Figure 1: We apply our time-series method to 133 years of monthly averaged GISS surface air temperature data from 1881 to 2013^27,28.

We analyze the global (black), Northern hemisphere (red) and Southern hemisphere (blue) averaged data and determine the (a) monthly stability a(t), (b) noise intensity N(t), and (c) long-term forcing f(τ) from the model . The model (red) is compared with the original time-series (blue) in (d) and via spectral power in (e). The spectral power of the stochastic model (red) and the data (blue) is calculated with Welch’s power spectral density estimate using 10-yr window size. Finally, in (f) we compare the seasonal standard deviation of the stochastic model (red) and the original data (blue). The overall comparison is good. The model assumptions that the surface energy flux balance can be considered as originating from weather, seasonal and decadal processes is well born out by the analysis. The high-frequency weather contribution is represented as the noise forcing N(t)ξ(t), wherein the intensity N(t) is related to the seasonal cycle of baroclinicity, being larger (smaller) winter (summer). The seasonality of the monthly stability a(t) is associated with that of the seasonality of the insolation. The September Northern hemisphere maximum of a(t) is commensurate with the minimum Arctic sea ice extent. Finally, the long-term forcing f(τ) is responsible for decadal variability, but as we see below, this contribution is not essential for understanding seasonal variability and predictability barriers and phase locking.