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. 

Uncertainty Estimates for SIRS, SKYRAD, & 

GNDRAD Data and Reprocessing the 

Pyrgeometer Data 

ASR Science Team Meeting 2012 

Ibrahim Reda, Tom Stoffel, and Aron Habte 

3/12/2012
 
 

 

 

 

 

 

The Guide to the Expression of Uncertainty in 

Measurement (GUM)*
 

Basic Steps: 

1.	 Determine the measurement equation. 

2.	 Estimate the standard uncertainty (ui

) associated with each variable in the 

measurement equation and for each component that might introduce uncertainty 

to the measurement process (e.g. interpolation, environmental conditions). 

3.	 Calculate the combined standard uncertainty (uc) by summing in quadrature the 

standard uncertainties in step 2. 

4.	 Calculate the expanded uncertainty (U) by multiplying the combined standard 

uncertainty by the coverage factor, k (typically known as Student’s “t”), or 

prescribed coverage factors for known distributions of measurements representing 

the single value of the quantity to be measured (e.g. Gaussian, triangular, 

rectangular). 

*BIPM; IEC; IFCC; ISO; IUPAP; OIML. (1995). 

Guide to the Expression of Uncertainty in Measurement, ISO TAG4, Geneva.
 

http://www.nrel.gov/docs/fy11osti/52194.pdf
 

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Uncertainty Estimates for SIRS, SKYRAD, & GNDRAD
 

Simple Expression: 

1. Determine the measurement equation: 

Pyrheliometers: Pyranometers:
 

W = V / Rs W = (V – Rnet * Wnet) / Rs
 

W = Flux (Wm-2) 

V = Thermopile Voltage (μV) 

Rs = Shortwave Responsivity (μV/Wm-2) 

Rnet = Longwave Responsity 

Wnet = Longwave Irradiance (Pyrgeometer) 

2. Estimate the standard uncertainty (ui) based on Type A and Type B error sources 

Calibration; Responses: Temperature, Spectral, Angular; Linearity, Stability, etc. 

3. Calculate the combined standard uncertainty (uc): 

uc = √ uA 

2 + uB 2 

4. Calculate the expanded uncertainty (U) 

U = k * uc (k = 1.96 for large degrees of freedom) 

http://www.nrel.gov/docs/fy11osti/52194.pdf 

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Calibration Uncertainty Estimates
 Traceable to SI Units 

Radiometer Expanded Uncertainty 

U95 = Uc * 1.96 

Pyranometer ±3% 

Pyrheliometer ±2% 

Pyrgeometer ± ( 1% + 4 Wm-2)* 

*Due to interim World Infrared Standard Group 

(WISG) 

http://www.nrel.gov/docs/fy11osti/52194.pdf
 

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Uncertainty Estimates for SIRS, SKYRAD & GNDRAD
 

Measurement Abbreviation 

Eppley 

Radiometer 

Model 

Typical 

Responsivity 

(μV/Wm-2) 

Estimated Measurement 

Uncertainty 

Value Added 

(correction for zenith, 

thermal offset, etc.) 

Direct Normal (Beam) DNI NIP 8 ±3.0% (>700 Wm-2) ±2.0% (>700 Wm-2) 

Diffuse Horizontal (Sky) DD PSP 9 +4.0% to -(4%+20 Wm-2) +2.0% to -(2%+4 Wm-2) 

Diffuse Horizontal (Sky) DD 8-48 8 +4.0% to -(4%+2Wm-2) +4.0% to -(4%+2Wm-2) 

Downwelling Shortwave 

(Global) DS PSP 9 +4.0% to -(4%+20 Wm-2) 

zenith < 80° 

+2.0% to -(2%+4 Wm-2) 

zenith < 80° 

Downwelling Longwave 

(Atmospheric) DIR PIR 4 ±(5%+4 Wm-2) * ±(1%+4 Wm-2 ) * 

Upwelling Shortwave 

(Reflected SW) US PSP 9 ±3.0% ±2.0% 

Upwelling Longwave 

(Reflected/Emitted LW) UIR PIR 4 ± 2 Wm-2 ±2 Wm-2 

* WISG uncertainty
 

All uncertainties are estimated with respect to the Système international d'unités (SI) and represent optimal maintenance and installation.
 

References:
 

- Reda, I. (2011). "Method to Calculate Uncertainty Estimate of Measuring Shortwave Solar Irradiance using Thermopile and Semiconductor Solar Radiometers". 20
 

pp.; NREL Report No. TP-3B10-52194
 

- Reda, I.; Zeng, J.; Scheuch, J.; Hanssen, L.; Wilthan, B.; Myers, D.; Stoffel, T., 2012. “An absolute cavity pyrgeometer to measure the absolute outdoor longwave
 

irradiance with traceability to International System of Units, SI”. Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 132-143.
 

http://dx.doi.org/10.1016/j.jastp.2011.12.011
 

5
 
 

 

lrradiance difference (Reference - Test) using the Manufacturer 

calibration coefficients for nine test pyrgeometers 

Outdoors at SGP from December 15, 2006 to January 31, 2007 

·- ·- ·- ·- · fMax: ten1p·.-Gradre·rrt - ·- ·- ·-· t ·-·-·-·-·-t·-·-· Mtn-:f temp-.· N:I t""'H or•'~'-

: =: =: =: =: ~: =: k~ : g ~a:= ~:= =:=:=: i: =: =: =: =: ~: =: =: =: = (K~ IY ~ g ~ . y). =: =: =: 

. . -.-;,..-. - +.-.-. --. -t.-.-.-.-. ~.-.-.-.-. 

-700 -600 -500 -400 -300 -200 -100 0 100 

VTP (uV) 

• 30836F3 • 30696F3 A29593F3 29147F3 X30020F3 • 30132F3 + 28630F3 29926F3 - 29927F3 

20 

17.5 

15 

12.5 

10 N 

E 7.5-

5 s 

2.5 

0 

-2.5 

-5 

Pyrgeometer Calibrations: WISG vs. Blackbody Results 

Dome coefficient = 3.5
 

Reference: Reda et al., 2007. “ARM/NREL Pyrgeometer Calibrations with Traceability to the World Infrared Standard Group (WISG)”. ARM-CONF2007, March 2007 Monterey, California 

6
 
 

 

Pyrgeometer Outdoor Calibration vs. Manufacturer Blackbody 

Calibration Histograms
 

0 

2000 

4000 

6000 

8000 

10000 

12000 

14000 

16000 

18000 

20000 

-6.7 -5.2 -3.7 -2.2 -0.7 0.8 2.3 3.8 5.3 6.8 8.3 9.8 11.3 

Frequency 

Difference = WWISG - WTe s t (Wm-2) 

All Dat a for 9 PI Rs 30836F3 30696F3 29593F3 29147F3 30020F3 30132F3 28630F3 29926F3 29927F3 

RMS of all data = 3.4 Wm-2 

Could be >> 8.5 Wm-2 

-1.96* Stdev = -4.1 Wm-2 1.96*Stdev = 4.1 Wm-2 

7
 
 

 

 

Pyrgeometer Aging Study 

Manufacturer BB re-calibration after seven years of field deployment
 

S/N Location 

Date 

Deployed 

Eppley Cal 

[uV/Wm-2] 

Date 

Returned 

from Eppley 

New Eppley 

Cal 

[uV/(W/m-2 )] 

%difference 

between 

cals 

%aging/year 

for a 7-year 

deployment 

Cal 

interval 

(Year) 

Error in 

Wincoming 

(Wm-2) 

30779F3 Ringwood, OK 8/17/2004 3.77 4/28/2011 3.79 0.53 0.08 1 0.15 

30832F3 Vici, OK 8/18/2004 3.71 4/28/2011 3.67 -1.08 -0.15 1 -0.31 

30688F3 Meeker, OK 8/19/2004 3.88 4/28/2011 3.9 0.52 0.07 1 0.15 

30785F3 Ashton, KS 12/14/2004 4.14 4/28/2011 4.09 -1.21 -0.17 1 -0.35 

30344F3 Pawhuska, OK 12/7/2004 3.95 4/28/2011 3.96 0.25 0.04 1 0.07 

30010F3 Lamont, OK 8/27/2004 3.2 4/28/2011 3.24 1.25 0.18 1 0.35 

From the inconsistency of the difference, no conclusion, yet a 2-year cal interval is reasonable 

8
 
 

 

 

 

 

 

Sampling Rate Effect for Correcting Historical Data
 

-Randomness of the data is a result of the nonlinearity of the basic variables in the pyrgeometer equation, i.e., resistanceto-temperature, (temperature)4, etc.
 

-Correcting the 1-min average might introduce > ± 2 W/m 2 randomness to the corrected data (site dependent)
 

-Correcting the present 20-sec irradiance data is more appropriate, yet it will introduce greater randomness than that
 

corrected using the 2-second irradiance, site dependent ... challenging for space/etc, yet it might not be an issue in the near
 

future.
 

9
 
Implementing a New Calibration System 
 

Broadband Outdoor Radiometer Calibration
 

System for Data Acquisition, Analyses, Reporting, Archival 

BORCAL/SW BORCAL/LW
 

• Pyrheliometers 

• Pyrgeometers 

• Pyranometers 

10
 
 

 

 

 

 

Implementing a New BORCAL/LW System
 

SRRL – 5 PIRs 

BORCAL/LW @ SRRL 

Data Acquisition + Auto Analyses + Certs + Reports + Archive 

SGP/RCF – 5 PIRs 

BORCAL/LW @ SGP/RCF
 

Hardware & Software Installation
 

Data Acquisition + Auto Analyses + Certs + Reports + Archive
 

Validation 

(5 PIRs) 

Operational 

31 March 2013 

11
 
What Happened to the Schedule?
 

•	 SRRL down for
 

8 months
 

instead of 6 

weeks!
 

•	 NPC-2011
 

•	 BORCAL-2012
 

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