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We have investigated the water abundance in shock-heated molecular gas,making use of $Herschel$ measurements of far-infrared CO and H$_2$O lineemissions in combination with $Spitzer$ measurements of mid-IR H$_2$ rotationalemissions. We present far-infrared line spectra obtained with $Herschel$'s PACSinstrument in range spectroscopy mode towards two positions in the protostellaroutflow NGC 2071 and one position each in the supernova remnants W28 and 3C391.These spectra provide unequivocal detections, at one or more positions, of 12rotational lines of water, 14 rotational lines of CO, 8 rotational lines of OH(4 lambda doublets), and 7 fine-structure transitions of atoms or atomic ions.We first used a simultaneous fit to the CO line fluxes, along with H$_2$rotational line fluxes measured previously by $Spitzer$, to constrain thetemperature and density distribution within the emitting gas; and we theninvestigated the water abundances implied by the observed H$_2$O line fluxes.The water line fluxes are in acceptable agreement with standard theoreticalmodels for nondissociative shocks that predict the complete vaporization ofgrain mantles in shocks of velocity $v \sim 25$ km/s, behind which thecharacteristic gas temperature is $\sim 1300$ K and the H$_2$O/CO ratio is 1.2

The water abundance behind interstellar shocks: results from $Herschel$/PACS and $Spitzer$/IRS observations of H$_2$O, CO, and H$_2$