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 (T
_{sky}), convective coefficient (h_{c}), air temperature (T_{a}) are the standard conditions defined in ASTM E1980 - Stefan Boltzman constant (σ) is a constant [5.66961 × 10
^{-8}W/(m^{2}K^{4})] - Surface temperature (T
_{s}) 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/m
^{2} - Sky temperature (T
_{sky}): 300 K - Air temperature (T
_{a}): 310 K - Convective coefficient (h
_{c}): 5, 12, or 30 W/(m^{2}K), corresponding to low-, medium- and high-wind conditions