General seasonal phase-locking of variance and persistence: application to tropical pacific, north pacific and global ocean

A stochastic climate model is used to explain the major features of seasonal phase-locking of climate variability in general. The model is the classical damped persistence model, generalized with seasonal cycles in the growth rate and noise forcing. Our theory predicts distinct phase-locking features for different seasonal forcing. With seasonal growth rate, the forced variance lags the growth rate within a season, with the initial persistence in phase with the variance. With seasonal noise forcing, the variance also lags the noise forcing within a season, but the initial persistence lags the variance by a season. The theory is further applied successfully to the phase-locking of SST variability over the tropical Pacific, North Pacific and the world ocean. Overall, the variance and persistence is forced predominantly by the seasonal growth rate in the tropics with the variance and persistence in phase, but they are forced by the seasonal noise forcing in the mid-latitude with the variance and persistence in quadrature or even out phase. Our theory provides a general framework and a null hypothesis for the understanding of phase locking of climate variability in general.