| 1. |
- Carbone, Francesco, et al.
(författare)
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Local dimensionality and inverse persistence analysis of atmospheric turbulence in the stable boundary layer
- 2022
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Ingår i: Physical review. E. - : American Physical Society. - 2470-0045 .- 2470-0053. ; 106:6
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Tidskriftsartikel (refereegranskat)abstract
- The dynamics across different scales in the stable atmospheric boundary layer has been investigated by means of two metrics, based on instantaneous fractal dimensions and grounded in dynamical systems theory. The wind velocity fluctuations obtained from data collected during the Cooperative Atmosphere-Surface Exchange Study- 1999 experiment were analyzed to provide a local (in terms of scales) and an instantaneous (in terms of time) description of the fractal properties and predictability of the system. By analyzing the phase-space projections of the continuous turbulent, intermittent, and radiative regimes, a progressive transformation, characterized by the emergence of multiple low-dimensional clusters embedded in a high-dimensional shell and a two-lobe mirror symmetrical structure of the inverse persistence, have been found. The phase space becomes increasingly complex and anisotropic as the turbulent fluctuations become uncorrelated. The phase space is characterized by a three-dimensional structure for the continuous turbulent samples in a range of scales compatible with the inertial subrange, where the phase-space-filling turbulent fluctuations dominate the dynamics, and is low dimensional in the other regimes. Moreover, lower-dimensional structures present a stronger persistence than the higher-dimensional structures. Eventually, all samples recover a three-dimensional structure and higher persistence level at large scales, far from the inertial subrange. The two metrics obtained in the analysis can be considered as proxies for the decorrelation time and the local anisotropy in the turbulent flow.
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| 2. |
- De Luca, Paolo, et al.
(författare)
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Compound warm-dry arid cold-wet events over the Mediterranean
- 2020
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Ingår i: Earth System Dynamics. - : Copernicus GmbH. - 2190-4979 .- 2190-4987. ; 11:3, s. 793-805
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Tidskriftsartikel (refereegranskat)abstract
- The Mediterranean (MED) Basin is a climate change hotspot that has seen drying and a pronounced increase in heatwaves over the last century. At the same time, it is experiencing increased heavy precipitation during wintertime cold spells. Understanding and quantifying the risks from compound events over the MED is paramount for present and future disaster risk reduction measures. Here, we apply a novel method to study compound events based on dynamical systems theory and analyse compound temperature and precipitation events over the MED from 1979 to 2018. The dynamical systems analysis quantifies the strength of the coupling between different atmospheric variables over the MED. Further, we consider compound warm-dry anomalies in summer and cold-wet anomalies in winter. Our results show that these warm-dry and cold-wet compound days are associated with large values of the temperature-precipitation coupling parameter of the dynamical systems analysis. This indicates that there is a strong interaction between temperature and precipitation during compound events. In winter, we find no significant trend in the coupling between temperature and precipitation. However in summer, we find a significant upward trend which is likely driven by a stronger coupling during warm and dry days. Thermodynamic processes associated with long-term MED warming can best explain the trend, which intensifies compound warm-dry events.
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| 3. |
- Faranda, Davide, et al.
(författare)
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A climate-change attribution retrospective of some impactful weather extremes of 2021
- 2022
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Ingår i: Weather and Climate Dynamics. - : European Geosciences Union (EGU). - 2698-4024 .- 2698-4016. ; 3:4, s. 1311-1340
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Tidskriftsartikel (refereegranskat)abstract
- The IPCC AR6 report outlines a general consensus that anthropogenic climate change is modifying the frequency and intensity of extreme events such as cold spells, heat waves, storms or floods. A pertinent question is then whether climate change may have affected the characteristics of a specific extreme event or whether such event would have even been possible in the absence of climate change. Here, we address this question by performing an attribution of some major extreme events that occurred in 2021 over Europe and North America: the Winter Storm Filomena, the French spring cold spell, the Westphalia floods, the Mediterranean summer heat wave, Hurricane Ida, the Po Valley tornado outbreak, Medicane Apollo and the late-autumn Scandinavian cold spell. We focus on the role of the atmospheric circulation associated with the events and its typicality in present (factual world) and past climate conditions (counterfactual world) – defined using the ERA5 dataset 1950 to present. We first identify the most similar sea-level pressure patterns to the extreme events of interest in the factual and counterfactual worlds – so-called analogues. We then compute significant shifts in the spatial characteristics, persistence, predictability, seasonality and other characteristics of these analogues. We also diagnose whether in the present climate the analogues of the studied events lead to warmer/cooler or dryer/wetter conditions than in the past. Finally we verify whether the El Niño–Southern Oscillation and the Atlantic Multidecadal Oscillation may explain interdecadal changes in the analogues' characteristics. We find that most of the extreme events we investigate are significantly modified in the present climate with respect to the past, because of changes in the location, persistence and/or seasonality of cyclonic/anticyclonic patterns in the sea-level pressure analogues. One of the events, Medicane Apollo, appears to be a black swan of the atmospheric circulation, with poor-quality analogues. Our approach, complementary to the statistical extreme-event attribution methods in the literature, points to the potentially important role of the atmospheric circulation in attribution studies.
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| 4. |
- Faranda, Davide, et al.
(författare)
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Atmospheric circulation compounds anthropogenic warming and impacts of climate extremes in Europe
- 2023
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Ingår i: Proceedings of the National Academy of Sciences of the United States of America. - : Proceedings of the National Academy of Sciences. - 0027-8424 .- 1091-6490. ; 120:13
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 5. |
- Faranda, Davide, et al.
(författare)
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Attractor dimension of time-averaged climate observables : insights from a low-order ocean-atmosphere model
- 2019
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Ingår i: Tellus. Series A, Dynamic meteorology and oceanography. - : Stockholm University Press. - 0280-6495 .- 1600-0870. ; 71:1
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Tidskriftsartikel (refereegranskat)abstract
- The ocean and atmosphere have very different characteristic timescales and display a rich range of interactions. Here, we investigate the sensitivity of the dynamical properties of the coupled atmosphere-ocean system when time-averaging of the trajectories of the original system is performed. We base our analysis on a conceptual model of the atmosphere-ocean dynamics which allows us to compute the attractor properties for different coupling coefficients and averaging periods. When the averaging period is increased, the attractor dimension initially shows a non-monotonic behaviour, but ultimately decreases for windows longer than 1year. The analysis of daily, monthly and annual instrumental and reconstructed indices of oceanic and atmospheric circulation supports our results. This has important implications for the analysis and interpretation of long climate timeseries with a low temporal resolution, but also for the possible convergence of climate observables subjected to long time-averages towards attractors close to hyperbolicity.
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| 6. |
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| 7. |
- Faranda, Davide, et al.
(författare)
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Correcting biases in tropical cyclone intensities in low-resolution datasets using dynamical systems metrics
- 2023
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Ingår i: Climate Dynamics. - : Springer Nature. - 0930-7575 .- 1432-0894. ; 61, s. 4393-4409
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Tidskriftsartikel (refereegranskat)abstract
- Although the life-cycle of tropical cyclones is relatively well understood, many of the underlying physical processes occur at scales below those resolved by global climate models (GCMs). Projecting future changes in tropical cyclone characteristics thus remains challenging. We propose a methodology, based on dynamical system metrics, to reconstruct the statistics of cyclone intensities in coarse-resolution datasets, where maximum wind speed and minimum sea-level pressure may not be accurately represented. We base our analysis on 411 tropical cyclones occurring between 2010 and 2020, using both ERA5 reanalysis data and observations from the HURDAT2 database, as well as a control simulation of the IPSL-CM6A-ATM-ICO-HR model. For both ERA5 and model data, we compute two dynamical system metrics related to the number of degrees of freedom of the atmospheric flow and to the coupling between different atmospheric variables, namely the local dimension and the co-recurrence ratio. We then use HURDAT2 data to develop three bias-correction approaches for SLP minima: a univariate, unconditional quantile–quantile bias correction, a quantile–quantile bias correction conditioned on the two dynamical systems metrics, and a multivariate correction method. The conditional approach generally outperforms the unconditional approach for ERA5, pointing to the usefulness of the dynamical systems metrics in this context. We then show that the multivariate approach can be used to recover a realistic distribution of cyclone intensities from comparatively coarse-resolution model data.
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| 8. |
- Faranda, Davide, et al.
(författare)
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Diagnosing concurrent drivers of weather extremes : application to warm and cold days in North America
- 2020
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Ingår i: Climate Dynamics. - : Springer Science and Business Media LLC. - 0930-7575 .- 1432-0894. ; 54:3-4, s. 2187-2201
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Tidskriftsartikel (refereegranskat)abstract
- A fundamental challenge in climate science is decomposing the concurrent drivers of weather extremes in observations. Achieving this can provide insights into the drivers of individual extreme events as well as into possible future changes in extreme event frequencies under greenhouse forcing. In the present work, we exploit recent results from dynamical systems theory to study the co-variation and recurrence statistics of different atmospheric variables. Specifically, we present a methodology to quantify the recurrences of bivariate variables and the coupling between distinct univariate variables in terms of their joint recurrences. The coupling is defined by a parameter which varies according to the chosen variables, season, and domain and can be understood in terms of the underlying physics of the atmosphere. For suitably chosen variables, this approach enables to decompose the different drivers of weather extremes. Here, we compute the above metrics for near-surface temperature and sea level pressure, and use them to study warm or cold days over North America. We first identify states where temperature is strongly or weakly coupled to the large-scale atmospheric circulation, and then elucidate the interplay between coupling and the occurrence of temperature extremes.
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| 9. |
- Faranda, Davide, et al.
(författare)
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Dynamical properties and extremes of Northern Hemisphere climate fields over the past 60 years
- 2017
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Ingår i: Nonlinear processes in geophysics. - : Copernicus GmbH. - 1023-5809 .- 1607-7946. ; 24:4, s. 713-725
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Tidskriftsartikel (refereegranskat)abstract
- Atmospheric dynamics are described by a set of partial differential equations yielding an infinite-dimensional phase space. However, the actual trajectories followed by the system appear to be constrained to a finite-dimensional phase space, i.e. a strange attractor. The dynamical properties of this attractor are difficult to determine due to the complex nature of atmospheric motions. A first step to simplify the problem is to focus on observables which affect - or are linked to phenomena which affect - human welfare and activities, such as sea-level pressure, 2m temperature, and precipitation frequency. We make use of recent advances in dynamical systems theory to estimate two instantaneous dynamical properties of the above fields for the Northern Hemisphere: local dimension and persistence. We then use these metrics to characterize the seasonality of the different fields and their interplay. We further analyse the large-scale anomaly patterns corresponding to phase-space extremes - namely time steps at which the fields display extremes in their instantaneous dynamical properties. The analysis is based on the NCEP/NCAR reanalysis data, over the period 1948-2013. The results show that (i) despite the high dimensionality of atmospheric dynamics, the Northern Hemisphere sea-level pressure and temperature fields can on average be described by roughly 20 degrees of freedom; (ii) the precipitation field has a higher dimensionality; and (iii) the seasonal forcing modulates the variability of the dynamical indicators and affects the occurrence of phase-space extremes. We further identify a number of robust correlations between the dynamical properties of the different variables.
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| 10. |
- Faranda, Davide, et al.
(författare)
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Dynamical proxies of North Atlantic predictability and extremes
- 2017
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Ingår i: Scientific Reports. - : Springer Science and Business Media LLC. - 2045-2322. ; 7
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 11. |
- Faranda, Davide, et al.
(författare)
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Minimal dynamical systems model of the Northern Hemisphere jet stream via embedding of climate data
- 2019
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Ingår i: Earth System Dynamics. - : Copernicus GmbH. - 2190-4979 .- 2190-4987. ; 10:3, s. 555-567
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Tidskriftsartikel (refereegranskat)abstract
- We derive a minimal dynamical systems model for the Northern Hemisphere midlatitude jet dynamics by embedding atmospheric data and by investigating its properties (bifurcation structure, stability, local dimensions) for different atmospheric flow regimes. The derivation is a three-step process: first, we obtain a 1-D description of the midlatitude jet stream by computing the position of the jet at each longitude using ERA-Interim. Next, we use the embedding procedure to derive a map of the local jet position dynamics. Finally, we introduce the coupling and stochastic effects deriving from both atmospheric turbulence and topographic disturbances to the jet. We then analyze the dynamical properties of the model in different regimes: one that gives the closest representation of the properties extracted from real data; one featuring a stronger jet (strong coupling); one featuring a weaker jet (weak coupling); and one with modified topography. Our model, notwithstanding its simplicity, provides an instructive description of the dynamical properties of the atmospheric jet.
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| 12. |
- Faranda, Davide, et al.
(författare)
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The hammam effect or how a warm ocean enhances large scale atmospheric predictability
- 2019
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Ingår i: Nature Communications. - : Springer Science and Business Media LLC. - 2041-1723. ; 10
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Tidskriftsartikel (refereegranskat)abstract
- 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 x 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.
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| 13. |
- Ginesta, Mireia, et al.
(författare)
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A methodology for attributing severe extratropical cyclones to climate change based on reanalysis data : the case study of storm Alex 2020
- 2023
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Ingår i: Climate Dynamics. - : Springer Science and Business Media LLC. - 0930-7575 .- 1432-0894. ; 61:1-2, s. 229-253
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Tidskriftsartikel (refereegranskat)abstract
- Extreme event attribution aims at evaluating the impact of climate change on specific extreme events. In this work, we present an attribution methodology for severe extratropical cyclones, and test it on storm Alex. Alex was an explosive extratropical cyclone that affected Southern France and Northern Italy at the beginning of October 2020. The methodology exploits mathematical properties of circulation analogues, and identifies changes in physical and statistical properties. We first divide 6-hourly ERA5 data into two periods: a counterfactual period (1950–1984) and a factual period (1986–2021). We then identify the 30 cyclones in each period whose sea-level pressure maps are closest to Alex’s map by selecting those with the lowest Euclidean distance from Alex. We term these “analogues” of Alex. We find that analogues in the factual period are more persistent than in the counterfactual period, which may favour severe impacts resulting from persistent strong winds and heavy precipitation, as was the case for Alex. This effect is compounded by the doubling in accumulated daily precipitation detected in Northern Italy between the counterfactual and factual analogues. In the factual period, the analogues display an increase in the eddy kinetic energy in their growth phase, with poleward-shifted backward tracks. We also identify a seasonal shift of the analogues, from spring to autumn. Finally, the analogues in the factual period are closer to Alex than in the counterfactual period. These changes collectively point to high-impact storms like Alex having become more common in a changing climate.
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| 14. |
- Holmberg, Emma, et al.
(författare)
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The link between European warm-temperature extremes and atmospheric persistence
- 2023
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Ingår i: Earth System Dynamics. - : Copernicus Publications. - 2190-4979 .- 2190-4987. ; 14:4, s. 737-765
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the link between warm-temperature extremes in Europe and the persistence of large-scale atmospheric-circulation patterns for both winter and summer, along with some possible physical mechanisms connecting the two. We assess atmospheric persistence, leveraging concepts from dynamical systems theory, and reconcile this approach with the more conventional meteorological views of persistence. We find that wintertime warm spells are partly associated with persistent zonal advection at the surface level but display no statistically significant persistence anomaly in the mid-troposphere. For summertime heatwaves, we find a weak yet significant link to anomalously persistent circulation patterns in the mid-troposphere, while there are few significant persistence anomalies of the surface circulation pattern. We further find no evidence of a strong warm-temperature advection signal. This suggests that other radiative and dynamical processes, for example sensible heating and adiabatic warming, as well as local effects, could play a more important role than large-scale warm-temperature advection for these events. We thus argue that persistent atmospheric configurations are not a necessary requirement for warm-temperature extremes and that the results depend to a considerable extent on region and tropospheric level.
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| 15. |
- Messori, Gabriele, et al.
(författare)
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A dynamical systems approach to studying midlatitude weather extremes
- 2017
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Ingår i: Geophysical Research Letters. - 0094-8276 .- 1944-8007. ; 44:7, s. 3346-3354
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Tidskriftsartikel (refereegranskat)abstract
- Extreme weather occurrences carry enormous social and economic costs and routinely garner widespread scientific and media coverage. The ability to predict these events is therefore a topic of crucial importance. Here we propose a novel predictability pathway for extreme events, by building upon recent advances in dynamical systems theory. We show that simple dynamical systems metrics can be used to identify sets of large-scale atmospheric flow patterns with similar spatial structure and temporal evolution on time scales of several days to a week. In regions where these patterns favor extreme weather, they afford a particularly good predictability of the extremes. We specifically test this technique on the atmospheric circulation in the North Atlantic region, where it provides predictability of large-scale wintertime surface temperature extremes in Europe up to 1week in advance. Plain Language Summary Extreme weather occurrences carry enormous social and economic costs and routinely garner widespread scientific and media coverage. The ability to predict these events is therefore a topic of crucial importance. Here we propose a novel analysis technique for improving the prediction of extreme events, which identifies the large-scale atmospheric circulation configurations affording the best predictability. We specifically test our technique on the atmospheric circulation in the North Atlantic region, where it provides predictability of large-scale wintertime surface temperature extremes in Europe up to 1week in advance.
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| 16. |
- Messori, Gabriele, et al.
(författare)
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A dynamical systems characterization of atmospheric jet regimes
- 2021
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Ingår i: Earth System Dynamics. - : Copernicus GmbH. - 2190-4979 .- 2190-4987. ; 12:1, s. 233-251
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Tidskriftsartikel (refereegranskat)abstract
- Atmospheric jet streams are typically separated into primarily eddy-driven (or polar-front) jets and primarily thermally driven (or subtropical) jets. Some regions also display merged jets, resulting from the (quasi-)collocation of the regions of eddy generation with the subtropical jet. The different locations and driving mechanisms of these jets arise from very different underlying mechanisms and result in very different jet characteristics. Here, we link the current understanding of dynamical jet maintenance mechanisms, mostly arising from conceptual or idealized models, to the phenomena observed in reanalysis data. We specifically focus on developing a unitary analysis framework grounded in dynamical systems theory, which may be applied to both idealized models and reanalysis, as well as allowing for direct intercomparison. Our results illustrate the effectiveness of dynamical systems indicators to diagnose jet regimes.
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| 17. |
- Messori, Gabriele, et al.
(författare)
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Compound Climate Events and Extremes in the Midlatitudes Dynamics, Simulation, and Statistical Characterization
- 2021
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Ingår i: Bulletin of The American Meteorological Society - (BAMS). - : American Meteorological Society. - 0003-0007 .- 1520-0477. ; 102:4, s. E774-E781
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- The workshop, conducted virtually due to travel restrictions related to COVID-19, gathered scientists from six countries and focused on the mechanistic understanding, statistical characterization, and modeling of societally relevant compound climate events and extremes in the midlatitudes. These ranged from co-occurring hot–humid or wet–windy extremes, to spatially compounding wet and dry extremes, to temporallycompounding hot–wet events and more. The aim was to bring together selected experts studying a diverse range of compound climate events and extremes to present their ongoing work and outline challenges and future developments in this societally relevant field of research.
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| 18. |
- Messori, Gabriele, et al.
(författare)
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On the Systematic Occurrence of Compound Cold Spells in North America and Wet or Windy Extremes in Europe
- 2023
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Ingår i: Geophysical Research Letters. - : American Geophysical Union (AGU). - 0094-8276 .- 1944-8007. ; 50:7
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Tidskriftsartikel (refereegranskat)abstract
- The repeated co-occurrence of cold spells over Eastern North America and wet or windy extremes over Western Continental Europe during recent winters, has led to hypothesize a link between the two. Here, we analyze the interplay between the large-scale atmospheric circulation and co-occurring cold spells in North America and wet or windy extremes in Europe. We collectively term these occurrences compound cold–wet–windy extremes. We leverage a recent approach grounded in dynamical systems theory, which provides an analytically and computationally efficient analysis of spatially resolved, multivariate climate extremes. We find that there are specific, recurrent large-scale atmospheric circulation patterns systematically associated with both the individual extremes and co-occurring cold–wet–windy anomalies. Evidence for this is also found when focusing on compound cold–wet–windy extremes, although with a weaker signal. This motivates further analyses focusing specifically on the statistics and drivers of these compound extreme occurrences.
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| 19. |
- Messori, Gabriele, et al.
(författare)
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Technical note : Characterising and comparing different palaeoclimates with dynamical systems theory
- 2021
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Ingår i: Climate of the Past. - : Copernicus Publications. - 1814-9324 .- 1814-9332. ; 17:1, s. 545-563
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Tidskriftsartikel (refereegranskat)abstract
- Numerical climate simulations produce vast amounts of high-resolution data. This poses new challenges to the palaeoclimate community - and indeed to the broader climate community - in how to efficiently process and interpret model output. The palaeoclimate community also faces the additional challenge of having to characterise and compare a much broader range of climates than encountered in other subfields of climate science. Here we propose an analysis framework, grounded in dynamical systems theory, which may contribute to overcoming these challenges. The framework enables the characterisation of the dynamics of a given climate through a small number of metrics. These may be applied to individual climate variables or to several variables at once, and they can diagnose properties such as persistence, active number of degrees of freedom and coupling. Crucially, the metrics provide information on instantaneous states of the chosen variable(s). To illustrate the framework's applicability, we analyse three numerical simulations of mid-Holocene climates over North Africa under different boundary conditions. We find that the three simulations produce climate systems with different dynamical properties, such as persistence of the spatial precipitation patterns and coupling between precipitation and large-scale sea level pressure patterns, which are reflected in the dynamical systems metrics. We conclude that the dynamical systems framework holds significant potential for analysing palaeoclimate simulations. At the same time, an appraisal of the framework's limitations suggests that it should be viewed as a complement to more conventional analyses, rather than as a wholesale substitute.
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| 20. |
- Pons, Flavio Maria Emanuele, et al.
(författare)
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Sampling Hyperspheres via Extreme Value Theory : Implications for Measuring Attractor Dimensions
- 2020
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Ingår i: Journal of statistical physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 179, s. 1698-1717
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Tidskriftsartikel (refereegranskat)abstract
- The attractor Hausdorff dimension is an important quantity bridging information theory and dynamical systems, as it is related to the number of effective degrees of freedom of the underlying dynamical system. By using the link between extreme value theory and Poincare recurrences, it is possible to estimate this quantity from time series of high-dimensional systems without embedding the data. In general d <= n, where n is the dimension of the full phase-space, as the dynamics freezes some of the available degrees of freedom. This is equivalent to constraining trajectories on a compact object in phase space, namely the attractor. Information theory shows that the equality d = n holds for random systems. However, applying extreme value theory, we show that this result cannot be recovered and that d < n. We attribute this effect to the curse of dimensionality, and in particular to the phenomenon of concentration of the norm observed in high-dimensional systems. We derive a theoretical expression for d(n) for Gaussian random vectors, and we show numerically that similar curse of dimensionality effects are found for random systems characterized by non-Gaussian distributions. Finally, we show that the effect of the curse of dimensionality can be quantified using the extreme value theory, thus enabling to retrieve the degree of nonrandomness of a system. We provide examples issued from real-world climate and financial datasets.
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| 21. |
- Pons, Flavio, et al.
(författare)
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Statistical performance of local attractor dimension estimators in non-Axiom A dynamical systems
- 2023
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Ingår i: Chaos. - : American Institute of Physics (AIP). - 1054-1500 .- 1089-7682. ; 33:7
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 22. |
- Rodrigues, David, et al.
(författare)
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Dynamical Properties of the North Atlantic Atmospheric Circulation in the Past 150 Years in CMIP5 Models and the 20CRv2c Reanalysis
- 2018
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Ingår i: Journal of Climate. - 0894-8755 .- 1520-0442. ; 31:15, s. 6097-6111
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Tidskriftsartikel (refereegranskat)abstract
- It is of fundamental importance to evaluate the ability of climate models to capture the large-scale atmospheric circulation patterns and, in the context of a rapidly increasing greenhouse forcing, the robustness of the changes simulated in these patterns over time. Here we approach this problem from an innovative point of view based on dynamical systems theory. We characterize the atmospheric circulation over the North Atlantic in the CMIP5 historical simulations (1851-2000) in terms of two instantaneous metrics: local dimension of the attractor and stability of phase-space trajectories. We then use these metrics to compare the models to the Twentieth Century Reanalysis version 2c (20CRv2c) over the same historical period. The comparison suggests that (i) most models capture to some degree the median attractor properties, and models with finer grids generally perform better; (ii) in most models the extremes in the dynamical systems metrics match large-scale patterns similar to those found in the reanalysis; (iii) changes in the attractor properties observed for the ensemble-mean 20CRv2c are artifacts resulting from inhomogeneities in the standard deviation of the ensemble over time; and (iv) the long-term trends in local dimension observed among the 56 members of the 20CR ensemble have the same sign as those observed in the CMIP5 multimodel mean, although the multimodel trend is much weaker.
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