This modelling study aims to gain an improved understanding of the processes that determine the water vapour budget in the stratosphere by means of the investigation of water isotope ratios. At first, a separate hydrological cycle has been introduced into the chemistry-climate model EMAC, including the water isotopologues HDO and H218O and their physical fractionation processes. Additionally, an explicit computation of the contribution of methane oxidation to HDO has been incorporated. EMAC simulates explicit stratospheric dynamics and a highly resolved tropical tropopause layer. These model expansions, now allow detailed analyses of water vapour and its isotope ratio with respect to deuterium (deltaD(H2O)), throughout the stratosphere and in the transition region to the troposphere. In order to assure the correct representation of the water isotopologues in the model's hydrological cycle, the expanded system has been evaluated in several steps. The physical fractionation effects have been evaluated by comparison of the simulated isotopic composition of precipitation with measurements from a ground-based network (GNIP) and with the results from an isotopologue-enabled ECHAM5 general circulation model version. The model's representation of the chemical HDO precursor CH3D in the stratosphere has been confirmed by a comparison with chemical transport models (CHEM1D, CHEM2D) and measurements from radiosonde flights. Finally, the simulated HDO and deltaD(H2O) have been evaluated in the stratosphere, with respect to retrievals from three different satellite instruments (MIPAS, ACE-FTS, SMR). Discrepancies in stratospheric deltaD(H2O) between two of the three satellite retrievals can now partly be explained. The simulated seasonal cycle of tropical deltaD(H2O) in the stratosphere exhibits a weak tape recorder signal, which fades out at altitudes around 25 km. This result ranges between the pronounced tape recorder signal in the MIPAS observations and the missing upward propagation of the seasonal variations in the ACE-FTS retrieval. Revisions of different insufficencies in the respective satellite measurements, however, are expected to alter both observational datasets towards the results of the EMAC model. Extensive analyses of the water isotope ratios have revealed the driving mechanisms of the stratospheric deltaD(H2O) tape recorder signal in the EMAC simulation. A sensitivity study without the impact of methane oxidation on deltaD(H2O) demonstrates the damping effect of this chemical process on the tape recorder signal. An investigation of the origin of the enhanced deltaD(H2O) in the lower stratosphere during boreal summer, shows isotopically enriched water vapour, crossing the tropopause over the subtropical Western Pacic. A correlation analysis confirms this link, and thus the Asian Summer Monsoon could be identified to be the major contributing process for the stratospheric deltaD(H2O) tape recorder. This finding contradicts an analysis of ACE-FTS satellite data, which assigns the lower stratospheric deltaD(H2O) increase during boreal summer to the North American Monsoon. A possible explanation for this discrepancy has been found to be an underrepresentation of convective ice overshooting in the applied convection scheme.