1. Introduction
Surface solar radiation is an important factor determining the thermal conditions and the circulation of the atmosphere. Accurate measurement of surface solar radiation is essential for understanding the present climate and potential climatic changes. There are a large number of solar radiation observation sites across the world for measuring shortwave global, direct, and scattering irradiances (GSI, DSI and SSI, respectively) using pyranometers and pyrheliometers. Observations began in the 1880s (Roosen et al. 1973; Stothers 1996). The Global Energy Balance Archive (GEBA) produces quality-controlled monthly datasets of surface energy fluxes, which are available on the Internet stretching back to October 1997 (Gilgen and Ohmura 1999). To provide surface solar radiation for validating satellite retrievals and model simulations, as well as monitor long-term changes in surface irradiance, the World Meteorological Organization/International Council of Scientific (WMO/ICSU) Joint Scientific Committee for the World Climate Research Programme (WCRP) proposed in October 1988 the establishment of an international Baseline Surface Radiation Network (BSRN) (Ohmura et al. 1998). The on-site pyranometer and pyrheliometer are usually calibrated once every one or two years through a calibration transfer process, in which they are compared with world or national standard instruments to determine their calibration coefficients. There are some uncertainties associated with field solar radiometer measurements caused by instrument stability, detector contamination, temperature effects, and so on (Dutton et al. 2001; Ji and Tsay 2010). For example, one would expect a significant influence of heavy aerosol loading on solar radiometer measurements in China if the detector dome is not cleaned very often. Therefore, a reliable method to monitor radiometer performance is highly desirable. Such a method would also be very useful for evaluating the data quality of historical solar radiation measurements.
Based on the fact that GSI is weakly sensitive to aerosol optical parameters in the case of aerosol optical thickness (AOT) < 0.2, Qiu et al. (2008) presented a method to estimate the uncertainties of historic GSI data in China. This evaluation method is not completely independent of DSI data quality, so further study on this issue is still required. More specifically, we need a simple yet effective calibration method that, as far as possible, is independent of radiation data quality. We developed a new method to fulfill this goal. One of the features of this method is that we can calibrate DSI, GSI, and SSI simultaneously. The method directly takes the World Radiation Reference (WRR) as the calibration standard and uses on-site radiation measurements as inputs. It does not assume a priori accuracy of any DSI, GSI, and SSI measurements using the following two key techniques. The first is to scale SSI and GSI detection sensitivities under overcast conditions. The assumption behind this step is that SSI and GSI measurements should be equal to each other if DSI is completely scattered and absorbed. The function of this step is to obtain a good estimation of SSI/GSI and thereby the ratio of the horizontal DSI (HDSI) to GSI. The HDSI is defined to be the difference between GSI and SSI. The second is to retrieve AOT from HDSI/GSI. The reason for the retrieval of AOT using HDSI/GSI is that this ratio is very sensitive to AOT, but not too sensitive to aerosol optical properties, such as single scattering albedo (SSA) and scattering phase function. The retrieved AOT is then used to drive a radiative transfer model (RTM) to calculate atmospheric transmittance, and then finally solar radiometers are calibrated.
The paper is organized as follows. An introduction to the method is presented in the following section. Section 3 presents an application and evaluation of this new calibration method. The conclusions of the study are presented in section 4.
2. Method
The calibration method is introduced as follows: first, the principle and calibration formula used in the two key techniques are explained; second, the criteria used for the selection of radiation data in the calibration are described; and finally, the calibration processes are presented.
a. The principle and calibration formula
b. Criteria for the selection of radiation data in the calibration
As analyzed above, solar radiation data in the case of a smaller AOT and a larger 
SSI-to-GSI ratio 
Citation: Journal of Atmospheric and Oceanic Technology 31, 6; 10.1175/JTECH-D-13-00114.1
Selecting smaller 
c. Major calibration processes
An important part of the calibration is the AOT retrieval from 
In summary, the calibration algorithm consists of the following steps:
- Determine the sensitivity scaling factor,
- Use SSI and GSI data with
- Use
- Use the RTM with the AOT retrieval from step 3 to calculate the transmittances
- Use
- Select calibrations according to the above-mentioned criteria.
It should be emphasized that the “calculated” 
3. Application and evaluation
a. Site and measurements
The new calibration method is applied to the measurements of surface solar radiation during 2005 at Xianghe, China, one of the BSRN sites and Aerosol Robotic Network (AERONET) sites (Holben et al. 1998). Kipp–Zonen CM21 radiometers are used to measure the GSI. The GSI can also be derived by summing the direct and diffuse components of radiation, which are measured separately by an Eppley Normal Incidence Pyrheliometer (NIP) and a black-and-white radiometer (B&W), both mounted on an EKO STR-22 solar tracker (Xia et al. 2007). The radiometers take samples every second, but 1-min means and standard deviations are saved to a Campbell datalogger. A redundant set of broadband radiometers is used to ensure the precision of measurements and to rule out possible biases by physical problems (e.g., misaligned solar shadowing disk). The data are quality checked using the BSRN quality control procedures (Ohmura et al. 1998) and submitted to the BSRN archive. It is estimated that the field measurement uncertainties are 3%, 6%, and 6% for direct, diffuse, and global measurements, respectively, using NIP and B&W radiometers (Stoffel 2005).
AOTs at seven wavelengths (340, 380, 440, 500, 670, 870, and 1020 nm) are derived with an uncertainty of 0.01–0.02 from Cimel Electronique sun-photometer measurements (Eck et al. 1999). The measurements at 940 nm are used for the derivation of the column water vapor amount. Aerosol size distribution, the refractive index, and SSA are retrieved from the sky radiance measurements and AOTs (Dubovik and King 2000; Eck et al. 2005). The data used here are level 2.0 quality-assured data that have been prefield and postfield calibrated, automatically cloud screened (Smirnov et al. 2000), and manually inspected. If AERONET water vapor data are not available, then we can use operational meteorological observations of surface water vapor pressure to derive them (Yang and Qiu 2002).
Comparisons of AOT retrievals by the present 
b. Radiation calibrations
A modified cloud-screening method is used for detecting clear skies from surface solar radiation measurements (Xia et al. 2006). Furthermore, we use two additional criteria to select radiation measurements in the calibration. The first and also most essential criterion is that 
As pointed out in the last section, the calibration requires the scaling of SSI and GSI detection sensitivities under overcast skies. To weaken the effect of radiation measurement noises on the scaling, only the SSI and GSI data that are larger than 100 W m−2 and measured on overcast days with DSI < 1 W m−2 are selected in the scaling.
As mentioned earlier, solar radiation data associated with large 
Sixty-one sets of 
Citation: Journal of Atmospheric and Oceanic Technology 31, 6; 10.1175/JTECH-D-13-00114.1
Figure 3 shows the monthly-mean transfer coefficients of GSI, DSI, and SSI. The monthly mean is calculated from calibrations on more than 3 days in each month. It is not surprising that the transfer coefficients for the GSI, DSI, and SSI in summer are larger than those in winter, which is likely caused by lower instrument sensitivity when the temperature is high (Coulson 1975). Temperature affects CM21 accuracy by 2%–3%, and instrumental uncertainty can be reduced to below 1% following correction of the temperature effect (Ji and Tsay 2010; Ji et al. 2011). The mean nighttime offset of the CM21 radiometer used in this study—an indicator of the magnitude of the infrared loss in global measurements—is about −2 W m−2 (Xia et al. 2007), which is corrected using the method suggested by Dutton et al. (2001). Monthly-mean transfer coefficients of GSI, DSI, and SSI change between 0.98 and 1.06, 0.97, and 1.04, and 0.95 and 1.06, implying their uncertainties vary between −5.9% and 2.4%, −4.0% and 2.9%, and −6.1% and 4.9%, respectively. The estimations are in good agreement with the measurement uncertainties of 3%, 6%, and 6% for DSI, GSI, and SSI, respectively, as suggested by Stoffel (2005). The annual mean transfer coefficients of GSI, DSI, and SSI are 1.02, 1.01, and 1.03, respectively.
Monthly-mean transfer coefficients of GSI, DSI, and SSI.
Citation: Journal of Atmospheric and Oceanic Technology 31, 6; 10.1175/JTECH-D-13-00114.1
c. Comparisons of AOT between BEM retrievals and AERONET products
AOT data used in comparisons should meet the following four requirements: 1) the measurement time difference between our retrieval and AERONET should be less than 30 s; 2) 
Two kinds of AOT at 750-nm retrievals are used to compare with AERONET AOTs. The first consists of retrievals based on the 
Figure 4 compares the AOT retrievals from 
Comparison of AOT retrievals from the new method based on HDSI/GSI with AERONET AOTs.
Citation: Journal of Atmospheric and Oceanic Technology 31, 6; 10.1175/JTECH-D-13-00114.1
Figure 5 compares BEM AOTs from the original and recalibrated HDSI with AERONET AOTs. The monthly-mean transfer coefficients (see Fig. 3) are used to recalibrate GSI and SSI data and then to retrieve AOT. There are a total of 234 days with BEM AOT retrievals. A good agreement between AOTs from BEM and AERONET is obtained. The deviation of monthly-mean BEM AOTs using the original HSDI data from AERONET AOTs varies from −0.048 to 0.044. The deviations using recalibrated HSDI varies from −0.029 to 0.029, which is about one-half of the former values. The RMS deviations of BEM AOTs from the original and recalibrated HDSI are 0.030 and 0.016, respectively, and the annual mean deviations are 0.012 and −0.001, respectively. It is clear that better retrievals of AOT are obtained from recalibrated HDSI data, as compared with that from original HDSI data.
Comparisons of monthly-mean BEM AOTs with Cimel Electronique AOTs.
Citation: Journal of Atmospheric and Oceanic Technology 31, 6; 10.1175/JTECH-D-13-00114.1
d. Effect of uncertainties in the AWE and aerosol imaginary index
Note that in the RTM calculation for the AOT retrievals and calibrations, the AWE is set to 1 and the aerosol imaginary index (AII) is set to 0.01 in the RTM calculations. The uncertainties associated with these parameters are the two most essential error sources in the calibration. If the AWE is set to 0.5 or 1.5 instead of 1.0, then the RMS deviations of the GSI and DSI calibration coefficients in those 36 days (compared with those using 1.0) are within 1.03% and 1.17%, respectively. If the AII is set 0.005 or 0.015 instead of 0.01, then the RMS deviations of the GSI and DSI calibration coefficients are 1.14% and 1.22%, respectively. Therefore, the calibration uncertainty is estimated to be less than 2%, caused by a ±0.5/±0.005 deviation in AWE/AII values. It should be noted that the smaller the AOT is, the smaller the uncertainty is of the AOT retrieval by the BEM, as caused by the AWE uncertainty (Qiu 1998, 2001). Therefore, as shown in Fig. 6, a better calibration accuracy is achieved in cases of smaller AOT. Figure 6 compares deviations of GSI transfer coefficients using AWEs of 0.0, 0.5, 1.5, and 2.0 with that using an AWE of 1.0 on 2 particular days (18 August and 21 April). The AERONET 670-nm AOTs on those 2 days are 0.062 and 0.168, and their AWEs are 1.134 and 0.715, respectively. When the AWE changes from 0.0 to 1.5, the GSI transfer coefficient deviations are within ±0.43% for 18 August and ±1.89% for 21 April. The deviations evidently increase when an AWE of 2.0 is set, being 1.95% and 9.92% for 18 August and 21 April, respectively. The uncertainty in the larger AOT case (21 April) is much larger. Furthermore, the DSI transfer coefficient deviations are almost the same as the GSI ones, being within ±0.46% and ±1.98% for 18 August and 21 April, respectively, when the AWE changes from 0% to 1.5%, and from 1.91% to 10.2%, respectively, when an AWE of 2.0 is set. In addition, we find that the transfer coefficient deviation, caused by the AII uncertainty, also increases with increasing AOT. The deviations are within ±0.65% for both the GSI and DSI calibrations when AIIs of 0, 0.005, 0.015, and 0.02 are set instead of 0.01 in the 0.062 AOT case (18 August), and they raise to within the range ±2.16% in the 0.168 AOT case (21 April). The above deviation is an analysis of the GSI and DSI transfer coefficient uncertainties for the suburban aerosol type over a site at Xianghe, near Beijing, based on an assumed AWE of 1.0 and an AII of 0.01. On the basis of the analysis, we now estimate the uncertainties caused by these assumptions for different aerosol types.
Deviations of GSI calibration transfer coefficients using AWEs of 0.0, 0.5, 1.5, and 2.0 with the coefficient using an AWE of 1.0.
Citation: Journal of Atmospheric and Oceanic Technology 31, 6; 10.1175/JTECH-D-13-00114.1
Using AERONET data, Dubovik et al. (2002) studied the variability of absorption and optical properties of key aerosol types observed at a number of locations throughout the world. The study indicated that AII changes between 0 and 0.02, except for biomass-burning aerosol over the African savanna in Zambia, where AII is within 0.021 ± 0.004. As analyzed above, when AIIs ranging from 0 to 0.02 are set instead of 0.01, the GSI and DSI transfer coefficient deviations are within ±0.65% for the case of the below 0.062 AOT at the 670-nm wavelength (18 August), or ±2.16% for 0.168 (21 April). Therefore, if radiation measurements in below 0.062 (or 0.168) AOT conditions are used in the calibrations, then a below 1% (or below 2%) uncertainty, caused by assuming an AII of 0.01, can be achieved for a wide variety of aerosol types, except for biomass-burning aerosol. As also analyzed by Dubovik et al. (2002), the AWE ranges from −0.1 to 2.5 for worldwide aerosol types. Larger AWEs (1.2–2.5) are found for urban–industrial and mixed aerosol over National Aeronautics and Space Administration (NASA)’s Goddard Space Flight Center (GSFC) in Greenbelt, Maryland, and much lower AWEs (<0.9) for desert and oceanic aerosol over Solar Village, Saudi Arabia. The AOT over GSFC is often very small. According to AERONET data at GSFC in 2005, there are a total of 73 days with below 0.062 AOT conditions at the 670-nm wavelength. The mean 750-nm AOT on these 73 days is 0.034, and the mean AWE is 1.686. The smaller the AOT is, the weaker the effect of AWE uncertainty on the radiation calibrations. If the radiation measurements on the 73 days are used, then a below −2% calibration uncertainty is estimated when an AWE of 1.0 is inputted. In the case of desert and oceanic aerosol over Solar Village, there are a total 274 days of AOT and AWE data in 2005, in which AWE changes from −0.003 to 1.276 and the mean AWE is 0.519. There are 14 days under below 0.062 AOT (670 nm) conditions. When using radiation measurements from those 14 days, and inputting an AWE of 1.0 into the calibrations, a below 0.5% uncertainty is estimated according to Fig. 6. Therefore, a below 2% uncertainty, caused by assuming an AWE of 1.0 and an AII of 0.01, can be achieved for a wide variety of aerosol types when radiation measurements under below 0.062 AOT (670 nm) conditions are used in the calibrations. The calibration accuracy should be improved further by using AWE and AII values that are close to their real values for a given aerosol type.
4. Summary
A new method has been proposed to simultaneously calibrate GSI, DSI, and SSI measurements. The method directly takes the WRR as the calibration standard and uses on-site radiation measurements as inputs. Two simple but effective techniques are used to achieve this goal. The first is to scale the SSI and GSI detection sensitivities under overcast skies, which is based on the fact that SSI should be equal to GSI when DSI is completely scattered and absorbed. The second is to retrieve the AOT under clear yet relatively clean conditions from 
The calibration uncertainties of DSI, GSI, and SSI were estimated to be within −4.0% to 2.9%, −5.9% to 2.4%, and −6.1% to 4.9%, respectively. The estimations were basically coincident with 3%, 6%, and 6% uncertainties (DSI, GSI, and SSI) (Stoffel 2005).
The maximum deviation of AOT retrievals based on 
The calibration transfer coefficients for the GSI, DSI, and SSI in summer are larger than those in winter, which is likely caused by lower instrument sensitivity when the temperature is high. The temperature effect will be further investigated in future work.
Sensitivity analysis showed the calibration uncertainty to be below 2% for suburban aerosol over the Xianghe site if there were ±0.5/±0.005 deviations in AWE/AII. The smaller the AOT was, the weaker the effect of AWE and AII uncertainty on the calibration. A below −2% uncertainty, caused by assuming an AWE of 1.0 and AII of 0.01, can be achieved for a wide variety of aerosol types when radiation measurements under below 0.062 AOT (670 nm) conditions are used in calibrations. Furthermore, a better calibration accuracy should be obtained if the AWE and AII inputs are even closer to their real values for a given aerosol type. How to select more suitable AWE and AII values in calibrations remains a problem to be further studied in future work.
The outstanding feature of this method is that prior calibrations of DSI, GSI, and SSI measurements are not required. Furthermore, AOT, the most important factor determining the atmospheric transmittance under clear and clean conditions, is retrieved from the pyranometer measurements. Therefore, the method can potentially be used to calibrate historical pyranometer measurements if water vapor content is available. The unique advantage of this method also lies in that it can be used to correct historic radiation measurements and monitor radiometer performance. It is especially suitable in cases with more clear days and smaller AOT. We intend to use the method to recalibrate DSI, GSI, and SSI measurements from Chinese meteorological observatories since 1960, and then retrieve AOTs from the recalibrated radiation data. The effects of input parameter uncertainties will also be further investigated.
This research was supported by the National Basic Research Program (Grant 2011CB403401), the National Natural Science Foundation of China (Grants 41175029 and 41175031), and the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA05100300). Maintenance of the solar radiometers by Mr. Weidong Nan and other staff members at the Xianghe Observatory is greatly appreciated. Special appreciation is also extended to the NASA AERONET group for processing the AERONET data.
REFERENCES
Coulson, K. L., 1975: Solar and Terrestrial Radiation: Methods and Measurements. Academic Press, 322 pp.
Dubovik, O., , and King M. , 2000: A flexible inversion algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements. J. Geophys. Res., 105, 20 673–20 696, doi:10.1029/2000JD900282.
Dubovik, O., , Holben B. N. , , Eck T. F. , , Smirnov A. , , Kaufman Y. J. , , King M. D. , , Tanre D. , , and Slutsker I. , 2002: Variability of absorption and optical properties of key aerosol types observed in worldwide locations. J. Atmos. Sci., 59, 590–608, doi:10.1175/1520-0469(2002)059<0590:VOAAOP>2.0.CO;2.
Dutton, E., , Michalsky J. J. , , Stoffel T. , , Forgan B. W. , , Hickey J. , , Nelson D. W. , , Alberta T. L. , , and Reda I. , 2001: Measurement of broadband diffuse solar irradiance using current commercial instrumentation with a correction for thermal offset errors. J. Atmos. Oceanic Technol., 18, 297–314, doi:10.1175/1520-0426(2001)018<0297:MOBDSI>2.0.CO;2.
Eck, T. F., , Holben B. N. , , Reid J. S. , , Dubovik O. , , Smirnov A. , , O’Neill N. T. , , Slutsker I. , , and Kinne S. , 1999: Wavelength dependence of the optical depth of biomass burning, urban, and desert dust aerosols. J. Geophys. Res., 104, 31 333–31 349, doi:10.1029/1999JD900923.
Eck, T. F., and Coauthors, 2005: Columnar aerosol optical properties of AERONET sites in central eastern Asia and aerosol transport to the tropical mid-Pacific. J. Geophys. Res.,110, D06202, doi:10.1029/2004JD005274.
Gilgen, H., , and Ohmura A. , 1999: The global energy balance archive. Bull. Amer. Meteor. Soc., 80, 831–850, doi:10.1175/1520-0477(1999)080<0831:TGEBA>2.0.CO;2.
Holben, B. N., and Coauthors, 1998: AERONET—A federated instrument network and data archive for aerosol characterization. Remote Sens. Environ., 66, 1–16, doi:10.1016/S0034-4257(98)00031-5.
Ji, Q., , and Tsay S.-C. , 2010: A novel nonintrusive method to resolve the thermal dome effect of pyranometers: Instrumentation and observational basis. J. Geophys. Res., 115, D00K21, doi:10.1029/2009JD013483.
Ji, Q., , Tsay S.-C. , , Lau K. M. , , Hansell R. A. , , Butler J. J. , , and Cooper J. W. , 2011: A novel nonintrusive method to resolve the thermal dome effect of pyranometers: Radiometric calibration and implications. J. Geophys. Res., 116, D24105, doi:10.1029/2011JD016466.
Ohmura, A., and Coauthors, 1998: Baseline Surface Radiation Network (BSRN/WCRP): New precision radiometry for climate research. Bull. Amer. Meteor. Soc., 79, 2115–2136, doi:10.1175/1520-0477(1998)079<2115:BSRNBW>2.0.CO;2.
Qiu, J., 1998: A method to determine atmospheric aerosol optical depth using total direct solar radiation. J. Atmos. Sci., 55, 744–758, doi:10.1175/1520-0469(1998)055<0744:AMTDAA>2.0.CO;2.
Qiu, J., 2001: Broadband extinction method to determine atmospheric aerosol optical properties. Tellus, 53B, 72–82, doi:10.1034/j.1600-0889.2001.01064.x.
Qiu, J., 2003: Broadband extinction method to determine aerosol optical depth from accumulated solar direct radiation. J. Appl. Meteor., 42, 1611–1623, doi:10.1175/1520-0450(2003)042<1611:BEMTDA>2.0.CO;2.
Qiu, J., , Xu X. , , and Yang J. , 2008: Accuracy estimations of global solar irradiance measurements at seven meteorological observatories of Beijing. J. Appl. Meteor. Sci., 19, 287–295.
Roosen, R. G., , Angione R. J. , , and Klemeke C. H. , 1973: Worldwide variations in atmospheric transmission: Baseline results from Smithsonian observations. Bull. Amer. Meteor. Soc., 54, 307–316, doi:10.1175/1520-0477(1973)054<0307:WVIATB>2.0.CO;2.
Schaaf, C. B., and Coauthors, 2002: First operational BRDF, albedo nadir reflectance products from MODIS. Remote Sens. Environ., 83, 135–148, doi:10.1016/S0034-4257(02)00091-3.
Smirnov, A., , Holben B. , , Eck T. , , Dubovik O. , , and Slutsker I. , 2000: Cloud screening and quality control algorithms for the AERONET database. Remote Sens. Environ., 73, 337–349, doi:10.1016/S0034-4257(00)00109-7.
Stamnes, K., , Tsay S.-C. , , Wiscombe W. J. , , and Jayaweera K. , 1988: Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media. Appl. Opt., 27, 2502–2509, doi:10.1364/AO.27.002502.
Stoffel, T., 2005: Solar infrared radiation station handbook. ARM Tech. Rep. ARM-TR-025, National Renewable Energy Laboratory, 29 pp.
Stothers, R. B., 1996: Major optical thickness perturbations to the stratosphere from volcanic eruptions: Pyrheliometric period, 1881-1960. J. Geophys. Res., 101, 3901–3920, doi:10.1029/95JD03237.
WMO, 1982: Abridged final report of the eighth session. WMO Series, No. 590, Commission for Instruments and Methods of Observation, World Meteorological Organization, 89 pp.
Xia, X., , Chen H. , , Wang P. , , Zhang W. , , Goloub P. , , Chatenet B. , , Eck T. F. , , and Holben B. N. , 2006: Variation of column-integrated aerosol properties in a Chinese urban region. J. Geophys. Res., 111, D06204, doi:10.1029/2005JD006203.
Xia, X., , Li Z. , , Wang P. , , Chen H. , , and Cribb M. , 2007: Estimation of aerosol effects on surface irradiance based on measurements and radiative transfer model simulations in northern China. J. Geophys. Res., 112, D22S10, doi:10.1029/2006JD008337.
Yang, J., , and Qiu J. , 2002: A method for estimating precipitable water and effective water vapor content from ground humidity parameters. Chin. J. Atmos. Sci., 26, 81–96.
