What's the mathmatical concept to calculate solar irradiance in Ladybug Tools?

A building surface can receive three kinds of radiance, i.e., direct, diffuse and reflect componnents. But how are they determined/calculated? Is there any academic reference to explain it with mathmatical equations?
So far as I know, Ladybug Tools relies on the Radiance engine to calculate the solar radiance, and Radiance engine uses the Pedez model to determine the diffuse component. How about the direct and reflect components?

Hi @Nate,

There’s usually references in the components or the Ladybug Tools primer. The page in the primer for the Cumulative Sky Matrix explains how the sky dome is generated.

The Incident Radiation component then has details of how the sky domes is used to calculate the incident radiation, and what it accounts for.

You can also click on the source code in the primer to read the code versions if you want a more detailed understanding of the calculation

The examples above are just for the Ladybug components, to account for reflections you need to use Honeybee which uses Radiance as a calculation engine. The Honeybee primer explains more on that, although you may need to get more details from the Radiance documentation for full calculation methodologies.


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Many thanks!
But I still cannot find any mathmatical explanation from those primer.

You can refer to the source code on this website

And the paper

And the References

  1. Perez, R., Seals, R., and Michalsky, J. All-weather model for sky luminance distribution. Solar Energy, 50:3, pp235-245, 1993.
  2. Kittler, R., Perez, R. and Darula, S. A new generation of sky standards. Proc. Lux Europa Conf., pp359-373, 1997.
  3. Darula S, Kittler R., CIE general sky standard defining luminance distributions, Proc. Conf. eSim 2002, Montreal, Canada.

This is great!
Thanks man.