We present the results of models that were designed to study all possible water maser transitions in the frequency range 0-1.91THz, with particular emphasis on maser transitions that may be generated in evolved-star envelopes and observed with the ALMA and SOFIA telescopes. We used tens of thousands of radiative transfer models of both spin species of H2O, spanning a considerable parameter space in number density, kinetic temperature and dust temperature. Results, in the form of maser optical depths, have been summarized in a master table, Table 6. Maser transitions identified in these models were grouped according to loci of inverted regions in the density/kinetic temperature plane, a property clearly related to the dominant mode of pumping. A more detailed study of the effect of dust temperature on maser optical depth enabled us to divide the maser transitions into three groups: those with both collisional and radiative pumping schemes (22,96,209,321,325,395,941 and 1486\,GHz), a much larger set that are predominantly radiatively pumped, and another large group with a predominantly collisional pump. The effect of accelerative and decelerative velocity shifts of up to 5km/s was found to be generally modest, with the primary effect of reducing computed maser optical depths. More subtle asymmetric effects, dependent on line overlap, include maximum gains offset from zero shift by >1km/s, but these effects were predominantly found under conditions of weak amplification. These models will allow astronomers to use multi-transition water maser observations to constrain physical conditions down to the size of individual masing clouds (size of a few astronomical units).< Réduire