Arctic amplification‐induced intensification of planetary wave modulational instability: A simplified theory of enhanced large‐scale waviness

In the mid–high latitude atmosphere, the instability of planetary waves characterizes enhanced planetary wave activity or amplified large‐scale waviness leading to increased regional weather extremes. In this paper, a nonlinear Schrödinger equation is derived to describe the evolution of planetary waves. Then the consequences of Arctic amplification (AA)‐induced meridional background potential vorticity (PVy) changes on the modulational instability of planetary waves are examined. It is found that the modulational instability of uniform planetary wave trains mainly results from the presence of high‐order dispersion and nonlinearity, even though such an instability depends on the amplitude, vertical structure and zonal wavenumber of uniform planetary waves and the atmospheric stratification. Because the nonlinearity and high‐order dispersion depend on the magnitude of PVy, the modulational instability of planetary waves is significantly influenced by the variation of PVy associated with AA. It is also revealed that stronger modulational instability of planetary waves tends to occur in the smaller PVy region or in higher latitudes due to both stronger nonlinearity and weaker high‐order dispersion for fixed background and planetary wave parameters, which is conducive to more intense large‐scale waviness. However, because AA can reduce PVy in the mid–high latitudes mainly in the lower troposphere via reductions of winter zonal winds and meridional temperature gradients, the reduced PVy under AA can significantly enhance the modulational instability. Thus, the role of AA is to amplify planetary wave activity in mid–high latitudes through strengthening the modulational instability of planetary waves due to reduced PVy, which further enhances large‐scale waviness.