We have now reduced all the good data, and have arrived at the intrinsic properties of each image. We extract now the ratio of the DS-patch to the total flux and divide this by the similar ratio extracted from the synthetic model. This ratio of ratios is the same as the ‘Lambertian sphere terrestrial albedo’ and is the quantity published by e.g. Goode et al.

We select data for airmasses less than 2 and for statistical error less than 1.5%. This error is that due to mainly pixel-selection inside the ‘patches’ on the lunar surface (one near Grimaldi, one inside Crisium). Monte Carlo bootstrap sampling of the pixels inside a lon-lat box were resampled, with replacement, and the standard deviation of the consecutive means calculated. Errors due to image alignment, improper scattered-light removal, synthetic model problems and so on, are not included.

Here is the plot of extracted albedo against lunar phase for the VE1 filter (the filter with least scatter: IRCUT is almost identical to this plot): [scroll down for discussion]

The colours designate the method used for scattered light removal: red is the EFM method, orange or yellow is the ‘linear BBSO method’, and green are the raw data. Crosses and diamonds indicate the sign of the lunar phase – crosses are for positive phase. Error bars (error due to counting noise, not image alignment etc) have been plotted over the symbols, but are all smaller than the symbols themselves.

What do we see? There is scatter and there is dependence on lunar phase.

First, let us discuss the lunar phase dependency: For small phases we are essentially getting closer to Full Moon and the scattered light is more and more of a problem. The Raw data are doubled by phase 80 degrees, showing the importance of removing the scattered light. BBSO-linear is better than no removal all while EFM is better than BBSO-linear. There is also another lunar phase dependency – notice how the albedo rises for large lunar phases. Since the halo is smallest here this is not an effect of scattered light! The albedo is a composite quantity, consisting of quantities measured in observed and modelled images. The scattered light influences mainly the model, and mainly at small lunar phases. The reflectance model soley influences the synthetic lunar image, of course – I think we are seeing the influence of the (inadequate) reflectance model at large lunar phases – the albedo rises artificially due to this.

The there is the scatter. We see ‘daily progressions’ for some connected lines of data points. For instance, by 90 and 95 degrees phase. These points represent our candidates for geophysics! I think the ‘progression’ along these lines are due to different parts of Earth )oceans, clouds, continents) rotating into view for these observing sequences.

Below is the same plot, for the B filter. Apart from more scatter we see that the EFM seems able to remove most effects of scattered light, compared to the BBSO-linear method. A stronger ‘upturn’ is possibly seen at large phase.