Reducing Broadband Shortwave Radiometer Calibration-Bias Caused by Longwave Irradiance in the Reference Direct Beam

Shortwave radiometers such as pyranometers, pyrheliometers, and photovoltaic cells are calibrated with traceability to consensus reference, maintained by Absolute Cavity Radiometers (ACRs). The ACR is an open cavity with no window that measures the extended broadband spectrum of the terrestrial direct solar beam irradiance, unlike shortwave radiometers that cover a limited range of the spectrum. The difference between the two spectral ranges may lead to calibration bias that can exceed 1%. This article describes a method to reduce the calibration bias resulting from using broadband ACRs to calibrate shortwave radiometers by using an ACR with Schott glass window to measure the reference broadband shortwave irradiance in the terrestrial direct solar beam from 0.3 μm to 3 μm. Reducing the calibration bias will result in lowering the historical solar irradiance by at least 0.9%. The published results in this article might 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.


Introduction
Shortwave radiometers such as pyranometers, pyrheliometers, and photovoltaic cells are calibrated with traceability to the World Radiometric Reference (WRR) (ISO, 1990) [1].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 [2].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 [3].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 [4] [5] 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 [6].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 manufacturer design.The reference broadband longwave irradiance in the direct solar beam (W LW ) 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 (W SW ) is calculated by subtracting the measured reference W LW from the broadband irradiance (W BB ), measured by broadband ACR (ACR BB ) (i.e.W SW = W BB − W LW ).The reference W SW is then used to calibrate an ACR with Schott glass window (ACR SW ), which is then used to calibrate a set of shortwave radiometers.The difference between using ACR BB and ACR SW to calibrate the radiometers is shown in Section 3 below.

Calibration Procedure
The shaded and unshaded pyrgeometers, the two ACRs (ACR BB and ACR SW ), 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 ACR SW.The ACR BB was calibrated with traceability to WRR during NREL Pyrheliometer Comparisons, NPC-2014 [7].The same outdoor dataset was used to calibrate the shortwave radiometers; their responsivity was calculated using the ACR BB , then re-calculated using the ACR SW .The calibration results of the shortwave radiometers by using ACR BB and ACR SW are compared to show the bias between the two calibration methods.measure the reference longwave irradiance in the solar beam (W LW ) as:

ACRSW Calibration
where, -W unsh is the longwave irradiance measured by the unshaded pyrgeometer (W•m −2 ) -W sh is the longwave irradiance measured by the shaded pyrgeometer with the Schott glass shading mechanism, see Figure 1 -Θ is the solar zenith angle (˚).
Detailed derivation of the equation is presented in Reda et al., 2015.Figure 2 shows the measured reference W LW 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 (W BB ) is measured by the ACR BB that was calibrated during NREL Pyrheliometer Comparison (NPC-2014) with traceability to WRR [7].The ACR BB 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 [8].The reference broadband shortwave irradiance (W SW ) is then calculated as: Figure 3 shows the W BB and W SW for the four clear days; the reference W SW irradiance is then used to calculate the window factor for the ACR SW at each data point where, -M is the sensitivity reciprocal (1/Sensitivity) of the ACR SW (W/m 2 /mV).Similar to  the ACR BB the ACR SW self-calibrates every hour to calculate M [8].-V tp is the thermopile output voltage when the shutter of the ACR SW is open (mV) (i.e. the direct solar beam is incident on the thermopile's receiving junctions).
-V 0 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 F SW , and its standard deviation (SD).
The uncertainty with 95% confidence level (U 95,SW ) for the ACR SW calibration is then calculated using the ISO Guide to the Expression of Uncertainty in Measurement (GUM) [9].
Table 1 shows the results of calibration and its uncertainty, where u 95,BB is the standard uncertainty of ACR BB from NPC-2014 [7] and u 95,LW is the standard uncertainty of W LW [6].From the Table, the F SW of the ACR SW equals 1.05655 and U 95,SW equals 0.41%.

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 ACR BB and ACR SW , W BB and W SW (W•m −2 ).-Reference diffuse irradiance measured by a shaded pyranometer, D (W•m −2 ).
The responsivity of each shortwave radiometer is then calculated using two methods: Using the ACR BB as a reference and using the ACR SW as the reference.The following equation is used to calculate the broadband responsivity (RS BB ) [11]: where R net is the pyranometer's net infrared responsivity calculated using the method described in [12], in µV/(W•m −2 ).The shortwave responsivity (RS SW ) is then calculated using Equation ( 4) by replacing RS BB and W BB by RS SW and W SW , respectively.).From the figures, pyrheliometers RS SW is larger than RS BB by at least 0.75%, and for pyranometers RS SW is larger than RS BB by at least 0.6%.Historically, direct solar beam and global irradiance is calculated using the RS BB for all radiometers.This implies that when the radiometers are deployed in the field after being calibrated using ACR SW , 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  Plains (SGP) site, which is at an elevation of 318 meters above sea level.Figure 9 shows the difference between the RS BB and RS SW for the same five radiometers.From the figure it is noted that for pyrheliometers RS SW is larger than RS BB by at least 1.1%, and for pyranometers RS SW is consistently larger than RS BB by at least 0.9%.Again, historical direct beam and global irradiance is calculated using the RS BB for all radiometers, which implies that when the radiometers are deployed in the field after being calibrated using  ACR SW , 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%.

Conclusion
We find that by using the historical calibration method of broadband shortwave radi-   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.

Discussion
While most users of such radiometers are interested in measuring the broadband short-

Figure 1 Figure 1 .
Figure1show the shaded and unshaded pyrgeometers set up, which was used to

Figures 5 -
Figures 5-8 show the difference between the RS BB and RS SW 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 RS SW is larger than RS BB by at least 0.75%, and for pyranometers RS SW is larger than RS BB by at least 0.6%.Historically, direct solar beam and global irradiance is calculated using the RS BB for all radiometers.

Table 1 .
Figure 4. Window factor (FSW) for the absolute cavity radiometer with Schott glass window from June 15 to June 18, 2016.Calibration results of the ACR SW .