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I want to compute the brightness in LUX based on solar irradiance depending on the Sun's altitude above the horizon.

I used the formula, which is here:

https://www.pveducation.org/pvcdrom/properties-of-sunlight/calculation-of-solar-insolation

It calculates the solar radiation through the atmosphere.

Next, when I use the air mass formula:

https://en.wikipedia.org/wiki/Air_mass_(astronomy)**strong text**

Function to fit solar radiation data

https://en.wikipedia.org/wiki/Air_mass_(solar_energy)

My final formula looks like

enter image description here

and works well only when the zenith angle is 0 degrees!

At solar elevation of 90 degrees the value obtained is 128858 Lux, which is fine against the value presented on this website:

https://stjarnhimlen.se/comp/radfaq.html#11

although for other angles, the situation doesn't look good

Brightness of the light source at twilight computation

Let's say, for the solar altitude of 60 degrees, it should be 103000lux, whereas in my case, it is 124100 lux

The error becomes more significant as the altitude of the Sun is lower.

At an altitude of 15 degrees, my value is almost 65000 lux, whereas the correct one should be 19200Lux.

Could anyone explain to me what I am missing in this formula?

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