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Interaction between the large-scale circulation and the convective pattern is investigated in a coupled system governed by the linearized primitive equations. Convection is represented in terms of two components of heating:A “climatological component” is prescribed stochastically to represent convection that is maintained by fixed distributions of land and sea and SST. An “induced comonent” is defined in terms of the column-integrated moisture flux convergence to represent convection that is produced through feedback with the circulation. Each component describes the envelope organizing mesoscale convective activity. As SST on the equator is increased, induced heating amplifies in the gravest zonal wavenumbers at eastward frequencies, where positive feedback offsets dissipation. Under barotropic stratification, a critical SST of 29.5°C results in positive feedback exactly cancelling dissipation in wavenumber 1 for an eastward phase speed of 6 m s−1. The neutral disturbance is dominated by Kelvin structure along the equator and Rossby gyres in the subtropics of each hemisphere. Heating induced by the neutral disturbance is magnified in a neighborhood of the equator, where nearly geostrophic balance in the boundary layer gives way to frictional balance. Moisture convergence induced by the Kelvin and Rossby structures fuels heating that is positively correlated with the temperature anomaly. Induced heating then generates eddy available potential energy, which offsets dissipation in the neutral disturbance. This sympathetic interaction between the circulation and the induced heating is the basis for “frictional waveCISK,” which is distinguished from classical wave-CISK by rendering the gravest zonal dimensions most unstable. Under baroclinic stratification, the coupled system exhibits similar behavior. The critical SST is only 26.5°C for conditions representative of equinox, but in excess of 30°C for conditions representative of solstice. However, the neutral disturbance is then no longer confined to the tropical troposphere. Forced by the induced heating, wave activity radiates poleward into extratropical westerlies and vertically into the stratosphere. Having the form of an unsteady Walker circulation, the disturbance produced by frictional wave-CISK compares favorably with the observed life cycle of the Madden–Julian oscillation (MJO). SST above the critical value produces an amplifying disturbance in which enhanced convection coincides with upper-tropospheric westerlies and is positively correlated with temperature and surface convergence. Conversely, SST below the critical value produces a decaying disturbance in which enhanced convection coincides with upper-tropospheric easterlies and is nearly in quadrature with temperature and surface convergence. The observed convective anomaly, which propagates across the Eastern Hemisphere at some 5 m s−1, undergoes a similar shift between amplifying and decaying stages of the MJO. During the same transition, enhanced convection remains phase-locked to inviscid convergence above the boundary layer, as does induced heating in the calculations. Frictional wave-CISK also predicts seasonality in accord with that observed. The coupled system is most unstable under equinoctial conditions, for which climatological convection and maximum SST neighbor the equator. While sharing essential features with the MJO in the Eastern Hemisphere, frictional wave-CISK does not explain observed behavior in the Western Hemisphere, where the convective signal is largely absent. Comprised of Kelvin structure with the same frequency, observed behavior in the Western Hemisphere can be understood as a propagating response that is excited in and radiates away from the fluctuation of convection in the Eastern Hemisphere.
Salby et al. (Mon,) studied this question.