Definitions and Terms


Solar Reflectance
Solar Reflectance is the fraction of the incident solar energy which is reflected by the surface in question. The best standard technique for its determination uses spectrophotometric measurements, with an integrating sphere to determine the reflectance at each different wavelength. The average reflectance is then determined by an averaging process, using a standard solar spectrum. This method is documented by ASTM (Amer. Soc. for Testing and Materials) as Standards E903 and E892. When this data is not available, other, less detailed measurements are utilized. The visible reflectance is sometimes measured by manufacturers. This is the reflectance in the visual part of the solar spectrum, wavelengths of 400 to 700 nanometers. Usually the visible reflectance is correlated with the solar reflectance, but the two quantities are not equal. For example, a good white coating with a solar reflectance of 0.8 typically has a visible reflectance of about 0.9.
Infrared Emittance
Infrared Emittance is a parameter between 0 and 1 which measures the ability of a warm or hot material to shed some of its heat in the form of infrared radiation. The wavelength range for this radiant energy is roughly 5 to 40 micrometers. Most building materials (including glass!) are opaque in this part of the spectrum, and have an emittance of roughly 0.9. Materials such as clean, bare metals are the most important exceptions to the 0.9 rule. Thus clean, untarnished galvanized steel has a very low emittance, and aluminum roof coatings have intermediate levels of emittance. A material with an emittance of unity ("black body"), emits about 6.1 watts per square meter, for each degree C above ambient temperature.
Temperature Rise
Formula for estimation of maximum roof temperature rise.

We have used simple, basic heat transfer equations to estimate peak roof temperatures, based on the assumptions listed below. Lower peak roof temperatures contribute less thermal stress, and likely lead to longer roof lifetimes in some systems. Actually, we estimate and tabulate the maximum temperature rise above ambient air temperature. To obtain the absolute maximum roof temperature, add the maximum temperature rise in the table to your estimate of the maximum air temperature.

Assumptions are:

The maximum roof temperature is primarily determined by external heat transfers (as, for example, for an insulated roof.)
Heat storage effects in the roof are neglected. (Heat storage, as for example, in a concrete roof, does reduce peak roof temperatures, but the offset air conditioning load tends to appear in the evening hours, as heat is released from storage.)
Solar flux is Io = 1 kW per square meter of roof.
Sky temperature is 10 deg. C (18 deg. F) below air temperature.
The heat transfer coefficient for infrared radiative cooling is hr = 6.1 W /(sq. meter . deg. C) times the thermal emittance (this parameter is derived from the Stefan-Boltzmann constant).
The maximum temperature rise of an exposed black surface (solar reflectance = 0.05, infrared emittance = 0.90) is 50 deg. C (90 deg. F). This number is based on observations by a number of observers of the maximum temperature rise of black surfaces in full sun and with low wind speed. The uncertainty in this number is roughly 30%. This assumption allows us to mathematically solve for the heat transfer coefficient for roof cooling by convection, which is then found to be hc = 12.4 W/(sq. meter . deg. C). This is in the range that would be expected if we simply estimated this parameter from engineering textbooks on heat transfer. The weak temperature dependence of this parameter is henceforth neglected.

With these assumptions the heat transfer equation reads

(1-R)Io = (hc + hr) (max. temp. rise) + hr (10 deg. C),

where R is the solar reflectance, and 10 deg. C is the sky temperature depression below air temperature. Thus the maximum temperature rise is found by solving this equation for each material, using the solar reflectance and infrared emittance values from the tables.

Solar Reflectance Index
The Solar Reflectance Index (SRI.) is a measure of the roof's ability to reject solar heat, as shown by a small temperature rise. It is defined so that a standard black (reflectance 0.05, emittance 0.90) is 0 and a standard white (reflectance 0.80, emittance 0.90) is 100. For example, the standard black has a temperature rise of 90 deg. F (50 deg. C) in full sun, and the standard white has a temperature rise of 14.6 deg. F (8.1 deg. C). Once the maximum temperature rise of a given material has been computed, the SRI can be computed by interpolating between the values for white and black.

Materials with the highest SRI values are the coolest choices for roofing. Due to the way SRI is defined, particularly hot materials can even take slightly negative values, and particularly cool materials can even exceed 100.


    Letter report from Atlas/DSET, August 4, 1999, Normal infrared emittance from ASTM E408-71, converted to hemispherical emittance using eqns. 4 and 5 provided by the National Fenestration Rating Council in NFRC 301-93. Solar reflectance from ASTM method E903, using the air mass 1.5 global spectrum of ASTM E892.
    D. S. Parker, J. E. R. McIlvaine, S. F. Barkaszi, and D. J. Beal, "Laboratory Testing of Reflectance Properties of Roofing Materials", Report No. FSEC-CR-670-93 (1993), Florida Solar Energy Center, 300 State Rd. 401, Cape Canaveral, FL 32920.
    David W. Yarbrough and Robert W. Anderson, "Use of Radiation Control Coatings to Reduce Building Air-Conditioning Loads." Energy Sources, Volume 15, pp 59-66
   Paul Berdahl and Sarah E. Bretz; "Preliminary Survey of the Solar Reflectance of Cool Roofing Materials," Energy and Buildings, Vol. 25, 149-158 (1997).
    Lawrence Berkeley National Laboratory, Unpublished results (Craig Smith, 1996).
Sarah E. Bretz and Hashem Akbari; "Long-term Performance of High-Albedo Roof Coatings," Energy and Buildings, Vol. 25, 159-167 (1997).
    Lawrence Berkeley National Laboratory, Unpublished results (Shea Rose and Paul Berdahl, 1998).
    Lawrence Berkeley National Laboratory, Unpublished results ( Paul Berdahl, D & S instrument, 1998).
    J.A.Reagan and D.M.Acklam; "Solar Reflectivity of Common Building Materials and its Influence on the Roof Heat Gain of Typical  Southwestern USA. Residences." Energy and Buildings, 2 (1979) 237-248.