Leaky Convectively Coupled Kelvin Waves

Abstract:

The rigid-lid approximation, which asserts an unmoving lid at the upper boundary of the troposphere, is often used to simplify the mathematical analysis of theoretical models of the atmosphere. In reality, the tropopause does not act as a rigid-lid on the troposphere, but rather as a leaky lid, as wave energy can radiate into the stratosphere. This study analyzes the effect of removing the rigid-lid on equatorial waves by coupling a previously developed set of linear, quasi-equilibrium tropospheric equations, with a dry, passive stratosphere. Analysis of the eastward-moving, convectively coupled Kelvin-wave (v = 0) modes finds that the inclusion of a stratosphere strongly damps the growth of the higher-order modes, greatly reddening the energy spectrum of the Kelvin-waves. The barotropic mode, which cannot be excited in linear models without surface friction, survives the quasi-equilibrium assumption and is present in this model. The superposition of the barotropic and phase-shifted first baroclinic modes leads to a vertical tilt in the dynamical fields. The vertical tilt is shown to be strongest for faster waves destabilized by the surface enthalpy flux feedback, and weaker for slower waves destabilized by cloud-radiation interaction. Results from near-global aqua-planet simulations that explicitly simulate Kelvin waves are also shown. The vertical structure of the numerically simulated equatorial Kelvin waves also exhibit a vertical tilt, and the structures are compared to those of the theoretical model.