How to handle negative cosine of Solar Zenith Angle while calculating clear-sky UV Index?

Decoding the Sun: What to Do When the Math Goes Dark on UV Index

Ever wondered how they calculate that UV Index number you see on weather reports? It’s more than just a guess – it’s a complex calculation that helps us understand the sun’s potential to damage our skin. But what happens when the math throws a curveball, especially when dealing with something called the “cosine of the solar zenith angle”? Sounds complicated, right? Let’s break it down.

The UV Index is basically a warning system, telling you how strong the sun’s harmful rays are on any given day. Getting it right is super important so we know when to slather on the sunscreen or seek shade i. A key ingredient in figuring this out is the cosine of the solar zenith angle (SZA). Think of the SZA as the sun’s angle in the sky, measured from straight overhead i. The cosine of that angle helps us pinpoint the sun’s position, ranging from 1 (directly above) to 0 (on the horizon) i. So far, so good.

But here’s the snag: what happens when the sun dips below the horizon? Suddenly, that cosine value turns negative ii. Now, you can’t have a negative UV Index – it’s like saying you have negative sunshine! So, what’s a sun-savvy person to do?

The problem is that many UV Index calculations use that cosine value directly ii. Imagine a simplified formula like this:

UVI ≈ 12.5 * (cos(SZA))^2.42 * (Ozone/300)^-1.23

See that cos(SZA) in there? If it’s negative, the whole equation goes haywire, spitting out nonsense numbers. We need to fix this!

Luckily, there are a few clever ways to handle this: