The concept of time-dependent vertical coordinates is used to upgrade conventional terrain-following 
sigma-coordinates to arbitrary hybrid coordinates. The method presented here has been implemented into
the WRF-ARW model and combines unrestricted applicability to nonhydrostatic dynamics with retaining the 
mass conservation property of the WRF-ARW dynamical core. The coordinate is based on a three-dimensional field
carrying the vertical position of the coordinate surfaces, which is made time-dependent by introducing a prognostic
equation. As a specific example, the adaptive coordinate is used to emulate a hybrid-isentropic system.
Idealized tests in which the coordinate surfaces are artificially moved reveal that the ensuing spurious
motions are small enough to be negligible in realistic applications. Mountain-wave tests demonstrate that
the hybrid coordinate remains numerically stable under strong forcing. However, the model layer distribution 
established with the hybrid-isentropic coordinate is not 
optimal for representing the dynamics of breaking gravity waves because the vertical distance between the model 
levels tends to be too large in the wave-breaking region. On the other hand, real-case studies 
demonstrate that the hybrid coordinate significantly improves the representation of the 
tropopause because of enhanced vertical resolution in the tropopause region.