Evaporation-Wind Feedback and the Organizing of Tropical Convection on the Planetary Scale. Part I: Quasi-Linear Instability

Abstract

Recent GCM experiments have suggested the existence of a zonal wavenumber one convective mode in the aqua-planet atmosphere. This paper reports that a planetary-scale mode can be generated in a very simple reduced 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 be independent of the perturbation amplitude so that a constant growth rate can be defined. This amplitude-independent nonlinear system is here called the quasi-linear (QL) system. An instability is found in a moist 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 structure, growing exponentially and propagating eastward at a speed close to that of the neutral, linear moist Kelvin wave. A new type of evaporation-wind feedback (EWFB) is responsible for the instability, which 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 calculations 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 selected. The instability has several observed features of the Madden-Julian oscillations, including the slow eastward propagation and wavenumber one structure. Its phase speed, growth rate, and spatial structure are insensitive to model resolution, suggesting its relevance to the planetary-scale modes reported in aqua-planet GCMs.