Presentation given at the 21st EGU General Assembly (EGU2019), published on the Proceedings from ... more Presentation given at the 21st EGU General Assembly (EGU2019), published on the Proceedings from the conference held 7-12 April, 2019 in Vienna, Austria, id.17414.
<p>Coupled ocean-atmosphere teleconnections are characteristics of internal... more <p>Coupled ocean-atmosphere teleconnections are characteristics of internal variability which have a forced response just like mean states. It is not trivial how to correctly and optimally estimate the forced response and changes of the El Niño-Southern Oscillation (ENSO)-Indian summer monsoon (ISM) teleconnection under greenhouse forcing. Here we use two different approaches to address it. The first approach, based on the conventional temporal method applied to 30 model simulations in Coupled Model Intercomparison Project Phase 6, suggests no model consensus on changes in the teleconnection on interannual timescale under global warming. The second approach is based on a converged infinite single model initial condition large ensemble (SMILE) and defines the relationship in an instantaneous climatological sense. In view of several characteristics of the teleconnection, a robust long-term strengthening of the teleconnection is found in the MPI-GE but not in the CESM1-LE. We discuss appropriateness and limitations of the two methods. </p>
The weakening of zonal atmospheric circulation, a widely accepted projection of climate change in... more The weakening of zonal atmospheric circulation, a widely accepted projection of climate change in response to global warming, features a weakening of the Indian Ocean Walker circulation (IWC), with an anomalous ascending motion over the western and anomalous descending motion over the eastern Indian Ocean. The projected IWC weakening has previously been attributed to slower warming in the east than the west, that is, to a positive Indian Ocean Dipole (IOD)-like warming pattern. However, such a warming pattern can also be induced by IWC weakening. As a result, the cause-and-effect relationship cannot be easily determined, and the projected change is poorly constrained and highly uncertain. Here, using a suite of coupled climate model simulations under a high-emission scenario, we find that the IWC slowdown is accompanied by not only a positive IOD-like warming pattern but also anomalous meridional circulation that is associated with anomalous descending motion over the eastern Indian...
We give here a brief summary of classical Extreme Value Theory for random variables, followed by ... more We give here a brief summary of classical Extreme Value Theory for random variables, followed by that for deterministic dynamical systems, which is a rapidly developing area of research. Here we would like to contribute to that by conducting a numerical analysis designed to show particular features of extreme value statistics in dynamical systems, and also to explore the validity of the theory. We find that formulae that link the extreme value statistics with geometrical properties of the attractor hold typically for high-dimensional systems-whether a so-called geometric distance observable or a physical observable is concerned. In very low-dimensional settings, however, the fractality of the attractor prevents the system from having an extreme value law, which might well render the evaluation of extreme value statistics meaningless and so ill-suited for application.
We study the forced response of the teleconnection between the El Niño–Southern Oscillation (ENSO... more We study the forced response of the teleconnection between the El Niño–Southern Oscillation (ENSO) and the Indian summer monsoon (IM) in the Max Planck Institute Grand Ensemble, a set of Earth system ensemble simulations under historical and Representative Concentration Pathway (RCP) forcing. The forced response of the teleconnection, or a characteristic of it, is defined as the time dependence of a correlation coefficient evaluated over the ensemble. We consider the temporal variability of spatial averages and that with respect to dominant spatial modes in the sense of Maximal Covariance Analysis, Canonical Correlation Analysis and Empirical Orthogonal Function analysis across the ensemble. A further representation of the teleconnection that we define here takes the point of view of the predictability of the spatiotemporal variability of the Indian summer monsoon. We find that the strengthening of the ENSO-IM teleconnection is robustly or consistently featured in view of various te...
Multistability is a ubiquitous feature in systems of geophysical relevance and provides key chall... more Multistability is a ubiquitous feature in systems of geophysical relevance and provides key challenges for our ability to predict a system's response to perturbations. Near critical transitions small causes can lead to large effects and - for all practical purposes - irreversible changes in the properties of the system. The Earth climate is multistable: present astronomical and astrophysical conditions support two stable regimes, the warm climate we live in, and a snowball climate, characterized by global glaciation. We first provide an overview of methods and ideas relevant for studying the climate response to forcings and focus on the properties of critical transitions. Following an idea developed by Eckhardt and co. for the investigation of multistable turbulent flows, we study the global instability giving rise to the snowball/warm multistability in the climate system by identifying the climatic edge state, a saddle embedded in the boundary between the two basins of attracti...
The Ghil-Sellers energy balance model of Earth's climate, features -- for a considerable rang... more The Ghil-Sellers energy balance model of Earth's climate, features -- for a considerable range of the solar intensity -- two stable climate states (a warm and a cold snowball Earth), where the bistability results from the celebrated ice-albedo feedback. The unstable solution is obtained and characterized in this paper. We find such unstable states by applying for the first time in a geophysical context the so-called edge tracking method that has been used for studying multiple coexisting states in shear flows. We examine robustness, efficiency, and accuracy properties of the edge tracking algorithm. We find that the procedure is the most efficient when taking a single bisection per cycle. Due to the strong diffusivity of the system trajectories of transient dynamics, initialized between the stable states with respect to the mean temperature, are confined to the heteroclininc trajectory, one which connects the fixed unstable and stable states, after relatively short transient tim...
In a low-order model of the general circulation of the atmosphere we examine the predictability o... more In a low-order model of the general circulation of the atmosphere we examine the predictability of threshold exceedance events of certain observables. The likelihood of such binary events -- the cornerstone also for the categoric (as opposed to probabilistic) prediction of threshold exceedences -- is established from long time series of one or more observables of the same system. The prediction skill is measured by a summary index of the ROC curve that relates the hit- and false alarm rates. Our results for the examined systems suggest that exceedances of higher thresholds are more predictable; or in other words: rare large magnitude, i.e., extreme, events are more predictable than frequent typical events. We find this to hold provided that the bin size for binning time series data is optimized, but not necessarily otherwise. This can be viewed as a confirmation of a counterintuitive (and seemingly contrafactual) statement that was previously formulated for more simple autoregressiv...
We investigate the effects of random perturbations on fully chaotic open systems. Perturbations c... more We investigate the effects of random perturbations on fully chaotic open systems. Perturbations can be applied to each trajectory independently (white noise) or simultaneously to all trajectories (random map). We compare these two scenarios by generalizing the theory of open chaotic systems and introducing a time-dependent conditionally-map-invariant measure. For the same perturbation strength we show that the escape rate of the random map is always larger than that of the noisy map. In random maps we show that the escape rate κ and dimensions D of the relevant fractal sets often depend nonmonotonically on the intensity of the random perturbation. We discuss the accuracy (bias) and precision (variance) of finite-size estimators of κ and D, and show that the improvement of the precision of the estimations with the number of trajectories N is extremely slow (∝ 1/ N). We also argue that the finite-size D estimators are typically biased. General theoretical results are combined with ana...
We search for the signature of universal properties of extreme events, theoretically predicted fo... more We search for the signature of universal properties of extreme events, theoretically predicted for Axiom A flows, in a chaotic and high dimensional dynamical system by studying the convergence of GEV (Generalized Extreme Value) and GP (Generalized Pareto) shape parameter estimates to a theoretical value, expressed in terms of partial dimensions of the attractor, which are global properties. We consider a two layer quasi-geostrophic (QG) atmospheric model using two forcing levels, and analyse extremes of different types of physical observables (local, zonally-averaged energy, and the average value of energy over the mid-latitudes). Regarding the predicted universality, we find closer agreement in the shape parameter estimates only in the case of strong forcing, producing a highly chaotic behaviour, for some observables (the local energy at every latitude). Due to the limited (though very large) data size and the presence of serial correlations, it is difficult to obtain robust statis...
The Earth is well-known to be, in the current astronomical configuration, in a regime where two a... more The Earth is well-known to be, in the current astronomical configuration, in a regime where two asymptotic states can be realised. The warm state we live in is in competition with the ice-covered snowball state. The bistability exists as a result of the positive ice-albedo feedback. In a previous investigation performed on a intermediate complexity climate model we have identified the unstable climate states (Melancholia states) separating the co-existing climates, and studied their dynamical and geometrical properties. The Melancholia states are ice-covered up to the mid-latitudes and attract trajectories initialised on the basins boundary. In this paper, we study how stochastically perturbing the parameter controlling the intensity of the incoming solar radiation impacts the stability of the climate. We detect transitions between the warm and the snowball state and analyse in detail the properties of the noise-induced escapes from the corresponding basins of attraction. We determi...
We conjecture for a linear stochastic differential equation that the predictability of threshold ... more We conjecture for a linear stochastic differential equation that the predictability of threshold exceedances (I) improves with the event magnitude when the noise is a so-called correlated additivemultiplicative (CAM) noise, no matter the nature of the stochastic innovations, and also improves when (II) the noise is purely additive obeying a distribution that decays fast, i.e., not by a power-law, and (III) deteriorates only when the additive noise distribution follows a power-law. The predictability is measured by a summary index of the receiver operating characteristic (ROC) curve. We provide support to our conjecture, to compliment reports in the existing literature on (II), by a set of case studies. Calculations for the prediction skill are conducted in some cases by a direct numerical time-series-data-driven approach, and in other cases by an analytical or semianalytical approach developed here.
In a low-order chaotic global atmospheric circulation model the effects of deterministic chaotic ... more In a low-order chaotic global atmospheric circulation model the effects of deterministic chaotic driving are investigated. As a result of driving, peak-over-threshold type extreme events, e.g. cyclonic activity in the model, become more extreme, with increased frequency of recurrence. When the characteristic time of the driving is comparable to that of the undriven system, a resonance effect with amplified variance shows up. For very fast driving we find a reduced enhancement of variance, which is also the case with white noise driving. Snapshot attractors and their natural measures are determined as a function of time, and a resonance effects is also identified. The extreme value statistics of group maxima is found to follow a Weibull distribution.
The authors argue that the concept of snapshot attractors and of their natural probability distri... more The authors argue that the concept of snapshot attractors and of their natural probability distributions are the only available tools by means of which mathematically sound statements can be made about averages, variances, etc., for a given time instant in a changing climate. A basic advantage of the snapshot approach, which relies on the use of an ensemble, is that the natural distribution and thus any statistics based on it are independent of the particular ensemble used, provided it is initiated in the past earlier than a convergence time. To illustrate these concepts, a tutorial presentation is given within the framework of a low-order model in which the temperature contrast parameter over a hemisphere decreases linearly in time. Furthermore, the averages and variances obtained from the snapshot attractor approach are demonstrated to strongly differ from the traditional 30-yr temporal averages and variances taken along single realizations. The authors also claim that internal va...
We show that a known condition for having rough basin boundaries in bistable 2D maps holds for hi... more We show that a known condition for having rough basin boundaries in bistable 2D maps holds for high-dimensional bistable systems that possess a unique nonattracting chaotic set embedded in their basin boundaries. The condition for roughness is that the cross-boundary Lyapunov exponent λ_x on the nonattracting set is not the maximal one. Furthermore, we provide a formula for the generally noninteger co-dimension of the rough basin boundary, which can be viewed as a generalization of the Kantz-Grassberger formula. This co-dimension that can be at most unity can be thought of as a partial co-dimension, and, so, it can be matched with a Lyapunov exponent. We show in 2D noninvertible- and 3D invertible minimal models, that, formally, it cannot be matched with λ_x. Rather, the partial dimension D_0^(x) that λ_x is associated with in the case of rough boundaries is trivially unity. Further results hint that the latter holds also in higher dimensions. This is a peculiar feature of rough fra...
We study the forced response of the teleconnection between the El NioSouthern Oscillation (ENSO) ... more We study the forced response of the teleconnection between the El NioSouthern Oscillation (ENSO) and global precipitation in general and the Indian summer monsoon (IM) in particular in the Max Planck Institute Grand Ensemble. The forced response of the teleconnection is defined as the time-dependence of a correlation coefficient evaluated over the ensemble. The ensemble-wise variability is taken either wrt. spatial averages or dominant spatial modes in the sense of Maximal Covariance Analysis or Canonical Correlation Analysis or EOF analysis. We find that the strengthening of the ENSO-IM teleconnection is robustly or consistently featured in view of all four teleconnection representations, whether sea surface temperature (SST) or sea level pressure (SLP) is used to characterise ENSO, and both in the historical period and under the RCP8.5 forcing scenario. The main contributor to this strengthening in terms of a linear regression model is the regression coefficient, which can outcompete even a declining ENSO variability in view of using the SLP. We also find that the forced change of the teleconnection is typically nonlinear by (1) formally rejecting the hypothesis that ergodicity holds, i.e., that expected values of temporal correlation coefficients with respect to the ensemble equal the ensemble-wise correlation coefficient itself, and also showing that (2) the trivial contributions of the forced changes of e.g. the mean SST and/or precipitation to temporal correlations are insignificant here. We also provide, in terms of the test statistics, global maps of the degree of nonlinearity/nonergodicity of the forced change of the teleconnection between local precipitation and ENSO.
Edge states in the climate system: exploring global instabilities and critical transitions To cit... more Edge states in the climate system: exploring global instabilities and critical transitions To cite this article: Valerio Lucarini and Tamás Bódai 2017 Nonlinearity 30 R32 View the article online for updates and enhancements. Related content Response formulae for n-point correlations in statistical mechanical systems and application to a problem of coarse graining Valerio Lucarini and Jeroen Wouters-Statistical and dynamical properties of covariant lyapunov vectors in a coupled atmosphere-ocean model-multiscale effects, geometric degeneracy, and error dynamics Stéphane Vannitsem and Valerio Lucarini-Multiple Climate States of Habitable Exoplanets: The Role of Obliquity and
Presentation given at the 21st EGU General Assembly (EGU2019), published on the Proceedings from ... more Presentation given at the 21st EGU General Assembly (EGU2019), published on the Proceedings from the conference held 7-12 April, 2019 in Vienna, Austria, id.17414.
<p>Coupled ocean-atmosphere teleconnections are characteristics of internal... more <p>Coupled ocean-atmosphere teleconnections are characteristics of internal variability which have a forced response just like mean states. It is not trivial how to correctly and optimally estimate the forced response and changes of the El Niño-Southern Oscillation (ENSO)-Indian summer monsoon (ISM) teleconnection under greenhouse forcing. Here we use two different approaches to address it. The first approach, based on the conventional temporal method applied to 30 model simulations in Coupled Model Intercomparison Project Phase 6, suggests no model consensus on changes in the teleconnection on interannual timescale under global warming. The second approach is based on a converged infinite single model initial condition large ensemble (SMILE) and defines the relationship in an instantaneous climatological sense. In view of several characteristics of the teleconnection, a robust long-term strengthening of the teleconnection is found in the MPI-GE but not in the CESM1-LE. We discuss appropriateness and limitations of the two methods. </p>
The weakening of zonal atmospheric circulation, a widely accepted projection of climate change in... more The weakening of zonal atmospheric circulation, a widely accepted projection of climate change in response to global warming, features a weakening of the Indian Ocean Walker circulation (IWC), with an anomalous ascending motion over the western and anomalous descending motion over the eastern Indian Ocean. The projected IWC weakening has previously been attributed to slower warming in the east than the west, that is, to a positive Indian Ocean Dipole (IOD)-like warming pattern. However, such a warming pattern can also be induced by IWC weakening. As a result, the cause-and-effect relationship cannot be easily determined, and the projected change is poorly constrained and highly uncertain. Here, using a suite of coupled climate model simulations under a high-emission scenario, we find that the IWC slowdown is accompanied by not only a positive IOD-like warming pattern but also anomalous meridional circulation that is associated with anomalous descending motion over the eastern Indian...
We give here a brief summary of classical Extreme Value Theory for random variables, followed by ... more We give here a brief summary of classical Extreme Value Theory for random variables, followed by that for deterministic dynamical systems, which is a rapidly developing area of research. Here we would like to contribute to that by conducting a numerical analysis designed to show particular features of extreme value statistics in dynamical systems, and also to explore the validity of the theory. We find that formulae that link the extreme value statistics with geometrical properties of the attractor hold typically for high-dimensional systems-whether a so-called geometric distance observable or a physical observable is concerned. In very low-dimensional settings, however, the fractality of the attractor prevents the system from having an extreme value law, which might well render the evaluation of extreme value statistics meaningless and so ill-suited for application.
We study the forced response of the teleconnection between the El Niño–Southern Oscillation (ENSO... more We study the forced response of the teleconnection between the El Niño–Southern Oscillation (ENSO) and the Indian summer monsoon (IM) in the Max Planck Institute Grand Ensemble, a set of Earth system ensemble simulations under historical and Representative Concentration Pathway (RCP) forcing. The forced response of the teleconnection, or a characteristic of it, is defined as the time dependence of a correlation coefficient evaluated over the ensemble. We consider the temporal variability of spatial averages and that with respect to dominant spatial modes in the sense of Maximal Covariance Analysis, Canonical Correlation Analysis and Empirical Orthogonal Function analysis across the ensemble. A further representation of the teleconnection that we define here takes the point of view of the predictability of the spatiotemporal variability of the Indian summer monsoon. We find that the strengthening of the ENSO-IM teleconnection is robustly or consistently featured in view of various te...
Multistability is a ubiquitous feature in systems of geophysical relevance and provides key chall... more Multistability is a ubiquitous feature in systems of geophysical relevance and provides key challenges for our ability to predict a system's response to perturbations. Near critical transitions small causes can lead to large effects and - for all practical purposes - irreversible changes in the properties of the system. The Earth climate is multistable: present astronomical and astrophysical conditions support two stable regimes, the warm climate we live in, and a snowball climate, characterized by global glaciation. We first provide an overview of methods and ideas relevant for studying the climate response to forcings and focus on the properties of critical transitions. Following an idea developed by Eckhardt and co. for the investigation of multistable turbulent flows, we study the global instability giving rise to the snowball/warm multistability in the climate system by identifying the climatic edge state, a saddle embedded in the boundary between the two basins of attracti...
The Ghil-Sellers energy balance model of Earth's climate, features -- for a considerable rang... more The Ghil-Sellers energy balance model of Earth's climate, features -- for a considerable range of the solar intensity -- two stable climate states (a warm and a cold snowball Earth), where the bistability results from the celebrated ice-albedo feedback. The unstable solution is obtained and characterized in this paper. We find such unstable states by applying for the first time in a geophysical context the so-called edge tracking method that has been used for studying multiple coexisting states in shear flows. We examine robustness, efficiency, and accuracy properties of the edge tracking algorithm. We find that the procedure is the most efficient when taking a single bisection per cycle. Due to the strong diffusivity of the system trajectories of transient dynamics, initialized between the stable states with respect to the mean temperature, are confined to the heteroclininc trajectory, one which connects the fixed unstable and stable states, after relatively short transient tim...
In a low-order model of the general circulation of the atmosphere we examine the predictability o... more In a low-order model of the general circulation of the atmosphere we examine the predictability of threshold exceedance events of certain observables. The likelihood of such binary events -- the cornerstone also for the categoric (as opposed to probabilistic) prediction of threshold exceedences -- is established from long time series of one or more observables of the same system. The prediction skill is measured by a summary index of the ROC curve that relates the hit- and false alarm rates. Our results for the examined systems suggest that exceedances of higher thresholds are more predictable; or in other words: rare large magnitude, i.e., extreme, events are more predictable than frequent typical events. We find this to hold provided that the bin size for binning time series data is optimized, but not necessarily otherwise. This can be viewed as a confirmation of a counterintuitive (and seemingly contrafactual) statement that was previously formulated for more simple autoregressiv...
We investigate the effects of random perturbations on fully chaotic open systems. Perturbations c... more We investigate the effects of random perturbations on fully chaotic open systems. Perturbations can be applied to each trajectory independently (white noise) or simultaneously to all trajectories (random map). We compare these two scenarios by generalizing the theory of open chaotic systems and introducing a time-dependent conditionally-map-invariant measure. For the same perturbation strength we show that the escape rate of the random map is always larger than that of the noisy map. In random maps we show that the escape rate κ and dimensions D of the relevant fractal sets often depend nonmonotonically on the intensity of the random perturbation. We discuss the accuracy (bias) and precision (variance) of finite-size estimators of κ and D, and show that the improvement of the precision of the estimations with the number of trajectories N is extremely slow (∝ 1/ N). We also argue that the finite-size D estimators are typically biased. General theoretical results are combined with ana...
We search for the signature of universal properties of extreme events, theoretically predicted fo... more We search for the signature of universal properties of extreme events, theoretically predicted for Axiom A flows, in a chaotic and high dimensional dynamical system by studying the convergence of GEV (Generalized Extreme Value) and GP (Generalized Pareto) shape parameter estimates to a theoretical value, expressed in terms of partial dimensions of the attractor, which are global properties. We consider a two layer quasi-geostrophic (QG) atmospheric model using two forcing levels, and analyse extremes of different types of physical observables (local, zonally-averaged energy, and the average value of energy over the mid-latitudes). Regarding the predicted universality, we find closer agreement in the shape parameter estimates only in the case of strong forcing, producing a highly chaotic behaviour, for some observables (the local energy at every latitude). Due to the limited (though very large) data size and the presence of serial correlations, it is difficult to obtain robust statis...
The Earth is well-known to be, in the current astronomical configuration, in a regime where two a... more The Earth is well-known to be, in the current astronomical configuration, in a regime where two asymptotic states can be realised. The warm state we live in is in competition with the ice-covered snowball state. The bistability exists as a result of the positive ice-albedo feedback. In a previous investigation performed on a intermediate complexity climate model we have identified the unstable climate states (Melancholia states) separating the co-existing climates, and studied their dynamical and geometrical properties. The Melancholia states are ice-covered up to the mid-latitudes and attract trajectories initialised on the basins boundary. In this paper, we study how stochastically perturbing the parameter controlling the intensity of the incoming solar radiation impacts the stability of the climate. We detect transitions between the warm and the snowball state and analyse in detail the properties of the noise-induced escapes from the corresponding basins of attraction. We determi...
We conjecture for a linear stochastic differential equation that the predictability of threshold ... more We conjecture for a linear stochastic differential equation that the predictability of threshold exceedances (I) improves with the event magnitude when the noise is a so-called correlated additivemultiplicative (CAM) noise, no matter the nature of the stochastic innovations, and also improves when (II) the noise is purely additive obeying a distribution that decays fast, i.e., not by a power-law, and (III) deteriorates only when the additive noise distribution follows a power-law. The predictability is measured by a summary index of the receiver operating characteristic (ROC) curve. We provide support to our conjecture, to compliment reports in the existing literature on (II), by a set of case studies. Calculations for the prediction skill are conducted in some cases by a direct numerical time-series-data-driven approach, and in other cases by an analytical or semianalytical approach developed here.
In a low-order chaotic global atmospheric circulation model the effects of deterministic chaotic ... more In a low-order chaotic global atmospheric circulation model the effects of deterministic chaotic driving are investigated. As a result of driving, peak-over-threshold type extreme events, e.g. cyclonic activity in the model, become more extreme, with increased frequency of recurrence. When the characteristic time of the driving is comparable to that of the undriven system, a resonance effect with amplified variance shows up. For very fast driving we find a reduced enhancement of variance, which is also the case with white noise driving. Snapshot attractors and their natural measures are determined as a function of time, and a resonance effects is also identified. The extreme value statistics of group maxima is found to follow a Weibull distribution.
The authors argue that the concept of snapshot attractors and of their natural probability distri... more The authors argue that the concept of snapshot attractors and of their natural probability distributions are the only available tools by means of which mathematically sound statements can be made about averages, variances, etc., for a given time instant in a changing climate. A basic advantage of the snapshot approach, which relies on the use of an ensemble, is that the natural distribution and thus any statistics based on it are independent of the particular ensemble used, provided it is initiated in the past earlier than a convergence time. To illustrate these concepts, a tutorial presentation is given within the framework of a low-order model in which the temperature contrast parameter over a hemisphere decreases linearly in time. Furthermore, the averages and variances obtained from the snapshot attractor approach are demonstrated to strongly differ from the traditional 30-yr temporal averages and variances taken along single realizations. The authors also claim that internal va...
We show that a known condition for having rough basin boundaries in bistable 2D maps holds for hi... more We show that a known condition for having rough basin boundaries in bistable 2D maps holds for high-dimensional bistable systems that possess a unique nonattracting chaotic set embedded in their basin boundaries. The condition for roughness is that the cross-boundary Lyapunov exponent λ_x on the nonattracting set is not the maximal one. Furthermore, we provide a formula for the generally noninteger co-dimension of the rough basin boundary, which can be viewed as a generalization of the Kantz-Grassberger formula. This co-dimension that can be at most unity can be thought of as a partial co-dimension, and, so, it can be matched with a Lyapunov exponent. We show in 2D noninvertible- and 3D invertible minimal models, that, formally, it cannot be matched with λ_x. Rather, the partial dimension D_0^(x) that λ_x is associated with in the case of rough boundaries is trivially unity. Further results hint that the latter holds also in higher dimensions. This is a peculiar feature of rough fra...
We study the forced response of the teleconnection between the El NioSouthern Oscillation (ENSO) ... more We study the forced response of the teleconnection between the El NioSouthern Oscillation (ENSO) and global precipitation in general and the Indian summer monsoon (IM) in particular in the Max Planck Institute Grand Ensemble. The forced response of the teleconnection is defined as the time-dependence of a correlation coefficient evaluated over the ensemble. The ensemble-wise variability is taken either wrt. spatial averages or dominant spatial modes in the sense of Maximal Covariance Analysis or Canonical Correlation Analysis or EOF analysis. We find that the strengthening of the ENSO-IM teleconnection is robustly or consistently featured in view of all four teleconnection representations, whether sea surface temperature (SST) or sea level pressure (SLP) is used to characterise ENSO, and both in the historical period and under the RCP8.5 forcing scenario. The main contributor to this strengthening in terms of a linear regression model is the regression coefficient, which can outcompete even a declining ENSO variability in view of using the SLP. We also find that the forced change of the teleconnection is typically nonlinear by (1) formally rejecting the hypothesis that ergodicity holds, i.e., that expected values of temporal correlation coefficients with respect to the ensemble equal the ensemble-wise correlation coefficient itself, and also showing that (2) the trivial contributions of the forced changes of e.g. the mean SST and/or precipitation to temporal correlations are insignificant here. We also provide, in terms of the test statistics, global maps of the degree of nonlinearity/nonergodicity of the forced change of the teleconnection between local precipitation and ENSO.
Edge states in the climate system: exploring global instabilities and critical transitions To cit... more Edge states in the climate system: exploring global instabilities and critical transitions To cite this article: Valerio Lucarini and Tamás Bódai 2017 Nonlinearity 30 R32 View the article online for updates and enhancements. Related content Response formulae for n-point correlations in statistical mechanical systems and application to a problem of coarse graining Valerio Lucarini and Jeroen Wouters-Statistical and dynamical properties of covariant lyapunov vectors in a coupled atmosphere-ocean model-multiscale effects, geometric degeneracy, and error dynamics Stéphane Vannitsem and Valerio Lucarini-Multiple Climate States of Habitable Exoplanets: The Role of Obliquity and
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