Physics of the Eddy Memory Kernel of a Baroclinic Midlatitude Atmosphere

In recent theory trying to explain the origin of baroclinic low-frequency atmospheric variability, the concept of eddy memory has been proposed. In this theory, the effect of synoptic scale heat fluxes on the planetary-scale mean flow depends on the history of the mean meridional temperature gradient. Mathematically, this involves the convolution of a memory kernel with the mean meridional temperature gradient over past times. However, the precise shape of the memory kernel and its connection to baroclinic wave dynamics remains to be explained. In this study we use linear and proxy response theory to determine the shape of the memory kernel of a truncated two-layer quasi-geostrophic atmospheric model. We find a memory kernel that relates the eddy heat flux to the zonal mean meridional temperature gradient on timescales greater than 2 days. Although the shape of the memory kernel is complex, we show that it may be well approximated as an exponential, particularly when reproducing baroclinic low-frequency intraseasonal modes of variability. By computing the terms in the Lorenz energy cycle, we find that the shape of the memory kernel can be linked to the finite time that growing baroclinic instabilities require to adapt their growth properties to the local zonal mean atmospheric flow stability. Regarding the explanation for observed baroclinic annular modes in the Southern Hemisphere, our results suggest that it is physical for these modes to be derived directly from the thermodynamic equation by considering an exponentially decaying memory kernel, provided accurate estimates of the necessary parameters are incorporated.