  In the near-future, atmospheric characterization of Earth-like planets in the
habitable zone will become possible via reflectance spectroscopy with future
telescopes such as the proposed LUVOIR and HabEx missions. While previous
studies have considered the effect of clouds on the reflectance spectra of
Earth-like planets, the molecular detectability considering a wide range of
cloud properties has not been previously explored in detail. In this study, we
explore the effect of cloud altitude and coverage on the reflectance spectra of
Earth-like planets at different geological epochs and examine the detectability
of $\mathrm{O_2}$, $\mathrm{H_2O}$, and $\mathrm{CH_4}$ with test parameters
for the future mission concept, LUVOIR, using a coronagraph noise simulator
previously designed for WFIRST-AFTA. Considering an Earth-like planet located
at 5 pc away, we have found that for the proposed LUVOIR telescope, the
detection of the $\mathrm{O_2}$ A-band feature (0.76 $\mathrm{\mu}$m) will take
approximately 100, 30, and 10 hours for the majority of the cloud parameter
space modeled for the atmospheres with 10\%, 50\%, and 100\% of modern Earth
O$_2$ abundances, respectively. Especially, for {the case of $\gtrsim 50$\%} of
modern Earth O$_2$ abundance, the feature will be detectable with integration
time $\lesssim 10$ hours as long as there are lower altitude ($\lesssim 8$ km)
clouds with a global coverage of $\gtrsim 20\%$. For the 1\% of modern Earth
$\mathrm{O_2}$ abundance case, however, it will take more than 100 hours for
all the cloud parameters we modeled.
