Observation of Waves in the Climate System with Nontrivial Topology

The rotation of the earth breaks time-reversal and parity symmetries in an opposite sense north and south of the equator, leading to a topological origin for certain atmospheric and oceanic equatorial waves. Away from the equator the shallow water and stably-stratified primitive equations exhibit Poincaré-gravity waves that have nontrivial topology as evidenced by a phase singularity in frequency-wavevector space. This non-trivial topology then predicts, via the principle of bulk-boundary correspondence, the existence of two equatorial waves along the equatorial interface, the Kelvin and Yanai waves. To verify the nontrivial topology of Poincaré-gravity waves, we examine ERA5 reanalysis data and study cross-correlations between the wind velocity and geopotential height of the mid-latitude stratosphere at the 50 hPa height, and find the predicted vortex and anti-vortex in the phase of the correlations at the high frequencies of the waves. By contrast, lower frequency planetary waves are found to have trivial topology. These results demonstrate a new way to understand of waves in the stratosphere, and provides a new qualitative tool for the investigation of waves in other components of the climate system.