Switching dynamics in atmospheric flow

The jet stream is a band of air that flows around the Earth at high-altitude, moving West to East in mid-latitude regions. This so-called “zonal” flow typically has cyclones and anticyclones embedded within it, which last for a few days. But a few times per year, particularly in winter, these structures slow-down or stop to travel eastward, persisting for long periods over the same region. Atmospheric scientists refer to these episodes as “blocking events,” as they’re associated with a disruption or blocking of the mid-latitude jet stream; the jet may be forced to move towards higher latitudes, or may split into two branches. Blocking episodes often have extreme consequences for the climate, such as the December 2010 cold spell in northern and central Europe, or the summer 2003 prolonged heatwave over western Europe.
But the atmospheric mechanism behind blocking events remains unknown. Some researchers have proposed that mid-latitude atmospheric dynamics may naturally alternate between two distinct equilibria, one associated with normal westerly flow of the jet stream, and another with blocked flow. Some laboratory experiments lend support this idea. However, a host of other mechanisms have also been considered. For example, some theoretical work suggests that blocking events could arise through the resonant amplification of Rossby waves, the common wave-like distortions of the jet stream’s path as it circles the Earth. Alternatively, others have suggested that blocking events may arise through instabilities driven by non-linear interactions between a variety of other distinct atmospheric flows or waves.
In a recent paper, a team of researchers including LML Fellows Davide Faranda, Nicholas Moloney and Yuzuru Sato attempt to identify the mechanism at work by using an approach inspired by dynamical systems theory. During blocked flow, they note, atmospheric variables are highly predictable. Weather conditions persist for several days, whereas in the normal flow they mostly have a chaotic alternation between cyclonic and anticyclonic phases. Qualitatively, such behaviour looks very much like that of a number of archetypal dynamical systems including the Henon map or the Lorenz equations, orbits of which generally exhibit chaotic dynamics, but sometimes become trapped near an unstable fixed point. When this happens, an orbit stays in the vicinity of the fixed point for a time that depends on the distance from the fixed point and the system experiences a temporary suppression of chaos. Faranda and colleagues explore the possibility that a similar dynamic could underlie blocked flow, and and test the idea by analysing data on mid-latitude atmospheric flows over several decades.
To run this test, they exploit ideas from extreme value theory – the branch of statistics looking at the extreme events of stochastic processes. In particular, they argue that the existence of unstable fixed points in the mid-latitude atmospheric circulation should be evident in the statistics of recurrent events, in which the system’s trajectory returns close to an earlier state. A trajectory of a dynamical system will repeatedly pass close to any point  on the attractor of that system. But recurrences for unstable fixed points should be strongly distinguished from recurrences for typical points of the attractor. In particular, recurrences for unstable fixed points should be strongly clustered in time, with many coming one after the other. Earlier studies using this technique found that the statistics of recurrences in temperature records obey one of the three classical patterns of extreme values, demonstrating that the atmosphere behaves as a chaotic system.
Here, in the context of blocking events, the authors look for possible unstable fixed points by studying blocking indices – low dimensional measures of the atmospheric flow, such as the pressure difference between two different locations at the same longitude. When the flow is zonal (typical, non-blocked flow), this difference always has the same sign because anticyclones are generally located at lower latitudes. Conversely, when the flow is blocked, low pressure systems tend to move to low latitudes and anticyclones to high latitudes, reversing the meridional gradient in pressure. A blocking event is identified as the persistence of such conditions for several days. As the study shows, the data do reveal significant evidence that the switching between atmospheric and blocked circulation can be associated with the existence of an unstable (saddle) fixed point of the atmospheric dynamics.
The novelty of this approach lies in the use of observations, rather than more complex atmospheric flow models. Significantly, the analysis appears to point to one of the mechanisms invoking non-linear interactions, either between zonal flow and eddies or between Rossby waves, as the driving mechanism for the blocking phenomena. Moreover, the study finds a complex spatial distribution of unstable fixed points, which suggests that simple bi-stability mechanisms are likely unable to explain the transitions between blocked and zonal flow.
Davide Faranda, Giacomo Masato, Nicholas Moloney, Yuzuru Sato, François Daviaud, et al. The switching between zonal and blocked mid-latitude atmospheric circulation: a dynamical system perspective. Climate Dynamics, Springer Verlag, 2015, 2015 (6), pp.2921. <10.1007/s00382-015-2921-6>.

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