Statistical performance of local attractor dimension estimators in non-Axiom A dynamical systems.

We investigate various estimators based on extreme value theory (EVT) for determining the local fractal dimension of chaotic dynamical systems. In the limit of an infinitely long time series of an ergodic system, the average of the local fractal dimension is the system's global attractor dimension. The latter is an important quantity that relates to the number of effective degrees of freedom of the underlying dynamical system, and its estimation has been a central topic in the dynamical systems literature since the 1980s. In this work, we propose a framework that combines phase space recurrence analysis with EVT to estimate the local fractal dimension around a particular state of interest. While the EVT framework allows for the analysis of high-dimensional complex systems, such as the Earth's climate, its effectiveness depends on robust statistical parameter estimation for the assumed extreme value distribution. In this study, we conduct a critical review of several EVT-based local fractal dimension estimators, analyzing and comparing their performance across a range of systems. Our results offer valuable insights for researchers employing the EVT-based estimates of the local fractal dimension, aiding in the selection of an appropriate estimator for their specific applications.

Atmospheric circulation compounds anthropogenic warming and impacts of climate extremes in Europe.

Diagnosing dynamical changes in the climate system, such as those in atmospheric circulation patterns, remains challenging. Here, we study 1950 to 2021 trends in the frequency of occurrence of atmospheric circulation patterns over the North Atlantic. Roughly 7% of atmospheric circulation patterns display significant occurrence trends, yet they have major impacts on surface climate. Increasingly frequent patterns drive heatwaves across Europe and enhanced wintertime storminess in the northern part of the continent. Over 91% of recent heatwave-related deaths and 33% of high-impact windstorms in Europe were concurrent with increasingly frequent atmospheric circulation patterns. While the trends identified are statistically significant, they are not necessarily anthropogenic. Atmospheric patterns which are becoming rarer correspond instead to wet, cool summer conditions over northern Europe and wet winter conditions over continental Europe. The combined effect of these circulation changes is that of a strong, dynamically driven year-round warming over most of the continent and large regional and seasonal changes in precipitation and surface wind.

The life cycle of meridional heat flux peaks.

Covariance between meridional wind and air temperature in the lower troposphere quantifies the poleward flux of dry static energy in the atmosphere; in the midlatitudes, this is primarily realised by baroclinic weather systems. It is shown that strong covariance between temperature and meridional wind results from both enhanced correlation and enhanced variance, and that the two evolve according to a distinct temporal structure akin to a life-cycle. Starting from a state of low correlation and variance, there is first a gradual build-up to modal growth at constant, high correlation, followed by a rapid decay at relatively low correlation values. This life-cycle evolution is observed most markedly over oceanic regions, and cannot be explained on purely statistical grounds. We find that local peaks of meridional heat flux are not exclusively linked to the action of individual weather systems and can affect the atmospheric circulation on larger length-scales through wave propagation along waveguides.

Scenarios of Human Responses to Unprecedented Social-Environmental Extreme Events.

In a rapidly changing world, what is today an unprecedented extreme may soon become the norm. As a result, extreme-related disasters are expected to become more frequent and intense. This will have widespread socio-economic consequences and affect the ability of different societal groups to recover from and adapt to rapidly changing environmental conditions. Therefore, there is the need to decipher the relation between genesis of unprecedented events, accumulation and distribution of risk, and recovery trajectories across different societal groups. Here, we develop an analytical approach to unravel the complexity of future extremes and multiscalar societal responses-from households to national governments and from immediate impacts to longer term recovery. This requires creating new forms of knowledge that integrate analyses of the past-that is, structural causes and political processes of risk accumulation and differentiated recovery trajectories-with plausible scenarios of future environmental extremes grounded in the event-specific literature. We specifically seek to combine the physical characteristics of the extremes with examinations of how culture, politics, power, and policy visions shape societal responses to unprecedented events, and interpret the events as social-environmental extremes. This new approach, at the nexus between social and natural sciences, has the concrete advantage of providing an impact-focused vision of future social-environmental risks, beyond what is achievable within conventional disciplinary boundaries. In this paper, we focus on extreme flooding events and the societal responses they elicit. However, our approach is flexible and applicable to a wide range of extreme events. We see it as the first building block of a new field of research, allowing for novel and integrated theoretical explanations and forecasting of social-environmental extremes.

A new dynamical systems perspective on atmospheric predictability: Eastern Mediterranean weather regimes as a case study.

The atmosphere is a chaotic system displaying recurrent large-scale configurations. Recent developments in dynamical systems theory allow us to describe these configurations in terms of the local dimension-a proxy for the active number of degrees of freedom-and persistence in phase space, which can be interpreted as persistence in time. These properties provide information on the intrinsic predictability of an atmospheric state. Here, this technique is applied to atmospheric configurations in the eastern Mediterranean, grouped into synoptic classifications (SCs). It is shown that local dimension and persistence, derived from reanalysis and CMIP5 models' daily sea-level pressure fields, can serve as an extremely informative qualitative method for evaluating the predictability of the different SCs. These metrics, combined with the SC transitional probability approach, may be a valuable complement to operational weather forecasts and effective tools for climate model evaluation. This new perspective can be extended to other geographical regions.

The hammam effect or how a warm ocean enhances large scale atmospheric predictability.

The atmosphere's chaotic nature limits its short-term predictability. Furthermore, there is little knowledge on how the difficulty of forecasting weather may be affected by anthropogenic climate change. Here, we address this question by employing metrics issued from dynamical systems theory to describe the atmospheric circulation and infer the dynamical properties of the climate system. Specifically, we evaluate the changes in the sub-seasonal predictability of the large-scale atmospheric circulation over the North Atlantic for the historical period and under anthropogenic forcing, using centennial reanalyses and CMIP5 simulations. For the future period, most datasets point to an increase in the atmosphere's predictability. AMIP simulations with 4K warmer oceans and 4 × atmospheric CO2 concentrations highlight the prominent role of a warmer ocean in driving this increase. We term this the hammam effect. Such effect is linked to enhanced zonal atmospheric patterns, which are more predictable than meridional configurations.

Dynamical proxies of North Atlantic predictability and extremes.

Atmospheric flows are characterized by chaotic dynamics and recurring large-scale patterns. These two characteristics point to the existence of an atmospheric attractor defined by Lorenz as: "the collection of all states that the system can assume or approach again and again, as opposed to those that it will ultimately avoid". The average dimension D of the attractor corresponds to the number of degrees of freedom sufficient to describe the atmospheric circulation. However, obtaining reliable estimates of D has proved challenging. Moreover, D does not provide information on transient atmospheric motions, such as those leading to weather extremes. Using recent developments in dynamical systems theory, we show that such motions can be classified through instantaneous rather than average properties of the attractor. The instantaneous properties are uniquely determined by instantaneous dimension and stability. Their extreme values correspond to specific atmospheric patterns, and match extreme weather occurrences. We further show the existence of a significant correlation between the time series of instantaneous stability and dimension and the mean spread of sea-level pressure fields in an operational ensemble weather forecast at lead times of over two weeks. Instantaneous properties of the attractor therefore provide an efficient way of evaluating and informing operational weather forecasts.