We benefited considerably from the discussions with Alan Plumb, Ari Solomon, and Walt Robinson. We are grateful to anonymous reviewers and editor Ming Cai for comments and suggestions, and to Noboru Nakamura for a careful review of our manuscript that helped tighten the relationship between the Lagrangian PV gradient and effective diffusivity changes. GC is supported by NSF Grant AGS-1064079, and JL is supported by NSF Grant AGS-1064045. GC and LS are also partially supported by a startup fund at Cornell University.
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As there is no change in the CO2 concentration, the minor stratospheric cooling has to be attributed to a dynamical cause, and it could provide additional cooling to the stratospheric radiative cooling of CO2 under climate warming (e.g., Sigmond et al. 2004).
The climatological-mean countergradient PV flux at the jet core in Fig. 11a seems to disagree with Eq. (14). This can be attributed to that Eq. (14) ignores the diabatic heating term in Eq. (24a) of Nakamura and Zhu (2010). Plate 5 of Haynes and Shuckburgh (2000) showed the effective diffusivity is very small at the jet core (i.e., a mixing barrier), where the diabatic term can be equally important.