## 4 Discussion  
In China, annual mean \(R_{\rm d}\) has increased during the past 30 years [25]. An increase in \(R_{\rm d}\) leads to an increase in canopy LUE because photosynthetic saturation is reduced, thereby enhancing the ecosystem GPP [3; 5]. Therefore, investigating the effect of \(R_{\rm d}\) on GPP is important in studies of the carbon cycle [5; 8; 9]. There are many causes of radiation changes, such as changes in the solar constant, clouds, aerosols, and water vapor [55]. As the world's largest developing country, rapid economic development and rapid population growth in China have led to the emission of increasing quantities of man-made aerosols into the atmosphere. Aerosols can simultaneously change the amounts of direct and diffuse radiation reaching the surface [56]. [PERSON] et al. [57] reported that radiation decreased by about 24.1 W m\({}^{-2}\) from September 2004 to September 2005 because of the higher aerosol concentration by using aerosol observation data from the Xianghe Station in China. In addition, volcanic eruptions can  
Figure 9: Spatial distribution of the mean annual GPP simulated by scenario 2 (**a**); spatial distribution of the difference between the mean annual GPP in simulations 1 and 2 (**b**); spatial distribution of the annual mean GPP in simulation 3 (**c**); and spatial distribution of the difference between the mean annual GPP in simulations 1 and 3 (**d**) (unit: g C m\({}^{-2}\) y\({}^{-1}\)). Simulation 1 assumed that the global radiation and diffuse radiation ratio changed with time; simulation 2 assumed that global radiation remained unchanged from 1981 to 2012; and simulation 3 assumed that the diffuse radiation fraction remained unchanged from 1981 to 2012 with a spatial resolution of 0.0727\({}^{\circ}\). also strongly affect global and diffuse radiation [58; 59]. [PERSON] et al. [25] observed that the eruption of Mount Pinatubo in the Philippines in 1991 caused a rapid increase in the amount of diffuse radiation in China in the early 1990s. The TL-LUE model, which provides a distinct means to investigate the effects of \(R_{\rm d}\) changes on GPP, simulates GPP for sunlit (diffuse and direct radiation) and shaded leaves (diffuse radiation) separately. In the present study, during the period 1981-2012, the average GPP contributed by \(R_{\rm d}\) in China was 5.69 Pg C y\({}^{-1}\), which accounted for 74.48% of the total annual GPP. This finding shows that the contribution of \(R_{\rm d}\) to GPP in China was greater than that of direct radiation. The higher contribution of \(R_{\rm d}\) to GPP was largely because of the high fraction of \(R_{\rm d}\) and was also associated with the higher LUE of \(R_{\rm d}\). The present results showed that the increase in \(R_{\rm d}\) ratio could compensate for the reduction in GPP because of the lower photosynthetically effective radiation. These results will help to quantify the impacts of \(R_{\rm d}\) on GPP and enhance knowledge of the possible causes of carbon budget variation. Although the mean annual GPP and the GPP of each vegetation type are comparable to those reported by many previous studies (Table 4), some marked differences are apparent. The possible reasons are, first, that model structures are different, not only between process models and LUE models, but also among various LUE models. Second, the modeling area and period are set differently. For example, in the Carnegie-Ames-Stanford approach (CASA) (Table 4), [PERSON] et al. [50] estimated that the total amount of GPP for the period 1982-2009 only varied by 2.66-3.16 Pg C y\({}^{-1}\), whereas the average annual GPP reported by [PERSON] et al. [51] for 1993 was 6.24 Pg C y\({}^{-1}\), in which maximum LUE was retrieved based on observations at 690 sites. Third, the types of input data used are inconsistent, covering different time ranges and differing in spatial and temporal resolutions. Several uncertainties in the present study are acknowledged.