ASTM G213-17(2023)

Standard Guide for Evaluating Uncertainty in Calibration and Field Measurements of Broadband Irradiance with Pyranometers and Pyrheliometers

SIGNIFICANCE AND USE
5.1 The uncertainty in outdoor solar irradiance measurement has a significant impact on weathering and durability and the service lifetime of materials systems. Accurate solar irradiance measurement with known uncertainty will assist in determining the performance over time of component materials systems, including polymer encapsulants, mirrors, Photovoltaic modules, coatings, etc. Furthermore, uncertainty estimates in the radiometric data have a significant effect on the uncertainty of the expected electrical output of a solar energy installation.  
5.1.1 This influences the economic risk analysis of these systems. Solar irradiance data are widely used, and the economic importance of these data is rapidly growing. For proper risk analysis, a clear indication of measurement uncertainty should therefore be required.  
5.2 At present, the tendency is to refer to instrument datasheets only and take the instrument calibration uncertainty as the field measurement uncertainty. This leads to over-optimistic estimates. This guide provides a more realistic approach to this issue and in doing so will also assists users to make a choice as to the instrumentation that should be used and the measurement procedure that should be followed.  
5.3 The availability of the adjunct (ADJG021317)5 uncertainty spreadsheet calculator provides real world example, implementation of the GUM method, and assists to understand the contribution of each source of uncertainty to the overall uncertainty estimate. Thus, the spreadsheet assists users or manufacturers to seek methods to mitigate the uncertainty from the main uncertainty contributors to the overall uncertainty.
SCOPE
1.1 This guide provides guidance and recommended practices for evaluating uncertainties when calibrating and performing outdoor measurements with pyranometers and pyrheliometers used to measure total hemispherical- and direct solar irradiance. The approach follows the ISO procedure for evaluating uncertainty, the Guide to the Expression of Uncertainty in Measurement (GUM) JCGM 100:2008 and that of the joint ISO/ASTM standard ISO/ASTM 51707 Standard Guide for Estimating Uncertainties in Dosimetry for Radiation Processing, but provides explicit examples of calculations. It is up to the user to modify the guide described here to their specific application, based on measurement equation and known sources of uncertainties. Further, the commonly used concepts of precision and bias are not used in this document. This guide quantifies the uncertainty in measuring the total (all angles of incidence), broadband (all 52 wavelengths of light) irradiance experienced either indoors or outdoors.  
1.2 An interactive Excel spreadsheet is provided as adjunct, ADJG021317. The intent is to provide users real world examples and to illustrate the implementation of the GUM method.  
1.3 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Published
• Publication Date: 31-Dec-2022
• ICS: 07.060 - Geology. Meteorology. Hydrology
• Technical Committee: G03 - Weathering and Durability
• Drafting Committee: G03.09 - Radiometry

Relations

• Refers: ASTM G113-14 - Standard Terminology Relating to Natural and Artificial Weathering Tests of Nonmetallic Materials
• Effective Date: 01-Mar-2014
• Refers: ASTM E772-13 - Standard Terminology of Solar Energy Conversion
• Effective Date: 01-Sep-2013
• Refers: ASTM E772-11 - Standard Terminology of Solar Energy Conversion
• Effective Date: 01-Sep-2011
• Refers: ASTM G167-05(2010) - Standard Test Method for Calibration of a Pyranometer Using a Pyrheliometer
• Effective Date: 01-Dec-2010
• Refers: ASTM G113-09 - Standard Terminology Relating to Natural and Artificial Weathering Tests of Nonmetallic Materials
• Effective Date: 15-Jun-2009
• Refers: ASTM G113-08 - Standard Terminology Relating to Natural and Artificial Weathering Tests of Nonmetallic Materials
• Effective Date: 01-Aug-2008
• Refers: ASTM G113-06 - Standard Terminology Relating to Natural and Artificial Weathering Tests of Nonmetallic Materials
• Effective Date: 01-Dec-2006
• Refers: ASTM G113-06e1 - Standard Terminology Relating to Natural and Artificial Weathering Tests of Nonmetallic Materials
• Effective Date: 01-Dec-2006
• Refers: ASTM G167-05 - Standard Test Method for Calibration of a Pyranometer Using a Pyrheliometer
• Effective Date: 01-Oct-2005
• Refers: ASTM G113-05 - Standard Terminology Relating to Natural and Artificial Weathering Tests of Nonmetallic Materials
• Effective Date: 15-Aug-2005
• Refers: ASTM E772-05 - Standard Terminology Relating to Solar Energy Conversion
• Effective Date: 01-Apr-2005
• Refers: ASTM G113-03 - Standard Terminology Relating to Natural and Artificial Weathering Tests of Nonmetallic Materials
• Effective Date: 10-Feb-2003
• Refers: ASTM G113-94 - Standard Terminology Relating to Natural and Artificial Weathering Tests of Nonmetallic Materials
• Effective Date: 10-Jul-2001
• Refers: ASTM G113-01 - Standard Terminology Relating to Natural and Artificial Weathering Tests of Nonmetallic Materials
• Effective Date: 10-Jul-2001
• Refers: ASTM G167-00 - Standard Test Method for Calibration of a Pyranometer Using a Pyrheliometer
• Effective Date: 10-Feb-2000

Overview

ASTM G213-17(2023), titled Standard Guide for Evaluating Uncertainty in Calibration and Field Measurements of Broadband Irradiance with Pyranometers and Pyrheliometers, is an international standard developed by ASTM. The guide addresses the crucial need for properly evaluating measurement uncertainties in solar irradiance data, particularly when using pyranometers and pyrheliometers. Accurate uncertainty estimates are essential for applications in weathering testing, durability assessment, photovoltaic power prediction, and economic risk analyses related to solar energy systems. Adhering to best practices for uncertainty evaluation helps stakeholders ensure that decisions based on solar irradiance data are reliable and defensible.

Key Topics

• Measurement Uncertainty in Solar Irradiance: The guide covers sources of uncertainty in both the calibration and field deployment of broadband solar radiometers, describing why rigorous evaluation is essential for trustworthy data.
• Focus on Pyranometers and Pyrheliometers: Specialized guidance is provided for these instruments, widely used to measure total hemispherical (global) and direct solar irradiance.
• Importance for Economic Risk and Performance Analysis: Accurate solar measurements, accompanied by confidence in their uncertainty estimates, impact not only scientific results but also the financial modeling and long-term performance predictions for solar installations.
• Realistic Uncertainty Assessment: The standard counters the common and overly simplistic practice of equating field measurement uncertainty with calibrator-reported uncertainty alone, guiding users to a more nuanced and accurate approach.
• ISO-aligned Methodology: The approach follows international uncertainty evaluation practices, referencing the Guide to the Expression of Uncertainty in Measurement (GUM) and ISO/ASTM 51707.
• Practical Application Tools: An interactive Excel spreadsheet (adjunct ADJG021317) is included to help users calculate overall uncertainty and understand how different uncertainty sources contribute to the total value.

Applications

ASTM G213-17(2023) is widely applicable across:

• Materials Weathering and Durability Testing: Accurately assess how materials (e.g., polymer encapsulants, coatings, mirrors) degrade under outdoor solar exposure, incorporating known measurement uncertainty into performance and lifetime estimates.
• Photovoltaic and Solar Thermal System Performance: Precise uncertainty evaluation in solar resource measurements directly affects energy yield estimates, system design decisions, and long-term monitoring of solar installations.
• Economic Risk Analysis: Quantifying the confidence in irradiance measurements improves risk modeling for investments in solar infrastructure, supporting informed decision-making.
• Instrument Calibration Laboratory Procedures: Provides guidance for calibration labs on best practices for uncertainty estimation, ensuring traceable and reproducible results.
• Field Deployment and Operation: Users in practical settings, such as solar farms or meteorological stations, can use the guide to document uncertainty budgets, select appropriate instruments, and establish robust measurement protocols.

Related Standards

ASTM G213-17(2023) references and complements several key international standards:

• ISO/IEC Guide 98-3: Guide to the Expression of Uncertainty in Measurement (GUM)
• ISO/ASTM 51707: Standard Guide for Estimating Uncertainties in Dosimetry for Radiation Processing
• ISO 9060: Solar Energy - Specification and Classification of Instruments for Measuring Hemispherical Solar and Direct Solar Radiation
• ASTM E772 and G113: Terminology standards related to solar energy and natural/artificial weathering tests
• ASTM G167: Test Method for Calibration of a Pyranometer Using a Pyrheliometer

By integrating these related documents, users can achieve comprehensive uncertainty analysis, consistent terminology, and harmonized metrological procedures across solar radiometry applications.

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Keywords: ASTM G213, solar irradiance measurement, pyranometer uncertainty, pyrheliometer calibration, broadband solar radiometry, GUM method, measurement uncertainty, risk analysis, photovoltaic performance, solar energy standards.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: G213 − 17 (Reapproved 2023)
Standard Guide for
Evaluating Uncertainty in Calibration and Field
Measurements of Broadband Irradiance with Pyranometers
and Pyrheliometers
This standard is issued under the fixed designation G213; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope Development of International Standards, Guides and Recom-
mendations issued by the World Trade Organization Technical
1.1 This guide provides guidance and recommended prac-
Barriers to Trade (TBT) Committee.
tices for evaluating uncertainties when calibrating and per-
forming outdoor measurements with pyranometers and pyrhe-
2. Referenced Documents
liometers used to measure total hemispherical- and direct solar
2.1 ASTM Standards:
irradiance. The approach follows the ISO procedure for evalu-
E772Terminology of Solar Energy Conversion
atinguncertainty,theGuidetotheExpressionofUncertaintyin
G113Terminology Relating to Natural andArtificial Weath-
Measurement (GUM) JCGM 100:2008 and that of the joint
ering Tests of Nonmetallic Materials
ISO/ASTM standard ISO/ASTM 51707 Standard Guide for
G167Test Method for Calibration of a Pyranometer Using a
Estimating Uncertainties in Dosimetry for Radiation
Pyrheliometer
Processing,butprovidesexplicitexamplesofcalculations.Itis
Guide for Estimating Uncertainties in Dosimetry for Radia-
up to the user to modify the guide described here to their
tion Processing
specific application, based on measurement equation and
2.2 ASTM Adjunct:
known sources of uncertainties. Further, the commonly used
ADJG021317CD Excel spreadsheet- Radiometric Data Un-
concepts of precision and bias are not used in this document.
certainty Estimate Using GUM Method
Thisguidequantifiestheuncertaintyinmeasuringthetotal(all
2.3 ISO Standards
angles of incidence), broadband (all 52 wavelengths of light)
ISO 9060Solar Energy—Specification and Classification of
irradiance experienced either indoors or outdoors.
Instruments for Measuring Hemispherical Solar and Di-
1.2 An interactive Excel spreadsheet is provided as adjunct,
rect Solar Radiation
ADJG021317. The intent is to provide users real world
ISO/IEC Guide 98-3 Uncertainty of Measurement—Part 3:
examples and to illustrate the implementation of the GUM
Guide to the Expression of Uncertainty in Measurement
method.
(GUM:1995)
1.3 The values stated in SI units are to be regarded as
ISO/IEC JCGM 100:2008 GUM 1995, with Minor
standard. No other units of measurement are included in this Corrections, Evaluation of Measurement Data—Guide to
standard.
the Expression of Uncertainty in Measurement
1.4 This standard does not purport to address all of the
3. Terminology
safety concerns, if any, associated with its use. It is the
3.1 Standard terminology related to solar radiometry in the
responsibility of the user of this standard to establish appro-
fields of solar energy conversion and weather and durability
priate safety, health, and environmental practices and deter-
testing are addressed inASTMTerminologies E772 and G113,
mine the applicability of regulatory limitations prior to use.
respectively.Someofthedefinitionsoftermsusedinthisguide
1.5 This international standard was developed in accor-
may also be found in ISO/ASTM 51707.
dance with internationally recognized principles on standard-
ization established in the Decision on Principles for the
3.2 Definitions of Terms Specific to This Standard:
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
This test method is under the jurisdiction of ASTM Committee G03 on contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
Weathering and Durability and is the direct responsibility of Subcommittee G03.09 Standards volume information, refer to the standard’s Document Summary page on
on Radiometry. the ASTM website.
Current edition approved Jan. 1, 2023. Published January 2023. Originally Available from International Organization for Standardization (ISO), ISO
approved in 2017. Last previous edition approved in 2017 as G213–17. DOI: Central Secretariat, BIBC II, Chemin de Blandonnet 8, CP 401, 1214 Vernier,
10.1520/G0213-17R23. Geneva, Switzerland, http://www.iso.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
G213 − 17 (2023)
3.2.1 aging (non-stability), n—a percent change of the organization(suchastheWorldRadiationCenter(WRC)ofthe
responsivityperyear;itisameasureoflong-termnon-stability. World Meteorological Organization (WMO)).
3.2.2 azimuth response error, n—ameasureofdeviationdue
3.2.13 reference radiometer, n—radiometer of high metro-
to responsivity change versus solar azimuth angle. logical quality, used as a standard to provide measurements
traceable to measurements made using primary standard radi-
NOTE 1—Often cosine and azimuth response are combined as “Direc-
ometer.
tional response error,” which is a percent deviation of the radiometer’s
responsivity due to both zenith and azimuth responses.
3.2.14 response function, n—mathematical or tabular repre-
3.2.3 broadband irradiance, n—the solar radiation arriving
sentation of the relationship between radiometer response and
at the surface of the earth from all wavelengths of light
primary standard reference irradiance for a given radiometer
(typically wavelength range of radiometers 300 nm to 3000
system with respect to some influence quantity. For example,
nm).
temperature response of a pyrheliometer, or incidence angle
response of a pyranometer.
3.2.4 calibration error, n—the difference between values
indicatedbytheradiometerduringcalibrationand“truevalue.”
3.2.15 routine (field) radiometer, n—instrument calibrated
against a primary-, reference-, or transfer-standard radiometer
3.2.5 cosine response error, n—a measure of deviation due
and used for routine solar irradiance measurement.
to responsivity change versus solar zenith angle. See Note 1.
3.2.6 coverage factor, n—numerical factor used as a multi- 3.2.16 sensitivity coeffıcient (function), n—describes how
sensitivetheresultistoaparticularinfluenceorinputquantity.
plierofthecombinedstandarduncertaintyinordertoobtainan
expanded uncertainty. 3.2.16.1 Discussion—Mathematically,itispartialderivative
of the measurement equation with respect to each of the
3.2.7 data logger accuracy error, n—a deviation of the
independent variables in the form:
voltage or current measurement of the data logger due to
resolution, precision, and accuracy. δy
y x 5 c 5 (2)
~ !
i i
δx
3.2.8 effective degrees of freedom, n—ν , for multiple (N) i
eff
where y(x,x , …x) is the measurement equation in inde-
1 2 i
sources of uncertainty, each with different individual degrees
pendent variables, x.
i
of freedom, ν that generate a combined uncertainty u , the
i c
3.2.17 soiling effect, n—a percent change in measurement
Welch-Satterthwaite formula is used to compute:
due to the amount of soiling on the radiometer’s optics.
u
c
v 5 (1)
i
eff 3.2.18 spectral mismatch error, radiometer, n—a deviation
u
N
Σ
i51
introduced by the change in the spectral distribution of the
v
i
incident solar radiation and the difference between the spectral
3.2.9 expanded uncertainty, n—quantity defining the inter-
response of the radiometer to a radiometer with completely
val about the result of a measurement that may be expected to
homogeneous spectral response in the wavelength range of
encompass a large fraction of the distribution of values that
interest.
could reasonably be attributed to the measurand.
3.2.19 temperature response error, n—a measure of devia-
3.2.9.1 Discussion—Expanded uncertainty is also referred
tion due to responsivity change versus ambient temperature.
to as “overall uncertainty” (BIPM Guide to the Expression of
Uncertainty in Measurement). To associate a specific level of
3.2.20 tilt response error, n—a measure of deviation due to
confidence with the interval defined by the expanded uncer-
responsivity change versus instrument tilt angle.
tainty requires explicit or implicit assumptions regarding the
3.2.21 transfer standard radiometer, n—radiometer, often a
probability distribution characterized by the measurement
reference standard radiometer, suitable for transport between
result and its combined standard uncertainty. The level of
different locations, used to compare routine (field) solar radi-
confidencethatmaybeattributedtothisintervalcanbeknown
ometer measurements with solar radiation measurements by
only to the extent to which such assumptions may be justified.
the transfer standard radiometer.
3.2.10 leveling error, n—a measure of deviation or asym-
3.2.22 Type A standard uncertainty, adj—method of evalu-
metryintheradiometerreadingduetoimpreciselevelingfrom
ation of a standard uncertainty by the statistical analysis of a
the intended level plane.
series of observations, resulting in statistical results such as
3.2.11 non-linearity, n—a measure of deviation due to
sample variance and standard deviation.
responsivity change versus irradiance level.
3.2.23 Type B standard uncertainty, adj—method of evalu-
3.2.12 primary standard radiometer, n—radiometer of the
ation of a standard uncertainty by means other than the
highest metrological quality established and maintained as an
statistical analysis of a series of observations, such as pub-
irradiance standard by a national (such as National Institute of
lished specifications of a radiometer, manufacturers’
Standards and Technology (NIST)) or international standards
specifications, calibration, or previous experience, or combi-
nations thereof.
3.2.24 zero offset A, n—a deviation in measurement output
InternationalBureauofWeightsandMeasures(BIPM)WorkingGroup1ofthe 2
(W/m ) due to thermal radiation between the pyranometer and
Joint Committee for Guides in Metrology (JCGM/WG 1).2008. “Evaluation of
the sky, resulting in a temperature imbalance in the pyranom-
Measurement Data—Guide to the Expression of Uncertainty in Measurement
(GUM).” JCGM 100:2008 GUM 1995 with minor corrections. eter.
G213 − 17 (2023)
3.2.25 zero offset B, n—a deviation in measurement output deriving the sensitivity coefficient using a partial derivative
(W/m ) due to a change (or ramp) in ambient temperature. approach from the measurement equation, and combining the
standarduncertaintyandthesensitivitytermusingtherootsum
NOTE 2—Both Zero Offset A and Zero Offset B are sometimes
of the squares, and lastly calculating the expanded uncertainty
combined as “Thermal offset,” which are due to energy imbalances not
directly caused by the incident short-wave radiation. by multiplying the combined uncertainty by a coverage factor
(Fig. 1). Some of the possible sources of uncertainties and
4. Summary of Test Method
associated errors are calibration, non-stability, zenith and
4.1 The evaluation of the uncertainty of any measurement
azimuth response, spectral mismatch, non-linearity, tempera-
system is dependent on two specific components: a) the
ture response, aging per year, datalogger accuracy, soiling, etc.
uncertainty in the calibration of the measurement system, and
These sources of uncertainties were obtained from manufac-
b) the uncertainty in the routine or field measurement system.
turers’ specifications, previously published reports on radio-
This guide provides guidance for the basic components of
metricdatauncertainty,orexperience,orcombinationsthereof.
uncertainty in evaluating the uncertainty for both the calibra-
4.2.1 Both calibration and field measurement uncertainty
tion and measurement uncertainty estimates. The guide is
employ the GUM method in estimating the expanded uncer-
based on the International Bureau of Weights and Measures
tainty (overall uncertainty) and the components mentioned
(acronym from French name: BIPM) Guide to the Uncertainty
above are applicable to both. The calibration of broadband
in Measurements, or GUM.
radiometers involves the direct measurement of a standard
4.2 The approach explains the following components; de- source (solar irradiance (outdoor) or artificial light (indoor)).
The accuracy of the calibration is dependent on the sky
fining the measurement equation, determining the sources of
uncertainty, calculating standard uncertainty for each source, condition or artificial light, specification of the test instrument
FIG. 1 Calibration and Measurement Uncertainty Estimation Flow Chart
Modified from Habte A., Sengupta M., Andreas A., Reda I., Robinson J. 2016. “The Impact of Indoor and Outdoor Radiometer Calibration on Solar Measurements,”
NREL/PO-5D00-66668. http://www.nrel.gov/docs/fy17osti/66668.pdf.
G213 − 17 (2023)
(zenith response, spectral response, non-linearity, temperature engineering units for measurements). Eq 3 and Eq 4 are
response, aging per year, tilt response, etc.), and reference equations used for calculating responsivity or irradiance and
instruments.All of these factors are included when estimating
they are used here for example purposes.
calibration uncertainties.
Calibration Equation: Field Measurement Equation:
sV 2 R 3 W
net net
NOTE 3—The calibration method example mentioned in Appendix X1 R5
V 2 R 3 W
s d
net net
G
G5 (3)
is based on outdoor calibration using the solar irradiance as the source.
R
5. Significance and Use
G5N3Cos Z 1 D
s d
5.1 The uncertainty in outdoor solar irradiance measure-
where R is the pyranometer’s responsivity, in microvolt per
−2
menthasasignificantimpactonweatheringanddurabilityand
watt per square meter µV/(Wm ),
the service lifetime of materials systems. Accurate solar
V is the pyranometer’s sensor output voltage, in µV
irradiance measurement with known uncertainty will assist in
N is the beam irradiance measured by a primary or standard
determiningtheperformanceovertimeofcomponentmaterials
reference standard pyrheliometer, measuring the beam irradi-
systems, including polymer encapsulants, mirrors, Photovol- −2
ance directly from the sun’s disk in Wm ,
taic modules, coatings, etc. Furthermore, uncertainty estimates
Z is the solar zenith angle, in degrees,
in the radiometric data have a significant effect on the uncer-
D is the diffuse irradiance, sky irradiance without the beam
tainty of the expected electrical output of a solar energy
irradiance from the sun’s disk, measured by a shaded
installation.
pyranometer,
5.1.1 This influences the economic risk analysis of these
−2
G is the calculated irradiance, in Wm ,
systems. Solar irradiance data are widely used, and the
Rnet is the pyranometer’s net infrared responsivity, in µV/
economic importance of these data is rapidly growing. For
−2
(Wm ), and
proper risk analysis, a clear indication of measurement uncer-
Wnet is the net infrared irradiance measured by a collocated
tainty should therefore be required.
−2
pyrgeometer, measuring the atmospheric infrared, in Wm ,if
5.2 At present, the tendency is to refer to instrument
known. If not known, or not applicable, explicit magnitude
datasheets only and take the instrument calibration uncertainty
(even if assumed to be zero, e.g., for a silicon detector
as the field measurement uncertainty. This leads to over-
radiometer) for the uncertainty associated with these terms
optimistic estimates. This guide provides a more realistic
must be stated. G is the calculated irradiance. The measure-
approach to this issue and in doing so will also assists users to
ment equation with unknown or not applicable Wnet and Rnet
makeachoiceastotheinstrumentationthatshouldbeusedand
is:
the measurement procedure that should be followed.
V
5.3 The availability of the adjunct (ADJG021317) uncer- G 5 (4)
R
tainty spreadsheet calculator provides real world example,
implementation of the GUM method, and assists to understand
6.1.2 Determine Sources of Uncertainties—Most of the
the contribution of each source of uncertainty to the overall
sources of uncertainties (expanded uncertainties, denoted by
uncertainty estimate. Thus, the spreadsheet assists users or
U) were obtained from manufacturers’ specifications, previ-
manufacturerstoseekmethodstomitigatetheuncertaintyfrom
ously published reports on radiometric data uncertainty or
the main uncertainty contributors to the overall uncertainty.
professional experience. Some of the common sources of
uncertainties are:
6. Basic Uncertainty Components for Evaluating
Solar Zenith Angle Response: pyranometer specification
Measurement Uncertainty of Pyranometers and
sheet
Pyrheliometers
SpectralResponse:userestimate/pyranometerspecification
6.1 As described in the BIPM GUM and summarized in
sheet
6 7
Reda et al. 2008, and Reda 2011, the process for both
Non-linearity: pyranometer specification sheet
calibrationandfieldmeasurementuncertaintyfollowssixbasic
Temperature response: pyranometer specification sheet
uncertainty components:
Aging per year: pyranometer specification sheet
6.1.1 Determine the Measurement Equation for the Calibra-
Data logger accuracy: data logger specification sheet
tion Measurement System (or both)—Mathematical description
Maintenance (for example, soiling): user estimate
of the relation between sensor voltage and any other indepen-
Calibration: calibration certificate
dent variables and the desired output (calibration response, or
6.1.3 Calculate the Standard Uncertainty, u—calculateufor
each variable in the measurement equation, using either statis-
Available from ASTM International Headquarters. Order Adjunct No. tical methods (Type A uncertainty component) or other than
ADJG021317. Original adjunct produced in ADJG021317. Adjunct last revised in
statistical methods (Type B uncertainty component), such as
2017.
manufacturer specifications, calibration results, and experi-
Reda, I.; Myers, D.; Stoffel, T. (2008).” Uncertainty Estimate for the Outdoor
mental or engineering experience.
Calibration of Solar Pyranometers: A Metrologist Perspective. Measure.” NCSLI
Journal of 100 Measurement Science. Vol. 3(4), December 2008; 58-66.
6.1.3.1 V: Sensor output voltage: from either the manufac-
Reda, I. Technical Report NREL/TP-3B10–52194. Method to Calculate Un-
turer’s specifications of the data acquisition manual, specifica-
certainties in Measuring Shortwave Solar Irradiance Using Thermopile and
Semiconductor Solar Radiometers. 2011. tion data, or the most recent calibration certificate.
G213 − 17 (2023)
6.1.3.2 Rnet: From the manufacturer’s specifications, ex- irradiance value. Therefore, the sensitivity coefficient for each
perimental data, or an estimate based on experience. inputiscalculatedbypartialdifferentiationwithrespecttoeach
6.1.3.3 Wnet: From an estimate based on historical net input variable in the measurement equation. The respective
infrared at the site using pyrgeometer data and experience. sensitivity coefficient equations based on Eq 3 are:
6.1.3.4 N: From the International Pyrheliometer Compari-
Calibration Sensitivity Equations Field Measurement Sensitivity
son (IPC) report described in reference or a pyrheliometer Equations
δR 1 δG 2 V 2 R net 3 W net
s d
comparisons certificate based on annual calibrations or com-
c 5 5 c 5 5
v R
δV N CossZd 1 D δR R
parisons to primary reference radiometers traceable to the
δR 2Wnet δG 2Wnet
world radiometric reference, or combinations thereof.
c 5 5 c 5 5
Rnet Rnet
δRnet N Cos Z 1 D δRnet R
s d
6.1.3.5 Z: From a solar position algorithm for calculating
solar zenith angle and a time resolution of 1 second. δR 2Rnet δG 2Rnet
c 5 5 c 5 5
Wnet Wnet
δWnet NCossZd 1D δWnet R
6.1.3.6 D:Fromadiffusepyranometercalibrationdescribed
in Test Method G167.
δR δG 1
c 5 c 5 5
N v
6.1.3.7 Discussion—Type A and Type B classification are δN δV R
2sV 2 R net W net d CossZd
basedondistributionofthemeasurement,andarequirementof 5
sN Cos sZd 1 Dd
theGUMapproachistoassociateeachsourceofuncertaintyto
δR
a specific distribution, either measured or assumed. See Ap-
c 5
Z
δZ
pendix X2 for a summary of typical distribution types (rectan-
N SinsZdsV 2 R net W net d
gular or uniform, Gaussian or normal, triangular, etc.) and the sN Cos sZd 1 Dd
associated form of standard uncertainty calculation.
δR 2 V 2 R net W net
s d
c 5 5
IntheTypeB,whenthedistributionoftheuncertaintyisnot D
δD sN Cos sZd 1 Dd
known, it is common to assume a rectangular distribution. In
this case, the expanded uncertainty of a source of uncertainty
6.1.5 Combined Standard Uncertainty, u —Calculate the
c
with unknown distribution is divided by the square root of
combined standard uncertainty using the propagation of errors
three.
formula and quadrature (root-sum-of-squares) method.
6.1.5.1 ThecombineduncertaintyisapplicabletobothType
U 3a
u 5 (5)
A and Type B sources of uncertainties. Standard uncertainties
=3
(u) multiplied by their sensitivity factors (c) are combined in
where U is the expanded uncertainty of a variable, and a is
quadrature to give the combined standard uncertainty, u .
the variable in a unit of measurement. For normal c
distribution, the equation is as follows:
n21
u 5 Σ u 3 c (8)
~ !
Œ
c i i
U 3a
i50
u 5 (6)
k
6.1.6 Calculate the Expanded Uncertainty (U ) by multi-
TypeAstandard uncertainty is calculated by taking repeated
plyingthecombinedstandarduncertaintybyacoveragefactor,
measurement of the input quantity value, from which the
k, based on the equivalent degrees of freedom (see section
sample mean and sample standard deviation (SD) can be
3.2.9).
calculated. The Type A standard uncertainty (u) is estimated
U 5 u 3k (9)
95 c
by:
6.1.6.1 Typically, k = 1, 2, or 3 implies that the true value
n 2
Σ x 2 x¯
~ !
i51 i
lies within the confidence interval defined by y 6 U with
SD 5Π(7)
n 2 1
confidence level of either 68.27 %, 95.45 %, or 99.73 % of the
where X represents individual input quantity, x¯ is the mean
time, respectively. These ranges are meant to be analogous to
of the input quantity, and n equals the number of repeated
the relation of the coverage of a normally distributed data set
measurement of the quantity value.
by numbers of standard deviations of such a data set. Thus U
6.1.4 Sensitivity Coeffıcient, c—The GUM method requires
is often denoted as U or U .
95 99
calculating the sensitivity coefficients (c) of the variables in a
i
7. Keywords
measurement equation. These coefficients affect the contribu-
tion of each input factor to the combined uncertainty of the
7.1 GUM; irradiance; pyranometers; pyrheliometers
G213 − 17 (2023)
APPENDIXES
(Nonmandatory Information)
X1. EXAMPLE OF CALIBRATION AND MEASUREMENT UNCERTAINTY ESTIMATION
X1.1 Overview and sensitivity functions for influencing quantities. Lastly,
report the combined standard uncertainties and expanded
X1.1.1 This section provides examples of a) evaluating the
uncertainty.
uncertainty in the calibration of pyranometers for measuring
total hemispherical solar radiation, and b) evaluating the
X1.2 Evaluating Field Measurement Uncertainty: As
uncertaintyinaroutinepyranometerfieldmeasurementsystem
calibration uncertainty is propagated as an element of field
for measuring total hemispherical solar radiation. The ex-
measurement uncertainty; and that to start with a somewhat
amples follow the approach described in Reda et al. 2008 for
simpler example, looking at the field measurement uncertainty
calibration, and Reda 2011, for measuring solar irradiance
as an introduction is suggested because the calibration uncer-
using thermopile or semiconductor radiometers.
ta
...