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In order to evaluate the ground-based infrared telescope sensitivity affectedby the noise from the atmosphere, instruments and detectors, we construct asensitivity model that can calculate limiting magnitudes and signal-to-noiseratio ($S/N$). The model is tested with tentative measurements of $\rm M'$-bandsky brightness and atmospheric extinction obtained at the Ali and Daochengsites. We find that the noise caused by an excellent scientific detector andinstruments at $-135^\circ \rm C$ can be ignored compared to the $\rm M'$-bandsky background noise. Thus, when $S/N=3$ and total exposure time is 1 secondfor 10 m telescopes, the magnitude limited by the atmosphere is $13.01^{\rm m}$at Ali and $12.96^{\rm m}$ at Daocheng. Even under less-than-idealcircumstances, i.e., the readout noise of a deep cryogenic detector is lessthan $200e^-$ and the instruments are cooled to below $-87.2^\circ \rm C$, theabove magnitudes decrease by $0.056^{\rm m}$ at most. Therefore, according toobservational requirements with a large telescope in a given infrared band,astronomers can use this sensitivity model as a tool for guiding site surveys,detector selection and instrumental thermal-control.

The estimate of sensitivity for large infrared telescopes based on measured sky brightness and atmospheric extinction