The evaluation of the GPP models was performed using in situ observations from eddy covariance stations. Test sites were selected from the FLUXNET2015 dataset and the ICOS “2018 drought initiative” dataset . It was ensured that the sites had a homogeneous land cover, which could be captured by the remote sensing products. A site was considered homogeneous when in 1 km × 1 km area surrounding the station location was dominated by a unique vegetation type (i.e. grassland, deciduous forest, evergreen forest). The site homogeneity was visually evaluated using high-resolution satellite images in Google Earth. Additionally, the sites were required to have a minimum of 3 years of GPP data since 1 January 2007 (i.e. the start of the SIF time series). This resulted in a selection of 61 sites, listed in Table . The dataset contained 461 years worth of GPP data, in which evergreen needleleaf forest (ENF) and the mid-latitude temperature-driven hydro-climatic biome (MidL_T; ) were dominantly represented.

All data were pre-processed with the ONEFLUX pipeline . The observed net ecosystem exchange was partitioned into the ecosystem respiration and GPP components using the daytime fluxes and a constant friction velocity threshold across years (labelled as GPP_DT_CUT in the database). Depending on site data quality, the reference GPP (GPP_DT_CUT_REF) or mean GPP (GPP_DT_CUT_MEAN) method was selected.

Daily data with a quality flag indicating poor gap filling (QF < 0.1) were discarded in the analysis. It was ensured that the same time periods were considered for all models at each site.

The test sites were classified per plant functional type (PFT; taken from the FLUXNET/ICOS International Geosphere–Biosphere Programme (IGBP) metadata) and hydro-climatic biome (HCB; ); see Table . The distribution of the sites across PFT and HCB is shown in Tables S1 and S2 in the Supplement). Seven PFT-HCB classes were selected for extra detailed analysis, given their importance and/or data quantity: evergreen broadleaf forest in tropical biome (EBF-Tropic), deciduous broadleaf forest in mid-latitude temperature-driven biome (DBF-MidL_T), evergreen needleleaf forest in boreal water–temperature-driven biome (ENF-Bor_WT), evergreen needleleaf forest in mid-latitude temperature-driven biome (ENF-MidL_T), evergreen needleleaf forest in transitional energy-driven biome (ENF-Trans_E), savanna in transitional energy-driven biome (SAV-Trans_E) and croplands in mid-latitude temperature-driven biome (CRO-MidL_T).

Incoming short-wave radiation, long-wave radiation and precipitation data, required by the meteo-driven and hybrid GPP models, were taken from the half-hourly tower observations. Due to large gaps in the atmospheric humidity time series, ERA5 was used as an alternative source for air temperature, atmospheric humidity, wind speed and atmospheric pressure . It was verified that the impact of the use of ERA5 instead of local observations was limited for these variables (Fig. S2 and Tables S3 and S4 in the Supplement). The forcing from ERA5 (hourly resolution) was linearly interpolated to match the 30 min temporal resolution from the tower observations. The atmospheric CO2 concentration was taken from the TRENDY time series (; https://sites.exeter.ac.uk/trendy, last access: 12 May 2023).

The simplest models considered were the linear regressions based on remotely sensed proxies of GPP, including VI and SIF. Remote sensing data were gathered from SPOT Vegetation+PROBA-V (SPV) for each tower location (the nearest pixel). This data product has a 10 d interval and 1 km resolution. The SPV decadal synthesis product is derived using the “maximum value composite” procedure after quality check of SPV native data and gives the best reflectance value on the 10 d time interval. Though daily data are available, they were not used here. The use of daily data would introduce gaps and noise in the SPV time series (in case of cloudy conditions at satellite overpass time, for instance) while not adding significant information on the vegetation status throughout the study period.

Derived from the SPV data, the normalized difference vegetation index (NDVI), the enhanced vegetation index (EVI) and near-infrared of vegetation (NIRv) are given below, according to , and : 1NDVI=R770-800-R630-670R770-800+R630-670,2EVI=2.5R770-800-R630-670R770-800+6⋅R630-670+7.5⋅R460-475+1,3NIRv=NDVI⋅R770-800, where R is the reflectance between the wavelengths in the subscript (in nm). Wavelength range 770–800 nm was used for the NIR reflectance, 630–670 nm was used for red reflectance, and 460–475 nm was used for blue band reflectance.

Additionally, the canopy structure-related near-infrared reflectance of vegetation multiplied by incoming sunlight (NIRvP) was included . It was calculated as follows: 4NIRvP=NIRv⋅PAR, where PAR is the daily mean photosynthetically active radiation, calculated as a constant fraction (0.45) of the in situ incoming short-wave radiation observations . For remotely sensed SIF data, we relied on the downscaled GOME-2 SIF product by (8 d interval, 0.05∘ resolution), given the coarse spatial resolution of the GOME-2 SIF product (> 40 km), sparse global coverage (only a dozen of GOME-2 observations for all tower locations were available per year) and the limited available time series of TROPOMI (starting in May 2018). The downscaling procedure involves a LUE methodology, involving NIRv, normalized difference water index (NDWI; ) and land surface temperature (LST) data from MODIS. demonstrated that this product has a high spatio-temporal agreement with TROPOMI SIF observations, so the impact of the artefacts due to the downscaling procedure are assumed to be limited.

A range of models to estimate GPP was selected, representing RS-driven, meteo-driven and hybrid approaches. An overview is given in Table .

To evaluate the performance of the models to capture the temporal variability, the time series in the dataset were decomposed in two ways: (1) by separating the inter-site variability, seasonal variability, and variability of seasonal anomalies and (2) by separating daily, weekly, monthly, seasonal, and interannual components with singular spectral analysis (SSA).

The performance at these timescales was evaluated by comparing the simulated variability (quantified by the standard deviation, σ) in observations and simulations and by computing the Pearson correlation (r). Additionally, the covariance (cov) between GPP and its driver variables was used to assess the sensitivity of GPP to these variables. It was evaluated whether the models reproduce the observed patterns.

Finally, the accuracy of the simulated carbon phenology was evaluated by comparing the timing of the simulated seasonal GPP cycle with observations. Details on the methodology are given below.

A comparison of the variability of GPP in observations and simulations is given in Table . The overall observed variability of σ = 4.18 gCm-2d-1 was underestimated in all models, except LSA SAF. After decomposing the observed GPP dataset, the inter-site variance represented 18 % of the total variance, the seasonal cycles represented 62 % and the anomalies represented 24 % (the sum of these fractions is larger than 100 % due to covariances; see Tables S8 and S9). This partitioning was not well represented in the NDVI, EVI or NIRv time series, where a large fraction of the variance (> 30 %) was attributed to the inter-site component and a very small fraction (< 12 %) to the anomalies. In the NDVI observations, the inter-site variance was even larger than the seasonal variance. In SIF, the contribution of the spatial and seasonal components was reasonably accurate, but the relative variance of the anomalies was too low (10 %). The relative variance of the seasonal pattern was strongly overestimated in the FluxCom products (∼ 80 %), whereas the contribution of the anomalies was the lowest of all datasets (∼ 5 %). The closest match with the observed variance partitioning was found in NIRvP, MOD17, LSA SAF and the DGVMs. To ensure that these results were not affected by the temporal resolution of the time series, the same analysis was performed after downsampling to a 10 d interval. This did not result in substantial changes in the variability or its partitioning (Table S6).

Depending on the land cover type, the variability and its partitioning between different components varied (Table ). As expected, limited seasonal variability was observed in the EBF-Tropic sites (σseason = 0.68 gCm-2d-1) compared to DBF-MidL_T sites (σseason = 5.11 gCm-2d-1). Still, the variability of the anomalies of the tropical sites was comparable to that in other sites (σanom≈ 2.00 gCm-2d-1). The CRO-MidL_T sites had the largest variability in the anomalies (σanom = 3.43 gCm-2d-1).

The Taylor diagram of the modelled GPP and its seasonal anomalies is shown in Fig. . In terms of correlation, the DGVMs, LSA SAF and the FluxCom products achieved a distinctly better performance (r>0.83, median for all sites) compared to the linear-regression-based models (and MOD17). The NDVI-based model had the weakest correlation with observations (r=0.57, median for all sites). The correlation of the simulated GPP was substantially reduced after subtracting the mean seasonal cycle. For NDVI, EVI, NIRv and SIF, ranom was smaller than 0.2 (median for all sites). LSA SAF and ISBA were the only models with ranom>0.5 (median for all sites). The performance of FluxCom to estimate the anomalies was similar to the NDVI-, EVI- and NIRv-based models. Though FluxComRSMet achieved ranom=0.43 (median for all sites), the variability of the anomalies was strongly underestimated.

A notable difference emerged in the anomalies simulated with NIRvP and SIF. While both datasets showed a similar performance in the full GPP time series, SIF performed much poorer than NIRvP in the anomalies.

The RS-driven models, which relied purely on RS observation of the vegetation state, had a significantly lower σanom (Wilcoxon p<0.05) compared to the models that used meteorological forcing. This difference in performance was most pronounced in the forest sites (Fig. ). In sites dominated by (water-limited) herbaceous vegetation, this was less the case; GPP estimations based on simple greenness sensitive NDVI-, EVI- and NIRv-based models often even outperformed DGVMs.

The variability of the time series after SSA decomposition is given in Table . In agreement with the variability of the seasonal GPP and its anomalies, the largest variability was explained by the annual timescale (77 %, median for all sites). At daily, weekly and monthly timescales, the relative variance was roughly 10-fold smaller. The least variability was found for the interannual timescale (1 %, median for all sites). More detailed results per land cover type are given in Table S6. Most land covers followed the same pattern, with the exception of the EBF-Tropic sites, where seasonal variance was smaller than the variance at daily, weekly, monthly or even annual timescales.

The RS-driven models underestimated the variance at all timescales, especially at the annual scale. Furthermore, very limited variability was found at the interannual scale, and the relative variance at monthly scale was overestimated in these models. NDVI was the least suitable proxy to capture this variability, whereas the relative variance partitioning in SIF approximated most closely the observations. Notably, the inclusion of PAR in NIRvP improved the GPP variability but degraded the variance partitioning across timescales.

The FluxCom products contained a too strong annual signal and underestimated variability at other scales. The incorporation of daily meteorological forcing in FluxComRSMet added variability at the daily timescale but reduced variability at weekly and monthly timescales. The annual variability was approximated relatively well, but the variability at shorter timescales was roughly 3-fold too small.

The variability across all timescales was best represented by the meteo-driven DGVMs (Table ). There were minor differences between ORCHIDEE and ISBA, as the variance at daily and weekly timescales was slightly more accurate in ISBA, and the variance at monthly and annual timescales was more accurate in ORCHIDEE. This trend was confirmed in most land covers (see Table S6). LSA SAF also estimated the variability reasonably accurately but overestimated the daily variability.

The correlation of the simulations at these timescales is given in Fig. . Note that the strength of the signal at interannual scale was relatively low (in observed and simulated GPP). Evaluating the correlation of this component should thus be done with caution, as the SSA itself can induce errors of comparable magnitude . It is shown here but not discussed in detail.

Most models had a good correlation with GPP at the annual timescale (r>0.80, median for all sites), except the NDVI-based model. At monthly the timescale, the correlation dropped to r≈0.25 for all models (median for all sites). At weekly timescale, the models that relied solely on remote sensing observations were very poorly correlated to the observed GPP. Compared to these models, the models that included meteorological data achieved a significantly higher correlation (Wilcoxon p<0.05). At daily scale, r increased again. LSA SAF and ISBA achieved r>0.65 (median for all sites) at this spectral range.

Separating the results by PFT (Fig. ) shows that the correlation at monthly and seasonal timescales was generally larger for DBF sites compared to ENF sites. At seasonal scale, this was most pronounced for the greenness-sensitive VI proxies (NDVI, EVI and NIRv).

Dryland sites, such as the SAV sites, generally showed a higher correlation at the interannual scale for the RS-driven models. Not all models manage to capture these interannual patterns. For example, ORCHIDEE obtained only a very low correlation at this scale. Regardless, the interannual scale had only a minor contribution to the total variability.

In the CRO sites, the RS-driven models had a significantly lower r at weekly timescale compared to the DGVMs (Wilcoxon p<0.05, with the exception of NIRv vs. ORCHIDEE and MOD17 vs. ORCHIDEE). However, at the monthly timescale, the RS-driven models had a higher r than the DGVMs (significantly for SIF, FluxComRS and MOD17), and at the annual scale this trend persisted (significantly for EVI, NIRv, FluxComRSMet and MOD17).

Given the different performances across timescales, the covariance between the GPP and its key drivers (SWrad, TA, VPD and SWC) was evaluated. The observed and simulated covariances are shown in Fig. . These are the median covariances for all sites. The covariance is impacted by the variance of the GPP estimates, as opposed to the Pearson correlation. For completeness, the latter is computed as well and is given in Fig. S5.

In the observations, all drivers had the highest covariance with GPP at the seasonal scale. SWrad and VPD had a stronger covariance at daily scale compared to weekly and monthly timescales, whereas TA had a slightly stronger covariance at weekly timescale. The covariance between SWC and GPP was negative, indicating that GPP was smaller during wet root-zone soil moisture anomalies (and higher during dry anomalies). This was largely attributed to the negative covariance between SWC and the other drivers, as wet conditions are associated with periods of rain and cloudy weather (Fig. S4). The covariance between GPP and SWC was similar at daily, weekly and monthly timescales. For all drivers and GPP, the interannual signal was very weak, resulting in a negligibly small covariance.

Substantial differences in the observed correlations were found between different biomes, as highlighted in the plots of the weekly, monthly and annual covariance (Fig. ). For example, the covariance between SWrad and GPP at the annual scale was very strong for most biomes, but it was very weak for EBF-Tropic (due to a small variability of the GPP signal at this scale) and SAV-Trans_E sites (due to downregulation of photosynthesis by other constraining factors). Another clear trend was the shift in covariance between SWC and GPP from negative in biomes where water is not a constraining factor (e.g. DBF-MidL_T) to water-limited biomes (e.g. SAV-Trans_E).

The accuracy of the models to reproduce these patterns was quantified by RMSE (see Tables S10 and S11 for detailed results). The RS-driven models generally had a very low sensitivity to all drivers at weekly and monthly timescales. The covariances at annual scale were underestimated as well. This can be attributed partly to the lower variance of the RS-driven GPP estimates at annual scale, but the Pearson r also indicated a too low sensitivity (Fig. S6). Conversely, the sensitivity of the meteo-driven models was generally more accurate. Some oversensitivity to the meteorological drivers was found in ISBA, whereas ORCHIDEE was generally among the most accurate models. The covariance with soil moisture was more accurate in ISBA than ORCHIDEE (e.g. RMSE at weekly, monthly and annual scales 10 %–30 % more accurate)

The performance of the hybrid models was highly variable. LSA SAF was generally too sensitive to meteorological drivers, whereas MOD17 (also a LUE model) was too insensitive to all drivers (though more sensitive than the RS-driven models). The covariance of GPP with its drivers was generally most accurate in the FluxCom products. Their largest shortcoming was a too low sensitivity to SWrad at daily and weekly timescales.

The dynamics in temperate DBF forest sites were reproduced fairy well by most models. The strong annual covariances were represented well by all models. Even the RS-driven models had a relatively high covariance at this scale. At annual scale, the DGVMs and LSA SAF were most accurate in this biome (RMSE 3- to 4-fold lower than RS-driven models). In contrast, the high annual covariance was not represented well by the NDVI-, EVI- and NIRv-based models in the ENF sites. The covariance between GPP and the drivers at annual scale was generally too weak. FluxCom and the DGVMs were more accurate (RMSE 4- to 5-fold lower than in VI-based models).

VPD and SWC were strong drivers for annual variability in the savanna sites. This was reproduced accurately by the RS-driven models and ISBA. NIRvP, FluxComRSMet and ORCHIDEE did not capture the annual covariance with VPD and SWC (RMSE for SWC and VPD 2- to 3-fold higher than ISBA, i.e. the most accurate model).

In the EBF-Tropic biome, all models had a too strong relation with the drivers at annual scale. A resemblance with the observed annual relations was found only in the FluxComRSMet product. It was the only model with an accurate positive GPP-SWC annual covariance for the EBF-Tropic sites.

The results for the FluxCom products highlight the importance of incorporating meteorological forcings in the GPP product. FluxComRSMet was superior to FluxComRS in the reproduction of GPP at different timescales. The coarser spatial resolution of FluxComRSMet did not have a negative impact on the performance in this study.

This analysis gives a coarse estimate of the (linear) sensitivity of the simulated GPP to the drivers impacting GPP. Note that many effects were not accounted for, including compound effects, legacy effects or the impact of other constraining variables (e.g. LAI in the DGVMs).

The accuracy of the simulated timing of the seasonal GPP cycle (start, max and end of season) is plotted in Fig.  (RMSE scores are calculated for every site individually). Generally, the simulations of SOS and EOS were generally less accurate in the RS-driven models (RMSE SOS ≈ 30–38 d, EOS ≈ 25–50 d; except FluxComRS) compared to the meteo-driven models (RMSE SOS ≈ 24–28 d, EOS ≈ 17–21 d). The phenology in the NDVI-based model was the least accurate, which was largely attributed to a bias in the timing, especially in the EOS (≈ 50 d delayed; see Fig. S7). This bias was also observed in EVI and NIRv but was smaller (≈ 10 d delayed). Notably, the most accurate simulations of SOS and EOS were obtained with FluxComRS, which purely relied on remote sensing observations.

To highlight differences between biomes, the mean annual cycle of DBF-MidL_T, ENF-MidL_T and SAV-Trans_E is plotted in Fig.  (the annual cycle of the other biomes can be found in Figs. S8 and S9). The DBF-MidL_T had a very distinct SOS around the fifth month of the year. The interannual variability of the observed GPP cycle was limited compared to other biomes. Most models reproduced the phenology fairly accurately. In the NDVI time series, an evident illustration of the so-called “saturation effect” was observed, as the simulated GPP reached a plateau during mid-summer.

In the ENF-MidL_T biome, the coupling between canopy greenness and GPP was less strong than in DBF-MidL_T. Consequently, the meteo-driven and hybrid models were generally more accurate to simulate the timing of the GPP cycle in this biome (RMSE SOS ≈ 10–18 d, EOS ≈ 10–18 d; see also Fig. ) than the RS-driven models (RMSE SOS ≈ 35–50 d, EOS ≈ 22–50 d). Also note the delayed MOS in the ISBA simulations for this biome. This was largely associated with the delay in the prognostic LAI seasonal cycle .

A strong variability of the annual GPP cycle was observed in the SAV-Trans_E biome (Fig. ), making it very challenging to capture the timing of the GPP cycle accurately (Fig. ). However, in these sites, a stronger coupling existed between GPP and the canopy greenness. At the SOS, a distinct difference between the RS-driven models and the meteo-driven models emerged. The RS-driven models were more accurate (RMSE SOS ≈ 20–30 d for NDVI, EVI and NIRv) compared to the DGVMs (RMSE SOS ≈ 46–82 d). In this biome, the inclusion of PAR in NIRvP resulted in a less accurate phenology compared to NIRv. In NIRv, the reduced photosynthesis due to water-limiting conditions in the second half of the growing season was evident, whereas GPP remained high in NIRvP.

Depending on the biome, the vegetation state is tightly coupled (e.g. in water-limited herbaceous sites), more loosely coupled (e.g. deciduous broadleaf forests) or completely decoupled (e.g. tropical evergreen broadleaf forests) to GPP . Vegetation indices, such as NDVI, EVI and NIRv are effective proxies to track the vegetation state via remote sensing. They have proven to be an effective, low-cost proxy for GPP in biomes with an evident coupling between canopy greenness and photosynthesis .

However, an important discrepancy was found between the RS observations and the observed GPP in the spatio-temporal partitioning of their variability. The inter-site variability of NDVI, EVI, NIRv and (to a lesser extent) SIF was substantially higher than that of the GPP observations. Furthermore, the variability of the anomalies in the models was relatively small (see Tab ). This high inter-site variability indicated that there was a need to use land-cover-dependent relations to estimate GPP from the remotely sensed vegetation proxies. Several studies have confirmed that PFT-specific relations considerably improved the GPP estimates from NDVI , EVI , NIRv and SIF . FluxComRS also relied on land cover data to estimate GPP from RS observations and captured the spatial and seasonal variability more accurately (see Table ). Results from explorative tests with PFT-specific regression models are shown in Figs. S10 and S11. They indicated that improved results were largely caused by improved spatial correlation. The variability of the seasonal signal and anomalies remained underestimated.

The biome-dependent relation between vegetation greenness and GPP was also evident in the seasonal cycle (Fig. ) and in the annual timescale (Fig. ). For DBF and CRO biomes, the coupling between VI and GPP resulted in high correlations at these timescales, whereas the decoupling in other biomes emerged. This was most pronounced in evergreen forest sites (ENF and EBF), and the decoupling increased as the climate was increasingly water-limited (ENF-Bor_WT < ENF-MidL_T < ENF-Trans_E; see Figs.  and ). Opposed to herbaceous sites in the same arid biomes (e.g. SAV-Trans_E), the photosynthesis downregulation in ENF sites was not translated into rapid changes in vegetation greenness.

As often reported, the decoupling of leaf phenology and carbon phenology was also poorly captured in the VI-based models. This was most pronounced in the senescent phase, where photosynthesis halts, due to decrease in SWrad and TA, before canopy greenness drops .

All VIs were insensitive to the decoupling of canopy greenness and photosynthesis at seasonal timescale, but NDVI performed significantly worse than EVI and NIRv in this respect. Saturation in dense canopies, background effects and atmospheric influences likely explain the underestimated variability of the seasonal cycle in NDVI time series, especially in forest biomes (illustrated in Fig. ). Between EVI and NIRv, no substantial differences in performance were found.

SIF is a more direct proxy for photosynthesis and is therefore expected to capture the decoupling between vegetation greenness and GPP more accurately than VIs . However, SIF did not perform significantly better than EVI or NIRv at the annual timescale (Figs.  and ). Exceptions were the arid biomes, ENF_Trans-E and SAV_Trans-E, where SIF outperformed EVI and NIRv. It remains unclear in what measure the downscaling processing is responsible for the moderate SIF scores. Future missions with high-resolution SIF, such as European Spatial Agency's Earth Explorer – FLEX (FLuorescence EXplorer, due to be launched in 2025), will provide further insights .

The results with the VI-based models seemed to indicate that the remotely sensed observations of the vegetation state were insufficient to describe GPP in evergreen vegetation. However, FluxComRS relied exclusively on these observations as predictors and managed to capture GPP patterns in ENF. Furthermore, it produced the most accurate results regarding the GPP phenology. This product illustrated that, in combination with land cover information and non-linear relations, accurate estimates of GPP at the seasonal timescale can be obtained from optical remote sensing .

Conversely, it is very challenging to accurately model the state of the vegetation without RS observations . In a detailed evaluation of the water, energy and carbon modelling in ISBA and ORCHIDEE, it was reported that the leaf phenology in ISBA and ORCHIDEE was delayed compared to observations and that it failed to capture the observed seasonal variability. reported that these errors were strongly correlated to errors in GPP. Despite these inaccuracies, the performance of the DGVMs was generally better than the VI-based models. The dominant impact of meteorological forcings and the decoupling of greenness and photosynthesis was captured accurately in the DGVMs.

Next to the complexity of plant physiology and biomass allocation; there can be a substantial impact of management practices (e.g. crop rotations, sowing and harvest in croplands; ). The lack of these practices in the configuration of the DGVMs in this study also resulted in a poorer performance of the monthly and annual-scale GPP in croplands (see Fig. ). Observations of these practices in remote sensing contribute to a better performance in croplands with RS-driven models. At a global scale, the lack of an adequate description of land management contributes considerably to uncertainties associated with the global carbon cycle in earth system models .

In summary, based on the observed vegetation state, a coarse estimate of the annual-scale GPP can be made. However, vegetation indices and linear regressions are insufficient to capture the decoupling of greenness and photosynthesis due to other confounding factors. Information on the hydrometeorological conditions is needed to capture this variability in all biomes, even at the seasonal scale.

Meteorological conditions are the main drivers of variability of GPP at sub-seasonal scale . At daily timescale, patterns were largely dominated by SWrad and VPD (see Fig. ). The impact of TA was more pronounced at weekly and monthly timescales (though still dominated by SWrad).

The RS-driven models had a very low performance to simulate these sub-seasonal patterns (Fig. ). They had a temporal resolution of 8–10 d, so the variability at daily timescale was absent. At weekly and monthly timescales, they had nearly no sensitivity to the driver variables (Fig. ). Consequently, the correlation of the anomalies was very weak in comparison to other models (Fig. ).

NIRvP was the most simplistic approach to incorporate SWrad (as PAR) as key driver for photosynthesis (Eq. ). Compared to NIRv (and SIF), NIRvP captured anomalies in GPP more accurately, in particular at the weekly timescale (Figs.  and ).

Alternatively, light-use efficiency models ingest more meteorological variables, such as VPD and TA, in addition to SWrad and vegetation state variables. Consequently, the quality of the simulated GPP strongly depended on the quality of the meteorological forcings. The MOD17 product relied on the coarse GMAO/NASA reanalysis dataset for the meteorological forcing and failed to achieve a better performance than the VI-based models (Fig. ). The LSA SAF GPP model, here forced by in situ SWrad observations, excelled in the simulation of temporal variability at all timescales and in all domains. Although there were other factors that impact the performance (e.g. the incorporation of soil moisture stress, which was absent in MOD17), the difference in SWrad forcings likely contributed substantially to the difference in performance, given the sensitivity of the models to SWrad and the quality of SWrad in reanalysis products .

The incorporation of meteorological forcings in FluxComRSMet improved the algorithm's ability to capture the anomalies compared to FluxComRS (Fig. ). This was most evident in forest sites (Fig. ), though the improvement was restricted to the weekly timescale (Fig. ). Still, despite the introduction of meteorological variables, the variance of the anomalies remained strongly underestimated (Table ).

In contrast, the meteo-driven DGVMs represented the variability of GPP accurately across timescales. A significant difference between ISBA and ORCHIDEE was found in the performance at daily timescale (Fig. ). The superior performance of ISBA at this timescale seemed to be originating from a more accurate sensitivity to SWrad than ORCHIDEE (Fig. ). Conversely, the sensitivity to atmospheric drivers at weekly and monthly timescales was more accurate in ORCHIDEE, whereas ISBA was generally oversensitive (Figs.  and ). Though the performance of ORCHIDEE to simulate GPP at these longer timescales was not superior (due to other confounding factors, e.g. soil moisture or LAI), ORCHIDEE is likely more accurate in assessing the impact larger meteorological anomalies, such as heat waves, on GPP. Further research addressing the performance of the models under extreme conditions is needed to confirm this.

At sub-seasonal scale, the RS-driven models demonstrated a big difference in performance between forest and herbaceous biomes. A substantially better performance was achieved in herbaceous sites (Fig. ), where the coupling between vegetation greenness and GPP is much tighter than in forest sites . The indirect observation of soil moisture stress in VIs allowed for accurate sub-seasonal-scale modelling of GPP in these strongly water-limited biomes . In other biomes, the combination with a drought indicator is required to simulate GPP in such conditions .

No downregulation due to soil moisture or temperature stress is considered explicitly in NIRvP. However, changes in light-use efficiency are partly reflected in changes in the canopy structure . Consequently, NIRvP can yield similar results than SIF, as demonstrated in the work by . Regardless, in water-limited herbaceous sites (e.g. SAV-Trans_E), the sensitivity to soil moisture stress in NIRv was eliminated in NIRvP, due to a too high sensitivity to SWrad (Fig. ). An illustration of this lack of soil moisture stress downregulation was evident in the mean annual cycle of NIRvP, where GPP was consistently overestimated during the dry season (Fig. ). The downregulation was more accurately reflected in the SIF model.

The seasonal GPP patterns in water-limited sites (e.g. ENF-Trans_E or SAV-Trans_E) were generally simulated less accurately (see Fig. ) in DGVMs, indicating that the soil moisture dynamics or the soil moisture stress response of the vegetation were an important source of errors . In the arid biomes, differences between ISBA and ORCHIDEE were most evident. The soil moisture dynamics and response to soil moisture stress in ORCHIDEE were demonstrated to be less accurate compared to ISBA in a previous study by .

The in situ observation uncertainty may contribute to the disagreement between models and observations. The eddy covariance observations are associated with site-dependent random errors due to instrumentation, stochastic nature of turbulence and varying footprint . Additionally, the typical non-closure of the energy balance might indicate that the observed carbon fluxes suffer from a similar bias , and there are significant uncertainties associated with the carbon flux partitioning in the ONEFLUX preprocessing pipeline .

Though land cover homogeneity and data quality were criteria for site selection, the discrepancy between the spatial scale of the in situ and remote sensing observations may contribute to the disagreement between observed and simulated GPP . Furthermore, there is a representation bias in the selection of test sites used here. There are limited sites included from South America, Africa and Asia. Consequently, some of the results reported here might be biased due to the dominant representation of (needleleaf) forest sites in temperate climates.

Lag effects of the drivers were not investigated in the frame of this study. Generally, it is mainly precipitation which leads to time lag effects , but that effect was largely accounted for by considering soil moisture. However, severe drought extremes can have a legacy effect, with a substantial impact on the interannual variability of GPP in terrestrial ecosystems . These effects fall out of the scope of this study.

The interannual variability in the SSA-decomposed time series was relatively small, in agreement with the results of . Given the associated uncertainty and relatively short time series in most sites, interpretation of the results at these timescales should be done with caution. In savanna biomes, there was an indication that RS-driven models captured the interannual variability better than meteo-driven models (see Fig. ). In other biomes, the interannual correlation was very weak.

This study evaluated the ability of the models to capture the variability in GPP. It relied on analysis of the variance, the Pearson correlation and metrics for phenology. The absolute errors were not evaluated here. These results give no guidance on the bias or accuracy of the simulated GPP itself.