Beyond Rigid Lids: Baroclinic Modes in a Structured Atmosphere

The baroclinic mode decomposition, a fixture of the tropical dynamics literature, is derived by assuming that the tropopause is a rigid lid. In this framework, a buoyancy anomaly in the troposphere composed of a single baroclinic mode will remain coherent for all time in the absence of dissipation. This behavior is often ameliorated in simple models by employing strong linear damping, but we argue that a more physical solution is to allow wave energy to propagate out of the troposphere by relaxing the rigid lid assumption. To demonstrate this point, we derive a Green’s function for a simple representation of the tropical atmosphere that allows for vertical propagation of wave energy out of the troposphere: a 2-dimensional, non-rotating, Boussinesq fluid comprised of two layers of constant but differing stratification. For earth-like parameter choices, the horizontal spreading of buoyancy due to upward propagation of wave energy happens very quickly. A first-baroclinic pulse of buoyancy the size of the tropical warm pool (about 8000 km across) will spread throughout the tropics in less than 8.5 days, after having made only one trip around the equator. For a mesoscale (about 100 km across) buoyancy pulse, this happens even faster: it spreads throughout the tropics in less than 2.5 hours, after having traveled only 500 km.