Differentiable land model reveals global environmental controls on latent ecological functions

Abstract

The spatial distributions of plant functional traits observed today are living imprints of current environmental gradients and past selection, offering insight into how plants have adapted to their environments. What remains insufficiently understood is how traits combine and coordinate across environments, and whether such coordination reflects organizing principles in ecology that can improve modeling of ecosystem functional diversity and decadal-scale carbon exchange. Here we present DifferLand, a differentiable hybrid model that learns high-dimensional, coordinated environment–trait relationships directly from multi-modal satellite and in situ observations. DifferLand reveals a small number of latent axes that represent how suites of plant traits jointly shape vegetation dynamics and carbon–water fluxes, enabling the model to capture both long-term adaptation patterns and short-term responses to meteorological variability, and to outperform models that rely solely on plant functional types in spatial generalization. The spatialization network learns nonlinear interactions between plant functional attributes and environmental gradients, organizing latent ecological parameters that represent functional traits at the global scale. This latent environment–trait structure reveals large-scale patterns of ecosystem functional diversity and improves the spatial generalization of terrestrial biosphere models.

Plants exhibit global patterns shaped by environment and evolution, yet how vegetation traits organize to produce observed ecological functions remains unclear. This study introduces DifferLand, which learns global environment–trait relationships from observations, reveals latent axes of ecological function, and improves the spatial generalization of carbon–water fluxes.

Introduction

Understanding how spatial gradients in abiotic and biotic drivers, such as climate, soils, and forest age, shape the distribution of plant functional traits is a long-standing question in ecological and climate research. Modern ecology theory posits that abiotic environmental filters¹ constrain viable plant functional trait combinations within bioclimatic envelopes, while local biotic interactions, dispersal limits, and disturbance histories further shape current plant trait distributions². These interacting eco-evolutionary processes underpin an ongoing debate (Fig. S1): are spatial variations in plant traits and the ecological functions they provide primarily explained by universal scaling relationships with spatial gradients of abiotic factors (i.e., the functional convergence hypothesis)³, or do species or plant functional type (PFT)-specific controls dominate⁴, limiting the ability of environmental gradients⁴ to predict within-PFT trait variation and their roles in the carbon cycle?

If climate and other environmental gradients constrain the set of viable functional traits, it follows that they should strongly predict the current distribution of physiological and morphological plant traits. However, evaluations of univariate environment–trait relationships found environmental variables, such as mean temperature, water availability, and soil properties, typically each explained <10–20% of the trait variations⁴. In contrast, global multivariate analyses of trait–trait relationships reveal that plant functional traits covary along key axes^5–7—such as the leaf economics spectrum⁸ and the allometry continuum⁹, reflecting the coexistence of multiple adaptive strategies shaped by trade-offs under natural selection. These contrasting patterns suggest that while abiotic gradients influence trait distributions, their effects are often expressed through integrated trait combinations shaped by multiple constraints, rather than through universal relationships between individual traits and single environmental predictors⁴.

Capturing the complex interplay between plant traits and environmental drivers requires moving beyond fixed PFT or univariate trait–environment relationships¹⁰, toward models that represent how multiple traits jointly shape vegetation dynamics through biological interactions and biome-specific influences. However, current terrestrial biosphere models (TBMs) typically prescribe fixed parameter sets for each PFT, assuming uniform trait distributions within broad life-form categories (e.g., deciduous vs. evergreen, broadleaf vs. needleleaf)¹¹. This assumption has long been criticized for neglecting local adaptation and within-generation response to microclimate, topography, and disturbance—as within-PFT variation can be as large as differences among PFTs^12–14. Directly specifying multiple spatially explicit trait-based parameters is also impractical due to the high dimensionality of trait diversity and the challenge of scaling from species to ecosystem levels^15,16.

Nonetheless, despite these limitations, mechanistic TBMs encode key physiological processes including photosynthesis, respiration, allocation, turnover, and responses to environmental stress. As a result, they provide our best process-based approximation of how traits, represented as model parameters, jointly mediate carbon and water exchanges with the atmosphere⁴. This perspective motivates our central hypothesis: that multivariate trait–environment relationships may be learned by inverting a TBM using observed global vegetation dynamics and spatial environmental predictors of plant traits. The tradeoffs and covariation among high-dimensional ecological parameters, together with the nonlinear interactions of environmental gradients, can be effectively represented in an ‘ecological latent space’¹⁷, a physics-informed machine learning-derived low-dimensional embedding^18,19 of global ecological functions, that enhances predictions of land–atmosphere carbon and water exchange beyond models relying on PFT-based parameterizations.

In this study, we introduce DifferLand, a differentiable terrestrial biosphere model that learns global trait–environment relationships directly from satellite and in situ observations. These relationships allow the model to capture both the long-term adaptation of vegetation to prevailing environmental conditions and its short-term sensitivity to seasonal and interannual meteorological variability, yielding more accurate predictions of global vegetation dynamics and carbon exchange than models that rely solely on PFT classifications or a few specific trait–environment linkages. We find that the retrieved environment–trait relationships arise from nonlinear interactions between PFT-specific attributes and local environmental gradients. Moreover, the organization of traits along major ecological axes emerges naturally from observed vegetation dynamics, providing a key source of predictability for spatial variations in ecosystem functioning within the high-dimensional space of plant functional diversity.

Results

Learning environment–trait relationships via differentiable modeling

DifferLand is a fully differentiable hybrid terrestrial biosphere model that unifies neural-network learning of global trait–environment relationships with process-based simulation of local carbon–water dynamics (Fig. 1). A global spatialization network (Fig. 1b) infers latent ecological parameters (Fig. 1c) from environmental predictors (Fig. 1a), which are then passed to a mechanistic model (Fig. 1d) that resolves monthly carbon uptake, respiration, fire carbon emissions, and associated changes in land carbon pools. Differentiability enables end-to-end optimization of these trait–environment relationships by propagating observation–model mismatches (Fig. 1e) back through the mechanistic model at each timestep.

Fig. 1. Schematics of the DifferLand framework.

a DifferLand integrates spatial information from four groups of environmental predictors: plant functional types (PFTs), climatology and elevation (CLIM), forest age and maximum canopy height (AGE), and soil texture properties (SOIL). b During a forward pass (black arrows), a spatialization neural network learns environment–parameter relationships, mapping these predictors to c global fields of ecological model parameters, which act as model representations of plant functional traits and regulate vegetation processes such as photosynthesis, carbon allocation, carbon turnover in different carbon pools, and sensitivities to drought and fire. d A terrestrial biosphere model uses these parameters together with meteorological forcing to simulate ecosystem state variables and fluxes, including leaf area index, biomass pools, photosynthesis, respiration, and carbon and water exchange. e DifferLand then evaluates the simulated states and fluxes against multiple streams of satellite and in situ observations. Its differentiable structure (orange arrows) provides gradients of the model–data mismatch with respect to the ecological parameters. These gradients update the spatialization network through iterative optimization of the inferred environment–parameter relationships. “Schematics of the DifferLand framework” created in BioRender. Fang, J. (https://BioRender.com/ne0dr93) is licensed under CC BY 4.0.

By coupling spatial environmental gradients, which structure trait distributions on decadal timescales, with grid-cell-level process representation, DifferLand reveals functional relationships linking plant traits to climate, soils, and vegetation history while retaining sensitivity to transient local meteorological forcing at monthly timescales. Its flexible data assimilation framework integrates diverse constraints, including satellite observations, eddy covariance fluxes, global soil carbon, and atmospheric inversions, as illustrated in Fig. S4, allowing the learned relationships to capitalize on spatial correlations, trait covariation, and the physical consistency of process-based modeling. This approach provides a unified, observation-constrained framework for uncovering the environmental determinants of vegetation function and improving predictions of the terrestrial carbon cycle.

Environmental control of ecological functional parameters

To evaluate whether trait–environment relationships provide independent information for predicting global ecological dynamics beyond what is captured by PFT-based categories, we trained models using either only PFT fractions as spatial predictors or a combination of PFT fractions and environmental predictors reflecting climatology, forest age and growth potential, and soil properties. Note that in both cases, all tunable ecological parameters in the process-based model, as well as the initial values of the carbon and water pools, are optimized against observations using the same meteorological forcings via the spatialization network. Thus, the performance differences reflect the information content of the spatial predictors rather than differences in default parameter choices, model initialization, or structural assumptions.

We train and evaluate the model on satellite-based indices that include leaf area index (LAI)²⁰ as a measure of canopy structure, a solar-induced fluorescence (SIF)-based photosynthesis proxy²¹, a top-down inversion of net biosphere exchange (NBE) constrained by column-integrated CO₂ concentration from satellites²², satellite gravimetry-based anomalies of total equivalent water thickness (EWT) over land²³, and a global evapotranspiration (ET) product derived from a satellite-data-constrained model²⁴. We performed detailed sensitivity analyses and found the results to be robust to the choices of alternative datasets (Supplementary Note 4 and Fig. S29).

Experiment results demonstrate that environmental gradients provide essential spatial information beyond plant functional types (PFTs) for predicting vegetation trait distributions. When incorporating all environmental predictors (PFTs, climate variables, forest age, and soil properties), DifferLand effectively captures the spatial and temporal patterns of both in situ and remotely sensed observations of vegetation dynamics from 2001 to 2023 (Figs. S14−S17). It generalizes well to held-out pixels, achieving total spatiotemporal R² values of 0.88 ± 0.01 for LAI, 0.76 ± 0.01 for SIF, 0.71 ± 0.03 for NBE, 0.68 ± 0.02 for ET, and 0.45 ± 0.01 for EWT. The model also accurately captures the mean global biomass (Fig. S23a) and reasonably reproduces the assimilated trends in biomass over the past two decades (Fig. S23b). Notably, the model demonstrates minor differences in predictive performance between the training and test pixels, suggesting the model generalizes well at unseen pixels (Figs. S14−S17). In contrast, the baseline model relying solely on PFT fractions yields lower total R² scores of 0.86 ± 0.01, 0.73 ± 0.01, 0.60 ± 0.03, 0.52 ± 0.02, and 0.42 ± 0.01 for LAI, SIF, NBE, ET, and EWT respectively, when evaluated over held-out pixels, and exhibits a total spatiotemporal mean absolute error (MAE) that is 3–20% higher than those of the full environmental predictor configuration (Fig. 2a). These findings indicate PFTs alone do not fully capture the spatial variability in ecological parameters required to explain the observed global vegetation dynamics recorded by satellite and atmospheric inversion data.

Fig. 2. Hierarchical partitioning of explained variance by four predictor groups.

Panel a compares the total spatiotemporal mean absolute error on held-out pixels for LAI, NBE, SIF, EWT, and ET across three model configurations between 2003 and 2023: PFT-only, environmental variables only (CLIM + SOIL + AGE), and combined PFT and environmental variables (PFT + CLIM + SOIL + AGE). Each bar shows the mean absolute error (MAE) normalized relative to the PFT-only configuration, averaged over 10 out of 20 ensemble members that achieved the best loss on the validation set; dots represent metrics of individual members; error bars denote the corresponding normalized standard deviation across the ensemble. Panels b–f show the proportion of temporal variance explained in LAI, NBE, SIF, EWT, and ET within each grid cell during the same period, attributed to the model using ecological parameters predicted from spatial information in PFT, CLIM, AGE, and SOIL variables, respectively. The inset shows the proportion of pixels where each predictor group (PFT or environmental variables) has the dominant effect.

However, the results also indicate that environmental variables alone are insufficient to capture spatial variations in latent ecological traits represented by the model parameters. While using only climatology, soil, and age predictors reduces MAE for ET predictions by 15% compared to the PFT-only baseline, PFT-specific information remains crucial for explaining variability in canopy structure, as reflected in LAI, and in photosynthetic activity, as measured by SIF (Fig. 2a). When both PFT fractions and environmental variables are used as predictors, we observe larger reduction in errors compared to using either PFTs or environmental variables alone (Fig. 2a). For EWT, changes are relatively minor regardless of the choice of spatial predictors, likely because total water storage anomalies at the coarse spatial scale (4° × 5°) are primarily driven by meteorological anomalies rather than spatial variations in ecological parameters. Overall, these findings suggest that interactions between PFTs and environmental variables are key to explaining variations in ecological functions related to vegetation growth and the carbon cycle, while water cycle dynamics are more strongly governed by environmental conditions or meteorological forcings. We also confirmed that the improved performance when including additional environmental variables cannot be explained solely by the increased degrees of freedom in the spatialization network or spatial autocorrelation in the predictors (Figs. S21 and S22).

To evaluate the independent contributions of different groups of spatial predictors, we performed a full-factorial experiment in which we systematically included or excluded each group of predictors—PFT, CLIM, AGE, and SOIL—and assessed their impact on the model’s ability to capture global ecological dynamics. Because of potential confounding signals among these predictor groups, we applied a hierarchical partitioning algorithm (see the “Methods” section) to disentangle their unique contributions. This method accounts for the interaction effects across different predictor groups and ensures that the sum of independent effects attributed to each predictor group equals the model’s performance when using the full set of predictors. With these metrics, we mapped the dominant predictor group across regions to identify which spatial predictors most strongly explain ecological dynamics within different biomes (Fig. 2b–f).

Hierarchical partitioning reveals that plant functional type (PFT) distribution plays a dominant role in regulating carbon cycle dynamics, emerging as the most important predictor for LAI (Fig. 2b), NBE (Fig. 2c), and SIF (Fig. 2d), dominating across 41–43% of land pixels. Spatially, the explanatory power of PFTs is positively correlated with local land cover heterogeneity (Spearman’s r = 0.32, p < 0.001), particularly in regions with sharp ecotones or steep land-use intensity gradients, such as the periphery of the Amazon Basin and the Sahel, where PFT fractions explain the largest variance. In contrast, the relative importance of PFTs is lower for water cycle variables such as EWT and ET, dominating the explanation in only 27–30% of the pixels. Environmental predictors, on the other hand, provide crucial information for regional variations in ecological parameters within each PFT (Figs. S24 and S25). Specifically, CLIM variables exert greater influence in mid-latitude herbaceous biomes characterized by strong climatological gradients, such as the Eurasian Steppe and the North American Great Plains. AGE variables (e.g., estimated forest age and maximum canopy height) are important for perennial vegetation and help differentiate vegetation function in mixed tree–grass systems. While SOIL variables play a minor role in explaining carbon cycle dynamics, they are essential for predicting EWT and ET, particularly in sparsely vegetated regions (Fig. 2e, f).

To understand the implications of parameter spatialization for simulated carbon dynamics, we evaluated DifferLand’s simulated carbon and water fluxes against eddy covariance observations and an ensemble of state-of-the-art land surface models. Comparison of model prediction of gross primary productivity (GPP), ET, and ecosystem respiration (RECO) against a subset of n = 128 eddy covariance sites with at least 12 months of record for all three variables during the simulation period (Supplementary Data 1 and Fig. S36) suggests the model achieved good agreement with site-level fluxes in mean spatial gradients (Fig. S20), attaining spatial correlation of 0.87 for GPP, 0.81 for RECO, and 0.72 for ET across all sites (spatial correlation of 0.78, 0.85, and 0.87 on n = 17 held-out sites) and effectively captured temporal variations of GPP, ET, and RECO across the eddy covariance sites (Figs. S18 and S19). These results are consistent across different filtering thresholds to reduce the spatial mismatch between the eddy covariance tower and the model grid cells (Supplementary Note 5). Furthermore, DifferLand closely reproduced the seasonal cycle (Fig. S11), annual anomalies (Fig. S10), and decadal trajectories (Fig. S9) of the assimilated CMS-Flux NBE dataset derived from atmospheric inversions for 2010–2022. The model also showed robust performance across different atmospheric inversion products and was able to largely reproduce global interannual variability in carbon fluxes during periods preceding the availability of satellite observations of column-integrated CO₂ (Supplementary Note 5). Despite its comparatively simplified process representation, DifferLand achieved significantly lower root mean squared errors and comparable correlation with the atmospheric inversion dataset than the much more structurally sophisticated dynamic global vegetation models (DGVMs) in the TRENDYv12 S3 ensemble²⁵ (Table S4), both globally and regionally, after assimilating the CMS-Flux (Figs. S7–S11). These results suggest that uncertainties in model parameters are a major source of error in simulating land–atmosphere carbon fluxes at decadal timescales, and that learning environment–trait relationships with differentiable model–data fusion can effectively reduce parameter uncertainties and improve alignment with top-down observational constraints.

Spatial coordination of ecological parameters

DifferLand’s ability to robustly predict vegetation dynamics across space by leveraging environment–parameter relationships suggests that global vegetation patterns may give rise to globally convergent plant functional traits, which in turn enable spatial predictability of the terrestrial carbon cycle. To investigate this hypothesis, we conducted a principal component analysis (PCA) on 13 ecologically meaningful and spatially identifiable parameters (see the subsection “Parameter identifiability analysis” in the “Methods” section and Supplementary Note 6) retrieved from the model using the full set of spatial predictors to identify covarying traits and the primary axes of spatial variability (Fig. 3a). To further examine how environmental drivers influence the covariation among ecological parameters, we applied Shapley Additive exPlanations (SHAP) to the ecological axes obtained by projecting the predicted parameters onto the principal components (PCs) using the loadings from the PCA (Fig. 3e–g). We assessed the overall importance of each spatial predictor by calculating its mean absolute SHAP value and quantified the strength and directionality of its influence using the difference in SHAP values between the upper (Q3) and lower (Q1) quantiles. This approach retains the nonlinear trait–environment relationships captured by the spatialization network while simplifying the analysis of parameter covariation through a linear transformation of the ecological space.

Fig. 3. Coordination of latent ecological functional traits along three principal axes.

a Principal component analysis (PCA) of 13 latent ecological parameters inferred from the ensemble mean of the PFT + CLIM + SOIL + AGE model configuration. The loadings that project each parameter onto the first three PCs are plotted in the 3D plot. The 13 parameters include canopy photosynthetic efficiency (ce), underlying water use efficiency (uWUE), temperature sensitivity of heterotrophic respiration (Q10), autotrophic respiration fraction (f_auto), litter turnover rate (k_litter), leaf carbon mass per area (LCMA), leaf onset (c_ronset) and fall duration (c_rfall), leaf lifespan (τ_foliar), and allocation fraction of GPP to labile (A_labile), foliar (A_foliar), wood (A_wood), and fine roots (A_root) pools. b–d Spatial distribution of PC1–PC3 scores projected from the spatialization neural network onto the PCA axes, with the proportion of variance explained by each component labeled. e–g SHAP-based feature attribution for each principal component, showing the influence of spatial predictors. Bars represent mean absolute SHAP values (feature importance), while colors indicate the direction and strength of association, calculated as the median SHAP difference between the upper (Q3) and lower (Q1) quartiles of each predictor.

The first principal component (PC1), explaining 53.2% of the variance, reflects the well-established leaf economics spectrum, distinguishing between plants that invest in long-lived leaves with high leaf carbon mass per area (LCMA) and those with shorter-lived leaves characterized by lower carbon investment and greater allocation to labile carbohydrates supporting seasonal leaf onset (Fig. 3b). The second component (PC2), explaining 22.1% of the variance (Fig. 3a,c), captures the tall–short vegetation gradient (Fig. 3g): short, often herbaceous vegetation exhibits high photosynthetic capacity and rapid litter turnover, whereas taller vegetation tends to have lower photosynthetic efficiency and allocates more carbon to woody biomass. These two ecological axes are well documented in trait databases at the species and community levels^5,6,9, but here we show they also emerge from satellite-observed vegetation dynamics without imposing explicit trait–environment relationships. The analysis also revealed a third component (PC3), orthogonal to the two natural trait coordination axes, which explains 10.5% of the variance (Fig. 3d) and is associated with regions of high photosynthetic efficiency and intensive cropland use, such as the U.S. Midwest, Southern Europe, and Eastern China. This pattern is consistent with the widespread cultivation of high-yield crop varieties and the prevalence of photosynthetically efficient C4 crops in these regions.

Mean annual temperature emerged as the primary predictor for all three principal components (PCs; Fig. 3e–g), reflecting a first-order energy control on plant functional traits. In warmer climates, plants tend to exhibit traits that support longer growing seasons, higher photosynthetic efficiency, greater allocation to woody biomass, and taller canopy height—strategies advantageous for light competition and perennial growth. In contrast, plants in colder environments adopt traits such as shorter stature, reduced leaf lifespan, and increased carbon allocation to belowground biomass. Maximum canopy height, a proxy for growth potential, is most strongly associated with PC2. Despite the dominant role of climate, PFT predictors also play a key role in shaping the ecological axes. Although a model configuration using only environmental predictors (CLIM + SOIL + AGE) can broadly reproduce the spatial patterns of PC1 and PC2 (Fig. S27), the inclusion of plant functional type (PFT) information, particularly cropland extent, is essential to capture the spatial variability related to managed crop productivity represented in PC3. In contrast, model configurations using only PFT-based predictors cannot capture the same set of coordinated axes (Fig. S28). These findings suggest that while the covariation of ecological parameters primarily reflects macroecological environmental gradients, it also bears the imprint of present-day PFT distributions and land-use legacies.

Apparent global vs. PFT-specific relationships

To further interpret how ecological parameters depend on climate, soil, and age predictors, we applied SHAP explainable AI analysis (see the “Methods” section) to the spatialization neural network to isolate specific trait–environment relationships. When incorporating both plant functional type (PFT) classes and environmental variables, the combined PFT classes explain ~35–50% of the spatial variability, as measured by absolute SHAP values (Fig. S26), consistent with the hierarchical partition results (Fig. 2). To investigate the interaction between PFTs and environmental predictors, we compared functional relationships derived from model configurations with and without PFT predictors. The PFT-agnostic configuration (CLIM + SOIL + AGE) attempts to identify apparent global relationships between latent ecological parameters and spatial predictors, representing a hypothetical scenario where environment–trait relationships are uniform across PFTs. Conversely, the PFT-aware model captures PFT-specific dependencies between ecological parameters and environmental variables.

For a clearer extraction of environment–parameter relationships within each vegetation type, we restricted the SHAP analysis to pixels where a single PFT occupies at least 80% of the grid cell. Our analysis focused on three key ecological parameters that are robustly identifiable from global vegetation dynamics and exhibit distinct spatial patterns: photosynthetic efficiency, carbon use efficiency, and root carbon allocation ratio. Among the environmental predictors, mean annual temperature and maximum canopy height were the most influential, followed by mean annual precipitation to a lesser extent. We therefore examined their specific relationships with the selected ecological parameters (Fig. 4).

Fig. 4. Comparison of global and PFT-specific trait–environment relationships.

SHAP-derived dependencies of a–c nitrogen-limited photosynthetic efficiency (gC m⁻² leaf day⁻¹), d–f carbon use efficiency (unitless, 0–1), and g–i fine-root carbon allocation ratio (unitless, 0–1) on a, d, g mean annual temperature, b, e, h mean annual precipitation, and c, f, i maximum canopy height. The global relationships (dashed lines) represent ensemble-mean SHAP-derived dependencies from the CLIM + SOIL + AGE model configuration. PFT-specific relationships are derived from the PFT + CLIM + SOIL + AGE model configuration, using samples where the specified PFT comprises at least 80% of the pixel. Solid lines denote smoothed relationships obtained using a univariate spline fit to the ensemble mean (M_ens) SHAP after excluding the 1st and 99th percentile of the predictor range. Note the baseline is added back to each SHAP value. Shaded regions indicate ±1 standard deviation of residuals between the observations and the fitted spline. PFT abbreviations: GRA grassland, SH shrubland, DBF deciduous broadleaf forest, NF needleleaf forest, EBF evergreen broadleaf forest.

Mean annual temperature exerts a dominant and often nonlinear influence on all three ecological parameters (Fig. 4a, d, g), indicating strong temperature regulation of ecosystem function, consistent with the PC-level analysis (Fig. 3). Photosynthetic efficiency rises with MAT from –10 to 15 °C before plateauing (Fig. 4a), while carbon use efficiency (NPP/GPP) declines from 0.45 to 0.35 and then stabilizes (Fig. 4d). Although global patterns are broadly mirrored within plant functional types (PFTs), notable differences exist in both mean values and temperature sensitivity. Grasslands and shrublands, spanning wide thermal ranges, generally exhibit higher photosynthetic efficiency (Fig. 4a), carbon use efficiency (Fig. 4d), and fine root allocation ratios (Fig. 4g) than forests—traits reflecting acquisitive growth strategies in open habitats. In contrast, evergreen broadleaf forests show conservative strategies with low photosynthetic efficiency (Fig. 4a) and low carbon use efficiency (Fig. 4d), adapted to humid tropical conditions. Deciduous broadleaf forests and needleleaf forests exhibit sharp internal temperature sensitivity despite lower mean photosynthetic efficiencies than grasslands and shrublands. These PFT-specific patterns highlight that PFT-specific responses can diverge from global trends, underscoring the need to account for both within- and across-PFT variations in modeling trait–temperature relationships.

In contrast, the apparent global sensitivity of the three ecological parameters to mean annual precipitation largely reflects differences among distinct PFTs distributed along the precipitation gradient, rather than variations within PFTs. For example, grasslands and shrublands, typically characterized by higher photosynthetic efficiency, are more common in drier regions than forests, resulting in an apparent global decline in photosynthetic efficiency with increasing precipitation (Fig. 4b). However, within-PFT variation in precipitation is generally small. For carbon use efficiency (Fig. 4e) and root carbon allocation ratio (Fig. 4h), we still observe negative relationships with precipitation within most PFTs, consistent with global trends, though the within-PFT sensitivities are generally smaller than the differences across PFTs. The divergence between global and within-PFT patterns is most pronounced in the relationship between maximum canopy height and photosynthetic capacity: while the global negative relationship is driven by differences in photosynthetic efficiency across PFTs (Fig. 4c), the within-PFT relationship is positive, suggesting that regions with greater resource availability support both higher canopy stature and photosynthetic potential. These retrieved relationships are broadly consistent with independent upscaled datasets, despite differences due to scale mismatch, observation uncertainties, and different physical meanings between individual plant trait measurements and model parameters representing effective traits at the ecosystem level (Fig. S48 and Supplementary Note 6). These contrasting patterns underscore the complementary roles of PFT and environmental gradients in shaping ecological parameter variation, reflecting distinct ecological processes operating at different organizational scales.

Discussion

DifferLand demonstrates a scalable method for retrieving the dependencies of global ecological parameters to climate, age, and soil. Unlike most model–data fusion studies that either optimize parameters independently at each grid cell^14,26 or rely on prescribed environment–trait functional forms for individual parameters²⁷, DifferLand captures the spatial coordination of ecological traits and their responses to environmental gradients through a unified latent space. This enables the derivation of a physically consistent, data-constrained set of ecological parameters that generalizes better to unseen locations than traditional PFT-based approaches used in most current TBMs, thereby improving predictions of carbon and water fluxes across finer environmental gradients.

We note that the conclusions drawn from this research are dependent on the timeframe considered for the observations. In this 23-year study, spatial predictors were treated as temporally invariant, under the assumption that their temporal variations are negligible compared to their mean spatial gradients. Furthermore, we assumed that the relationships between parameters and the environment remained stable throughout the study period, implying that adaptation to environmental changes occurs on much longer timescales. However, these assumptions may not always hold for long-term predictions, in which case environmental conditions, land use patterns, population distributions²⁸, community compositions²⁹, and plant functional responses³⁰ could all undergo significant shifts. At multidecadal to centennial timescales, slow processes such as CO₂ fertilization³¹, nutrient limitation³², evolving forest demography^33,34, and belowground carbon dynamics^35,36 can dominate the trajectories of land-atmosphere carbon exchange, yet most of these slow processes can be constrained only with long-term observations or by making equilibrium assumptions. Future work should further investigate shifts in ecological parameters in response to a changing environment using long-term observational records.

Analysis on identifiable model parameters unveiled correlations between them (Fig. 3). From a modeling perspective, inter-parameter correlation reduces the effective dimensionality of model parameters, and the sparsity of the latent parameter space is crucial for effective out-of-sample generalization in conditions unseen in the observational record^37–40. Essentially, our ability to model high-dimensional physical worlds relies on the fact that most systems have much lower intrinsic dimensions governed by a few fundamental variables^37,41–44. Natural selection, self-organization, and entropy maximization have been proposed as three organizing principles that introduce predictability to vegetation dynamics^45,46, giving rise to optimality-based trait spectra of photosynthesis^47,48, leaf size and economics^8,49–51, plant hydraulics^52–55, and carbon allocations^56–58 that reflect trade-offs under multiple selection forces.

Previous studies have leveraged dimensionality reduction algorithms on surface gas exchange measurements⁷ and global trait databases^5,9 to extract the main axes of ecosystem traits and functions, yet they are limited by the available set of observable plant traits and uneven spatial sampling. By integrating the spatialization neural network with a differentiable TBM and assimilating diverse observations, DifferLand imposes a comprehensive set of constraints on the latent space, capturing both observed and unobserved dynamics and process dependencies. The two dominant axes of latent parameter variation correspond to leaf economics and plant stature, while a third diagnostic axis captures residual effects of human land use. Together, these axes highlight that environment–parameter relationships governing carbon and water fluxes emerge from the interaction between macroecological gradients and PFT-specific effects. It has been shown that state-of-the-art land models using PFT-based parameterizations overestimate the correlation between ecosystem functions compared with observations⁷, limiting their capacity to simulate the full diversity of ecosystem function space, such as the spatial variations of carbon-use efficiency and water use strategies, and therefore likely their response to climate change⁷. Despite its parsimonious process representation (Supplementary Note 7), DifferLand showcases how data-constrained hybrid differentiable modeling can retrieve complex environment–trait relationships from observations and provide a more comprehensive view of the vegetation–environment relationships.

We propose that hybrid-physics modeling offers a promising pathway for parameter calibration in operational land surface models (LSMs), a process that is currently constrained by the high dimensionality of the parameter space and the substantial computational costs involved⁵⁹. Many existing parameter estimation studies in LSMs have focused on only one or a few parameters at a time, often assigning uninformative and independent priors (represented by diagonal prior covariance matrices), which misrepresent potential parameter covariation and confounding effects⁵⁹. By first identifying parameters that are both observationally constrained and climatically sensitive within an intermediate-complexity framework, researchers can prioritize a tractable subset of candidate parameters for subsequent analysis in full-complexity LSMs. Moreover, the robust spatial coordination of ecological traits revealed in our study provides a meaningful source of predictability to help address the “curse of dimensionality” in complex models^15,16. By encoding these correlation relationships between parameters into an informative prior covariance matrix, we can robustly constrain the parameter search space for more complex models and reduce equifinality.

In the long term, the differentiable programming paradigm explored in DifferLand offers a promising avenue for addressing the structural and parametric biases that currently limit confidence in long-term projections of the terrestrial carbon sink⁶⁰. Differentiable programming enables end-to-end learning of ecological functional relationships within an ecologically consistent modeling framework, creating new opportunities to uncover emergent patterns in ecosystem processes⁶¹. By integrating multi-modal observations of today’s climatic, ecological, and hydrological states, these emergent patterns may provide tighter constraints on uncertainties in future climate projections than constraints from traditional emergent-constraint studies, which largely depend on simple univariate linear relationships between current and projected climate⁶². Furthermore, coupling differentiable land models with differentiable general circulation models, such as NeuralGCM⁶³, opens a powerful future pathway for jointly learning biophysical and biogeochemical feedbacks between land and atmosphere across sub-seasonal to decadal timescales. While implementing a differentiable land model may require substantial initial technical and numerical investment, particularly in translating legacy components written in C or Fortran into modern differentiable frameworks, the potential long-term benefits are considerable. Such integration has the potential to improve the fidelity of simulating both the terrestrial carbon cycle and the broader climate system in next-generation hybrid Earth System Models⁶⁴.

Methods

DifferLand: a hybrid-ML terrestrial biosphere modeling framework

The DifferLand configuration used in this study includes three main components: a spatialization neural network that maps spatial predictors to ecological model parameters, a process-based dynamical terrestrial biosphere model, and a loss function that computes the distance between simulated variables and observational constraints. We note that the DifferLand framework is flexible, and it can accommodate different process-based or neural network components to model ecological functional relationships⁶⁵. The spatialization network ($f_{\mathrm{nn}}$) (Fig. S3) consists of, first, a fully-connected neural network (FCNN) with three hidden layers and 32 neurons that maps the input predictors ($\mathbf{P}$) to a 32-dimensional embedding. This embedding is then passed into three output layers, predicting the ecological model parameters of the Data Assimilation Linked Ecosystem Carbon (DALEC) model (${\mathit{\theta }}_{\mathrm{e}},$ n = 31), the initial pool values (${\mathit{\theta }}_{\mathrm{i}}$, n = 7), and two phenology parameters (${\mathit{\theta }}_{\mathrm{p}}$, n = 2), respectively. ${\mathit{\theta }}_{\mathrm{e}}$ and ${\mathit{\theta }}_{\mathrm{p}}$ together constitute the model parameters of the DALEC model (${\mathit{\theta }}_{\mathrm{M}}$). The rectified linear unit (ReLU) is used as the activation function of all NN layers. NN parameters (${\mathit{\theta }}_{\mathrm{nn}}$) include weights and biases in each layer. Weights are randomly initialized using the Xavier initializer⁶⁶, and biases are set to one. A transform function (Supplementary Note 1) is used to convert each parameter from the real space to its physical range (see Table S2 for a list of the parameters and their physical range). In mathematical form (Eq. (1)), the spatialization network can be expressed as

$${{\mathit{\theta }}_{\mathrm{M}}^k,{\mathit{\theta }}_{\mathrm{i}}^k=f}_{\mathrm{nn}}\left({\mathbf{P}}^{\mathbf{k}},\left.∣\right),{\mathit{\theta }}_{\mathrm{nn}}\right)$$ 1

where k denotes the kth pixel in spatial coverage. Note that ${\mathit{\theta }}_{\mathrm{nn}}$ is not spatially varying, as we assume a global relationship between environmental predictors and model parameters in this hierarchical framework.

The centerpiece of DifferLand is an automatically differentiable version of the DALEC model, meaning that the model has the capacity to compute gradients and the sensitivity to any parameter or variable in the model with respect to a model output using back-propagation (adapted from model version 1006, see Fig. S5 for model schematics). DALEC is an intermediate-complexity dynamical terrestrial biosphere model that simulates photosynthesis, carbon allocation, leaf phenology, autotrophic and heterotrophic respiration, turnover, decomposition, and fire disturbance. Labile, foliar, wood, fine roots, litter, and soil carbon pools are prognostically computed at each time step based on mass balance principles^14,67,68. The model also simulates ET based on an underlying water use efficiency formulation^69,70, and computes a prognostic water bucket as a balance between precipitation, runoff, and ET. The water bucket feeds back into photosynthesis to represent soil water limitation on GPP^65,71. Versions of the DALEC model have been used in the CARbon DAta MOdel fraMework (CARDAMOM) to conduct model-data fusion studies at local^67,72,73, regional^71,74, and global scales¹⁴. At each time step t for location k, this TBM ($f_{\mathrm{M}}$) uses meteorological forcing variables (${\mathbf{m}}^{k,t}$) to prognostically evolve state variables ($\mathbf{x}$) and compute observable ($\overline{{\mathbf{y}}_{\mathbf{o}}}$) and unobservable ($\overline{{\mathbf{y}}_{\mathbf{u}}}$) ecological variables and fluxes (Eq. (2)). We note that at t = 0, ${\mathbf{x}}^{k,0}={\mathit{\theta }}_{\mathrm{i}}$

$$\widehat{{\mathbf{y}}_{\mathrm{o}}^{k,t}},\widehat{{\mathbf{y}}_{\mathrm{u}}^{k,t}},{\mathbf{x}}^{k,t+1}=f_{\mathrm{M}}\left({\mathbf{x}}^{k,t},{\mathbf{m}}^{k,t},\left.∣\right),{\mathit{\theta }}_{\mathrm{M}}^k\right)$$ 2

Substituting Eq. (1) into Eq. (2) and considering the legacy effects of meteorological forcing on ecological states, we have

$$\widehat{{\mathbf{y}}_{\mathrm{o}}^{k,t}},\widehat{{\mathbf{y}}_{\mathrm{u}}^{k,t}},{\mathbf{x}}^{k,t+1}=f_{\mathrm{M}}\left({\mathbf{m}}^{k,1},{\mathbf{m}}^{k,2},\dots {,\mathbf{m}}^{k,t},\left.∣\right),f_{\mathrm{nn}}\left({\mathbf{P}}^{\mathbf{k}},\left.∣\right),{\mathit{\theta }}_{\mathrm{nn}}\right)\right)=f_{\mathrm{M}}\left({\mathbf{m}}^{k,1},{\mathbf{m}}^{k,2},\dots {,\mathbf{m}}^{k,\mathrm{t}},\left.∣\right),{\mathbf{P}}^{\mathbf{k}},{\mathit{\theta }}_{\mathrm{nn}}\right)$$ 3

Equation (3) essentially states that the ecological fluxes and states at any time and location are a function of the environmental background (${\mathbf{P}}^{\mathbf{k}}$), the environment-parameter relationships learned through the spatialization network (${\mathit{\theta }}_{\mathrm{nn}}$), the current and legacy meteorological forcings up to that time (${\mathbf{m}}^{k,1},{\mathbf{m}}^{k,2},\dots {,\mathbf{m}}^{k,t}$), and the ecological process dependencies encoded in the TBM (${\mathrm{f}}_{\mathrm{M}}$).

By selecting a parsimonious TBM, we aim to include mechanistic representations that capture essential ecological processes while minimizing equifinality and the high computational costs associated with more sophisticated models. Despite its relative simplicity, DALEC has shown strong performance in capturing global carbon flux dynamics within ranges comparable to much more complex dynamic global vegetation models (DGVMs) and fully coupled Earth System Models (ESMs)⁷⁵. A brief summary of the DALEC model can be found in Supplementary Note 2, and additional details about the adaptations made to convert DALEC into a differentiable model have been described in previous work⁶⁵. We present a worked example from a site in Finland illustrating the inner mechanism of the DifferLand framework: the spatialization network maps environmental predictors into ecological parameters, which then parameterize the DALEC model to simulate trajectories of ecological states and fluxes under monthly meteorological forcing (Fig. S3).

The loss function (Eq. (4)) calculates a weighted sum of mean squared error (MSE) between model-simulated ($\widehat{{\mathbf{y}}_{\mathbf{o}}}$) and observed (${\mathbf{y}}_{\mathbf{o}}$) NEE, LAI, SIF, ET, RECO, VOD, live biomass, fire C emission, and soil organic carbon from gridded datasets. It also compares the differences between simulated and observed GPP, RECO, and ET at a global network of eddy covariance sites where grid cells overlap with tower sites (Fig. S36). Among the variables that are not directly simulated by DALEC but assimilated to inform carbon dynamics, (reconstructed) SIF is assumed to have a linear relationship between modeled GPP at the monthly level⁷⁶, with the slope and intercept of the GPP–SIF relationships treated as model parameters to be predicted from the spatialization neural network⁷¹.

Live biomass was computed as the sum of the labile, foliar, wood, and fine roots carbon pools. In addition, we included two soft constraint terms (${\mathcal{L}}_{\mathrm{constraint}}$) to prevent excessive drying of the water pool and penalize spurious exponential growth and decay in carbon and water pools, as this was previously found important for predicting water dynamics in semi-arid regions and prevent excessive excursions in carbon pool trajectories due to implausible initial conditions (Supplementary Note 3)⁶⁵.

Thus, we have

$$\mathcal{L}={\sum }_{k,t,v}{\alpha }_v{\left(\widehat{y_{\mathrm{o}}^{k,t,v}}-y_{\mathrm{o}}^{k,t,v}\right)}^2+{\mathcal{L}}_{\mathrm{constraint}}$$ 4

Index v denotes the vth variable in the loss function. The gradient of the loss function with respect to the NN parameters in the spatialization network (${\mathit{\theta }}_{\mathrm{nn}}$) is used to optimize the entire framework. We heuristically tuned the weights for different loss terms (${\alpha }_v$) to achieve a balanced performance all observational constraints. The complete set of hyperparameters used in this study is listed in Table S3. We implemented DifferLand in JAX⁷⁷, an automatic differentiation software package built in Python. All code and data used in this study can be accessed with the links provided in the “Code availability and Data availability” sections.

Datasets

DifferLand requires three types of data inputs: spatial predictors ($\mathbf{P}$), forcing variables ($\mathbf{m}$), and observational constraints (${\mathbf{y}}_{\mathbf{o}}$).

Spatial predictors

Spatial variables are classified into four groups: PFT, CLIM, AGE, and SOIL (i.e., $\mathbf{P}\mathit{\subseteq }\mathit{\{}\mathrm{PFT},\mathrm{CLIM},\mathrm{SOIL},\mathrm{AGE}\mathit{\}}$). PFT fractions are derived from MCD12C1.v061 MODIS/Terra + Aqua Yearly Land Cover Type⁷⁸, with the percentage of underlying 500 m classes aggregated to 0.05° grid cells. We further averaged the product to 0.25° to match the modeling grid. We consolidated the International Geosphere Biosphere Program (IGBP) fractions into 10 classes, including needleleaf forest (ENF + DNF), deciduous broadleaf forest (DBF), evergreen broadleaf forest (EBF), mixed forest (MF), shrubland (SH), savanna (WSA + OSA), grassland (GRA), wetland (WET), cropland (CRO + CNM), and a non-vegetated land surface class encompassing all other land cover types (URB + SNO + BSV). Pixels where the area of permanent water bodies exceeds 50% or the non-vegetated surface exceeds 20% were excluded from the analysis.

The CLIM group includes mean annual temperature (MAT, °C) and mean annual precipitation (MAP, mm/year) averaged over 2001–2023 from ERA5 reanalysis by ECMWF⁷⁹. We also include elevation (ELE, m) derived from the Global 30 Arc-Second Elevation dataset (GTOPO30)^80,81.

The AGE predictor group includes forest age (year) estimates obtained from a global 1 km forest age dataset (circa 2010)^82,83, which used a machine learning algorithm and data from more than 40,000 forest inventory plots to estimate global forest age. We used tree age estimates with 10% tree cover correction for our analysis, whereas non-forest pixels were assigned an age value of 1 year, assuming annual vegetation turnover. Also in this group is the maximum canopy height (MCH, m) from the ETH Global Sentinel-2 10-m Canopy Height dataset⁸⁴, accessed from Google Earth Engine. We first computed the 95th-percentile canopy height at 1 km spatial resolution to represent forest growth potential while avoiding single-pixel outliers, followed by calculating the maximum value among the 1 km pixels within each 0.25° grid cell.

SOIL predictors include soil bulk density and soil sand, silt, clay, and gravel fractions derived from the Regridded Harmonized World Soil Database v1.2⁸⁵ available at 0.05° resolution. We combined surface soil (0–30 cm) and deeper soil values (30–100 cm) to a top 1 m value (0–100 cm) by computing a depth-weighted mean. All spatial predictors are assumed to be temporally invariant and converted to a common spatial resolution of 0.25°.

Overall, our predictor selection process prioritized parsimony and interpretability by iteratively adding spatial predictors that enhance model performance across multiple observational constraints (Figs. S14–S17). While we recognize that incorporating additional predictors, such as bioclimatic variables^86,87, might further enhance prediction, we opted to use a limited set of climatological predictors to minimize confounding effects and maintain interpretability. We excluded variables that are only incidentally correlated with spatial variation but do not represent causal controls on the parameters (for example, latitude and longitude), because such predictors encourage the model to learn spurious spatial structure and thereby reduce its ability to generalize in out-of-sample spatial extrapolation (Fig. S22).

Forcing data

Monthly-averaged forcing data used to drive the DALEC model include daily minimum temperature (°C), daily maximum temperature (°C), shortwave solar radiation downward (W/m²), precipitation rate (mm/day), and vapor pressure deficit (kPa) computed from ERA5 reanalysis⁷⁹ between 2001 and 2023 at 0.25° resolution. Globally averaged monthly CO₂ concentration (ppm) was obtained from NOAA Global Monitoring Laboratory measurements⁸⁸. Fire dynamics were driven by burned area from the Fifth Version of Global Fire Emissions Database (GFED5)⁸⁹ at 0.25° resolution between 2001 and 2020. We divided the burned area by the burnable area estimated in GFED5 to obtain the burned area fraction. Because GFED5 burned area data are not yet fully available after 2020, we cross-calibrated GFED5 with monthly MODIS burned area fraction⁹⁰ data resampled to 0.25° to extend the burned area fraction record through 2021–2023.

Observational constraints

We assimilated 12 globally gridded or in situ datasets to constrain various aspects of the terrestrial biosphere represented in DifferLand (Fig. S4). We used 0.05° biweekly MODIS-based Long-term Continuous SIF-informed Photosynthesis Proxy (LCSPP-MODIS) as a proxy of photosynthesis between 2010 and 2023⁹¹. Reprocessed MODIS Version 6.1 Leaf Area Index^92,93, which exhibited enhanced spatial and temporal continuity compared with the original MCD15A2H, was used to constrain modeled foliar dynamics from 2001 to 2023. Evapotranspiration from Global Land Evaporation Amsterdam Model (GLEAM) v4.2a at 0.1° resolution was used to constrain modeled ET between 2001 and 2023²⁴. Monthly GFED5 Beta total fire carbon emission at 0.25° is used to constrain modeled carbon emission. The aforementioned global datasets were regridded to 0.25° grid cells at monthly intervals to match DifferLand output.

Annual live woody biomass (B_w) maps from 2001-2021 were obtained from a dataset reconstructed with an array of inventory plots, airborne, and satellite observations⁹⁴. Herbaceous biomass (B_h) is estimated under an equilibrium assumption with ${B_{\mathrm{h}}=f}_{\mathrm{h}}\times \overline{\mathrm{GPP}}\times \tau \times \left(1-\alpha \right)$, where $f_{\mathrm{h}}$ is the area fraction of herbaceous vegetation within each grid cell estimated from MCD12C1, $\overline{\mathrm{GPP}}$ is annual GPP climatology estimated from FLUXCOM upscaling⁹⁵, $\alpha$ is the respiration cost of carbon (assumed to be 0.5), and $\tau$ is the mean residence time taken as one year for annual plants⁹⁶. Total live biomass (B_l) is computed as B_l = B_h + B_w. In the absence of temporal observations, this use of the equilibrium assumption provides an estimate of the spatial gradient of live biomass density. The lack of temporal variability in biomass estimates is partially compensated for by assimilated LAI and VOD dynamics in those regions. We aggregated annual live biomass density to a 0.25° spatial resolution.

Monthly NBE from the NASA Carbon Monitoring System Flux (CMS-Flux) GCP 2023 submission^22,25,97 was used to constrain DifferLand modeled NBE from 2010-2022. CMS-Flux is a top-down flux inversion system constrained by column CO₂ observations from the Greenhouse Gases Observing Satellite (GOSAT) and Orbiting Carbon Observatory-2 (OCO-2), which have broader and more even spatial coverage compared with ground-based CO₂ observations^98,99. Due to the computational cost of the atmospheric transport model, CMS-Flux has a native resolution of 4° × 5°. We derived NBE in DifferLand as the sum of (negative) gross primary productivity (GPP), ecosystem respiration (RECO, which is itself the sum of autotrophic respiration, R_a, and heterotrophic respiration, R_h), and carbon emission from fire (F_fire). The first three terms constitute net ecosystem exchange (NEE), whereas fire carbon emission was additionally constrained by the GFED5 beta dataset. A negative NBE represents a net flux of carbon from the atmosphere to the land (i.e., land carbon sink).

$$\mathrm{NBE}=-\mathrm{GPP}+R_{\mathrm{a}}+R_{\mathrm{h}}+F_{\mathrm{fire}}=-\mathrm{GPP}+\mathrm{RECO}+F_{\mathrm{fire}}=\mathrm{NEE}+F_{\mathrm{fire}}$$ 5

To constrain DifferLand simulated terrestrial water storage, we assimilated monthly satellite-gravimetry based JPL GRACE and GRACE-FO Mascon Equivalent Water Height (GRACE EWT) from 2002 to 2023 (RL06.3)²³. Although GRACE EWT was provided on 0.5° grids, the product has an effective resolution of 3° × 3°. We thus assimilated both CMS-Flux NBE and GRACE EWT at the 4° × 5° batch level to prevent signal aliasing (see the next section for details). To evaluate the robustness of model performance to different observational constraints, we conducted sensitivity analyses with alternative assimilated datasets, including LAI, live biomass, NBE, fire carbon emissions, and optimally assimilated VOD. Detailed results are presented in Supplementary Note 4.

We also assembled monthly eddy-covariance-based observations GPP, RECO, and ET by combining the FLUXNET2015¹⁰⁰, ICOS, OzFlux¹⁰¹, and AmeriFlux FLUXNET datasets. For GPP and RECO, we used night-time partitioned values with variable u^* threshold and removed months where more than 30% of the NEE measurements were gap-filled¹⁰². For ET, we removed months where more than 30% of the latent heat flux measurements were gap-filled. Sites representing managed landscapes that are highly uncharacteristic of the surrounding grid cell ecosystems are excluded from the data assimilation. After filtering, we retained 180 sites during the simulation period (Fig. S36). Whenever available, we gridded the site-level data to 0.25°. If observations from multiple sites within a grid cell were available in a specific month, we used the mean value across these sites to fill the grid cell. To investigate the contributions of eddy covariance data and potential uncertainties due to spatial mismatch between model grid and tower footprints, we further performed a set of sensitivity analyses by either not assimilating eddy covariance data or testing the effects of more stringent or relaxed site representativeness filtering criteria (Supplementary Note 5). We found that while assimilating eddy covariance data is essential for constraining both the absolute magnitude and latitudinal gradient of GPP and RECO, the results are largely insensitive to the specific thresholds used for site representativeness filtering (Figs. S37 and S38). A complete list of the eddy covariance sites used in this study is provided in Supplementary Data 1 with detailed citations.

Model training and evaluation

To assimilate multi-resolution observational constraints at both fine (0.25°) and coarse (4° × 5°) resolutions, we first divided the globe into 3240 4° × 5° patches, each corresponding to the grid of coarse-resolution datasets. Each 4° × 5° patch contains 320 nested fine-resolution grid cells (Fig. S5). We filtered these patches to retain only those with at least 32 valid vegetated fine-resolution grid cells. Out of the 944 patches meeting this criterion, 10% of the patches (n = 95) were randomly selected and reserved for model testing (Fig. S5c). Prior to training each ensemble member, we randomly sampled 90% of the remaining 849 patches for training, while the unselected patches formed a development set used for hyperparameter tuning and monitoring training progress (Fig. S5a). The final training and development sets contain 164,152 grid cells with a total of 45,305,952 pixel-months. All spatial predictors were standardized by subtracting their means and dividing by their standard deviations, calculated from the training dataset, to accelerate model convergence. After evaluating model performance, we retrained each ensemble on the combined training and development sets (excluding the test set) to derive latent ecological parameters and their relationships with spatial predictors for subsequent analysis.

We developed a customized gradient-based algorithm to train the multi-resolution model. This approach first permutes the fine-resolution grids within each patch and then shuffles the patches within the training set to introduce stochasticity, while ensuring that all fine-resolution grid cells within a patch remain grouped. As a result, each patch forms a minibatch (batch size ≈ 320) during model training, allowing fine-resolution datasets to serve as sample-level constraints, and coarse-resolution datasets as batch-level constraints. We assimilate coarse resolution constraints at the patch level only if at least 80% of the fine resolution grid cells within the patch are valid. The model was trained using the Adam optimizer, with a learning rate of 0.0005. Each ensemble member underwent 199 epochs of training, a choice balanced among computational cost, model convergence, and overfitting risk.

After training, we evaluated model performance on the held-out test datasets. We used R²-score as a measure of overall model fitting on each variable

$$R^2=1-\frac{{\sum }_{i=1}^n{\left(y_i-\widehat{y_i}\right)}^2}{{\sum }_{i=1}^n{\left(y_i-ȳ\right)}^2}$$ 6

With $y_i$ being ith observed value, $\widehat{y_i}$ being the ith modeled value, and $ȳ$ being the observed mean. The R²-score is mathematically equivalent to the Nash–Sutcliffe efficiency (NSE) metric commonly used in hydrology, which accounts for both correlation and systematic offsets between modeled and observed values. A perfect model would have R² = 1, but the R²-score can approach negative infinity for arbitrarily bad predictions. Thus, we also used, the square of the Pearson correlation coefficient between modeled and observed values (range 0–1), for hierarchical partition and pixelwise temporal correlations. We made explicit in our manuscript which metric was used when reporting the results. We excluded the first two years of simulations (2001–2002) to reduce the potential influence of initialization uncertainties on performance metrics.

Hierarchical partition of explained variance

Hierarchical partition¹⁰³ enables a decomposition of the explained variance on target variables by a multivariate regression model into the independent contributions of different groups of variables. To segregate the independent contributions of PFT, CLIM, SOIL, and AGE, we performed a full factorial experiment by including or excluding each group of variables, resulting in a total of 15 setups (i.e., |P({PFT, CLIM, SOIL, AGE})\{∅} | = 2⁴−1, where P (·) denotes power set).

For each setup, we ran 20 experiments with random initializations and selected the 10 with the lowest training loss, minimizing the impact of poor initializations and forming a robust model ensemble. The mean performance metric across these 10 ensemble members is used to represent a setup. Under the hierarchical theorem, the independent effect of a variable group j within a set containing N groups of variables can be computed as the mean explained variance difference between N pairs of setups within a predictor group hierarchy, where j is either included or excluded from the predictor set, averaged over all possible (N−1)! sequences of hierarchies¹⁰³. We conducted a hierarchical partitioning analysis on explained variance for each of SIF, LAI, ET, NBE, and EWT on both global and pixel levels. We then derived the proportion of explained variance that can be independently attributed to each predictor group, assuming a baseline explained variance of 0.

Parameter identifiability analysis

We conducted parameter identifiability analyses on the three setups using either the full set of predictors (PFT + CLIM + SOIL + AGE, Fig. S39), the environmental predictors only (CLIM + SOIL + AGE, Fig. S40), or the PFT predictors only (PFT, Fig. S41). For each model parameter and initial pool value, we computed the pixelwise coefficient of variance (CV) across ensemble members and used the spatial median CV as a diagnostic for predictor robustness. The rationale of this test is that if a latent ecological parameter is well constrained by the assimilated observations, it should converge to relatively stable values across independently initialized runs. Conversely, non-identifiable parameters with low sensitivity to the observational constraints can be expected to take substantially different values across independently initialized runs. We used a spatial median CV < 0.6 to select parameters for subsequent analyses to balance parameter robustness with process coverage under the available constraints.

Principal component analysis (PCA) on ecological parameters

We performed a principal component analysis (PCA) on 13 ecologically significant and spatially consistent parameters that passed the identifiability threshold to determine the underlying dimensions controlling their spatial variability. These parameters include canopy photosynthetic efficiency (ce), underlying water use efficiency (uWUE), temperature sensitivity of heterotrophic respiration (Q10), autotrophic respiration fraction (f_auto), leaf carbon mass per area (LCMA), leaf onset (c_ronset) and fall duration (c_rfall), leaf lifespan (τ_foliar), litter turnover rate (k_litter), and allocation fraction of GPP to labile (A_labile), foliar (A_foliar), wood (A_wood), and fine roots (A_root) pools. Overall, these parameters characterize ecosystem functions related to photosynthesis and leaf phenology, carbon allocation, residence time, and water use efficiency. We projected these parameters into the space defined by the first three principal components to explore their interrelationships (Fig. 3)

SHAP analysis for feature importance and environment–parameter relationships

We applied kernel SHapley Additive exPlanations (SHAP) to extract the learned environment–parameter relationship from the spatialization neural network for a selection of latent ecological parameters¹⁰⁴. Kernel SHAP estimates Shapley values, informed by cooperative game theory, to quantify each feature’s marginal contributions, which sum additively to the model output minus a baseline. To ensure robustness of SHAP results and reduce the random uncertainties associated with individual model members, we calculated ensemble-based SHAP by first defining an ensemble-averaged model M_ens from 10 out of 20 model members for each configuration that best converges on the training dataset.

$$M_{\mathrm{ens}}=\frac{1}{10}{\sum }_{i=1}^{10}M\left(\mathbf{x},{\mathit{\theta }}_{\mathbf{i}}\right)$$ 7

where M is the spatialization network, x denotes the spatial predictors, and ${\mathit{\theta }}_{\mathbf{i}}$ are the neural network weights and biases of member i within the ensemble. From M_ens we sampled 100 grid cells to compute the background distribution, and then computed the SHAP values from 1000 randomly selected grid cells within the training dataset. The feature importance of different predictors was determined by ranking the mean absolute SHAP values from the 1000 samples. This procedure is repeated for each selected parameter to obtain global environment–trait relationships. To derive PFT-specific SHAP results, we further computed conditional SHAP values by sampling from grid cells where a specified plant functional type constitutes at least 80% of the area. For SHAP analysis on the principal components, we linearly projected $M_{\mathrm{ens}}$ into the principal component space using the PCA loadings and computed the SHAP analysis within this projected space.

Author contributions

J.F. and P.G. conceived the study. J.F. collected and curated the data, developed and implemented the model, performed the experiments, analyzed the results, and wrote the original draft. J.F., K.B., W.Z., X.L., and P.G. reviewed and edited the manuscript and contributed to the interpretation of the results. J.F. and P.G. acquired funding.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.

Funding

J.F. and P.G. were supported by the NASA ROSES-22 Future Investigators in NASA Earth and Space Science and Technology (FINESST) Program (Grant Number: 80NSSC24K0023). Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004). The authors acknowledge support from the NASA Greenhouse Gas Earth Information System and the Carbon Monitoring System Program (NNH22ZDA001N-CMS). J.F., P.G., W.Z., and X.L. were also funded by the Land Ecosystem Models based On New Theory, obseRvations, and ExperimEnts (LEMONTREE) project (UREAD 1005109-LEMONTREE) supported by Schmidt Sciences, the European Research Council grant USMILE (ERC CU18-3746), the Max-Planck Caltech Carnegie Columbia (MC³) Center funded by the Max Planck Foundation, and National Science Foundation Science and Technology Center LEAP, Learning the Earth with Artificial intelligence and Physics (AGS-2019625). W.Z., J.F., and P.G. were also supported by NASA under Grant No. 80NSSC26K0079. Funding for the AmeriFlux data portal was provided by the U.S. Department of Energy Office of Science.

Data availability

The DifferLand driver files, including processed spatial predictors, forcing data, and model configuration files, are publicly accessible on Zenodo at 10.5281/zenodo.13984225. Additionally, the processed model output used to generate the figures is also deposited in the same Zenodo repository. Datasets used in this study are publicly available from their respective repositories. Key datasets and their DOIs include: MODIS land cover product MCD12C1, ERA5 reanalysis (10.24381/cds.adbb2d47), Global 30 Arc-Second Elevation dataset GTOPO30 (10.5066/F7DF6PQS), global forest age 1 km dataset (10.17871/ForestAgeBGI.2021), Harmonized World Soil Database v1.2 (10.3334/ORNLDAAC/1247), NOAA global CO₂ record (10.15138/9N0H-ZH07), GRACE/GRACE-FO terrestrial water storage (10.5067/TEMSC-3JC63), the LCSPP-MODIS photosynthesis proxy (10.5281/zenodo.11658088), the reprocessed MODIS Version 6.1 Leaf Area Index dataset (http://globalchange.bnu.edu.cn/research/laiv061), CMS-Flux Net Biome Exchange (NBE) (https://cmsflux.jpl.nasa.gov/get-data/gcp-2023/), and GLEAM v4.2a evapotranspiration data (https://www.gleam.eu/#downloads). GFED5 burned area data are available at https://zenodo.org/records/7668424, while GFED5 fire emissions data are available from the Global Fire Data portal (https://www.globalfiredata.org/). MODIS burned area fraction data are available via NASA EarthData Search (https://search.earthdata.nasa.gov/). Global live biomass dataset from Xu et al.⁹⁴ can be accessed at https://zenodo.org/records/4161694 or by contacting the authors of the dataset. Additional datasets include: Copernicus Atmosphere Monitoring Service (CAMS) global inversion-optimized greenhouse gas fluxes and concentrations (10.24381/ed2851d2); Copernicus Leaf Area Index 1999–2020, 1 km, 10-daily (10.2909/d5fdc595-2e03-4cbe-a39e-5f006f9cef07); Copernicus Leaf Area Index 2014–present, 300 m, 10-daily (10.2909/219fdc9f-616b-444b-a495-198f527b4722); IB-AGC global live biomass carbon product (10.5281/zenodo.15676176); GLAB-VOD vegetation optical depth dataset (10.5281/zenodo.10306094); and CMS-Flux Fire L4 V2 carbon fluxes (10.5067/HO07ZJEQBMHE). Eddy covariance observations used in this study were compiled from the FLUXNET2015 dataset, AmeriFlux FLUXNET, ICOS, and OzFlux networks. These datasets are publicly available under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Detailed site-level citations, dataset access links, and metadata are provided in Supplementary Data 1.

Code availability

The code of the DifferLand model is available at https://github.com/JianingFang/DifferLand_Global, and the model version used for this study is deposited in a Zenodo repository¹⁰⁵ (10.5281/zenodo.19410423).

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-73395-4.