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Aims: Our aim is to determine the critical parameters in water chemistry andthe contribution of water to the oxygen budget by observing and modelling watergas and ice for a sample of eleven low-mass protostars, for which both forms ofwater have been observed.  Methods: A simplified chemistry network, which is benchmarked against moresophisticated chemical networks, is developed that includes the necessaryingredients to determine the water vapour and ice abundance profiles in thecold, outer envelope in which the temperature increases towards the protostar.Comparing the results from this chemical network to observations of wateremission lines and previously published water ice column densities, allows usto probe the influence of various agents (e.g., FUV field, initial abundances,timescales, and kinematics).  Results: The observed water ice abundances with respect to hydrogen nuclei inour sample are 30-80ppm, and therefore contain only 10-30% of the volatileoxygen budget of 320ppm. The keys to reproduce this result are a low initialwater ice abundance after the pre-collapse phase together with the fact thatatomic oxygen cannot freeze-out and form water ice in regions with T(dust)>15K. This requires short prestellar core lifetimes of less than about 0.1Myr. Thewater vapour profile is shaped through the interplay of FUV photodesorption,photodissociation, and freeze-out. The water vapour line profiles are aninvaluable tracer for the FUV photon flux and envelope kinematics.  Conclusions: The finding that only a fraction of the oxygen budget is lockedin water ice can be explained either by a short pre-collapse time of less than0.1 Myr at densities of n(H)~1e4 cm-3, or by some other process that resets theinitial water ice abundance for the post-collapse phase. A key for theunderstanding of the water ice abundance is the binding energy of atomic oxygenon ice.

Water in Low-Mass Star-Forming Regions with Herschel: The Link Between Water Gas and Ice in Protostellar Envelopes