  High-resolution far-infrared and sub-millimetre spectroscopy of water lines
is an important tool to understand the physical and chemical properties of
cometary atmospheres. We present observations of several rotational ortho- and
para-water transitions in comet C/2008 Q3 (Garradd) performed with HIFI on
Herschel. These observations have provided the first detection of the
2_{12}-1_{01} (1669 GHz) ortho and 1_{11}-0_{00} (1113 GHz) para transitions of
water in a cometary spectrum. In addition, the ground-state transition
1_{10}-1_{01} at 557 GHz is detected and mapped. By detecting several water
lines quasi-simultaneously and mapping their emission we can constrain the
excitation parameters in the coma. Synthetic line profiles are computed using
excitation models which include excitation by collisions, solar infrared
radiation, and radiation trapping. We obtain the gas kinetic temperature,
constrain the electron density profile, and estimate the coma expansion
velocity by analyzing the map and line shapes. We derive water production rates
of 1.7-2.8 x 10^{28} s^{-1} over the range r_h = 1.83-1.85 AU.
