A deep-atmosphere extension in a nonhydrostatic dynamical core: formulation and idealized tests

We have developed a deep-atmosphere extension within the GMCORE (Grid-Model dynamical CORE) using a dry terrain-following mass-based coordinate. The new dycore retains the full three-dimensional Coriolis force, accounts for the height dependence of gravity, and introduces radial metric corrections into the discrete operators, while preserving the main structure of the original solver. Numerical consistency is examined through convergence and balanced-state stability tests. Two idealized test cases are used for evaluation: a baroclinic wave test and a tropical cyclone test. In the standard Earth-radius baroclinic wave experiment, the deep- and shallow-atmosphere solutions are similar, whereas in the reduced-radius X20 experiment the GMCORE deep-atmosphere dycore reproduces the clear separation reported in earlier studies. In the tropical-cyclone experiment, the deep-atmosphere formulation has little effect on storm intensity and warm-core structure, but leads to a systematic south-westward trajectory shift relative to the shallow-atmosphere simulation. The trajectory difference is linked to an organised inner asymmetry. This includes a dipole-like pattern connected to 2Ωcosφ∂w∂y and a low-level easterly anomaly. These results support the numerical consistency of the GMCORE deep-atmosphere implementation and suggest that nontraditional Coriolis effects can influence low-latitude vortex motion, although a complete dynamical attribution requires further diagnosis.