## 1 Introduction  
Carbon sequestration is extremely important for global change studies [1]. Terrestrial gross primary productivity (GPP), which indicates the ability of vegetation to use light energy through fixation of carbon dioxide during photosynthesis, is a primary component of the terrestrial carbon cycle [2]. Solar radiation substantially affects the ecosystem GPP [3]. Global radiation (\(R_{\rm g}\)) includes both direct and diffuse components. Compared with direct radiation, diffuse radiation (\(R_{\rm d}\)) is more readily distributed evenly in the canopy and shows higher photosynthetic saturation. Therefore, higher \(R_{\rm d}\) increases the canopy light use efficiency (LUE) and thus leads to the enhancement of GPP [4; 5; 6; 7]. Consequently, under cloudy or severe haze conditions, even if \(R_{\rm g}\) decreased, vegetation GPP can increase as a result of the higher \(R_{\rm d}\) component. Many studies have quantitatively or mechanistically assessed the influence of changes in \(R_{\rm d}\) on GPP at the site scale. An increase in \(R_{\rm d}\) results in enhanced canopy LUE and hence leads to an increase in vegetation productivity. For example, [PERSON] et al. [8] confirmed that canopy LUE under \(R_{\rm d}\) was higher than that under direct radiation for six vegetation types. [PERSON] et al. [9] observed that after a volcanic eruption, changes in \(R_{\rm d}\) on the GPP of Harvard Forest increased by 3-21% because of the increase in the diffuse radiation fraction. Previous studies have evaluated the effects of \(R_{\rm d}\) on GPP at the regional scale with ecological models. [PERSON] et al. [10] investigated the impact of radiation on GPP over the past 50 years. The effect was greater for agricultural lands and grasslands than for forests, as demonstrated by flux data. [PERSON] et al. [5] observed that the reduction in global photosynthetically active radiation (PAR) reduced global terrestrial carbon sinks by 14.4%, whereas an increase in \(R_{\rm d}\) increased global terrestrial carbon sinks by 9.3%. [PERSON] et al. [11] coupled a terrestrial ecological model and an atmospheric radiation transmission model to study the direct radiation effect on terrestrial ecosystems from 2003 to 2010, and reported that enhanced \(R_{\rm d}\) led to an increase of global GPP by 4.9 Pg C. Thus, previous studies clearly show that the impacts of \(R_{\rm d}\) on the carbon cycle should be considered in ecological models. In recent years, given the important influence of \(R_{\rm d}\) on GPP, an increasing body of research has attempted to improve ecological models for simulation of GPP with the inclusion of \(R_{\rm d}\) with LUE models. The two-leaf light use efficiency model (TL-LUE) simulates GPP with the differentiation of direct radiation and \(R_{\rm d}\)[12]. [PERSON] et al. [13; 14] incorporated \(R_{\rm d}\) into a LUE model. [PERSON] et al. [15] also established a two-leaf model Terrestrial Ecosystem Carbon flux (DTEC) to separately simulate GPP for sunlit and shaded leaves. [PERSON] et al. [16] upgraded a large-leaf model, Eddy Covariance - Light Use Efficiency (EC-LUE), into a two-leaf model to separately simulate GPP for sunlit and shaded leaves. The above-mentioned models show that incorporation of \(R_{\rm d}\) into GPP models clearly improves the GPP simulation. In China, previous studies of changes in \(R_{\rm g}\) and \(R_{\rm d}\) have been based on meteorological data, including global radiation measurements, or global radiation derived from sunshine duration. With regard to \(R_{\rm g}\), studies of trends in \(R_{\rm g}\) that were conducted around or before 2000 were inconsistent because of limited radiation measurement stations.