A global 0.05° gross primary production dataset from 2001 to 2024 generated using a hybrid LSTM framework

Abstract

Gross primary production (GPP), the total carbon fixed through plant photosynthesis, is a central component of the global energy and carbon cycles. While substantial divergences persist among inter-model GPP estimates, especially in their seasonal and interannual behaviours, more precise estimation approaches are urgently required. The present study introduces TRAX GPP, a new global GPP dataset with 0.05° spatial resolution and monthly coverage from 2001 to 2024. The dataset is generated using a hybrid Long Short–Term Memory (LSTM) framework that integrates Robust Seasonal–Trend decomposition (RSTL) with a loss function optimized for temporal learning. The model integrates satellite-derived vegetation and meteorological drivers, further enhanced by atmospheric CO₂ assimilation constraints to better capture CO₂ fertilization effects. TRAX GPP dataset aligns well with tower flux measurements and outperforms standard LSTM models in capturing both seasonal dynamics and interannual fluctuations. Compared with previous GPP products, TRAX GPP alleviates the common biases in global GPP totals and interannual trends. This dataset provides a new pathway for global GPP estimation and supports refined monitoring of terrestrial carbon dynamics.

Background & Summary

Gross Primary Productivity (GPP), typically quantified in flux-tower measurements as the apparent CO₂ uptake partitioned from net ecosystem exchange (NEE), represents the total carbon fixed via photosynthesis and serves as a fundamental indicator of ecosystem carbon cycling and energy flow¹. Understanding its spatiotemporal variability is essential for improving carbon budgets, climate models, and sustainability policies^2–4. However, owing to limited observations and substantial methodological differences, considerable divergence exists among GPP estimates⁵, reflected in global totals spanning approximately 90 to 160 Pg C yr⁻¹ and widely inconsistent long-term trends^6,7. The magnitude of this inter-model spread is pronounced, exceeding even the scale of global fossil-fuel emissions⁷. These discrepancies highlight the critical need for accurate, long-term, and temporally robust global GPP products.

Eddy-covariance (EC) flux towers represent the most direct observational constraints on terrestrial GPP, providing systematic measurements of net ecosystem CO₂ exchange that can be partitioned to derive GPP⁸. Yet, their utility is constrained by two major limitations: (1) the sparse and uneven spatial distribution, and (2) the inherently small observational footprint (~1 km). Accordingly, many studies have upscaled site-based records to global GPP products using high-resolution auxiliary data, approaches that can be grouped into empirical light-use efficiency (LUE) models, process-based biophysical models, and machine-learning (ML) models. In LUE models, GPP is derived as the product of absorbed photosynthetically active radiation (APAR) and light-use efficiency (ε)^9,10. Although simple and efficient, these models typically rely on prescribed empirical sensitivity functions to represent the environmental variability of ε, which can still introduce uncertainties in GPP estimation^11,12. Rooted in biophysical principles, process-based models integrate carbon, water, and energy fluxes, providing strong mechanistic interpretability^13,14. However, their structural and parametric complexity, together with high data demands, poses significant challenges to balancing predictive accuracy and mechanistic fidelity¹⁵.

Data-driven ML models infer relationships from site-level measurements and apply them to fine-resolution grids. Despite limited mechanistic interpretability, they offer greater objectivity by requiring less subjective parameterization^16,17. In addition, their capacity to generalize over complex, nonlinear systems renders ML models well-suited for global ecological applications¹⁸. However, existing ML-based global GPP products remain far from consistent, owing to: (1) differences in model and algorithmic architectures, and (2) differences in data setups, including tower-site selection and input features. At the modelling level, traditional ML algorithms used in GPP estimation commonly include tree-based ensemble methods (e.g., Random Forest), Artificial Neural Networks (ANN), and Support Vector Machines (SVM). These algorithms do not encode temporal memory or state evolution and thus capture only static input–output associations¹⁹. Consequently, they are disadvantaged in tasks requiring reconstruction of continuous time series or characterization of long-term and interannual variability²⁰. In contrast, Long Short-Term Memory (LSTM) networks are specifically designed to retain and update internal states over time, enabling them to learn lagged dependencies, persistence, and memory effects in sequential data^21,22. By modelling temporal evolution directly rather than relying on static input–output mappings, LSTM is better suited to capturing seasonal cycles, interannual fluctuations, and long-term trends in GPP. Although LSTM-based methods have proven effective for NEE²³, their application to global-scale products remains largely unexplored. Furthermore, training schemes that do not stratify by plant functional type (PFT), but instead mix multiple PFTs in a single model, can smooth or distort seasonal and interannual dynamics and lead to unstable, and often underestimated, long-term trends²⁴. At the data level, given the direct physiological coupling between CO₂ fertilization and GPP, the omission of CO₂ fertilization effects, along with inputs that lack a proper representation of vegetation functioning and abiotic disturbances, can substantially weaken temporal signal fidelity. A typical example is the FLUXCOM GPP product, which does not account for CO₂ fertilization effects and uses vegetation inputs prescribed from a climatological mean seasonal cycle, so the inferred long-term GPP trends should be interpreted with caution^25,26. However, the column-averaged dry air mole fraction of atmospheric carbon dioxide (XCO₂), despite being an effective proxy for CO₂ concentration, is limited by the lack of continuous observational records, posing a challenge for imposing sustained CO₂ constraints on long-term GPP estimates.

The objective of this study is to validate and introduce a novel algorithmic framework for GPP estimation that markedly strengthens its performance in reconstructing and predicting temporal trajectories. To achieve this, a hybrid model integrating robust Seasonal-Trend decomposition using Loess (STL) decomposition and LSTM algorithms was developed to upscale site-based measurements to the global scale. STL was employed to resolve the non-stationary signals embedded within GPP estimates, where pronounced seasonality and multi-year trajectories are modulated by climate variability²⁷. Robustly partitioning these signals facilitates a precise distillation of phenological patterns and long-term ecological responses²⁶, ensuring the structural stability of our hybrid framework. In contrast to earlier studies that typically adopt standard loss functions, such as Mean Squared Error (MSE) and Mean Absolute Error (MAE), we propose a new loss function designed to better capture interannual fluctuations and reinforce the model’s memory of historical dynamics. Ultimately, we generated a new continuous global GPP dataset at 0.05° spatial resolution covering 2001–2024, with support for ongoing updates, hereafter referred to as TRAX GPP (A Temporal–Robust LSTM Architecture combining XCO₂ constraint for GPP estimation). TRAX GPP can be used for global analyses of spatiotemporal GPP variability and to support multi-model integration and intercomparison.

Methods

Data input

Eddy covariance data

GPP derived from eddy covariance measurements were used as the target variable to train the model. We obtained monthly GPP records spanning 2001–2024 from well-established flux network datasets, including FLUXNET2015²⁸, AmeriFlux FLUXNET²⁹, and ICOS Warm Winter 2020 database³⁰. The daytime-partitioned GPP (GPP_DT_VUT_REF) was employed for its consistency with daytime remote sensing drivers and its robust representation of VPD-stomatal coupling³¹. All data were standardized with the ONEFLUX pipeline²⁸. To enhance sampling coverage, we further introduced flux sites from the Heihe River Basin (HRBFlux) in China³². We followed the quality-control procedures in previous research³³, retaining monthly averages where no more than 20% of values were gap-filled, and restricting the analysis to NEE uncertainties below 3 g C m⁻² d⁻¹. The mismatch between EC tower footprints and 0.05° × 0.05° pixels introduces scale uncertainties that challenge model accuracy. To mitigate this scale-driven bias, flux sites were rigorously screened using the MODIS Land Cover Type product (MCD12C1)³⁴. We selected only those sites where the dominant IGBP (International Geosphere-Biosphere Programme) pixel class (LC_Type1) within the 0.05° grid cell aligned with the site-reported ecosystem type. Our study collected data from a total of 105 sites across diverse ecosystems, encompassing a cumulative 10176 site-months (Fig. 1). Details of the EC sites are provided in Table 1.

Fig. 1.

Location of 105 eddy covariance sites used in this study. The inset boxplot illustrates the distribution of data record lengths (in years) across all study sites.

Table 1.

Summary of the study sites across FLUXNET2015, AmeriFlux, ICOS, and HRBFlux networks.

Sites	IGBP	Latitude	Longitude	Dataset	Duration	Reference
CA-Obs	ENF	53.9872	−105.1178	FLUXNET2015	2006–2010	64
CA-SF1	ENF	54.4850	−105.8176	FLUXNET2015	2003–2006	65
NL-Loo	ENF	52.1666	5.7436	FLUXNET2015	2003–2008	66
CA-Ca1	ENF	49.8673	−125.3336	AmeriFlux	2001–2010	67
CA-Ca2	ENF	49.8705	−125.2909	AmeriFlux	2001–2010	68
US-Me2	ENF	44.4526	−121.5589	AmeriFlux	2002–2022	69
US-Me6	ENF	44.3233	−121.6078	AmeriFlux	2012–2014	70
CZ-BK1	ENF	49.5021	18.5369	ICOS	2019–2020	71
DE-Obe	ENF	50.7867	13.7213	ICOS	2009–2020	72
DE-RuW	ENF	50.5049	6.3310	ICOS	2012–2016	73
FI-Hyy	ENF	61.84741	24.2948	ICOS	2001–2020	74
FI-Let	ENF	60.6418	23.9595	ICOS	2009–2020	75
IT-Ren	ENF	46.5869	11.4337	ICOS	2001–2018	76
SE-Ros	ENF	64.1725	19.7380	ICOS	2014–2018	77
GF-Guy	EBF	5.2787	−52.9248	ICOS	2004–2020	78
AU-Wac	EBF	−37.4259	145.1878	FLUXNET2015	2005–2008	79
AU-Wom	EBF	−37.4222	144.0944	FLUXNET2015	2010–2014	80
BR-Sa1	EBF	−2.8567	−54.9589	FLUXNET2015	2002–2006	81
BR-Sa3	EBF	−3.0180	−54.9714	FLUXNET2015	2001–2004	82
CN-Din	EBF	23.1733	112.5361	FLUXNET2015	2003–2005	83
MY-PSO	EBF	2.9730	102.3062	FLUXNET2015	2003–2009	84
CA-Oas	DBF	53.6289	−106.1978	FLUXNET2015	2003–2005	85
US-Bar	DBF	44.0646	−71.2881	AmeriFlux	2004–2022	86
US-Ha1	DBF	42.5378	−72.1715	AmeriFlux	2001–2020	87
US-MMS	DBF	39.3232	−86.4131	AmeriFlux	2001–2020	88
US-MOz	DBF	38.7441	−92.2000	AmeriFlux	2007–2011	89
US-SSH	DBF	40.6658	−77.9041	AmeriFlux	2016–2021	90
US-UMB	DBF	45.5598	−84.7138	AmeriFlux	2007–2021	91
US-UMd	DBF	45.5625	−84.6975	AmeriFlux	2008–2022	92
US-xBR	DBF	44.0639	−71.2873	AmeriFlux	2017–2021	93
US-xHA	DBF	42.5369	−72.1727	AmeriFlux	2017–2021	94
CZ-Stn	DBF	49.0360	17.9699	ICOS	2010–2018	95
DE-Hai	DBF	51.0794	10.4521	ICOS	2001–2018	96
JP-SMF	MF	35.2617	137.0788	FLUXNET2015	2002–2006	97
US-PFa	MF	45.9459	−90.2723	FLUXNET2015	2013–2014	98
CA-Gro	MF	48.2167	−82.1556	AmeriFlux	2003–2014	99
US-Syv	MF	46.2420	−89.3477	AmeriFlux	2012–2023	100
BE-Vie	MF	50.3050	5.9981	ICOS	2001–2020	101
RU-Cok	SHR	70.8291	147.4943	FLUXNET2015	2011–2013	102
US-EML	SHR	63.8784	−149.2536	AmeriFlux	2011–2019	103
US-ICt	SHR	68.6063	−149.3041	AmeriFlux	2016–2021	104
US-Jo1	SHR	32.5820	−106.6350	AmeriFlux	2011–2022	105
US-Ses	SHR	34.3349	−106.7442	AmeriFlux	2008–2015	106
US-xHE	SHR	63.8757	−149.2133	AmeriFlux	2017–2021	107
US-xJR	SHR	32.5907	−106.8425	AmeriFlux	2017–2023	108
ES-LJu	SHR	36.9266	−2.7521	ICOS	2004–2008	109
AU-Gin	SAV	−31.3764	115.7138	FLUXNET2015	2011–2014	110
AU-GWW	SAV	−30.1913	120.6541	FLUXNET2015	2013–2014	111
AU-How	SAV	−12.4943	131.1523	FLUXNET2015	2001–2014	112
CG-Tch	SAV	−4.2892	11.6564	FLUXNET2015	2008–2009	113
US-Ton	SAV	38.4309	−120.9660	AmeriFlux	2001–2023	114
BR-Npw	SAV	−16.4980	−56.4120	AmeriFlux	2013–2017	115
ES-LM1	SAV	39.9427	−5.7787	ICOS	2014–2020	116
ES-LM2	SAV	39.9346	−5.7759	ICOS	2014–2020	117
AU-DaP	GRA	−14.0633	131.3181	FLUXNET2015	2007–2011	118
AU-Rig	GRA	−36.6499	145.5759	FLUXNET2015	2011–2014	119
CN-Cng	GRA	44.5934	123.5092	FLUXNET2015	2007–2010	120
CN-Dan	GRA	30.4978	91.0664	FLUXNET2015	2004–2005	121
CN-HaM	GRA	37.3700	101.1800	FLUXNET2015	2002–2004	122
US-AR1	GRA	36.4267	−99.4200	AmeriFlux	2009–2012	123
US-Cop	GRA	38.0900	−109.3900	AmeriFlux	2001–2003	124
US-Fwf	GRA	35.4454	−111.7718	AmeriFlux	2005–2010	125
US-Kon	GRA	39.0824	−96.5603	AmeriFlux	2004–2015	126
US-Seg	GRA	34.3623	−106.7020	AmeriFlux	2007–2009	127
US-SRG	GRA	31.7894	−110.8277	AmeriFlux	2009–2010	128
US-Wkg	GRA	31.7365	−109.9419	AmeriFlux	2007–2021	129
US-xAE	GRA	35.4106	−99.0588	AmeriFlux	2019–2021	130
US-xCL	GRA	33.4012	−97.5700	AmeriFlux	2018–2021	131
US-xKA	GRA	39.1104	−96.6129	AmeriFlux	2017–2021	132
CA-MA3	GRA	50.1774	−97.8686	AmeriFlux	2009–2011	133
CH-Aws	GRA	46.5832	9.790417	ICOS	2013–2020	134
CH-Cha	GRA	47.2102	8.4104	ICOS	2017–2020	135
IT-Tor	GRA	45.8444	7.5781	ICOS	2019–2020	136
ARo	GRA	38.0443	100.4646	HRBFlux	2010-2011	32
ARS	GRA	38.0473	100.4643	HRBFlux	2014–2021	32
DDS	GRA	38.0142	100.2421	HRBFlux	2015-2022	32
JYL	GRA	37.8384	101.1160	HRBFlux	2021–2022	32
SDQ	GRA	42.0012	101.1374	HRBFlux	2017-2022	32
HHL	GRA	41.9903	101.1335	HRBFlux	2014–2015	32
US-Twt	CRO	38.1087	−121.6531	FLUXNET2015	2011–2013	137
CA-ER1	CRO	43.6405	−80.4123	AmeriFlux	2015–2020	138
US-ARM	CRO	36.6058	−97.4888	AmeriFlux	2004–2014	139
US-CF1	CRO	46.7815	−117.0821	AmeriFlux	2017–2021	140
US-CF2	CRO	46.7840	−117.0908	AmeriFlux	2017–2020	141
US-CF3	CRO	46.7551	−117.1261	AmeriFlux	2017–2021	142
US-CF4	CRO	46.7518	−117.1285	AmeriFlux	2017–2021	143
US-Lin	CRO	36.3566	−119.0922	AmeriFlux	2009–2010	144
US-Mo1	CRO	39.2298	−92.1167	AmeriFlux	2015–2023	145
US-Mo3	CRO	39.2322	−92.1493	AmeriFlux	2016–2021	146
US-Ne1	CRO	41.1651	−96.4766	AmeriFlux	2001–2020	147
US-Ro1	CRO	44.7143	−93.0898	AmeriFlux	2004–2016	148
US-Ro2	CRO	44.7288	−93.0888	AmeriFlux	2008–2013	149
US-Ro5	CRO	44.6910	−93.0576	AmeriFlux	2017–2023	150
US-Ro6	CRO	44.6946	−93.0578	AmeriFlux	2017–2023	151
US-Tw3	CRO	38.1152	−121.6469	AmeriFlux	2013–2018	152
BE-Lon	CRO	50.5516	4.7462	ICOS	2004–2020	153
CH-Oe2	CRO	47.2864	7.7338	ICOS	2009–2020	154
CZ-KrP	CRO	49.5733	15.0788	ICOS	2014–2020	155
DE-Geb	CRO	51.0997	10.9146	ICOS	2001–2020	156
DE-Kli	CRO	50.8931	13.5224	ICOS	2004–2020	157
DE-RuS	CRO	50.8659	6.4471	ICOS	2011–2020	158
FR-Aur	CRO	43.5496	1.1061	ICOS	2005–2020	159
FR-Lam	CRO	43.4964	1.2379	ICOS	2005–2020	160
DMS	CRO	38.8555	100.3722	HRBFlux	2015.1	32
YKe	CRO	38.8571	100.4103	HRBFlux	2008.1	32

Included are Site IDs, plant functional types, geographic coordinates, dataset versions, and observation periods. References and DOIs for each site are provided in the final column.

Vegetation and meteorological drivers

Several vegetation indices were calculated based on the MODIS Nadir BRDF-adjusted reflectance (NBAR) daily dataset with the resolution of 0.05° (MCD43C4)³⁵.Vegetation indices selected includes the normalized difference vegetation index (NDVI)³⁶, Enhanced Vegetation Index (EVI)³⁷, Normalized Difference Water Index (NDWI)³⁸, and the near-infrared reflectance of vegetation (NIRv)³⁹. Furthermore, we added the leaf area index (LAI) and the fraction of photosynthetically active radiation (fPAR) from Terra and Aqua satellites (MCD15A3H)⁴⁰.

Meteorological factors were also included as essential predictors in the model. We obtained air temperature (TMP), precipitation (PRE), shortwave radiation downwards (SWR), soil moisture (SM), and vapor pressure deficit (VPD), all derived from the ERA5-Land reanalysis dataset⁴¹. Notably, VPD was not directly provided by the ERA5-Land dataset, but was instead calculated by the ERA5-Land T2m and dewpoint temperature data using the August–Roche–Magnus formula⁴². The 0–100 cm soil moisture was estimated by integrating the moisture content across layers, weighted by layer thickness⁴³.

CO₂ concentration constraint

To better track long-term trends, XCO₂ were incorporated as a key model input. Due to the absence of a continuous XCO₂ observation product covering 2001–2024, we merged two assimilation datasets: NOAA’s CarbonTracker version CT2022 (2000–2020, 3° × 2°)⁴⁴ and the Copernicus Atmosphere Monitoring Service (CAMS) global inversion-optimized greenhouse gas dataset (2015–2024, 1.4° × 0.7°)^45,46. Both products integrate multi-source observations with atmospheric transport models, yielding reliable global XCO₂ fields with continuous spatial and temporal coverage. It should be noted that CAMS does not account for COVID-19-induced emission perturbations in its prescribed emission fields, which may cause deviations in trend estimates during the period around 2019⁴⁷. Accordingly, we used CT2022 as the reference and applied mean–variance matching (MVM) method over the overlap period (2015–2020) to derive monthly linear adjustments for CAMS. Specifically, the MVM adjustment was applied using a monthly linear transformation that matches the mean ($\mu$) and standard deviation ($\sigma$) of CAMS to those of CT2022, expressed as:

$$X_{\mathit{CAMS}}^{*}={\mu }_{\mathit{CT}}+\frac{{\sigma }_{\mathit{CT}}}{{\sigma }_{\mathit{CAMS}}}\left(X_{\mathit{CAMS}}-{\mu }_{\mathit{CAMS}}\right)$$ 1

where $X_{\mathit{CAMS}}^{*}$ refers to the adjusted CAMS XCO₂ fields. We finally achieved the fusion of CT2022 (2001–2020) with CAMS (2021–2024) into a global continuous XCO₂ record (See Supplementary Fig. 1 for detailed evaluation before and after fusion).

Other supporting data

Plant functional types (PFTs) were identified using the MODIS Land Cover product (MCD12C1)³⁴ based on the classification system of IGBP. Considering the sparse distribution of EC sites, some similar PFT categories were grouped. Closed shrublands and open shrublands were combined into a single shrublands class. Woody savannas and savannas were combined into a single savannas class.

Global GPP datasets were also incorporated to support the analysis. The FLUXCOM_GPP dataset provides global estimates of GPP by upscaling site-level eddy covariance flux measurements through an ensemble of machine learning models. Two versions are available: FLUXCOM_RS, driven by MODIS remote sensing data, and FLUXCOM_RS + METEO, which integrates both remote sensing and meteorological data⁴⁸. In this study, we adopted the RS+METEO product to ensure consistency with our predicted GPP. We used the MOD17A2H v061 GPP dataset from MODIS³⁵. We additionally incorporated the latest FLUXCOM-X product, an advanced machine-learning ensemble that upscales EC measurements using ERA5 meteorological forcing⁴⁹. Two CEDAR-GPP products were also included: ST_Baseline_DT, which estimates GPP from satellite reflectance and meteorological inputs, and ST_CFE-Hybrid_DT, which augments the baseline setup with CO₂-fertilization constraints to improve long-term responsiveness⁵⁰. Finally, we used the Revised_EC_LUE_GPP dataset, an enhanced LUE-based product featuring updated representations of environmental stress⁵¹. All the above gridded inputs were aggregated to a monthly time step and 0.05° spatial grid to ensure consistency in resolution for subsequent GPP generation. In the gap-filling step, short-term missing values were filled using a moving-window median filter, followed by seasonal mean imputation based on multi-year monthly averages to handle longer-term gaps. A comprehensive summary of all input datasets utilized for TRAX GPP generation is provided in Table 2 of the Supporting Information.

Table 2.

Summary of the input datasets and metadata used for TRAX GPP generation.

Category	Dataset	Spatial resolution	Temporal resolution	Temporal coverage
Vegetation drivers	MODIS Nadir BRDF-adjusted reflectance (MCD43C4 v006)35	0.05° × 0.05°	Daily	2000-present
	MODIS Terra and Aqua LAI/fPAR (MCD15A3H, v006)40	500 m	4-days	2000-present
Meteorological drivers	ERA5-Land monthly averaged data from 1950 to present41	0.1° × 0.1°	Monthly	1950-present
CO2 constraints	NOAA’s CarbonTracker version CT202244	3° × 2°	Monthly	2000–2020
	CAMS global inversion-optimised greenhouse gas fluxes and concentrations45	1.4° × 0.7°	Monthly	2015–2024
Other supporting data	MODIS Land Cover (MCD12C1 v006)34	0.05° × 0.05°	Yearly	2001-present
	FLUXCOM GPP (RS + METEO)161	0.5° × 0.5°	Monthly	2001–2018
	MODIS GPP (MOD17A2H v061)162	500 m	8-days	2000-present
	FLUXCOM-X GPP (X-BASE)49	0.05° × 0.05°	Monthly	2001–2021
	CEDAR-GPP (ST_Baseline_DT / ST_CFE-Hybrid_DT)50	0.05° × 0.05°	Monthly	1982–2020
	Revised_EC_LUE GPP51	0.05° × 0.05°	8-days	1982–2018

The Hybrid LSTM Model

LSTM algorithm

Recurrent Neural Networks (RNNs) are widely used for sequential prediction due to their capacity to capture temporal dependencies, including in climate and Earth system studies⁵². Nevertheless, conventional RNNs are constrained by issues such as vanishing and exploding gradients, impeding ability to learn long-term patterns²¹. Unlike RNNs, LSTM networks overcome these limitations by introducing memory cells regulated by input, forget, and output gates (Figure S1). These gating mechanisms enable LSTMs to filter irrelevant information, update cell states with new inputs, and control output contributions, thereby maintaining stable gradients and effectively modelling long-term dependencies⁵³.

Robust STL

RSTL has emerged as a reliable and flexible technique for extracting temporal components from multivariate time series⁵⁴. The time-series data y_t is expressed as:

$$y_t={\tau }_t+s_t+r_t,t=1,2,\dots ,n$$

where τ_t captures the long-term trend, s_t describes the periodic seasonal variations, and r_t comprises residuals that signify anomalies and noise. The robust variant of STL applies iterative reweighting to diminish the impact of outliers, improving decomposition accuracy under noisy conditions. The procedure is summarized as follows:

Step 1: Detrending. Remove the current trend estimate ${\tau }_t^{\left(k\right)}$ from the original series to obtain a detrended signal: $y_t^{\left(k\right)}$ = y_t - ${\tau }_t^{\left(k\right)}$.

Step 2: Subseries Seasonal Smoothing. Split $y_t^{\left(k\right)}$ into seasonal subseries according to the cycle period (e.g., monthly), and apply locally weighted regression smoothing (LOESS) to each subseries to estimate the preliminary seasonal component ${\tilde{S}}_t^{(k+1)}$.

Step 3: Low-Pass Filtering. Apply a low-pass filter to the preliminary seasonal estimate ${\tilde{S}}_t^{(k+1)}$ to extract the residual low-frequency trend component ${\tilde{T}}_t^{(k+1)}$.

Step 4: Seasonal Component Estimation. Obtain the seasonal component $S_t^{(k+1)}$ by removing ${\tilde{T}}_t^{(k+1)}$ from ${\tilde{S}}_t^{(k+1)}$: $S_t^{(k+1)}$ = ${\tilde{S}}_t^{(k+1)}$ - ${\tilde{T}}_t^{(k+1)}$

Step 5: De-seasonalizing. Subtract the estimated seasonal component from the original series to obtain the de-seasonalized signal.

Step 6: Trend Smoothing. Estimate the updated trend component ${\tau }_t^{(k+1)}$ by applying LOESS smoothing to the de-seasonalized series Y_t - $S_t^{(k+1)}$.

Model setup

We developed a hybrid RSTL–LSTM framework, consisting of four main steps (Fig. 2). Site-level GPP records were used as targets, while 12 satellite-derived variables served as features. Both targets and features were decomposed by RSTL into trend, seasonal, and residual components, each normalized separately with Min–Max scaling. Independent LSTM models were trained for each component, and their outputs were summed to produce final predictions.

Fig. 2.

Schematic overview of the hybrid LSTM framework for GPP estimation. The architecture integrates eight PFT-specific models with a unified nonPFT model that handles ecosystems excluded from the training stage during global upscaling. All 12 input features are satellite-derived while only the target variable (EC-GPP) is obtained from tower-based measurements.

We adopted a single-layer LSTM with a dropout and a fully connected layer. The LSTM module extracts temporal dependencies from multivariate inputs, with dropout mitigating overfitting and the output layer mapping hidden states to GPP estimates. We developed an Adaptive Expanding Window Cross-Validation (AEW-CV) scheme for training, validation, and testing. In AEW-CV, the trailing portion of each site’s record is reserved as the test set, while the remainder forms the validation set, where the validation segment length is adaptively determined by data availability. Validation follows a standard expanding-window scheme, with progressively extended training and advancing validation segments⁵⁵. AEW-CV maximizes the use of limited samples without violating temporal structure and introducing data leakage. We adopt a six-month sliding window (input length = 6) as the empirical look-back period, using the previous six months of input features to predict GPP for the current month, a strategy shown effective in prior studies^23,56.

To optimize model performance, we employed Bayesian Optimization for hyperparameter tuning. The method builds a probabilistic surrogate of the objective function and iteratively selects promising configurations, enabling efficient exploration of complex hyperparameter spaces⁵⁷. Unlike conventional grid search, this approach lowers computational cost and explores the hyperparameter space more efficiently. Key hyperparameters were tuned within the following ranges: hidden size (32–512), the number of LSTM layers (1–3), dropout rate (0.1–0.5), batch size (8–64), learning rate (0.00001–0.01), and weight decay (0.00001–0.01). We employed the AdamW optimizer to drive training loss reduction, based on its decoupled weight decay for potentially enhanced generalization⁵⁸.

We built separate RSTL-LSTM model for 8 representative PFTs (ENF, EBF, DBF, MF, SHR, SAV, GRA, CRO). We also trained a global model (nonPFT) using all available samples without differentiating by PFTs, serving one purpose as the comparison model to evaluate the benefit of PFT-specific modelling, and another to support predictions in areas not classified under the selected 8 PFT types. Model performance was assessed using R², MAE, and RMSE, and the optimal models were used to generate the final gridded product.

Loss function design

In contrast to prior research using sample-wise error metrics (e.g., MSE, MAE) for model training and evaluation, we propose a loss function explicitly designed to enhance model fidelity in annual totals and long-term trends (Eq. 1). Interannual differences between predicted and observed values at t and t−12 were computed, ensuring that both the magnitude and direction of interannual changes were considered in model training. The discrepancies were quantified using the Huber loss (Eq. 2), which is well established in statistics⁵⁹. The final loss integrates MSE and the interannual difference term in the trend branch, whereas the seasonal and residual branches rely solely on MSE. The customized loss function, L_trend, is formulated as follows:

$$L_{\mathit{trend}}=\frac{1}{N}\sum _{t=1}^N{\left({\hat{y}}_t-y_t\right)}^2+\frac{1}{N-12}\sum _{t=13}^N{\mathcal{H}}_{\delta }\left(\left({\hat{y}}_t-{\hat{y}}_{t-12}\right)-\left(y_t-y_{t-12}\right)\right)$$ 2

$${\mathcal{H}}_{\delta }\left(x\right)=\left\{\begin{array}{l}\frac{1}{2}{x}^2,\left|\mathit{x}\right|\le \delta \\ \delta \left|\mathit{x}\right|-\frac{1}{2}{\delta }^2,\left|\mathit{x}\right|>\delta \end{array}\right)$$ 3

where $y_t$ and ${\hat{y}}_t$ denote the observed and predicted GPP values at month t respectively. The term $\left({\hat{y}}_t-{\hat{y}}_{t-12}\right)-\left(y_t-y_{t-12}\right)$ represents the discrepancy between predicted and observed interannual differences. N is the total number of monthly samples, and $\delta$ is the threshold parameter in the Huber loss, which in this study was set to 1. The Huber loss ($\mathcal{H}$) is a composite loss function, acting like MSE for small errors ($\left|\mathit{x}\right|>\delta$) and like MAE for large errors ($\left|\mathit{x}\right|>\delta$), which has proved robust to outliers⁶⁰.

Data Records

The TRAX GPP dataset is provided at a 0.05° spatial resolution, covering global land areas with a grid of 3600 × 7200 latitude–longitude cells. It contains monthly gross primary production (GPP) estimates from January 2001 to December 2024, comprising 288 time steps and forming a continuous 24-year global time series. The dataset is publicly available in the Zenodo repository⁶¹ at: 10.5281/zenodo.18632859.

Each NetCDF file contains three primary dimensions representing latitude, longitude, and time. The main variable, GPP, is stored in integer form and requires the application of a uniform scaling factor of 0.01 to obtain values expressed in g C m⁻² d⁻¹. This scaling approach ensures numerical consistency across all files while reducing storage size. Missing or invalid grid cells are marked using a fill value of −9999 for easy masking.

Technical Validation

Performance assessment at the PFT Level

To ensure the robustness of the dataset, we compared two modelling strategies: a single global model (TRAX-nonPFT) and PFT-specific models (TRAX-PFTs) (Fig. 3). The global strategy trained a single unified model using all available sites, whereas in the PFT-specific strategy, separate models were trained for each PFT and applied adaptively during prediction based on land-cover data. To assess the model performance, monthly GPP was predicted on the test set and validated against records from EC sites. Overall, models with distinguished PFT robustly outperformed the non-differentiated models in prediction accuracy. Compared to the TRAX-nonPFT results, modelling PFTs individually improved the R² from 0.78 to 0.81, reduced the MAE from 1.09 to 0.99 g C m⁻² d⁻¹, and decreased the RMSE from 1.61 to 1.58 g C m⁻² d⁻¹ (Fig. 3a,b). When evaluated across different PFTs, models trained separately for each PFT generally achieve higher accuracy than the unified non-PFT model (Fig. 3c).

Fig. 3.

Predictive performance of two modelling strategies. (a) Results from the model trained separately for individual PFTs (TRAX-PFTs). (b) Results from the unified model without PFT distinction (TRAX-nonPFT). (c) Comparison of PFTs and nonPFT models across eight PFT groups. Marginal panels with kernel density estimates (KDE) depict the data distribution density for both axes. MAE and RMSE are in g C m⁻² d⁻¹.

Figure 4 shows more specific results, by distinguishing PFTs, the average values of R² ranged from 0.65 to 0.93, with corresponding MAE from 0.37 to 1.71 g C m⁻² d⁻¹, and RMSE from 0.52 to 2.71 g C m⁻² d⁻¹. In contrast, for models without distinguishing PFTs, the average values of R² ranged from 0.53 to 0.88, while MAE and RMSE ranged from 0.58 to 1.67 and 0.83 to 2.67 g C m⁻² d⁻¹ respectively (See detailed results for each PFT in Supplementary Table S1). Notably, DBF had the highest prediction accuracy (R² = 0.93), whereas EBF (R² = 0.82) and CRO (R² = 0.65) appear to be the most challenging to estimate, particularly for CRO, which showed markedly lower quality than other biomes. The lower accuracy in CRO is primarily attributed to complex anthropogenic management, including physiological differences between C3/C4 pathways and diverse crop rotation patterns. Additionally, the spatial scale mismatch between 0.05° pixels and localized site footprints is a potential contributing factor to this discrepancy. Overall, the hybrid LSTM model trained with PFT stratification outperform the unified model and achieves consistently strong accuracy across the eight PFT groups.

Fig. 4.

Evaluation of model performance across different PFTs. All scatter points are based on test-set predictions. Marginal panels with kernel density estimates (KDE) depict the data distribution density for both axes. MAE and RMSE are in g C m⁻² d⁻¹.

Model capability in tracking temporal dynamics

By integrating Robust STL with LSTM, our model is designed to effectively capture nonlinear trends and temporal variations. For validation, we examined two key aspects: (1) the ability to track seasonal dynamics and (2) the ability to reproduce interannual trends. In this section, we implemented comparative experiments across three LSTM model configurations: (1) a baseline LSTM model without incorporating XCO₂ information; (2) RSTL-LSTM, which integrates the RSTL module but still excludes XCO₂ and retaining MSE as its loss function; (3) an RSTL-LSTM model augmented with the XCO₂ constraint and the enhanced loss function (RSTL-LSTM-X). We also included two widely used global GPP products, FLUXCOM_GPP and MODIS_GPP, as external benchmarks. Figure 5 illustrates the cross-site GPP predictive performance across the evaluated models, providing a comprehensive assessment of their spatial generalization and temporal dynamics tracking capability. RSTL-LSTM-X achieved the best performance, showing the highest median R² (0.82) and the lowest MAE (0.84 g C m⁻² d⁻¹) and RMSE (1.08 g C m⁻² d⁻¹), and performing slightly better than RSTL-LSTM, reflecting robust generalization ability in cross-site prediction. In comparison, FLUXCOM and MODIS exhibited reduced predictive consistency, with median R² values of 0.61 and 0.62 respectively, and higher corresponding error metrics. We additionally introduced the Kling-Gupta Efficiency (KGE) to assess fidelity in annual magnitudes and interannual variability. KGE integrates correlation, bias, and variability for a rigorous evaluation of GPP dynamics, retaining only sites with test records exceeding 24 months. The results indicate that RSTL-LSTM-X exhibits a more consistent KGE distribution compared to FLUXCOM and MODIS. While outliers are present at certain sites, which could be attributed to the complexity of local environmental conditions, the results overall suggest that the integration of all modules contributes to an improved temporal tracking capability.

Fig. 5.

Cross-site evaluation of temporal dynamics tracking capability for the compared GPP models, where each point corresponds to a single site. Comparisons are shown between three proposed model variants (LSTM, RSTM-LSTM, and RSTL-LSTM-X), and two external benchmarks (FLUXCOM and MODIS). Among these, RSTL-LSTM-X is the final model used to generate the global product. R², MAE, and RMSE are computed against EC-GPP, with MAE and RMSE expressed in g C m⁻² d⁻¹. KGE is calculated based on annual GPP totals per site to evaluate fidelity in annual magnitudes and variations.

The seasonal amplitude (SA), defined as the difference between the maximum and minimum monthly GPP values within a year, was employed to evaluate the capacity of different modeling frameworks to track seasonal dynamics. Overall, the SA exhibited pronounced variations across different PFTs and models (Fig. 6). Among the three proposed model variants and the two external benchmarks, RSTL-LSTM-X and RSTL-LSTM exhibited the best overall alignment with EC-derived GPP records (EC-GPP), followed by the single LSTM. However, MODIS and FLUXCOM systematically underestimated SA, particularly for DBF, GRA, and CRO, where the amplitudes were markedly lower than EC-GPP. The average deviation in SA between each product and EC-GPP was further quantified, as summarized in Table S2 of Supplementary Information. RSTL-LSTM-X showed the smallest SA deviation ranging from 0.218 to 2.513 g C m⁻² d⁻¹, while FLUXCOM and MODIS exhibited significantly larger errors ranging from 0.513 to 6.301 and 0.420 to 6.633 g C m⁻² d⁻¹ respectively.

Fig. 6.

Seasonal amplitude (SA) across eight PFT groups for the test dataset. SA is defined as the difference between annual maximum and minimum GPP. Comparisons are shown between EC-GPP, three proposed model variants (LSTM, RSTM-LSTM, RSTL-LSTM-X), and two external benchmarks (FLUXCOM and MODIS). Among these, RSTL-LSTM-X is the final model used to generate the global product. SA is in g C m⁻² d⁻¹.

We further evaluated the model’s capability to predict long-term trends. To achieve this, we employed a two-step selection procedure to mitigate the uneven local conditions and data quality of EC sites. The first criterion, only the sites with more than 15 years of continuous records were retained. Second, we applied the Mann-Kendall (MK) test⁶² to the annual mean GPP time series, selecting sites with Z-values ≥ 1.65, corresponding to a 90% confidence level. To prevent potential data leakage, we independently trained a separate model for each site, ensuring that the test site was excluded from the training set. Figure 7 illustrates the GPP time series from different products at three representative sites: FI-Hyy (ENF), IT-Ren (ENF), and BE-Vie (MF). The interannual trends were quantified using Sen’s slope estimator⁶³, a robust non-parametric method widely employed for detecting monotonic trends. Among all evaluated models, RSTL-LSTM-X achieved the best agreement with EC-GPP, maintaining a high degree of consistency in long-term trends. While RSTL-LSTM and the standard LSTM model provided overall satisfactory results, it consistently underperformed relative to RSTL-LSTM-X. MODIS and FLUXCOM failed to reproduce the observed trends in most cases, typically showing near-zero or even negative slopes. The proposed RSTL-LSTM-X and RSTL-LSTM models consistently outperformed the others, achieving mean correlation coefficients (r) values of 0.64 and 0.60, respectively. These results were significantly higher than those of the base LSTM and external benchmarks (≤0.31).

Fig. 7.

Comparison of long-term GPP predictions across all evaluated models at representative sites. Comparisons are shown between EC-GPP, three proposed model variants (LSTM, RSTM-LSTM, RSTL-LSTM-X), and two external benchmarks (FLUXCOM and MODIS). Among these, RSTL-LSTM-X is the final model used to generate the global product. Red lines represent EC-GPP, and the blue lines correspond to predicted GPP. β_Sen denotes the Theil–Sen slope of the annual GPP series; z and p are the Mann–Kendall test statistic and its two-sided significance level, respectively; r is the Pearson correlation between observed and predicted GPP. The units of GPP are g C m⁻² d⁻¹.

These results suggest that the integration of RSTL decomposition effectively improves the model’s ability to track seasonal dynamics, and that incorporating the optimized loss function together with the XCO₂ constraint further strengthens its capability to capture long-term trends. It should be noted that the precise capture of every annual fluctuation across all independent sites remains difficult, partly due to the sparse and uneven coverage of monitoring sites. Nevertheless, the enhanced framework demonstrates a positive impact on estimation consistency.

Temporal and spatial pattern of TRAX GPP

Regions with high mean annual GPP are mainly distributed in southeastern Asia, central Africa, western Europe, South America and eastern North America (Fig. 8a). The spatial pattern and latitudinal distributions of mean annual GPP from TRAX generally align with results from MODIS, FLUXCOM, FLUXCOM-X, CEDAR-GPP and Revised_EC_LUE, with only slight regional deviations (Supplementary Fig. S2). One clear example is the evident underestimation in MODIS, especially in tropical ecosystems.

Fig. 8.

Spatiotemporal patterns of TRAX GPP and comparison with previous products. (a) Global distributions of mean annual GPP. (b) Long-term trends in annual GPP for 2002–2024; hatched areas indicate pixels with statistically significant trends at p < 0.05 based on the Mann–Kendall test. Global annual total GPP across products, presented in (c) for their complete temporal coverage and in (d) for the common overlapping period (2002–2018).

The global annual GPP estimation for the period 2002–2024 averages 125.33 Pg C yr⁻¹ (ranging from 118.88 to 131.10 Pg C yr⁻¹) and exhibits a significant positive trend of 0.45 Pg C yr⁻² (p < 0.01) (Fig. 8c). The spatial pattern reveals increases across most global regions, except for central Asia, which demonstrates a marked downward trend (Fig. 8b). TRAX GPP shows high interannual consistency with newer products such as FLUXCOM-X and CEDAR-GPP, in terms of overall trends and interannual fluctuations. Figure 8d presents the results of all products over the same period. ST_CFE-ML_DT has the highest trend (0.60 Pg C yr⁻²), followed by TRAX GPP (0.48 Pg C yr⁻²) and MODIS (0.41 Pg C yr⁻²). ST_Baseline_DT and FLUXCOM-X show weaker positive trends of 0.34 and 0.32 Pg C yr⁻². In contrast, both FLUXCOM and Revised_EC-LUE exhibit negative trends and substantially lower total GPP estimates. It should be noted that gaps in the MCD43C4 reflectance data during winter in certain high-latitude regions lead to missing values in the TRAX GPP. This results in a modest underestimation of the global total, although the impact is expected to be small given that these regions correspond to the non-growing season. It should also be noted that although TRAX GPP is available from 2001, the first six months are used to initialize the hybrid LSTM rolling temporal window. As a result, valid predictions begin in July 2001, and annual GPP totals are reported from 2002 onward.

In summary, TRAX GPP captures seasonal and interannual variability with acceptable accuracy and outperforms traditional global GPP products such as FLUXCOM and MODIS. In terms of global long-term trends, it substantially reduces the typical underestimation bias and produces estimates that are broadly consistent with recent advanced datasets. Together, these results indicate that LSTM-based frameworks offer a promising and viable pathway for carbon-flux prediction.

Author contributions

Shaoyang Chen and Liangyun Liu designed the research and wrote the manuscript. Liangyun Liu, Xinjie Liu, and Yanhong Wu revised the manuscript. Qizhi Han provided assistance with the eddy-covariance flux data.

Data availability

The TRAX GPP dataset generated and analyzed during the current study is available in the Zenodo repository at 10.5281/zenodo.17745655. The dataset is provided in NetCDF-4 format as a series of yearly files covering the period from 2001 to 2024. The GPP values (units: g C m⁻² day⁻¹) are stored as 32-bit integers (int32) with a scale factor of 0.01 and a fill value of -9999.0, following the Climate and Forecast (CF) Metadata Conventions. The dataset is released under a Creative Commons Attribution 4.0 International License (CC BY 4.0). All third-party input datasets used for model driving and validation are publicly available from their respective sources, as detailed in the Methods section.

Code availability

The TRAX GPP dataset was generated using Python 3.11, and the corresponding source code is publicly available at: https://github.com/liuly01/TRAX_GPP_code.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41597-026-07046-0.