The importance of surface pressure changes in the response of the atmosphere to zonally‐symmetric thermal and mechanical forcing

Abstract The classical problem of the response of a balanced, axisymmetric vortex to thermal and mechanical forcing is re‐examined, paying special attention to the lower boundary condition. The correct condition is DΦ/Dt = 0, where Φ is the geopotential and D/Dt the material derivative, which explicitly accounts for a mass redistribution as part of the mean‐flow response. This redistribution is neglected when using the boundary condition Dp/Dt = 0, which has conventionally been applied in this problem. It is shown that applying the incorrect boundary condition, and thereby ignoring the surface pressure change, leads to a zonal wind acceleration δū/δt that is too strong, especially near the surface. The effect is significant for planetary‐scale forcing even when applied at tropopause level. A comparison is made between the mean‐flow evolution in a baroclinic life‐cycle, as simulated in a fully nonlinear, primitive‐equation model, and that predicted by using the simulated eddy fluxes in the zonally‐symmetric response problem. Use of the correct lower boundary condition is shown to lead to improved agreement.