Characterization of first and higher order statistics of mesoscales and sub-mesoscales in the MLT usingPhysics-informed machine learning

The mesosphere and lower thermosphere (MLT) represent a dynamically complex region governed by multiscale, nonlinear processes, including interactions between gravity waves and turbulence. Observing these dynamics at sufficient resolution is challenging due to instrumental and physical limitations at high altitudes. Common observational techniques often rely on assumptions such as horizontal homogeneity or negligible vertical motion, which are not always valid.Despite substantial advancements in upper atmospheric research, key physical quantities in the MLT remain poorly constrained. One example is the dissipation rate of kinetic energy, a critical quantity that governs the cascade of turbulent energy but is extremely difficult to estimate. It remains unknown whether dissipation rates vary with season, latitude, or local dynamical regimes. Additionally, it is unclear whether second-order statistics and spectral slopes alone can fully characterize dissipation, or whether higher-order statistics—such as third-order structure functions—are the only way to infer the presence of energy fluxes and anisotropy in the turbulence.To address these challenges, the HYPER (HYdrodynamic Point‐wise Environment Reconstructor) framework was recently developed to produce high-fidelity 4D reconstructions of wind fields (time, altitude, latitude, longitude) compliant with the Navier-Stokes equations. While effective for case studies, HYPER’s resolution (~30 km) and computational demands make it impractical for long-term statistical analyses. This project proposes extending HYPER by incorporating Reynolds-Averaged Navier-Stokes (RANS) formulations to estimate second and higher-order wind statistics. This will enable the statistical characterization of mesoscales and sub-30 km scales while reducing computational cost.In addition, the project plans to integrate MAARSY radar measurements directly into HYPER to improve coverage and resolution, and leverages collaboration with Dr. Victor Avsarkisov researcher at the University of Hamburg working on related themes.