Introduction

Solar radiation is the ultimate energy source of the earth's climate system, which drives weather and climate change and vegetation growth1. Due to its importance, surface incident solar radiation (Rs) has been widely measured since the late 1950s. These observations have been archived by the Global Energy Balance Archive (GEBA)2. They have suggested a widespread decrease between the 1950s and 1980s (“global dimming”)2 with the subsequent brightening3,4.

Recent studies5,6 have compared the Coupled Model Intercomparison Project phase 3 (CMIP3) and phase 5 (CMIP5)7 decadal variability of simulated Rs with observations collected by GEBA over land for the last half century and have reported large discrepancies. In particular, it was found that all of the 42 models of CMIP5 underestimated the trend of the observed Rs and none of the simulations of the CMIP5 models could reproduce the magnitude of the observed dimming trend over China and India5. From these comparisons, it could be inferred that the models are seriously flawed in their determination of the decadal variability of Rs. If this is so, their reported good ability to reproduce twentieth century climate could be called into question because Rs has an important contribution to decadal variability of surface air temperature8,9,10.

In this study, we examine the decadal variability of observed Rs in China and find that the observed Rs may have overestimated the dimming rate due to the degradation problem of instruments before 1990 and overestimated the brightening rate due to instrument replacement from 1990 to 1993. When these sources of error are accounted for, the inference that there is serious disagreement between models and observations becomes much weaker.

Results

Here, we evaluate the decadal variability of the observed Rs with an independent measurement of sunshine duration (SunDu). SunDu is a conventional meteorological observation that records the time duration during a day when the direct solar beam is greater than 120 W m−2, which is defined by the world meteorological organization. The light-sensitive paper of a SunDu recorder is burned when the direct solar beam is higher than a threshold, i.e., 120 W m−2. SunDu is measured through reading the length of the burned mark during a day.

Rs can be calculated from SunDu, i.e., with the method (Eq. (1)) proposed by Yang et al.11, which has been regarded as having the capability of reflecting the impacts of clouds and aerosols on Rs accurately12,13,14,15,16,17. To apply the method globally or regionally, existing studies12,13 tried to derive a suite of parameters by calibrating the equations with the observed Rs.

However, the burning threshold depends on the types of SunDu recorders and the sitting environment, i.e., its geographical location16. To address this issue, we calibrate the Eq. (1) to estimate Rs from SunDu at each station. We find 122 stations where both Rs and SunDu were measured for more than 10 years from 1958 to 2012 (Fig. 1), from which a reliable relationship between Rs and SunDu can be established at each station (Eq. (1) of Method Section). The relationship between Rs and SunDu may vary with geo-location and types of SunDu recorders. However, this relationship is expected to be stable for a station given the same SunDu recorder has been used. Under the assumption that the relationship between Rs and SunDu is stable for a station, the calibrated equation can be used to calculate Rs from SunDu for a longer time period, as SunDu has a longer observation history than Rs16.

Figure 1
figure 1

A map of the stations (red square) where data durations of both surface incident solar radiation (Rs) and Sunshine Duration (SunDu) were longer than 120 months from 1958 to 2012.

There are 122 stations in total. The figure was produced using MATLAB.

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Fig. 2 shows scatterplots of SunDu-derived Rs as a function of the observed Rs at four stations. The biases are near zero because Eq. (1) used to estimate Rs from SunDu was calibrated with the observed Rs at each station. The statistical results of the standard deviation and correlation coefficients of all the stations are shown in Fig. 3, which shows Rs can be accurately estimated from SunDu at daily and monthly time scales. SunDu has difficulty in estimating Rs at time scales shorter than one day, as only daily SunDu was documented.

Figure 2
figure 2

Scatterplots of monthly averages of Sunshine Duration (SunDu) derived surface incident solar radiation (Rs) as a function of the observed Rs at four stations.

The biases, standard deviations and correlation coefficients of the comparisons between SunDu-derived Rs and observed Rs at the four stations are: (a): −0.3 W m−2, 12.0 W m−2, 0.99, (b) −0.6 W m−2, 12.9 W m−2, 0.98, (c) −0.8 W m−2, 12.5 W m−2, 0.98 and (d) −0.4 W m−2, 7.9 W m−2, 0.99. The biases are near zero because Eq. (1) used to calculate Rs from SunDu was calibrated at each station with the observed Rs. Four examples are shown here and the statistical results of all the stations are shown in Fig. 3. The figure was produced using MATLAB.

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Figure 3
figure 3

Histograms of the statistical parameters of the comparisons between daily and monthly observed surface incident solar radiation (Rs) and Rs derived from Sunshine Duration (SunDu).

The correlation coefficients and relative standard deviations (normalized by multi-year averages at each station) calculated from daily data are shown in panels (a) and (b) and those calculated from monthly data are shown in panels (c) and (d). As the Eq. (1) used to calculate Rs from SunDu was calibrated at each station, the biases of the comparisons are near zero and are not shown here. The medians of the correlation coefficients and the relative standard deviations between observed and calculated daily Rs are 0.89 and 17.32%, respectively and the values are 0.94 and 9.11% for monthly Rs. The figure was produced using MATLAB.

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To provide accurate decadal variability of Rs, it is necessary to regularly and properly calibrate the instruments (i.e., the pyranometers) to measure Rs. However, a world-wide radiometric reference for such a calibration was not established until the year 197918,19. Without an accurate and regular calibration, the instruments would lose their sensitivity and introduce a false dimming trend of the observed Rs3. SunDu recorders do not have this issue20 as their recording material, the light-sensitive paper, is replaced every day. Fig. 4 shows that there were obvious instrument degradation problems for the observed Rs at the four stations in the Tibetan Plateau, while the SunDu-derived Rs were more stable and more homogeneous.

Figure 4
figure 4

Time series of 12-month smoothed monthly anomalies of observed surface incident solar radiation (Rs) and Rs calculated from Sunshine Duration (SunDu) at four stations in the Tibetan Plateau.

Observations of Rs are impacted by the performance of instruments (pyrheliometer and pyranometers). These instruments should be accurately and regularly calibrated. Otherwise, they would lose their sensitivity and produce a spurious dimming trend of Rs. On the contrary, the measurements of SunDu are much less sensitive to instrument calibration, as its recording material is replaced each day. There is significant evidence that the instruments used to measure Rs at these four stations had important calibration problems before 1992 when the new instruments were deployed. The figure was produced using MATLAB.

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These instrument degradation issues were very common for the Rs measurements in China before 1990. Fig. 5 shows that trends of Rs from observations are substantially more negative than those of the SunDu-derived Rs from 1960 to 1989. There are four stations where the observed Rs had a near-zero trend while SunDu-derived Rs had significant positive or negative trends. Fig. 6 shows that this is because the instruments used to measure Rs were inaccurately calibrated at the stations at certain years.

Figure 5
figure 5

Scatterplot of the linear trends of observed Rs as a function of trends of SunDu-derived Rs.

Each red star represents a station in China where the data duration of both the observed and calculated Rs were longer than 120 months during 1960 to 1989. There are 76 stations in total. Linear trends of observed surface incident solar radiation (Rs) are significantly more negative than those from sunshine duration (SunDu) derived Rs. The figure was produced using MATLAB.

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Figure 6
figure 6

Time series of observed surface incident solar radiation (Rs) and Rs calculated from Sunshine Duration (SunDu) at four stations where the observed Rs showed a near-zero trend while SunDu-derived Rs had significant positive or negative trends (see Fig. 5).

It is obvious that the instruments used to measure Rs were inaccurately calibrated at the DaLian station in the early 1970s and the early 1990s, YanTai station in the late 1960s and ChamDo station in the late 1980s to the early 1990s. At these stations, the trends of SunDu-derived Rs are more reliable than those of observed Rs. The figure was produced using MATLAB.

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Figs. 4–6 indicate that the lack of calibration or inaccurate calibration made the observed Rs values highly uncertain. Fig. 7 further shows that measurement biases may explain the discrepancies between the observed and simulated decadal variability of Rs. The linear trend of the observed Rs averaged over China from 1960 to 1989 was −8.5 W m−2 per decade, with a 95% confidence interval from −9.8 W m−2 per decade to −7.3 W m−2 per decade. None of the 48 Earth System Models of CMIP5 (CMIP5 ESM)7,21 reproduced the observed trend (Fig. 7).

Figure 7
figure 7

Histogram of the linear trends of surface incident solar radiation (Rs, blue bars) over China from 1960 to 1989 simulated by 48 CMIP5 models (see Ma et al.21 for details of these models).

None of the models reproduced the observed trend of −8.5 W m−2 per decade (thick red line, with the red box showing its 95% confidence interval) based on the raw data of Rs observations. However, some CMIP5 models, including NASA Goddard Institute for Space Studies (GISS) models, National Center for Atmospheric Research (NCAR) Community Earth System Models (CESM-CAM5) and Centre National de Recherches Meteorologiques Climate Model 5 (CNRM-CM5), reproduced our new estimates of the trend based on Sunshine Duration (SunDu) derived Rs, −2.8 W m−2 per decade (thick green line, with the green box showing its 95% confidence interval). The figure was produced using MATLAB.

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However, many high-quality CMIP5 ESMs reproduced the trend of SunDu-derived Rs very well. The linear trend of the SunDu-derived Rs averaged over China during the same period was −2.8 W m−2 per decade, with a 95% confidence interval from −3.7 W m−2 per decade to −1.9 W m−2 per decade (Fig. 7). The Rs from NASA Goddard Institute for Space Studies (GISS) models show the best agreement with the SunDu-derived values. The four versions of GISS ESM simulated an average trend of Rs by −2.8 W m−2 per decade. Other CMIP5 ESMs, including the Centre National de Recherches Meteorologiques Climate Model 5 (CNRM-CM5-2, −2.9 W m−2 per decade) and National Center for Atmospheric Research (NCAR) Community Earth System Models (CESM1-CAM5-1-FV2, −2.4 W m−2 per decade and CESM1-CAM5, −2.0 W m−2 per decade), also had consistent simulations of Rs trend with SunDu-derived Rs. However, the interannual variability of Rs of CMIP5 is much less than those from the observed Rs and SunDu derived Rs because the models have difficulty in simulating variability of clouds22.

It has been shown that aerosol is the dominating factor for the dimming of Rs in China from 1960 to 199023,24 although cloud has been believed to be the key factor for the decadal variability of Rs in the U.S.25,26 and India27 during recent decades. A recent study has shown that the CMIP5 models perform significantly different in simulating atmospheric aerosols over India28. This is because the atmospheric aerosol loading was interactively calculated by each individual model10, although the same emission inventory29,30,31,32 was used for all of the CMIP5 models7. Our results show that the GISS models perform best, which is partly because the GISS model team has made great effort in simulating aerosols33,34,35,36.

Fig. 8 shows that the agreement of the long-term trends between SunDu-derived Rs and CMIP5 simulations is significantly better than those between observations and CMIP5 simulations over China from 1960 to 1989. The brightening rate of the measured Rs was impaired by instrument replacement between 1990 and 199313, as shown in Fig. 4. The observations of diurnal temperature range8,37 confirmed that the observed brightening from 1990 to 1993 was not real. The observed increase in Rs is inconsistent with the observed increase in stratospheric aerosols because of Pinatubo volcano eruption in 199138 either. After 1995, variability of the three estimates of Rs from the observations, the SunDu and the CMIP5 model simulations agreed well because issues of the instruments used to measure Rs had been eliminated. During this period, the impact of increased aerosols on Rs39 has been offset by the decreasing cloud cover fraction13 and in turn Rs kept near constant.

Figure 8
figure 8

Time series of observed surface incident solar radiation (Rs, in red), Rs calculated from Sunshine Duration (SunDu, in green) and Rs simulated by CMIP5 GISS (in blue) averaged over China.

The observed Rs overestimated the dimming trend from 1960 to 1989. The instrument replacement in China from 1990 to 1993 resulted in an abrupt increase to the observed Rs. The agreement of the long-term trends of Rs between sunshine duration (SunDu) derived Rs and CMIP5 NASA Goddard Institute for Space Studies (GISS) model simulations (averaged from four different model versions) is much better than those between observations and CMIP5 simulations. After 1995, variability of the three estimates of Rs from the observations, the SunDu and the CMIP5 model simulations agreed well because issues of the instruments used to measure Rs had been eliminated. The figure was produced using MATLAB.

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Discussion

The overestimation of the dimming trend of the observed Rs over China has been corroborated by independent studies on clouds and aerosols. Observed Rs was reported to have decreased by 21 W m−2 in eastern China from 1961 to 199040, with changes in aerosols regarded as the primary reason for this dimming trend13,41. Changes in cloud cover showed a decreasing trend41, implying an increasing trend of Rs. The aerosol optical depth (AOD, vertical integration of optical extinction) over the same region during the same time has increased by 0.1642. Analyses have shown that Rs under clear sky conditions decreases by 8 Wm−2 in the winter seasons or 9 Wm−2 in the summer seasons for an AOD increase of 0.1 over China43. The change in AOD can explain at most a reduction of 1.6 × 9 = 14.4 Wm−2 of Rs, which is approximately two-thirds of the observed value, but probably considerably less because of masking by clouds. This is confirmed by the SunDu-derived Rs, which showed a decrease of 8.4 W m−2 during the period.

Globally distributed DTR observations show that since 1985, brightening was only significant over Europe and there was a lack of brightening over other continents8. Furthermore, AOD derived from visibility observations has increased globally since 1973 except for Europe39. This explains why the CMIP5 ESM could only reproduce the observed brightening over Europe5.

The inhomogeneity of observed Rs caused by inaccurate instrument calibration also impacted the observed Rs over Europe before 1990. A homogeneity test was applied to Rs measurements at 56 stations over Europe where at least 30 years of data of Rs were available at each station44. Sixteen of the 56 series (28.6% of the total) were found to be inhomogeneous44. After these datasets were appropriately adjusted, the dimming trend over Europe from 1961 to 1984 became −2.0 W m−2 per decade, substantially less than the −3.1 W m−2 per decade derived from raw data of the observed Rs45.

Methods

Sunshine Duration (SunDu) records the time during a day that the direct solar beam irradiance exceeds 120 Wm−2. It was initiated 150 years ago and is one of the oldest and most robust measurements related to radiation3. Measurement of SunDu is insensitive to instrument calibration as its recording material is replaced each day.

SunDu has long been used to estimate Rs and the earliest and most popular methods are those developed by Ångström46 and subsequently modified by Prescott47, which assumed a linear relationship between relative Rs and SunDu. Yang et al. proposed a revised Ångström-Prescott to estimate daily mean Rs from SunDu11:

where n is the measured SunDu; N is the theoretical values of SunDu and Rc is the daily solar radiation at the surface under clear-sky conditions:

where Rcb is the daily mean direct solar radiation at the surface, Rcd is the daily mean diffuse solar radiation at the surface, I0 is the solar radiation at the extraterrestrial level, is the atmospheric transmittance for direct solar radiation, is the atmospheric transmittance for diffuse solar radiation, h(rad) is the altitude angle of sun and t(s) is the time. The atmospheric transmittances and depend on Rayleigh scattering, aerosol extinction, ozone absorption, water vapor absorption and permanent gas absorption. Rayleigh scattering and water vapor absorption can be calculated from surface meteorological observations and ozone and permanent gas absorption can be calculated using their climatological values. In the calculation of aerosol extinction, winter- and summer-averaged aerosols based on Hess et al.48 were included but the inter-annual variation of aerosols was not incorporated. Please refer to reference 11 for detailed information of the calculations.

The calculation of Rc does not include time varying aerosols because SunDu is impacted by changes in both clouds and aerosols. Direct solar radiation is generally lower than 120 W m−2 for scattered clouds (cumulus, stratocumulus)20. High and thin cirrus, as well as aerosols can reduce SunDu at low solar elevations, i.e., at times when the incident clear sky solar radiation is not much larger than 120 W m−2. Recent studies confirmed such an inference and have shown that SunDu can accurately reflect the impact of change of aerosols and clouds on Rs12,13,14,15,16,17 at time scales ranging from daily to decadal.

The parameters of Eq. (1), namely a0, a1 and a2, can be obtained by tuning this equation with measurements of Rs and SunDu. In the existing studies, a suite of parameters are derived by calibrating Eq. (1) and then the method is applied regionally or globally12,13. This may limit the accuracy of the Rs estimates. In contrast, in this study, we calibrate Eq. (1) at each station in China where both Rs and SunDu observations were available at more than 10 years. We then apply Eq. (1) to calculate Rs from 1958 to 2012 at each station when observations of SunDu were available. Figs. 2–3 show that Rs can be calculated accurately from SunDu data at daily and monthly time scales. These two estimates of Rs allow us to investigate the homogeneity of these two estimates, which are shown in Figs. 4–8. In this study, we show that the Rs decreased at a rate of −2.8 W m−2 per decade from 1960 to 1989 over the 76 stations where both the observed Rs and SunDu were available at more than 120 months during the study period. In a previous study, Tang et al.12 calculated Rs from SunDu with a suite of parameters of Eq. (1) for 716 weather stations in China and estimated an averaged trend of −2.3 W m−2 per decade from 1961 to 2000, which is a little weaker than our current estimate because Rs stopped decreasing after 1990 (Fig. 8).

In this study, we propose to combine the advantages of the observations of Rs and SunDu. The observed Rs can accurately quantify the variation of Rs in higher temporal resolution, i.e., hourly and daily. However, it is impaired by the sensitivity drift of its measurement instruments. This limits its usage in climatic study. The SunDu is nearly free from the sensitivity drift problem. We use the observed Rs to calibrate Eq. (1) used to estimate Rs from SunDu at each station. This makes up the disadvantages of SunDu: (1) SunDu does not directly provide an estimate of Rs, (2) threshold of a SunDu recorder changes with recorder types and their sitting environment. In this paper, we show that the SunDu-derived Rs has an advantage of long-term stability and can be used to climatic studies, i.e., to evaluate climate model simulations, which only require estimates of Rs at coarse time resolution (monthly or annually). However, SunDu has difficulty in estimating Rs at time scales shorter than daily.