DM-5660: Add motivated model fits to validate_drp photometric and astrometric scatter/repeatability analysis and plots

[wmwv]

Implements well-motivated theoretical fits to the astrometric and photometric performance measurements based on derivations from LSST Overview paper.
http://arxiv.org/pdf/0805.2366v4.pdf
Photometric errors described by
Eq. 5
sigma_(rand) = (0.039 - gamma) * x + gamma * x^2 [mag^2]
where x = 10^(0.4*(m-m_5))
Eq. 4
sigma_1^2 = sigma_sys^2 + sigma_rand^2
Astrometric Errors
error = C * theta / SNR
Based on helpful comments from Zeljko Ivezic
"""
I think eq. 5 from the overview paper (with gamma = 0.039 and m5 = 24.35;
the former I assumed and the latter I got from the value of your
analytic fit that gives err=0.2 mag) would be a much better fit than
the adopted function for mag < 21 (and it is derived from first principles).
Actually, if you fit for the systematic term (eq. 4) and gamma and m5,
it would be a nice check whether there is any “weird” behavior in
analyzed data (and you get the limiting depth, m5, even if you don’t
go all the way to the faint end).
Similarly, for the astrometric random errors, we’d expect
error = C * theta / SNR,
where theta is the seeing (or a fit parameter), SNR is the photometric
SNR (i.e. 1/err in mag), and C ~ 1 (empirically, and 0.6 for the idealized
maximum likelihood solution and gaussian seeing).
"""

[danielsf]

Just sticking my nose where it doesn't belong:

If it would help,the calcSNR_m5 method here

https://github.com/lsst/sims_photUtils/blob/master/python/lsst/sims/photUtils/SignalToNoise.py

can calculate the photometric signal to noise given m5 and a few system parameters and throughputs. It has been checked to be consistent with equations 4 and 5 in the overview paper. There is also a method calcGamma to calculate the appropriate value of gamma given m5.

Take it or leave it. I just wanted to make sure you were aware that these methods existed.

[wmwv]

@danielsf Thanks, I didn't know about that and very much appreciate your note!

I unfortunately don't think I can use that here as sims_photUtils has some substantial dependencies that I don't want to add here:

setupRequired(sims_sed_library)
setupRequired(sims_maps)
setupRequired(sims_utils)
setupRequired(throughputs)

If it would be possible to expose some of these utility functions without requiring the large and substantial sims_sed_library and sims_maps then I might be interested in adopting some of these routines this to ensure consistency.

[danielsf]

@wmv That (stripping out the massive data file dependencies from sims_photUtils) is on our list of things to do in the near future (I guess we hadn't considered removing sims_maps; definitely sims_sed_library). I will ping you when it is accomplished.

[jonathansick]

Typo: move this into previous sentence.

[jonathansick]

Aside from the issues mentioned in the line notes this all seems okay. I haven't independently run the code to check the plots, though.

I don't have a good feel for how robust these fits are. If there's a weird dataset is it possible for the fits to go crazy? I'm not sure it's necessary to add in either code to check the robustness of the fits (even if it's a basic bootstrap); depends on the use cases of the fitted values.

[jonathansick]

Also, it might be useful to capture the provenance of the model for astrometric scatter somewhere in the docstrings.