Sunlight intensity during a day What simple mathematical function would reasonably well simulate sunlight intensity (disregarding weather) from dawn till dusk in relative numbers, 0-100 %. Are there significant differences (apart from maximum power and daylight duration) between temperate winter, summer or tropical days? The goal is more natural LED lighting for captive wild animals.
Well, there are three parameters of interest to be evaluated to get intensity of sunlight.


Sinusoidal variation of sun vector on earth's surface througout the year
The latitude variation. Which is also sinusoidal
The time variation. Which is also sinusoidal


$$ Intensity = A_0 \sin(\theta - \theta_0) \sin(\pi/2(1 - |t-12|/6))$$

Where,

$$ \theta_0 = A_1\sin(2\pi|d/365.25|)$$

Here $d$ is the day and starts from vernal equinox. $t$ is the time from 00:00 - 23:59. $A_0$ and $ A_1$ are constants. Also when Intensity is negative, obviously there it means darkness.

This is very crude approximation. It assumes circular orbit.