Dynamical analysis of blocking events: spatial and temporal fluctuations of covariant Lyapunov vectors

Abstract

One of the most relevant weather regimes in the mid-latitudes atmosphere is the persistent deviation from the approximately zonally symmetric jet stream to the emergence of so-called blocking patterns. Such configurations are usually connected to exceptional local stability properties of the flow which come along with an improved local forecast skills during the phenomenon. It is instead extremely hard to predict onset and decay of blockings. Covariant Lyapunov Vectors (CLVs) offer a suitable characterization of the linear stability of a chaotic flow, since they represent the full tangent linear dynamics by a covariant basis which explores linear perturbations at all time scales. Therefore, we assess whether CLVs feature a signature of the blockings. As a first step, we examine the CLVs for a quasi-geostrophic beta-plane two-layer model in a periodic channel baroclinically driven by a meridional temperature gradient ∆T . An orographic forcing enhances the emergence of localized blocked regimes. We detect the blocking events of the channel flow with a Tibaldi-Molteni scheme adapted to the periodic channel. When blocking occurs, the global growth rates of the fastest growing CLVs are significantly higher. Hence, against intuition, the circulation is globally more unstable in blocked phases. Such an increase in the finite time Lyapunov exponents with respect to the long term average is attributed to stronger barotropic and baroclinic conversion in the case of high temperature gradients, while for low values of ∆T , the effect is only due to stronger barotropic instability. In order to determine the localization of the CLVs we compare the meridionally averaged variance of the CLVs during blocked and unblocked phases. We find that on average the variance of the CLVs is clustered around the center of blocking. These results show that the blocked flow affects all time scales and processes described by the CLVs.

Integrated Regional Enstrophy and Block Intensity as a Measure of Kolmogorov Entropy

“…However, the timing of onset, intensification and decay will be governed by synoptic-scale processes [35,36]. Additionally, Schubert et al [19] suggested that blocked flows were identifiable using Lyapunov exponents and are more unstable and more difficult to predict in their simplified model. This agrees with [2,12], and the results found here show that the Lyapunov exponents were relatively high at onset and intensification.…”

“…Although relatively high values of IRE derived from an atmospheric flow field in the study of atmospheric blocking were identified with the onset or demise of blocking events, IRE can also be associated with transitions of the large-scale flow in general, and thus are not exclusive to blocking [12]. Recently [19], however, used covariant Lyapunov vectors to identify blocking flows in a simple channel model with orography. As stated in [19], each covariant Lyapunov vector is associated with a Lyapunov exponent, representing the growth or decay rates in blocked or zonal flows.…”

“…Recently [19], however, used covariant Lyapunov vectors to identify blocking flows in a simple channel model with orography. As stated in [19], each covariant Lyapunov vector is associated with a Lyapunov exponent, representing the growth or decay rates in blocked or zonal flows. They found growth rates corresponding to more unstable flow during blocked flows.…”

A new mathematical framework for atmospheric blocking events

“…Such an increase in the finite time LEs (FTLEs) with respect to typical, zonal conditions is attributed to a combination of stronger barotropic and baroclinic conversions, see also an earlier analysis by Frederiksen and Bell (1990). Schubert and Lucarini (2016) interpreted such a counterintuitive finding -blockings are usually thought as being characterized by anomalously high predictability -as resulting from the difficulty of predicting the specific timing of onset (Mauritsen et al 2004) and decay (Quandt et al 2017) of the blocking event. Kwasniok (2018, personal communication) found that atmospheric flows associated with anomalously high values of finite time largest LE resemble correspond to blocked conditions.…”

Detecting Regime Transitions in Time Series Using Dynamic Mode Decomposition

“…More recently methods from dynamical systems theory have been employed. In particular, covariant Lyapunov vectors and unstable periodic orbits were shown to capture blocking events [43,28]. More closely related to our approach of DMD, methods based on the transfer operator, the formal L 2 -adjoint of the Koopman operator, and the behaviour of its point spectrum were used to study transitions to individual blocking event [44].…”