Atmospheric Instability and Its Associated Oscillations in the Tropics

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The interaction between tropical clouds and radiation is studied in the context of the weak temperature gradient approximation, using very low order systems (e.g., a two-column two-layer model) as a zeroth-order approximation. Its criteria for the instability are derived in the systems. Owing to the connection between the instability (unstable fixed point) and the oscillation (limit cycle) in physics (phase) space, the systems suggest that the instability of tropical clouds and radiation leads to the atmospheric oscillations with distinct timescales observed. That is, the instability of the boundary layer quasi-equilibrium leads to the quasi-two-day oscillation, the instability of the radiative convective equilibrium leads to the Madden–Julian oscillation (MJO), and the instability of the radiative convective flux equilibrium leads to the El Niño–southern oscillation. In addition, a linear model as a first-order approximation is introduced to reveal the zonal asymmetry of the atmospheric response to a standing convective/radiative heating oscillation. Its asymmetric resonance conditions explain why a standing ~45-day oscillation in the systems brings about a planetary-scale eastward travelling vertical circulation like the MJO. The systems, despite of their simplicity, replicate the oscillations with the distinct timescales observed, providing a novel cloud parameterization for weather and climate models. Their instability criteria further suggests that the models can successfully predict the oscillations if they properly represent cirrus clouds and convective downdrafts in the tropics.