Designation: E1980 − 11Standard Practice forCalculating Solar Reflectance Index of Horizontal and Low-Sloped Opaque Surfaces1This standard is issued under the fixed designation E1980; 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.INTRODUCTIONThe steady-state surface temperature (Ts) under the sun is strongly correlated to solar reflectivityand thermal emissivity of the surface. For equivalent conditions, the Tsof dark surfaces (with low solarreflectance) is higher than light-colored surfaces (with high solar reflectance); and surfaces with lowthermal emissivity have higher Ts’s than surfaces with high thermal emissivity. The procedurerecommended in this standard will allow a direct comparison of Tsof surfaces under the sun. Theprocedure defines a Solar Reflectance Index (SRI) that measures the relative Tsof a surface withrespect to the standard white (SRI = 100) and standard black (SRI =0) under the standard solar andambient conditions.1. Scope1.1 This practice covers the calculation of the Solar Reflec-tance Index (SRI) of horizontal and low-sloped opaque sur-faces at standard conditions. The method is intended tocalculate SRI for surfaces with emissivity greater than 0.1.1.2 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.3 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.2. Referenced Documents2.1 ASTM Standards:2G173 Tables for Reference Solar Spectral Irradiances: DirectNormal and Hemispherical on 37° Tilted Surface3. Terminology3.1 Definitions:3.1.1 convective coeffıcient (hc)—the rate of heat transferfrom the surface to air induced by the air movement, expressedin watts per square metre per degree Kelvin, W·m–2·K–1.3.1.2 low-sloped surfaces—surfaces with a slope smallerthan 9.5° from the horizontal.3.1.3 reference black surface temperature (Tb)—is thesteady-state temperature of a black surface with solar reflec-tance of 0.05 and thermal emissivity of 0.9, under the standardsolar and ambient conditions.3.1.4 reference white surface temperature (Tw)—is thesteady-state temperature of a white surface with solar reflec-tance of 0.80 and thermal emissivity of 0.9, under the standardsolar and ambient conditions.3.1.5 sky temperature (Tsky)—is the temperature of a blackbody that would radiate the same power toward the earth asdoes the sky.3.1.6 solar absorptance (α)—the fraction of solar flux ab-sorbed by a surface. For an opaque surface α =1−a.3.1.7 solar flux (I)—is the direct and diffuse radiant powerfrom the sun received at ground level over the solar spectrum,expressed in watts per square metre, W·m–2.3.1.8 solar reflectance (a)—the fraction of solar flux re-flected by a surface.3.1.9 solar reflectance index (SRI)—is the relative Tsof asurface with respect to the standard white (SRI = 100) andstandard black (SRI = 0) under the standard solar and ambientconditions.3.1.10 solar spectrum—spectral distribution of typical ter-restrial sunlight at air mass 1.5 as defined in Tables G173.1This test method is under the jurisdiction ofASTM Committee D08 on Roofingand Waterproofing and is the direct responsibility of Subcommittee D08.18 onNonbituminous Organic Roof Coverings.Current edition approved Jan. 1, 2011. Published January 2011. Originallypublished in 1998. Last previous edition approved in 2001 as E1980–01, which waswithdrawn in January 2010 and reinstated in January 2011. DOI: 10.1520/E1980-11.2For 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.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.1.11 standard solar and ambient conditions— for thepurpose of this calculation, is defined as a solar flux of 1000W·m–2, ambient air temperature of 310 Kelvin (K), and skytemperature of 300 K. Three convective coefficient of 5, 12, 30W·m–2·K–1, corresponding to low- (0 to 2 ms–1), medium- (2to6ms–1), and high-wind (6 to 10 ms–1) conditions, respec-tively.3.1.12 steady-state surface temperature (Ts)—is the tem-perature of the surface, in K, under the standard solar andambient conditions.3.1.13 thermal emissivity (ε)—the ratio of radiant flux emit-ted by a surface at a given temperature to that emitted by ablack body radiator at the same temperature. For thiscalculation, the thermal emissivity is for a temperature below150°C.4. Summary of Practice4.1 For a surface exposed to the sun, when the conductioninto the material is zero, the steady-state surface temperature isobtained by:αI 5 εσ~Ts42 Tsky4!1hc~Ts2 Ta! (1)where:α = solar absorptance=1−solar reflectance,I = solar flux, W·m–2,ε = thermal emissivity,σ = Stefan Boltzmann constant, 5.66961 ×10–8W·m–2·K–4,Ts= steady-state surface temperature, K,Tsky= sky temperature, K,hc= convective coefficient, W·m–2·K–1, andTa= air temperature, K.4.2 Given the solar reflectivity and thermal emissivity of asurface, and the convective coefficient, Eq 1 needs to be solvediteratively for surface temperature. Alternatively, one can usethe following equation to obtain the surface temperature:Ts5 309.071~1066.07α 2 31.98ε!~6.78ε1hc!(2)2~890.94α212153.86αε!~6.78ε1hc!2Surface temperature estimated by Eq 2 is accurate within 1K.4.3 In this practice, Solar Reflectance Index is defined as:SRI 5 100Tb2 TsTb2 Tw(3)where: Tband Tware the steady-state temperature of blackand white surfaces.Under the standard solar and ambient conditions, Eq 3 isregressed to:SRI 5 123.97 2 141.35χ19.655χ2(4)where:χ 5~α 2 0.029ε!~8.7971hc!9.5205ε1hc(5)For α greater than 0.1, and excluding collector surfaces(surface with high solar absorptance and low thermalemittance, that is, α greater than 0.8 and ε less than 0.2), Eq 4estimates SRI with an average error of 0.9 and maximum errorof 2.5. Significance and Use5.1 Solar reflectance and thermal emittance are importantfactors affecting surface and near-surface ambient air tempera-ture. Surfaces with low solar reflectance, absorb a high fractionof the incoming solar energy.Afraction of this absorbed energyis conducted into ground and buildings, a fraction is convectedto air (leading to higher air temperatures), and a fraction isradiated to the sky. For equivalent conditions, the lower theemissivity of a surface the higher its steady-state temperature.Surfaces with low emissivity cannot effectively radiate to thesky and, therefore, get hot. Determination of solar reflectanceand thermal emittance, and subsequent calculation of therelative temperature of the surfaces with respect to black andwhite reference temperature (defined as Solar ReflectanceIndex, SRI), may help designers and consumers to choose theproper materials to make their buildings and communitiesenergy efficient. The method described here gives the SRI ofsurfaces based on measured solar reflectances and thermalemissivities of the surfaces.6. Procedure6.1 Given the solar reflectance and thermal emissivity of atest surface, calculate the SRI for three convective coefficientsof 5, 12, 30 W·m–2·K–1, corresponding to low-, medium-, andhigh-wind conditions, respectively. The following alternateapproaches can be used to calculate SRI:6.1.1 Approach I—Calculate the steady-state surface tem-peratures for the test surface and black and white referencesurfaces. Either Eq 1 (with iterative approach) or Eq 2 can beused. Calculate the SRI from Eq 3.6.1.2 Approach II— Calculate SRI from Eq 4.7. Report7.1 The report shall include the following:7.1.1 The solar reflectance and the thermal emittance of thetest surface.7.1.2 The calculated SRI for three convective coefficients of5, 12, 30 W·m–2·K–1, corresponding to low-, medium-, andhigh-wind conditions, respectively.8. Precision and Bias8.1 The SRI of a test surface varies with two materialproperties, solar reflectance and thermal emissivity, and fourenvironmental conditions, solar flux, convection coefficient, airE1980 − 112temperature, and sky temperature. A detailed sensitivity analy-sis for the variation of SRI with respect to the above environ-mental conditions has been reported.3The following is asummary of the results and may be used as a guideline forpractitioners.8.1.1 SRI is an excellent predictor of solar reflectance formaterials with high emissivity (ε 0.8), that is, non-metals.Under these conditions, a 61 % error in solar reflectance willresult in a maximum error of 61.4 in SRI. Similarly, a 61%error in ε will result in a maximum error of 60.6 in SRI.8.1.2 For non-metallic surfaces, SRI is insensitive to choiceof convective coefficient.8.1.3 For metallic surfaces that are characterized with low ε,the SRI calculated by the above procedure varies significantlywith the choice of convection coefficient. Hence, the SRIshould be reported for three convective coefficients corre-sponding to low-, medium-, and high-wind conditions.8.1.4 SRI is insensitive to choice of sky temperature,ambient temperature, and solar flux.9. Keywords9.1 solar flux; solar reflectance; solar reflectance index;thermal emittanceBIBLIOGRAPHY2(1) ASTM E408 Test Methods for Total Normal Emittance of Sur-faces Using Inspection-Meter Techniques(2) ASTM E772 Terminology Relating to Solar Energy Conversion(3) ASTM E903 Test Method for Solar Absorptance, Reflectance, andTransmittance of Materials Using Integrating Spheres(4) ASTM E1918 Test Method for Measuring Solar Reflectance ofHorizontal and Low-Sloped Surfaces in the FieldASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or

[email protected] (e-mail); or through the ASTM website(www.astm.org). Permission rights to photocopy the standard may also be secured from the Copyright Clearance Center, 222Rosewood Drive, Danvers, MA 01923, Tel: (978) 646-2600; http://www.copyright.com/3Akbari, H., R. Levinson, and P. Berdahl, “ASTM Standards for MeasuringSolar Reflectance and Infrared Emittance of Construction Materials and Comparingtheir Steady-State Surface Temperatures,” Proceedings of the ACEEE 1996 SummerStudy on Energy Effıciency in Buildings, Vol. 1, p. 1, Pacific Grove, CA, August1996.E1980 − 113