Designation: G213 − 17Standard Guide forEvaluating Uncertainty in Calibration and FieldMeasurements of Broadband Irradiance with Pyranometersand Pyrheliometers1This standard is issued under the fixed designation G213; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This guide provides guidance and recommended prac-tices for evaluating uncertainties when calibrating and per-forming outdoor measurements with pyranometers and pyrhe-liometers used to measure total hemispherical- and direct solarirradiance. The approach follows the ISO procedure for evalu-ating uncertainty, the Guide to the Expression of Uncertainty inMeasurement (GUM) JCGM 100:2008 and that of the jointISO/ASTM standard ISO/ASTM 51707 Standard Guide forEstimating Uncertainties in Dosimetry for RadiationProcessing, but provides explicit examples of calculations. It isup to the user to modify the guide described here to theirspecific application, based on measurement equation andknown sources of uncertainties. Further, the commonly usedconcepts of precision and bias are not used in this document.This guide quantifies the uncertainty in measuring the total (allangles 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 worldexamples and to illustrate the implementation of the GUMmethod.1.3 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.1.5 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2E772 Terminology of Solar Energy ConversionG113 Terminology Relating to Natural and Artificial Weath-ering Tests of Nonmetallic MaterialsG167 Test Method for Calibration of a Pyranometer Using aPyrheliometerGuide for Estimating Uncertainties in Dosimetry for Radia-tion Processing2.2 ASTM Adjunct:2ADJG021317 CD Excel spreadsheet- Radiometric Data Un-certainty Estimate Using GUM Method2.3 ISO Standards3ISO 9060 Solar Energy—Specification and Classification ofInstruments for Measuring Hemispherical Solar and Di-rect Solar RadiationISO/IEC Guide 98-3 Uncertainty of Measurement—Part 3:Guide to the Expression of Uncertainty in Measurement(GUM:1995)ISO/IEC JCGM 100:2008 GUM 1995, with MinorCorrections, Evaluation of Measurement Data—Guide tothe Expression of Uncertainty in Measurement3. Terminology3.1 Standard terminology related to solar radiometry in thefields of solar energy conversion and weather and durabilitytesting are addressed in ASTM Terminologies E772 and G113,respectively. Some of the definitions of terms used in this guidemay also be found in ISO/ASTM 51707.3.2 Definitions of Terms Specific to This Standard:1This test method is under the jurisdiction of ASTM Committee G03 onWeathering and Durability and is the direct responsibility of Subcommittee G03.09on Radiometry.Current edition approved Feb. 1, 2017. Published May 2017. DOI: 10.1520/G0213–17.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3Available from International Organization for Standardization (ISO), ISOCentral Secretariat, BIBC II, Chemin de Blandonnet 8, CP 401, 1214 Vernier,Geneva, Switzerland, http://www.iso.org.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.13.2.1 aging (non-stability), n—a percent change of theresponsivity per year; it is a measure of long-term non-stability.3.2.2 azimuth response error, n—a measure of deviation dueto responsivity change versus solar azimuth angle.NOTE 1—Often cosine and azimuth response are combined as “Direc-tional response error,” which is a percent deviation of the radiometer’sresponsivity due to both zenith and azimuth responses.3.2.3 broadband irradiance, n—the solar radiation arrivingat the surface of the earth from all wavelengths of light(typically wavelength range of radiometers 300 to 3000 nm).3.2.4 calibration error, n—the difference between valuesindicated by the radiometer during calibration and “true value.”3.2.5 cosine response error, n—a measure of deviation dueto responsivity change versus solar zenith angle. See Note 1.3.2.6 coverage factor, n—numerical factor used as a multi-plier of the combined standard uncertainty in order to obtain anexpanded uncertainty.3.2.7 data logger accuracy error, n—a deviation of thevoltage or current measurement of the data logger due toresolution, precision, and accuracy.3.2.8 effective degrees of freedom, n—νeff, for multiple (N)sources of uncertainty, each with different individual degreesof freedom, νithat generate a combined uncertainty uc, theWelch-Satterthwaite formula is used to compute:veff5uc4Σi51Nu4ivi(1)3.2.9 expanded uncertainty, n—quantity defining the inter-val about the result of a measurement that may be expected toencompass a large fraction of the distribution of values thatcould reasonably be attributed to the measurand.3.2.9.1 Discussion—Expanded uncertainty is also referredto as “overall uncertainty” (BIPM Guide to the Expression ofUncertainty in Measurement).4To associate a specific level ofconfidence with the interval defined by the expanded uncer-tainty requires explicit or implicit assumptions regarding theprobability distribution characterized by the measurementresult and its combined standard uncertainty. The level ofconfidence that may be attributed to this interval can be knownonly to the extent to which such assumptions may be justified.3.2.10 leveling error, n—a measure of deviation or asym-metry in the radiometer reading due to imprecise leveling fromthe intended level plane.3.2.11 non-linearity, n—a measure of deviation due toresponsivity change versus irradiance level.3.2.12 primary standard radiometer, n—radiometer of thehighest metrological quality established and maintained as anirradiance standard by a national (such as National Institute ofStandards and Technology (NIST)) or international standardsorganization (such as theWorld Radiation Center (WRC) of theWorld Meteorological Organization (WMO)).3.2.13 reference radiometer, n—radiometer of high metro-logical quality, used as a standard to provide measurementstraceable to measurements made using primary standard radi-ometer.3.2.14 response function, n—mathematical or tabular repre-sentation of the relationship between radiometer response andprimary standard reference irradiance for a given radiometersystem with respect to some influence quantity. For example,temperature response of a pyrheliometer, or incidence angleresponse of a pyranometer.3.2.15 routine (field) radiometer, n—instrument calibratedagainst a primary-, reference-, or transfer-standard radiometerand used for routine solar irradiance measurement.3.2.16 sensitivity coeffıcient (function), n— describes howsensitive the result is to a particular influence or input quantity.3.2.16.1 Discussion—Mathematically, it is partial derivativeof the measurement equation with respect to each of theindependent variables in the form:y~xi! 5 ci5δyδxi(2)where y(x1,x2, …xi) is the measurement equation in inde-pendent variables, xi.3.2.17 soiling effect, n—a percent change in measurementdue to the amount of soiling on the radiometer’s optics.3.2.18 spectral mismatch error, radiometer, n—a deviationintroduced by the change in the spectral distribution of theincident solar radiation and the difference between the spectralresponse of the radiometer to a radiometer with completelyhomogeneous spectral response in the wavelength range ofinterest.3.2.19 temperature response error, n—a measure of devia-tion due to responsivity change versus ambient temperature.3.2.20 tilt response error, n—a measure of deviation due toresponsivity change versus instrument tilt angle.3.2.21 transfer standard radiometer, n—radiometer, often areference standard radiometer, suitable for transport betweendifferent locations, used to compare routine (field) solar radi-ometer measurements with solar radiation measurements bythe transfer standard radiometer.3.2.22 Type A standard uncertainty, adj—method of evalu-ation of a standard uncertainty by the statistical analysis of aseries of observations, resulting in statistical results such assample variance and standard deviation.3.2.23 Type B standard uncertainty, adj—method of evalu-ation of a standard uncertainty by means other than thestatistical analysis of a series of observations, such as pub-lished specifications of a radiometer, manufacturers’specifications, calibration, or previous experience, or combi-nations thereof.3.2.24 zero offset A, n—a deviation in measurement output(W/m2) due to thermal radiation between the pyranometer andthe sky, resulting in a temperature imbalance in the pyranom-eter.3.2.25 zero offset B, n—a deviation in measurement output(W/m2) due to a change (or ramp) in ambient temperature.4International Bureau of Weights and Measures (BIPM) Working Group 1 of theJoint Committee for Guides in Metrology (JCGM/WG 1).2008. “Evaluation ofMeasurement Data—Guide to the Expression of Uncertainty in Measurement(GUM).” JCGM 100:2008 GUM 1995 with minor corrections.G213 − 172NOTE 2—Both Zero Offset A and Zero Offset B are sometimescombined as “Thermal offset,” which are due to energy imbalances notdirectly caused by the incident short-wave radiation.4. Summary of Test Method4.1 The evaluation of the uncertainty of any measurementsystem is dependent on two specific components: a) theuncertainty in the calibration of the measurement system, andb) the uncertainty in the routine or field measurement system.This guide provides guidance for the basic components ofuncertainty in evaluating the uncertainty for both the calibra-tion and measurement uncertainty estimates. The guide isbased on the International Bureau of Weights and Measures(acronym from French name: BIPM) Guide to the Uncertaintyin Measurements, or GUM.44.2 The approach explains the following components; de-fining the measurement equation, determining the sources ofuncertainty, calculating standard uncertainty for each source,deriving the sensitivity coefficient using a partial derivativeapproach from the measurement equation, and combining thestandard uncertainty and the sensitivity term using the root sumof the squares, and lastly calculating the expanded uncertaintyby multiplying the combined uncertainty by a coverage factor(Fig. 1). Some of the possible sources of uncertainties andassociated errors are calibration, non-stability, zenith andazimuth response, spectral mismatch, non-linearity, tempera-ture response, aging per year, datalogger accuracy, soiling, etc.These sources of uncertainties were obtained from manufac-turers’ specifications, previously published reports on radio-metric data uncertainty, or experience, or combinations thereof.4.2.1 Both calibration and field measurement uncertaintyemploy the GUM method in estimating the expanded uncer-tainty (overall uncertainty) and the components mentionedabove are applicable to both. The calibration of broadbandradiometers involves the direct measurement of a standardsource (solar irradiance (outdoor) or artificial light (indoor)).The accuracy of the calibration is dependent on the skycondition or artificial light, specification of the test instrument(zenith response, spectral response, non-linearity, temperatureFIG. 1 Calibration and Measurement Uncertainty Estimation Flow ChartModified 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 − 173response, aging per year, tilt response, etc.), and referenceinstruments. All of these factors are included when estimatingcalibration uncertainties.NOTE 3—The calibration method example mentioned in Appendix X1is based on outdoor calibration using the solar irradiance as the source.5. Significance and Use5.1 The uncertainty in outdoor solar irradiance measure-ment has a significant impact on weathering and durability andthe service lifetime of materials systems. Accurate solarirradiance measurement with known uncertainty will assist indetermining the performance over time of component materialssystems, including polymer encapsulants, mirrors, Photovol-taic modules, coatings, etc. Furthermore, uncertainty estimatesin the radiometric data have a significant effect on the uncer-tainty of the expected electrical output of a solar energyinstallation.5.1.1 This influences the economic risk analysis of thesesystems. Solar irradiance data are widely used, and theeconomic importance of these data is rapidly growing. Forproper risk analysis, a clear indication of measurement uncer-tainty should therefore be required.5.2 At present, the tendency is to refer to instrumentdatasheets only and take the instrument calibration uncertaintyas the field measurement uncertainty. This leads to over-optimistic estimates. This guide provides a more realisticapproach to this issue and in doing so will also assists users tomake a choice as to the instrumentation that should be used andthe measurement procedure that should be followed.5.3 The availability of the adjunct (ADJG021317)5uncer-tainty spreadsheet calculator provides real world example,implementation of the GUM method, and assists to understandthe contribution of each source of uncertainty to the overalluncertainty estimate. Thus, the spreadsheet assists users ormanufacturers to seek methods to mitigate the uncertainty fromthe main uncertainty contributors to the overall uncertainty.6. Basic Uncertainty Components for EvaluatingMeasurement Uncertainty of Pyranom