Estimation of GPP in northern hemisphere terrestrial ecosystems based on light use efficiency model and chlorophyll fluorescence

1 Introduction

Gross Primary Productivity (GPP) refers to the amount of organic carbon fixed by green plants through photosynthesis per unit time and is also known as total primary productivity (Garbulsky et al., 2014). As the initial input of matter and energy into terrestrial ecosystems, GPP is a key parameter for understanding biosphere-atmosphere interactions. Accurate monitoring of GPP is essential for studying the global carbon cycle and assessing climate feedback mechanisms (Bai et al., 2022). Given the vast extent and environmental complexity of Northern Hemisphere terrestrial ecosystems, estimating GPP using remote sensing data based on various environmental factors has become the primary method at the ecological scale.

As remote sensing technology advances and remote sensing data at various spatial scales accumulates, remote sensing-driven GPP models are adopted predominately in current ecosystem carbon cycle research (Bandopadhyay et al., 2021; Chen et al., 2021). These models are generally categorized into three types: Mathematical-statistical models, which are simple in structure and require few parameters, but their accuracy can be limited under heterogeneous conditions; process-based models, which incorporate numerous variables and provide detailed mechanistic understanding, yet their application is often constrained by the availability of extensive ground-based observations; and LUE models, which offer a balance of mechanistic clarity, structural simplicity, and practical applicability (Chen et al., 2024a; Chen et al., 2024b). The theoretical basis for LUE model was first proposed by Monteith, who introduced the concept of estimating primary productivity based on the efficiency of solar radiation utilization by plants (Chen et al., 2022; Monteith, 1972). The Carnegie-Ames-Stanford Approach (CASA) model, developed by Potter et al., 1993 estimates FAPAR using the Normalized Difference Vegetation Index (NDVI) and adjusts LUE using temperature and moisture stress factors (Potter et al., 1993). The Eddy Covariance-Light Use Efficiency (EC-LUE) model, proposed by Yuan et al., 2007 further incorporates CO₂ fertilization effects and vapor pressure deficit factors to refine LUE, and calibrates maximum LUE (LUEmax) using eddy covariance (EC) flux data (Yuan et al., 2007). Other representative LUE models include the Vegetation Photosynthesis Model (VPM), which uses the Enhanced Vegetation Index (EVI) for FAPAR estimation and the Land Surface Water Index (LSWI) for water stress modulation, as well as the MODIS GPP product based on biome-specific maximum LUE values (Running et al., 2004). All these models estimate FAPAR using vegetation indices. Derived from reflectance data, vegetation indices primarily represent canopy greenness and structural characteristics. However, they have a weak correlation with short-term photosynthetic activity and conflate multiple biophysical signals. As a result, they are limited in their ability to capture rapid changes in vegetation photosynthetic status. Given these limitations, a more comprehensive review of recent modeling advances is warranted, particularly those incorporating physiological signals.

Sun-induced chlorophyll fluorescence (SIF) refers to the red and near-infrared photons re-emitted by chlorophyll molecules after absorbing solar radiation. Extensive research has shown that SIF emitted by plants under natural sunlight serves as an ideal proxy for instantaneous photosynthetic activity and holds great potential for assessing plant physiological status and responses to environmental stress (Xiao et al., 2005). Examining the relationship between chlorophyll fluorescence yield and photochemical yield offers a novel approach for monitoring actual photosynthesis using SIF and for estimating GPP in terrestrial ecosystems (Chen et al., 2021). Compared to greenness-based vegetation indices, SIF—being a direct byproduct of photosynthesis—is more sensitive to vegetation photosynthesis and provides more timely indications of photosynthetic dynamics. Advanced remote sensing algorithms enables numerous high-spectral resolution spectrometers mounted on satellite platforms to retrieve SIF signals in the near-infrared band, leading to the generation of SIF products at various spatial and temporal scales. Numerous studies have confirmed a strong correlation between large-scale SIF data from various sensors and GPP. For example, Guanter et al., 2012. utilized GOME-2 SIF data and demonstrated that SIF is more sensitive to crop photosynthesis than any other existing remote sensing parameter or model (Guanter et al., 2012). Joiner et al., 2014. showed strong seasonal consistency between GOME-2 SIF data and GPP measured by flux towers (Joiner et al., 2014). Sun et al., 2018. further demonstrated that OCO-2 SIF data exhibit strong correlations with flux tower-derived GPP at daily time scales across ecosystems (Sun et al., 2018).

Currently, SIF-based GPP estimation models can be broadly categorized into three types: Linear regression models, which are directly built on the strong correlation between SIF and GPP. These models are simple but lack general applicability (Guanter et al., 2012). LUE model, which features clear mechanisms, simple structure, and strong practicality, has been extensively studied and widely applied. The Soil-Canopy Observation of Photosynthesis and Energy fluxes (SCOPE) model, which simulates the radiative transfer processes of both reflected and emitted radiation (including thermal and fluorescence emissions). It calculates leaf-level photosynthetic rates and the proportion of absorbed radiation converted into fluorescence using both C₃ and C₄ photosynthesis models. These calculations are then scaled up to the canopy level, enabling quantitative studies of the relationship between canopy GPP and SIF (Verrelst et al., 2015).

However, the relationship between canopy SIF and GPP is influenced by multiple factors, and the widely used empirical linear models lack general applicability (Chen et al., 2024a). Meanwhile, the SCOPE model is constrained by its dependence on numerous parameters required by mechanistic modeling. To address these limitations, this study introduces the Photochemical Reflectance Index (PRI) and vegetation indices that reflect canopy structure to develop LUE model. By leveraging various SIF datasets obtained from satellite platforms, the study explores the models’ applicability across different vegetation types under varying combinations of SIF products and vegetation indices. Furthermore, the LUE model is applied to estimate GPP in Northern Hemisphere terrestrial ecosystems, aiming to improve the spatiotemporal accuracy of GPP estimations. The results are expected to provide valuable references for ecosystem carbon cycle research at global and regional scales, and to contribute to advancing understanding of global carbon cycling and climate change.

2 Dara collection and processing

2.1 Observed GPP_EC data and selection of flux sites

The ground-based flux observation data used in this study were obtained from the FLUXNET2015 dataset published by the Global Flux Observation Network (Pastorello et al., 2020). A total of 177 flux sites located in the Northern Hemisphere were selected for analysis, with their spatial distribution shown in Figure 1. Monthly GPP data from these Northern Hemisphere sites for the period 2007–2014 were downloaded from http://fluxnet.fluxdata.org/. Specifically, the GPP_NT_VUT_REF product (nighttime partitioning method with variable friction velocity threshold) was used. Negative GPP values, which indicate measurement or partitioning errors, were removed. All available data were aggregated to monthly temporal resolution to match the satellite SIF products. No interpolation was performed for missing values, and no further outlier exclusion was applied to preserve data continuity. After aggregating to monthly temporal resolution to match the satellite SIF products, the number of available flux tower sites decreased from 177 to 106.

2.2 SIF datasets

Three SIF products—GOSIF, GOME-2 SIF, and TCSIF—are used to construct the LUE model. The GOSIF data, developed by the Global Ecology Group (http://data.globalecology.unh.edu/data/GOSIF_v2/Monthly/), is a high-resolution product generated using machine learning methods based on discrete SIF observations from the OCO-2 satellite (Li and Xiao, 2019). GOME-2 SIF data are derived from the far-red SIF signal at 740 nm (SIF740), extracted by the GOME-2 hyperspectral instrument onboard the MetOp-A/B satellites. In this study, the GOME-2 SIF Level 3 (L3) product is used (http://acdb-ext.gsfc.nasa.gov/People/Joiner/my_gifs/GOME_F/GOME-F.htm) (Köhler et al., 2015). TCSIF data come from the Time-consistent Corrected SIF Dataset (https://zenodo.org/records/8242928), a globally consistent, temporally harmonized dataset spanning 2007–2021. This dataset was developed by Zou et al., 2024. by calibrating the temporal degradation of the GOME-2A instrument using a quasi-invariant calibration method, with quasi-invariant regions in the Sahara Desert serving as reference points. SIF retrieval within the 735–758 nm window is performed using a data-driven singular value decomposition (SVD) approach (Zou et al., 2024). Detailed product information is provided in Table 1. After the monthly data for the three SIF products covering 2007–2014 were downloaded, pixel values corresponding to flux tower sites were extracted using ArcGIS with Python. The three SIF products have inconsistent spatiotemporal resolutions (Table 1). To enable cross-product comparison, all SIF data were aggregated to monthly and resampled to a common 0.05° resolution.

TABLE 1. Information of SIF product datasets.

2.3 Vegetation indices and MODIS surface reflectance

PRI, calculated as the ratio of the difference between vegetation reflectance at 531 nm and 570 nm to their sum, is used to estimate the photochemical light use efficiency (LUEP) of vegetation (Demmig-Adams and Adams, 1996; Hall et al., 2012). However, the MCD19A1 dataset provides only daily-scale reflectance at 531 nm and does not include a standard 570 nm band. Therefore, Band 4 (545–564 nm), the closest available to 570 nm, is selected as the reference band. Daily PRI is computed on the Google Earth Engine (GEE) platform, then aggregated to monthly scale by averaging, resampled to 0.05°, and mathematically scaled to obtain sPRI.NDVI, EVI, Modified Soil-Adjusted Vegetation Index (MSAVI), and Near-Infrared Reflectance of Vegetation (NIRv) have demonstrated good performance in canopy leaf area index (LAI) retrieval and can effectively represent the influence of vegetation canopy optical structure (Peng et al., 2011; Haboudane et al., 2004; Badgley et al., 2017). In addition to these established indices, we empirically tested the combined index NDVI × NIRv, which showed improved sensitivity to canopy structure compared to NIRv alone. Although NIRv already incorporates NDVI information, a multiplicative enhancement may nonlinearly amplify greenness signals. Similar to the relationship between NDVI and EVI, where the latter was developed to reduce saturation in high-biomass regions while sharing the same spectral bands (Huete et al., 2002), NDVI × NIRv may offer additional predictive power for LAI retrieval beyond individual indices. Monthly EVI and NDVI data, along with reflectance in red, blue, near-infrared, and shortwave-infrared bands, are obtained from the MOD13A3 dataset via the Google Earth Engine (GEE) platform and resampled to 0.05°. Subsequently, MSAVI, NIRv, and the combined index NDVI × NIRv are calculated using the formulas described in Table 2. After downloading the monthly vegetation indices data for 2007–2014, pixel values corresponding to the flux tower sites were extracted using ArcGIS with Python.

TABLE 2. Formulas for relevant vegetation indices.

2.4 LUEmax and land cover product

In constructing the LUE model, this study introduces maximum light use efficiency (LUEmax) to represent the maximum photosynthetic potential of different vegetation types, following the estimation approach of the MODIS-GPP (MOD17) models (Running et al., 2004). Based on the FLUXNET2015 dataset, the 177 flux tower sites selected in the Northern Hemisphere are initially classified into 11 IGBP vegetation types. To account for similarities in vegetation physiological and ecological characteristics, as well as to ensure sufficient sample sizes, several vegetation types are merged following the classification method proposed by Frankenberg et al., (2011) resulting in a total of 9 vegetation categories. The LUEmax values for each vegetation type are determined based on the empirical parameters from the UMD classification scheme in the MODIS land cover product (MOD12Q1), as well as the findings of Yu et al., (2009), and are listed in Table 3. To estimate GPP across the Northern Hemisphere, the spatial distribution of vegetation types is required in order to assign appropriate LUEmax values globally. Therefore, the MODIS land cover product MCD12C1 for the period 2007–2014, with a spatial resolution of 0.05°, is used in this study.

TABLE 3. Empirical parameter for different vegetation types (kg C/m²/d/MJ/1000).

2.5 Global GPP products

Two GPP products are used to validate the GPP estimated by the LUE model at the Northern Hemisphere scale. The first is GLASS-GPP, developed based on the EC-LUE model, sourced from the UMD GLASS Laboratory (http://www.glass.umd.edu/Download.html), with a spatial resolution of 500 m × 500 m and a temporal resolution of 8 days (Du et al., 2021). The second is MODIS-GPP, a global, high-temporal-resolution product derived from MODIS satellite data, obtained from the LP DAAC data center (https://lpdaac.usgs.gov/), also with a spatial resolution of 500 m × 500 m and an 8-day temporal resolution. After downloading the datasets for the period 2007–2014, both products are aggregated to monthly temporal resolution and resampled to a spatial resolution of 0.05 ° × 0.05 ° using ArcGIS and the GEE platform to match the model output scale.

3 Materials and methods

This study focuses on the Northern Hemisphere and develops SIF-based LUE model to estimate terrestrial ecosystem GPP. First, the LUE model is constructed using multiple SIF products and vegetation indices, with nonlinear relationships fitted through Support Vector Regression (SVR). Next, the performance of different SIF-VI combinations across vegetation types is evaluated, and their monthly-scale estimation accuracy is compared to identify the optimal combination. Finally, based on the best-performing SIF-VI model, GPP across the Northern Hemisphere from 2007 to 2014 is estimated, followed by an analysis of its spatial and temporal variation.

A three-stage methodological framework is followed: data acquisition and pre-processing, model construction and nonlinear fitting, and data analysis and validation (Figure 2). Data preprocessing includes denoising, resampling, and harmonizing the spatial resolution of flux tower observations, SIF products, MODIS, and GLASS data. For model construction, SVR is used to fit the SIF-VI relationship and to estimate site-level GPP. Finally, the performance of different models is compared to identify the optimal SIF-VI combination. This optimal model is then applied to estimate monthly GPP across the Northern Hemisphere, followed by validation against existing GPP products and an analysis of spatial and temporal patterns.

3.1 LUE model development

A SIF-based GPP estimation model is developed within the framework of the LUE model (Du et al., 2018). The basic form of the model is expressed as Equation 1 where PAR denotes solar radiation in the 400–700 nm wavelength range, FAPAR represents the fraction of absorbed photosynthetically active radiation (PAR), and LUE _*P* is the actual light use efficiency. Similarly, SIF can be expressed as Equation 2 where LUE _*F* denotes the light use efficiency for SIF, and f _*esc* represents the canopy escape fraction. Combining these two yields this fundamental relationship Equation 3:

G P P = S I F λ × L U E P L U E F λ × f e s c λ (1)

S I F λ = P A R × F A P A R × L U E F λ × f e s c λ (2)

GPP = APAR × LUE = PAR × FAPAR × L U E P (3)

During model development, the Photochemical Reflectance Index (PRI) was introduced as an indicator for estimating LUE _*P*. Studies have shown that variations in vegetation LUE trigger adjustments in photosynthetic pigments through mechanisms such as the xanthophyll cycle. This process produces a characteristic reflectance response near the 531 nm wavelength. PRI effectively captures this physiological response and has demonstrated strong correlations across multiple spatial scales. To account for the influence of canopy structure and chlorophyll content on the relationship between PRI and LUE, a vegetation index correction function, f _*1* (VI), is introduced. In addition, because the photosynthetic capacity varies among vegetation types, LUEmax is species-dependent (Gamon et al., 1997). Following the approaches of MODIS-GPP (MOD17) and the VPM model, LUEmax is assigned based on land cover classification (MOD12Q1). Accordingly, LUEp can be expressed as Equation 4 where sPRI = (PRI + 1)/2 denotes the standardized PRI index. For SIF yield, existing studies suggest that LUE _*F* can be considered a relatively stable constant under non-stressed environmental conditions. In contrast, f _*esc* is influenced by structural parameters such as the Leaf Area Index (LAI). To quantify this effect, a vegetation index function f _*2* (VI), designed to characterize canopy structure, is introduced. Based on these components, the GPP estimation model is formulated as Equation 5 where λ represents the wavelength of the extracted SIF data; LU E _max denotes the maximum light use efficiency; sPRI is the scaled photochemical reflectance index; f _*1* (VI) describes the composite relationship between PRI and LUE constructed using vegetation indices; a is a constant representing LUE _*F*; f _*2* (VI) is a function quantifying the effect of canopy structure on escape fraction based on vegetation indices; c denotes the fitted constant for different vegetation types; and f(VIs) reflects the influence of canopy structural characteristics on the modeled relationship.

L U E P = L U E max × s P R I × f 1 V I (4)

G P P = c × S I F λ × L U E max × s P R I × f V I s (5)

3.2 Fitting methods for LUE model

In the LUE model, the relationship between sPRI and LUE _*P*, as well as the influence of vegetation indices representing canopy structure on SIF, are generally nonlinear. Machine learning techniques are well-suited for capturing complex nonlinear relationships and performing feature learning. In particular, SVR, grounded in Vapnik-Chervonenkis (VC) dimension theory and the principle of structural risk minimization, effectively addresses challenges such as small sample sizes, nonlinearity, high dimensionality, and local minima—issues that often limit conventional regression algorithms (Chen et al., 2024b). Therefore, this study adopts SVR with Particle Swarm Optimization (PSO) for hyperparameter selection. The SVR model used a grid search with 5-fold cross-validation to optimize the penalty parameter C and kernel coefficient γ. Vegetation indices are used as input variables xk, while the output variable yk is defined as GPP _*EC* /[LUEmax × SIF (λ) × sPRI]. This framework is used to fit the nonlinear function f in Formulas.

3.3 Accuracy evaluation

To ensure the reproducibility of the results, the site data in this study are divided into a training set and a validation set in a 7:3 ratio. The accuracy evaluation includes the Coefficient of Determination (R ^*2*) and the Root Mean Square Error (RMSE), with their formulas given as follows Equations 6, 7: where y _*i* is the observed value of GPP, yˆ_*i* is the predicted value, y¯ are the means of y _*i* respectively, and n is the sample size. R ^*2* indicates the explanatory power of the model (ranging from 0 to 1), while RMSE and MAE measure the absolute error—with smaller values indicating better model performance.

R 2 = 1 − ∑ i = 1 n y i − y ^ i 2 ∑ i = 1 n y i − y ¯ 2 (6)

RMSE = 1 n ∑ i = 1 n y i − y ^ i 2 (7)

4 Result and discussion

4.1 Comparative analysis of three SIF products in relation to GPP_EC

Based on the site information, this study analyzes the correlation between three SIF products and GPP at a monthly scale across nine vegetation types (Figure 3). GPP from the flux tower sites shows a statistically significant linear relationship (P < 0.01) with all three SIF products across all vegetation types. The corresponding R ^*2* values are presented in (Figure 4).

The correlations between GPP and different SIF products vary. GOSIF exhibits the best overall performance, with a mean R ^*2* of 0.63, followed by GOME-2 SIF (mean R ^*2* = 0.50), while TCSIF shows the weakest correlation (mean R ^*2* = 0.42). However, the performance of these products varies across vegetation types. GOSIF shows significantly stronger correlations than GOME-2 SIF and TCSIF in evergreen broadleaf forests (EBF), savannas (SAV), shrublands (SHR), and wetlands (WET). In contrast, GOME-2 SIF slightly outperforms GOSIF in evergreen needleleaf forests (ENF) and mixed forests (MF), while TCSIF outperforms GOME-2 SIF in SAV and SHR. Overall, the three SIF products demonstrate stronger correlations with GPP in MF, deciduous broadleaf forests (DBF), and grasslands (GRA), and weaker correlations in SHR and SAV.

4.2 Comparative analysis of model fitting performance

4.2.1 Comparison of model fitting using different methods

Based on different SIF types, this study employs NDVI, EVI, MSAVI, NIRv, and the combined vegetation index NDVI × NIRv to construct the models. The SVR algorithm is used to fit the nonlinear functional relationships. Two approaches are applied to control model input data: Approach 1 involves training the data from all flux sites collectively without distinguishing vegetation types, resulting in a single model. The corresponding GPP prediction results are denoted as GPPGlobal_Vegetation index. Approach 2 partitions the flux site data by nine vegetation types. For each type, a separate model is trained, and the prediction results are subsequently merged to obtain the overall GPP prediction, denoted as GPPV_type_Vegetation index. The R ^*2* values between the predicted GPP from both approaches and the observed GPP_EC are presented in Table 4.

TABLE 4. R² between GPP estimation results from two methods and GPP_EC at flux sites.

For the same SIF type and vegetation index, the R ^*2* of GPPV_type_Vegetation index is significantly higher than that of GPPGlobal_Vegetation index, with accuracy improvements ranging from 8.55% to 14.43%, and an average increase of 12.17%. The R ^*2* values are significantly influenced by the type of SIF product, showing a consistent pattern under the same modeling method and vegetation index: GOSIF > GOME-2 SIF > TCSIF. In contrast, the influence of vegetation indices on R ^*2* is relatively weak; under the same modeling approach and SIF type, the R ^*2* values across different vegetation indices are similar. In summary, Approach 2 provides better overall fitting performance and substantially improves model estimation accuracy.

4.2.2 Comparison of model estimation accuracy using different SIF products and vegetation indices

Approach 2 significantly improves the overall model estimation accuracy. Therefore, this study adopts Approach 2 to build the LUE model based on three SIF products, using NDVI, EVI, MSAVI, NIRv, and the combined vegetation index NDVI × NIRv. These models are then used to estimate GPP across nine vegetation types, and their correlations with observed GPP_EC values from flux towers are analyzed.

To compare the performance of different models, this study evaluates the model fitting results based on GOSIF (Figure 5). Compared with the empirical linear model, the GOSIF model shows limited overall improvements in accuracy, but their performance varies notably across vegetation types. SHR exhibit the most significant improvement, with the average accuracy gain across the five vegetation indices reaching 8.47%, and NDVI contributing the highest individual improvement of 13.12%. EBF follow, with an average gain of 5.00%, again with NDVI showing the best performance (6.35%). For GRA, the average improvement is 2.78%, with the NDVI × NIRv combination providing the highest increase (3.68%). Although this model performs poorly overall in WET, integrating NDVI still results in a 2.87% improvement. In summary, although the overall accuracy improvement of the GOSIF model is limited, at least one vegetation index consistently outperforms the empirical linear model in each of the nine vegetation types.

Model fitting results based on GOME-2 are developed to further evaluate the impact of GOME-2 SIF data (Figure 6). Compared with the empirical linear model, the GOME-2 SIF models demonstrate a substantial overall improvement in estimation accuracy, with performance varying across vegetation types. SHR show the most dramatic improvement, with R ^*2* increasing from 0.096 in the linear model to 0.593 in the SVR-based model (an absolute gain of approximately 0.497). EBF exhibit significant improvements as well, with an average increase of 54.55% (or alternatively, R ^*2* rising from 0.458 to 0.715). SAV follow closely, with R ^*2* increasing from 0.287 to 0.468 (an absolute gain of approximately 0.181). Moderate gains are observed in WET and CRO, with average improvements of 17.96% and 13.72%, respectively.

The model fitting results based on TCSIF are presented to analyze the impact of TCSIF data (Figure 7). Compared with the empirical linear model, TCSIF-based models generally yield improved estimation accuracy across most vegetation types and indices. The only exception is the ENF × NDVI combination, where a slight accuracy decrease of 0.47% is observed. In all other cases, accuracy improves to varying extents. SHR exhibits the greatest gains, with R ^*2* increasing from 0.133 in the linear model to 0.545 in the SVR-based model (an absolute gain of approximately 0.412). EBF follows with an average improvement of 72.26% (or alternatively, R ^*2* rising from 0.406 to 0.739). WET shows moderate improvement, with an average increase of 20.91%, led by the NDVI × NIRv combination (30.66%). ENF shows the smallest improvement, with an average gain of just 1.22%, among which EVI performs best (2.87%).

In summary, compared to the empirical linear model, the LUE model constructed using different SIF products and vegetation indices demonstrates significant accuracy improvements across various vegetation types. TCSIF, exhibiting the strongest adaptability, achieves the most pronounced accuracy gains, with only a minimal accuracy loss of 0.47% observed in the NDVI × ENF combination. GOME-2 SIF also performs well, with minor average R ^*2* reductions of 0.0248 and 0.0037 observed in ENF and DBF, respectively. While GOSIF provides relatively limited overall accuracy enhancement, it achieves notable improvements of 8.47% in SHR and 5.00% in EBF. Importantly, for each vegetation type, at least one vegetation index yields better fitting performance than the empirical linear model. This is primarily because GOSIF more directly captures the co-variability between GPP and SIF, resulting in relatively effective simple empirical models. In contrast, TCSIF may lose some true signal due to sensor time degradation correction, which affects its correlation with GPP_EC.

Furthermore, comparisons among different vegetation indices applied to the same SIF product indicate that optimizing vegetation index combinations specific to the SIF type can enhance GPP estimation accuracy across ecosystems. The combinations of GOSIF with NDVI, and both GOME-2 SIF and TCSIF with NDVI × NIRv, yield the greatest overall accuracy improvements. This can be mainly attributed to NDVI’s superior sensitivity to leaf area index (LAI) compared to EVI and MSAVI. Since NIRv inherently contains NDVI information and has been demonstrated to disentangle confounding factors such as soil background brightness, LAI, and the vertical distribution of photosynthetic capacity within the canopy, the combined index NDVI × NIRv effectively leverages the advantages of both components. Consequently, it provides a more robust representation of vegetation photosynthetic activity.

4.2.3 Interannual variations of estimates from the three optimal combinations at a single site

Figures 8–10 present the models developed using the GOSIF-NDVI, GOME-2 SIF-NDVI × NIRv, and TCSIF-NDVI × NIRv combinations, respectively. These models estimate GPP at the site with the largest sample size within each vegetation type and compare the seasonal variation curves of estimated GPP with measured GPP_EC. The results show that all three models effectively capture the interannual variation characteristics of GPP at individual sites across different vegetation types. Among them, the DBF site FR-Fon demonstrates the best performance, with the estimated GPP temporal variation curve closely matching that of GPP_EC. For other vegetation-type sites, the estimated GPP generally aligns well with the temporal pattern of GPP_EC, although some overestimation or underestimation occurs at seasonal peaks and troughs. The SHR site US-SRC exhibits the largest discrepancies in this regard.

4.3 Validation and pattern analysis of model-estimated northern hemisphere GPP

This study evaluated the applicability of three SIF–vegetation index models—GOSIF-NDVI, GOME-2 SIF–NDVI × NIRv, and TCSIF–NDVI × NIRv—across Northern Hemisphere terrestrial ecosystems. Monthly SIF, sPRI, multiple vegetation indices, and annual land cover products from 2007 to 2014 were input into the vegetation-type-specific GPP models to generate monthly GPP datasets for this period. Missing values in the model outputs are interpolated using the mean of adjacent months. In addition, 2000 random sampling points are generated across the Northern Hemisphere’s land areas using the ArcGIS tool, and the corresponding monthly GPP estimates at these points are extracted to assess the spatiotemporal accuracy of each model.

4.3.1 Spatial distribution of model-estimated northern hemisphere GPP

The monthly GPP datasets from 2007 to 2014, estimated using three combinations—GOSIF with NDVI, GOME-2 SIF with NDVI × NIRv, and TCSIF with NDVI × NIRv—along with the processed GLASS-GPP and MODIS-GPP product datasets for the same period, are first aggregated on a monthly basis to obtain annual total GPP. The average over 2007–2014 is then calculated to produce the corresponding annual mean GPP datasets (Figure 11).

The spatial distribution of annual mean GPP estimated by the three optimal SIF-VI models is generally consistent with that of the GLASS-GPP and MODIS-GPP products, showing a clear latitudinal gradient of decreasing values from the equator to the Arctic, though with significant spatial heterogeneity. High-GPP regions in the Northern Hemisphere (>2000 g C·m^-2·a⁻¹) are primarily located in tropical rainforest zones near the equator—such as the Congo Basin in Africa, the Amazon Basin in South America, and the Indochina Peninsula and Malay Archipelago in Southeast Asia—collectively accounting for less than 10% of the land area. These areas are characterized by consistently high temperatures and abundant rainfall throughout the year, which fully meet the thermal and moisture requirements for vigorous vegetation photosynthesis. Medium-GPP regions (1000–2000g C·m^-2·a⁻¹) mainly include South and Southeast Asia influenced by monsoon climates, the southeastern coastal regions of North America, most of Europe under Mediterranean or temperate maritime climates, and certain green belts in Central Asia formed by rivers and other water sources. These regions, covering about 20% of the Northern Hemisphere’s land area, feature relatively flat terrain, favorable climate conditions, and relatively abundant water resources—factors conducive to vegetation growth and agricultural productivity. Low-GPP regions (<1000 g C·m^-2·a⁻¹) are predominantly found in high-latitude cold zones or arid inland areas with scarce precipitation, such as Arctic territories, interior regions of North America and Eurasia, and desert areas across the Arabian Peninsula and Central Asia. These areas, accounting for over 70% of the Northern Hemisphere’s land area, are characterized by extreme cold or heat, extensive ice, snow, or desert coverage, low precipitation, arid climates, and sparse surface vegetation.

The proportions of land area corresponding to high and low annual mean GPP estimated by each model and product are shown in Figure 12. As illustrated, compared with GLASS-GPP and MODIS-GPP models, the GOSIF-NDVI estimates a larger proportion of high-GPP areas (>2000 g C·m^-2·a⁻¹) and a smaller proportion of low-GPP areas (<1000 g C·m^-2·a⁻¹). In comparison, the GPP estimated by the other two SIF–VI models lie between those of MODIS-GPP and GLASS-GPP.

To further validate the reliability of the GPP estimates across the Northern Hemisphere derived from the models in this study, the annual mean GPP model from each model is compared with two existing GPP products (Figure 13). This figure presents the spatial distribution of differences between the model-derived annual mean GPP and the GPP products. Positive values indicate that GPP models exceeds the GPP product, while negative values indicate the opposite.

GPP-GOSIF aligns well with GPP-GLASS and GPP-MODIS in medium-value GPP regions, but shows higher values in high-GPP areas and lower values in low-GPP areas. GPP-GOME-2SIF corresponds well with GPP-GLASS and GPP-MODIS in low-GPP inland arid zones, but overestimates in high-GPP areas and underestimates in cold high-latitude low-GPP regions and medium-GPP zones. In contrast, GPP-TCSIF matches GPP-GLASS and GPP-MODIS in cold high-latitude low-GPP regions, but underestimates in high-GPP areas and overestimates in inland arid low-GPP zones.

Overall, among the models evaluated in this study, the combination of GOSIF with NDVI combination is better suited for estimating GPP in regions with high annual mean values; GOME-2 SIF and NDVI × NIRv performs more accurately in inland arid regions with low GPP; and TCSIF is more appropriate for cold, high-latitude regions with low annual mean GPP.

4.3.2 Temporal patterns of model-estimated GPP in the northern hemisphere

Using ARCGIS, 2,000 random sample points are generated across the Northern Hemisphere land area. Monthly GPP data from 2007 to 2014 are extracted at these locations from three models, GOSIF-NDVI, GOME-2 SIF-NDVI × NIRv, and TCSIF-NDVI × NIRv—as well as from post-processed GPP products, GPP-GLASS and GPP-MODIS, specifically MOD17A2H. For each model and product, annual total GPP and monthly mean GPP are calculated.

The interannual variability of annual total GPP (2007–2014) is presented in Figure 14, comparing estimates from the three SIF-VI models with the GPP-GLASS and GPP-MODIS products. Among them, GPP-GOME-2SIF displays a distinct three-phase fluctuation: a decline from 2007 to 2009, a rise from 2009 to 2011, and a subsequent decline from 2011 to 2014. In contrast, the other models and products show a consistent trend—reaching their lowest GPP in 2008, followed by a steady increase, culminating in peak values in 2014. The interannual trend of GPP-GOSIF closely resembles that of GPP-GLASS, while GPP-TCSIF aligns more closely with GPP-MODIS. Quantitatively, GPP-GOSIF maintains a consistently higher annual total than both GPP-GOME-2SIF and GPP-TCSIF across the entire period. Between 2007 and 2011, GPP-GOME-2SIF slightly exceeds GPP-TCSIF, but from 2012 to 2014, GPP-TCSIF overtakes it significantly.

Collectively, excluding GPP-GOME-2SIF, the annual total GPP across the Northern Hemisphere estimated by other models and products shows a consistent pattern: reaching a minimum in 2008, followed by a steady increase that peaks in 2014. This trend suggests a general improvement in vegetation conditions across Northern Hemisphere terrestrial ecosystems. In contrast, GPP-GOME-2SIF exhibits a distinct three-phase fluctuation, which is likely attributable to the degradation of the GOME-2A sensor.

A comparison of the monthly mean GPP (2007–2014) derived from the three SIF-VI-based models, GPP-GLASS, and GPP-MODIS is provided in Figure 15. All datasets exhibit a typical unimodal seasonal pattern, with minimum values occurring in January. Except for GPP-GOSIF, which peaks in August, all other models and products reach their maximum in July. This consistency in seasonal dynamics reflects strong agreement between the SIF-VI models and mainstream GPP products. In terms of magnitude, the monthly mean GPP values generally follow this order, GPP-GOISF > GPP-GLASS > GPP-GOME-2SIF > GPP-TCSIF > GPP-MODIS.

Additionally, in this study, the monthly GPP estimated by the three SIF-VI models from 2007 to 2014 is compiled into corresponding monthly mean datasets. According to standard climatic seasonal divisions (March-May as spring, June-August as summer, September-November as autumn, and December-February as winter), seasonal GPP values are derived by summing the respective monthly means. Panel A illustrates seasonal GPP from the GOSIF-NDVI model, Panel B from the GOME-2 SIF-NDVI × NIRv model and Panel C from the TCSIF-NDVI × NIRv model (Figure 16).

The results reveal clear seasonal patterns across all models. From winter to spring to summer, GPP increases progressively from south to north and east to west; from summer to autumn to winter, this trend reverses, decreasing from north to south and west to east. summer exhibits the highest GPP, coinciding with peak vegetation growth and photosynthetic activity in the Northern Hemisphere. spring follows, marked by vegetation revival and rapid development. GPP is lower in autumn and winter, as vegetation in temperate and northern regions enters dormancy due to leaf fall or snow and ice cover. Overall, the GPP estimated by the three SIF-VI models effectively captures seasonal dynamics in the Northern Hemisphere and aligns well with climate-driven vegetation phenology.

5 Discussion

Before discussing the limitations, it is worth examining why TCSIF exhibits the lowest correlation with GPP_EC among the three SIF products (mean R ^*2* = 0.42). One contributing factor lies in the TROPOMI SIF retrieval algorithm. As documented in the TROPOSIF dataset specification, the baseline retrieval uses a 743–758 nm fitting window, which avoids atmospheric absorption lines and is therefore more stable under varying atmospheric conditions, but it comes with larger random errors. The alternative 735–758 nm window reduces random errors by including more spectral channels, yet becomes more easily disturbed by water vapor and clouds (Guanter et al., 2021). This trade-off between stability and precision in the TROPOMI retrieval introduces uncertainties in TCSIF, which may partially explain why it performs worse than GOME-2 and GOSIF.

Several critical limitations of the SIF-based GPP estimation models warrant further investigation. First, the model assumes that LUEF(λ) remains constant under non-stressed and non-light-limited conditions. While this assumption simplifies model structure, it restricts applicability to healthy and undisturbed vegetation and fails to represent photosynthetic downregulation under stressors such as high vapor pressure deficit (VPD), soil drought, leaf temperature rise, or enhanced non-photochemical quenching (NPQ). Empirical evidence has shown that SIF often remains relatively stable under drought conditions, whereas GPP can decline substantially, indicating a decoupling of the SIF–GPP relationship under stress (Pan et al., 2025). In addition, differences in the responses of SIF and GPP to radiation and canopy geometry further complicate the retrieval of LUE from SIF signals (Doughty et al., 2022). Incorporating stress-related parameters is therefore essential to improve model generalizability in future research.

Second, the FLUXNET2015 dataset used for model calibration exhibits uneven spatial distribution, with monitoring sites concentrated primarily in Western Europe, Eastern Asia, and Central North America (Middleton et al., 2012; Barton and North, 2001; Drolet et al., 2005). A related limitation is that our validation is constrained by the availability of flux tower sites. The 2,000 sampling points are not arbitrary but reflect the existing FLUXNET2015 observations. While more data would improve model confidence, we are limited by the current network. This should be considered when interpreting the validation results. Crucially, vegetation types such as SAV, SHR, and EBF are significantly underrepresented, each accounting for less than 5% of the total sites. ENF (24 sites) and GRA (23 sites) are well-represented, whereas SAV (2 sites), EBF (4 sites), SHR (5 sites), and MF (6 sites) have relatively fewer sites. This imbalance in sample size may bias the performance metrics: vegetation types with fewer sites are more sensitive to outlier influences and may yield less reliable R ^*2* estimates. Therefore, the superior performance observed for certain vegetation types should be interpreted with caution (Alton, 2020). This limited biome representation introduces substantial uncertainty when extrapolating model results to diverse vegetation types across the Northern Hemisphere (van der Tol et al., 2016). Future research should therefore prioritize the inclusion of data from under-sampled ecosystems and adopt domain-adaptive or hierarchical Bayesian approaches to enhance model robustness in poorly constrained vegetation types (Xu et al., 2023).

Finally, a critical limitation lies in the spatial scale mismatch between tower-based flux measurements and satellite SIF products. Flux towers typically cover source areas of 1–10 km, whereas GOME-2 SIF and TROPOMI/TCSIF operate at coarser 0.5°or larger resolutions (Qiu et al., 2020). Directly matching these mixed-pixel satellite signals with point-based flux tower observations—while ignoring subpixel vegetation heterogeneity—can significantly compromise model accuracy. Recent high-resolution missions such as OCO-2/3 provide finer-scale SIF retrievals (∼1.6 × 2.2 km) and, in the case of OCO-3, Snapshot Area Mapping (SAM) mode enables dense regional coverage aligned with flux tower footprints (Eldering et al., 2019). Leveraging these higher-resolution datasets, combined with flux footprint modeling and downscaling methods using auxiliary reflectance, could reduce uncertainties and enhance the consistency of tower–satellite comparisons.

The proposed model shows a larger improvement in SHR than a linear SIF–GPP relationship, mainly because the model accounts for both canopy structure and physiological stress, two factors that strongly affect SHR but are ignored by linear models. Structural corrections using vegetation indices help capture non-linear escape fraction effects (Rangel Pinagé et al., 2022), while PRI captures stress-induced changes in light use efficiency (Hall et al., 2012). Based on the limitations above, future studies should prioritize expanding flux tower networks, incorporating stress-related parameters, and leveraging high-resolution SIF missions.

6 Conclusion

In this study, the LUE models are developed to estimate GPP across Northern Hemisphere terrestrial ecosystems using various SIF products and vegetation indices. SVM are employed to fit nonlinear relationships, and the performance of different SIF-VI combinations is systematically evaluated. The results have revealed that all three SIF products—GOSIF, GOME-2 SIF, and TCSIF—exhibit significant linear correlations with flux tower-measured GPP, with GOSIF demonstrating the best overall performance. Particularly strong correlations are observed in MF, DBF, and GRA. Training models by vegetation type significantly improvs estimation accuracy, with gains ranging from 8.55% to 14.43%. Among the combinations, TCSIF with NDVI × NIRv shows the highest compatibility and best captured the interannual variability of GPP across vegetation types. In terms of spatial patterns, GPP estimates from all three SIF-VI combinations align well with those from MODIS-GPP and GLASS-GPP products, showing a clear latitudinal gradient—decreasing from the equator to the Arctic. High GPP estimates are found in tropical rainforests, intermediate values in monsoon-affected regions, and low values in cold high-latitude areas. As for temporal dynamics, all models except for GOME-2 SIF indicate a sustained increase in Northern Hemisphere GPP after 2008. Monthly GPP estimates exhibit a unimodal seasonal pattern, with the lowest estimates in January and peaks in July-August. The overall magnitude of GPP estimates follows this order, GPP-GOSIF > GPP-GLASS > GPP-GOME-2 SIF > GPP-TCSIF > GPP-MODIS, highlighting distinct seasonal variation. These findings suggest that SIF-based LUE models offer an effective means for estimating the spatial and temporal dynamics of GPP, providing a promising technical approach for advancing carbon cycle research in terrestrial ecosystems.

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Footnotes

Edited by: Xing Li, Seoul National University, Republic of Korea

Reviewed by: Jingyu Lin, Sun Yat-sen University, China

Enjun Gong, Northwest University, China