Discussion

4.1 Adequacy of model structure in representing processes

The understanding of the processes involved in GPP is fundamental to building a reliable GPP model. For example, we found that failed incorporation of the effect of clouds on GPP in some existing models significantly underestimated GPP in areas with frequent cloudy cover. Under clear sky conditions, the upper canopy leaves are close to light saturation, while the lower canopy leaves are shaded and have limited light (26). In contrast, under cloudy conditions, a higher proportion of the light in the form of diffuse radiation can reach the lower parts of the canopy, thus increasing the total photosynthetic use of PAR by the vegetation (27). Some studies indicated that a 1% increase in diffuse radiation induces a 0.94% increase in GPP (29, 30). In addition, many studies have shown that CO2 fertilization has a significant effect on vegetation production, a dominant factor contributing to the 31% increase in global GPP since 1990 (30). Nevertheless, many LUE models have not explicitly accounted for the effect of increasing atmospheric CO2 concentration(32, 33). In our study, after incorporating the impacts of both cloud cover and CO2, the performance of the LUE-EF and LUE-NDWI models improved compared with the original EC-LUE model: R2 improved from 0.61 to 0.68 for LUE-NDWI and from 0.61 to 0.74 for LUE-EF, respectively.
Water availability is an important factor that affects GPP(33). In this study, we adopted two alternative parameterized expressions to represent the impact of water stress on GPP. First, the evaporative fraction (EF) of total energy, closely related to the Bowen ratio, was used in the LUE-EF model. The relevance of LUE-EF is grounded on the fact that less energy used for ecosystem evaporation (i.e., smaller evaporative fraction) implies a stronger water limitation (35), which has largely been verified using flux tower measurements(35). Nevertheless, the application of the LUE-EF model is hindered by the derivation of EF that required multiple steps and input data layers and therefore prone to error propagation (36). In order to get a direct measure of water stress, and therefore minimize error propagation, from satellite observations we replaced the EF using NDWI in the LUE-NDWI model, based on the evidence that NDWI is closely related to the plant water content and thus a good proxy for plant water stress (37). The direct use of NDWI in the LUE-NDWI model makes it ideal for mapping GPP at the regional to global scales.

4.2 input data biases and possible impacts on GPP simulations

In this study, we found that the spatial data at the EC-tower sites had various systematic deviations, which seriously affected GPP estimates. For example, the spatial data fields of PAR explained only 57% of the PAR variation observed at the EC-tower sites. Reasons for the data biases are mainly rooted in the influence of sensor errors and atmospheric factors (e.g., cloud and snow) (39, 40, 41). In addition, attempts unifying data from different spatial and temporal resolutions also bring biases as we found that data at different resolutions sometimes had poor correlations. The reason for the existence of resolution mismatch is mainly caused by mixed pixels and/or different time scales (e.g., daily, 8-day, or monthly data), compared to the spatio-temporal resolution that applies to ground conditions (42, 43). In general, spatial data errors are an important cause of the uncertainty of GPP simulation, which might have contributed to the large differences in GPP estimates among existing GPP models (44). Thus, improving the quality of input data fields should be a major research component in reducing the uncertainty in GPP simulations at regional to global scales.
The comparison of existing global GPP products shows a huge variation from 92.7 to 178.9 Pg C yr-1, which might be related to data biases (45). One should realize that the sensitivities of models to data biases are usually different, depending on model structure. In our study, it was found that the LUE-EF model is more susceptible to data errors, while the LUE-NDWI model is less affected by data biases (Fig.3d). There are many GPP models in the world, and the sensitivity of each model to data biases has not been effectively evaluated and compared. The sensitivities of the models to data deviations should be systematically investigated in future research. Another research area that deserves more attention is how to improve data quality. Data bias should be a primary concern in modeling GPP from site to region scales. The existence bias of spatial data not only effects the GPP simulation, but more importantly it hinders the observation and understanding of the earth system. Therefore, effective correction of spatial data is critical for reducing the uncertainty in GPP simulations, and research on improving data quality should be encouraged. In this regard, our research cautions using currently available spatial data for relevant research.

4.4 Improving GPP simulation capability: the ways forward

In this study, after data correction, the coefficients of determination for the LUE-EF and LUE-NDWI models at site scale reached 0.80 and 0.79, respectively. The evaporative fraction parameter of the LUE-EF model involves more steps than the NDWI of the LUE-NDWI model, and consequently the risk of the error accumulation increases. The direct observation and continuous recording of NDWI as a remote sensing product is one of the main advantages of the LUE-NDWI model. The risk of error propagation of the LUE-NDWI model at the regional to global scale is small. Therefore, the LUE-NDWI model is more practical and attractive in spatially-explicit simulations of GPP. In addition, many studies now show that Sun-Induced chlorophyll Fluorescence (SIF) has a strong near linear relationship with GPP (43), indicating SIF can be used as a direct indicator of GPP. In principle, the simple forms of GPP models and widely available inputs, as compared with more complex global models, make them more practical for applications over large areas and better suited for attribution and uncertainty analysis (46, 47).
Should a balance or combination of multiple approaches be considered in the study of GPP simulation improvement? The comparison of global GPP products shows that there are differences among the three types of GPP models. The biophysical models showed the greatest inter-annual variability, followed by LUE models, and the machine learning models had minimal. Some research shows the machine learning models rely on empirical relationships between forcing variables and fluxes, which causes them barely captured the inter-annual variation of GPP (45). In contrast, LUE models assume that GPP is only related to environmental factors (e.g., temperature, water, etc.) and light use efficiency in relatively straightforward forms. Compared with the biophysical models, LUE models have less parameters, and simpler structures. This means that biophysical models have higher probability of error expansion in the processes of GPP simulations. In addition, studies have shown that the combination of machine learning models with other type of models have more potential to improve GPP estimation, which implies a balance or combination of multiple approaches might be the choice to reduce the uncertainty in GPP simulation.
Vastly different GPP products, as shown by the means, trends, and interannual variabilities of GPP, generated by the 22 models suggest our current ability in simulating global GPP is not encouraging (Fig.4c). For nearly 40 years committed to the global simulation of GPP, there does not seem to have a clear direction of the improvement of GPP simulation. This is mainly reflected in the fact that the models did not converge in GPP simulations with the advance of time. GPP model development is not explicitly directed, despite the constant emergence of new models. Our research indicates that neither the structure of the model nor the quality of the input data are error prone. Therefore, specific standards need to be developed to optimize model structures as well as sufficient validation and calibration of the input data. Research into efficacy of model structures and the precision of input data may be more important than the development of new models for global GPP estimation.