  The characterization of rocky, Earth-like planets is an important goal for
future large ground- and space-based telescopes. In support of developing an
efficient observational strategy, we have applied Bayesian statistical
inference to interpret the albedo spectrum of cloudy true-Earth analogs that
include a diverse spread in their atmospheric water vapor mixing ratios. We
focus on detecting water-bearing worlds by characterizing their atmospheric
water vapor content via the strong 0.94$\,\mu$m H$_2$O absorption feature, with
several observational configurations. Water vapor is an essential signpost when
assessing planetary habitability, and determining its presence is important in
vetting whether planets are suitable for hosting life. We find that R=140
spectroscopy of the absorption feature combined with a same-phase green optical
photometric point at $0.525-0.575\,\mu$m is capable of distinguishing worlds
with less than $0.1\times$ Earth-like water vapor levels from worlds with
$1\times$ Earth-like levels or greater at a signal-to-noise ratio of 5 or
better with $2\sigma$ confidence. This configuration can differentiate between
$0.01\times$ and $0.1\times$ Earth-like levels when the signal-to-noise ratio
is 10 or better at the same confidence. However, strong constraints on the
water vapor mixing ratio remained elusive with this configuration even at
signal-to-noise of 15. We find that adding the same-phase optical photometric
point does not significantly help characterize the H$_2$O mixing ratio, but
does enable an upper limit on atmospheric ozone levels. Finally, we find that a
0.94$\,\mu$m photometric point, instead of spectroscopy, combined with the
green-optical point, fails to produce meaningful information about atmospheric
water content.
