The Madden-Julian oscillation and nonlinear moisture modes

Abstract

The Madden-Julian oscillation (MJO), the dominant tropical intraseasonal variability with widespread meteorological impacts, continues to puzzle the climate research community on both theoretical and modeling fronts. Motivated by a recent interest in the role of humidity in tropical dynamics, this thesis hypothesizes that the MJO is a nonlinear moisture mode whose existence depends on moisture-convection feedback (the feedback between deep convection and environmental free-tropospheric humidity), and that weak moisture convection feedback in general circulation models accounts for their deficiencies with the MJO simulations. Moisture modes are found to exist in a large class of linear primitive equation models on the equatorial beta-plane. For models with standard quasi-equilibrium parameterizations,perturbation expansion analyses demonstrate that the weak temperature gradient (WTG) approximation of Sobel et al. describes the small-scale limit of the moisture mode accurately,with the small expansion parameter being the ratio between temperature tendency and adiabatic cooling. Under the WTG balance, the only leading order variables are humidity and vertical motion. Analyses of three models in the literature show that a moisture mode is unstable if moist static energy (MSE) sources such as cloud radiative forcing or gust-enhanced surface heat flux exceed the MSE export. Numerical calculations of a single-column model under the WTG configuration show that a realistic convective scheme can reproduce moisture mode instability. Sensitivity tests on the strength of moisture-convection feedback in the Emanuel scheme indicate that such a feedback is essential for moisture mode instability, confirming the prediction from simple models. To explore the nonlinear regime of a moisture mode, numerical calculations of a simplified Quasi-equilibrium Tropical Circulation Model on the equatorial beta-plane have been performed.

A classical Gill model augmented with a prognostic humidity variable can capture nonlinear dynamics of the moisture mode. In particular, nonlinear advection of dry air by Rossby gyres is found to move the moisture mode eastward. Notwithstanding progress made in the present thesis, numerous difficulties abound. The most significant issue is that moisture mode instability favors the smallest scale in the linear regime. The author suggests that scale interaction and its effect on the humidity budget might be an important research topic.