Variability in Direct and Diffuse Solar Radiation Across China From 1958 to 2017

Long‐term variability of direct and diffuse solar radiation (Rdir and Rdif) is essential for climate change study. However, Rdir and Rdif observations suffer from low spatiotemporal coverage and inhomogeneity. This study improved hybrid models to calculate Rdir and Rdif from sunshine duration and meteorological data at ~2,000 stations from 1958 to 2017 over China and demonstrated their reliability. We identified that Rdir observations show a spurious steep downtrend before 1990 due to the sensitivity drift of the measuring instruments, implying an overestimation of global dimming. Long‐term trends and spatiotemporal details in Rdir and Rdif were also revealed. From 1958 to 1989, our results show that Rdir displays a significant downtrend (−3.52 W m−2 per decade), whereas Rdif shows a significant increasing trend (0.84 W m−2 per decade), especially over the North China Plain. From 1990 to 2017, Rdir decreases nonsignificantly by −0.47 W m−2 per decade but Rdif shows a slight decline of −0.28 W m−2 per decade.


Introduction
The surface incident solar radiation (R s ) is an indispensable energy source on the Earth, consisting of direct solar radiation (R dir ) and diffuse solar radiation (R dif ) (Wild et al., 2005). They dominate plant photosynthesis (Alados et al., 2002;Stanhill & Cohen, 2001), land-atmosphere carbon (Mercado et al., 2009;Roderick et al., 2001), water exchange (Hong et al., 2015;Wang et al., 2007), and solar energy production (Kaygusuz, 2002;. In particular, due to higher light-use efficiency for canopy photosynthesis under R dif than R dir , changes of fraction of R dif to R dir could substantially alter plant productivity and the efficiency of canopy gas exchange (Knohl & Baldocchi, 2008;Mercado et al., 2009;Roderick et al., 2001;Wang et al., 2008). It has shown that the increase in the diffuse fraction enhanced the global land carbon sink by 23.7% during the period from 1960-1990 when R s substantially decreased during the global dimming period (Mercado et al., 2009).
The global coordinated measurement of R s started in the 1950s at high level weather stations (Ohmura et al., 1989;Wild et al., 2017). The stations routinely observing R s are very sparsely distributed (Tang et al., 2011;Wang et al., 2015). Even worse, R dir and R dif are not routinely observed due to the cost, maintenance, and calibration of the equipment (Chukwujindu, 2017;Khorasanizadeh & Mohammadi, 2016). Especially in China, some issues with recorded observations existed including instrument aging and sensitivity drift before 1990, probably resulting in spurious dramatic downtrends in R s observation in China (Pandey & Katiyar, 2013;Tang et al., 2011;Wang, 2014). During the period of 1990-1993, China has replaced its instruments to address the problem of instruments aging. To benefit calibration processes, an absolute pyrheliometer  and two H-F-type cavity pyrheliometers making up the national reference group of China, have been calibrated by references at the World Radiation Center every 5 years since 1991, and then they are used to calibrate all working instruments in China (Yang et al., 2007). Even though these instruments are better calibrated using a multistep method, the observations of solar radiation still lack spatiotemporal representation due to sparse sites and poor management of the network (Shi et al., 2008;Wang et al., 2015).
The Baseline Surface Radiation Network (BSRN) has a reputation of providing high-accuracy data with good maintenance protocols and frequent calibration (Augustine & Dutton, 2013;Wang et al., 2012a). It measures R s , R dir , and R dif directly and simultaneously according to the specifications of the World Climate Research Programme. Nonetheless, the BSRN was established in the early 1990s and only has approximately 50 sites worldwide (Ohmura et al., 1998).
Satellite retrievals can provide R s with continuous and high spatiotemporal resolution properties (Sanchez-Lorenzo et al., 2017), whereas satellite measurements are limited, as they only have available data dating back to the 1980s (Pinker et al., 2005). Satellite measurements also suffer from inhomogeneity issues due to different amounts and capabilities of data acquired from geostationary and polar orbit satellites (Dai et al., 2006). It was also suggested that R s data from satellite retrievals generally have worse agreement with ground-based observations where it snows (Pfeifroth et al., 2018;. Few satellite products provide estimates of R dir and R dif for China. A great deal of existing models can estimate R dir and R dif based on empirical statistical methods and physical mechanisms (El Mghouchi et al., 2016;Monteith, 1962). The establishment of diffuse radiation model usually correlates the diffuse fraction with the clearness index or relative sunshine duration. However, most existing models are only suitable for single weather condition (Yao et al., 2015), and they seem to lack universal applicability (Dervishi & Mahdavi, 2012;Khorasanizadeh & Mohammadi, 2016). Therefore, it is of significance to offset the deficiencies of poor spatial coverage and temporal discontinuity existing in other data sets of R dir and R dif . Sunshine duration (SunDu), as a useful proxy of R s , has been measured at approximately 2,400 stations over China since 1951 and does not suffer from the problem of instrument sensitivity drift and influences of instrument replacement (Sanchez-Lorenzo & Wild, 2012;Stanhill & Cohen, 2005;Wild, 2009), due to the advantage of recording SunDu (Wang et al., 2015). SunDu-derived R s has been proven to accurately depict the long-term variability in R s (He et al., 2018). Furthermore, certain impacts of both aerosols and clouds are also reflected in the derived R s data from this method [Tang et al., 2011;Wang et al., 2012b;Yang et al., 2006]. Previous research has estimated R dir (Tang et al., 2018) or R dif (Feng et al., 2018) based on sunshine duration, but they did not address the variability in long-term trends of R dir and R dif .
This study could improve methods to estimate R dir and R dif based on routine meteorological observations. The derived data are evaluated by in two steps that show their reliability at monthly and annual time scales. We then apply the models to~2,000 stations over China from 1958 to 2017, which shows that R dir decreases by −3.52 W m −2 per decade and R dif increases 0.84 W m −2 per decade from 1958 to 1989, and the trend in R dir after 1990 is nonsignificant.

Data
The observed R s , R dir , and R dif data sets were obtained from the BSRN (at 55 stations) and the China Meteorological Administration (CMA, at 122 stations). SunDu and other meteorological data (e.g., air temperature, relative humidity, and surface pressure) were also obtained from the CMA to estimate R dir and R dif at approximately 2,400 meteorological stations from 1958 to 2017. Note that total cloud cover data were from 1958 to 2014.
After preliminary quality checks including continuity and data length (at least 80% of the record duration at all timescales, that is, ≥24 days per month, ≥292 days per year, and ≥48 years during the study period of 1958-2017), 62 sites from the CMA stations during the period 1970-1989 were involved in this study. Data during the period 1990-1993 were here excluded because of large errors from instrument replacement issues (Tang et al., 2011;Wang, 2014). Most of the CMA stations stopped observing R dir and R dif after 1993, and hence, only 16 stations (after the quality checks) continued to simultaneously monitor R s , R dir , and R dif . Accordingly, 32 sites were selected from 55 BSRN global radiation stations from 1994 to 2015, whose instruments are of high accuracy, with good maintenance, frequent calibrations, and separate measurements of R s , R dir , and R dif (Ohmura et al., 1998). The spatial distribution of solar radiation stations is shown in Figure S1 in the supporting information. The stations used to study the long-term variability and more spatial details of R dir and R dif across China from 1958 to 2017 were also selected based on the above quality checks, with 2,188 sites in total.

Methods
The equations of R dir and R dif are regressed based on the observed direct and diffuse solar radiation from 16 CMA stations during the period 1994-2014. Analogously, the calculation formula for the monthly derived R dir data set is improved based on that for the derived R s data set (He et al., 2018;Tang et al., 2018;Yang et al., 2006), as shown in equation (1): where a 0 , a 1 , and a 2 represent the regression coefficients of SunDu against the observed R dir values in equation (1); n and N are the actual sunshine duration and the theoretical value of the sunshine duration without clouds, respectively. I 0 is the solar irradiance on a horizontal surface at the top of the atmosphere. R c_dir is the direct solar radiation under clear-sky conditions.τ c_dir is the direct radiation transmittance under clear-sky conditions and is calculated using other meteorological data (including relative humidity, air temperature, and surface pressure) from the CMA stations, turbidity coefficient based on Hess et al. (1998), and ozone thickness based on the satellite products provided by National Aeronautics and Space Administration/Goddard Space Flight Center Ozone Processing Team [K Yang et al., 2006].
For the estimates of R dif , based on the relationship of transmittances between R dif /R s and R dir /R 0 , this study develops a model equation (3): where b 0 , b 1 , and b 2 represent regression coefficients of R dir /R 0 R dir /R 0 against the observed R dif /R s values in equation (3); R s is calculated by using the sunshine duration and other meteorological data from He et al. (2018); R 0 is the solar radiation on a horizontal surface at the top of the atmosphere.
We used the observed R dir (R dif ), sunshine duration, and other climatic factors from 1994 to 2014 to obtain the 16 sets of regression coefficients based on equation (1) (3) (Table S1); and their spatial distribution is illustrated in Figure S2. Then, approximately 2,000 sites were matched to 16 radiation observations stations based on distance, ensuring that each site can be assigned a set of the regression coefficient from its nearest site among the 16 radiation stations ( Figure S3). Finally, we applied equation (1) (3) again to calculate the R dir (R dif ) values from 1958 to 2017 for each station (~2,000 stations in China) when the observed sunshine duration and other climatic factors (e.g., air temperature, relative humidity, and surface pressure) were available.

Models Performances
To assess the derived R dir and R dif , the estimations of monthly averages at the 16-pair stations were compared with the observations from 1994 to 2014 over China. Considering the uncertainty of the annual timescale of CMA observations due to the impacts of problems such as instrument sensitivity drift, we utilized the observations from 32 BSRN stations to further verify the reliability of the long-term changes in the derived data by examining the sensitivity of R dif to R dir . We calculated a polynomial regression model to assess the sensitivity of R dif to R dir at the annual timescale, which is the slope of the liner regression line between annual anomaly R dif and R dir . Other statistical indicators include the following: the correlation coefficient (r), mean bias error (bias), root-mean-square error, and relative root-mean-square error.

Comparisons of the Observed and Derived R s , R dir , and R dif
Compared to previous studies, the derived data show good performance to reproduce the monthly R dir (R dif ) estimates with a higher correlation coefficient of 0.96 (0.98) and a smaller mean bias of 3.41 W m −2 (−0.02 W m −2 ) (Figures 1a and 1b and Table S4) (Li et al., 2011;Tang et al., 2018). The observed trends in R s and R dir appear to be steeper (likely spurious) than the derived trends during the period 1970-1989 (Figures 1c1 and 1d1). It has been verified that the spurious trend in the observed R s may be due to the observations from the CMA radiation stations experiencing the negative influence of instrument sensitivity drift and instrument aging before 1990 (Wang, 2014;Wang et al., 2015;Yang et al., 2018), and the same is true for the pyrheliometer used to measure R dir in this study, implying an overestimation of global dimming in China. However, this issue is almost not present in the SunDu-derived radiation data sets. The light sensitive paper used to measure SunDu is replaced each day, and therefore, SunDu-derived R dir does not have such a sensitivity drift problem. After 1993 when the CMA stations have finished the instrument replacement activity and improved calibrations, the derived and observed radiation have similar variations (Figures 1c2, 1d2, and 1e2). In brief, the derived radiation data can effectively describe the monthly average values and temporal variability as proxies of the observation data.
To further confirm the dependence of the derived R dif to R dir at the annual timescale, a higher-accuracy radiation observation data set from the BSRN stations was adopted as a criterion. Based on the annual anomalies in R dif and R dir , the sensitivities of R dif to R dir are shown in Figure 2. More than 57% of the BSRN stations and derived stations both have sensitivities of less than 0.0. The overall sensitivity of R dif to R dir is −0.06 ± 0.03 (p < 0.001) for the~2,000 derived radiation stations in China and −0.08 ± 0.03 (p < 0.001) for the BSRN radiation stations, which indicates that the annual variation of R dif and R dir is roughly negative correlated. Therefore, the derived data based on SunDu might accurately describe the relationship between R dif and R dir . These results can also prove that the derived R dif and R dir are credible to depict the long-term variability of solar radiation.  Table 1 describes the decadal trends in the derived R s , R dir , and R dif from approximately 2,000 stations over China during the three periods. The period of 1958-1989 is known as global dimming (Gilgen et al., 1998;Ohmura, 2009;Ohmura et al., 1998;Wild, 2009), when the trends are declining for both R s (−2.68 W m −2 per decade, p < 0.05) and R dir (−3.52 W m −2 per decade, p < 0.05) but increasing for R dif (0.84 W m −2 per decade, p < 0.05) (Figure 3a and Table 1) almost without the influence of the sensitivity drift. The average trend in R s of the four models from Coupled Model Intercomparison Project Phase 5 Goddard Institute for Space Studies is consistent with our result during the period of global dimming (Wang et al., 2015). For seasonal variations, R dir in the warm season decreases more greatly than that in the cold season (−4.14 vs. −2.75 W m −2 per decade) (Figures 3b and 3c and Table 1). R dif correspondingly shows a

Geophysical Research Letters
HE AND WANG larger increasing trend in the warm season (1.12 W m −2 per decade, p < 0.05) than that in the cold season (0.51 W m −2 per decade, p < 0.05), which may enhance plant photosynthesis in the warm season through the diffuse radiation fertilization thereby increasing global primary production (Rap et al., 2018).
In the period of 1990-2017, the derived R s data depict a downward trend (−0.76 W m −2 per decade, p < 0.10). The satellite retrievals of R s (Wu & Fu, 2011)  Particularly, in the warm season of 1990-2017, the negative trend in R s is more apparent (by −2.09 W m −2 per decade, p < 0.05) ( Table 1). R dir decreases nonsignificantly by −0.47 W m −2 per decade (p > 0.10) during the period of 1990-2017 over China, likely because the estimations of R dir have opposite trends between those in the warm season (−1.72 W m −2 per decade, p < 0.05) and cold season (0.78 W m −2 per decade, p < 0.10) to offset their effect (Figures 3b and 3c and Table 1). However, R dif declines slightly by −0.28 W m −2 per decade (p < 0.05) at the annual timescale, with downtrends in the warm season (−0.37 W m −2 per decade, p < 0.05) and cold season (−0.20 W m −2 per decade, p > 0.10).
In general, the variation in R dir is steeper than that in R s during the period 1958-2017, showing a significant decreasing trend (Table 1). R dif increases by 0.53 W m −2 per decade (p < 0.05) in the warm season, and increases by 0.16 W m −2 per decade (p < 0.05) in the cold season from 1958 to 2017 (Figures 3b and 3c and Table 1). Our results are similar to Feng and Li (2018) who utilized a backpropagation artificial neural network (BP network) to estimate R s , R dir , and R dif at 45 stations from 1958 to 2016 over China. Figure 4 shows the spatial distribution of the trends in R s , R dir , and R dif and total cloud cover over China at different timescales. The derived R s and R dir data show an overall decline over China during the period of   1958-1989, and (c) 1990-2017 (1990-2014 for c4, c8, and c12). The sites with significant trends (p < 0.05) are distributed in Figure S4 (in the supporting information).

Geophysical Research Letters
1958-2017 (with more than 78% of sites) at annual and seasonal timescales, especially in the North China Plain. However, R dif data show significant increasing trends there (Figure 4a), likely because of the increasing trend in aerosol loading in the areas (Li et al., 2016). It is worth noting that the spatial difference of their trends seems not be affected by the spatial pattern of~2,000 meteorological stations in China matching the 16 radiation observation stations ( Figures S3 and 4).
From 1958 to 1989, the spatial pattern of the derived R dir is similar to that of the derived R s , with a significant decrease over most parts of China (with more than 75% of sites) at annual and seasonal timescales (Figure 4b). In contrast to the R dir data, the derived R dif data show significant continuous increasing trends, especially over the North China Plain. In the southern China, there are nonsignificant decreasing trends in R dif at annual timescale (Figures 4b and S4), mainly due to the offset effect of its opposite trends in different seasons, that is, the trends of R dif are negative in the cold season but positive in the warm season.
From 1990 to 2017, R s shows decreasing trends over China at annual and warm seasonal timescales, except in the Pearl River Basin (Figure 4c). These trend patterns at the annual timescales are consistent with the findings of Xia (2010) and Wang and Wild (2016). For R dir , the spatial distribution of its trends is similar to R s at different timescales. In the warm season, R s and R dir data both appear negative trends in almost whole China (Figures 4c and S4).In the cold season, however, they show significant positive trends over the Loess Plateau, the Szechwan Basin, and the Yangtze River Basin (Figures 4c and S4). The seasonal differences also occur in R dif during this period, but mainly over the Szechwan Basin, the North China Plain, and parts of the southeastern China. The trends in R dif are significant with the 95% confidence level in the northern China at different timescales ( Figure S4). These seasonal and regional details in solar radiation variability could provide effective information for the analysis of plant photosynthesis.

Variation of Solar Radiation in Relation to Key Factors
It is obvious that R s is affected mostly by clouds, aerosols, and water vapor through the atmosphere (Horseman et al., 2008;Qian et al., 2015;Ramanathan et al., 1989;Warren et al., 2007). Clouds directly reduce R s by reflecting a large portion of solar radiation into space and scattering a small portion of solar radiation (Cess et al., 1995;Kasten & Czeplak, 1980); aerosols and water vapor reduce R s through absorption and scattering effects. The scattering portion eventually arrives at the Earth's surface in the form of R dif (Ramanathan et al., 2001).
The variations in total cloud cover (at the rightmost column of Figure 4) can only explain the trend changes in solar radiation during the period of 1990-2014, which is in agreement with the previous studies (Luo et al., 2000;Yang et al., 2013). The contribution of aerosols to long-term solar radiation variations should be considered, but it is difficult to be quantified due to aerosol direct and indirect effect on solar radiation. Based on the model only considering aerosol direct plus first indirect effect, increasing air pollution alone can account for 2.6 W m −2 of the decreasing solar radiation in the part of United States (Liepert, 2002). Li et al. (2018) found that R s may be highly sensitive to aerosol-related parameters (such as single scattering albedo), by analyzing a station with collocated R s and aerosol observations in Xianghe, China. After the volcanic eruption in 1991, significant decreasing R s should appear due to the effect of the large amount of aerosols. However, the total cloud cover declines significantly much from 1991 to 1992 in China ( Figure S5 in the supporting information), which could weaken the decreasing extent of solar radiation caused by aerosols from the volcanic eruptions. The changes of water vapor can also lead to the reduction in R dir and an increase in R dif .

Conclusions
This study reconstructed a comprehensive data set of R dir and R dif over most of all China to offset the deficiencies of poor spatial coverage and temporal discontinuity. Due to the simple physical models and mathematical methods involved, the derived data sets in this study show better performance in temporal variability and spatial details with high correlation coefficients (0.96 and 0.98) and relatively small standard deviations (15.49 and 5.93 W m −2 ) at the monthly timescale. Simultaneously, the derived data can describe the relationship between R dif and R dir at the annual timescale, increasing the credibility of the derived R dif and R dir from sunshine duration. Furthermore, we estimated the long-term trends of R dir and R dif , suggesting that the sensitivity drift of the pyrheliometer used to measure R dir implies an overestimation of global dimming in China before 1990. From 1958 to 1989, the new and more believable R dir decreases by −3.52 W m −2 per decade and R dif increases by 0.84 W m −2 per decade. After that, the trend in R dir does not change significantly (−0.47 W m −2 per decade, p > 0.10), but R dif shows a slight decline (−0.28 W m −2 per decade, p < 0.05). Moreover, R dir and R dif from estimated data both have steeper trends in the warm season than those in the cold season.
These regional details and seasonal differences in the R dir and R dif trends will be beneficial to advance the current understanding of variability in solar radiation and the study of plant photosynthesis and landatmosphere interaction. Actually, due to the use of local meteorological parameters to estimate R dir and R dif , the models should also be adapted to different terrain areas and climate zones around the world.

Author Contributions
K. W. conceived the study. Y. H. conducted the analysis and wrote the initial draft of the paper. All authors participated in interpreting and revising the paper.