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Principles of the Measurement of Solar Reflectance, Thermal Emittance, and Color

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Principles of the Measurement of Solar Reflectance, Thermal Emittance, and Color Principles of the Measurement of Solar Reflectance, Thermal Emittance, and Color Contents Roof Heat Transfer Electromagnetic Radiation Radiative Properties of Surfaces Measuring Solar Radiation Measuring Solar Reflectance Measuring Thermal Emittance Measuring Color 1. Roof Heat Transfer 3 Roof surface is heated by solar absorption, cooled by thermal emission + convection Radiative Cooling Convective Solar Cooling Absorption Troof Insulatio n T Qin = U (Troof – inside Tinside) Most solar heat gain is dissipated by convective and radiative cooling… ...because the conduction heat transfer coefficient is much less than those for convection & radiation 2. Electromagnetic Radiation 7 The electromagnetic spectrum spans radio waves to gamma rays This includes sunlight (0.3 – 2.5 μm) and thermal IR radiation (4 – 80 μm) (0.4 – 0.7 All surfaces emit temperature-dependent electromagnetic radiation • Stefan-Boltzmann law • Blackbody cavity is a perfect absorber and emitter of radiation • Total blackbody radiation [W m-2] = σ T 4, where – σ = 5.67 10-8 W m-2 K-4 – T = absolute temperature [K] • At 300 K (near room temperature) σ T 4 = 460 W m-2 Higher surface temperatures → shorter wavelengths Solar radiation from sun's surface (5,800 K) peaks near 0.5 μm (green) Thermal radiation from ambient surfaces (300 K) peaks near 10 μm (infrared) Extraterrestrial sunlight is attenuated by absorption and scattering in atmosphere Global (hemispherical) solar radiation = direct (beam) sunlight + diffuse skylight Pyranometer measures global (a.k.a. Pyranometer hemi-spherical) sunlight on with horizontal surface sun-tracking shade Pyrheliometer measures measures direct (a.k.a. collimated, diffuse beam) light from sun skylight Let's compare rates of solar heating and radiative cooling Spectral heating rate of a black roof facing the sky on a 24-hour average basis, shown on a log scale. Equal areas represent equal radiant fluxes. The box in the upper right shows the area of 100 W m-2. 3. Radiative Properties of Surfaces A photon striking a surface is reflected, absorbed, or transmitted • Spectral reflectance r(λ): probability that an incident photon of wavelength λ is reflected • Spectral absorptance a(λ): probability that photon is absorbed • Spectral transmittance t(λ): probability that photon is transmitted r(λ) + a(λ) + t(λ) = 1 Averaging solar spectral reflectance r(λ) weighted with solar spectral irradiance i(λ) yields solar reflectance R • Solar reflectance R is fraction of incident sunlight that is reflected • Integrating over the solar spectrum, R = ∫ i(λ) r(λ) dλ / ∫ i(λ) dλ • Solar absorptance and solar transmittance can be calculated in the same way Emittance compares emission of surface to that of a perfect emitter (black body) • Spectral emittance ε(λ): radiant power at wavelength λ emitted by a surface divided by that emitted by a black body at the same temperature Kirchhoff’s law: at each wavelength, emittance equals absorptance • Opaque enclosure in equilibrium enclosure at – The enclosure filled with temperature T a blackbody radiation: BT (λ) – The surface emits B radiation at the rate B ε ε(λ) BT (λ) – The surface absorbs radiation at the rate photon gas at B λ λ temperature T a( ) BT ( ) a = ε • Hence, we have Kirchhoff’s law: ε(λ) = a(λ) If ε(λ) ≠ a(λ), the surface will spontaneously warm or cool, violating the 2nd law of thermodynamics! Solar absorptance and thermal emittance are independent parameters • Emittance and absorptance are equal at the same wavelength. For example, – Bare shiny metals, such as aluminum, have low thermal emittance – Therefore bare metals have low absorptance (and high reflectance) in the thermal infrared • However, typical terminology is to refer to – Solar absorptance (weighted average from 0.3 to 2.5 µm) – Thermal emittance (weighted average from 4 to 80 µm) Typical radiative properties of some roofing materials (unsoiled) Material Solar Thermal reflectance emittance Gray-rock fiberglass asphalt shingle 0.10 0.90 Bare gray-cement concrete tile 0.15 0.90 Terracotta clay tile 0.40 0.90 Bare zincalume steel 0.75 0.05 Resin-coated zincalume steel 0.60 0.15 Zincalume steel w/25-µm white coating 0.70 0.85 Wood shake 0.50 0.90 4. Measuring Solar Radiation A pyranometer is a thermal-electrical instrument that measures solar radiation Solar irradiance is assessed from solar heating of black sensing element • Sensor is black disk backed by thermopile • Output voltage is proportional to temperature rise of the black disk in sunlight • Glass dome(s) over sensor inhibits convective heat transfer, blocks thermal infrared radiation • Instrument can measure incident or reflected radiation • A recent review on measurement errors: Gueymard and Myers, Solar Energy 83 (2009), 171–185 5. Measuring Solar Reflectance CRRC-approved reflectometer techniques for measuring solar reflectance Methods based on Devices & Services Solar Spectrum Reflectometer • Homogeneous surfaces: ASTM C1549-09(2014) – Laboratory or in-situ measurement of the solar reflectance of a small surface (diameter ~ 25 mm) – Average three points on surfaces • Heterogeneous surfaces: CRRC-1 Test Method #1 – Laboratory or in-situ measurement of the solar reflectance of a heterogeneous surface, such as a variegated asphalt shingle – Averages many randomly located points • Heterogeneous tiles: Tile Template Method – Laboratory or in-situ measurement of the solar reflectance of a heterogeneous tile surface – Averages many fixed points Design of Devices & Services Solar Spectrum Reflectometer (SSR) Sample Lamp in center Unit may be 2.5 cm aperture at inverted top Primarily a lab Interior coated technique, but can be used in-situ white Detectors view sample through collimating tube Aggregate spectral response of SSR's filtered detectors mimics solar spectral irradiance Response of each filtered Aggregate response compared detector (version 5) to solar spectral irradiance SSR version 6 (current model) has 'G1' output for global solar reflectance AM1.5 solar reflectances measured with SSRv5, SSRv6 compared to E903 global (Note: final edition of SSRv6 measures global horizontal solar reflectance at AM1, rather than AM1.5) ASTM C1549: Standard test method for determination of solar reflectance near ambient temperature using portable solar reflectometer • Specimen diffusely illuminated by incandescent bulb inside a white cavity • Light reflected through a tube at 20o from normal is measured by 4 filtered detectors • Aggregate spectral response of 4 filtered detectors mimics solar spectral irradiance • Weighted average of 4 detector readings approximates solar reflectance • Suitable for homogeneous surfaces • C1549 describes operation of SSR version 5 – SSR version 6 weights six (rather than four) detector readings and has more outputs CRRC-1 Test Method #1: Standard practice for measuring solar reflectance of a flat, opaque, and heterogeneous surface using a portable solar reflectometer • Application of C1549 (reflectometer) to non-uniform surface (e.g., blended asphalt roofing shingle) • Measure reflectance at n ≥ 30 random locations • Compute mean and sampling error (standard error of mean) • Measure reflectances at additional locations (if necessary) until sampling error (proportional to n-1/2) is sufficiently small • Report mean reflectance Other CRRC-approved techniques for measuring solar reflectance Method based on solar (UV-VIS-NIR) spectrometer with integrating sphere • Small, homogenous surfaces: ASTM E903-12 – Laboratory measurement of the spectral and solar reflectance of a very small surface Method based on first-class pyranometer • Large, low-slope surfaces: ASTM E1918-06 (2015) – In-situ (field) measurement of the solar reflectance of a large surface (diameter ~ 4 m) ASTM E 903: Standard test method for solar absorptance, reflectance, and transmittance of materials using integrating spheres • Use spectrometer w/integrating sphere to measure spectral reflectance or transmittance • Spectral measurements are essential for in-depth studies • Weight spectral reflectance with solar spectral irradiance to obtain solar reflectance – Weight with ASTM E891 beam-normal irradiance—matches 1.5 output of SSRv5, 1.5E output of SSRv6 – Weight with air mass 1 (sun at zenith) global horizontal (AM1GH) irradiance—matches G1 output of SSRv6 Integrating sphere design Example of spectrometer with integrating sphere • Perkin-Elmer Lambda 900 UV-VIS-NIR Spectrometer – Solar: 300 - 2,500 nm – Ultraviolet: 300 - 400 nm – Visible: 400 - 700 nm – Near-infrared: 700 - 2,500 nm – LBNL measures reflectance at 5-nm intervals (balancing detail, speed) • Labsphere integrating sphere – Hollow sphere with very white interior (Spectralon coating, r ≈ 99%) – Collects all diffuse light reflected by sample • Two light sources, two detectors, several diffraction gratings • Solar spectral reflectance measured relative to a calibrated standard (Spectralon disk) Spectrometer design details Schematic of Perkin-Elmer Lambda 900 spectrometer (without integrating sphere) ASTM E1918: Standard test method for measuring solar reflectance of horizontal and low-sloped surfaces in the field • Step 1: Measure incident sunlight – Face pyranometer away from surface (sensor parallel to surface) • Step 2: Measure reflected sunlight – Face pyranometer toward surface (sensor parallel to surface) • Step 3: Calculate solar reflectance – R = reflected sunlight / incident sunlight • Requirements: – Unobstructed sunlight (clear skies) – High sun (solar zenith angle ≤ 45°) – Large surface (at least 4 m × 4 m) to
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