This paper develops a theoretical framework for understanding Arctic amplification through the lens of nonlinear potential vorticity (PV) dynamics, static stability feedbacks, and stratosphere-troposphere coupling. Using scaling arguments, Green’s function solutions, and a modified Eady model, we show how surface-warming-induced static stability perturbations modulate PV inversion efficiency and extend remote influences. We identify a critical threshold in the diabatic number \({\mathcal{D}}\) that marks the transition from a dry-nonlinear to a moist-nonlinear regime where diabatic PV generation outweighs baroclinic advection. A regime diagram constructed from the nonlinearity ratio \({\mathcal{R}}=| {\sigma }^{{\prime} }/\overline{\sigma }|\) (where σ is static stability) and \({\mathcal{D}}\) reveals four quadrants; the Arctic already resides in a nonlinear background (\({\mathcal{R}} > 0.3\) for most CMIP6 models) and under continued warming, it migrates vertically into the moist-nonlinear state via increasing \({\mathcal{D}}\). Under SSP2-4.5, the ensemble-mean \({\mathcal{D}}\) crosses the 0.03 threshold by mid-century (\({\mathcal{D}}=0.031\)); under SSP5-8.5, \({\mathcal{D}}\) reaches 0.039 by end-century, with 88% of models exceeding the threshold. Reduced stability amplifies baroclinic growth rates and shifts most unstable modes toward high-latitude blocking wavelengths. Extending the framework to the stratosphere, we show that the refractive index for vertically propagating Rossby waves decreases with weakened zonal winds, a robust signal across models, enabling deeper wave penetration. Observational support from ERA5 reanalysis reveals a vertical contrast in PV anomalies - strong positive anomalies in the lower troposphere and a wave-like pattern aloft, consistent with the transition to diabatically driven dynamics. A positive feedback loop linking surface warming, reduced stability, enhanced inversion efficiency, amplified streamfunction anomalies, increased poleward heat transport, and strengthened vertical wave coupling suggests a loop gain that would be arrested by nonlinear saturation. These results establish polar amplification as arising from coupled interactions of static stability, PV dynamics, diabatic heating, and stratosphere-troposphere coupling, with direct implications for predicting midlatitude extreme weather events.
