...
SNR scales as source flux in the numerator and (for unresolved objects) as seeing in the denominator. Flux at an airmass "a" is reduced by a factor f(a)=10^(x*(a-1)/2.5) where x is the extinction coefficient listed in the table above. So SNR vs. airmass at fixed exposure time for unresolved point sources scales as SNR(a)~10^(x*(a-1)/2.5)/(0.35+0.72a^2-0.07a)
flux attenuation
Some references
...