Solar spectra in ASTM E903 solar reflectance calculations

Various solar spectra (i.e. solar spectral irradiance distributions) could be used in solar reflectance (of course, solar transmittance and absorptance too) calculations according to ASTM E903, as listed below:

  • ASTM E891:
    • Default solar spectrum used by the building industry and by OTM in SRI testing.
    • It is the default solar spectrum due to historical reasons and for compatibility with existing practices, data and instruments.
    • ASTM E891 is withdrawn and the same data set is available in ISO 9845-1.
  • ASTM E892:
    • Default solar spectrum for solar reflectance testing of non-roofing materials, according to LEED (note: solar reflectance only, not SRI)
    • Similarly, ASTM E892 is withdrawn and the data set is availble in ISO 9845-1.
    • ASTM E891 and E892 are different. ASTM E891 is in terms of direct normal solar radiation (no diffuse radiation); ASTM E892 is in terms of hemispherical solar radiation (with diffuse radiation).
  • ASTM G173:
    • Default solar spectrum included in ASTM E903, including both direct normal solar spectrum (equivalent to ASTM E891) and hemispherical solar spectrum (equivalent to ASTM E892)
    • It is not often used in the buidling industry, due to the historical reasons stated under ASTM E891.
  • ASTM E490:
    • Used in extraterrestrial applications, with AM0.
    • All other spectra mentioned above are with AM1.5 (refer to this article on air mass).

Surface temperature calculation model in SRI calculation (ASTM E1980)

As discussed in What is SRI, solar reflectance index (SRI) can be understood as the surface temperature on a 0 – 100 scale. We have an online SRI calculator, which calculates the surface temperatures and SRIs under 3 standard conditions. This post aims to explain the surface temperature calculation model in SRI calculation according to ASTM E1980.

Surface temperature calculation model

Below is the surface temperature calculation model in ASTM E1980.

The absorbed solar radiation (the term on the left hand side) is splitted to 3 components:

  • Low-wave radiation to sky (the first term on the right hand side)
  • Convection to air (the second term on the right hand side)
  • Conduction to materials beneath the surface (ignored)

For the quantities in the equation below:

  • Solar absorptance (α) and emissivity (ε) are material properties (tested in the laboratory)
  • Solar flux (I), sky temperature (Tsky), convective coefficient (hc), air temperature (Ta) are the standard conditions defined in ASTM E1980
  • Stefan Boltzman constant (σ) is a constant [5.66961 × 10-8 W/(m2K4)]
  • Surface temperature (Ts) is the unknown to be solved

The equation can be solved iteratively to get the surface temperature. ASTM E1980 also provides an alternative solution to the equation.

Standard conditions

For the standard conditions, the following are defined in ASTM E1980:

  • Solar flux (I): 1000 W/m2
  • Sky temperature (Tsky): 300 K
  • Air temperature (Ta): 310 K
  • Convective coefficient (hc): 5, 12, or 30 W/(m2K), corresponding to low-, medium- and high-wind conditions

Dirt collection index testing of architectural coatings

Dirt pickup resistance (DPUR)

Dirt pickup resistance (DPUR) represents the ability of an architectural coating (e.g. paint) to resist dirt in exposure to natural environments.

Though it is named “dirt pickup”, it is not defined in terms of the amount of dirt accumulated on a surface, but in terms of the color change of a surface before and after a period of exposure. Due to this definition, surface color changes due to other factors, such as exposure to UV radiation, also impact DPUR.

A detailed description of the dirt pickup mechanism is available in this article: Towards a comprehensive understanding of dirt pickup resistance.

In simple words, DPUR is the color change of an architectural coating due to exposure to the natural environment.

Dirt collection index?

Dirt collection index, Dc, is a property defined in ASTM D3719 for DPUR characterization:

Dc = L*exposed / L*unexposed

where:

  • Dc: dirt collection index
  • L*exposed: L* value of the exposed surface
  • L*unexposed: L* value of the unexposed surface

L* is the lightness of a color in the CIELAB color space. L* = 0 for a perfect black surface and L* = 100 for a perfect white surface.

There are other similar properties characterizing DPUR. To the author’s knowledge, dirt collection index is the only one defined in an international standard. Unfortunately, ASTM D3719 was withdrawn in 2019 and there is no replacement standard at the moment of writing (please leave your comment at the bottom of this page, if you are aware of some alternative international standards on DPUR characterization).

Laboratory testing of dirt collection index

For laboratory testing of dirt collection index, a test sample needs to be measured two times, in the unexposed state and in the exposed state, with the following 3 steps:

  1. Unexposed sample measurement: a new sample is measured before weathering
  2. Weathering: the sample is weathered outdoors for a certain period
  3. Exposed sample measurement: the exposed sample is measured after weathering

For the weathering part, the customers may perform the weathering by themselves according to their preferred conditions.

The colors can be measured with either a handheld spectrophotometer or our UV/VIS/NIR spectrophotometer.

Most customers perform the dirt collection index together with the solar reflectance index (SRI) testing (also in the unexposed and exposed states). In that case, the spectral reflectance data collected in the SRI testing can be re-used to calculate the dirt collection index.

SRI testing: Can membrane products be tested without substrate?

We are often requested to test the solar reflectance index (SRI) of membrane products, particularly liquid applied membrane products.

Unlike paints, membrane products can be free-standing. A membrane product sample can be prepared either as a standalone membrane layer or with a substrate. The question from many customers is whether the SRI of membrane products can be tested without substrate.

Two examples

To answer this question, two examples are illustrated below:

A translucent membrane sample
An opaque membrane sample

The sample on the left is translucent (with large transmission). For such samples, a substrate is required.

The sample on the right is opaque (with zero transmission). For such samples, a substrate is not required.

The theory

For a material, we have the following relationship:

Solar transmittance + solar reflectance + solar absorptance = 1

In SRI calculations, the solar transmittance is assumed 0 (solar transmittance = 0). The solar reflectance is directly measured by the instrument. Therefore, we use the following relationship to calculate the solar absorptance:

Solar absorptance = 1 – solar reflectance

However, if the material is not opaque (solar transmittance ≠ 0, for example, the left example), the equation above is not valid.

For such translucent samples, the calculated solar absorptance is higher than the actual solar absorptance, as the solar transmittance is counted as part of the solar absorptance, and the resultant SRI is therefore lower.

In order to eliminate this error, translucent samples shall not be used for SRI testing. If a membrane product is translucent, it shall be applied onto a suitable substrate for testing.

The practice

To determine if a membrane sample is translucent, a simple method is to check if the flashlight from a phone can transmit through the sample, as shown in the examples above.

Theoretical range of solar reflectance index (SRI)

In our website, we explain that the solar reflectance index (SRI) is the surface temperature in a 0 – 100 scale. In the same section, we also mention that It is possible for SRI to be negative or larger than 100. So, what is the theoretical range of SRI? What is the possible minimum SRI and maximum SRI?

We can easily find the minimum and maximum SRIs with our online SRI calculator.

  • Minimum SRI: the minimum SRI is the SRI of a surface with solar reflectance = 0 (perfect black color in the solar radiation spectrum) and emittance = 0 (perfect white body in the infrared radiation spectrum)
    • Mininum SRI = -244.6 (low-wind), -99.7 (medium-wind), or -44.9 (high-wind)
  • Maximum SRI: the maximum SRI is the SRI of a surface with solar reflectance = 1 (100%, perfect white color in the solar radiation spectrum) and emittance = 1 (perfect black body in the infrared radiation spectrum)
    • Maximum SRI = 133.0 (low-wind), 129.6 (medium-wind), or 128.0 (high-wind)

Therefore, the theoretical range of SRI is:

  • Low-wind: -244.6 ~ 133.0
  • Medium-wind: -99.7 ~ 129.6
  • High-wind: -44.9 ~ 128.0

Shown below are the calculation screenshots.

Minimum SRI calculation results
maximum SRI calculation results

With the theoretical SRI range presented above, is it still valid to say that the SRI is the surface temperature in a 0 – 100 scale?

Yes, it is still valid. As most natural surfaces are with high emissivity (emittance > 0.8), the SRIs of most natural materials are in the range of 0 – 100.

Surfaces with low emissivity (low-e, e.g. emissivity < 0.2) are typically bare metal surfaces (e.g. aluminum or stainless steel). In practice, they are rarely directly used as the top layer of roof or pavement materials. When such low-e surfaces are painted, the emissivity is high (as the paint layer becomes the top layer).

Why the SRI of a low-e surface is low?

There are 3 heat transfer modes: conduction, convection, and radiation. For a low-e surface, the radiative heat exchange between the surface and the ambient environment is weak (i.e. less heat transfer via radiation). More heat is kept on the low-e surface and it results in higher surface temperature and, therefore, lower SRI.

In the low-wind condition, the convection is weak and the radiation is more dominant. This is the reason that the dependence of SRI on emittance is stronger at the low-wind condition.

New release of lab profile 2020 edition

We are pleased to release our 2020 edition of laboratory profile, which is a 56-page comprehensive document, with rich information on our capabilities and many technical insights.

What are in the laboratory profile?

  • A comprehensive overview of the laboratory
  • Detailed introduction of 10 popular tests
  • 14 informative technical insights articles

You may download a soft copy of our lab profile.