Re: UV Index vs. angle of sun?
- From: bobg@xxxxxxxxx (Robert Grumbine)
- Date: Fri, 01 Jun 2007 17:28:37 -0000
In article <1180547634.905965.234680@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<hellman@xxxxxxxxxxxx> wrote:
I recently bought an Oregon Scientific UV meter and made some
measurements which surprised me by showing a much higher UV index than
I expected when the sun was low in the sky. My experience had been
that, when the sun was lower than 45 degrees above the horizon, I
could spend considerably more time in the sun without burning. For
example, I was in Sweden many years ago near the summer soltice,
forgot sun screen (it was 1976 after all!), being in the sun for a
number of hours, and not burning)
At first this surprised me because at 45 degrees, there is only 41%
more atmospheric path for the sun's rays to penetrate. But then I
realized the attenuation is exponential and needs to be measured in
dB. If the atmosphere attenuates UV by 20 dB at high solar noon, then
that extra 41% translates to 8.2 dB of extra attenuation, for an
equivalent SPF of 6.6. With the sun 30 degrees above the horizon there
would be 100% more atmospheric path since 1/sin(30 deg) = 2, and that
would add 20 dB, equivalent to an SPF of 100. Of course, if the basic
attenuation were 10 dB instead of 20, all the SPF's would be reduced
accordingly.
Based on my experience I guesstimated that the basic attenuation was
closer to 20 dB than to 10. But my UV meter seems to indicate an
effective SPF of only about 3 when the sun is 30 degrees above the
horizon, which would correspond to a basic attenuation of about 5 dB.
Is the UV meter right? Does anyone know the basic attenuation, as I am
calling it?
Thanks for any help.
Martin
PS I realize that due to the different absorption rates for UVA and
UVB, the problem is more complex than I've phrased it here --
especially at high altitude. But this is already complex enough for a
first post.
You might look for some articles by Forest Mims III. I don't
remember the details, but do recall that he explored a fair number
of factors controlling ground level UV (adjacent buildings, trees,
clouds, as reflectors for instance). It was also done by a
UV meter you could build yourself if you're in to that sort of
thing.
One thing that you don't describe, and is not a small detail, is
how you were getting the angle of the sun to the horizon. Eyeball
estimation is notoriously inaccurate, with an estimated 45 degrees
turning out to be anything from 30 to 60 (usually towards 60).
An element of the physics you'll want to look up is how strongly
absorbed the UV that you're measuring is. You've implicitly
assumed that you're in the linear regime -- that the path length
is so small that having twice as much path through the absorbing
layer will double the absorption. Offhand, I think this isn't the
case for your integrated radiometer. There's enough ozone at mid-latitudes
(my inference from your stanford address) that I think it's in the
exponential regime. That is, the transmission is proportional to
exp(-L) where L is proportional to both some coefficient and the path
length itself. For small enough L, it's linear. But for large values,
it's distinctly not:
L Transmission
0 1.00
1 0.37
2 0.14
3 0.05
I don't follow you through the SPF and dB.
But, as there was no other response, maybe this can give you a
couple of useful starting points.
--
Robert Grumbine http://www.radix.net/~bobg/ Science faqs and amateur activities notes and links.
Sagredo (Galileo Galilei) "You present these recondite matters with too much
evidence and ease; this great facility makes them less appreciated than they
would be had they been presented in a more abstruse manner." Two New Sciences
.
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