Abstract We investigate similarities and differences between natural and simulated slow earthquakes using nonlinear dynamical system tools. We use spatio‐temporal slip potency rate data derived from Global Navigation Satellite System (GNSS) position time series in the Cascadia subduction zone and numerical simulations intended to reproduce their pulse‐like behavior and scaling laws. We provide metrics to evaluate the accuracy of simulations in mimicking slow earthquake dynamics. We investigate the influence of spatio‐temporal coarsening as well as observational noise. Despite the use of many degrees of freedom, numerical simulations display a surprisingly low average dimension, akin to natural slow earthquakes. Instantaneous dynamical indices can reach large values (>10) instead, and differences persist between numerical simulations and natural observations. We propose to use the suggested metrics as an additional tool to narrow the divergence between slow earthquake observations and dynamical simulations.

Statistical physics and dynamical systems theory are key tools to study high-impact geophysical events such as temperature extremes, cyclones, thunderstorms, geomagnetic storms and many more. Despite the intrinsic differences between these events, they all originate as temporary deviations from the typical trajectories of a geophysical system, resulting in well-organised, coherent structures at characteristic spatial and temporal scales. While statistical extreme value analysis techniques are capable to provide return times and probabilities of occurrence of certain geophysical events, they are not apt to account for their underlying physics. Their focus is to compute the probability of occurrence of events that are large or small with respect to some specific observable (e.g. temperature, precipitation, solar wind), rather than to relate rare or extreme phenomena to the underlying anomalous geophysical regimes. This paper outlines this knowledge gap, presenting some related challenges, new formalisms and briefly commenting on how stochastic approaches tailored to the study of extreme geophysical events can help to advance their understanding.

Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of deterministic chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively by studying the properties of the underlying attractor, the compact object asymptotically hosting the trajectories of the system with their invariant density in the phase space. This multi-scale nature of natural systems makes it practically impossible to get a clear picture of the attracting set. Indeed, it spans over a wide range of spatial scales and may even change in time due to non-stationary forcing. Here, we combine an adaptive decomposition method with extreme value theory to study the properties of the instantaneous scale-dependent dimension, which has been recently introduced to characterize such temporal and spatial scale-dependent attractors in turbulence and astrophysics. To provide a quantitative analysis of the properties of this metric, we test it on the well-known low-dimensional deterministic Lorenz-63 system perturbed with additive or multiplicative noise. We demonstrate that the properties of the invariant set depend on the scale we are focusing on and that the scale-dependent dimensions can discriminate between additive and multiplicative noise despite the fact that the two cases have exactly the same stationary invariant measure at large scales. The proposed formalism can be generally helpful to investigate the role of multi-scale fluctuations within complex systems, allowing us to deal with the problem of characterizing the role of stochastic fluctuations across a wide range of physical systems.

We analyze frictional motion for a laboratory fault as it passes through the stability transition from stable sliding to unstable motion. We study frictional stick-slip events, which are the lab equivalent of earthquakes, via dynamical system tools in order to retrieve information on the underlying dynamics and to assess whether there are dynamical changes associated with the transition from stable to unstable motion. We find that the seismic cycle exhibits characteristics of a low-dimensional system with average dimension similar to that of natural slow earthquakes (<5). We also investigate local properties of the attractor and find maximum instantaneous dimension ≳10, indicating that some regions of the phase space require a high number of degrees of freedom (dofs). Our analysis does not preclude deterministic chaos, but the lab seismic cycle is best explained by a random attractor based on rate- and state-dependent friction whose dynamics is stochastically perturbed. We find that minimal variations of 0.05% of the shear and normal stresses applied to the experimental fault influence the large-scale dynamics and the recurrence time of labquakes. While complicated motion including period doubling is observed near the stability transition, even in the fully unstable regime we do not observe truly periodic behavior. Friction's nonlinear nature amplifies small scale perturbations, reducing the predictability of the otherwise periodic macroscopic dynamics. As applied to tectonic faults, our results imply that even small stress field fluctuations (≲150 kPa) can induce coefficient of variations in earthquake repeat time of a few percent. Moreover, these perturbations can drive an otherwise fast-slipping fault, close to the critical stability condition, into a mixed behavior involving slow and fast ruptures.

Hurricanes—and more broadly tropical cyclones—are high-impact weather phenomena whose adverse socio-economic and ecosystem impacts affect a considerable part of the global population. Despite our reasonably robust meteorological understanding of tropical cyclones, we still face outstanding challenges for their numerical simulations. Consequently, future changes in the frequency of occurrence and intensity of tropical cyclones are still debated. Here, we diagnose possible reasons for the poor representation of tropical cyclones in numerical models, by considering the cyclones as chaotic dynamical systems. We follow 197 tropical cyclones which occurred between 2010 and 2020 in the North Atlantic using the HURDAT2 and ERA5 data sets. We measure the cyclones instantaneous number of active degrees of freedom (local dimension) and the persistence of their sea-level pressure and potential vorticity fields. During the most intense phases of the cyclones, and specifically when cyclones reach hurricane strength, there is a collapse of degrees of freedom and an increase in persistence. The large dependence of hurricanes dynamical characteristics on intensity suggests the need for adaptive parametrization schemes which take into account the dependence of the cyclone’s phase, in analogy with high-dissipation intermittent events in turbulent flows.

The description and analysis of compound extremes affecting mid- and high latitudes in the winter requires an accurate estimation of snowfall. This variable is often missing from in situ observations and biased in climate model outputs, both in the magnitude and number of events. While climate models can be adjusted using bias correction (BC), snowfall presents additional challenges compared to other variables, preventing one from applying traditional univariate BC methods. We extend the existing literature on the estimation of the snowfall fraction from near-surface temperature, which usually involves binary thresholds or nonlinear least square fitting of sigmoidal functions. We show that, considering methods such as segmented and spline regressions and nonlinear least squares fitting, it is possible to obtain accurate out-of-sample estimates of snowfall over Europe in ERA5 reanalysis and to perform effective BC on the IPSL_WRF high-resolution EURO-CORDEX climate model when only relying on bias-adjusted temperature and precipitation. In particular, we find that cubic spline regression offers the best tradeoff as a feasible and accurate way to reconstruct or adjust snowfall observations, without requiring multivariate or conditional bias correction and stochastic generation of unobserved events.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Compound climate events and extremes in the mid-latitudes: dynamics, simulation and statistical characterisation Gabriele Messori, Emanuele Bevacqua, Rodrigo Caballero, Dim Coumou, Paolo de Luca, Davide Faranda, Kai Kornhuber, Olivia Martius, Flavio Pons, Colin Raymond, et al.

We study analytically and numerically the extreme value distribution of observables defined along the temporal evolution of a dynamical system. The convergence to the Gumbel law of observable recurrences gives information on the fractal structure of the image of the invariant measure by the observable. We provide illustrations on idealized and physical systems.

Extreme Aleutian Low (AL) events have been associated with major ecosystem reorganisations and unusual weather patterns in the Pacific region, with serious socio-economic consequences. Yet, their future evolution and impacts on atmosphere–ocean interactions remain uncertain. Here, a large ensemble of historical and future runs from the Community Earth System Model is used to investigate the evolution of AL extremes. The frequency and persistence of AL extremes are quantified and their connection with climatic variables is examined. AL extremes become more frequent and persistent under the RCP8.5 scenario, associated with changes in precipitation and air temperature patterns over North America. Future changes in AL extremes also increase the variability of the sea surface temperature and net heat fluxes in the Kuroshio Extension, the most significant heat and energy flux region of the basin. The increased frequency and persistence of future AL extremes may potentially cause substantial changes in fisheries and ecosystems of the entire Pacific region as a knock-on effect.

A heatwave struck Northern Europe in summer 2018. The probability of this event increased with human-induced climate change primarily due to thermodynamic changes.

We propose a novel approach to the study of compound extremes, grounded in dynamical systems theory. Specifically, we present the co-recurrence ratio (α), which elucidates the dependence structure between maps by quantifying their joint recurrences. This approach is applied to daily climate extremes, derived from the ERA-Interim reanalysis over the 1979-2018 period. The analysis focuses on concurrent (i.e. same-day) wet (total precipitation) and windy (10m wind gusts) extremes in Europe and concurrent cold (2m temperature) extremes in Eastern North America and wet extremes in Europe. Results for wet and windy extremes in Europe, which we use as a test-bed for our methodology, show that α peaks during boreal winter. High αvalues correspond to wet and windy extremes in north-western Europe, and to large-scale conditions resembling the positive phase of the North Atlantic Oscillation (NAO). This confirms earlier findings which link the positive NAO to a heightened frequency of extra-tropical cyclones impacting north-western Europe, resulting in frequent wet and windy extremes. For the Eastern North America-Europe case, α extremes once again reflect concurrent climate extremes -- in this case cold extremes over North America and wet extremes over Europe. Our analysis provides detailed spatial information on regional hotspots for these compound extreme occurrences, and encapsulates information on their spatial footprint which is typically not included in a conventional co-occurrence analysis. We conclude that α successfully characterises compound extremes by reflecting the evolution of the associated meteorological maps. This approach is entirely general, and may be applied to different types of compound extremes and geographical regions.

Slow earthquakes, like regular earthquakes, result from unstable frictional slip. They produce little slip and can therefore repeat frequently. We assess their predictability using the slip history of the Cascadia subduction between 2007 and 2017, during which slow earthquakes have repeatedly ruptured multiple segments. We characterize the system dynamics using embedding theory and extreme value theory. The analysis reveals a low-dimensional (<5) nonlinear chaotic system rather than a stochastic system. We calculate properties of the underlying attractor like its correlation and instantaneous dimension, instantaneous persistence, and metric entropy. We infer that the system has a predictability horizon of the order of days weeks. For the better resolved segments, the onset of large slip events can be correctly forecasted by high values of the instantaneous dimension. Longer-term deterministic prediction seems intrinsically impossible. Regular earthquakes might similarly be predictable but with a limited predictable horizon of the order of their durations.

Turbulent Rayleigh-Bénard convection in a 2D square cell is characterized by the existence of a large-scale circulation which varies intermittently. We focus on a range of Rayleigh numbers where the large-scale circulation experiences rapid non-trivial reversals from one quasi-steady (or meta-stable) state to another. In previous work [B. Podvin and A. Sergent, J. Fluid Mech. 766, 172201 (2015); B. Podvin and A. Sergent, Phys. Rev. E 95, 013112 (2017)], we applied proper orthogonal decomposition (POD) to the joint temperature and velocity fields at a given Rayleigh number, and the dynamics of the flow were characterized in a multi-dimensional POD space. Here, we show that several of those findings, which required extensive data processing over a wide range of both spatial and temporal scales, can be reproduced, and possibly extended, by application of the embedding theory to a single time series of the global angular momentum, which is equivalent here to the most energetic POD mode. Specifically, the embedding theory confirms that the switches among meta-stable states are uncorrelated. It also shows that, despite the large number of degrees of freedom of the turbulent Rayleigh Bénard flow, a low dimensional description of its physics can be derived with low computational efforts, providing that a single global observable reflecting the symmetry of the system is identified. A strong connection between the local stability properties of the reconstructed attractor and the characteristics of the reversals can also be established.

Regime shifts are abrupt changes in an ecosystem that may propagate through multiple trophic levels and have pronounced effects on the biotic and abiotic environment, potentially resulting in ecosystem reorganization. There are multiple mechanisms that could cause such abrupt events including natural and anthropogenic factors. In the North Pacific a major shift in the physics of the system, including a sudden increase in sea surface temperature, was reported in 1977 with a prominent biological response in the lower trophic levels and subsequent effects on the fisheries and economy of the region. Here we investigate the statistics of physical processes that could have triggered and maintained the late 1970’s shift. The hypothesis of an extreme sea level pressure event abruptly changing the oceanic conditions in winter 1976-1977, which was maintained by long-term changes in air-sea interaction processes, is tested. Using a novel statistical and dynamical approach, we show the occurrence of an extreme atmospheric event, specifically a persistent Aleutian Low during winter 1976-77, which constitutes a substantial part of the triggering mechanism of the regime shift. Subsequent sudden changes in the net heat flux occurred in the western North Pacific, particularly in the Kuroshio Extension region, which contributed to the maintenance of the new regime.

We examine the connection between the singularities or quasisingularities in the solutions of the incompressible Navier-Stokes equation (INSE) and the local energy transfer and dissipation, in order to explore in detail how the former contributes to the phenomenon of intermittency. We do so by analyzing the velocity fields (a) measured in the experiments on the turbulent von Kármán swirling flow at high Reynolds numbers and (b) obtained from the direct numerical simulations of the INSE at a moderate resolution. To compute the local interscale energy transfer and viscous dissipation in experimental and supporting numerical data, we use the weak solution formulation generalization of the Kármán-Howarth-Monin equation. In the presence of a singularity in the velocity field, this formulation yields a nonzero dissipation (inertial dissipation) in the limit of an infinite resolution. Moreover, at finite resolutions, it provides an expression for local interscale energy transfers down to the scale where the energy is dissipated by viscosity. In the presence of a quasisingularity that is regularized by viscosity, the formulation provides the contribution to the viscous dissipation due to the presence of the quasisingularity. Therefore, our formulation provides a concrete support to the general multifractal description of the intermittency. We present the maps and statistics of the interscale energy transfer and show that the extreme events of this transfer govern the intermittency corrections and are compatible with a refined similarity hypothesis based on this transfer. We characterize the probability distribution functions of these extreme events via generalized Pareto distribution analysis and find that the widths of the tails are compatible with a similarity of the second kind. Finally, we make a connection between the topological and the statistical properties of the extreme events of the interscale energy transfer field and its multifractal properties.

We show that the probability of the appearance of synchronization in chaotic coupled map lattices is related to the distribution of the maximum of a certain observable evaluated along almost all orbits. We show that such a distribution belongs to the family of extreme value laws, whose parameters, namely the extremal index, allow us to get a detailed description of the probability of synchronization. Theoretical results are supported by robust numerical computations that allow us to go beyond the theoretical framework provided and are potentially applicable to physically relevant systems.

We establish a link between the maximization of Kolmogorov Sinai entropy (KSE) and the minimization of the mixing time for general Markov chains. Since the maximisation of KSE is analytical and easier to compute in general than mixing time, this link provides a new faster method to approximate the minimum mixing time dynamics. It could be interesting in computer sciences and statistical physics, for computations that use random walks on graphs that can be represented as Markov chains.