Studying barotropic instability of the 30 hPa level: unstable eigenmodes

This dataset contains the results of a long-term analysis of the unstable eigenmodes of the shallow water system linearized around the 30 hPa zonal mean flow. Such data provides opportunity to study the barotropic instability of the QBO region and the relation between unstable eigenmodes and mixed Rossby-gravity waves. 

We linearize the spherical shallow water equations around the 30 hPa zonal mean zonal wind for 5-day timesteps within the period of 1990-1999, which is followed by the computation of the eigenmodes of the linearized equations  by using the BGHough software, whose description can be found in https://doi.org/10.1175/JAS-D-24-0033.1 (Appendix A therein). The procedure of BGHough is based on the algorithm proposed by https://doi.org/10.1175/1520-0469(1980)037<0917:EOZFOT>2.0.CO;2. We apply 10 km as equivalent depth corresponding to the barotropic vertical mode. The 30 hPa zonal wind field, used for the computations is taken from ERA5 reanalysis (https://doi.org/10.1002/qj.3803).

We compute the background eigenmodes for the zonal wavenumers k=1-12. Among these eigenmodes we take into account only the two most unstable ones, i.e. the modes with the largest imaginary part of the complex eigenfrequency.