Connecting the Energy and Momentum Flux Response to Climate Change Using the Eliassen and Palm Relation

Energy and momentum flux by transient eddies can be used to define the storm track and eddy-driven jet stream, respectively. While comprehensive climate models project a poleward shift of the storm tracks and eddy-driven jet in response to increased CO₂, currently there does not exist a theoretical framework that connects changes in the storm track and jet.

Eliassen and Palm (EP) derived a relation connecting energy and momentum fluxes for stationary eddies that was subsequently extended to transient eddies. The EP relation, which is fundamentally connected to pseudoenergy flux, states that the eddy potential energy flux is equal to the Doppler shifted phase speed times the eddy momentum flux. When applied to climate change, the EP relation suggests any change in eddy potential energy flux is due to either a change in eddy momentum flux times the climatological Doppler shifted phase speed or a change in the Doppler shifted phase speed times the climatological momentum flux. Here we use the EP relation to examine the response of eddy potential energy and momentum flux to climate change using aquaplanet general circulation model simulations with idealized (gray radiation) and sophisticated (RRTMG) radiative transfer.

The latitude of maximum eddy potential energy flux shifts poleward in response to increased long wave optical depth in the gray radiation model and increased CO₂ concentration in the sophisticated radiative transfer model, consistent with the shift of the eddy moist static energy flux. The latitude of maximum eddy momentum flux also shifts poleward in response to increased CO₂. Interestingly, the latitude of maximum eddy momentum flux shifts equatorward in response to increased optical depth in the gray radiation model. According to the EP relation, the eddy momentum flux response is dominated by the change in eddy potential energy flux divided by the climatological Doppler shifted phase speed. The paradox regarding opposite eddy momentum flux shifts is ultimately traced to different climatological Doppler shifted phase speeds. The climatological jet in the gray radiation model involves a strong stratospheric jet alongside a weaker tropospheric midlatitude jet whereas there is a merged tropospheric jet with sophisticated radiative transfer. Overall the results suggest that the eddy momentum flux response can be constrained given the energetic response to climate change and the climatological mean flow.