The sol-air temperature expression includes the long-wave correction term defined as the product of (the hemispherical emittance of the surface) and (the difference between long-wave radiation incident on the surface from sky and surroundings and radiation emitted by a blackbody at the outdoor air temperature) devided by (the coefficient of heat transfer by long-wave radiation and convection at the outer surface).
It is common practice (from reference ASHRAE) to assume this correction term equal to 0K for vertical surfaces and equal to 4K for horizontal surfaces.
Could anyone help me with a more precise model to estimate this correction term?