How far light survives — haze and clear air

Whether an evening glows or fizzles isn’t only about the light and the clouds — it’s about the clarity of the air in between. Every kilometre of air takes a little of the light away.

Every kilometre takes a cut

As light crosses the air, a little is scattered or absorbed out of the beam at every step. The more air — and the more dust and haze suspended in it — the more is lost. And the loss isn’t gentle: a beam fades exponentially with the amount of stuff in its path, not in a straight line. Double the murk, or double the distance, and you don’t lose twice as much light — you lose far more.

The Goldilocks amount of haze

Much of that work is done by aerosols — dust, sea salt, smoke, pollution. For a sunset they cut both ways. Too little, and the air is so clean the light passes almost untouched: the sky is clear, but the colour is pale and thin. Too much, and the haze greys everything into a flat, muddy horizon. In between sits a sweet spot where the air strips just enough blue to leave the reds deep and saturated — the difference between a forgettable evening and a burning one. (Meteorologists track this aerosol load as aerosol optical depth, or AOD.)

Why it’s the horizon that counts

Here is where it ties back to the geometry. At sunset the light reaches you along a long, grazing path — through many times more air than the beam overhead at noon. So the clarity that matters isn’t the air above your head; it’s the air stretched out toward the horizon, often hundreds of kilometres away, over ground where the sun has already set. A sky that looks hazy straight up can still deliver if the long path toward the sun happens to be clean — and a crisp blue overhead can disappoint if there’s a wall of haze sitting out where the light is coming from.

The maths, briefly

The fraction of light that survives a path is set by its optical depth \(\tau\) — a running total of everything scattering and absorbing along the way:

$$ T = e^{-\tau}. $$

\(\tau\) is small for a short, clean path and large for a long or hazy one, and the exponential is why a little extra haze over a long path snuffs the light so fast. The aerosol share of \(\tau\) is the aerosol optical depth (AOD) — the number that separates a pale sky from a saturated one.

The light, the clouds, and a clean path to the sun — a fire sky needs all three to line up. This is the third.