Assessing Bjerknes Compensation for Climate Variability and Its Time-Scale Dependence

Abstract

Abstract The Bjerknes compensation (BJC) refers to the tendency for changes in the atmosphere heat transport (AHT) and ocean heat transport (OHT) to compensate each other. However, the nature of this compensation varies with the time scale of changes. In this study, a new approach was developed to diagnose BJC for climate variability by considering the correlation between AHT and OHT and their relative magnitudes. The correlation is equivalent to the cosine of phase difference between AHT and OHT. For high-frequency climate variability, AHT lags or leads OHT by π/2, the correlation is zero, and BJC does not occur concurrently. For low-frequency climate variability, AHT lags or leads OHT by π, the correlation is −1, and BJC is concurrent. With increasing time scale, the phase difference between AHT and OHT changes from π/2 to π, and the BJC reaches equilibrium. A coupled box model is used to justify the approach and to understand the temporal change of BJC from a theoretical perspective. The correlation and BJC rate derived from theory and from the box model exhibit similar transient behaviors, approaching equilibrium monotonically with increasing time scale. The equilibrium BJC is established at decadal time scale. Since the BJC is closely related to climate feedback, a proper identification of BJC processes in climate variability can reveal the nature of dominant climate feedback processes at different time scales.