Stochastic modelling of stratospheric temperature

A stochastic model for daily-spatial mean stratospheric temperature over a given area is suggested. The model is a sum of a deterministic seasonality function and a Lévy driven vectorial Ornstein-Uhlenbeck process, which is a mean-reverting stochastic process. More specifically, the model is an order 4 continuous-time autoregressive (CAR(4)) process, derived from data analysis suggesting an order 4 autoregressive (AR(4)) process to model the deseasonalized stochastic temperature data empirically. In this analysis, temperature data as represented in ECMWF re-analysis model products are considered. The residuals of the AR(4) process turn out to be normal inverse Gaussian distributed random variables scaled with a time dependent volatility function. In general, it is possible to show that the discrete time AR(p) process is closely related to CAR(p) processes, its continuous counterpart. An equivalent effort is made in deriving a dual stochastic model for stratospheric temperature, in the sense that the year is divided into summer and winter seasons. However, this seems to further complicate the modelling, rather than obtaining a simplified analytic framework. A stochastic characterization of the stratospheric temperature representation in model products, such as the model proposed in this paper, can be used in geophysical analyses to improve our understanding of stratospheric dynamics. In particular, such characterizations of stratospheric temperature may be a step towards greater insight in modelling and prediction of large-scale middle atmospheric events like sudden stratospheric warmings. Through stratosphere-troposphere coupling, this is important in the work towards an extended predictability of long-term tropospheric weather forecasting.