Re: What wavelengths of the sun's radiation are filtered by overcast skies?

Clouds are white. This means they scatter light of all wavelengths equally in the visible spectrum.

But you want a more specific answer than that. In general, particles of anything will tend to scatter light most strongly at wavelengths equal to or smaller than the size of the particle. Larger waves go right through without noticing the particles are there. Cloud droplets tend to be a few microns in diameter, so we'd expect visible light and near-infrared to be strongly absorbed, with larger wavelengths less affected.

The precise answer to your question can be found in "Principles of Atmospheric Physics and Chemistry", by Richard Goody, ISBN 0-19-509362-3. (This is not a cheap book, and it's written for people who've taken lots of college-level physics and chemistry -- you're better off looking for it in a university library rather than buying it.) Figure 8.10 shows the optical properties of a typical cumulus cloud. The important quantity is the "extinction coefficient", which shows the fraction of an incoming beam of light which is absorbed or scattered per unit distance the beam travels through a given density of particles. The larger this value is, the less light reaches the ground.

The figure shows that between 300 nanometers and 2 microns (sunburn-ultraviolet and the entire visible and near-infrared range), the cloud's extinction coefficient is nearly constant. This agrees with the earlier statement that "clouds are white". There is a peak in the extinction at around 5 microns -- there, extinction is 50% higher than in the visible. This corresponds to mid-infrared light. Between 5 and 100 microns (the "thermal infrared"), extinction gradually decreases, reaching about 20% of the visible-light value at 100 microns. Keep in mind I've only described the general shape of the curve: there are lots of peaks and wiggles I've ignored.

This figure does not show cloud extinction in the middle and far ultraviolet, but those wavelengths are almost entirely eliminated by ozone in the atmosphere. Beyond 100 nanometers (the microwave and radio range), both clouds and air are pretty much transparent (except for a few specific wavelengths).

You've mentioned an idea for treatment of S.A.D. which seems to rely on exposing people to different wavelengths of light. You need to justify this idea scientifically, and (since human perception is involved) you must be very careful doing so. You need to do a controlled experiment which compares your light box with something which you expect to have no effect (a placebo). Since human perceptions can change wildly based on human knowledge, you must have a "blind control": the people in the experiment must not know whether they are being treated with the "real" light box or the placebo. (If your treatment involves colored light, I have no idea how you could do this.) Otherwise people will feel better because they think they ought to. Needless to say, you must do this experiment with many people, and you cannot use yourself as a subject. Finally, your experiment must be able to distinguish between your hypothesis (S.A.D. is caused by color changes in daylight which are due to clouds) and alternative hypotheses (for example, S.A.D. is caused by changes in light level, not color). One piece of data which argues for the second hypothesis: lots of people report S.A.D. symptoms here in Boston in the wintertime, when there's less daylight, but it's not noticeably cloudier.

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