  Aims: By performing a detailed radiative transfer analysis, we determine
fractional abundances of circumstellar H2O in the envelopes around six M-type
asymptotic giant branch stars. The models are also used to predict H2O spectral
line emission for the upcoming Herschel/HIFI mission.
  Methods: We use Infrared space observatory long wavelength spectrometer
spectra to constrain the circumstellar fractional abundance distribution of
ortho-H2O, using a non-local thermal equilibrium, and non-local, radiative
transfer code based on the accelerated lambda iteration formalism. The
mass-loss rates and kinetic temperature structures for the sample stars are
determined through radiative transfer modelling of CO line emission based on
the Monte-Carlo method. The density and temperature profiles of the
circumstellar dust grains are determined through spectral energy distribution
modelling using the publicly available code Dusty.
  Results: The determined ortho-H2O abundances lie between 1e-4 and 1.5e-3
relative to H2, with the exception of WX Psc, which has a much lower estimated
ortho-H2O abundance of only 2e-6, possibly indicating H_2O adsorption onto dust
grains or recent mass-loss-rate modulations. The estimated abundances are
uncertain by, at best, a factor of a few.
  Conclusions: The high water abundance found for the majority of the sources
suggests that either the `normal' chemical processes are very effective in
producing H2O, or else non-local thermal equilibrium atmospheric chemistry,
grain surface reactions, or a release of H_2O (e.g. from icy bodies like Kuiper
belt objects) play a role. We provide predictions for ortho-H2O lines in the
spectral window of Herschel/HIFI.
