We use synthetic models of the Moon, illuminated by a model Earth, to generate fits to our observations. The properties of the theoretical models determine not only the fit itself but also the quality of the fit. Two important choices are made in generating the theoretical models – the lunar
surface albedo map has to be chosen, and the lunar reflectance model has
to be chosen.
We can choose surface albedo either directly from
the Clementine map, or as this map scaled visually to better match the
1970s albedo map by Wildey.
We can choose the reflectance models
in several ways – current models being tested are ‘the new Hapke 63’ and
the ‘Hapke-X’ reflectance model.
We test how well these choices work by considering the RMSE of the ‘edge-profile fits’
generated between the theoretical Moon models and the observed ones.
Combing the two choices above in all possible wasy we get these results:
There are four histograms here but pairwise hide behind the other. The major effect is that due to the choice of albedo map (blue vs green above) – the scaled Clementine map has 25% lower RMSE than does the un-scaled map.
The effect of reflectance model is very minor and can barely be seen
The RMSE is calculated from the profile of 20-row averaged ‘cuts’ at the dark side edge, starting 50 pixels from the edge and ending 50 pixels onto the disc. Fitting was performed vith the MPFITFUN routine in IDL, using a 4-parameter fitting model where intensity offset, horisontal pixel shift, terrestrial albedo and PSF-parameter ‘alfa’ were varied to obtain the optimal fit. RMSE was then calculated from the residuals between observed edge-profile and model same.
The Clementine map was scaled (see http://earthshine.thejll.com/#post253 ) against the Wildey map in the sense that the lower-resolution grid from the Wildey map was interpolated by the Clementine map and the scatter-plot generated. An obvious offset and slope difference existed and from the robust linear regression of one onto the other a scaling relationship for the Clementine map pixel values was generated and applied to all pixels in the Clementine map.
So, we may be able to help constrain the sort of work current space-missions do! We should not avoid to point this aspect of the work out, in the ‘big article’.
Puzzling, at first, is the almost complete absence of an effect due to the choice of reflectance model. I can see effect clearly when total flux vs phase angle is plotted, so we simply do not have a large sensitivity to reflectance at the edge of the disc. Fair enough, only a local set of pixels are involved and the flux of the model bay be quite wrong while the fit at the edge is till very nice. So we should constrain our models by fitting many different aspects of our data – both the reflectance model against observed total flux as function of phase, and the albedo map by edge-fitting.
The subject of Clementine vs Wildey has been discssed in this blog before. Here: