This study investigates a climate dynamics model that incorporates topographical effects and the phase transformation of water vapor. The system comprises the Navier–Stokes equations, the temperature equation, the specific humidity equation, and the water content equation, all adhering to principles of energy conservation. Applying energy estimation methods, the Helmholtz–Weyl decomposition theorem, and the Brezis–Wainger inequality, we derive high-order a priori estimates for state functions. Subsequently, based on the initial data assumptions V0H4(Ω), T0,q0,mw0H2(Ω), we can prove that a strong solution to this system exists globally in time and establish the uniqueness of the global strong solution.

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