Temporal variation in UVB
Figure 1 shows the seasonal variation of UVB in Beijing from November 2010 to October 2011. The values of UVB began increasing in the spring, and the maximum values appeared during the summer due to the small zenith angle. Conversely, UVB began decreasing in autumn and reached its lowest value in winter, in conjunction with the increasing zenith angle. The seasonal variability in UVB was similar to that of G. The seasonal fluctuation of UVB and G was largely regulated by the trend in the variability in the solar zenith angle. The maximum daily value of UVB was observed in April and August when the zenith angle was small, and the minimum was observed in December. The average SZA in summer and winter was 69.8° and 51.5° respectively. The monthly average of daily total UVB ranged from 4.69 to 28.37 kJ m−2 d−1, with an annual average value of 6.13 kJ m−2. The maximum daily total UVB for each month ranged from 6.52 kJ m−2 d−1 in November to 54.22 kJ m−2 d−1 in July. The monthly minimum of daily total UVB varied from 0.5 kJ m−2 d−1 in February to 11.52 kJ m−2 d−1 in July.
The ranges of maximum and minimum UVB radiation were the same as those measured at the Valladolid station (40°40′N, 4°50′W, 840 m a.s.l.) in Spain, which located in a wide-open area, 40 km northwest of Valladolid city. The climate characteristics and observation environment of Valladolid station were similar to those of Beijing station. However, the annual average value of UVB was smaller than that of the Valladolid station with a measured value of 7.04 MJ m−2 . This result may be partially explained by the higher ozone column concentration and fine aerosol particle loading in Beijing than those in Valladolid . As we know, the amount of UVB received at the earth's surface is predominantly influenced by the solar zenith angle, then the concentration of the total ozone column, aerosol loading and cloud cover in the atmosphere. The difference in the variation in the solar zenith angle between Beijing and Valladolid was very small due to the similar altitudes of these two observation sites. The difference in solar radiation flux was only about 0.45% that caused by the difference in latitude of these two sites. Consequently, the difference in UVB radiation between these two observation sites was probably attributed to the differences in the amount of ozone and aerosol loadings. The annual ozone average in Beijing was calculated from TOMS data. The difference in the amount of ozone between these two sites was small with the annual averages of 344 and 338 DU in Beijing and Valladolid respectively. The effect of aerosols on UVB radiation was mainly caused by scattering and absorption processes—and can be amplified with higher concentration of aerosols that results in more abatement of UVB radiation in the optical path [20, 21]. The concentration level of aerosol particles was higher in Beijing than that in Valladolid. At Beijing, the annual average aerosol optical depth (AOD) at 380 nm and the Angstrom wavelength exponent (α) were 0.75 and 1.48, respectively, whereas at Valladolid, they were only 0.4 and 0.6 respectively. The AOD in Beijing was twice higher as that of Valladolid. Meanwhile, the aerosol in Beijing was finer with higher extinction efficiencies than those in Valladolid, causing more intensive scattering effect on UVB radiation and resulting in lower UVB radiation values in Beijing.
The monthly statistics for UVB radiation in Beijing is presented in box plots in Fig. 2. There was significant monthly variation in UVB radiation levels. The monthly UVB radiation level increased gradually from December to June and then gradually decreased. The pattern of seasonal variation in UVB was the same as that of UV radiation (16). It showed an increasing trend in the spring and a decreasing trend in the autumn, until reached its winter minimum.
Figure 2. Distributions of UVB radiant exposure at different months in Beijing station. In each box, the central bar is the median, and the lower and upper limits are the maximum and minimum respectively.
Download figure to PowerPoint
The statistical properties of the monthly averages of daily total UVB radiation are presented in Table 1. The following statistics was evaluated: the arithmetic mean, M; median, Md; standard deviation, SD; maximum, Mx; minimum, Mn; 5th and 95th percentiles, P5 and P95, respectively; first and third quartile, Q1 and Q3, respectively; interquartile range, Q1 − Q3 and the coefficient of quartile variation, V, which is defined by the following expression:
. These parameters are the most common statistical parameters used to evaluate the variability in solar radiation.
Table 1. The statistical results of monthly daily UVB (kJ m−2) in Beijing
| ||M||SD||Mx||Mn||Md|| Q 1 || Q 3 ||Q3 − Q1|| V ||P95||P5|
In general, the UVB radiation showed a symmetrical variation around the month of June, when radiation reached its peak. However, the decreasing trend showed some differences in spring and autumn. The amounts of UVB radiation in September and October were evidently higher than that in March and February. This asymmetrical variation was probably attributed to the different reduction in ozone loading during these two periods. Usually, the highest value of stratospheric ozone occurs in April, and the lowest value appears in November in the Northern Hemisphere.
The median values of UVB radiation were close to the averages except during the summer season, which indicated that the distribution of UVB values was relatively uniform in each month in most time of the year. The lower median values in July and August were mainly attributed to the increased cloudy or rainy days in these months that lead to more low UVB radiation appeared in this period. In Beijing area, most rainfall in the year is concentrated in these 2 months. The differences between the P5 percentile and the minimum values were quite large. In some cases, P5 or the first quartile was up to 300% higher than the minima. The abnormally low values of the minima could be due to overcast skies. The maximum values of UVB radiation varied from 6.55 kJ m−2 in November to 54.22 kJ m−2 in June. The differences in monthly maximum UVB values were greater than the average values. The differences in UVB radiation between the maximum values and the P95 percentile or the third quartile were generally fairly small. These results indicate that the maximum values can represent the variation properties of UVB radiation characteristics.
Relation between UVB radiation and G
Figure 3 shows the linear regression results for daily UVB radiation and G. There was a high correlation between UVB radiation and G, which indicated that one of these two solar parameters can be estimated from the other. In other words, UVB radiation can be calculated from more routinely measured data for G based on linear regression equation. Bilbao and Miguel  reported that the root mean square error and mean bias error of linear regressions between estimated and measured UVB radiation were 9.18% and 2.16% respectively.
To obtain more UVB radiation data, many other studies have addressed R and developed an empirical estimation model for estimation UVB radiation based on the variability in R [8, 20]. At the top of the atmosphere there is negligible variability in UVB and G, so the R can be treated as a constant parameter. The value of UVB radiation at the top of the atmosphere can be integrated from the spectral solar values provide by Bilbao and Miguel . The constant for UVB radiation and G at the top of atmosphere is 10.3 Wm−2  and 1367 Wm−2 respectively (23). Thus, only 0.75% of the total solar spectrum is UVB radiation at the top of the atmosphere. The atmospheric attenuation factors are solely responsible for the variability in R at the earth's surface.
The daily mean R values are shown in Fig. 4. There was an obvious seasonal trend of R in Beijing. R increased in the spring, reached its maximum in summer and then decreased gradually, arrived at its minimum in the winter.
The monthly average R ranged from 0.007% in December to 0.017% in July, with an annual average of 0.012%. This seasonal variability was similar as that of UVB radiation. However, there were still some differences between seasonal variations in R and UVB radiation. For example, the maximum of R 0.024% appeared in July, which was 1 month later than the maximum of UVB radiation occurred. This seasonal feature of R may be influenced by the variation of water vapor content, which is predominantly controlled by the East Asian monsoon. The southeast wind coming from the Pacific Ocean carries water vapor to mainland China in spring and generally reaches its maximum in summer. Beginning in August, the winds decrease as the monsoon withdraws. There seasonal variation characteristic of water vapor content was similar to that of R . Long-wave radiation can preferentially absorb water vapor, leaving a shorter solar spectrum UVB radiation unchanged and resulting in a higher R during periods with higher water vapor content.
The annual mean R value was only 0.012% in Beijing, significantly lower than R at top of atmosphere. At that location, more than 90% of R was abated during atmospheric transmission processes. The annual average R in Beijing was smaller than that in Valladolid, with a value of 0.017% . The difference in R between the Beijing and Valladolid sites was probably caused by the high fine aerosol particle load and low humidity in Beijing. The influence of aerosols on UVB radiation is caused by scattering and absorption effects, which depends on the size distribution of aerosol particles. Fine particles cause short-wave radiation to be preferentially scattered. The higher load of fine aerosol particles made selective scattering much stronger in Beijing. Conversely, the relative humidity was lower in Beijing, which reduced the absorption effect on long-wave radiation. Therefore, the enhanced attenuation of short-wave radiation, including UVB radiation, and the weaker attenuation of long-wave radiation created a lower R in Beijing.
Influence of ozone on R
The spatiotemporal characteristics of UVB radiation and G can be influenced by many parameters such as the ozone column, clouds and aerosol due to these parameters have significant spatiotemporal variability characteristics. Consequently, the value of R has a large spatiotemporal variability. In this section, the effect of the ozone column and clouds on the variation of R are discussed in detail.
The ozone column near noon can be calculated from the TOMS instrument. To discuss the effect of the ozone column on R, the average measured UVB radiation and G between 1100 and 1300 h (true solar time) were considered to be the daily average values.
The length of the optical path of total ozone is the primary factor attenuating solar radiation, especially in the shorter wavelength UVB radiation. The length of the optical path of total ozone is defined as the slant ozone column (Os), and this parameter is calculated using the following equation:
where μ is the average value of the cosine of the solar zenith angle from 1100 to 1300 h, Os is the slant ozone column and TOC is the total ozone column from TOMS.
From Fig. 5, it is apparent that the seasonal variability in the slant ozone column was opposite to the seasonal variability in R. There was an evident inverse correlation between the slant ozone column and R. The maximum value of the slant ozone column appeared in December and then decreased gradually until it reached its lowest value in July. The monthly mean value of noon R ranged from 0.0081 ± 0.0001% (December) to 0.0208 ± 0.005% (August) in Beijing. This variability in the slant ozone column and noon R was similar to that of the Cáceres station and Plasencia in Spain. From Figs. 4 and 5, it is apparent that the high R values appeared during the summer, which may be largely attributable to the low slant ozone values during this season.
In Figs. 4 and 5, the seasonal variability in R followed the same pattern as the solar elevation angle. The values of the slant ozone column and aerosol loading were lower in the summer than in the winter.
The variation characteristics of UVB radiation and R may lead scientists to pay more attention to predicting summer UVB radiation levels to advise people on how to protect themselves against UVB radiation overexposure.
Influence of the clearness index on R
As previously mentioned, cloud cover is another notable factor that attenuates UVB radiation. The dependence of UVB radiation on clouds is investigated in this section. Unfortunately, direct measures of cloud cover are scarce in Beijing, so a clearness index was used instead of cloud cover. The clearness index is defined as the ratio of G to extraterrestrial radiation at the same geographical coordinates. In theory, the variability in the field clearness index is usually used to characterize the cloud variation. The clearness index can be considered an indicator of scattering and absorption processes caused by aerosols, gases and clouds. The clearness index can also be used to indicate the interruption of the transmission of solar radiation through the atmosphere [25, 26].
To be consistent with the ozone column data, the average of the clearness index between 1100 and 1300 h was used instead of the daily clearness index. The classification of the sky condition followed the results of Alados . The sky condition was classified into three types: overcast (0.02 ≤ Ks ≤ 0.35), intermediate (0.35 < Ks ≤ 0.7) and clear (0.70 < Ks ≤ 1.0).
Figure 6 shows the variability in UVB radiation and G under different sky conditions based on an hourly data set. The highest value of R (0.0212) appeared with clear sky conditions, and the lowest value of R (0.0175) appeared with cloudy sky conditions. The value of R with intermediate sky conditions fell between those with clear and cloudy sky conditions. R decreased by ca 17% when the sky condition changed from clear to cloudy. This result indicated that the effect of clouds on UVB radiation and G due to the strong extinction properties of clouds on solar radiation, such as cloud location, percent cover and cloud optical thickness. The influence of clouds on UVB radiation and R will be studied in future works.