EVAPORATION WIND FEEDBACK AND THE ORGANIZING OF TROPICAL CONVECTION ON THE PLANETARY SCALE .1. QUASI-LINEAR INSTABILITY

Recent GCM experiments have suggested the existence of a zonal wavenum ber one convective mode in the aqua-planet atmosphere. This paper repo rts that a planetary-scale mode can be generated in a very simple redu ced gravity model that is linear except for two nonlinearities in its cumulus parameterization: conditional heating and wind speed-dependent surface evaporation. The behavior of the model solution is shown to b e independent of the perturbation amplitude so that a constant growth rate can be defined. This amplitude-independent nonlinear system is he re called the quasi-linear (QL) system. An instability is found in a m oist stable atmosphere at rest, which is stable in existing theories. A global integral theorem confirms the existence of the QL instability . The instability has an equatorially trapped, zonal wavenumber one st ructure, growing exponentially and propagating eastward at a speed clo se to that of the neutral, linear moist Kelvin wave. A new type of eva poration-wind feedback (EWFB) is responsible for the instability, whic h does not require the existence of mean easterlies and arises from an in-phase relation between temperature perturbation and condensational heating directly due to surface evaporation. By performing calculatio ns in zonally periodic spherical triangles of various zonal sizes, an increasing relation between the growth rate and the zonal size of the domain is found, which explains why the wavenumber one mode is selecte d. The instability has several observed features of the Madden-Julian oscillations, including the slow eastward propagation and wavenumber o ne structure. Its phase speed, growth rate, and spatial structure are insensitive to model resolution, suggesting its relevance to the plane tary-scale modes reported in aqua-planet GCMs.