arXiv subjects

Valerio Lucarini

Publications and source records attributed to Valerio Lucarini.

At least 37 records · Page 2Linked to original sources

arXiv2025

Time-Lagged Recurrence: a data-driven method to estimate the predictability of dynamical systems

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales. Classical approaches based on the Lyapunov spectrum rely on the knowledge of the dynamic forward operator, or of a data-derived approximation of it. This operator is typically unknown, or the data are too noisy to derive its faithful representation. Here we propose a new data-driven approach to analyze the local predictability of dynamical systems. This method, based on the concept of recurrence, is closely linked to the well-established framework of local dynamical indices. When applied to both idealized systems and real-world datasets arising from large-scale atmospheric fields, our new approach proves its effectiveness in estimating local predictability. Additionally, we discuss its relationship with other local dynamical indices, and how it reveals the scale-dependent nature of predictability. Furthermore, we explore its link to information theory, its extension that includes a weighting strategy, and its real-time application. We believe these aspects collectively demonstrate its potential as a powerful diagnostic tool for complex systems.

nlin.CD↗

arXiv2025

Spatio-temporal Dynamical Indices for Complex Systems

Complex systems span multiple spatial and temporal scales, making their dynamics challenging to understand and predict. This challenge is especially daunting when one wants to study localized and/or rare events. Advances in dynamical systems theory, including the development of state-dependent dynamical indices, namely local dimension and persistence, have provided powerful tools for studying these phenomena. However, existing applications of such indices rely on a predefined and fixed spatial domain, that provides a single scalar quantity for the entire region of interest. This aspect prevents understanding the spatially localized dynamical behavior of the system. In this work, we introduce Spatio-temporal Dynamical Indices (SDIs), that leverage the existing framework of state-dependent local dimension and persistence. SDIs are obtained via a sliding window approach, enabling the exploration of space-dependent properties in spatio-temporal data. As an example, we show that, through this framework, we are able to reconcile previously different perspectives on European summertime heatwaves. This result showcases the importance of accounting for spatial scales when performing scale-dependent dynamical analyses.

physics.ao-ph↗

arXiv2025

Deficiency of equation-finding approach to data-driven modeling of dynamical systems

Finding the governing equations from data by sparse optimization has become a popular approach to deterministic modeling of dynamical systems. Considering the physical situations where the data can be imperfect due to disturbances and measurement errors, we show that for many chaotic systems, widely used sparse-optimization methods for discovering governing equations produce models that depend sensitively on the measurement procedure, yet all such models generate virtually identical chaotic attractors, leading to a striking limitation that challenges the conventional notion of equation-based modeling in complex dynamical systems. Calculating the Koopman spectra, we find that the different sets of equations agree in their large eigenvalues and the differences begin to appear when the eigenvalues are smaller than an equation-dependent threshold. The results suggest that finding the governing equations of the system and attempting to interpret them physically may lead to misleading conclusions. It would be more useful to work directly with the available data using, e.g., machine-learning methods.

nlin.CD↗

arXiv2025

Interpretable and Equation-Free Response Theory for Complex Systems

Response theory provides a pathway for understanding the sensitivity of a system and for predicting how its statistical properties change when a perturbation is applied. In the case of complex and multiscale systems, to achieve enhanced practical applicability, response theory should be interpretable, capable of focusing on relevant timescales, and amenable to data-driven and equation-agnostic implementations. Along these lines, in the spirit of Markov state modelling, we present linear and nonlinear response formulas for Markov chains. We obtain simple and easily implementable expressions that can be used to predict the response of observables as well as of higher-order correlations. The methodology proposed here can be implemented in a purely data-driven setting and even if the underlying evolution equations are unknown. The use of algebraic expansions inspired by Koopmanism allows to elucidate the role of different time scales and modes of variability, and to find explicit and interpretable expressions for the Green's functions at all orders. This is a major advantage of the framework proposed here. We illustrate our methodology in a very simple yet instructive metastable system. Finally, our results provide a dynamical foundation for the Prony method, which is commonly used for the statistical analysis of discrete time signals.

cond-mat.stat-mech↗

arXiv2025

A General Framework for Linking Free and Forced Fluctuations via Koopmanism

The link between forced and free fluctuations for nonequilibrium systems can be described via a generalized version of the celebrated fluctuation-dissipation theorem. The use of the formalism of the Koopman operator makes it possible to deliver an intepretable form of the response operators written as a sum of exponentially decaying terms, each associated one-to-one with a mode of natural variability of the system. Here we showcase on a stochastically forced version of the celebrated Lorenz '63 model the feasibility and skill of such an approach by considering different Koopman dictionaries, which allows us to treat also seamlessly coarse-graining approaches like the Ulam method. Our findings provide support for the development of response theory-based investigation methods also in an equation-agnostic, data-driven environment.

cond-mat.stat-mech↗

arXiv2025

Bridging the Gap between Koopmanism and Response Theory: Using Natural Variability to Predict Forced Response

The fluctuation-dissipation theorem is a cornerstone result in statistical mechanics that can be used to translate the statistics of the free natural variability of a system into information on its forced response to perturbations. By combining this viewpoint on response theory with the key ingredients of Koopmanism, it is possible to deconstruct virtually any response operator into a sum of terms, each associated with a specific mode of natural variability of the system. This dramatically improves the interpretability of the resulting response formulas. We show here on three simple yet mathematically meaningful examples how to use the Extended Dynamical Mode Decomposition (EDMD) algorithm on an individual trajectory of the system to compute with high accuracy correlation functions as well as Green functions associated with acting forcings. This demonstrates the great potential of using Koopman analysis for the key problem of evaluating and testing the sensitivity of a complex system.

cond-mat.stat-mech↗

arXiv2025

The role of edge states for early-warning of tipping points

Tipping points (TP) are often described as low-dimensional bifurcations, and are associated with early-warning signals (EWS) due to critical slowing down (CSD). CSD is an increase in amplitude and correlation of noise-induced fluctuations away from a reference attractor as the TP is approached. But for high-dimensional systems it is not obvious which variables or observables would display the critical dynamics and carry CSD. Many variables may display no CSD, or show changes in variability not related to a TP. It is thus helpful to identify beforehand which observables are relevant for a given TP. Here we propose this may be achieved by knowledge of an unstable edge state that separates the reference from an alternative attractor that remains after the TP. This is because stochastic fluctuations away from the reference attractor are preferentially directed towards the edge state along a most likely path (the instanton). As the TP is approached the edge state and reference attractor typically become closer, and the fluctuations can evolve further along the instanton. This can be exploited to find observables with substantial CSD, which we demonstrate using conceptual dynamical systems models and climate model simulations of a collapse of the Atlantic Meridional Overturning Circulation (AMOC).

nlin.CD↗

arXiv2024

Detecting and Attributing Change in Climate and Complex Systems: Foundations, Green's Functions, and Nonlinear Fingerprints

Detection and attribution (D&A) studies are cornerstones of climate science, providing crucial evidence for policy decisions. Their goal is to link observed climate change patterns to anthropogenic and natural drivers via the optimal fingerprinting method (OFM). We show that response theory for nonequilibrium systems offers the physical and dynamical basis for OFM, including the concept of causality used for attribution. Our framework clarifies the method's assumptions, advantages, and potential weaknesses. We use our theory to perform D&A for prototypical climate change experiments performed on an energy balance model and on a low-resolution coupled climate model. We also explain the underpinnings of degenerate fingerprinting, which offers early warning indicators for tipping points. Finally, we extend the OFM to the nonlinear response regime. Our analysis shows that OFM has broad applicability across diverse stochastic systems influenced by time-dependent forcings, with potential relevance to ecosystems, quantitative social sciences, and finance, among others.

physics.ao-ph↗

arXiv2024

The Typicality of Regimes Associated with Northern Hemisphere Heatwaves

We study the hemispheric to continental scale regimes that lead to summertime heatwaves in the Northern Hemisphere. By using a powerful data mining methodology - archetype analysis - we identify characteristic spatial patterns consisting of a blocking high pressure systems embedded within a meandering upper atmosphere circulation that is longitudinally modulated by coherent Rossby Wave Packets. Periods when these atmospheric regimes are strongly expressed correspond to large increases in the likelihood of extreme surface temperature. Most strikingly, these regimes are shown to be typical of surface extremes and frequently reoccur. Three well publicised heatwaves are studied in detail - the June-July 2003 western European heatwave, the August 2010 "Russian" heatwave, and the June 2021 "Heatdome" event across western North America, and are shown to be driven by blocking high pressure systems linked to stalled Rossby Wave Packets. We discuss the implications of our work for long-range prediction or early warning, climate model assessment and post-event diagnosis.

physics.ao-ph↗

arXiv2024

Melancholia States of the Atlantic Meridional Overturning Circulation

The Atlantic Meridional Overturning Circulation (AMOC) is a much studied component of the climate system, because its suspected multistability is associated with tipping behaviour yielding potentially large regional and global climatic impacts. In this paper we investigate the global stability properties of the system using an ocean general circulation model. We construct an unstable AMOC state, i.e., an unstable solution of the flow that resides between the stable regimes of a vigorous and collapsed AMOC. Such a solution, also known as a Melancholia or edge state, is a dynamical saddle embedded in the boundary separating the competing basins of attraction. It is physically relevant since it lies on the most probable path of a noise-induced transition between the two stable regimes, and because tipping occurs when one of the attractors and the Melancholia state collide. Its properties may thus give hints towards physical mechanisms and predictability of the critical transition. We find that while the AMOC Melancholia state as viewed from its upper ocean properties lies between the vigorous and collapsed regimes, it is characterized by an Atlantic deep ocean that is fresher and colder compared to both stable regimes. The Melancholia state has higher dynamic enthalpy than either stable state, representing a state of higher potential energy that is in good agreement with the dynamical landscape view on metastability.

physics.ao-ph↗

arXiv2024

Saddle avoidance of noise-induced transitions in multiscale systems

In multistable dynamical systems driven by weak Gaussian noise, transitions between competing states are often assumed to pass via a saddle on the separating basin boundary. By contrast, we show that timescale separation can cause saddle avoidance in non-gradient systems. Using toy models from neuroscience and ecology, we study cases where sample transitions deviate strongly from the instanton predicted by Freidlin-Wentzell theory, even for weak finite noise. We attribute this to a flat quasipotential and present an approach based on the Onsager-Machlup action to aptly predict transition paths.

math.DS↗

arXiv2024

Agnostic detection of large-scale weather patterns in the northern hemisphere: from blockings to teleconnections

Detecting recurrent weather patterns and understanding the transitions between such regimes are key to advancing our knowledge on the low-frequency variability of the atmosphere and have important implications in terms of weather and climate-related risks. We adapt an analysis pipeline inspired by Markov State Modelling and detect in an unsupervised manner the dominant winter mid-latitude Northern Hemisphere weather patterns in the Atlantic and Pacific sectors. The daily 500 hPa geopotential height fields are first classified in $\sim 200$ microstates. The weather dynamics is then represented in the basis of these microstates and the slowest decaying modes are identified from the spectral properties of the transition probability matrix. These modes are defined on the basis of the nonlinear dynamical processes of the system and not as tentative metastable states as often done in Markov state analysis. In the Atlantic and Pacific sectors slow relaxation processes are mainly related to transitions between blocked regimes and zonal flow. We also find strong evidence of a dynamical regime associated with the simultaneous Atlantic-Pacific blocking. When the analysis is performed in a broader geographical region of the Atlantic sector, we discover that the slowest relaxation modes of the system are associated with transitions between dynamical regimes that resemble teleconnection patterns like the North Atlantic Oscillation and weather regimes like the Scandinavian and Greenland blocking, yet have a much stronger dynamical foundation than classical methods based e.g. on EOF analysis. Our method clarifies that, as a result of the lack of a time-scale separation in the atmospheric variability of the mid-latitudes, there is no clear-cut way to represent the atmospheric dynamics in terms of few, well-defined modes of variability.

physics.ao-ph↗

arXiv2023

Limits to predictability of the asymptotic state of the Atlantic Meridional Overturning Circulation in a conceptual climate model

Anticipating critical transitions in the Earth system is of great societal relevance, yet there may be intrinsic limitations to their predictability. For instance, from the theory of dynamical systems possessing multiple chaotic attractors, it is known that the asymptotic state depends sensitively on the initial condition in the proximity of a fractal basin boundary. Here, we approach the problem of final-state sensitivity of the Atlantic Meridional Overturning Circulation (AMOC) using a conceptual climate model, composed of a slow bistable ocean coupled to a fast chaotic atmosphere. First, we explore the occurrence of long chaotic transients in the monostable regime, which can mask a loss of stability near bifurcations. In the bistable regime, we explicitly construct the chaotic saddle using the edge tracking technique. Quantifying the final-state sensitivity through the maximum Lyapunov exponent and the lifetime of the saddle, we find that the system exhibits a fractal basin boundary with almost full phase space dimension, implying vanishing predictability of the second kind near the basin boundary. Our results demonstrate the usefulness of studying non-attracting chaotic sets in the context of predicting climatic tipping points, and provide guidance for the interpretation of higher-dimensional models such as general circulation models.

nlin.CD↗

arXiv2023

Probabilistic Measures for Biological Adaptation and Resilience

This paper introduces a novel approach to quantifying ecological resilience in biological systems, particularly focusing on noisy systems responding to episodic disturbances with sudden adaptations. Incorporating concepts from non-equilibrium statistical mechanics, we propose a measure termed `ecological resilience through adaptation,' specifically tailored to noisy, forced systems that undergo physiological adaptation in the face of stressful environmental changes. Randomness plays a key role, accounting for model uncertainty and the inherent variability in the dynamical response among components of biological systems. Our measure of resilience is rooted in the probabilistic description of states within these systems, and is defined in terms of the dynamics of the ensemble average of a model-specific observable quantifying success or well-being. Our approach utilizes stochastic linear response theory to compute how the expected success of a system, originally in statistical equilibrium, dynamically changes in response to a environmental perturbation and a subsequent adaptation. The resulting mathematical derivations allow for the estimation of resilience in terms of ensemble averages of simulated or experimental data. Finally, through a simple but clear conceptual example, we illustrate how our resilience measure can be interpreted and compared to other existing frameworks in the literature. The methodology is general but inspired by applications in plant systems, with the potential for broader application to complex biological processes.

q-bio.QM↗

arXiv2023

Multistability and Intermediate Tipping of the Atlantic Ocean Circulation

Tipping points (TP) in climate sub-systems are usually thought to occur at a well-defined, critical forcing parameter threshold, via destabilization of the system state by a single, dominant positive feedback. However, coupling to other sub-systems, additional feedbacks, and spatial heterogeneity may promote further small-amplitude, abrupt reorganizations of geophysical flows at forcing levels lower than the critical threshold. Using a primitive-equation ocean model we simulate a collapse of the Atlantic Meridional Overturning Circulation (AMOC) due to increasing glacial melt. Considerably prior to the collapse, various abrupt, qualitative changes in AMOC variability occur. These intermediate tipping points (ITP) are transitions between multiple stable circulation states. Using 2.75 million years of model simulations, we uncover a very rugged stability landscape featuring parameter regions of up to nine coexisting stable states. The path to an AMOC collapse via a sequence of ITPs depends on the rate of change of the meltwater input. This challenges our ability to predict and define safe limits for TPs.

physics.ao-ph↗

arXiv2023

Response Theory Identifies Reaction Coordinates and Explains Critical Phenomena in Noisy Interacting Systems

We consider a class of nonequilibrium systems of interacting agents with pairwise interactions and quenched disorder in the dynamics featuring, in the thermodynamic limit, phase transitions. We provide conditions on the microscopic structure of interactions among the agents that lead to a dimension reduction of the system in terms of a finite number of reaction coordinates. Such reaction coordinates prove to be proper nonequilibrium thermodynamic variables as they carry information on correlation, memory and resilience properties of the system. Phase transitions can be identified and quantitatively characterised as singularities of the complex valued susceptibility functions associated to the reaction coordinates. We provide analytical and numerical evidence of how the singularities affect the physical properties of finite size systems.

cond-mat.stat-mech↗

arXiv2023

Modelling the effect of aerosol and greenhouse gas forcing on the South and East Asian monsoons with an intermediate complexity climate model

The South and East Asian summer monsoons are globally significant meteorological features, creating a strongly seasonal pattern of precipitation. The stability of the monsoon is of extreme importance for a vast range of ecosystems and for the livelihoods of a large share of the world's population. Simulations are performed with an intermediate complexity climate model, PLASIM, to assess the future response of the monsoons to changing concentrations of aerosols and greenhouse gases. The aerosol loading consists of a mid-tropospheric warming and a surface cooling, which is applied to India, Southeast Asia and East China, both concurrently and independently. The primary effect of increased aerosol loading is a decrease in summer precipitation in the vicinity of the applied forcing, although the regional response varies significantly. The decrease in precipitation is only partially ascribable to a decrease in the precipitable water, and instead derives from a reduction of the precipitation efficiency, due to changes in the stratification of the atmosphere. When the aerosol loading is added in all regions simultaneously, precipitation in East China is most strongly affected, with a quite distinct transition to a low precipitation regime as the radiative forcing increases beyond 60 W/m^2. The response is less abrupt as we move westward, with precipitation in South India being least affected. This lower sensitivity in South India is attributed to aerosol forcing over East China. Additionally, the effect on precipitation is approximately linear with the forcing. The impact of doubling carbon dioxide levels is to increase precipitation over the regions and weaken the circulation. When the carbon dioxide and aerosol forcings are applied at the same time, the carbon dioxide forcing partially offsets the surface cooling and reduction in precipitation associated with the aerosol response.

physics.ao-ph↗

arXiv2023

A strategy to compute convective timescales of the Indian monsoon with the WRF model

The Indian monsoon brings around 80% of the annual rainfall over the summer months June--September to the Indian subcontinent. The timing of the monsoon onset and the associated rainfall has a large impact on agriculture, thus impacting the livelihoods of over one billion people. To improve forecasting the monsoon on sub-seasonal timescales, global climate models are in continual development. One of the key issues is the representation of convection, which is typically parametrised. Different convection schemes offer varying degrees of performance, depending on the model and scenario. Here, we propose a method to compute a convective timescale, which could be used as a metric for comparison across different models and convection schemes. The method involves the determination of a vertical convective flux between the lower and upper troposphere through moisture budget analysis, and then relating this to the total column moisture content. The method is applied to a WRF model simulation of the 2016 Indian monsoon, giving convective timescales that are reduced by a factor of 2 when the onset of the monsoon occurs. The convective timescale can also be used as an indicator of monsoon transitions from pre-onset to full phase of the monsoon, and to assess changes in monsoon phases under future climate scenarios.

physics.ao-ph↗