Steady Linear Response to Tropical Heating in Barotropic and Baroclinic Models

The atmospheric response to tropical heating is examined using both the linear, multilevel baroclinic model with an imposed tropical heat source, and the one-level barotropic model with a tropical divergence forcing. The divergent component of the response in the baroclinic model is characterized by a tropical divergence confined to the heated region, plus convergence and divergence centers away from the tropical heated region at the outflow level. The rotational component of the response is depicted by a local baroclinic response in the Tropics and a remote equivalent barotropic wave train in the extratropics. The barotropic model responses to a fixed tropical divergence are highly sensitive to the strength of the zonal mena zonal flow at different vertical levels in the upper troposphere. The sensitivity is induced by the dependence of the propagation speed of the stationary Rossby wave rays on the strength of the zonal mean zonal flow. The barotropic response to a tropical divergence when linearized about the zonal mean state at the outflow level differs significantly from the equivalent barotropic wave train in the baroclinic model. However, when the barotropic model is linearized about the zonal mean flow at the equivalent barotropic level, around 350 mb in winter and 500 mb in summer, its response to tropical divergence forcing is very similar to the baroclinic model result. The similarity confirms that the nature of the remote atmospheric response is indeed equivalent barotropic, but it is important to apply the barotropic model at the appropriate upper-tropospheric level. The barotropic Rossby wave energy dispersion can be applied to the baroclinic atmosphere when the equivalent barotropic level is chosen.