Facing the Sun

Does the angle of attack matter for skin damage by UV?

A reader, I’ll call him Michael, raised some interesting points after this post about the UVI and exposure time for skin damage. He first commented.

… the UV dose our skin experiences cannot be calculated from the UVI by a simple formula because UVI does not represent the intensity of radiation on the skin. It represents the intensity of radiation on a flat horizontal surface which is not the same as the radiation directly impinging on the skin.

Good point. I used to wonder about this myself and decided to do some measurements to check it out. We used a pair of instruments to simultaneously measure skin-damaging UV at Lauder. One was set up as usual, to measure the UVI arriving on a horizontal surface. The other was mounted on a sun-tracker, so it always pointed directly towards the sun.

The short answer to his question is yes, but …

Let’s start with the clear-sky situation.

The main clear-sky result, which we first published in 1997, is updated below. The top panel shows the variation in sun elevation over the day, and the second panel shows that the corresponding variation in UVI for both instrument orientations. You can see that while the peak values are similar, the readings from the sun-pointing instrument (in blue) are indeed somewhat larger than the official UVI values (in red). So the time for damage to skin with that orientation will be shorter. So Michael is correct. But how important is it?

Of course for any other orientations, the readings would be somewhat lower. Facing the sun directly is the worst case scenario. If you’re facing away from the sun, you’ll receive less than indicated by the official UVI.

The differences are rather small given those huge differences in orientation, especially for smaller sun elevations. You might find them surprisingly small. That’s because, unlike the visible radiation (light) that you’re more familiar with, most of the UV is from scattered skylight. When the sun is near the horizon, virtually none of the direct beam makes it through the long atmospheric path.

The lower two panels in the figure show the discrepancies in more detail. The third shows the ratios, and the fourth shows the differences. As expected, near noon, the ratio is close to one, showing that both instruments gave similar readings; while at other times, the UV measured by the instrument that pointed directly towards the sun was indeed greater.

But the opposite is true near sunrise and sunset when the UVI is close to zero. In this case, the signal from the sun-pointing instrument becomes smaller because it can ‘see’ only half the sky. The greatest discrepancy was in the mid-morning and afternoon when readings from the sun-facing meter were higher by more than 30 percent (i.e., the ratio plotted was greater than 1.3). But overall, it turns out (rather fortuitously) that the effect isn’t all that important - at least for summer conditions - because the amount of UV arriving outside the midday period is only a small fraction of the total.

For example, at noon this day the peak value was around UVI = 12, whereas by at 8 and 18 NZST (i.e., 9 am and 7 pm local daylight-saving time) when the ratio is largest, it had dropped to around UVI = 2. So, although the ratio is large, the difference in UVI is never more than 1 unit, as shown in the lowest panel.

The two instrument orientations therefore give similar results when the sun is high in the sky, which is when the UV is most problematic. The biggest differences are for small sun elevation angles - around 20 to 30 degrees. This means that while the daily doses of UV aren’t greatly affected in summer, they will be significantly underestimated in winter, when the maximum sun elevation remains low.

What about cloudy skies …. (the more normal situation in Aotearoa New Zealand?) 😊

Under cloudy conditions, larger differences (in either sense) are possible. I decided to have a closer look at that. The results for the entire inter-comparison period are summarised in the plots below. The time series in the first panel includes several bell-shaped curves corresponding to cloudless days, including December 31, 1995, as shown above. The cloudiest was three days later, on January 3, 1996.

In the other 3 panels above, I’ve plotted results as functions of sun elevation angle, which is the most important determinant of clear-sky UV for both orientations. They show that under-estimations by the horizontal instrument during clear skies are approximately compensated by over-estimations during cloudy skies, so the overall effect on inferred UV doses is relatively small. The mean UVI ratio is 0.98, which means that the overall difference between the two instrument orientations is less than 2 percent, which corresponds to less than 0.1 of a UVI unit.

Michael went on to say …

… when UVI is only slightly more than zero at sunrise or sunset the actual ultraviolet radiation intensity UVA + UVB on the skin can be as much as 4 W/cm2 on a clear day, not near zero. Actual ultraviolet intensity radiating the face or exposed parts of the body can be as much as 4 W/cm2 when standing in direct sunlight at sunrise or sunset and around 20% to 30% more when the sun reflects off water onto our skin.

Here he’s talking about something quite different - and less relevant for skin damage. The total UV radiation he’s talking about (UVA + UVB) is dominated by the UVA component, rather than the short wavelength UVB component that’s responsible for most skin damage (I think his units above should be W/m2 rather than W/cm2).

For overhead sun there’s about 66 W/m2 of UVA, while the amount of UVB (which depends on ozone) is around 2.2 W/m2. So, for overhead sun, only around 3 percent of the UV is within the damaging UVB range. Because of its stronger atmospheric attenuation, that fraction reduces markedly as the sun gets lower in the sky. For example, if the sun is 30 degrees above the horizon, only 1.5 percent of the UV is in the UVB range, and if the sun’s on the horizon it’s less than 0.3 percent. So, of that 4 W/m2 of UV in the direct beam at sunrise or sunset, only a tiny fraction is in the UVB region.

The UVI does include a contribution from UVA wavelengths, but as you can see from the 2nd panel above, even for sun elevations as high as 10 degrees above the horizon, the UVI remains close to zero for both instrument orientations. In fact, whenever the sun’s less than 20 degrees above the horizon, you don’t need to worry about UV damage to your skin.

His last bit - in the italics above - about reflections off water is also interesting. While reflections from water (or snow) can increase the UV you receive, it turns out to be not a problem for skin-damaging UV when the sun is close to the horizon because, as I mentioned earlier, at those times there’s virtually no UVB in the direct beam of sunlight. What hasn’t been absorbed is scattered out of the beam by air molecules in the long atmospheric path. When the sun’s low in the sky, virtually all the UVB is from radiation scattered from air molecules in the sky above.

It has to be said that differences in orientation would be much larger for instruments measuring radiation at longer wavelengths (e.g., in the visible, or infra-red regions), where most of the radiation is from the direct solar beam.

This all goes to show that, while not perfect, the approximation of measuring UV incident on a horizontal surface wasn’t such a bad choice after all. Whew!

Thanks for raising these points Michael. It’s all very interesting. Well worth thinking about. As we’ve seen, the answers are sometimes counter intuitive.

Sorry if it was a bit complicated for some …. 😊