A Simple Model of the 40-50 Day Oscillation

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Abstract
The effects of a positive-only cumulus heating parameterization on equatorially trapped waves are investigated using both nonlinear and linear single vertical mode models. In the linear model the cumulus heating is shown to slow down the equatorial waves. In particular the eastward moving Kelvin wave is readily slowed from the free phase speed (45 m s−1) to the intrinsic speed associated with the observed 40–50 day oscillation (−1). Slow eastward propagating Kelvin waves only occur for stable cumulus heating (stable meaning that adiabatic cooling is able to compensate for the cumulus heating). However these linear moist waves decay rapidly and are thus an unlikely explanation of the observed oscillation. The observed meridional wind perturbation is also unexplained by this mechanism. For unstable cumulus heating, growing linear CISK waves develop but remain stationary. Thus no satisfactory explanation of the 40–50 day oscillation is possible with this single vertical mode linear model. For unstable cumulus heating in the nonlinear model, the growing CISK modes rapidly stabilize the atmosphere. The stability increases greatest to the west of the CISK heating which thus leads to eastward propagation. Upon equilibration, the CISK mode propagates eastward ≲10 m s−1 for a wide range of parameters. The mode has a substantial meridional velocity perturbation and appears to be a horizontally coupled Rossby-Kelvin wave. These propagating modes are quite similar to the observed 40–50 day oscillation. Various experiments are conducted to elucidate the mode of propagation. Experiments relevant to the observed atmosphere (i.e., moisture parameters that are a function of space and time) are also discussed.

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