biodiversity measurements (Marselis et al., 2020). The metrics developed here could be used to identify areas with unique structural features that harbour high levels of biodiversity. Furthermore, integrating them with data from other sensors, such as Sentinel 1 and Sentinel 2, offers a promising avenue for generating accurate spatial explicit estimates of different indicators, thus paving the way for the development of frameworks for monitoring long-term biodiversity changes.

Secondly, the dataset offers a valuable resource for quantifying the observed impacts of global change drivers on the functioning of European forest ecosystems. The increasing recognition of the role of structural diversity in driving ecosystem processes (Ali et al., 2016; Aponte et al., 2020; Listopad et al., 2015) underscores the importance of our metrics. Consequently, our dataset provides a crucial tool for enabling comprehensive, data-driven assessments of the impact of climate and land cover changes on the functioning of forest ecosystems across large scales, addressing the previous limitations posed by the unavailability of structural diversity data over extensive spatial scales.

Thirdly, the dataset could be used for improving Earth system models. Historically, plant canopy structure has not been adequately represented in these models (Atkins et al., 2018; Schneider et al., 2020). This lack of detailed representation can lead to significant errors in predicting energy balance, carbon cycling, and ecosystem responses to environmental changes (Duveiller et al., 2023). Integrating structural diversity into these models has the potential to enhance the accuracy of simulations by incorporating more realistic representations of light interception, photosynthetic rates, and energy fluxes. In particular, these applications are directly relevant to contemporary Earth system modelling frameworks such as CMIP6 and forthcoming CMIP7 simulations, which underpin IPCC climate assessments and projections.