Abstract
We use a simple yet Earth-like hemispheric atmospheric model to propose a new framework for the mathematical properties of blocking events. Using finite-time Lyapunov exponents, we show that the occurrence of blockings is associated with conditions featuring anomalously high instability. Longer-lived blockings are very rare and have typically higher instability. In the case of Atlantic blockings, predictability is especially reduced at the onset and decay of the blocking event, while a relative increase of predictability is found in the mature phase. The opposite holds for Pacific blockings, for which predictability is lowest in the mature phase. Blockings are realised when the trajectory of the system is in the neighbourhood of a specific class of unstable periodic orbits (UPOs), natural modes of variability that cover the attractor the system. UPOs corresponding to blockings have, indeed, a higher degree of instability compared to UPOs associated with zonal flow. Our results provide a rigorous justification for the classical Markov chains-based analysis of transitions between weather regimes. The analysis of UPOs elucidates that the model features a very severe violation of hyperbolicity, due to the presence of a substantial variability in the number of unstable dimensions, which explains why atmospheric states can differ a lot in term of their predictability. Additionally, such a variability explains the need for performing data assimilation in a state space that includes not only the unstable and neutral subspaces, but also some stable modes. The lack of robustness associated with the violation of hyperbolicity might be a basic cause contributing to the difficulty in representing blockings in numerical models and in predicting how their statistics will change as a result of climate change. This corresponds to fundamental issues limiting our ability to construct very accurate numerical models of the atmosphere, in term of predictability of the both the first and of the second kind in the sense of Lorenz.
Highlights
The dominant mechanism controlling the mid-latitude synoptic variability is the baroclinic instability, due to the presence of a strong equator-to-pole temperature difference
In this paper we wish to advance the mathematical understanding of blockings and reconcile some of the dynamical points of view proposed so far, in order to clarify their properties in terms of predictability, to understand to what extent blockings can be associated with specific modes of the atmospheric circulation
The statistics with respect to time duration and geographical prevalence is similar to what obtained with the T18 model
Summary
The dominant mechanism controlling the mid-latitude synoptic variability (time scales of 3–7 days) is the baroclinic instability, due to the presence of a strong equator-to-pole temperature difference. Blockings are persistent, localized departures from the quasi-zonally symmetric flow in the mid-latitudes associated with the presence of large-amplitude, almost-stationary pressure anomalies (Rossby 1951), and are a key feature of the atmospheric low-frequency variability; see Tibaldi and Molteni (2018) and references therein. They are usually observed in either the Atlantic or in the Pacific sector, and, much more rarely, in both sectors at the same time (global blockings). The phenomenology of blockings is very complex and will not be recapitulated here; see, e.g., Hoskins (1987), Pelly and Hoskins (2003a, b), Masato et al (2012), Tibaldi and Molteni (2018), Woolings et al (2018), and references therein
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