Skin damage and SPF

How UVA as well as UVB is implicated.

This one’s in response to requests from a couple of readers …

SPF - short for Sun-Protection-Factor - is the protection rating against skin-damage (erythema) for sunscreens. The shortest wavelengths are most damaging, so the action spectrum for skin damage decreases with wavelength.

The relative importance of different wavelengths in causing skin damage is given by the so-called action spectrum - or weighting function - for erythema, which is shown by the grey curve in the upper panel below. Whether it is the most accurate curve for describing skin damage is up for debate, but it has become widely accepted because it is well defined. It can be accurately described by three simple equations: one for each straight-line segment of the grey curve. There’s therefore no argument about its values (unlike other weighting functions).

Note that the curve spans the entire UVA and UVB regions. And as is normal for plots involving UVB in sunlight, it’s shown with a logarithmic y-axis rather than the usual linear one. This is done because with a linear axis, the details at the shorter wavelengths wouldn’t be discernible. In this case, the lowest value shown is less than 0.0001 of the maximum value plotted. On a linear scale, any details smaller than 0.01 become indistinguishable from the x-axis. Try drawing it.

The other three curves in that upper panel show the extra-terrestrial spectrum of sunlight just outside Earth’s atmosphere (black); and the noon spectra at Lauder New Zealand (latitude 45 S, altitude 370 metres) in summer (red) and winter (blue). The features common to all are ‘Fraunhofer’ lines due to absorption by gases in the Sun’s atmosphere; and the sharp drop-off at shorter wavelengths in the UVB is due to absorption by ozone in our own atmosphere. At wavelength 300 nm, the winter irradiance is about 1 percent of that in summer and about 0.01 percent of the extra-terrestrial value. Differences are even more pronounced at shorter wavelengths where ozone absorption is larger.

The spectral dependence of skin damage in summer and winter sunlight is found by multiplying the grey curve with the red or blue curve respectively. The results are shown in the lower panel of the plot, this time with the more familiar linear axes. But because the winter values are so much smaller, I’ve had to scale them up by a factor of ten so you can better see the detail.

Notice that although the peak wavelengths for skin-damaging radiation fall within the UVB region - with maxima in the range 305 to 310 nm - there is a significant contribution from UVA wavelengths.

The overall skin damage is proportional to the area under the curves. For the noon summer and winter spectra shown, this amounts to 0.3 and 0.03 watts per square metre respectively, corresponding to UVIs 12 and 1.2 respectively.

To clarify my own thoughts (and hopefully yours 😊), I’ve plotted below, the cumulative percentage contribution to the total skin-damaging UV as a function of wavelength for both the summer and winter spectra. For the summer spectrum (red) about 80 percent of that total is from UVB wavelengths, and the remaining 20 percent from UVA wavelengths. But, for the winter spectrum (blue) only 40 percent is from UVB wavelengths, with the remaining 60 percent of the total coming from UVA wavelengths. The reduced contribution from shorter wavelengths is because they are preferentially blocked by the longer atmospheric path.

Clearly, any effective sunscreens must block some UVA (as well as nearly all the UVB). Many popular sunscreens are rated as SPF20. What does that mean in terms of the wavelengths blocked?

A sunscreen with SPF20 means that if its correctly applied, your skin is protected by a factor of twenty. Which is another way of saying it transmits only 5 percent of the skin-damaging radiation, and therefore blocks 95 percent of it. But, as I’ve just pointed out, for high sun conditions about 20 percent of that damage is caused by UVA wavelengths. It therefore follows that any sunscreen with an advertised SPF of 5 or more must block some UVA.

From the previous figure, you can deduce that a sunscreen with SPF20 would have to block all radiation at wavelengths less than 350 nm (to limit the overall transmission to only 5 percent), and an SPF of 50 or more implies there must be good ‘broad-band’ blocking right out to 380 nm.

The long-wave blocking isn’t as effective for the winter spectrum (blue) as for the summer spectrum (red). For example, with blocking out to wavelength 350 nm, 15 percent of the skin damaging UV still gets through, corresponding to an SPF less than 10 (rather than the advertised 20 for high sun). Fortunately, at such times the UVI is already very small (around 1), due to the long path through the atmosphere, so even that smaller blocking factor is sufficient to avoid skin damage.

The term ‘SPF’ is usually applied only to sunscreens, but the principle applies equally well to other materials, including clothing, windows, or eyeglasses.