Stochastic Geostrophic Relaxation Dynamics from ERA5 Wind Fields

Compared to previous versions, this release introduces a unified stochastic relaxation framework validated across multiple geographic regions, along with residual-based diagnostics. This repository provides a reproducible analysis of atmospheric directional dynamics using ERA5-derived wind and pressure gradient fields. We show that the temporal evolution of the alignment between pressure gradient force (PGF) and wind can be described by a simple stochastic dynamical system: dcos(t+1) = -k(shear) * cos(t) + b(wind, PGF) + noise where:- k represents a restoring strength linked to flow deformation (shear),- b represents an external forcing term associated with wind speed and PGF magnitude. Key findings:- A consistent restoring structure is observed across all analyzed regions.- The restoring strength varies systematically with shear.- The forcing term is primarily controlled by wind speed and PGF magnitude.- Residual variability decreases with increasing forcing strength. All figures and analysis workflows are fully reproducible using the provided notebooks. ERA5 data is not redistributed due to licensing restrictions.