ASTM G213-17(2023)

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 service@astm.org. 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
i
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