Stable water isotopologues, mainly 1H2O, 1H2HO (HDO), and , are useful tracers for processes in the global hydrological cycle. The incorporation of water isotopes into Atmospheric General Circulation Models (AGCMs) since 1984 has helped scientists gain substantial new insights into our present and past climate. In recent years, there have been several significant advances in water isotopes modeling in AGCMs. This paper reviews and synthesizes key advances accomplished in modeling (1) surface evaporation, (2) condensation, (3) supersaturation, (4) postcondensation processes, (5) vertical distribution of water isotopes, and (6) spatial δ18O-temperature slope and utilizing (1) spectral nudging technique, (2) higher model resolutions, and (3) coupled atmosphere-ocean models. It also reviews model validation through comparisons of model outputs and ground-based and spaceborne measurements. In the end, it identifies knowledge gaps and discusses future prospects of modeling and model validation. 1. Introduction Stable water isotopologues, mainly 1H2O, 1H2HO (HDO), and 1H218O, differ by their mass and molecular symmetry. As a result, during phase transitions, they have slightly different behaviors. The heavier molecules prefer to stay in the liquid or solid phase while the lighter ones tend to evaporate more easily. This unique characteristic makes water isotopologues the ideal tracers for processes in the global hydrological cycle. In the past three decades, the incorporation of water isotopes into Atmospheric General Circulation Models (AGCMs) has helped scientists gain substantial new insights into our present and past climate. AGCMs (or more generally, GCMs) numerically represent our current understanding of the physical processes in the atmosphere on a rotating planet. They usually contain main modules for advection, diffusion, convection, radiation, cloud formation, and other physics. Much effort has been put into model development to ensure numerical simulations do reflect our physical understanding of the atmosphere. In addition to model development, model validation with real-world data is of paramount importance because it ensures that what is simulated are real physical phenomena in nature, not artifacts caused by inadequate model parameterizations. Only after AGCMs are validated with global measurements of water isotopes could they be deployed with confidence to address new scientific questions such as changes in the global precipitation patterns and large-scale atmospheric circulations. When Hoffmann et al. [1] published their review on water
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