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European Journal of Applied Sciences – Vol. 10, No. 2
Publication Date: April 25, 2022
DOI:10.14738/aivp.102.12098. Reda, I., Andreas, A., & Gotseff, P. (2022). A Procedure to Correct the Historical Atmospheric Longwave Irradiance Data When the
World Reference Is Established with Respect to the International System of Units. European Journal of Applied Sciences, 10(2). 274-
281.
Services for Science and Education – United Kingdom
A Procedure to Correct the Historical Atmospheric Longwave
Irradiance Data When the World Reference Is Established with
Respect to the International System of Units
Ibrahim Reda
National Renewable Energy Laboratory, Golden, CO
Afshin Andreas
National Renewable Energy Laboratory, Golden, CO
Peter Gotseff
National Renewable Energy Laboratory, Golden, CO
ABSTRACT
Historical atmospheric longwave irradiance data sets with traceability to the
International System of Units (SI) are essential for renewable energy and
atmospheric science research and applications. To date, all pyrgeometers used to
measure the irradiance are traceable to the interim World Infrared Standard Group
(WISG), not to SI units. In 2013, the Absolute Cavity Pyrgeometer (ACP) (Reda et al.
2012) was developed at the National Renewable Energy Laboratory (NREL) to
measure the atmospheric longwave irradiance. The ACP has been compared against
the InfraRed Integrating Sphere (IRIS), developed by the Physikalisch- Meteorologisches Observatorium Davos/World Radiation Center (PMOD/WRC)
(Gröbner 2012). The ACP and the IRIS are absolute instruments traceable to SI units
through the International Temperature Scale of 1990. Results of six comparisons
between the ACP and the IRIS at different locations have shown that the irradiance
measured by WISG pyrgeometers underestimates clear-sky atmospheric longwave
irradiance by 2 W/m2 to 6 W/m2 (Gröbner et al. 2014); therefore, once the world
reference is established with traceability to SI units, the WISG would be corrected,
then used to calibrate field pyrgeometers with traceability to SI units. The following
described method is used to correct the historical atmospheric longwave irradiance
data sets in anticipation of the WISG scale change.
SIGNIFICANCE STATEMENT
The purpose of using the described method in the submitted manuscript is to correct the
historical atmospheric longwave irradiance data sets in anticipation of changing the world
reference with traceability to the International System of Units (SI). Pyrgeometers are
radiometers that measure the atmospheric longwave irradiance are deployed worldwide for
renewable energy and atmospheric science research and applications. All deployed
pyrgeometers have been calibrated using the present world reference that underestimates the
measured atmospheric longwave irradiance; therefore, once the world reference is re- established with traceability to SI, the historical data sets would be corrected with lower
uncertainty; this would undoubtedly improve the validation of satellite surface products and
climate model outputs used for renewable energy and atmospheric science applications.
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275
Reda, I., Andreas, A., & Gotseff, P. (2022). A Procedure to Correct the Historical Atmospheric Longwave Irradiance Data When the World Reference
Is Established with Respect to the International System of Units. European Journal of Applied Sciences, 10(2). 274-281.
URL: http://dx.doi.org/10.14738/aivp.102.12098
PROCEDURE
a. Measurement Equations
1) National Renewable Energy Laboratory Equation
From Reda et al. (2002):
�!"# = �$� + �%�& + �'(�( − �&) (1)
where:
• Watm is the atmospheric longwave radiation in W/m2.
• K2 and K3 are the calibration coefficients of the pyrgeometer, calibrated at the PMOD.
• K1 is the reciprocal of the pyrgeometer’s responsivity, calculated from the outdoor
calibration described below.
• V is the pyrgeometer thermopile output, in microvolts.
• Wr is the pyrgeometer receiver radiation = s * Tr
4, and Tr = Tc + K4 * V, where:
o s is Stefan-Boltzman constant = 5.6704 * 10-8 W/m2/K4
o Tc is the pyrgeometer case temperature, in Kelvin.
o S is the Seebeck coefficient = 39 V/K.
o n is the number of thermopile junctions = 56 junctions.
o E is the thermopile efficiency factor = 0.65.
o K4 is the thermopile efficiency factor equal to 1/(S * n * E) = 0.0007044 K.uV- 1.
• Wd is the pyrgeometer dome radiation = s * Td4, where Td is the dome temperature
in Kelvin.
Equation (1) is rewritten in the following form:
�)*" = �!"# − �+," = �!"# − �$� (2)
where:
• Wnet is the net irradiance measured by the pyrgeometer thermopile:
�+," = −�$� (3)
• Wout is the outgoing irradiance from the pyrgeometer:
�)*" = �% �& + �'( �( − �&) (4)
2) Physikalisch-Meteorologisches Observatorium Davos Equation
From Philipona, Fröhlich, and Ch. Betz (1995):
�!"# = -
. (1 + �$s�/
') + �%�/ + �'(�( − �/) (5)
where C is the pyrgeometer responsivity, and Tb is the case temperature.
Similar to Eq. (2) and Eq. (3):
�+," = -
. (1 + �$s�/
') (6)
�)*" = �%�/ + �'(�( − �/) (7)
b. Step-by-Step Procedure for Each Site
1. Download the data for at least 2 years. Data include pyrgeometer serial number and
calibration coefficients traceable to the WISG, V, Tcase, and Tdome.
2. Calculate Wnet using Eq. (3) or Eq. (6).
3. Calculate the minimum and maximum values of Wnet = Min and Max.
4. Choose a site where Wnet is the smallest minimum value.
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European Journal of Applied Sciences (EJAS) Vol. 10, Issue 2, April-2022
Services for Science and Education – United Kingdom
5. Define the new scale from 0 W/m2 to X W/m2, where X is the consensus value
approved by the World Meteorological Organization Commission for Instruments
and Methods of Observation. Note that 0 W/m2 represents cloudy-sky conditions,
and X W/m2 represents clear-sky conditions and the lowest Wnet at the NREL site.
6. Calculate the slope:
� = 0!1203+
425 (8)
7. Calculate the Wnet correction:
� = 6!"#
7 (9)
8. Calculate the corrected Wnet:
�+,",9)&& = �+," − � (10)
9. Calculate the corrected Watm:
�!"#,9)&& = �+,",9)&& + �)*" (11)
10. Calculate the uncertainty of the irradiance measured by each pyrgeometer with
respect to the SI units, U95:
�:; = /�&,<
% + �",="
% (12)
where:
�&,< = 0�>.?&ABA7
% + �6A7C
% (13)
The estimated values of UACP&IRIS = ± 2 W/m2 and UWISG = ± 1 W/m2; and Utest is the calibration
uncertainty of the pyrgeometer under test.
RESULTS
Historical data were downloaded from NREL’s Solar Radiation Research Laboratory Baseline
Measurement System and three U.S. Department of Energy (DOE) Atmospheric Radiation
Measurement (ARM) program sites: sgpbrsC1, spgsirsE13, and sgpserisS01. In this method, X
= 5 W/m2 is used as an example to show the following results, the consensus value of X would
be used once it is approved.
Table 1 includes sites and the pyrgeometers calibration coefficients: Utest, slope, minimum Wnet,
and U95. NREL’s slope is applied to the three DOE ARM sites because NREL is one of the
international sites that has the lowest value of Wnet.
Table 1. Sites parameters and uncertainty
Site Serial # k1 k2 k3 k4 = kr Utest slope Wnet U95
NREL PIR31193F3 0.26317 1.0006 -4 7.04E- 04
2.7 42.3 -206.3 3.5
NREL CG410548 0.0737 1.0013 0 7.04E- 04
2.9 33.5 -167.5 3.7
sgpbrsC1 PIR30695F3 0.24487 0.9968 -3.6 7.04E- 04
3.1 42.3 -141.2 3.8
spgsirsE13 PIR38870F3 0.26379 0.9942 -4.6 7.04E- 04
3.0 42.3 -147.4 3.7
sgpserisS01 PIR30689F3 0.25271 0.9963 -3.6 7.04E- 04
3.1 42.3 -84.7 3.8