Figure 1 displays the geographical locations of the 20 flux sites selected for the study. These sites are situated in various climatic zones and ecosystem types including forest, grassland, and cropland. The observation data for these sites come from the Science Data Bank (SDB, https://www.scidb.cn/en/, last access: 7 May 2025). Detailed information about the sites is provided in Table 1.

Most LUE models typically incorporate four main groups of variables: PAR, fPAR, temperature, and water-related stress indicators. In previous studies, vegetation indices such as EVI, NDVI, or LAI have been widely used as proxies for fPAR, representing the fraction of PAR absorbed by the plant canopy (Chang et al., 2023; Qian et al., 2024). In this study, we selected six water-related indicators based on their ecological relevance: plant-based indicators (LSWI and EF), soil-based indicators (SW), and atmospheric indicators (VPD, precipitation, and relative humidity). Previous research has shown that plant-based indicators like LSWI and EF effectively capture canopy-level drought stress (Anderson et al., 2007; Xiao et al., 2004). Soil moisture regulates water availability at the root level, which strongly influences photosynthetic activity, particularly under water-limited conditions (Vicca et al., 2014; Reichstein et al., 2007). Meanwhile, atmospheric indicators such as VPD, precipitation, and RH influence stomatal conductance and transpiration by altering the vapor pressure gradient between the leaf surface and the surrounding air (Wang et al., 2018; Novick et al., 2016). To assess the relative importance of these different types of water stress indicators in estimating GPP, we developed machine learning models using each group individually. This allowed us to identify the most effective type of water-related variable for simulating GPP across diverse ecosystems within the LUE modeling framework.

The flowchart of this study is shown in Fig. 2.

To evaluate the model performance at the site level, the accuracy of the 18 FLAML-LUE models was assessed using test datasets from individual flux tower sites. The algorithms selected by each FLAML-LUE model are listed in Table S1 in the Supplement. Notably, the Extra Trees algorithm was most frequently chosen as the best-performing model. Extra Trees is an ensemble method that constructs multiple unpruned decision trees and introduces high randomness in both feature and threshold selection, which enhances generalization and reduces overfitting, particularly in noisy or high-dimensional datasets. The consistent selection of Extra Trees suggests that FLAML tends to favor models with higher stochasticity and ensemble structures under the given data and computational constraints.

Figure 3 presents the R, nuRMSE, and NSD values for the 18 models. As shown in Fig. 3u, the model performance shows relatively small differences across different combinations of input indicators. Specifically (Table 4), the overall R2 of the different FLAML-LUE models ranged from 0.78 to 0.82, while nuRMSE values ranged from 0.4240 to 0.4670.

Among the fPAR-related indices, the model driven by EVI performed slightly better (R2=0.82, nuRMSE=0.4265) than models driven by NDVI (R2=0.80, nuRMSE=0.4524) and LAI (R2=0.79, nuRMSE=0.4561). Regarding moisture stress indicators, the model using LSWI as input achieved the best performance (R2=0.82, nuRMSE=0.4298), followed by models using VPD (R2=0.80, nuRMSE=0.4455) and RH (R2=0.80, nuRMSE=0.4450). Models driven by EF (R2=0.80, nuRMSE=0.4487), SW (R2=0.80, nuRMSE=0.4505), and Pre (R2=0.80, nuRMSE=0.4503) performed slightly worse, though the differences were minimal.

As shown in Table 5, the performance of the FLAML-LUE model varies considerably across different sites, with the average R2 ranging from 0.17 at DXG to 0.92 at CBF and HBG_G01. Notably, this variation was primarily attributed to site-level differences rather than the combinations of input indicators (Fig. 3), highlighting the influence of land cover type and climatic conditions on model performance.

The best model performance was observed at the HZF, MEF, CBF, and HBG_G01 sites (R2>0.85, TSS>0.9), followed by QYF, DLG, JZA, and SYA (R2>0.75, TSS>0.88). Within forest ecosystems, the model performed better in MF, NF, and DBF than in EBF (ALF, BNF) and savannas (YJF). MF, which includes both evergreen conifers and deciduous broadleaf species, exhibits distinct seasonal variations that can be effectively captured by satellite imagery. In contrast, EBF shows minimal seasonal greenness variation, leading to larger modeling bias in GPP estimation.

In grassland ecosystems, the model performed better for shrublands and typical steppe than for alpine meadows (Tables S4 and S5). Alpine meadows, characterized by short growing seasons and harsh high-altitude climates, often experience strong environmental disturbances and large GPP fluctuations, making them more difficult to model accurately. In contrast, typical steppe and alpine shrublands display clearer phenological rhythms and stronger photosynthetic activity, making their GPP dynamics easier to capture.

In cropland ecosystems, all sites demonstrated relatively strong model performance (R2>0.6, TSS>0.80). Compared to natural grasslands or alpine meadows, croplands are usually monocultures with stable phenology and simpler canopy structures, which aid in more accurate GPP modeling.

Notably, at the DXG site, the model achieved a high TSS (0.8326) but a relatively low R2 (0.17), primarily due to the large performance variation among different index combinations. As shown in Table S4, all six NDVI-driven models (FLAML10-FLMAL15) have negative R2 values, significantly reducing the overall model accuracy at this site.

From an ecosystem perspective, Fig.  and Table 7 indicates that the FLAML-LUE model achieves the highest fitting accuracy in forest ecosystems (R2=0.83, nuRMSE=0.4162), followed by cropland ecosystems (R2=0.72, nuRMSE=0.5258) and the lowest in grassland ecosystems (R2=0.71, nuRMSE=0.5407). The slope of the fitted line in Fig. 7 is less than 1 for all ecosystem types, indicating that the FLAML-LUE model tends to underestimate GPP, particularly in croplands and grasslands.

Tables S2 and S3 and Table 6 collectively demonstrate that the model's performance varies across ecosystem types depending on the choice of fPAR-related variables. In forest ecosystems, the model is relatively insensitive to different fPAR and water-related inputs, with the LAI-driven model achieving the best performance. This can be attributed to LAI's ability to capture forest canopy structure, thereby improving fPAR estimates. In contrast, the model's performance is more sensitive to the choice of input variables in cropland and grassland ecosystems. In croplands, the EVI-driven model performs best, followed by LAI and then NDVI, although the performance differences are moderate. In grasslands, however, the NDVI-driven model performs worst, especially at the DXG site, likely due to NDVI's sensitivity to soil background and saturation in sparse and heterogeneous vegetation. EVI, with reduced saturation and higher sensitivity to biomass, shows better performance in structured cropland areas. Overall, the EVI- and LSWI-driven model (FLAML00) exhibits the best performance across all ecosystem types.

To further investigate model accuracy across different land cover types, Fig. 5 presents the R2 values of five forest types, three grassland types, and two cropland types under different models. In general, model performance varies little within the same land cover type but differs substantially across types. Specifically, DBF, NF, MF, and SC exhibit higher simulation accuracy, followed by GRA, SHR, and DC, while EBF, SAV, and MEA perform the worst. These results are consistent with the Taylor diagram in Fig. 3.

Regarding CV_RMSE, SHR shows the largest error, followed by MEA, GRA, SC, and DC, while the five forest types show the smallest errors. This may be attributed to the greater GPP variability in grassland and cropland ecosystems, which are more strongly influenced by climatic variability and anthropogenic activities, leading to higher model uncertainty. In contrast, forest ecosystems have more stable structures and continuous carbon exchange processes, resulting in more robust model performance. Although alpine meadow is classified as grassland ecosystems, their extreme climatic conditions, short growing season, and high sensitivity to temperature and precipitation further increase the uncertainty of GPP simulation, leading to higher errors.

In terms of PBias, SHR consistently shows a pronounced overestimation across all models. Similarly, SAV and MEA are also generally overestimated in all models, though to a lesser extent than SHR. EBF exhibits a slight overestimation as well. Other vegetation types display only minor underestimation or overestimation. Overall, the models perform best for DBF, NF, and MF, followed by EBF, MEA, SC, and DC, while the simulation accuracy is relatively poor for SAV, SC, and especially SHR.

Biases also differ among grassland ecosystems, especially for typical grasslands, alpine meadows, and shrublands. Typical grasslands tend to be underestimated, while alpine meadows and shrublands are often overestimated. These biases may result from the model's limited ability to capture seasonal changes in water availability and its interaction with temperature. Typical grasslands usually show high productivity when water is sufficient, especially in spring and summer. If the model fails to reflect these seasonal patterns, it can lead to underestimation. In contrast, productivity in alpine meadows is mainly limited by low temperatures and a short growing season. If the model does not fully consider these constraints, it may overestimate photosynthesis and thus GPP. For shrublands, overestimation may be due to high spatial heterogeneity, including a mix of shrubs, grasses, and bare soil. This complexity is difficult to capture in remote sensing data (e.g., fPAR) and model inputs, leading to possible overestimation of productivity.

Across the four temporal scales, the performance of the 18 FLAML-LUE models improves as the temporal resolution becomes coarser. The average R2 across 20 sites increases from 0.64 at the daily scale to 0.74 at the monthly scale (Table S8), while the average nuRMSE decreases from 0.5518 to 0.4088. Paired t tests show that, except for YJF, NMG, DMG, DXG, and YCA, the FLAML-LUE model exhibits significantly lower R2 at the daily scale than at longer temporal scales (p<0.05, Fig. 6). For these five sites, model performance remains relatively stable across different temporal scales.

Furthermore, compared to the daily scale, the nuRMSE decreases by 12.97 %, 16.52 %, and 25.92 % at the 8 d, 16 d, and monthly scales, respectively, indicating that the uncertainty of the FLAML-LUE model is significantly reduced at coarser temporal resolutions.

Overall, the accuracy of FLAML-LUE models constructed using different combinations of fPAR and water stress indicators showed limited variation, with the FLAML00 model (fPAR = EVI, water = LSWI) demonstrating the best performance. However, the model exhibited considerable differences in performance across ecosystem types, with the highest accuracy observed in forest ecosystems, followed by croplands and then grasslands. Further analysis by specific vegetation cover types revealed that the model performed best for DBF, NF, and MF, followed by GRA, MEA SC, and DC, while its performance was relatively poor for EBF, SAV, and particularly SHR (PBias>27 %, CVRMSE>1, R2<0.6). In addition, evaluation across different temporal scales indicated that model uncertainty decreased with increasing time intervals, suggesting that the FLAML-LUE model exhibits greater robustness and reliability at coarser temporal resolutions.

Numerous studies have demonstrated that climate extremes such as heat waves, droughts, and high atmospheric VPD can substantially alter ecosystem dynamics and reduce carbon uptake capacity (Frank et al., 2015; Reichstein et al., 2013). These extreme events can suppress photosynthesis, increase respiration, and disrupt the balance of carbon exchange between vegetation and the atmosphere. In order to evaluate the robustness and reliability of the FLAML-LUE models under such stress conditions, this study further investigates model performance in simulating GPP under three types of climate extremes: high temperature, high VPD, and drought. By analyzing the response of model accuracy and bias under these scenarios, we aim to assess its applicability and limitations in extreme environmental conditions.

In this study, FLAML-LUE models were constructed for different combinations of variables and different timescales based on AutoML algorithms. On the whole, the modeled GPP values agree well with the GPP estimated based on the EC tower, and the FLAML-LUE models performed better in capturing the magnitude and seasonal dynamics of the GPP, which indicated that it was feasible to estimate the GPP using AutoML algorithms. Further, all three ecosystems showed good model performance driven by observational data. Comparisons across various ecosystems indicate that the model exhibited superior performance over forest ecosystems compared to grassland and agricultural ecosystems, as evidenced by the average R2 values.

Although model performance differences across indicator combinations were minimal, EVI-driven FLAML-LUE models slightly outperformed those driven by NDVI. This highlights the key role of EVI in GPP estimation, as it offers more comprehensive atmospheric correction and is less susceptible to saturation from green reflectance compared to NDVI. Additionally, model performance varied significantly across sites.

Based on the evaluation metrics, the optimal model selected was FLAML00 (EVI + LSWI). Under this combination of indicators, the FLAML-LUE model demonstrated the best performance in mixed forests at CBF, deciduous broadleaf forests at MEF, and alpine meadows at HBG_G01, with R2 values of 0.92, 0.92, and 0.93, respectively. The next best performances were observed in coniferous forests at QYF and HZF, single-cropping farmland at JZA and SYA stations, double-cropping farmland at YCA, and typical grasslands at DLG and DMG sites. In contrast, the model performed poorly in alpine shrub and alpine ecosystems, with an R2 of 0.54, and the worst performance was observed at the BNF site, with an average R2 of only 0.28. Mixed forests exhibit distinct seasonal variations that satellite imagery can effectively capture, while evergreen broadleaf forests (ALF and BNF) show minimal seasonal changes in vegetation cover or greenness, making accurate predictions challenging. Alpine shrublands have more complex vegetation structures and less distinct seasonal variations in vegetation cover, which makes it harder for the model to capture the dynamics accurately. In contrast, alpine meadows exhibit more pronounced seasonal variations in vegetation cover, which makes the model more effective in capturing GPP dynamics. For non-forest ecosystems, the highest R2 values were observed in agricultural fields and typical grasslands, followed by alpine meadows and alpine shrublands.

Mixed forests display clear seasonal variations that satellite imagery can effectively capture. However, evergreen broadleaf forests (ALF) have slight seasonal variations in vegetation cover or greenness, making it difficult for the model to predict. For non-forest ecosystems, the highest R2 was found in agricultural fields and typical grasslands, followed by alpine meadows and alpine scrub. In addition, the differences in model performance were also reflected in different temporal scales. In general, the model simulation performance at the 16 d and monthly scales was better than that at the daily scale, and the performances of different temporal scales for forest, grassland, and cropland ecosystems were consistent with previous studies.

This study did not distinguish between rainfed and irrigated agricultural systems, considering only the crop rotation types. Specifically, JZA and SYA represent rainfed systems, whereas GCA, LCA, and YCA are irrigated. Future research could incorporate this distinction to improve the accuracy of carbon flux estimates in cropland ecosystems. This distinction is important for interpreting model results under water-limited conditions.

In addition, our results indicate that forest and agricultural fields have greater carbon sequestration capacity and higher annual fluxes than grasslands (Tables S9–S11), aligning with previous research outcomes (Wang et al., 2021b; Zhang et al., 2007). However, due to the annual harvest of crops, approximately 76 % of the on-farm biomass is removed, resulting in limited long-term carbon storage capacity (Zhang et al., 2007). With the exception of tropical rainforests (i.e., BNF), the annual carbon production of planted forests (i.e., QYF) is higher than that of natural forests (i.e., CBF, DHF), which implies that planted forests possess significant potential for carbon assimilation, functioning as robust carbon sinks.

In the context of global warming and the increasing frequency of extreme climate events, the adaptability and stability of GPP estimation models in extreme environments have become crucial. This study systematically evaluated the performance of the FLAML-LUE model under high-temperature, high-VPD, and drought scenarios by grouping the validation set. The results showed a general decline in the model's accuracy across all three extreme climate conditions, with varying performance depending on the scenario, highlighting the complexity of vegetation carbon absorption responses to climate stress.

In high-temperature conditions, the model generally underestimated GPP. This could be due to the suppression of photosynthesis caused by high temperatures. High temperatures increase transpiration stress, causing stomatal closure to reduce water loss, which limits CO2 input and lowers photosynthetic rates (Qu et al., 2020; Reichstein et al., 2013). Additionally, high temperatures can cause leaf damage and senescence, reducing LAI and overall photosynthetic potential (Chen et al., 2021a, b). Although the FLAML-LUE model accounts for fPAR and water stress factors, it may not fully capture rapid responses such as leaf damage or sudden declines in LAI, which likely contribute to the reduced accuracy under high-temperature conditions. Moreover, the model does not explicitly account for the lag effect of leaf senescence, which may further worsen estimation bias (Frank et al., 2015).

Under high-VPD conditions, the model showed significant uncertainty, with some areas overestimating GPP and others underestimating it. This inconsistency likely arises from the diverse water stress mechanisms induced by high VPD. Guo et al. (2015) noted that high VPD does not always reflect the true level of water stress in plants, leading to the potential overestimation of GPP. Conversely, in extreme VPD scenarios, where stomata close to reduce carbon absorption, the model may underestimate GPP if it fails to recognize this regulatory behavior (Li et al., 2016). Additionally, the FLAML-LUE model does not explicitly consider leaf energy load or light inhibition, which may contribute to the model's higher errors under high-VPD conditions (Rigden et al., 2020).

Although the model's performance decreased at some sites under drought conditions, its overall accuracy improved under these scenarios. This improvement may be due to the stronger limiting effect of drought on vegetation growth, allowing the model to more accurately capture the suppressive impact of water stress on photosynthesis. In drought conditions, water scarcity limits carbon absorption, leading to a substantial reduction in GPP (McDowell et al., 2008). As a result, the model's estimates are more likely to align with the actual limitation of carbon absorption. Thus, under drought conditions, the model may underestimate GPP, which can be more accurate, while in wetter environments, where water stress is less pronounced, the model may overestimate GPP, reducing its accuracy. Additionally, under drought, the model is likely better at capturing the direct effects of water shortage on plant physiology, reducing interference from other environmental variables and improving prediction accuracy (Zhou et al., 2019).

Although the FLAML-LUE model demonstrates strong predictive capabilities under normal climate conditions, there is still room for improvement under extreme scenarios. One potential limitation is the insufficient representation of rapid plant response mechanisms (e.g., leaf damage and sudden declines in LAI) in the current input features (Frank et al., 2015; Reichstein et al., 2013). Future research could incorporate high-temporal-resolution vegetation indices, such as solar-induced chlorophyll fluorescence (SIF), to better capture dynamic changes in plant metabolic activity and stress responses under extreme conditions (Yi et al., 2024; Pagán et al., 2019). Including lag variables or cumulative stress indices could also enhance the model's ability to handle delayed physiological responses after stress events (Frank et al., 2015). Furthermore, future studies should expand the scope to include a broader range of climate events that affect GPP, such as floods and low temperatures, in addition to high temperature, high VPD, and drought (Wang et al., 2023). Vegetation in different regions responds differently to these events, with low temperatures and frost being especially important for high-latitude ecosystems.

In this study, FLAML (Wang et al., 2021a) selected the Extra Trees algorithm as the best-performing model for GPP simulation in China. Extra Trees is an ensemble learning method that builds multiple unpruned decision trees and incorporates randomization in features selection and split thresholds determination. Compared to traditional decision tree ensembles such as Random Forests, Extra Trees typically achieves minimal variance while maintaining low bias, which makes it particularly well suited for complex, high-dimensional datasets (Geurts et al., 2006).

The adoption of FLAML provides several significant advantages. First, it automates the model selection and hyperparameter tuning process, eliminating the need for extensive manual trial and error and reducing reliance on domain expertise (Nakano and Liu, 2025; Wang et al., 2022). Instead of manually evaluating various algorithms and their configurations, FLAML efficiently explores a broad search space and identifies the most appropriate model for the dataset.

Moreover, FLAML employ a cost-aware hyperparameter optimization strategy, enabling it to find high-performing models with relatively low computational cost (Zhang et al., 2023a; Wang et al., 2021a). This feature is particularly advantageous in scenarios with limited computational resources or the need for rapid prototyping.

Compared to conventional machine learning workflows, FLAML significantly reduces human bias in model selection, improves reproducibility, and lowers the barrier to applying advanced modeling techniques (He et al., 2021). Overall, the use of FLAML in this study not only improved model performance but also streamlined the modeling process, supporting its broader applicability in ecological and climate-related research.

This study attempted to predict the GPP of different sites using the FLAML model based on the LUE model variables. The results showed that the AutoML algorithm is a promising GPP estimation method, which explains on average 75 %–98 % of the GPP variation.

Compared to two GPP products (MODIS GPP and PML GPP), the GPP from this study showed the highest precision (Table 8 and Fig. ) and better consistency with flux-tower-based GPP under different ecosystems. Overall, the FLAML-LUE model used in this study had the best simulation performance. These findings highlight the potential of the FLAML algorithm for accurately estimating GPP. The FLAML-LUE model is a data-driven ML approach that builds relationships based on dependent and explanatory variables. This enables it to effectively simulate the complex nonlinear interactions across diverse ecosystems (Tramontana et al., 2016). This advantage is even more prominent at the global scale, considering that more flux tower data are available for model construction.

However, further work is needed to evaluate the FLAML-LUE model's suitability and accuracy, considering its limitations. In particular, it tends to underestimate high GPP and overestimate low GPP. In addition, the model performance in GPP estimation is highly dependent on ecosystem type. Our findings indicated that mixed forests, deciduous broadleaf forests, and agricultural lands had higher prediction accuracies, while grass sites such as alpine scrub and alpine meadows were predicted with large uncertainties, consistent with results from other studies (Wang et al., 2021b; Yuan et al., 2014). This is still a big challenge in accurately estimating GPP.

In general, satellite imagery accurately captures the seasonal leaf phenology of DBF and MF canopies (e.g., spring leaf unfolding and fall senescence). Additionally, the key environmental factors influencing vegetation production during different phenological phases are well defined (Yuan et al., 2014), making them well suited for FLAML-LUE modeling. In contrast, the ambiguous seasonal leaf area changes in EBF and the low variability of GPP in NMG ecosystems result in poorer model performance, and empirical methods struggle to estimate GPP variability in these areas (Tramontana et al., 2016).

Model performance is heavily influenced by the quality of the driver data and the typicality of the flux towers. In this study, meteorological indices are obtained directly from spatially explicit reanalysis products. Remotely sensed variables (e.g., NDVI and EVI, LSWI) serve as proxies for vegetation growth and seasonal changes and are crucial for scaling simulations from site to regional levels. These gridded indices are directly derived from satellite reflectance bands. Large-area EFs can be obtained using LE and H calculations from ERA5 reanalysis data or can be derived using NDVI temperature triangulation (Venturini et al., 2004). LAI, VPD, Pre, and RH can be obtained from ERA5 reanalysis data. Thus, the model can be extended from the site scale to the regional and even global scale. Building on this foundation, we will develop a long-term gridded GPP dataset for China using the FLAML-LUE framework to analyze its spatiotemporal variations over multiple years. This dataset will allow us to investigate long-term GPP trends across different climate zones and vegetation types, as well as their responses to key environmental drivers. By comparing GPP estimates across regions and years, we will also assess model uncertainties and identify potential areas for improvement.