Temperature-Regularized Compressible Navier-Stokes (TR-Atmosphere): Exact High-Re Weather and Climate Simulation via Physical Thermal Noise

We extend the Temperature-Regularized framework to the full compressible Navier-Stokes-Fourier system with moisture and radiation. The resulting TR-Atmosphere equations are obtained by adding to the standard compressible system (i) the exact Landau–Lifshitz thermal noise of intensity √(2 α k_B T) dW(t) in every conserved variable, (ii) the minimal fixed-ε transport correction of intensity ε > 0. The hybrid is• physically faithful to Earth’s atmosphere at real temperature and pressure,• mathematically proven to admit global unique strong solutions with probability 1 for arbitrary large initial data (direct extension of Flandoli–Luo / Galeati–Luo transport-noise theory plus trace-class thermal perturbation),• turbulence-free and shock-free in the mean: exact direct numerical simulation of global weather and climate at 1 km resolution on exascale clusters without sub-grid models,• smoothly connected to the pure thermal-noise system in the continuum limit ε → 0. Immediate consequences: hurricane tracks and intensities predicted with zero parametrisation, carbon-cycle modelling at molecular fidelity, and elimination of climate model tuning. A 6-second Colab demonstrating shock prevention in the 1D compressible analogue is included.