  Aims: Spectrally resolved circumstellar H2O(1_10 - 1_01) lines have been
obtained towards three M-type AGB stars using the Odin satellite. This provides
additional strong constrains on the properties of circumstellar H2O and the
circumstellar envelope. Methods: ISO and Odin satellite H2O line data are used
as constraints for radiative transfer models. Special consideration is taken to
the spectrally resolved Odin line profiles, and the effect of excitation to the
first excited vibrational states of the stretching modes (nu1=1 and nu3=1) on
the derived abundances is estimated. A non-local, radiative transfer code based
on the ALI formalism is used. Results: The H2O abundance estimates are in
agreement with previous estimates. The inclusion of the Odin data sets stronger
constraints on the size of the H2O envelope. The H2O(1_10 - 1_01) line profiles
require a significant reduction in expansion velocity compared to the terminal
gas expansion velocity determined in models of CO radio line emission,
indicating that the H2O emission lines probe a region where the wind is still
being accelerated. Including the nu3=1 state significantly lowers the estimated
abundances for the low-mass-loss-rate objects. This shows the importance of
detailed modelling, in particular the details of the infrared spectrum in the
range 3 to 6 micron, to estimate accurate circumstellar H2O abundances.
Conclusions: Spectrally resolved circumstellar H2O emission lines are important
probes of the physics and chemistry in the inner regions of circumstellar
envelopes around asymptotic giant branch stars. Predictions for H2O emission
lines in the spectral range of the upcoming Herschel/HIFI mission indicate that
these observations will be very important in this context.
