  We have modeled the emission of H2O rotational lines from the extreme C-rich
star IRC+10216. Our treatment of the excitation of H2O emissions takes into
account the excitation of H2O both through collisions, and through the pumping
of the nu2 and nu3 vibrational states by dust emission and subsequent decay to
the ground state. Regardless of the spatial distribution of the water
molecules, the H2O 1_{10}-1_{01} line at 557 GHz observed by the Submillimeter
Wave Astronomy Satellite (SWAS) is found to be pumped primarily through the
absorption of dust-emitted photons at 6 $\mu$m in the nu2 band. As noted by
previous authors, the inclusion of radiative pumping lowers the ortho-H2O
abundance required to account for the 557 GHz emission, which is found to be
(0.5-1)x10^{-7} if the presence of H2O is a consequence of vaporization of
orbiting comets or Fischer-Tropsch catalysis. Predictions for other
submillimeter H2O lines that can be observed by the Herschel Space Observatory
(HSO) are reported. Multitransition HSO observations promise to reveal the
spatial distribution of the circumstellar water vapor, discriminating among the
several hypotheses that have been proposed for the origin of the H2O vapor in
the envelope of IRC+10216. We also show that, for observations with HSO, the
H2O 1_{10}-1_{01} 557 GHz line affords the greatest sensitivity in searching
for H2O in other C-rich AGB stars.
