Scaling UV damage to human skin

... is 10 x 1 always the same as 1 x 10?

In response to the question below, asked by subscriber Fabio, from Italy.

I've read that 1h with UVI 2 is the same as 30m with UVI 4, which in turn is the same as 15m with UVI 8. This is because UVI 2 means half the power of UVI 4, right? Does this mean that 15min with UVI 8 does the same damage as 1h UVI 2 because you get the same amount of photons/power?

Thanks, Fabio. This turns out to be a very interesting question. I’ll try to answer it, with some cautionary caveats.

As far as the amount of energy you’re exposed to is concerned, one hour of exposure to UVI =1 is, indeed, exactly the same as for one tenth of an hour (i.e., 6 minutes) at UVI =10. In both cases you’d receive a skin-damaging dose of 90 joules per square metre, or 0.9 SED (Standard Erythemal Dose)¹. And, after 10 hours of exposure to UVI =1 (which doesn’t normally happen because of the variations in sun angle over a day) the dose would be 9 SED, the same as a 1-hour exposure at UVI = 10. This poor little kid probably got at least that amount.

Found on Google Images. See https://premiermedicalocala.com/sunburn/.

But that ‘equality’ assumes that the weighting function for erythema that was applied in those calculations is absolutely correct. We know it’s not because in the original paper where it was first defined, it was clearly just an approximation to measured data, as shown in the telling figure below that was drawn a long time ago by my colleague Sasha Madronich. It shows (note the logarithmic y-axis) that at some wavelengths the line differs from the data points by more than a factor of 5, and that it’s consistently too high at wavelengths longer than 320 nm (throughout most of the UV-A region).

The action spectrum for erythema is the thick solid line. The solid symbols are the data points used to derive it, based on measurements published by McKinlay and Diffey, in 1987. For comparison, three other action spectra are also included..

What it all means as far as real skin damage is concerned is another question entirely. For the most sensitive skin types, the first signs of damage - as evidenced by skin-reddening (called ‘erythema’) - occur after exposures as small as 2 SED. That so-called Minimum Erythemal Dose (MED) of course varies from person to person depending on their skin type. For fair skin - like for the child pictured above - it could be achieved after an exposure to a UVI of 10 for a period of about 15 minutes; or a UVI of 1 for 150 minutes. But repair mechanisms are also at play, which probably work better at lower UVIs. I should add that for more serious outcomes, like skin cancer in its various forms, the damage may not scale proportionately because the effective wavelength dependence (sometimes called the ‘action spectrum’) for those outcomes won’t be the same as for erythema - as illustrated above. In fact, the action spectrum for the most serious outcome, melanoma induction in human skin, isn’t known. It would be impossible to get ethical approval to carry out the experiment.

In any case, it’s generally assumed that the skin damage is simply proportional to the dose received, regardless of whether it’s a low UVI for a long time, or a high UVI for a short time. That proportionality assumes there is so called ‘reciprocity’ between the UVI’s strength and its duration. The best study I’m aware of on the topic was published way back in 1989 so isn’t easily available on-line. Unfortunately, it doesn’t fully answer that question. The paper nicely shows that reciprocity for erythema applies, but only for exposure to a UV lamp for periods ranging from 40 minutes down to 2.5 seconds (which is 1000 times shorter). For fair-skinned people, those exposure times for skin-reddening correspond to UVIs ranging from about 3 to 3000.

That lower limit is problematic. Although UVIs in the range 0 to 3 are common, we can’t be sure that reciprocity then applies. It’s tacitly assumed that it does, but that may not be correct because below some UVI threshold, repair mechanisms may be able to cope adequately enough to avoid cumulative damage. We don’t yet know what that threshold is. The 1989 experiment should be extended to include lower UV levels and therefore longer times for erythema. The difficulty would be in finding volunteers prepared to subject themselves to consistently low illumination levels over periods of several hours. Even the 40-minute sittings in that study must have been trying.

That upper UV limit is fine. It far exceeds any realistic value for sunlight. The highest UVI reliably measured so far at Earth’s surface is 25 (in the high-altitude tropical altiplano region). Even in outer space, the UVI would be around 300, implying a time for skin damage of about half a minute (30 seconds).

Finally, harking back to the large uncertainties in the action spectrum for erythema showed above, the approximate reciprocity shown to hold for that laboratory light source won’t necessarily hold for sunlight because the shape of the spectrum of received sunlight changes throughout the day. The proportion of shorter, more damaging, UV wavelengths is larger for higher UVIs.

Wow. This all ended up being a lot more interesting than I thought when I started. The closer I look, the murkier it gets. It’s high time some of these issues were examined more closely. Go for it Europe. With tRump’s layoffs in the USA, progress there will probably have to wait until sanity resumes …

1. Here’s how the dose of sunburning UV is calculated:
To convert the UVI to erythemally-weighted UV in SI units, you need to divide by 40.
Therefore, a UVI of 1
= 0.025 watts per square meter
= 0.025 joules per square metre per second
After 1 hour (i.e., 60 x 60 seconds), the cumulative dose will be 0.025 * 60 * 60 joules per square meter
= 90 joules per square metre
= 0.9 SED (given that 1 SED = 100 joules per square metre).
For more details check out this post.