Using an Absolute Cavity Pyrgeometer to Validate the Calibration of a Secondary Standard Pyrgeometer Outdoors, Independent from the Reference Value of the Atmospheric Longwave Irradiance

Accurate measurements of broadband outdoor longwave irradiance are im-portant for renewable energy applications and the study of the atmosphere and climate change. A unique method of pyrgeometer calibration has been developed to improve the measurement uncertainty [1]. The results of this method yielded irradiance values within ±3 W/m 2 of those traceable to the World InfraRed Standard Group (WISG). This article describes a technique for validating this pyrgeometer calibration method using two Absolute Cavity Pyrgeometers (ACPs). The ACPs and pyrgeometer model PIR were deployed outdoors and the irradiance measured by the PIR was compared against the average irradiance measured by the two ACPs. The irradia nce measured by the PIR was calculated using two equations, NREL equation and the Physika-lisch Meteorologisches Observatorium Davos (PMOD) equation. The uncertainty with 95% confidence level (U 95 ) of the irradiance measured by the PIR using NREL equation equaled ±3.51 W/m 2 with respect to SI and using PMOD equation U 95 equaled ±2.99 W/m 2 with respect to SI. These results suggest that the PIR calibration method might be useful in addressing the international need for a secondary standard pyrgeometer traceable to SI.


Introduction
The pyrgeometer model PIR was installed outdoors on an aluminum plate that was connected to a temperature controller, see Photo 1. Adjusting the temperature controller to decrease the pyrgeometer's body temperature changed the pyrgeometer's thermopile output. If the incoming radiation was stable, then the slope of the change in the pyrgeometer's output irradiance (W out ) versus the change in the thermopile output voltage (V) would equal the pyrgeometer outdoors responsivity (RS), independent from the absolute value of the atmospheric longwave irradiance [1]. We then evaluated the results of the method using two Absolute Cavity Pyrgeometers (ACPs), ACP95F3 and ACP10F3. The ACPs were installed on temperature controllers and operated as described in [2]. The described method addressed the inherent problems related to the spectral difference between the blackbodies and the atmospheric irradiance by calculating RS from the clear sky outdoor calibration and using the actual atmospheric irradiance as the calibration source. Section 2 describes the procedure, equations, and the mathematical representation of the rate of change of V versus W out . Section 3 shows the procedure results and the outdoor evaluation of this procedure. The evaluation compared the measured irradiance by the PIR against the average irradiance measured by ACP95F3 and ACP10F3. Section 4 is the conclusion.

Procedure
The ACPs and PIR were deployed outdoors from July 20 to August 19, 2020.
Two equations were used to calculate the atmospheric longwave irradiance measured by the PIR, as described below in NREL and PMOD equations.  V is the pyrgeometer thermopile output, in microvolts. W r is the pyrgeometer receiver radiation = K 4 thermopile efficiency factor equal to ( ) Equation (1) is rewritten in the following form: where: W net is the net irradiance measured by the pyrgeometer thermopile. W out is the outgoing irradiance from the pyrgeometer.
( ) A fundamental principle for this calibration procedure is to lower the outgoing irradiance while the atmospheric longwave irradiance (W atm ) is constant, i.e., stable during clear sky conditions to within 1 W/m 2 from the start to end of the calibration, at least 7 minutes. Lowering W out was achieved by cooling the pyrgeometer's case using the temperature controller. While lowering W out , all signals from the pyrgeometer were measured every 10 seconds (i.e., thermopile output voltage, T d , and T r ). Differentiating Equation (2) with respect to time then yields: If W atm is assumed constant, Equation 4 then yields: Equation (5) implies that the change of W out versus the change of V yields K 1 , which is independent from the absolute value of W atm .
Once K 1 was calculated using the above procedure, Equation (1)  PMOD Equation [4] ( ) ( ) where C is the pyrgeometer responsivity and T b is the case temperature. As in the NREL method described above, where W atm is assumed to be constant, differentiating Equation 6 with respect to time yields: For simplicity, Equation (7) is rewritten as: Equation (8) implies that the change of F versus the change of W out yields C, which is independent from the absolute value of W atm .
The ACP's Measurement Equation [2] To measure the atmospheric longwave irradiance: where: W atm is the atmospheric longwave irradiance (W/m 2 ). K 1 is the reciprocal of the ACP's responsivity (W/m 2 /uV). V is the thermopile output voltage (uV). ε is the gold emittance. K 2 is the emittance of the black receiver surface. W r is the receiver irradiance (W/m 2 ). W c is the concentrator irradiance (W/m 2 ). τ is the ACP's throughput.

Results
The measurement uncertainty was calculated using the following equation: ( ) Photo 1 shows the outdoor set up of ACP95F3, ACP10F3, and PIR. Table 1 is a sample list of the calculated K 1 for the PIR (NREL), ACP95F3, ACP10F3, and C for PIR (PMOD). Figure 1 and Figure 2 show W net versus V for ACP95F3 and ACP10F3. Figure 3 shows W out versus V for the PIR using the NREL equation. Figure 4 shows W out versus F for the PIR using the PMOD equation. Figure 5 shows the average irradiance of the ACPs and the PIR using NREL and PMOD equations. Figure 6 shows the difference between the ACPs average irradiance and the PIR irradiance using NREL and PMOD Equations. Figure 7 shows the atmospheric water vapor content. Atmospheric and Climate Sciences

Conclusion
We conclude that using this procedure will result in calibration coefficients that are independent from the absolute value of the atmospheric longwave irradiance. Based on the results, it is possible to achieve an uncertainty of ±3.51 W/m 2 using the NREL equation and an uncertainty of ±2.99 W/m 2 using the PMOD equation with respect to SI. These results suggest that the PIR calibration method might be useful in addressing the international need for a secondary standard pyrgeometer traceable to SI.