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for a fixed integration time and in the sky-dominated regime. Taking the log of both sides, and incorporating the zenith-dependence of FWHM and also passband-dependent extinction A(zenith), and incorporating the attenuation due to clouds AC (in magnitudes), we compute a change in m5 relative to nominal conditions of
This includes the zenith-depedence of FWHM, which scales as airmass^0.6, and extinction in the various bands
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Some references
LSST science book
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