In this entry we introduced a Monte-Carlo based model for the spectrum of earthlight. We are able to use the model to estimate B-V for outgoing light, given input for cloud albedo, surface albedo and so on – and cloud fraction.

From the NCEP reanalysis project we can take the global total cloud fraction product (‘tcdc’) and calculate the global mean value for different times (we pick year 2011 here) and use the values for the B-V model.

I have done this. In 2011 TCDC varied between 50 and 55 percentage points. delta(B-V) [i.e. the differences between the solar spectrum B-V and the earthlight B-V, in the model] varied from 0.090 to 0.075 at the same time. That is, earthlight became more solar coloured for larger cloud cover – good – and implies that Earth is bluer when there are fewer clouds.

The change in B-V is 0.015 mags – can we measure that at all?

In our little paper we have relevant results. Uncertainties on B and V are at the 0.005 to 0.009 mags level, so that differences are at the 0.012 level (worst case) for a B-V value – on the ‘lucky night’.

But on the Full Moon night of 2455814 we have errors of just 0.001 and 0.002 on B-V.

We need to understand why the error can be so different. We promised 0.1% accuracies at the start of this project – and seem to be able to get it with 0.001 mags error – but why not on both nights?

Obviously, the error on the DS will be larger since there are much fewer photons – but this does not help explain why the errors are similar on the ‘lucky night’.

One point is that on 2455814 we measure B-V from one image generated by alignment of the B and V images in question. On 2455945 we measure B and V in seperate images and take the difference of those means. There are ‘cancellation’ issues at play here – surface structure will add to the variance of single -band images while some of the structures cancel (particularly if the images are well centred) in difference images.

Added later: yes, there is an effect (obviously, duuuh) – if we calculate the DS-BS difference from areas in the B-V image, instead of in the B and V images seperately, and perform bootstrap sampling on the pixels involved, we get the mean over the resamplings and its standard deviation to be

-0.155 +/- 0.005

whereas the difference between <B> and <V>, and its error calculated from error propagation, is

-0.154 +/- 0.014.

That is, we have a third the uncertainty. This will be used in the paper.

The uncertainty is still a bit high, though. (5 times what we promised, or to be fair about 5/sqrt(2)=3.5 times. since the above is a difference and not a directly measured quantity – which was the thing about which we made promises!).

It could be that noise on the low-flux DS is dominating here – this remains to be seen. And we still need to understand why it is still higher than for the Full Moon night – but things are making a bit more sense now.