One of the key aspects in our climate is the seasonal cycle, which is shown as the largest signal in most of climate time series. What we observe as a main characteristic in climate time-series is the combination of the seasonal cycle, short-time processes related to weather and slowly-varying signals caused by ocean circulation or global warming. Even though the myriad of processes are involved to shape the time-series, the simplest physical view is the Brownian particles moving through a slowly-varying seasonal cycle. The mathematical framework for this view could be a periodic non-autonomous stochastic dynamical system. This mathematical model consists of the deterministic part generating a reliable seasonal cycle and the stochastic forcing implying the impact of short-time scale processes. First, I will show how this model can be applied to understand the seasonal variability of Arctic sea ice. Analytic solutions constructed from a stochastic perturbation method reveal the basic physics, memory effect, controlling the seasonal variability. Due to the generality of the method, this formalism is used to construct a stochastic model to regenerate the statistics in a monthly-average surface temperature data which spans around 133 years from 1880 to present. Based on this model I will present current climate issues such as seasonal phase locking and seasonal predictability.