Large-scale modes in a rotating atmosphere with radiative-convective instability and WISHE

A highly simplified parameterization of diabatic processes is applied to linearized equations on a equatorial beta plane. The diabatic processes include moist convection, cloud-radiation interactions ( CRI), and wind-induced surface heat exchange ( WISHE). The precipitation rate is assumed to increase linearly as the vertically averaged saturation deficit decreases. The modeled modes are Matsuno's normal modes, that is, Kelvin waves, mixed Rossby- gravity waves, Rossby waves, and inertio-gravity waves, and an additional mode called here a slow moisture mode. All of the Matsuno modes are damped and remain stable even when CRI and WISHE are turned on. Their phase speeds do not vary much from Matsuno's adiabatic values except for very long wavelength Kelvin and Rossby modes, for which the phase speeds are reduced compared to the adiabatic values. The slow moisture modes are stationary and unstable under CRI, while WISHE causes them to propagate. Under CRI and WISHE together the slow moisture modes are unstable and eastward propagating for long wavelengths and slowly moving relative to the mean flow for short wavelengths. The dispersion relations of the slow moisture modes are one of nearly constant or decreasing frequency with increasing wavenumber. The most important model parameter is the tropospheric moisture relaxation time scale, which is chosen to be 1 day. The model failed to explain the observed phase speeds of convectively coupled Matsuno modes. Following Mapes, the authors suggest that other dynamics, more realistic than the one including only the first baroclinic mode, may be responsible for these modes.