NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Pyrgeometer Calibration for 

DOE-Atmospheric System Research 

program using NREL Method

Science Team Meeting

Ibrahim Reda

Tom Stoffel

Date 3/15/2010

NREL/PR-3B0-47756
National Renewable Energy Laboratory Innovation for Our Energy Future

Overview to address some ECR comments

Thermocouple/thermopile

Pyrgeometer thermodynamics

NREL & PMOD equations

NREL calibration method

Conclusion.
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Effect of increased junctions on thermopile

Vtp = n.s.e (Tr – Tref)

where,

n = number of junctions

s = Seebeck coefficient

e = thermopile efficiency. e=1 for n = 1, 2, or small number

n↑ to increase signal/noise ratio, thermal conductivity between 

receiving&reference junctions ↑, Tref effect on Tr ↑, therefore e ≠ 1

If n is not optimum → Vtp ↓ , n too large Vtp ~ zero volt
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Effect of increased thermal conductivity on PIRs

Vtp = n.s.e(Tr – Tcase)

where e = 0.65 for PIRs, measured by John Hickey for PIRs with n ~ 56 junctions 

and Seebeck coefficient ~39 μV/K, reported in:

Reda et al., (2002). Pyrgeometer Calibration at the National Renewable Energy Laboratory (NREL).

Journal of Atmospheric and Solar-Terrestrial Physics. Vol. 64(15), 2002; pp. 1623-1629.

therefore,

Tr = Tcase + 0.0007044 Vtp

Not to scale
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Simplified pyrgeometer thermodynamics

● Net Irradiance = Wnet= K1‘.Vtp

= Wincoming - Woutgoing = Wtransmitted + K3‘.(Wdome – Wr) – K2‘.Wr

where Wtransmitted = τ . Wdownwelling , and τ = Dome+Filter transmittance .. assumed to be constant

Other equations are based on assumptions: e = 1 and Woutgoing = Wcase instead of Wr !?!

● Arrange the above equation and Re-name constants, therefore,

Wdownwelling = K1.Vtp + K2.Wr – K3.(Wdome – Wr

)

This is NREL’s equation without K0 , Reda et al., (2002). Pyrgeometer Calibration at the National Renewable 

Energy Laboratory (NREL). Journal of Atmospheric and Solar-Terrestrial Physics. Vol. 64(15), 2002; pp. 1623-1629.

K0 is reserved for troubleshooting regressions & blackbody calibrations only

Not to scale
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Comparing NREL and PMOD equations

NREL Equation:

Wdownwelling = K1.Vtp + K2.Wr – K3(Wdome – Wr)

Expansion of NREL Equation to compare with PMOD equation: 

1. Tr = Tcase + 0.0007044 Vtp ..... for PIRs

2. Wdownwelling = K1.Vtp+K2.σ(Tcase + 0.0007044 Vtp )4 –K3[Wdome- σ(Tcase + 0.0007044Vtp )4]

Expand (Tcase + 0.0007044 Vtp )4 using (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4

3. Arrange terms and re-name coefficients, 

Wdownwelling = K1.Vtp + k’1 .Tcase

3. Vtp + k2.Wcase– k3(Wdome – Wcase) + k4 .Tcase2. Vtp2 +

k5 .Tcase. Vtp

3 + k6 . Vtp4

PMOD Equation:

Wdownwelling = Vtp(1 + k1.σ.Tcase

3)/c+ k2.Wcase – k3(Wdome – Wcase )

= K1.Vtp + k’1 .Tcase

3. Vtp + k2.Wcase – k3(Wdome – Wcase )

! PMOD equation = NREL equation without k4 , k5 , and k6 terms !

From many comparisons, U95 using NREL or PMOD equation = (1 to 3) W/m2 w.r.t. WISG
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NREL Calibration Procedure

Procedure is developed after many comparisons/validations with PMOD/NOAA 

Calibration is performed outdoor using a group of reference pyrgeometers with 

traceability to consensus reference, WISG

Recommended Measurement Equation:

Wdownwelling = K1.Vtp + K2.Wr – K3(Wdome – Wr

)

Process:

1. V = minimum negative magnitude (Cloudy sky), adjust K2 to minimize the 

difference between pyrgeometer under test (PUT) irradiance and reference 

irradiance

2. V = maximum negative magnitude (Clear sky), adjust K1 to minimize the 

difference between the PUT irradiance and reference irradiance

3. Adjust K3 to minimize the scatter of the differences between PUT irradiance 

and reference irradiance.

Future software development might include/evaluate regression, with uniform sets 

of data!!, to calculate the calibration coefficients
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NREL Calibration Method Validation

At least 40 pyrgeometers were calibrated using NREL method 

with uncertainty U95 < 3 W/m2 with respect to WISG, for all sky 

conditions, e.g.

-6

-4

-2

0

2

4

6

8

10

12

14

16

-500.00 -450.00 -400.00 -350.00 -300.00 -250.00 -200.00 -150.00 -100.00 -50.00 0.00

WWISG - Wtest (W/m2)

Vthermopile (uV)

Difference between the reference irradiance and the irradiance measured by 31197F3 using 

NREL method/equation
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Conclusions

NREL method achieves uncertainty of < 3 W/m2 for all sky 

conditions

NREL equation accounts for the pyrgeometer thermodynamics

Since Tr = Tcase + 0.0007044 Vtp, and response time of thermopile 

is faster than case temperature response, therefore, NREL equation 

reduces response time of measuring Wdownwelling .... needed for fast 

changes in sky conditions

At present, with the instruments/data-acquisition limitations, all 

equations might achieve U95= (1 to 3) W/m2 w.r.t. WISG

In the future, when U95 of measuring instruments and consensus 

reference is reduced, NREL equation might be a good candidate 

when uncertainty of fractions of W/m2 is needed

Manufacturers specifications to include thermopile efficiency, e, for 

accurate K2 and K3 derivation.