Calculations of the stratospheric quasi-biennial oscillation for time-varying wave forcing

One-dimensional calculations are carried out for the time evolution of the equatorial lower stratospheric mean zonal wind forced by time-varying equatorial Kelvin and mixed Rossby-gravity waves. If the time variation of the wave momentum forcing is given by a steady forcing plus a sinusoidal modulation, a tendency toward phase locking between the period of the wave forcing's modulation and the period of the resulting mean wind oscillation is found in some cases, depending on the period and magnitude of the wave forcing as well as the phase difference between variations of the easterly and westerly momentum fluxes. Regime diagrams are shown to make these dependences clearer. If the wave forcings are irregularly modulated, the resulting time variation of the wind oscillation shows no resemblance to the imposed time variation of the wave forcing. These simple calculations are used to indicate that for nonlinear phenomena, such as the quasi-biennial oscillation (QBO), one cannot conclude that a lack of correlation between two data records means that these are physically unrelated. When the equatorial wave momentum fluxes are modulated according to the eastern Pacific sea surface temperatures, the simulated time variation of the QBO period sometimes (depending on the phase relation between the easterly and westerly time-varying fluxes) shows a great resemblance to the observations. This suggests that easterly and westerly momentum fluxes into the equatorial lower stratosphere are related to SST variations.