Michael Ghil | University of California, Los Angeles (original) (raw)

Papers by Michael Ghil

arXiv (Cornell University), Nov 29, 1993

The Jupiter{Saturn 2:5 near{commensurability is analyzed in a fully analytic Hamiltonian planetar... more The Jupiter{Saturn 2:5 near{commensurability is analyzed in a fully analytic Hamiltonian planetary theory. Computations for the Sun{Jupiter{Saturn system, extending to the third order of the masses and to the 8th degree in the eccentricities and inclinations, reveal an unexpectedly sensitive dependence of the solution on initial data and its likely nonconvergence. The source of the sensitivity and apparent lack of convergence is this near{commensurability, the so{called great inequality. This indicates that simple averaging, still common in current semi{analytic planetary theories, may not be an adequate technique to obtain information on the long-term dynamics of the Solar System. Preliminary results suggest that these di culties can be overcome by using resonant normal forms.

Proceedings of SPIE, Feb 13, 2001

Los Alamos National Laboratory, an affirmative actiorkqual oppmb.mityemplo yer, is operated by th... more Los Alamos National Laboratory, an affirmative actiorkqual oppmb.mityemplo yer, is operated by the University of Califomiaforthe U.S. Deparlrnent of Energy under mntract W-7405-ENG-36. By acceptance of this artkle, the publisher rewgnizesthatthe U.S. Government retains a nonexclusive, royallyfree license to publish or reproduce the published form of this mntribution, or to allow otherato do so, for U.S. Government purposes. Los Alamos National Laboratory requests that the publisher identify this article as work performed under the auspices of the U.S. Department of Energy. Los Alamos National Laboratov strongly supporta academic freedom and a researcher's right to publisk as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness.

Journal of heat transfer, Aug 1, 1971

Nomenclature d = cylinder diameter upper bound for iVpe introduced inequation (5) = Nusselt numbe... more Nomenclature d = cylinder diameter upper bound for iVpe introduced inequation (5) = Nusselt number, hd/k = Peclet number, dU/a = Reynolds number, dll/v-Strouhal number, d/UT-Strouhal cycle period = velocity characteristic of penetration depth 5, see equation (1) main flow velocity thermal diffusivity penetration depth

Nonlinear Processes in Geophysics, Mar 22, 2010

We consider a highly idealized model for El Niño/Southern Oscillation (ENSO) variability, as intr... more We consider a highly idealized model for El Niño/Southern Oscillation (ENSO) variability, as introduced in an earlier paper. The model is governed by a delay differential equation for sea-surface temperature T in the Tropical Pacific, and it combines two key mechanisms that participate in ENSO dynamics: delayed negative feedback and seasonal forcing. We perform a theoretical and numerical study of the model in the three-dimensional space of its physically relevant parameters: propagation period τ of oceanic waves across the Tropical Pacific, atmosphere-ocean coupling κ, and strength of seasonal forcing b. Phase locking of model solutions to the periodic forcing is prevalent: the local maxima and minima of the solutions tend to occur at the same position within the seasonal cycle. Such phase locking is a key feature of the observed El Niño (warm) and La Niña (cold) events. The phasing of the extrema within the seasonal cycle depends sensitively on model parameters when forcing is weak. We also study coexistence of multiple solutions for fixed model parameters and describe the basins of attraction of the stable solutions in a one-dimensional space of constant initial model histories.

arXiv (Cornell University), Dec 29, 2022

HAL (Le Centre pour la Communication Scientifique Directe), May 28, 2008

We consider a delay differential equation (DDE) model for El-Niño Southern Oscillation (ENSO) var... more We consider a delay differential equation (DDE) model for El-Niño Southern Oscillation (ENSO) variability. The model combines two key mechanisms that participate in ENSO dynamics: delayed negative feedback and seasonal forcing. We perform stability analyses of the model in the three-dimensional space of its physically relevant parameters. Our results illustrate the role of these three parameters: strength of seasonal forcing b, atmosphere-ocean coupling κ, and propagation period τ of oceanic waves across the Tropical Pacific. Two regimes of variability, stable and unstable, are separated by a sharp neutral curve in the (b, τ) plane at constant κ. The detailed structure of the neutral curve becomes very irregular and possibly fractal, while individual trajectories within the unstable region become highly complex and possibly chaotic, as the atmosphere-ocean coupling κ increases. In the unstable regime, spontaneous transitions occur in the mean "temperature" (i.e., thermocline depth), period, and extreme annual values, for purely periodic, seasonal forcing. The model reproduces the Devil's bleachers characterizing other ENSO models, such as nonlinear, coupled systems of partial differential equations; some of the features of this behavior have been documented in general circulation models, as well as in observations. We expect, therefore, similar behavior in much more detailed and realistic models, where it is harder to describe its causes as completely.

Ecological Modelling, Dec 1, 2015

The Rosenzweig-MacArthur model is a set of ordinary differential equations (ODEs) that provides a... more The Rosenzweig-MacArthur model is a set of ordinary differential equations (ODEs) that provides an aggregate description of the dynamics of a predator-prey system. When including an Allee effect on the prey, this model exhibits bistability and contains a pitchfork bifurcation, a Hopf bifurcation and a heteroclinic bifurcation. We develop an agent-based model (ABM) on a two-dimensional, square lattice that encompasses the key assumptions of the aggregate model. Although the two modelling approaches-ODE and ABM-differ, both models exhibit similar bifurcation patterns. The ABM model's behaviour is richer and it is analysed using advanced statistical methods. In particular, singular spectrum analysis is used to robustly locate the transition between apparently random, smallamplitude fluctuations around a fixed point and stable, large-amplitude oscillations. Critical slowing down of model trajectories anticipates the heteroclinic bifurcation. Systematic comparison between the ABM and the ODE models' behaviour helps one understand the predator-prey system better; it provides guidance in model exploration and allows one to draw more robust conclusions on the nature of predator-prey interactions.

arXiv (Cornell University), Feb 9, 2009

This study is motivated by problems related to environmental transport on river networks. We esta... more This study is motivated by problems related to environmental transport on river networks. We establish statistical properties of a flow along a directed branching network and suggest its compact parameterization. The downstream network transport is treated as a particular case of nearest-neighbor hierarchical aggregation with respect to the metric induced by the branching structure of the river network. We describe the static geometric structure of a drainage network by a tree, referred to as the static tree, and introduce an associated dynamic tree that describes the transport along the static tree. It is well known that the static branching structure of river networks can be described by self-similar trees (SSTs); we demonstrate that the corresponding dynamic trees are also self-similar. We report an unexpected phase transition in the dynamics of three river networks, one from California and two from Italy, demonstrate the universal features of this transition, and seek to interpret it in hydrological terms.

Two novel statistical methods are applied to the prediction of transitions between weather regime... more Two novel statistical methods are applied to the prediction of transitions between weather regimes. The methods are tested using a long, 6 000-day simulation of a three-layer, quasi-geostrophic (QG3) model on the sphere at T21 resolution. The two methods are the k nearest-neighbor classifier and the random-forest method. Both methods are widely used in statistical classification and machine learning; they are applied here to forecast the break of a regime and subsequent onset of another one. The QG3 model has been previously shown to possess realistic weather regimes in its Northern Hemisphere and preferred transitions between these have been determined. The two methods are applied to the three more robust transitions; they both demonstrate a skill of 35-40% better than random and are thus encouraging for use on real data. Moreover, the random-forest method allows, while keeping the overall skill unchanged, to efficiently adjust the ratio of correctly predicted transitions to false alarms. A long-standing conjecture has associated regime breaks and preferred transitions with distinct directions in the reduced model phase space spanned by a few leading empirical orthogonal functions of its variability. Sensitivity studies for several predictors confirm the crucial influence of the exit angle on a preferred transition path. The present results thus support the paradigm of multiple weather regimes and of their association with unstable fixed points of atmospheric dynamics.

AGU Fall Meeting Abstracts, Dec 1, 2007

Recent refinements of models for the motions of the planets, including the Earth-Moon system, hav... more Recent refinements of models for the motions of the planets, including the Earth-Moon system, have led to the realization that the calculated cyclical changes in Earth's orbital eccentricity may be approximately correct for the whole of the Cenozoic. This raises the possibility of an astronomically-tuned geological timescale that extends to, and perhaps beyond, the Cretaceous-Tertiary (KT) boundary. In order to test the validity of these long numerical integrations, we compare calculations of Earth's orbital eccentricity 62-67 ...

RePEc: Research Papers in Economics, 2015

This paper presents a modeling framework for macroeconomic growth dynamics; it is motivated by re... more This paper presents a modeling framework for macroeconomic growth dynamics; it is motivated by recent attempts to formulate and study "integrated models" of the coupling between natural and socioeconomic phenomena. The challenge is to describe the interfaces between human activities and the functioning of the earth system. We examine the way that this interface works in the presence of endogenous business cycle dynamics, based on a non-equilibrium dynamic model. Recent findings about the macroeconomic response to natural disasters in such a nonequilibrium setting have shown a more severe response to natural disasters during expansions than during recessions. These findings raise questions about the assessment of climate change damages or natural disaster losses that are based purely on long-term growth models. In order to compare the theoretical findings with observational data, we analyze cyclic behavior in the U.S. economy, based on multivariate singular spectrum analysis. We analyze a total of nine aggregate indicators in a 52-year interval (1954-2005) and demonstrate that the behavior of the U.S. economy changes significantly between intervals of growth and recession, with higher volatility during expansions.

Springer eBooks, 2016

We present a data-adaptive spectral method-Monte Carlo Singular Spectrum Analysis (MC-SSA)-and it... more We present a data-adaptive spectral method-Monte Carlo Singular Spectrum Analysis (MC-SSA)-and its modification to tackle astrophysical problems. Through numerical simulations we show the ability of the MC-SSA in dealing with 1/ f β power-law noise affected by photon counting statistics. Such noise process is simulated by a first-order autoregressive, AR(1) process corrupted by intrinsic Poisson noise. In doing so, we statistically estimate a basic stochastic variation of the source and the corresponding fluctuations due to the quantum nature of light. In addition, MC-SSA test retains its effectiveness even when a significant percentage of the signal falls below a certain level of detection, e.g., caused by the instrument sensitivity. The parsimonious approach presented here may be broadly applied, from the search for extrasolar planets to the extraction of low-intensity coherent phenomena probably hidden in high energy transients.

Dynamics and Statistics of the Climate System, 2018

Decline in the Arctic sea ice extent (SIE) is an area of active scientific research with profound... more Decline in the Arctic sea ice extent (SIE) is an area of active scientific research with profound socioeconomic implications. Of particular interest are reliable methods for SIE forecasting on subseasonal time scales, in particular from early summer into fall, when sea ice coverage in the Arctic reaches its minimum. Here, we apply the recent data-adaptive harmonic (DAH) technique of Chekroun and Kondrashov, (2017), Chaos, 27 for the description, modeling and prediction of the Multisensor Analyzed Sea Ice Extent (MASIE, 2006-2016) data set. The DAH decomposition of MASIE identifies narrowband, spatio-temporal data-adaptive modes over four key Arctic regions. The time evolution of the DAH coefficients of these modes can be modelled and predicted by using a set of coupled Stuart-Landau stochastic differential equations that capture the modes' frequencies and amplitude modulation in time. Retrospective forecasts show that our resulting multilayer Stuart-Landau model (MSLM) is quite skilful in predicting September SIE compared to year-to-year persistence; moreover, the DAH-MSLM approach provided accurate real-time prediction that was highly competitive for the 2016-2017 Sea Ice Outlook.

Proceedings of the National Academy of Sciences of the United States of America, Nov 1, 2018

Reviews of Modern Physics, Jul 31, 2020

The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is ... more The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject to various external forcings, natural as well as anthropogenic. This paper reviews the observational evidence on climate phenomena and the governing equations of planetary-scale flow, as well as presenting the key concept of a hierarchy of models as used in the climate sciences. Recent advances in the application of dynamical systems theory, on the one hand, and of nonequilibrium statistical physics, on the other, are brought together for the first time and shown to complement each other in helping understand and predict the system's behavior. These complementary points of view permit a self-consistent handling of subgrid-scale phenomena as stochastic processes, as well as a unified handling of natural climate variability and forced climate change, along with a treatment of the crucial issues of climate sensitivity, response, and predictability.

We evaluate the contribution of natural variability to the modern decrease in foraminiferal δ 18 ... more We evaluate the contribution of natural variability to the modern decrease in foraminiferal δ 18 O by relying on a 2200-years-long, high-resolution record of oxygen isotopic ratio from a Central Mediterranean sediment core. Pre-industrial values are used to train and test two sets of algorithms that are able to forecast the natural variability in δ 18 O over the last 150 yr. These algorithms are based on autoregressive models and neural networks, respectively; they are applied separately to each of the δ 18 O series' significant variability components, rather than to the complete series. The separate components are extracted by singular-spectrum analysis and have narrowband spectral content, which reduces the forecast error. By comparing the sum of the predicted components to the actual values during the Industrial Era, we deduce that the natural contribution to the modern δ 18 O variation decreased gradually, until it reached roughly 40 % as early as the end of the 1970s.

Providing efficient and accurate parametrizations for model reduction is a key goal in many areas... more Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal perturbation expansions of the Koopman operator allow us to derive general stochastic parametrizations of weakly coupled dynamical systems. Such parametrizations yield a set of stochastic integro-differential equations with explicit noise and memory kernel formulas to describe the effects of unresolved variables. We show that the perturbation expansions involved need not be truncated when the coupling is additive. The unwieldy integro-differential equations can be recast as a simpler multilevel Markovian model, and we establish an intuitive connection with a generalized Langevin equation. This connection helps setting up a parallelism between the top-down, equations-based methodology herein and the well-established empirical model reduction (EMR) methodology that has been shown to provide efficient dynamical closures to partially observed systems. Hence, our findings support, on the one hand, the physical basis and robustness of the EMR methodology and, on the other hand, illustrate the practical relevance of the perturbative expansion used for deriving the parametrizations.

Proxy records from Greenland ice cores have been studied for several decades, yet many open quest... more Proxy records from Greenland ice cores have been studied for several decades, yet many open questions remain regarding the climate variability encoded therein. Here, we use a Bayesian framework for inferring inverse, stochastic-dynamic models from δ 18 O and dust records of unprecedented, subdecadal temporal resolution. The records stem from the North Greenland Ice Core Project (NGRIP) and we focus on the time interval 59 ka-22 ka b2k. Our model reproduces the dynamical characteristics of both the δ 18 O and dust proxy records, including the millennial-scale Dansgaard-Oeschger variability, as well as statistical properties such as probability density functions, waiting times and power spectra, with no need for any external forcing. The crucial ingredients for capturing these properties are (i) high-resolution training data; (ii) cubic drift terms; (iii) nonlinear coupling terms between the δ 18 O and dust time series; and (iv) non-Markovian contributions that represent shortterm memory effects. 1 Introduction Data-driven stochastic difference equation models have recently been successfully applied to a wide range of climatic phe

Climate of The Past, Apr 21, 2022

The relative role of external forcing and of intrinsic variability is a key question of climate v... more The relative role of external forcing and of intrinsic variability is a key question of climate variability in general and of our planet's paleoclimatic past in particular. Over the last 100 years since Milankovic's contributions, the importance of orbital forcing has been established for the period covering the last 2.6 Myr and the Quaternary glaciation cycles that took place during that time. A convincing case has also been made for the role of several internal mechanisms that are active on timescales both shorter and longer than the orbital ones. Such mechanisms clearly have a causal role in Dansgaard-Oeschger and Heinrich events, as well as in the mid-Pleistocene transition. We introduce herein a unified framework for the understanding of the orbital forcing's effects on the climate system's internal variability on timescales from thousands to millions of years. This framework relies on the fairly recent theory of non-autonomous and random dynamical systems, and it has so far been successfully applied in the climate sciences for problems like the El Niño-Southern Oscillation, the oceans' wind-driven circulation, and other problems on interannual to interdecadal timescales. Finally, we provide further examples of climate applications and present preliminary results of interest for the Quaternary glaciation cycles in general and the mid-Pleistocene transition in particular.