The work reported here was supported by the Swedish Research Council and is a contribution from the Bert Bolin Centre for Climate Research at Stockholm University. We thank Rodrigo Caballero and Peter Langen for discussions and two anonymous reviewers for constructive comments.
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To some degree this also applies for mass transport streamfunctions based on potential temperature: Held and Schneider (1999) show that near-ground equatorward flow in midlatitudes occurs at potential temperatures lower than the surface zonal-mean value.