A Theory for Seasonal Predictability Barrier：Threshold, Timing and Intensity

A theory is developed in a stochastic climate model for understanding the general features of seasonal predictability barrier (PB), which is characterized by a band of maximum decline in autocorrelation function phase-locked to a particular season. Our theory determines the forcing threshold, timing and intensity of the seasonal PB as a function of the damping rate and seasonal forcing. A seasonal PB is found to be an intrinsic feature of a stochastic climate system forced by either seasonal growth rate or seasonal noise forcing. A PB is generated when the seasonal forcing, relative to the damping rate, exceeds a modest threshold. Once generated, all the PBs occur on the same calendar month, forming a seasonal PB. The PB season is determined by the decline of the seasonal forcing as well as the delayed response associated with damping. As such, for a realistically weak damping, the PB season is locked close to the minimum SST variance under the seasonal growth rate forcing, but after the minimum SST variance under the seasonal noise forcing. The intensity of the PB is determined mainly by the amplitude of the seasonal forcing. The theory is able to explain the general features of the seasonal PB of the observed SST variability over the world. In the tropics, a seasonal PB is generated mainly by a strong seasonal growth rate, while in the extratropics, a seasonal PB is generated mainly by a strong seasonal noise forcing. Our theory provides a general framework for the understanding of the seasonal PB of climate variability.