Stam (A&A 482, pp.989-1007, 2008) has provided spectra of model Earths. From these we can construct B-V colours and compare to our observations.

Using the F0 and F1 model coefficients from Stam (cloud free and 100% cloudy, respectively) we combine these linearly as a function of cloud-cover fraction, and apply Johnson B and V filter transmission curves, and calculate B-V.

We check the method’s correctness on the Wehrli Solar spectrum (we get B-V=0.64) and for Vega (we get B-V=-0.014). Both are very close to the accepted values, so we trust the method for other spectra.

We generate a set of models going from cloud free to 100% cloudy, and get:

Is it just my eyes or is this a really lousy rendition? I wish the blog software allowed for better pictures! Anyway, what we (almost) see is that the observed B-V for earthlight corresponds to about 40% clouds on Earth, with our observational uncertainty of +/- 0.02 mags corresponding to quite a wide range of cloudiness: +/- 8%.

Colours are thus not the way to determine cloudiness on Earth!

Conversely – the variations in cloudiness on Earth is considerable from day to day (at some phase angles +/-20%) so we should be able to use colour variations as an indicator of cloud variations, along with the direct albedo measurements.

The Stam model is based on assuming a Lambertian forest surface; Earth seen at phase angle 90 degrees, and polarization ignored.

Our (considerable) errors on observed colour is due to the conversion from earthshine colours to earthlight colours and the problems of taking the effect of the lunar surface into account. Our observational error on earthshine colour is 0.005 mags. This would allow us to determine Earth’s cloud cover to about 2%-points from B-V colours alone.

A telescope in space (or on the Moon) looking directly at Earth could have colour errors that were even smaller.

The model has to account for orientation of Earth and so on, of course. This is not the case in the Stam model.