Shortwave radiometers such as pyranometers, pyrheliometers, and photovoltaic cells are calibrated with traceability to the World Radiometric Reference (WRR) (ISO, 1990)  . Photovoltaic cells have two traceability chains: the solar simulator method is traceable through a standard lamp to the National Institute of Standards and Technology (NIST) or other National Metrology Institute (NMI) while the solar irradiance method is traceable to the WRR  . The WRR is maintained by six Absolute Cavity Radiometers (ACR) that form the World Standard Group (WSG), which are located at the Physikalisch-Meteorologisches Observatorium in Davos, Switzerland  . The ACR is an open cavity with no windows and was developed to measure the extended broadband spectrum of the terrestrial direct solar beam irradiance that extends beyond the ultraviolet and infrared bands (i.e., below 0.2 µm and above 50 µm, respectively). On the other hand, pyranometers and pyrheliometers measure broadband shortwave irradiance from approximately 0.3 µm to 3 µm   and the silicon-based photovoltaic cells are limited to the spectral range of approximately 0.3 µm to 1 µm. The broadband spectral mismatch of the ACR versus the shortwave radiometers might result in a larger than 1% bias in the radiometers’ calibration methods, as shown in Reda, et al. 2015  . The method described in Reda, et al., 2015 summarizes using two pyrgeometers: one shaded with a Schott glass shading mechanism to block the spectral range greater than 3 µm from the direct solar beam, and the other unshaded with spectral range from approximately 3 µm to 50 µm. The Schott glass shading mechanism is used for broadband shortwave radiometers’ dome to transmit spectral range from 0.3 µm to 3 µm, per ma- nufacturer design. The reference broadband longwave irradiance in the direct solar beam (WLW) is then calculated by subtracting the irradiance measured by the shaded pyrgeometer from that measured by the unshaded pyrgeometer.
As will be described in section 2 below, the reference broadband shortwave irradiance (WSW) is calculated by subtracting the measured reference WLW from the broadband irradiance (WBB), measured by broadband ACR (ACRBB) (i.e. WSW = WBB − WLW). The reference WSW is then used to calibrate an ACR with Schott glass window (ACRSW), which is then used to calibrate a set of shortwave radiometers. The difference between using ACRBB and ACRSW to calibrate the radiometers is shown in Section 3 below.
2. Calibration Procedure
The shaded and unshaded pyrgeometers, the two ACRs (ACRBB and ACRSW), and fiveshortwave radiometers, two thermopile pyrheliometers (Eppley Laboratory, Inc., model NIP and Kipp and Zonen model CHP1), two thermopile pyranometers (Eppley Laboratory, Inc., model PSP and Kipp and Zonen model CMP22), and one photodiode pyranometer (Kipp and Zonen model SP Lite2),were set up outdoors at the National Renewable Energy Laboratory’s (NREL) Solar Radiation Research Laboratory (SRRL), which is at an elevation of 1828.8 meters above sea level. Data was collected simultaneously from all radiometers under clear sky conditions every 30 seconds, from June 15 to June 18, 2016. The following subsections describe the calibration of the ACRSW. The ACRBB was calibrated with traceability to WRR during NREL Pyrheliometer Comparisons, NPC-2014  . The same outdoor dataset was used to calibrate the shortwave radiometers; their responsivity was calculated using the ACRBB, then re-calculated using the ACRSW. The calibration results of the shortwave radiometers by using ACRBB and ACRSW are compared to show the bias between the two calibration methods.
2.1. ACRSW Calibration
Figure 1 show the shaded and unshaded pyrgeometers set up, which was used to
Figure 1. Set up of shaded and unshaded pyrgeometers to measure the longwave irradiance in solar beams.
measure the reference longwave irradiance in the solar beam (WLW) as:
- Wunsh is the longwave irradiance measured by the unshaded pyrgeometer (W・m−2)
- Wsh is the longwave irradiance measured by the shaded pyrgeometer with the Schott glass shading mechanism, see Figure 1 (W・m−2)
- Θ is the solar zenith angle (˚).
Detailed derivation of the equation is presented in Reda et al., 2015. Figure 2 shows the measured reference WLW varies from 3 W・m−2 to 12 W・m−2 due to time of day, solar irradiance level, and the atmospheric constituents, such as water vapor, aerosol optical depth, ozone, etc.
The broadband direct beam irradiance (WBB) is measured by the ACRBB that was calibrated during NREL Pyrheliometer Comparison (NPC-2014) with traceability to WRR  . The ACRBB was self-calibrating every hour to calculate its multiplication factor based on the changing environmental conditions during the outdoor measurement (e.g. temperature, pressure, humidity, irradiance level, and spectral distribution). Details about ACR self-calibration is presented in Reda, 1996  . The reference broadband shortwave irradiance (WSW) is then calculated as:
Figure 3 shows the WBB and WSW for the four clear days; the reference WSW irradiance is then used to calculate the window factor for the ACRSW at each data point (FSW),
- M is the sensitivity reciprocal (1/Sensitivity) of the ACRSW (W/m2/mV). Similar to
Figure 2. Reference longwave irradiance (Wsh-Wunsh) in solar beam from June 15 to June 18, 2016.
Figure 3. Broadband and shortwave irradiance from June 15 to June 18, 2016.
the ACRBB the ACRSW self-calibrates every hour to calculate M  .
- Vtp is the thermopile output voltage when the shutter of the ACRSW is open (mV) (i.e. the direct solar beam is incident on the thermopile’s receiving junctions).
- V0 is the thermopile output voltage when the cavity is self-calibrating and the shutter is closed [i.e. no solar irradiance (mV)].
Figure 4 shows the window factor, the average FSW, and its standard deviation (SD). The uncertainty with 95% confidence level (U95,SW) for the ACRSW calibration is then calculated using the ISO Guide to the Expression of Uncertainty in Measurement (GUM)  .
Table 1 shows the results of calibration and its uncertainty, where u95,BB is the standard uncertainty of ACRBB from NPC-2014  and u95,LW is the standard uncertainty of WLW  . From the Table, the FSW of the ACRSW equals 1.05655 and U95,SW equals 0.41%.
2.2. Shortwave Radiometer Calibration
During the calibration, each measurement data point consists of simultaneous recording of the following parameters:
- Output voltage from the test radiometer, V (µV).
- Reference irradiance measured by ACRBB and ACRSW, WBB and WSW (W・m−2).
Figure 4. Window factor (FSW) for the absolute cavity radiometer with Schott glass window from June 15 to June 18, 2016.
Table 1. Calibration results of the ACRSW.
- Net longwave irradiance measured by a pyrgeometer, Wnet (W・m−2).
- Reference diffuse irradiance measured by a shaded pyranometer, D (W・m−2).
- The solar zenith angle calculated using the Solar Position Algorithm (SPA), Θ(˚)  .
The responsivity of each shortwave radiometer is then calculated using two methods: Using the ACRBB as a reference and using the ACRSW as the reference. The following equation is used to calculate the broadband responsivity (RSBB)  :
where Rnet is the pyranometer’s net infrared responsivity calculated using the method described in  , in µV/(W・m−2).
The shortwave responsivity (RSSW) is then calculated using Equation (4) by replacing RSBB and WBB by RSSW and WSW, respectively.
Figures 5-8 show the difference between the RSBB and RSSW for five radiometers, two thermopile pyrheliometers (Eppley Laboratory, Inc., model NIP and Kipp and Zonen model CHP1), two thermopile pyranometers (Eppley Laboratory, Inc., model PSP and Kipp and Zonen model CMP22), and one photodiode pyranometer (Kipp and Zonen model SP Lite2). From the figures, pyrheliometers RSSW is larger than RSBB by at least 0.75%, and for pyranometers RSSW is larger than RSBB by at least 0.6%. Historically, direct solar beam and global irradiance is calculated using the RSBB for all radiometers.
Figure 5. Shortwave and broadband responsivities and percentage differences on June 15, 2016.
This implies that when the radiometers are deployed in the field after being calibrated using ACRSW, the measured direct broadband shortwave beam solar irradiance might be lower than the historical irradiance by at least 0.75%, and that the global broadband shortwave solar irradiance might be lower than the historical global irradiance by 0.6%.
The same calibration method was repeated at the USA-Department of Energy (DOE), Atmospheric Radiation Measurement (ARM) program at the Southern Great
Figure 6. Shortwave and broadband responsivities and percentage differences on June 16, 2016.
Plains (SGP) site, which is at an elevation of 318 meters above sea level. Figure 9 shows the difference between the RSBB and RSSW for the same five radiometers. From the figure it is noted that for pyrheliometers RSSW is larger than RSBB by at least 1.1%, and for pyranometers RSSW is consistently larger than RSBB by at least 0.9%. Again, historical direct beam and global irradiance is calculated using the RSBB for all radiometers, which implies that when the radiometers are deployed in the field after being calibrated using
Figure 7. Shortwave and broadband responsivities and percentage differences on June 17, 2016.
ACRSW, the measured direct beam solar irradiance might be lower than the historical irradiance by at least 1.1%, and the global solar irradiance might be lower than the historical global irradiance by 0.9%.
We find that by using the historical calibration method of broadband shortwave radi-
Figure 8. Shortwave and broadband responsivities and percentage differences on June 18, 2016.
ometers recommended by ISO 9059:1990 results in an overestimation in the field measurement of the direct broadband shortwave beam solar irradiance by at least 0.75% and the global broadband shortwave solar irradiance by at least 0.6%. This overestimation might exceed 1% based on the atmospheric conditions during the calibration, primarily water vapor and aerosols. Since shortwave radiometers are designed to measure the broadband shortwave solar irradiance in the spectral range from 0.3 µm to 3 µm,
Figure 9. Shortwave and broadband responsivities and percentage differences at SGP on August 17, 2016.
per ISO 9060:1990, the recommended calibration method by ISO 9059-1990 would result in biases in the calibration results. These biases might be significant in atmospheric science and solar energy applications.
While most users of such radiometers are interested in measuring the broadband short- wave irradiance, some users are interested in measuring the broadband solar irradiance (WBB). For the latter, it is recommended that radiometers be designed with domes or windows that transmit the broadband spectral range to avoid such calibration discrepancy. The purpose of this article is to raise the awareness of the calibration discrepancy to the users of such radiometers, and open a discussion within the solar and atmospheric science community to define their expectation from such radiometers to the radiometers’ manufacturers and calibration providers.
We would like to thank NREL’s solar program staff, NREL’s Quality Management Systems and Assurance Office, NREL Metrology Laboratory, and DOE-Atmospheric Radiation Measurement (ARM) program for providing the funds for this publication. We extend special appreciation to Martina Newman for providing the superb administrative support by taking care of all the logistics associated with this effort.
 Müllejans, H., Zaaiman, W., Merli, F., Dunlop, E.D. and Ossenbrink, H.A. (2015) Comparison of Traceable Calibration Methods for Primary Photovoltaic Reference Cells. Journal of Progress in Photovoltaics: Research and Applications, 13, 661-671.
 ISO 9060:1990. Solar Energy—Specification and Classification of Instruments for Measuring Hemispherical Solar and Direct Solar Radiation. International Organization for Standardization, Geneva, 11 p.
 Reda, I., Konings, J. and Xie, Y. (2015) Method to Measure the Broadband Longwave Irradiance in the Terrestrial Direct Solar Beam. Journal of Atmospheric and Solar-Terrestrial Physics, 129, 23-29.
 Reda, I., Hickey, J., Long, C., Myers, D., Stoffel, T., Wilcox, S., Michalsky, J.J., Dutton, E.G. and Nelson, D. (2005) Using a Blackbody to Calculate Net Infrared Responsivity of Shortwave Solar Pyranometers to Correct for Their Thermal Offset Error during Outdoor Calibration Using the Component Sum Method. Journal of Atmospheric and Oceanic Technology, 22, 1531-1540.