Equivalent optical depths of a standard continental aerosol model are defined as the indexes for atmospheric optical depths of absorption and scattering (ODA and ODS, respectively) under clear-sky condition and can be calculated with the routinely observed data of broadband surface solar irradiances. The ODS by definition is a proxy of the scattering component of atmospheric aerosol optical depth (AOD) and is shown to be largely free from influences of systematic errors of the radiation observing instruments and uncertainties in atmospheric absorption. The ODA accounts for contributions of aerosols, water vapor, and other gases with profiles deviating from the standard atmosphere model. Applied to the data from 36 observatories of China, from 1957 to 2007, the method provides the long-term variations of clear-sky atmospheric absorption and scattering, which are qualitatively compared with other AOD estimations with comparable regional and temporal coverage. The results show the method reasonably separates the absorption and scattering effects and captures the general features of their seasonal variation. The radiation dimming trend over China region during about 1970–1990 is shown to be associated with the increasing ODA and ODS. After 1990, there is not a significant trend in ODS but the ODA has been slightly decreased.
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 While the possible mechanisms of the trends are still to be understood, they must have functioned ultimately by affecting the atmospheric properties of absorption and scattering. The absorption and scattering of the atmosphere can force the climate system in different ways, especially through their differing effects on the vertical profile of the atmospheric heating rates, which require more comprehensive quantification of the radiative forcing [Forster et al., 2007]. Myhre  has reported the relative contribution of the aerosol absorption to the total aerosol extinction has been increasing globally since the pre-industrial era.
 For cloud-free condition, the downward diffused solar radiation is mainly contributed by the Rayleigh scattering of the atmospheric molecules, and by aerosols. The column integrated effect of molecular scattering is essentially determined by the surface pressure or atmospheric mass and can be assumed to be without significant long-term trends. The absorption of the atmosphere for cloud-free sky is contributed by aerosols and gases such as water vapor, ozone, carbon dioxide, etc., which are expected with both long-term and short-term variations. The scattering effect mainly contributed by aerosols and the combined absorbing effect by aerosols and other absorbers in principle can be diagnosed with the surface radiation data.
Qiu  has devised a method to determine atmospheric aerosol optical depth (AOD) using total direct solar radiation and applied the method to five observatories of China [Qiu and Yang, 2000]. After this method, Luo et al.  have estimated the AOD at 750 nm over China from 1961 to 1990, using the daily direct radiation data and the data of surface pressure, water vapor pressure and total ozone amount to account for the effects of the Rayleigh scattering and the absorbing gases. The advantage of using the routine observatory data is that it can make use of the data accumulated during the past decades when the satellite data and the other spectral radiation data were not available. Without the spectral information, however, aerosol size distribution or spectral properties have to be assumed. The absorption and scattering effects of the AODs cannot be verified with the pure extinction analysis.
 In this study, a set of indices of atmospheric absorption and scattering, defined as equivalent optical depths of a standard aerosol model, are calculated from the routine surface observations of solar direct and diffuse irradiances for the past 51 years (1957–2007) to provide a semiquantified reference for further studies of atmospheric radiative agents and the long-term trends of absorption and scattering over continental area of China. It should be noted that the indices, while defined with optical depth of aerosol, are indeed influenced by variations in aerosol as well as in all other radiative agents, though the scattering indices can be seen later to be a good proxy of aerosol scattering optical depth. In sections 2–5, the data set and the method adopted in the calculation are introduced; the results are described and compared with those of other works about aerosol optical depths (AODs) based on the similar data set but different methods; the limits and advantages of the method of this work are briefly discussed; finally the implications of the results are discussed.
2. Data and Method
 The data of daily solar radiation (DSR), defined as the temporal integration of surface downward solar irradiance during daytime (i.e., from local sunrise to sunset), are from the Meteorological Information Center of Chinese Meteorological Administration (MIC/CMA). Among the 753 observatories conducted by CMA, 122 observatories measure global solar radiation and 78 of them record direct and/or diffuse irradiances in addition. In most cases, only the diffuse irradiance is observed independently with the same type of pyranometer as the global irradiance, but with a shadow ring to screen out the direct beam. The portion of the diffuse irradiance blocked out by the shadow ring is routinely accounted with a set of empirical calibrating coefficients, which is obtained from comparisons with the more refined instruments (with a shadow ball instead of ring) and are well tabulated as functions of sites and the ordinal date. The calibrating coefficients therefore implicitly account for the effects of solar zenith angle and climatological scattering conditions (such as clouds and aerosols) for each sites. A comprehensive introduction to the instrumentation and in-depth quality assessment of the data set can be seen in the previous work [Shi et al., 2008].
 With the CMA data set, this work evaluates the atmospheric absorption and scattering and their long-term variations with a couple of indices, namely, the clear-sky atmospheric optical depths of absorption and scattering (ODA and ODS, respectively), defined as the respective optical depth components (absorption and scattering) of typical continental aerosol model that equivalently reproduce the three components of DSR. With the Rayleigh scattering effect taken into account, the ODS is in fact an equivalent scattering optical depth of atmospheric aerosols (i.e., the product of optical depth and single scattering albedos).
 The method is essentially interpolation of the observed (global, direct, and diffuse) DSRs to the precalculated look-up tables (LUTs) that relate the DSRs to the absorption and scattering indices of the atmosphere. The values of DSRs in the LUTs are calculated with a set of optical depths of scattering and absorption (i.e., ODSs and ODAs) of a standard aerosol model as well as the optical depths of atmospheric molecule scattering and absorption of dry air (contributed by O2, O3, and CO2 with climatological concentrations defined in the middle latitude model atmospheres [McClatchey et al., 1972]), and latitude, date and surface albedos for each observatory. The air masses for Rayleigh scattering calculations are estimated with the altitude data of the observatories.
 To facilitate the intercomparison between the sites, a uniform aerosol model is required to calculate the LUTs for all of the sites. The vertical profile and spectrum of the aerosol extinction and the asymmetry factor used here are after the continental model (CONT-I) of the Standard Radiation Atmosphere [Deepak and Gerber, 1983], and the single scattering albedos are prescribed according to the set of ODSs and ODAs in the LUTs. The CONT-I model, by its definition, is supposed to represent the average background condition of the global continental areas; therefore, it is a literally default choice when there is not any other data about aerosol optical properties available for such scales of space and time. Therefore the dimensions of the LUTs are in practice the global, direct, and diffuse DSRs versus ODA and ODS (specifically, the 0.55 micron optical depths of the CONT-I aerosol).
 The radiation transfer model used here is a delta-Eddington two-stream scheme for the absorbing and multiple scattering effects of atmospheric molecules, aerosols, and clouds, as well as the absorption effect of atmospheric gases represented with a k-distribution scheme. The model has been used in previous works about a general circulation model [Wang et al., 2000] and a conceptual climate model [Wang et al., 2008]. Since delta-scaling treatment in the scheme tends to exaggerate the direct beam, only the calculated global irradiance is kept in the results, while the direct irradiance has been recalculated with the exponential extinction formula and the same radiative agents as in the preceding calculations, so has the diffuse irradiance, as the difference between the global and the recalculated direct irradiance.
 The observed DSR data are processed through the following steps. First, all the observed data of DSRs are normalized with respective values of global DSRs calculated by the radiation transfer model that take account the absorption and scattering of dry air, surface reflectance, and the solar zenith angles during local daytime as a function of time and latitude. The normalization removes the regular annual cycle component arising from the variations of solar zenith angle from the DSR data so that the values of normalized DSRs of different dates reveal their relative extinction levels. The cloud-free days are selected then as the days with the highest direct DSRs for any consecutive 30 day period.
 The selected direct and diffuse DSRs for clear-sky condition are then interpolated against the LUTs to get the ODA and ODS indexes with the algorithm developed by Renka  that implements bivariate interpolation of scattered data.
 Among the 78 observatories, only 46 series are longer than 30 years and are processed as for the long-term variation study. However, 7 series from the 3 provinces to the southwest of China (i.e., Sichuan, Guizhou, and Yunnan) have been ignored for these areas are usually heavily cloudy so that the clear-sky condition cannot be guaranteed even with the 30 day criterion; 3 observatories from the Tibet areas (Lhasa, Qamdo, and Xining) have been excluded too because the data quality had been shown to be quite problematic for a substantial period in the previous study [Shi et al., 2008].
 The results for the adopted observatories with their locations, the available durations of the data, the mean optical depth levels, and the decadal linear trends are summarized in Table 1.
Table 1. List of the Sites Used in This Work, With Their Location, Lengths of Data Series, and the Mean Values and the Decadal Trends of ODA and ODS Results
Series Length (years)
The correlation with confidence level higher than 99%.
 Most of the sites show significant positive trends in the indices. For the ODS, the most significant sites (with trends greater than 0.1/decade) include Guangzhou, Hefei, Xian, Jinan, Taiyuan, Yichang, Houma, Ganzhou, Zhengzhou, Wuhan, Shantou, Fuzhou, Nanchang, in the descending order of the ODS. For the ODA, the most significant sites are Nanchang, Hefei, Jinan, Datong, Taiyuan. Most of them are the well-known industrial urban sites located in the middle east part of China. However, a few sites, mostly remote ones, do show no significant trends in both of the indices, including Erenhot, Yining, Minqin, Heihe, and Haiko. Among the 10 sites with records until 2007 (i.e., the top 10 in Table 1), most show the trends of the indices in agreement with the dimming and brightening radiation data before and after about 1990; several exceptions seem to be the ODA of Kashi, Golmud, and Harbin, and ODS of Zhengzhou, which have been increasing since 1990.
 The optical depths for the atmospheric absorption (ODAs) exhibit regular seasonal variation with a peak in summer and a minimum in winter (Figures 1a–1c), which is expected as the absorption is contributed mostly by water vapor. In contrast, the seasonal variation of the scattering optical depths (ODSs) shows site-specific features. The ODS's maxima occur in the spring (from February to May) for the remote sites of western China, such as Altay, Dunhuang, Golmud, Hame, Heihe, Hotan, Minqin, Rouqiang, Xi'an, Yining, etc., with the influence of dust weather widespread over those areas during spring seasons (Figure 1a). The data from urban sites of eastern China usually show comparable, if not higher, summer or autumn ODS peaks beside the spring ones, including Beijing, Changchun, Datong, Fuzhou, Ganzhou, Guangzhou, Haikou, Harbin, Hefei, Jiamusi, Jinan, Nanchang, Shanghai, Shantou, Shenyang, Taiyuan, Tianjin, Wuhan, Zhengzhou, etc., suggesting significant anthropogenic polluting sources (Figure 1b). A few of sites show ODS maxima during winter, such as Kashi, Lanzhou, Turpan, and Urumqi, where are all notably basin areas or surrounded by mountains with local pollutants dominating the atmospheric turbidity (Figure 1c). Almost all of the sites referred in Table 1 can be classified into the three groups.
Figure 2 illustrates the variation of the averaged ODA and ODS over all sites from 1957 to 2007. It can be seen that the ODS curve has clearly captured the influences of the two major volcanic eruptions: El Chichón (1982) and Pinatubo (1991) [Deshler, 2008], in contrast with the ODA curve, as expected that the volcanic aerosols essentially consist of sulfate particles and contribute much less to the atmospheric absorption than to the scattering. The reason for the much higher pikes of the ODS index than other observed AODs [e.g., Sato et al., 1993] is likely due to the much higher elevation and scattering efficiency of the stratospheric aerosols than those of the tropospheric aerosol model used here. On the other hand, the finer particle size spectrum of the CONT-I model (than that of general volcanic aerosols) may lead to the exaggerated results of the 0.55 micron optical depth.
 Also illustrated in Figure 2 is the AODs at 0.75 micron averaged for 46 sites of China from 1961 to 1990 estimated by Luo et al.  and AODs at 0.55 micron averaged for 31 urban sites of China from 1961 to 2007 derived from horizontal visibility data by Qin et al. . Despite the different definitions, methods, and sites selection, the curves of ODS and the AOD show reasonably similar long-term trends of overall increase and interannual variation features such as the local minimum around 1963, 1971, 1974, 1981, 1986, etc., but the ODS's variability seems more significant than those of AOD, especially in response to the volcanic impacts. The AODs estimated from the horizontal visibility by Qin et al., as expected, are not relevant to the volcanic aerosols.
 Both curves of ODA and ODS show generally increasing trends for the past 50 years, most significantly from 1968 to about 1990. As can be seen from Table 1, the increasing trends are mostly contributed by the industrial urban sites, indicating the roles of human activities. After 1990, there is no significant trend in ODS but a slightly decreasing trend in ODA. The ODA curve shows a decreasing trend before 1968, along with the short brightening trend during the period [Shi et al., 2008]. These agreements are not trivial because the indexes are based on a small subset of the radiation data, which is only for clear-sky condition.
 Two assumptions among others significantly affect the general levels of the resultant indexes. The first is the aerosol model (CONT-I here) used in the calculations. Since the single scattering albedos have been prescribed in the LUT calculations, the choice in fact affects the extinction spectrum and then the equivalent AOD at 0.55 micron. For example, the indices that have been calculated with the CONT-II model (representing the continental desert atmosphere under conditions of fairly heavy haze) are smaller because of the bigger particle size of the model, which implies more flatter extinction spectrum and hence more efficient extinction at the intense solar wavelengths. The indexes obtained with different aerosol models therefore are expected to be in proportion to each other with a constant ratio, so are their long-term trends.
 The other relevant assumption is that of clear-sky criterion. In general, the 30 day period criterion is stricter than the human eye observation of cloudiness and certainly overkill for many sites, especially for those in northern China, where some heavily polluted cases may be excluded. However, the criterion may be not strict enough for some sites in the southwest regions of China. To balance the spatial and temporal sampling sizes, the 30 day period is chosen here and some heavily cloudy sites are abandoned. The resultant indexes for most sites then can be regarded as background parameters and that may be one of the reasons for lower level of the indexes than the AODs obtained with other methods. Nevertheless, similar to the others without sufficient spectral resolution, this method in principle is not immune to the influence of minimal clouds decreasing direct beam or increasing diffuse irradiance, which might contribute long-term trend to the results of ODS.
 In contrast with the methods based on broadband direct radiation analyzed for atmospheric extinction, the method used in this work verifies the effects of absorption and scattering and then it in principle keeps the ODS results largely from the influence of uncertainties in the absorbing agents. The uncertainties includes the errors in the other data sources about water vapor, ozone, and others used by the extinction analysis methods, the errors in the parameterizations of atmospheric absorption in the radiative transfer models used in building the LUTs, and the uncertainties induced by any unknown absorption agent or mechanisms in the atmosphere. Most of the effects of the uncertainties are dumped in the results of ODA. Nevertheless, the ODA is still a useful index for long-term variation of atmospheric absorption due to aerosols, water vapor, and other gases.
 The ODSs obtained with this method can also largely reduce the influence of the instrument error. The global and diffuse irradiance data used in this work are measured with same type of pyranometers which undergo the same calibration procedure, so they are supposed to have shared same systematic error if there is any. Figure 3 shows the same results as in Figure 2 beside two additional sets of results with the solar radiation data with all their three components modified by the same magnitudes of relative deviation −5% and +5%. It can be seen that the same systematic relative errors in the pyranometers for global and diffuse irradiance observations have only minor influence on the ODSs, in contrast to that on the ODAs, which is much more sensitive to the errors. The ODSs are therefore a robust index for the atmospheric scattering of aerosols. The results also suggest that the AOD estimations based on broadband extinction analysis only [e.g., Luo et al., 2001] should be very careful when dealing with assumptions about atmospheric absorptions by gases, such as the empirical relation between the column water vapor amount and the near-surface water vapor pressure.
 Another advantage of indexes ODA and ODS is their immediate relevance to the clear-sky global, diffuse, and direct DSRs and to the radiative effects of the variation of the atmospheric absorption and scattering.
 In this work, the optical depths of a continental aerosol model at 550 nm are used as the indexes of atmospheric absorption and scattering. The ODS is shown to be a reasonable proxy of scattering component of AOD and largely free of systematic errors of the instruments observing the surface irradiances and the uncertainties in the information or modeling of other absorbing agents in the atmosphere. The ODA, though with its absolute values vulnerable to the various errors and uncertainties, is still a useful reference for long-term variation of the atmospheric absorption contributed by aerosols, water vapors, ozone, and others. Therefore the indexes can provide clues for the attribution studies of the long-term radiation variation studies. However, it should be kept in mind that the ODA is contributed and affected by many factors whose relative significances vary with space and time, which have to be considered when further analysis of the results can be done site by site with more data available.
 The method is applied to the data set of daily integrated surface solar irradiances observed over China continental area from 1957 to 2007. The ODAs show regular seasonal variation with peaks during summer season for all sites, as expected from water vapor variations. The long-term trend of average ODS agree reasonably with previous works on AOD by other methods. The results show that the dimming trend of global radiation over China from 1970s to the end of 1990s is associated with the increasing clear-sky atmospheric absorption and scattering, while the short period of brightening before the mid-1960s is largely correlated with a decreasing trend of atmospheric absorption of clear sky.
 This study was funded by the 973 Program of China with grant 2006CB403706 and MOST project 2007FY110700. The radiation data used in this work are provided by the Meteorological Information Center of Chinese Meteorological Administration (MIC/CMA).