The following treatment follows Okajima et al. (2012):
$$R_\mathrm{abs} = \alpha_\mathrm{s} (1 + r) S_\mathrm{sw} + \alpha_\mathrm{l} \sigma (T_\mathrm{sky} ^ 4 + T_\mathrm{air} ^ 4)$$
The incident longwave (aka thermal infrared) radiation is modeled from sky and air temperature \(\sigma (T_\mathrm{sky} ^ 4 + T_\mathrm{air} ^ 4)\) where \(T_\mathrm{sky}\) is function of the air temperature and incoming solar shortwave radiation:
$$T_\mathrm{sky} = T_\mathrm{air} - 20 S_\mathrm{sw} / 1000$$
Symbol | R | Description | Units | Default |
\(\alpha_\mathrm{s}\) | abs_s | absorbtivity of shortwave radiation (0.3 - 4 \(\mu\)m) | none | 0.80 |
\(\alpha_\mathrm{l}\) | abs_l | absorbtivity of longwave radiation (4 - 80 \(\mu\)m) | none | 0.97 |
\(r\) | r | reflectance for shortwave irradiance (albedo) | none | 0.2 |
\(\sigma\) | s | Stefan-Boltzmann constant | W / (m\(^2\) K\(^4\)) | 5.67e-08 |
\(S_\mathrm{sw}\) | S_sw | incident short-wave (solar) radiation flux density | W / m\(^2\) | 1000 |
\(S_\mathrm{lw}\) | S_lw | incident long-wave radiation flux density | W / m\(^2\) | calculated |
\(T_\mathrm{air}\) | T_air | air temperature | K | 298.15 |
\(T_\mathrm{sky}\) | T_sky | sky temperature | K | calculated |