Skip to main content
Open Access Publications from the University of California

UC Berkeley

UC Berkeley Previously Published Works bannerUC Berkeley

Beyond the Rigid Lid: Baroclinic Modes in a Structured Atmosphere


The baroclinic-mode decomposition is a fixture of the tropical-dynamics literature because of its simplicity and apparent usefulness in understanding a wide range of atmospheric phenomena. However, its derivation relies on the assumption that the tropopause is a rigid lid that artificially restricts the vertical propagation of wave energy. This causes tropospheric buoyancy anomalies of a single vertical mode to remain coherent for all time in the absence of dissipation. Here, the authors derive the Green's functions for these baroclinic modes in a two-dimensional troposphere (or, equivalently, a three-dimensional troposphere with one translational symmetry) that is overlain by a stratosphere. These Green's functions quantify the propagation and spreading of gravity waves generated by a horizontally localized heating, and they can be used to reconstruct the evolution of any tropospheric heating. For a first-baroclinic two-dimensional right-moving or left-moving gravity wave with a characteristic width of 100 km, its initial horizontal shape becomes unrecognizable after 4 h, at which point its initial amplitude has also been reduced by a factor of 1/p. After this time, the gravity wave assumes a universal shape that widens linearly in time. For gravity waves on a periodic domain the length of Earth's circumference, it takes only 10 days for the gravity waves to spread their buoyancy throughout the entire domain.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View