arXiv subjects

Valerio Lucarini

Publications and source records attributed to Valerio Lucarini.

At least 91 records · Page 5Linked to original sources

arXiv2019

Stochastic Resonance for Non-Equilibrium Systems

Stochastic resonance (SR) is a prominent phenomenon in many natural and engineered noisy system, whereby the response to a periodic forcing is greatly amplified when the intensity of the noise is tuned to within a specific range of values. We propose here a general mathematical framework based on large deviation theory, and, specifically, on the theory of quasi-potentials, for describing SR in noisy N-dimensional non-equilibrium systems possessing two metastable states and undergoing a periodically modulated forcing. The drift and the volatility fields of the equations of motion can be fairly general and the competing attractors of the deterministic dynamics and the edge state living on the basin boundary can, in principle, feature chaotic dynamics. Similarly, the perturbation field of the forcing can be fairly general. Our approach is able to recover as special cases the classical results previously presented in the literature for systems obeying detailed balance and allows for expressing the parameters describing SR and the statistics of residence times in the two-state approximation in terms of the unperturbed drift field, the volatility field, and the perturbation field. We clarify which specific properties of the forcing are relevant for amplifying or suppressing SR in a system, and classify forcings according to classes of equivalence. Our results indicate a route for a detailed understanding of SR in rather general systems.

cond-mat.stat-mech↗

arXiv2019

A New Mathematical Framework for Atmospheric Blocking Events

We use a simple yet Earth-like atmospheric model to propose a new framework for understanding the mathematics of blocking events. Analysing error growth rates along a very long model trajectory, we show that blockings are associated with conditions of anomalously high instability of the atmosphere. Additionally, the lifetime of a blocking is positively correlated with the intensity of such an anomaly, against intuition. In the case of Atlantic blockings, predictability is especially reduced at the onset and decay of the blocking, while a relative increase of predictability is found in the mature phase, while the opposite holds for Pacific blockings, for which predictability is lowest in the mature phase. We associate blockings to a specific class of unstable periodic orbits (UPOs), natural modes of variability that cover the attractor of the system. The UPOs differ substantially in terms of instability, which explains the diversity of the atmosphere in terms predictability. The UPOs associated to blockings are indeed anomalously unstable, which leads to them being rarely visited. The onset of a blocking takes place when the trajectory of the system hops into the neighbourhood of one of these special UPOs. The decay takes place when the trajectory hops back to the neighbourhood of usual, less unstable UPOs associated with zonal flow. This justifies the classical Markov chains-based analysis of transitions between weather regimes. The existence of UPOs differing in the dimensionality of their unstable manifold indicates a very strong violation of hyperbolicity in the model, which leads to a lack of structural stability. We propose that this is could be a generic feature of atmospheric models and might be a fundamental cause behind difficulties in representing blockings for the current climate and uncertainties in predicting how their statistics will change as a result of climate change.

physics.ao-ph↗

arXiv2019

Response and Sensitivity Using Markov Chains

Dynamical systems are often subject to forcing or changes in their governing parameters and it is of interest to study how this affects their statistical properties. A prominent real-life example of this class of problems is the investigation of climate response to perturbations. In this respect, it is crucial to determine what the linear response of a system is to small perturbations as a quantification of sensitivity. Alongside previous work, here we use the transfer operator formalism to study the response and sensitivity of a dynamical system undergoing perturbations. By projecting the transfer operator onto a suitable finite dimensional vector space, one is able to obtain matrix representations which determine finite Markov processes. Further, using perturbation theory for Markov matrices, it is possible to determine the linear and nonlinear response of the system given a prescribed forcing. Here, we suggest a methodology which puts the scope on the evolution law of densities (the Liouville/Fokker-Planck equation), allowing to effectively calculate the sensitivity and response of two representative dynamical systems.

nlin.CD↗

arXiv2019

Effects of Stochastic Parametrization on Extreme Value Statistics

Extreme geophysical events are of crucial relevance to our daily life: they threaten human lives and cause property damage. To assess the risk and reduce losses, we need to model and probabilistically predict these events. Parametrizations are computational tools used in Earth system models, which are aimed at reproducing the impact of unresolved scales on resolved scales. The performance of parametrizations has usually been examined on typical events rather than on extreme events. In this paper we consider a modified version of the two-level Lorenz'96 model and investigate how two parametrizations of the fast degrees of freedom perform in terms of the representation of extreme events. One parametrization is constructed following Wilks (2005) and is constructed through an empirical fitting procedure; the other parametrization is constructed through the statistical mechanical approach proposed by Wouters and Lucarini (2012, 2013). The two strategies show different advantages and disadvantages. We discover that the agreement between parametrized models and true model is in general worse when looking at extremes rather than at the bulk of the statistics. The results suggest that stochastic parametrizations should be accurately and specifically tested against their performance on extreme events, as usual optimization procedures might neglect them.

nlin.CD↗

arXiv2019

Spectral decomposition and extremes of atmospheric meridional energy transport in Northern Hemisphere midlatitudes

The atmospheric meridional energy transport in the Northern Hemisphere midlatitudes is mainly accomplished by planetary and synoptic waves. A decomposition into wave components highlights the strong seasonal dependence of the transport, with both the total transport and the contributions from planetary and synoptic waves peaking in winter. In both winter and summer months, poleward transport extremes primarily result from a constructive interference between planetary and synoptic motions. The contribution of the mean meridional circulation is close to climatology. Equatorward transport extremes feature a mean meridional equatorward transport in winter, while the planetary and synoptic modes mostly transport energy poleward. In summer, a systematic destructive interference occurs, with planetary modes mostly transporting energy equatorward and synoptic modes again poleward. This underscores that baroclinic conversion dominates regardless of season in the synoptic wave modes, whereas the planetary waves can be either free or forced, depending on the season.

physics.ao-ph↗

arXiv2019

Transitions across Melancholia States in a Climate Model: Reconciling the Deterministic and Stochastic Points of View

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 determine the most probable paths for the transitions and find evidence that the Melancholia states act as gateways, similarly to saddle points in an energy landscape.

physics.ao-ph↗

arXiv2019

A new diagnostic tool for water, energy and entropy budgets in climate models

This work presents a novel diagnostic tool for studying the thermodynamics of the climate systems with a wide range of applications, from sensitivity studies to model tuning. It includes a number of modules for assessing the internal energy budget, the hydrological cycle, the Lorenz Energy Cycle and the material entropy production, respectively. The routine receives as inputs energy fluxes at surface and at the Top-of-Atmosphere (TOA), for the computation of energy budgets at Top-of-Atmosphere (TOA), at the surface, and in the atmosphere as a residual. Meridional enthalpy transports are also computed from the divergence of the zonal mean energy budget fluxes; location and intensity of peaks in the two hemispheres are then provided as outputs. Rainfall, snowfall and latent heat fluxes are received as inputs for computing the water mass and latent energy budgets. If a land-sea mask is provided, the required quantities are separately computed over continents and oceans. The diagnostic tool also computes the Lorenz Energy Cycle (LEC) and its storage/conversion terms as annual mean global and hemispheric values. In order to achieve this, one needs to provide as input three-dimensional daily fields of horizontal wind velocity and temperature in the troposphere. Two methods have been implemented for the computation of the material entropy production, one relying on the convergence of radiative heat fluxes in the atmosphere (indirect method), one combining the irreversible processes occurring in the climate system, particularly heat fluxes in the boundary layer, the hydrological cycle and the kinetic energy dissipation as retrieved from the residuals of the LEC. A version of the diagnostic tool is included in the Earth System Model eValuation Tool (ESMValTool) community diagnostics, in order to assess the performances of soon available CMIP6 model simulations.

physics.ao-ph↗

arXiv2019

A Large Deviation Theory-based Analysis of Heat Waves and Cold Spells in a Simplified Model of the General Circulation of the Atmosphere

We study temporally persistent and spatially extended extreme events of temperature anomalies, i.e. heat waves and cold spells, using large deviation theory. To this end, we consider a simplified yet Earth-like general circulation model of the atmosphere and numerically estimate large deviation rate functions of near-surface temperature in the mid-latitudes. We find that, after a re-normalisation based on the integrated auto-correlation, the rate function one obtains at a given latitude by looking, locally in space, at long time averages agrees with what is obtained, instead, by looking, locally in time, at large spatial averages along the latitude. This is a result of scale symmetry in the spatial-temporal turbulence and of the fact that advection is primarily zonal. This agreement hints at the universality of large deviations of the temperature field. Furthermore, we discover that the obtained rate function is able to describe spatially extended and temporally persistent heat waves or cold spells, if we consider temporal averages of spatial averages over intermediate spatial scales. Finally, we find out that large deviations are relatively more likely to occur when looking at these spatial averages performed over intermediate scales, thus pointing to the existence of weather patterns associated to the low-frequency variability of the atmosphere. Extreme value theory is used to benchmark our results.

cond-mat.stat-mech↗

arXiv2019

Climate sensitivity to ozone and its relevance on the habitability of Earth-like planets

Atmospheric ozone plays an important role on the temperature structure of the atmosphere. However, it has not been included in previous studies on the effect of an increasing solar radiation on the Earth's climate. Here we study the climate sensitivity to the presence/absence of ozone with an increasing solar forcing for the first time with a global climate model. We show that the warming effect of ozone increases both the humidity of the lower atmosphere and the surface temperature. Under the same solar irradiance, the mean surface temperature is 7 K higher than in an analog planet without ozone. Therefore, the moist greenhouse threshold, the state at which water vapor becomes abundant in the stratosphere, is reached at a lower solar irradiance (1572 Wm^-2 with respect to 1647 Wm^-2 in the case without ozone). Our results imply that ozone reduces the maximum solar irradiance at which Earth-like planets would remain habitable.

astro-ph.EP↗

arXiv2019

Climate Sensitivity to Carbon Dioxide and Moist Greenhouse threshold of Earth-like planets under an increasing solar forcing

Carbon dioxide is one of the major contributors to the radiative forcing, increasing both the temperature and the humidity of Earth's atmosphere. If the stellar irradiance increases and water becomes abundant in the stratosphere of an Earth-like planet, it will be dissociated and the resultant hydrogen will escape from the atmosphere. This state is called the moist greenhouse threshold (MGT). Using a global climate model (GCM) of intermediate complexity, we explore how to identify this state for different CO2 concentrations and including the radiative effect of atmospheric ozone for the first time. We show that the moist greenhouse threshold correlates with the inflection point in the water vapor mixing ratio in the stratosphere and a peak in the climate sensitivity. For CO2 concentrations between 560 ppm and 200 ppm, the moist greenhouse threshold is reached at a surface temperature of 320 K. Despite the higher simplicity of our model, our results are consistent with similar simulations without ozone by complex GCMs, suggesting that they are robust indicators of the MGT. We discuss the implications for inner edge of the habitable zone as well as the water loss timescales for Earth analog planets.

astro-ph.EP↗

arXiv2019

Lyapunov analysis of multiscale dynamics: The slow bundle of the two-scale Lorenz 96 model

We investigate the geometrical structure of instabilities in the two-scales Lorenz 96 model through the prism of Lyapunov analysis. Our detailed study of the full spectrum of covariant Lyapunov vectors reveals the presence of a slow bundle in tangent space, composed by a set of vectors with a significant projection on the slow degrees of freedom; they correspond to the smallest (in absolute value) Lyapunov exponents and thereby to the longer time scales. We show that the dimension of the slow bundle is extensive in the number of both slow and fast degrees of freedom, and discuss its relationship with the results of a finite-size analysis of instabilities, supporting the conjecture that the slow-variable behavior is effectively determined by a non-trivial subset of degrees of freedom. More precisely, we show that the slow bundle corresponds to the Lyapunov spectrum region where fast and slow instability rates overlap, "mixing" their evolution into a set of vectors which simultaneously carry information on both scales. We suggest these results may pave the way for future applications to ensemble forecasting and data assimilations in weather and climate models.

nlin.CD↗

arXiv2018

Reconsidering the relationship of the El Niño--Southern Oscillation and the Indian monsoon using ensembles in Earth system models

We study the relationship between the El Niño--Southern Oscillation (ENSO) and the Indian summer monsoon in ensemble simulations from state-of-the-art climate models, the Max Planck Institute Earth System Model (MPI-ESM) and the Community Earth System Model (CESM). We consider two simple variables: the Tahiti--Darwin sea-level pressure difference and the Northern Indian precipitation. We utilize ensembles converged to the system's snapshot attractor for analyzing possible changes (i) in the teleconnection between the fluctuations of the two variables, and (ii) in their climatic means. (i) With very high confidence, we detect an increase in the strength of the teleconnection, as a response to the forcing, in the MPI-ESM under historical forcing between 1890 and 2005, concentrated to the end of this period. We explain that our finding does not contradict instrumental observations, since their existing analyses regarding the nonstationarity of the teleconnection are either methodologically unreliable, or consider an ill-defined teleconnection concept. In the MPI-ESM we cannot reject stationarity between 2006 and 2099 under the Representative Concentration Pathway 8.5 (RCP8.5), and in a 110-year-long 1-percent pure CO2 scenario; neither can we in the CESM between 1960 and 2100 with historical forcing and RCP8.5. (ii) In the latter ensembles, the climatic mean is strongly displaced in the phase space projection spanned by the two variables. This displacement is nevertheless linear. However, the slope exhibits a strong seasonality, falsifying a hypothesis of a universal, emergent relationship between these two climatic means, excluding applicability in an emergent constraint.

physics.ao-ph↗

arXiv2018

Revising and Extending the Linear Response Theory for Statistical Mechanical Systems: Evaluating Observables as Predictors and Predictands

Linear response theory has developed into a formidable set of tools for studying the forced behaviour of a large variety of systems - including out of equilibrium ones. In this paper we provide a new angle on the problem, by studying under which conditions it is possible to perform predictions on the response of a given observable of a system to perturbations, using one or more other observables of the same system as predictors, and thus bypassing the need to know all the details of the acting forcing. Thus, we break the rigid separation between forcing and response, which is key in linear response theory, and revisit the concept of causality. As a result, the surrogate Green functions one constructs for predicting the response of the observable of interest may have support that is not necessarily limited to the nonnegative time axis. This implies that not all observables are equally good as predictands when a given forcing is applied, as result of the properties of their corresponding susceptibility. In particular, problems emerge from the presence of complex zeros. We derive general explicit formulas that, in absence of such pathologies, allow one to reconstruct the response of an observable of interest to N independent forcings by using as predictors N other observables. We provide a thorough test of the theory and of the possible pathologies by using numerical simulations of the paradigmatic Lorenz '96 model. Our results are potentially relevant for problems like the reconstruction of data from proxy signals, like in the case of paleoclimate, and, in general, the analysis of signals and feedbacks in complex systems where our knowledge on the system is limited, as in neurosciences. Our technique might also be useful for reconstructing the response to forcings of a spatially extended system in a given location by looking at the response in a separate location.

cond-mat.stat-mech↗

arXiv2018

Equivalence of nonequilibrium ensembles in turbulence models

Understanding under what conditions it is possible to construct equivalent ensembles is key to advancing our ability to connect microscopic and macroscopic properties of non-equilibrium statistical mechanics. In the case of fluid dynamical systems, one issue is to test whether different models for viscosity lead to the same macroscopic properties of the fluid systems in different regimes. Such models include, besides the standard choice of constant viscosity, cases where the time symmetry of the evolution equations is exactly preserved, as it must be in the corresponding microscopic systems, when available. Here a time-reversible dynamics is obtained by imposing the conservation of global observables. We test the equivalence of reversible and irreversible ensembles for the case of a multiscale shell model of turbulence. We verify that the equivalence is obeyed for the mean values of macroscopic observables, up to an error that vanishes as the system becomes more and more chaotic.

physics.flu-dyn↗

arXiv2018

Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models

The stability properties of intermediate-order climate models are investigated by computing their Lyapunov exponents (LEs). The two models considered are PUMA (Portable University Model of the Atmosphere), a primitive-equation simple general circulation model, and MAOOAM (Modular Arbitrary-Order Ocean-Atmosphere Model), a quasi-geostrophic coupled ocean-atmosphere model on a beta-plane. We wish to investigate the effect of the different levels of filtering on the instabilities and dynamics of the atmospheric flows. Moreover, we assess the impact of the oceanic coupling, the dissipation scheme and the resolution on the spectra of LEs. The PUMA Lyapunov spectrum is computed for two different values of the meridional temperature gradient defining the Newtonian forcing. The increase of the gradient gives rise to a higher baroclinicity and stronger instabilities, corresponding to a larger dimension of the unstable manifold and a larger first LE. The convergence rate of the rate functional for the large deviation law of the finite-time Lyapunov exponents (FTLEs) is fast for all exponents, which can be interpreted as resulting from the absence of a clear-cut atmospheric time-scale separation in such a model. The MAOOAM spectra show that the dominant atmospheric instability is correctly represented even at low resolutions. However, the dynamics of the central manifold, which is mostly associated to the ocean dynamics, is not fully resolved because of its associated long time scales, even at intermediate orders. This paper highlights the need to investigate the natural variability of the atmosphere-ocean coupled dynamics by associating rate of growth and decay of perturbations to the physical modes described using the formalism of the covariant Lyapunov vectors and to consider long integrations in order to disentangle the dynamical processes occurring at all time scales.

physics.ao-ph↗

arXiv2018

A Statistical Mechanical Approach for the Parametrization of the Coupling in a Fast-Slow System

Constructing accurate, flexible, and efficient parametrizations is one of the great challenges in the numerical modelling of geophysical fluids. We consider here the simple yet paradigmatic case of a Lorenz 84 model forced by a Lorenz 63 model and derive a parametrization using a recently developed statistical mechanical methodology based on the Ruelle response theory. We derive an expression for the deterministic and the stochastic component of the parametrization and we show that the approach allows for dealing seamlessly with the case of the Lorenz 63 being a fast as well as a slow forcing compared to the characteristic time scales of the Lorenz 84 model. We test our results using both standard metrics based on the moments of the variables of interest as well as Wasserstein distance between the projected measure of the original system on the Lorenz 84 model variables and the measure of the parametrized one. By testing our methods on reduced phase spaces obtained by projection, we find support to the idea that comparisons based on the Wasserstein distance might be of relevance in many applications despite the curse of dimensionality.

cond-mat.stat-mech↗

arXiv2017

Crisis of the Chaotic Attractor of a Climate Model: A Transfer Operator Approach

The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are characterised by a single or a pair of characteristic exponents crossing the imaginary axis. The approach of such bifurcations in the presence of noise can be inferred from the slowing down of the correlation decay. On the other hand, little is known about global bifurcations involving high-dimensional attractors with positive Lyapunov exponents. The global stability of chaotic attractors may be characterised by the spectral properties of the Koopman or the transfer operators governing the evolution of statistical ensembles. It has recently been shown that a boundary crisis in the Lorenz flow coincides with the approach to the unit circle of the eigenvalues of these operators associated with motions about the attractor, the stable resonances. A second type of resonances, the unstable resonances, is responsible for the decay of correlations and mixing on the attractor. In the deterministic case, those cannot be expected to be affected by general boundary crises. Here, however, we give an example of chaotic system in which slowing down of the decay of correlations of some observables does occur at the approach of a boundary crisis. The system considered is a high-dimensional, chaotic climate model of physical relevance. Moreover, coarse-grained approximations of the transfer operators on a reduced space, constructed from a long time series of the system, give evidence that this behaviour is due to the approach of unstable resonances to the unit circle. That the unstable resonances are affected by the crisis can be physically understood from the fact that the process responsible for the instability, the ice-albedo feedback, is also active on the attractor. Implications regarding response theory and the design of early-warning signals are discussed.

nlin.CD↗

arXiv2017

A proof of concept for scale-adaptive parameterizations: the case of the Lorenz '96 model

Constructing efficient and accurate parameterizations of sub-grid scale processes is a central area of interest in the numerical modelling of geophysical fluids. Using a modified version of the two-level Lorenz '96 model, we present here a proof of concept of a scale-adaptive parameterization constructed using statistical mechanical arguments. By a suitable use of the Ruelle response theory and of the Mori-Zwanzig projection method, it is possible to derive explicitly a parameterization for the fast variables that translates into deterministic, stochastic and non-markovian contributions to the equations of motion of the variables of interest. We show that our approach is computationally parsimonious, has great flexibility, as it is explicitly scale-adaptive, and we prove that it is competitive compared to empirical ad-hoc approaches. While the parameterization proposed here is universal and can be easily analytically adapted to changes in the parameters' values by a simple rescaling procedure, the parameterization constructed with the ad-hoc approach needs to be recomputed each time the parameters of the systems are changed. The price of the higher flexibility of the method proposed here is having a lower accuracy in each individual case.

cond-mat.stat-mech↗