A new view on the trend of solar radiation in mainland China — based on the optimized empirical model

As a kind of renewable energy, the development and utilization of solar energy are valued by many countries. To accurately provide a basis for the use of solar energy in mainland China, the optimized empirical model is adopted to analyze the variation trends and spatial patterns in solar radiation (SR) during 1961–2016 based on the data of 31 SR sites and 500 sunshine duration (SD) stations. The results indicate that there are obvious discrepancies in the variation trends of annual SR and SD during 1961–2016, with trend conversion occurring in 1992 (SR) and 1980 (SD), respectively. Overall, annual SR decreases at the rate of −3.68 MJ/m2·a in China. Notably, SR declines at the rate of −16.95 MJ/m2·a during 1961–1989 (“dimming” stage), while it increases at the rate of 5.34 MJ/m2·a for 1990–2016 (“brightening” period). In addition, all seasons show a tendency of dimming first and then brightening except for autumn. Compared with SD, SR is more sensitive to changes in pollution, leading to a marked recovery with the reduction of pollution after the 1990s. This study provides a new perspective for the trend difference between SR and SD after the 1990s.


Introduction
The solar radiation reaching the surface of the earth is the main energy source of the planet, provides energy for the movement of the earth's atmosphere, and is also the main source of the earth's light and heat energy (Wild 2009). Recently, in order to maintain a sustainable development strategy, all energy industries are developing toward low-carbon applications (Pazikadin et al. 2020). Photovoltaic (PV), as a clean energy source, can effectively reduce the consumption of the ozone layer by traditional energy applications and also slow down global warming (Wilberforce et al. 2019). PV generating technology has always been a concern in China. Due to the abundant solar energy, especially in the Northwest region, the application of photovoltaic technology can effectively alleviate the carbon emissions caused by fossil fuels (Gao et al. 2020;Hou et al. 2016). SR is a key factor that determines electricity produced by photovoltaic (PV) systems (Rabaia et al. 2020). Chinese mainland has a vast area, with quite different distribution of SR. Proving the distribution and changes of solar energy in China is a necessary foundation for the stable development of the PV industry (Kazaz and Adiguzel Istil 2019).
Since the 1950s, the surface solar radiation has been on a downward trend, and this trend continued until the 1980s (global dimming) (Stanhill 2005). Recent studies have shown that this "dimming" phenomenon ceased in the 1990s (Pinker et al. 2005;Wild 2005). Additionally, quantities of studies have shown that this dimming stagnation has not continued but has turned into an upward trend (Augustine and Dutton 2013; Wild 2005). The phenomenon where SR decreases first and then increases is widespread all over the world (Augustine and Dutton 2013; Wild 2005), and there is a similar trend in China (Che et al. 2005;Wang and Wild 2016). Since the 1950s, SR has been decreasing in most parts of China (Wang and Wild 2016), among which the eastern and central regions have a faster rate of decline, while a few sites in western China show an upward trend (Che et al. 2005;Tao et al. 2016). This is because marginal brightening after 1990 fails to adequately compensate for strong dimming in the 1950s-1980s . During the dimming phase, SR shows a downward trend in almost all regions of China (Wang and Wild 2016); on the contrary, in the brightening period, only the western and northeastern regions of China showed a larger upward trend (Tao et al. 2016).
However, SR stations are scarce due to high costs of installation and difficulty in maintenance of measuring instruments (Akinoǧlu and Ecevit 1990). This has led to certain differences in the conclusions drawn by researchers when analyzing SR trends, especially seasonal trends . Insufficient data length and poor site coverage have become the difficult problems in analysis of SR changes in mainland China. In order to overcome the limitations of small data volume and low coverage when analyzing solar radiation changes, the method of using other meteorological elements for auxiliary analysis has gradually been recognized . SD is defined as the amount of time when the solar disk is above the horizon and is not obscured by natural obstacles (such as clouds and fog), which is one of the oldest types of radiation measurements (Kaiser and Qian 2002). SD is considered a high-quality indicator to measure SR (Kaiser and Qian 2002).
In 1924, Angström (1924) first used the climatological relationship between SD and SR to establish an empirical model. After Prescott's optimization, the model calculation was based on total radiation instead of clear sky radiation (Prescott 1940). Since then, various variants of the Angström model have evolved, such as logarithmic model (Black et al. 1954) and power function model (Coppolino 1994). These models have been widely used in the simulation of SR around the world (Fan et al. 2019;Zhang et al. 2017). Subsequently, SR calculation models based on various meteorological elements (cloud cover (Súri et al. 2005), temperature (Hassan et al. 2016), and combined weather model ) have also been established and applied. Although these models have better performance in some areas, they also have instability due to higher data requirements . Due to the validity and reliability of the SD data measured by most weather stations in the world, the empirical model based on SD is still the most extensively used model for SR estimation (Al-Mostafa et al. 2014).
The empirical model is a linear model, and it cannot adjust itself according to changes in element relationships. Due to the instability of SR and SD since the 1950s, their changes are not the same . This different trend change among the two elements is likely to cause errors in the calculation of SR. Liu et al. (2015) find that Angström model performs best when calibrated with a 10-year dataset. We can cautiously assume that the different relationship between SR and SD affects the calculation accuracy of the empirical model. However, there is no optimization of the empirical model based on the different trends of the two elements. Therefore, the objectives of this present study are to (1) address the similarities and differences between SR and SD from 1961 to 2016 and optimize the selected empirical model based on these results; (2) calculate the SR of mainland China and analyze the temporal and spatial change trends; and (3) explore the possible reasons for similarities and differences in SR and SD.

Study area
This study is conducted over mainland China, located within 73°41′-135°02′ E and 18°10′-53°33′ N. The geography of mainland China is variable, and the topography has obvious regional differences. There are many climate types in mainland China, covering monsoon climate, continental climate, and plateau climate from east to west. The climatic conditions of each climatic zone are obviously different. Therefore, based on indicators such as heat and precipitation, combined with China's main climate types, mainland China is divided into 8 climate regions (Table 1). Figure 1 shows the geographical details of each partition.

Data
Daily SR data from 130 stations and SD data from 753 stations during January 1961 to December 2016 have been provided by the National Meteorological Information Center of the China Meteorological Administration (http://data.cma.cn). All observations provided by these stations are subject to strict quality control. The stations with continuous data and time series length of 56 years or more are selected, and those sites are deleted with continuous missing measurement for more than 2 months or total missing measurement for more than 6 months. After screening, 31 SR and 500 SD stations are retained (Fig. 1). SR sites are evenly distributed except QT region, and SD sites have a similar distribution pattern, but the density is higher. The daily air pollution index (API) data of 120 cities in mainland China from March 2001 to December 2012 are obtained from China Environmental Monitoring Center (http://www.cnemc. cn/). In this study, seasons are defined as winter (December to February), spring (March to May), summer (June to August), and autumn (September to November).

Time series analysis method
In this study, the temporal trend is analyzed by using linear trend analysis, mutation test, and significance test, and universal kriging spatial interpolation method is used to analyze spatial changes (Hu et al. 2003;Ren et al. 2017). Mann-Kendall (M-K) nonparametric test can be very effective for testing time series (Kendall 1948). In this study, the changing trend and tendency significance of SR in mainland China are presented by using M-K test. The Mann-Kendall rank statistics is a common method for testing abrupt change in time series (Sang et al. 2014). In this method, the mutation time is usually determined by the intersection of the UF and UB curves. However, this single mutation time determination method is susceptible to disturbances such as the length of the time series and the step size. Therefore, this study combines Bernaola-Galvan (B-G) segmentation algorithm (Bernaola-Galván et al. 2000), Move-t, Yamamoto, and Lepage test methods to determine the mutation time of SD in mainland China. Among them, B-G test is an excellent visual mutation test method, which can divide the interval according to the mutation time (Feng et al. 2005).

Solar radiation simulation method
Six empirical models are used in this study, combined with the measured values of SR in mainland China to verify the applicability of the model. Firstly, the extraterrestrial radiation (S 0 ) and possible daily SD (H 0 ) are calculated.
where G sc is the solar constant (=1367 W/m 2 (Duffie et al. 1991)) and k is the eccentricity correction coefficient: where n is the day of the year starting on 1 January. The magnetic declination δ and the sunset angle ω s can be calculated according to Cooper's equation (Cooper 1969): where φ is the local latitude. The possible daily SD (H 0 ) can be calculated by the following formula (Iqbal 1983): According to Formulas 1-5, the extraterrestrial radiation (S 0 ) and possible daily SD (H 0 ) can be used to simulate SR. Considering the applicability of the model, six kinds of daily   Table 2). The performance of the models is evaluated on the basis of the following statistical error tests. Coefficient of determination (R 2 ): Mean absolute bias error (MABE): where R M and R S represent simulation and measured values, respectively, and n is the total number of observations. Root mean square error (RMSE): 3 Results

Comparison of variation characteristics of SR and SD
In order to optimize the empirical model of SR, the variation trends of SR and SD are compared in mainland China from 1961 to 2016 (Fig. 2). Both SR and SD show a downward trend after 1961. The decline trend of SR stops around 1990, and then there is an obvious rebound tendency. Wang et al. (2013) and Wild et al. (2009) reached a similar conclusion. However, SD shows a decreasing trend from 1961 to 2016, and an abrupt drop in the early 1980s. This tendency also has been drawn by Chen et al. (2010). Four mutation detection methods are used to detect the mutation of two meteorological elements. The main mutation time of SR occurs in 1992 and that of SD occurs in 1980 (Table 3).
SR and SD show a decreasing trend in mainland China during 1961-2016 (Table 4), with tendency rates of −4.485 MJ/m 2 ·a and −4.018 h/a, respectively. There are significant differences in trend rate between SR and SD in different time periods (divided by the mutation time). During 1961-1979, the decreasing rate of SR is the largest in all time periods (−20.468 MJ/m 2 ·a), while SD also shows a large downward trend (−6.170 h/a). In the 1980s, SD has a sudden decline tendency, and the downward trend increases (−8.344 h/a), while the decline trend of SR in the same period slightly slows down (−13.145 MJ/m 2 ·a). After that, SR shows an obvious rising trend (7.544 MJ/m 2 ·a). In the same period, the decreasing trend of SD slows down and tends to be stable (−0.418 h/a).

Model optimization and simulation of SR
In order to ensure the reliability of the simulation results, the consistency of six empirical models is evaluated. The measured values of 31 high-quality SR stations are selected as the real values. Firstly, the coefficients of the six empirical models are determined by the relationship between the measured SR/ extraterrestrial radiation (S/S 0 ) and the measured SD/ theoretical SD (H/H 0 ). According to the coefficient determined by regression relation, coefficient and R 2 of empirical models are obtained (Table 5).
The correlation between the predicted values and measured values of the six empirical models is analyzed (Fig. 3). It can be seen that all the six models can well estimate SR value, but Akinoglu (Akinoǧlu and Ecevit 1990) Bahel (Bahel et al. 1987) Modified logarithmic   1969199219921992SD 1980198019801980 with certain differences in fitting degree and error quantity. Among the six models, cubic model shows the best correlation. In addition, cubic model has the minimum error value, followed by the quadratic and linear logarithmic model. This indicates that cubic model has the best goodness of fit. Similar conclusion has been drawn by Zhang et al. (2017) and Yao et al. (2018). Therefore, cubic model is selected for SR simulation in this study. Obvious mutations in SD and SR occur in 1980and 1992, respectively, during 1961. The trends of SD and SR have obvious discrepancies in different periods separated by two time points. Four coefficients of the cubic model per year are calculated, and the changes of each coefficient in the study period (including B-G analysis) are given, respectively, (Fig.  4). B-G test shows that four coefficients in the empirical model all have the mean mutation in 1992, and b, c, d have an obvious mean mutation in 1980. This indicates that the correlation between SR and SD changes at these two time points. Therefore, combining the trend conversion of SR (1992) and SD (1980) and the mean mutation of empirical model coefficient (1980 and 1992), we conduct segmented simulations on SR to minimize estimation errors. Figure 5 shows the comparison of the agreement between predicted and measured values in different time periods before and after model optimization. The optimized model shows better coherence in all the three time periods. During 1980-1991, the consistency significantly improves after model optimization, with RMSE significantly reduced and R 2 increased. From 1992 to 2016, the tendency of SR changes from declining to increasing, and SD changes from a significant downward trend to a stable fluctuation trend. During this period, RMSE of the optimized model is also significantly lower than that of pre-optimized model. Overall, R 2 of the optimized model increases; MABE decreases, and RMSE significantly reduces.
In order to further analyze the estimation effect of the model before and after optimization, the annual average daily SR calculated by the models is compared with the measured value (Fig. 6a). The optimized model is obviously closer to the measured value. And the optimized model performs better in showing the rapid decline in SR from the late 1970s to the early 1990s. After the 1990s, both models show an upward trend of SR, but the difference between the optimized model and the measured value is smaller (Fig. 6b). To sum up, the optimized model has higher consistency with the observed value and therefore can better reflect the dimming and brightening trend of SR. Figure 7 shows the spatial distribution of annual average SR and tendency rate over mainland China during 1961-2016 (based on simulated data). The annual average SR in mainland China is more in the southeast and less in the northwest (Fig.  7a). In eight climate regions, GX and QT regions have the highest average annual SR (7000 MJ/m 2 ), which is due to the high altitudes of the two regions and climatic reasons that lead to scarce precipitation. In contrast, the area with the shortest annual average SR is located in the west of CC, and its minimum value is less than 3500 MJ/m 2 . This is because the basin topography and circulation factors accumulated a large number of clouds, fog (Lu and Ye 2011). Frequent precipitation is the main factor for low SR in CC.

Spatial variation of SR
Over the period 1961-2016, the annual average SR in most of the mainland China showed a downward trend (Fig. 7b). Among them, NC and CC have the largest decline in SR, especially in central NC and southern CC (trend rate exceeds −12MJ/ m 2 ·a). The largest drop in SR in these two regions is related to the pollution brought by the rapid development of economy ). On the contrary, there is an increasing trend in the west of QT and CD, and there are also some areas in the middle and west of GX presenting the same trend.
Since SR seasonal distribution is similar to annual distribution with only a difference in magnitude, this study only analyzes the seasonal variation trend of SR (Fig. 8). In general, the rising trend of SR is the most obvious in spring, while the decreasing trend is the largest in summer. And the SR decline rate in all seasons in the eastern region is higher than that in the western region. The northwest of QT region shows the largest upward trend in spring, while the area with more concentrated  downward trend is NC. Besides, the tendency of SR is similar in summer, autumn, and winter, and NC is the region with the largest decline, followed by CC. QT and CD show the largest upward trend. Figure 9a shows a suspected trend mutation of SR in mainland China in the late 1980s. MK test is used to test the change in SR trend (Fig. 9b). In this method, UF line is used to indicate the changing trend of the time series (Sang et al. 2014), and its turning point indicates that the SR has a significant trend change in 1989. This result is the same with that obtained by Wang et al. (2016). According to the time of the trend transformation, SR is divided into dimming stage  and brightening stage (1990-2016)   The seasonal trend of SR in mainland China is also analyzed (Fig. 10). In the dimming phase of 1961-1989, SR of each season has a significant downward trend, all passing the p<0.05 significance test. Among them, the maximum decline rate of SR is in summer (−6.22 MJ/ m 2 ·a), followed by spring, autumn, and winter, with trend rates of −4.55, −3.04, and −2.99 MJ/m 2 ·a, respectively. During the brightening period from 1990 to 2016, the season with the most significant SR upward trend is spring (3.76 MJ/m 2 ·a), followed by winter (1.34 MJ/m 2 · a). On the contrary, the upward trend in summer is not significant, and SR in autumn still shows a downward trend after a slight rebound in the early 1990s. Similar conclusion has been drawn by Wang and Wild (2016). Table 6 analyzes the variation trend of SR in eight climate regions in 1961-2016 based on simulated values. From 1961 to 2016, SR shows a downward trend in most regions of mainland China. Among them, SR decline trend rate in NC is the largest (−8.22 MJ/m 2 ·a), followed by CC and SC, with trend rates of −5.67 and −4.74 MJ/m 2 ·a, respectively. CD is the only region with an upward trend (2.46 MJ/m 2 ·a). Due to the instability of SR (dimming and brightening), only half of the regions have passed the p<0.05 significance test. Except for NC region, SR of all regions shows a trend of decreasing first and then increasing. Therefore, the phenomenon of dimming and brightening is very common in mainland China. From 1961 to 1989, SR has a significant downward trend in each subregion. Among them, CC, SC, and NC regions have the largest decline rates, with the values of −26.20, −24.38, and −20.13 MJ/m 2 ·a, respectively. In the brightening period, SR of the seven subregions all rebounds to a certain extent with the exception of North China. Among them, CD region has the largest upward trend rate (20.68 MJ/m 2 ·a), followed by SC and GX, with trend rates of 8.78 and 8.77 MJ/m 2 ·a, respectively. North China is the only region with a downward trend in both periods, which is similar to the conclusion by Zheng et al. (2012).

Discussion
Between 1961 and 2016, both SR and SD show a different downward trend in mainland China. The trend of SR changes in the late 1980s, from decreasing to increasing, consistent with the findings of Wang et al. (2013). However, after a rapid decline in SD in the 1980s, the trend gradually stabilizes, as is also reported by Song et al. (2019) and Feng et al. (2019).
Six empirical models are verified with the measured data of 31 radiation sites as true values, among which the cubic model shows the best consistency. In addition, this study finds the limitations of the linear regression model and then proposes to optimize the model based on the trend transition points of SR and SD. After optimization, the consistency of the model is obviously improved. Before and after the trend conversion point, the correlation between the two and the regression coefficient are significantly different (Table 3 and Fig. 4).
The obvious variation of correlation is caused by the unsynchronized trends in SR and SD. Based on the optimized model, SR shows an overall downward trend in mainland  1961-1979,1980-1991,1992-2016, and 1961-2016, respectively; 1 represents the pre-optimized model and 2 is the post-optimized model. Time period segmentation by primary mutation time of SR. The color of the dots indicates the density of the dots; the red dots are the area with higher density; black line is y=x) China from 1961 to 2016, divided into the dimming stage  and the brightening stage . This trend conversion phenomenon is also pointed out by Wild (2012). From 1961 to 2016, SR decline rate is the largest in NC, followed by CC and SC. Except for autumn, all seasons show a trend of dimming first and then brightening. The degree of dimming is the greatest in winter, and the trend of rebound is the most significant in spring. Similar conclusions have been drawn by Wang and Wild (2016).
Changes in SR and SD are always related to factors such as aerosol, wind speed, and precipitation (Fei and Xia 2015;Luo et al. 2019). As an indicator closely related to aerosol optical thickness (AOD), the level of air pollution index (API) has a significant impact on SR and SD . Fiftyeight API sites are selected in mainland China from 2001 to 2012 (Table 7), which are divided into two groups for comparison (based on a median of 75). It can be seen that the annual and seasonal declines in SR and SD are greater in areas with larger API. This also explains that as the most polluted area in mainland China, NC has the most significant decline in SR. Since 1990, AOD has declined in mainland Chinese (Wang et al. 2013), as is evidenced by the API trends of 2001-2012. This is one of the important reasons for the rebound of SR and SD. Besides, the trend shift is analyzed of wind speed, precipitation, and relative humidity around 1989 (Fig. 11). Among them, the trends of wind speed before and after 1989 are significantly different, and the relative humidity has the same performance. The decline rate of wind speed slows down significantly, and an abrupt change signal is detected in the MK test in 1989. Lin et al. (2015) point out that the reduction of wind speed magnifies the weakening effect of aerosol on SR and SD. The downward trend of wind speed slows down after 1989, and there is a trend of recovery around 2010. Relative humidity is closely related to water vapor which has a certain weakening effect on SR (Yang et al. 2009). The rapid decline of relative humidity has a certain correlation with the trend of SR recovery after 1989.
In addition to similar trends, there are significant differences in the trends of SR and SD after the 1980s (Fig. 2). Explanation of this phenomenon is attempted from the different response degrees of SR and SD to pollution. Cities with API stations, SD stations, and first-class SR stations are selected as research targets (Fig. 12). The percentage difference in clear sky conditions is compared between SR and SD under light pollution conditions and under heavy pollution conditions. When the amount of diffuse radiation reaching the earth's surface is less than or equal to 25% of global radiation, the sky is termed as clear sky (Ahmad and Tiwari 2011). The results indicate that SR and SD of the days with less pollution are greater than those of the days with severe pollution in almost all stations in each season. This shows that air pollution  has a certain weakening effect on SR and SD. The heavier the air pollution, the more obvious the weakening effect. Moreover, the difference of SR under the two pollution conditions is greater, indicating that the response degree of SR to pollution may be more sensitive than SD. From the early 1990s to 2005, various pollution indicators show a downward trend in China's large cities, as reported Chan and Yao (2008), and this is consistent with the trend of API change during 2001-2012 (Fig. 11). Combined with the difference in the response degree of SR and SD to pollution, the trend difference between SR and SD after the 1990s may be due to the fact that SR is more sensitive to pollution reduction. The  decline in SR (−9.74%) from 1961 to 1989 is significantly greater than SD (−6.34%), which also proves this point of view. A possible reason for the stronger response of SR to pollution is inferred: SD meter only responds to radiation greater than 120 W/m 2 (Xia 2010). Under clear sky conditions, the weakening effect of pollution on SD only has an effect at sunrise and sunset. In contrast, the response of SR, weakened by pollution throughout the day, is more obvious.
Though the main objectives of the study have been achieved, it must be acknowledged that there are still some uncertainties in the present study. (1) Due to data limitations, it is difficult to obtain pollution data before 2000, which also makes it impossible to quantitatively explain when analyzing the common downward trend of SR and SD. (2) Although the theory proposed in this study can explain the difference between SD and SR changes well, the sudden rise in SR around 1992 is still puzzling. Based on previous studies (Feng et al. 2019), we cautiously conjecture that this sudden change may be related to the dissipation of volcanic aerosols accumulated in the atmosphere from the 1980s to the early 1990s.

Conclusion
In this study, the similarities and differences between SR and SD during 1961-2016 are explored, and the cubic empirical    and brightening stage (1990-2016). Except for autumn, all seasons shows a tendency to dimming first and then brightening. The degree of dimming is the greatest in winter and the trend of rebound is the most significant in spring. From 1961 to 2016, the decline rate of SR is the largest in NC, followed by CC and SC. Except in NC, SR shows the trend of dimming and then brightening in mainland China. NC shows a downward trend in both periods, which may be related to worse local pollution. During the brightening period, most areas show an upward trend in spring; however, only western China shows a small upward trend in autumn. The downward trend of SR and SD from 1961 to 1989 may be due to more serious pollution, while the trend changes after the 1990s are related to the stagnation of the downward trend of wind speed, pollution mitigation, and the rapid decline of relative humidity. The trend difference between SR and SD after the 1990s may result from the fact that SR is more sensitive to pollution reduction.