FLUXNET is a global network composed of local regional networks that measures the exchanges of carbon dioxide, water vapor, and energy between the biosphere and atmosphere based on the eddy covariance method (Baldocchi et al., 2001; Friend et al., 2007). The daily GPP, NEE, ER, and heat fluxes, as well as meteorological data (including air temperature, shortwave radiation and VPD) were download from the FLUXNET database (https://fluxnet.org/). There are 12 FLUXNET sites in China, the distribution and overview of which can be seen in Figure 1 and Table 1, respectively. Due to the complex vertical structures of the forest canopy, it has a strong response to diffuse radiation (Strada et al., 2015; Zhang Y. et al., 2020). Therefore, we chose only four forest sites in this study: Cha, Qia, Din and MPM. We extracted flux data from the growing season (June–August) when physiological and phenological changes can be largely neglected (Alton et al., 2007). A detailed description of the geographical environment of the four sites is shown in Table 2. There are three kinds of plant functional types (PFT) at FLUXNET forest sites in China, which are mixed forests (MF), evergreen broadleaf forests (EBF) and evergreen needleleaf forests (ENF). The PFT of different sites is related to the local climate. The Cha site located in a higher latitude zone and has a temperate continental climate, forming a mixed forest of temperate coniferous forest and broad-leaved forest. The other three sites are located in the middle and low latitudes zone and have a subtropical monsoon climate, forming evergreen broad-leaved forests and evergreen coniferous forests. The vertical structure of the canopy plays an important role in diffuse fertilization effect. The response of carbon absorption to diffuse radiation is also related to canopy characteristics such as leaf area index (LAI), leaf angle and leaf optical characteristics. Some studies showed that diffuse fertilization effect increased with the increase of LAI (Gui et al., 2021). From the Table 2, Cha site has the largest LAI and canopy height (5.8 m² m⁻² and 26m, respectively), followed by Din and Qia sites. MPM sites had the smallest LAI and canopy height (1.75–2.455.8 m² m⁻² and 2–4 m, respectively). In terms of LAI and canopy height, Cha site has the most complex vertical canopy structure, while MPM site had the simplest canopy structure. In addition, it is worth paying attention to that the typical vegetation type of MPM site is different from other sites. The MPM site is a coastal mangrove ecological community, and mangrove is a woody wetland plant, which has higher requirements on hydrothermal conditions. In addition, the four sites provide data in different years. The Cha, Qia, and Din sites provide data from 2003 to 2005, and the MPM site provides data from 2016 to 2018.

The in situ-measured radiation dataset was obtained from the National Meteorological Information Center of the China Meteorological Administration (CMA) (https://data.cma.cn/). It provides daily solar radiation data including daily total radiation, diffuse radiation, and sunshine duration. Quality control was carried out for all data to reduce the impact of outliers on the result analysis. Among all these sites, only 19 sites provided diffuse radiation measurements (He and Wang, 2020). The spatial distribution of radiation sites is shown in Figure 1. For this study, we use daily measurements from 19 diffuse radiation sites during 2000–2017 to establish and verify an empirical model of K_d. Among them, the measurements from 2000 to 2011 were used for K_d modeling, and data from 2012 to 2017 were used for K_d validation. On the other hand, some of these radiation sites are adjacent to FLUXNET sites but they rarely overlap and they are a certain distance away from FLUXNET sites. Therefore, when we built the K_d model of FLUXNET sites, we chose the three nearest radiation sites.

According to the previous empirical model, we selected the K_d model based on K_t. K_t represents the diffusion and absorption effects caused by the presence of the atmosphere (Bortolini et al., 2013; Khorasanizadeh and Mohammadi, 2016). As K_t decreases, sky conditions vary from clear to cloudy (Tsubo and Walker, 2004; Apeh et al., 2021). The FLUXNET sites did not provide diffuse radiation data, but there were many CMA sites around the FLUXNET sites. According to Tobler’s First Law of Geography, everything is related to everything else, but things that are located near each other are more related than things located further away (Tobler, 1970). Therefore, we considered the FLUXNET sites as center points and chose the three CMA radiation sites nearest to the FLUXNET sites. The sky conditions and radiation conditions at the radiation sites were used to approximately represent those of FLUXNET sites. We used the data provided by the radiation sites to build the K_d model and then input the data from the FLUXNET sites to obtain the corresponding K_d. Therefore, according to the distribution of the forest FLUXNET sites, seven CMA sites were chosen. To obtain K_d, we first needed to calculate K_t, which is the ratio of total solar radiation (H) to extraterrestrial radiation (H₀). The equation of daily extraterrestrial radiation (H₀) was given as follows (Duffie and Beckman, 2020; Yang et al., 2020): H 0 = 24 × 3600 G S C π ⋅ ( 1 + 0.033 c o s 360 n 365 ) ⋅ ( c o s ∅   c o s δ   s i n ω s + π ω s 180 s i n ∅   s i n δ ) (1) δ = 23.45 ⋅ s i n ( 360 ( 284 + n ) 365 ) (2) ω s = a r c c o s ( − tan ∅ ⋅ tan ⁡ δ ) (3) where   G S C   is the solar constant (1367 W m⁻²),     ∅ is the latitude (°), δ is the solar declination (°),   ω s is the sunset hour angle (°), and n is the day number of the year. Based on this, we established a regression model of K_d and K_t in the form of a cubic polynomial function.

Because the measurement of radiation may be subject to errors and failures, it is necessary to perform quality control on the data to identify incorrect data (Yang et al., 2020). This study adopts the data quality control method proposed by Younes (Younes et al., 2005): First, data were rejected if the solar altitude was less than 7°; Second, data were rejected if the ratio of the sunshine duration to maximum possible sunshine was greater than 1; Third, the values of the K_t and K_d ranged between 0–1; Fourth, the envelope was drawn. The results are shown in Figure 2. After the quality control process, the percentage of valid data at the CMA sites was 95.36–97.34%. The remaining datasets were divided into two parts. The data from 2000 to 2011 were used for K_d modeling, and data from 2012 to 2017 were used for K_d validation.

PAR is the main energy source for plant photosynthesis, controlling the rate of effective photosynthesis of terrestrial organisms and directly affecting the growth of vegetation (Li et al., 1997). Its diffuse component can enhance the LUE of the vegetation canopy, thereby increasing carbon uptake. However, not all FLUXNET sites provided PAR observations; only the MPM site provided photosynthesis photon flux density (PPFD), so we converted quantum systems (μmol m⁻² s⁻¹) into energy systems (W·m⁻²) based on Formula (4). Other sites adopted the method proposed by (Zhu et al., 2010), which was based on geographical division. U P A R = μ ⋅ Q P A R (4) where U P A R is the PAR of quantum systems,   Q P A R is the PAR of energy systems, and μ is the conversion coefficient, usually 4.55 (Zhou et al., 1984). PAR consists of direct PAR and diffuse PAR, among which diffuse PAR is the most important component that promotes photosynthesis. It is generally estimated by multiplying PAR by the K_d (Spitters et al., 1986; Ren et al., 2014).

LUE connects solar radiation, photosynthesis and vegetation production, represents the ratio of plant fixation to light energy absorption, and represents the efficiency of converting the light energy captured by plants into chemical energy, that is, the efficiency of CO₂ fixation into organic matter, which can indicate vegetation productivity and carbon fixation efficiency (Monteith, 1972; Monteith, 1977; Baldocchi and Penuelas, 2019). We attempted to quantify the LUE to analyze the impact of diffuse radiation on the vegetation LUE, which can be defined as the ratio of the GPP to PAR, as shown in Formula (5) (Strada et al., 2015; Yue and Unger, 2017; Wang et al., 2018) (Strada et al., 2015; Yue and Unger, 2017; Wang et al., 2018). L U E = GPP PAR (5)

Changes in aerosol load and cloud cover not only change the PAR reaching the surface but also change the proportion of diffuse radiation, with uncertain overall effects on global plant productivity and the terrestrial carbon sink.

We first explored the relationship among the K_d, PAR and GPP, and the result is shown in Figure 7. Clouds and aerosols can increase diffuse radiation, thereby promoting K_d. As the K_d increased, GPP first increased and then decreased. It was closely related to PAR, and changes in the K_d caused changes in PAR and its components. Overall, the total PAR decreased with increasing K_d. However, the changes in its direct and diffuse components were more complicated during the different ranges of K_d. When K_d gradually increased to K_o (K_d corresponds to the maximum value of GPP), the direct PAR was higher than the diffuse PAR but decreased rapidly, while the diffuse PAR showed the opposite results and increased rapidly, and the two radiation components reached a balanced state near K_o. At this stage, the growth in GPP was mainly caused by the increase in diffuse PAR. The presence of clouds and aerosols increased the diffuse PAR, and the diffuse PAR in the canopy had a stronger transmittance, which can spread more incident radiation to shaded leaves, greatly promoting the photosynthesis of the shaded leaves. This diffuse fertilization effect leads to an increase in canopy GPP. Due to differences in vegetation PFTs, aerosol load and cloud cover, different regions had an optimal K_d (K_o) when the GPP reached a maximum value. The optimal K_d (K_o) values of the Cha (MF), Qia (ENF), Din (EBF), and MPM (EBF) sites were 0.54, 0.56, 0.57, and 0.43, respectively, and the sky conditions at this time were the most favorable for carbon assimilation. This result is consistent with the optimal K_d range of forests obtained by previous studies, which was between 0.4–0.6 (Alton et al., 2007; Alton, 2008; Zhang J. et al., 2020).

When the K_d exceeds K_o, the amount of aerosols and clouds in the sky is too high, which greatly reduces the total PAR reaching the surface, so the GPP begins to decrease with an increase in K_d. However, the root cause of the reduction in total PAR is the substantial reduction in direct PAR. The diffuse PAR first increases and then decreases with increasing K_d. This is because the moderate increase in aerosols and cloud cover promotes diffuse PAR. Once the increase becomes excessive, it greatly reduces the total PAR, resulting in no excess PAR becoming scattered. When the K_d is between K_o and K_diff-max (K_d corresponds to the maximum value of diffuse PAR), although the diffuse PAR is higher than the direct PAR, it grows slowly, while the direct PAR still decreases, and the diffuse fertilization effect is not enough to compensate for the loss of GPP caused by the reduction of direct PAR, so the overall GPP at this stage has a downward trend. When the K_d is greater than the K_diff-max, the diffuse PAR also begins to decrease, and because the total PAR has been drastically reduced, there is not enough radiation for the aerosols and clouds to scatter. The drop in diffuse PAR causes a weakening of photosynthesis in shaded leaves, while the direct PAR is still in a reduced state, which leads to a weakening of photosynthesis in sunlit leaves. The reduction in the superposition of the two radiation components results in the rapid decline of canopy GPP.

Hence, the net effect on the canopy carbon assimilation depends on a balance between the reduction in direct PAR (which tends to reduce photosynthesis) and the increase in diffuse PAR (which tends to increase photosynthesis).

Figure 7 shows that the LUE increases as the K_d increases. Furthermore, we compared the LUE under direct and diffuse radiation conditions. The sky conditions were separated into categories of predominantly diffuse (K_d ≥ 0.5) and predominantly direct (K_d < 0.5) sunlight. We divided the sky condition based on the K_d, and considered direct radiation to be dominant when the K_d was less than 0.5 and diffuse radiation to be dominant when the K_d was greater than 0.5 (Alton, 2008). The LUE of FLUXNET forest sites under different radiation conditions is shown in Figure 8. The LUE of the four forest sites from high to low was: Cha, MPM, Qia and Din. At all sites, the LUE was significantly higher under diffuse radiation dominated conditions than direct radiation dominated conditions. Specifically, when the sky radiance was dominated by diffuse sunlight, the LUE was found to be 5.52%, 3.38%, 2.58%, and 3.77% higher than that under direct sunlight at the Cha, Qia, Din and MPM sites, respectively. This observation indicated an enhanced LUE, with the greatest increase occurring in dense foliage, such as the Cha site dominated by MF. Table 2 shows that the Cha site has the most complex vertical structure among the four forest sites because it has the highest LAI (5.8 m²·m⁻²) and the highest canopy height (26 m), so it is more sensitive to the diffuse radiation response.

Under clear-sky conditions, there were fewer clouds and aerosols, and the K_d was low, so solar radiation was dominated by direct light and sunlight was too concentrated on sunlit leaves. This situation led to the sunlit leaves in the canopy being usually light-saturated, and since extra sunlight cannot be used efficiently for photosynthesis, the LUE was low. At the same time, shaded leaves are more efficient at using light, but they were limited by the low incident radiation that they have received. In contrast, under cloudy or aerosol sky conditions, sunlight is more scattered and incoming radiation is more diffuse, the irradiance of the canopy is more uniform, and shaded leaves can receive much more sunlight from all directions, so the light-saturated part of the canopy is reduced and the LUE increases. This also demonstrates the diffuse fertilization effect. In conclusion, canopy photosynthesis tends to be significantly more light-use efficient under diffuse sunlight than under direct sunlight. The LUE enhancement under diffuse sunlight can be explained by the sharing of the canopy radiation load, which is reduced under direct sunlight. A modest reduction in direct radiation does not reduce photosynthesis in sunlit leaves because the LUE remains light saturated. However, when the amount of the K_d is too high, the total PAR is greatly reduced, and both the diffuse and direct PAR components are reduced (Figure 7). Even though the LUE still increases, the available light is reduced, so the canopy GPP also decreases.