A New Mathematical Framework for Atmospheric Blocking Events

Abstract

<p>We use a simple yet Earth-like atmospheric model to propose a new framework for understanding the mathematics of blocking events, which are associated with low frequency, large scale waves in the atmosphere. Analysing error growth rates along a very long model trajectory, we show that blockings are associated with conditions of anomalously high instability of the atmosphere. Additionally, the lifetime of a blocking is positively correlated with the intensity of such an anomaly, against intuition. In the case of Atlantic blockings, predictability is especially reduced at the onset and decay of the blocking, while a relative increase of predictability is found in the mature phase, while the opposite holds for Pacific blockings, for which predictability is lowest in the mature phase. We associate blockings to a specific class of unstable periodic orbits (UPOs), natural modes of variability that cover the attractor of the system. The UPOs differ substantially in terms of instability, which explains the diversity of the atmosphere in terms predictability. The UPOs associated to blockings are indeed anomalously unstable, which leads to them being rarely visited. The onset of a blocking takes place when the trajectory of the system hops into the neighbourhood of one of these special UPOs. The decay takes place when the trajectory hops back to the neighbourhood of usual, less unstable UPOs associated with zonal flow. This justifies the classical Markov chains-based analysis of transitions between weather regimes. The existence of UPOs differing in the dimensionality of their unstable manifold indicates a very strong violation of hyperbolicity in the model, which leads to a lack of structural stability. We propose that this is could be a generic feature of atmospheric models and might be a fundamental cause behind difficulties in representing blockings for the current climate and uncertainties in predicting how their statistics will change as a result of climate change.<br><br>References:<br>V. Lucarini, A. Gritsun, A. A new mathematical framework for atmospheric blocking events. Climate Dynamics 54, 575–598 (2020). https://doi.org/10.1007/s00382-019-05018-2<br>M. Ghil, V. Lucarini, The Physics of Climate Variability and Climate, Rev. Modern Physics, 92, 035002 (2020). https://link.aps.org/doi/10.1103/RevModPhys.92.035002  <br>S. Schubert, V. Lucarini, Dynamical analysis of blocking events: spatial and temporal fluctuations of covariant Lyapunov vectors. Q. J. R. Meteorol. Soc. 142, 2143-2158 (2016). https://doi.org/10.1002/qj.2808</p>

A Topological Perspective on Weather Regimes

“…Hence it seems, to these authors, not to be possible to find a definition of regimes, using density or temporal persistence alone, that unifies all the systems we considered. While an alternative definition of regimes based on fixed points, UPOs or other 'exact solution' techniques might seem plausible, computing such solutions is extremely computationally demanding, and state-of-the-art techniques are only able to handle systems of significantly lower dimensionality than existing climate models [25]. More crucially, these techniques are inherently model features, in that they rely on being able to integrate the model dynamics.…”

“…While a more technical definition based on exact solutions (e.g., fixed-points and periodic orbits) of the flow can work and even be computationally tractable for relatively low-dimensional systems [23,24], they suffer from the 'curse of dimensionality', and are generally limited to simple systems. In a state-ofthe-art application of these concepts to atmospheric modelling, [25] identified unstable periodic orbits (UPOs) corresponding to zonal and blocking events in a low resolution quasi-geostrophic model. However, the dimensionality of this model still sits well below that of weather and climate models, let alone the physical system itself.…”

Chameleon attractors in a turbulent flow

“…So far, the search for an attractor underlying turbulent flows in general, and geophysical turbulence in particular has however proved only partially successful. Since the 1990s several studies have suggested that the observed dynamical processes can be associated with the existence of non-hyperbolic strange and possibly stochastic attractors having a dimensionality much lower than the number of degrees of freedom of the system [23,24]. Non-hyperbolicity manifests itself with the fact that the attractor is heterogeneous in terms of its local properties of persistence and predictability [24,25].…”

“…Since the 1990s several studies have suggested that the observed dynamical processes can be associated with the existence of non-hyperbolic strange and possibly stochastic attractors having a dimensionality much lower than the number of degrees of freedom of the system [23,24]. Non-hyperbolicity manifests itself with the fact that the attractor is heterogeneous in terms of its local properties of persistence and predictability [24,25]. When considering numerical models, this has important implications also in terms of error dynamics and efficiency of data assimilation [26].…”

A topological perspective on weather regimes

“…While a more technical definition based on exact solutions (e.g., fixed-points and periodic orbits) of the flow can work and even be computationally tractable for relatively low-dimensional systems [16,21], they suffer from the 'curse of dimensionality', and are generally limited to simple systems. In a stateof-the-art application of these concepts to atmospheric modelling, [32] identified unstable periodic orbits (UPOs) corresponding to zonal and blocking events in a low resolution quasi-geostrophic model. However, the dimensionality of this model still sits well below that of weather and climate models, let alone the physical system itself.…”