## 4 Discussion
First, the \(R_{\rm g}\) of 1981 as a baseline was used to investigate the effect of \(R_{\rm g}\) and diffuse radiation fraction on GPP in terrestrial ecosystems. The advantages of this method were that the annual \(R_{\rm g}\) remained unchanged from 1981 to 2012 and the variation tendency of daily \(R_{\rm g}\) variation to \(R_{\rm g}\) values in 1981 was consistent. However, this method would result in a degree of uncertainty regarding daily \(R_{\rm g}\). For example, for a year that included many cloudy days, the \(R_{\rm g}\) of a sunny day would be overestimated. Second, the TL-LUE model has been validated worldwide [42; 43; 44], showing that the model performance for GPP simulations is satisfactory. In the present study, we obtained a high \(R^{2}\) (0.82) value for comparisons between the model-simulated GPP and observed GPP values. However, an extremely limited number of flux sites in China were used to optimize \(\rm LUE_{sun}\) and \(\rm LUE_{shaded}\)[43], which would cause their underestimation for some ecosystems, especially for crops. Compared with \(\rm C_{3}\) plants, \(\rm C_{4}\) plants photosynthesize by the combination of vascular bundle sheath cells and mesophyll cells, which have a higher \(\rm CO_{2}\) assimilation rate, resulting in higher LUE [60]. Therefore, the inclusion of a few sites dominated by \(\rm C_{4}\) plants to parameterize the model would result in underestimation of \(\rm LUE_{sun}\) and \(\rm LUE_{shaded}\) used in the model and the subsequent simulation would underestimate GPP values at some sites in China (Figure 5). Therefore, additional flux tower sites in China should be used to validate the model in the future. In addition, underestimation of LAI values would result in underestimation of simulated GPP values. For example, the LAI values at the GRASS sites used in the present study were significantly lower than those of the MOD15A2 LAI product (Figure 10), which resulted in underestimation of GPP values at these sites. The GPP uncertainties caused by LAI uncertainties have been investigated and the sensitivity of GPP estimates derived from TL-LUE was lower than that of large-leaf LUE models at the site scale [43]. In the present study, the uncertainties of GPP simulated by the TL-LUE model caused by LAI uncertainties at the national scale were investigated (Figure 10). Overestimation of LAI by 10% would result in GPP overestimation by about 1.2-10%, whereas in most areas with higher LAI the overestimation of GPP was no more than 8%; similarly, underestimation of LAI by 10% would result in GPP overestimation by a similar magnitude to that mentioned above but in the inverse direction (Figure 11). Furthermore, radiation measurements in China are extremely limited, comprising 103 and 81 sites for global radiation and diffuse radiation, respectively; therefore, an interpolation method was used to infer the national-scale \(R_{\rm g}\) and \(R_{\rm d}\). The Angstrom model is commonly used for radiation  
Figure 11: Uncertainties in GPP simulated by the TL-LUE model caused by LAI uncertainties in China during the period 1981–2012 (unit: %). **(a)** Decrease in GPP simulated with the TL-LUE model (GPPTL) caused by a decrease in LAI by 10%; **(b)** increase in GPPTL caused by an increase in LAI by 10%; **(c)** decrease in GPPTL caused by a decrease in LAI by 20% and **(d)** increase in GPPTL caused by an increase in LAI by 20%. Figure 10: Comparison of leaf area index (LAI) data used in this study and the MODIS LAI product (MOD15A2) for grassland sites, as part of the validation process for estimation of GPP (details for each site were described in Table 3). interpolation [29; 30]. Interpolated radiation data are widely used for ecosystem-level simulations of water and carbon dynamics [44; 61].