We present and apply a novel method of describing and modeling complex multivariate datasets in the geosciences and elsewhere. Data-adaptive harmonic (DAH) decomposition identifies narrow-banded, spatio-temporal modes (DAHMs) whose frequencies are not necessarily integer multiples of each other. The evolution in time of the DAH coefficients (DAHCs) of these modes can be modeled using a set of coupled Stuart-Landau stochastic differential equations that capture the modes’ frequencies and amplitude modulation in time and space. This methodology is applied first to a challenging synthetic dataset and then to Arctic sea ice concentration (SIC) data from the US National Snow and Ice Data Center (NSIDC). The 36-year (1979–2014) dataset is parsimoniously and accurately described by our DAHMs. Preliminary results indicate that simulations using our multilayer Stuart-Landau model (MSLM) of SICs are stable for much longer time intervals, beyond the end of the twenty-first century, and exhibit interdecadal variability consistent with past historical records. Preliminary results indicate that this MSLM is quite skillful in predicting September sea ice extent.

%B Advances in Nonlinear Geosciences %I Springer %G eng %U http://doi.org/10.1007/978-3-319-58895-7_10 %0 Journal Article %J Journal of Atmospheric and Solar-Terrestrial Physics, %D 2018 %T Data-adaptive harmonic analysis and modeling of solar wind-magnetosphere coupling %A Kondrashov, Dmitri %A Chekroun, Mickaël D %X The solar wind-magnetosphere coupling is studied by new data-adaptive harmonic decomposition (DAHD) approach for the spectral analysis and inverse modeling of multivariate time observations of complex nonlinear dynamical systems. DAHD identifies frequency-based modes of interactions in the combined dataset of Auroral Electrojet (AE) index and solar wind forcing. The time evolution of these modes can be very efficiently simulated by using systems of stochastic differential equations (SDEs) that are stacked per frequency and formed by coupled Stuart-Landau oscillators. These systems of SDEs capture the modes' frequencies as well as their amplitude modulations, and yield, in turn, an accurate modeling of the AE index' statistical properties. %B Journal of Atmospheric and Solar-Terrestrial Physics, %V 177 %P 179-189 %G eng %U https://www.sciencedirect.com/science/article/pii/S136468261730295X %0 Journal Article %J Dynamics and Statistics of the Climate System %D 2018 %T Data-adaptive harmonic decomposition and prediction of Arctic sea ice extent %A Kondrashov, Dmitri %A Chekroun, Mickaël D. %A Ghil, Michael %X Decline in the Arctic sea ice extent (SIE) is an area of active scientific research with profound socio-economic 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,The multiscale variability of the ocean circulation due to its nonlinear dynamics remains a big challenge for theoretical understanding and practical ocean modeling. This paper demonstrates how the data-adaptive harmonic (DAH) decomposition and inverse stochastic modeling techniques introduced in (Chekroun and Kondrashov, (2017), Chaos, 27), allow for reproducing with high fidelity the main statistical properties of multiscale variability in a coarse-grained eddy-resolving ocean flow. This fully-data-driven approach relies on extraction of frequency-ranked time-dependent coefficients describing the evolution of spatio-temporal DAH modes (DAHMs) in the oceanic flow data. In turn, the time series of these coefficients are efficiently modeled by a family of low-order stochastic differential equations (SDEs) stacked per frequency, involving a fixed set of predictor functions and a small number of model coefficients. These SDEs take the form of stochastic oscillators, identified as multilayer Stuart–Landau models (MSLMs), and their use is justified by relying on the theory of Ruelle–Pollicott resonances. The good modeling skills shown by the resulting DAH-MSLM emulators demonstrates the feasibility of using a network of stochastic oscillators for the modeling of geophysical turbulence. In a certain sense, the original quasiperiodic Landau view of turbulence, with the amendment of the inclusion of stochasticity, may be well suited to describe turbulence.

%B Fluids %V 3 %P 21 %G eng %U https://www.mdpi.com/2311-5521/3/1/21/html %N 1 %0 Journal Article %J Ecological Economics %D 2018 %T Coupled Climate-Economic Modes in the Sahel's Interannual Variability %A Sainte Fare Garnot, Vivien %A Groth, Andreas %A Ghil, Michael %X We study the influence of interannual climate variability on the economy of several countries in the Sahel region. In the agricultural sector, we are able to identify coupled climate-economic modes that are statistically significant on interannual time scales. In particular, precipitation is a key climatic factor for agriculture in this semi-arid region. Locality and diversity characterize the Sahel's climatic and economic system, with the coupled climate-economic patterns exhibiting substantial differences from country to country. Large-scale atmospheric patterns — like the El Niño–Southern Oscillation and its quasi-biennial and quasi-quadrennial oscillatory modes — have quite limited influence on the economies, while more location-specific rainfall patterns play an important role. %B Ecological Economics %I Elsevier BV %V 153 %P 111–123 %8 nov %G eng %R 10.1016/j.ecolecon.2018.07.006 %0 Book Section %B The Gap between Weather and Climate Forecasting: Sub-Seasonal to Seasonal Prediction %D 2018 %T Extratropical sub-seasonal–to–seasonal oscillations and multiple regimes: The dynamical systems view %A Ghil, Michael %A Groth, Andreas %A Kondrashov, Dmitri %A Robertson, Andrew W. %E Robertson, Andrew W. %E Vitart, Frederic %XThis chapter considers the sub-seasonal–to–seasonal (S2S) prediction problem as intrinsically more difficult than either short-range weather prediction or interannual–to–multidecadal climate prediction. The difficulty arises from the comparable importance of atmospheric initial states and of parameter values in determining the atmospheric evolution on the S2S time scale. The chapter relies on the theoretical framework of dynamical systems and the practical tools this framework helps provide to low-order modeling and prediction of S2S variability. The emphasis is on mid-latitude variability and the complementarity of the nonlinear-waves vs. multiple-regime points of view in understanding this variability. Empirical model reduction and the forecast skill of the models thus produced in real-time prediction are reviewed.

%B The Gap between Weather and Climate Forecasting: Sub-Seasonal to Seasonal Prediction %7 1 %I Elsevier %P 119-142 %G eng %U https://doi.org/10.1016/B978-0-12-811714-9.00006-1 %& Extratropical sub-seasonal–to–seasonal oscillations and multiple regimes: The dynamical systems view %0 Book %B Focus Issue in Chaos %D 2017 %T Synchronization in Large Networks and Continuous Media – Data, Models, and Supermodels %E Duane, G. S. %E Grabow, C. %E Selten, F. %E Ghil, Michael %B Focus Issue in Chaos %7 27 %I American Institute of Physics, Melville, NY %G eng %0 Journal Article %J Chaos %D 2017 %T Data-adaptive harmonic spectra and multilayer Stuart-Landau models %A Chekroun, Mickaël D. %A Kondrashov, Dmitri %XHarmonic decompositions of multivariate time series are considered for which we adopt an integral operator approach with periodic semigroup kernels. Spectral decomposition theorems are derived that cover the important cases of two-time statistics drawn from a mixing invariant measure.

The corresponding eigenvalues can be grouped per Fourier frequency, and are actually given, at each frequency, as the singular values of a cross-spectral matrix depending on the data. These eigenvalues obey furthermore a variational principle that allows us to define naturally a multidimensional power spectrum. The eigenmodes, as far as they are concerned, exhibit a data-adaptive character manifested in their phase which allows us in turn to define a multidimensional phase spectrum.

The resulting data-adaptive harmonic (DAH) modes allow for reducing the data-driven modeling effort to elemental models stacked per frequency, only coupled at different frequencies by the same noise realization. In particular, the DAH decomposition extracts time-dependent coe cients stacked by Fourier frequency which can be e ciently modeled—provided the decay of temporal correlations is su ciently well-resolved—within a class of multilayer stochastic models (MSMs) tailored here on stochastic Stuart-Landau oscillators.

Applications to the Lorenz 96 model and to a stochastic heat equation driven by a space-time white noise, are considered. In both cases, the DAH decomposition allows for an extraction of spatio-temporal modes revealing key features of the dynamics in the embedded phase space. The multilayer Stuart-Landau models (MSLMs) are shown to successfully model the typical patterns of the corresponding time-evolving fields, as well as their statistics of occurrence.

%B Chaos %V 27 %P 093110 %G eng %U http://dx.doi.org/10.1063/1.4989400 %0 Journal Article %J Chaos %D 2017 %T Synchronization of world economic activity %A Groth, Andreas %A Ghil, Michael %XCommon dynamical properties of business cycle fluctuations are studied in a sample of more than 100 countries that represent economic regions from all around the world. We apply the methodology of multivariate singular spectrum analysis (M-SSA) to identify oscillatory modes and to detect whether these modes are shared by clusters of phase- and frequency-locked oscillators. An extension of the M-SSA approach is introduced to help analyze structural changes in the cluster configuration of synchronization. With this novel technique, we are able to identify a common mode of business cycle activity across our sample, and thus point to the existence of a world business cycle. Superimposed on this mode, we further identify several major events that have markedly influenced the landscape of world economic activity in the postwar era.

%B Chaos %V 27 %P 127002 %8 Dec 2017 %G eng %N 12 %R 10.1063/1.5001820 %0 Report %D 2017 %T Synchronization of world economic activity %A Groth, Andreas %A Ghil, Michael %XCommon dynamical properties of business cycle fluctuations are studied in a sample of more than 100 countries that represent economic regions from all around the world. We apply the methodology of multivariate singular spectrum analysis (M-SSA) to identify oscillatory modes and to detect whether these modes are shared by clusters of phase- and frequency-locked oscillators. An extension of the M-SSA approach is introduced to help analyze structural changes in the cluster configuration of synchronization. With this novel technique, we are able to identify a common mode of business cycle activity across our sample, and thus point to the existence of a world business cycle. Superimposed on this mode, we further identify several major events that have markedly influenced the landscape of world economic activity in the postwar era. These findings raise therefore questions about assessments of climate change impacts that are based purely on long-term economic growth models. A key conclusion is the importance of endogenous-dynamics e?ects at the interface between natural climate variability and economic fluctuations.

%I Chair Energy & Prosperity %C Paris %8 03/31 %G eng %U http://www.chair-energy-prosperity.org/en/publications-2/synchronization-of-world-economic-activity-2/ %0 Journal Article %J Journal of Climate %D 2017 %T Interannual variability in the North Atlantic ocean’s temperature field and its association with the wind stress forcing %A Groth, Andreas %A Feliks, Yizhak %A Kondrashov, Dmitri %A Ghil, Michael %XSpectral analyses of the North Atlantic temperature field in the Simple Ocean Data Analysis (SODA) reanalysis identify prominent and statistically significant interannual oscillations along the Gulf Stream front and in large regions of the North Atlantic. A 7–8-yr oscillatory mode is characterized by a basin-wide southwest-to-northeast–oriented propagation pattern in the sea surface temperature (SST) field. This pattern is found to be linked to a seesaw in the meridional-dipole structure of the zonal wind stress forcing (TAUX). In the subpolar gyre, the SST and TAUX fields of this mode are shown to be in phase opposition, which suggests a cooling effect of the wind stress on the upper ocean layer. Over all, this mode’s temperature field is characterized by a strong equivalent-barotropic component, as shown by covariations in SSTs and sea surface heights, and by phase-coherent behavior of temperature layers at depth with the SST field. Recent improvements of multivariate singular spectrum analysis (M-SSA) help separate spatio-temporal patterns. This methodology is developed further and applied to studying the ocean’s response to variability in the atmospheric forcing. Statistical evidence is shown to exist for other mechanisms generating oceanic variability of similar 7–8-yr periodicity in the Gulf Stream region; the latter variability is likewise characterized by a strongly equivalent-barotropic component. Two other modes of biennial variability in the Gulf Stream region are also identified, and it is shown that interannual variability in this region cannot be explained by the ocean’s response to similar variability in the atmospheric forcing alone.

%B Journal of Climate %V 30 %P 2655-2678 %8 21 mar 2017 %G eng %N 7 %R 10.1175/JCLI-D-16-0370.1 %0 Journal Article %J Discrete and Continuous Dynamical Systems - A %D 2017 %T The wind-driven ocean circulation: Applying dynamical systems theory to a climate problem %A Ghil, Michael %XThe large-scale, near-surface flow of the mid-latitude oceans is dominated by the presence of a larger, anticyclonic and a smaller, cyclonic gyre. The two gyres share the eastward extension of western boundary currents, such as the Gulf Stream or Kuroshio, and are induced by the shear in the winds that cross the respective ocean basins. This physical phenomenology is described mathematically by a hierarchy of systems of nonlinear partial differential equations (PDEs). We study the low-frequency variability of this wind-driven, double-gyre circulation in mid-latitude ocean basins, subject to time-constant, purely periodic and more general forms of time-dependent wind stress. Both analytical and numerical methods of dynamical systems theory are applied to the PDE systems of interest. Recent work has focused on the application of non-autonomous and random forcing to double-gyre models. We discuss the associated pullback and random attractors and the non-uniqueness of the invariant measures that are obtained. The presentation moves from observations of the geophysical phenomena to modeling them and on to a proper mathematical understanding of the models thus obtained. Connections are made with the highly topical issues of climate change and climate sensitivity.

%B Discrete and Continuous Dynamical Systems - A %V 37 %P 189-228 %8 2016 %G eng %N 1 %0 Journal Article %J Climatic Change %D 2016 %T DADA: data assimilation for the detection and attribution of weather and climate-related events %A Hannart, A. %A Carrassi, A. %A Bocquet, M. %A Ghil, Michael %A Naveau, P. %A Pulido, M. %A Ruiz, J. %A Tandeo, P. %XWe describe a new approach that allows for systematic causal attribution of weather and climate-related events, in near-real time. The method is designed so as to facilitate its implementation at meteorological centers by relying on data and methods that are routinely available when numerically forecasting the weather. We thus show that causal attribution can be obtained as a by-product of data assimilation procedures run on a daily basis to update numerical weather prediction (NWP) models with new atmospheric observations; hence, the proposed methodology can take advantage of the powerful computational and observational capacity of weather forecasting centers. We explain the theoretical rationale of this approach and sketch the most prominent features of a ``data assimilation–based detection and attribution'' (DADA) procedure. The proposal is illustrated in the context of the classical three-variable Lorenz model with additional forcing. The paper concludes by raising several theoretical and practical questions that need to be addressed to make the proposal operational within NWP centers.

%B Climatic Change %V 136 %P 155–174 %8 21 Mar 2016 %G eng %U http://dx.doi.org/10.1007/s10584-016-1595-3 %N 2 %R 10.1007/s10584-016-1595-3 %0 Journal Article %J Phys. Rev. E %D 2016 %T Comment on ``Nonparametric forecasting of low-dimensional dynamical systems'' %A Kondrashov, Dmitri %A Chekroun, Mickaël D. %A Ghil, Michael %B Phys. Rev. E %I American Physical Society %V 93 %P 036201 %8 Mar %G eng %U http://link.aps.org/doi/10.1103/PhysRevE.93.036201 %R 10.1103/PhysRevE.93.036201 %0 Journal Article %J Space Weather %D 2016 %T Data assimilation of low-altitude magnetic perturbations into a global magnetosphere model %A Merkin, V. G. %A Kondrashov, Dmitri %A Ghil, Michael %A Anderson, B. J. %K Data assimilation %K global MHD %K integration and fusion %K magnetosphere %K Magnetosphere/ionosphere interactions %K Models %K Numerical modeling %B Space Weather %V 14 %P 165–184 %G eng %U http://dx.doi.org/10.1002/2015SW001330 %N 2 %R 10.1002/2015SW001330 %0 Book Section %B The Universe of Digital Sky Surveys %D 2016 %T Singular Spectrum Analysis for astronomical time series: constructing a parsimonious hypothesis test %A Greco, G %A Kondrashov, Dmitri %A Kobayashi, S %A Ghil, Michael %A Branchesi, M %A Guidorzi, C %A Stratta, G %A Ciszak, M %A Marino, F %A Ortolan, A %B The Universe of Digital Sky Surveys %I Springer %P 105–107 %G eng %U http://link.springer.com/chapter/10.1007%2F978-3-319-19330-4_16 %0 Journal Article %J Journal of Business Cycle Research %D 2016 %T Economic Cycles and Their Synchronization: A Comparison of Cyclic Modes in Three European Countries %A Lisa Sella %A Gianna Vivaldo %A Groth, Andreas %A Ghil, Michael %XThe present work applies singular spectrum analysis (SSA) to the study of macroeconomic fluctuations in three European countries: Italy, The Netherlands, and the United Kingdom. This advanced spectral method provides valuable spatial and frequency information for multivariate data sets and goes far beyond the classical forms of time domain analysis. In particular, SSA enables us to identify dominant cycles that characterize the deterministic behavior of each time series separately, as well as their shared behavior. We demonstrate its usefulness by analyzing several fundamental indicators of the three countries' real aggregate economy in a univariate, as well as a multivariate setting. Since business cycles are international phenomena, which show common characteristics across countries, our aim is to uncover supranational behavior within the set of representative European economies selected herein. Finally, the analysis is extended to include several indicators from the U.S. economy, in order to examine its influence on the European economies under study and their interrelationships.

%B Journal of Business Cycle Research %I Springer %V 12 %P 25-48 %8 12 Aug 2016 %G eng %U http://dx.doi.org/10.1007/s41549-016-0003-4 %N 1 %R 10.1007/s41549-016-0003-4 %0 Journal Article %J Journal of the Atmospheric Sciences %D 2016 %T Interannual Variability in North Atlantic Weather: Data Analysis and a Quasigeostrophic Model %A Feliks, Yizhak %A Robertson, Andrew W. %A Ghil, Michael %XThis paper addresses the effect of interannual variability in jet stream orientation on weather systems over the North Atlantic basin (NAB). The observational analysis relies on 65 yr of NCEP–NCAR reanalysis (1948–2012). The total daily kinetic energy of the geostrophic wind (GTKE) is taken as a measure of storm activity over the North Atlantic. The NAB is partitioned into four rectangular regions, and the winter average of GTKE is calculated for each quadrant. The spatial GTKE average over all four quadrants shows striking year-to-year variability and is strongly correlated with the North Atlantic Oscillation (NAO).The GTKE strength in the northeast quadrant is closely related to the diffluence angle of the jet stream in the northwest quadrant. To gain insight into the relationship between the diffluence angle and its downstream impact, a quasigeostrophic baroclinic model is used. The results show that an initially zonal jet persists at its initial latitude over 30 days or longer, while a tilted jet propagates meridionally according to the Rossby wave group velocity, unless kept stationary by external forcing.A Gulf Stream–like narrow sea surface temperature (SST) front provides the requisite forcing for an analytical steady-state solution to this problem. This SST front influences the atmospheric jet in the northwest quadrant: it both strengthens the jet and tilts it northward at higher levels, while its effect is opposite at lower levels. Reanalysis data confirm these effects, which are consistent with thermal wind balance. The results suggest that the interannual variability found in the GTKE may be caused by intrinsic variability of the thermal Gulf Stream front.

%B Journal of the Atmospheric Sciences %V 73 %P 3227-3248 %G eng %N 8 %R 10.1175/JAS-D-15-0297.1 %0 Journal Article %J Journal of Geophysical Research: Solid Earth %D 2016 %T Data-Adaptive Detection of Transient Deformation in Geodetic Networks %A Walwer, Damian %A Calais, Eric %A Ghil, Michael %XThe recent development of dense and continuously operating Global Navigation Satellite System (GNSS) networks worldwide has led to a significant increase in geodetic data sets that sometimes capture transient-deformation signals. It is challenging, however, to extract such transients of geophysical origin from the background noise inherent to GNSS time series and, even more so, to separate them from other signals, such as seasonal redistributions of geophysical fluid mass loads. In addition, because of the very large number of continuously recording GNSS stations now available, it has become impossible to systematically inspect each time series and visually compare them at all neighboring sites. Here we show that Multichannel Singular Spectrum Analysis (M-SSA), a method derived from the analysis of dynamical systems, can be used to extract transient deformations, seasonal oscillations, and background noise present in GNSS time series. M-SSA is a multivariate, nonparametric, statistical method that simultaneously exploits the spatial and temporal correlations of geophysical fields. The method allows for the extraction of common modes of variability, such as trends with nonconstant slopes and oscillations shared across time series, without a priori hypotheses about their spatiotemporal structure or their noise characteristics. We illustrate this method using synthetic examples and show applications to actual GPS data from Alaska to detect seasonal signals and microdeformation at the Akutan active volcano. The geophysically coherent spatiotemporal patterns of uplift and subsidence thus detected are compared to the results of an idealized model of such processes in the presence of a magma chamber source.

%B Journal of Geophysical Research: Solid Earth %I Wiley Online Library %V 121 %P 2129-2152 %8 Mar 2016 %G eng %N 3 %R 10.1002/2015JB012424 %0 Journal Article %J Journal of Climate %D 2016 %T Diversity, nonlinearity, seasonality and memory effect in ENSO simulation and prediction using empirical model reduction %A Chen, C. %A Cane, M. A. %A Henderson, N. %A Lee, D. Eun %A Chapman, D. %A Kondrashov, Dmitri %A Chekroun, Mickaël D. %XA suite of empirical model experiments under the empirical model reduction framework are conducted to advance the understanding of ENSO diversity, nonlinearity, seasonality, and the memory effect in the simulation and prediction of tropical Pacific sea surface temperature (SST) anomalies. The model training and evaluation are carried out using 4000-yr preindustrial control simulation data from the coupled model GFDL CM2.1. The results show that multivariate models with tropical Pacific subsurface information and multilevel models with SST history information both improve the prediction skill dramatically. These two types of models represent the ENSO memory effect based on either the recharge oscillator or the time-delayed oscillator viewpoint. Multilevel SST models are a bit more efficient, requiring fewer model coefficients. Nonlinearity is found necessary to reproduce the ENSO diversity feature for extreme events. The nonlinear models reconstruct the skewed probability density function of SST anomalies and improve the prediction of the skewed amplitude, though the role of nonlinearity may be slightly overestimated given the strong nonlinear ENSO in GFDL CM2.1. The models with periodic terms reproduce the SST seasonal phase locking but do not improve the prediction appreciably. The models with multiple ingredients capture several ENSO characteristics simultaneously and exhibit overall better prediction skill for more diverse target patterns. In particular, they alleviate the spring/autumn prediction barrier and reduce the tendency for predicted values to lag the target month value.

%B Journal of Climate %V 29 %P 1809-1830 %8 Mar 2016 %G eng %N 5 %R 10.1175/JCLI-D-15-0372.1 %0 Journal Article %J Journal of Climate %D 2016 %T Exploring the pullback attractors of a low-order quasigeostrophic ocean model: The deterministic case %A Pierini, S. %A Ghil, Michael %A Chekroun, Mickaël D. %XA low-order quasigeostrophic double-gyre ocean model is subjected to an aperiodic forcing that mimics time dependence dominated by interdecadal variability. This model is used as a prototype of an unstable and nonlinear dynamical system with time-dependent forcing to explore basic features of climate change in the presence of natural variability. The study relies on the theoretical framework of nonautonomous dynamical systems and of their pullback attractors (PBAs), that is, of the time-dependent invariant sets attracting all trajectories initialized in the remote past. The existence of a global PBA is rigorously demonstrated for this weakly dissipative nonlinear model. Ensemble simulations are carried out and the convergence to PBAs is assessed by computing the probability density function (PDF) of localization of the trajectories. A sensitivity analysis with respect to forcing amplitude shows that the PBAs experience large modifications if the underlying autonomous system is dominated by small-amplitude limit cycles, while less dramatic changes occur in a regime characterized by large-amplitude relaxation oscillations. The dependence of the attracting sets on the choice of the ensemble of initial states is then analyzed. Two types of basins of attraction coexist for certain parameter ranges; they contain chaotic and nonchaotic trajectories, respectively. The statistics of the former does not depend on the initial states whereas the trajectories in the latter converge to small portions of the global PBA. This complex scenario requires separate PDFs for chaotic and nonchaotic trajectories. General implications for climate predictability are finally discussed.

%B Journal of Climate %V 29 %P 4185-4202 %8 Jun 2016 %G eng %N 11 %R 10.1175/jcli-d-15-0848.1 %0 Journal Article %J Discrete and Continuous Dynamical Systems - Series S %D 2016 %T Low-dimensional Galerkin approximations of nonlinear delay differential equations %A Chekroun, Mickaël D. %A Ghil, Michael %A Liu, Honghu %A Wang, Shouhong %XThis article revisits the approximation problem of systems of nonlinear delay differential equations (DDEs) by a set of ordinary differential equations (ODEs). We work in Hilbert spaces endowed with a natural inner product including a point mass, and introduce polynomials orthogonal with respect to such an inner product that live in the domain of the linear operator associated with the underlying DDE. These polynomials are then used to design a general Galerkin scheme for which we derive rigorous convergence results and show that it can be numerically implemented via simple analytic formulas. The scheme so obtained is applied to three nonlinear DDEs, two autonomous and one forced: (i) a simple DDE with distributed delays whose solutions recall Brownian motion; (ii) a DDE with a discrete delay that exhibits bimodal and chaotic dynamics; and (iii) a periodically forced DDE with two discrete delays arising in climate dynamics. In all three cases, the Galerkin scheme introduced in this article provides a good approximation by low-dimensional ODE systems of the DDE's strange attractor, as well as of the statistical features that characterize its nonlinear dynamics.

%B Discrete and Continuous Dynamical Systems - Series S %V 36 %P 4133-4177 %8 Mar 2016 %G eng %N 8 %R 10.3934/dcds.2016.36.4133 %0 Journal Article %J Oecologia %D 2016 %T Pathogens trigger top-down climate forcing on ecosystem dynamics %A Edeline, Eric %A Groth, Andreas %A Cazelles, Bernard %A Claessen, David %A Winfield, Ian J. %A Ohlberger, Jan %A Asbjørn Vøllestad, L. %A Stenseth, Nils C. %A Ghil, Michael %XEvaluating the effects of climate variation on ecosystems is of paramount importance for our ability to forecast and mitigate the consequences of global change. However, the ways in which complex food webs respond to climate variations remain poorly understood. Here, we use long-term time series to investigate the effects of temperature variation on the intraguild-predation (IGP) system of Windermere (UK), a lake where pike (Esox lucius, top predator) feed on small-sized perch (Perca fluviatilis) but compete with large-sized perch for the same food sources. Spectral analyses of time series reveal that pike recruitment dynamics are temperature controlled. In 1976, expansion of a size-truncating perch pathogen into the lake severely impacted large perch and favoured pike as the IGP-dominant species. This pathogen-induced regime shift to a pike-dominated IGP apparently triggered a temperature-controlled trophic cascade passing through pike down to dissolved nutrients. In simple food chains, warming is predicted to strengthen top–down control by accelerating metabolic rates in ectothermic consumers, while pathogens of top consumers are predicted to dampen this top–down control. In contrast, the local IGP structure in Windermere made warming and pathogens synergistic in their top–down effects on ecosystem functioning. More generally, our results point to top predators as major mediators of community response to global change, and show that size-selective agents (e.g. pathogens, fishers or hunters) may change the topological architecture of food webs and alter whole ecosystem sensitivity to climate variation.

%B Oecologia %P 1–14 %8 Feb 2016 %G eng %R 10.1007/s00442-016-3575-8 %0 Book %B Proceedings of the Royal Society A %D 2015 %T A collection on 'Climate Dynamics: Multiple Scales and Memory Effects' %A Ghil, Michael %A Chekroun, Mickaël D. %A Stepan, Gabor %B Proceedings of the Royal Society A %I Royal Society London %V 471 %G eng %U http://dx.doi.org/10.1098/rspa.2015.0097 %N 2176 %R 10.1098/rspa.2015.0097 %0 Journal Article %J Ecological Modelling %D 2015 %T Bifurcation analysis of an agent-based model for predator–prey interactions %A Colon, Célian %A Claessen, David %A Ghil, Michael %K Early-warning signals %XAbstract 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, small-amplitude 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.

%B Ecological Modelling %V 317 %P 93 - 106 %G eng %U http://www.sciencedirect.com/science/article/pii/S0304380015004111 %R http://dx.doi.org/10.1016/j.ecolmodel.2015.09.004 %0 Journal Article %J Journal of Climate %D 2015 %T Predicting critical transitions in ENSO models. Part I: Methodology and simple models with memory %A Mukhin, Dmitry %A Loskutov, Evgeny %A Mukhina, Anna %A Feigin, Alexander %A Zaliapin, Ilia %A Ghil, Michael %X A new empirical approach is proposed for predicting critical transitions in the climate system based on a time series alone. This approach relies on nonlinear stochastic modeling of the system’s time-dependent evolution operator by the analysis of observed behavior. Empirical models that take the form of a discrete random dynamical system are constructed using artificial neural networks; these models include state-dependent stochastic components. To demonstrate the usefulness of such models in predicting critical climate transitions, they are applied here to time series generated by a number of delay-differential equation (DDE) models of sea surface temperature anomalies. These DDE models take into account the main conceptual elements responsible for the El Niño–Southern Oscillation phenomenon. The DDE models used here have been modified to include slow trends in the control parameters in such a way that critical transitions occur beyond the learning interval in the time series. Numerical results suggest that the empirical models proposed herein are able to forecast sequences of critical transitions that manifest themselves in future abrupt changes of the climate system’s statistics. %B Journal of Climate %V 28 %P 1940–1961 %G eng %N 5 %R 10.1175/JCLI-D-14-00239.1 %0 Journal Article %J Journal of Climate %D 2015 %T Predicting critical transitions in ENSO models. Part II: Spatially dependent models %A Mukhin, Dmitry %A Kondrashov, Dmitri %A Loskutov, Evgeny %A Gavrilov, Andrey %A Feigin, Alexander %A Ghil, Michael %X The present paper is the second part of a two-part study on empirical modeling and prediction of climate variability. This paper deals with spatially distributed data, as opposed to the univariate data of Part I. The choice of a basis for effective data compression becomes of the essence. In many applications, it is the set of spatial empirical orthogonal functions that provides the uncorrelated time series of principal components (PCs) used in the learning set. In this paper, the basis of the learning set is obtained instead by applying multichannel singular-spectrum analysis to climatic time series and using the leading spatiotemporal PCs to construct a reduced stochastic model. The effectiveness of this approach is illustrated by predicting the behavior of the Jin–Neelin–Ghil (JNG) hybrid seasonally forced coupled ocean–atmosphere model of El Niño–Southern Oscillation. The JNG model produces spatially distributed and weakly nonstationary time series to which the model reduction and prediction methodology is applied. Critical transitions in the hybrid periodically forced coupled model are successfully predicted on time scales that are substantially longer than the duration of the learning sample. %B Journal of Climate %V 28 %P 1962–1976 %G eng %N 5 %R 10.1175/JCLI-D-14-00240.1 %0 Journal Article %J Physica D: Nonlinear Phenomena %D 2015 %T Low-frequency variability and heat transport in a low-order nonlinear coupled ocean–atmosphere model %A Vannitsem, Stéphane %A Demaeyer, Jonathan %A De Cruz, Lesley %A Ghil, Michael %X We formulate and study a low-order nonlinear coupled ocean–atmosphere model with an emphasis on the impact of radiative and heat fluxes and of the frictional coupling between the two components. This model version extends a previous 24-variable version by adding a dynamical equation for the passive advection of temperature in the ocean, together with an energy balance model. The bifurcation analysis and the numerical integration of the model reveal the presence of low-frequency variability (LFV) concentrated on and near a long-periodic, attracting orbit. This orbit combines atmospheric and oceanic modes, and it arises for large values of the meridional gradient of radiative input and of frictional coupling. Chaotic behavior develops around this orbit as it loses its stability; this behavior is still dominated by the LFV on decadal and multi-decadal time scales that is typical of oceanic processes. Atmospheric diagnostics also reveals the presence of predominant low- and high-pressure zones, as well as of a subtropical jet; these features recall realistic climatological properties of the oceanic atmosphere. Finally, a predictability analysis is performed. Once the decadal-scale periodic orbits develop, the coupled system’s short-term instabilities–as measured by its Lyapunov exponents–are drastically reduced, indicating the ocean’s stabilizing role on the atmospheric dynamics. On decadal time scales, the recurrence of the solution in a certain region of the invariant subspace associated with slow modes displays some extended predictability, as reflected by the oscillatory behavior of the error for the atmospheric variables at long lead times. %B Physica D: Nonlinear Phenomena %I Elsevier %V 309 %P 71–85 %G eng %R 10.1016/j.physd.2015.07.006 %0 Book %D 2015 %T Approximation of Stochastic Invariant Manifolds: Stochastic Manifolds for Nonlinear SPDEs I %A Chekroun, Mickaël D. %A Liu, Honghu %A Wang, S. %X[[{"fid":"280","view_mode":"default","type":"media","attributes":{"height":"232","width":"153","style":"float: right;","class":"media-element file-default"}}]]

This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.

%I Springer Briefs in Mathematics, Springer %C New York %G eng %U http://link.springer.com/book/10.1007/978-3-319-12496-4/page/1 %0 Book %D 2015 %T Climate Change: Multidecadal and Beyond %E C. P. Chang %E Ghil, Michael %E M. Latif %E J. M. Wallace %I World Scientific Publ. Co./Imperial College Press %G eng %0 Journal Article %J Physica D: Nonlinear Phenomena %D 2015 %T Data-driven non-Markovian closure models %A Kondrashov, Dmitri %A Chekroun, Mickaël D. %A Ghil, Michael %XThis paper has two interrelated foci: (i) obtaining stable and efficient data-driven closure models by using a multivariate time series of partial observations from a large-dimensional system; and (ii) comparing these closure models with the optimal closures predicted by the Mori–Zwanzig (MZ) formalism of statistical physics. Multilayer stochastic models (MSMs) are introduced as both a generalization and a time-continuous limit of existing multilevel, regression-based approaches to closure in a data-driven setting; these approaches include empirical model reduction (EMR), as well as more recent multi-layer modeling. It is shown that the multilayer structure of MSMs can provide a natural Markov approximation to the generalized Langevin equation (GLE) of the MZ formalism. A simple correlation-based stopping criterion for an EMR–MSM model is derived to assess how well it approximates the GLE solution. Sufficient conditions are derived on the structure of the nonlinear cross-interactions between the constitutive layers of a given MSM to guarantee the existence of a global random attractor. This existence ensures that no blow-up can occur for a broad class of MSM applications, a class that includes non-polynomial predictors and nonlinearities that do not necessarily preserve quadratic energy invariants. The EMR–MSM methodology is first applied to a conceptual, nonlinear, stochastic climate model of coupled slow and fast variables, in which only slow variables are observed. It is shown that the resulting closure model with energy-conserving nonlinearities efficiently captures the main statistical features of the slow variables, even when there is no formal scale separation and the fast variables are quite energetic. Second, an MSM is shown to successfully reproduce the statistics of a partially observed, generalized Lotka–Volterra model of population dynamics in its chaotic regime. The challenges here include the rarity of strange attractors in the model’s parameter space and the existence of multiple attractor basins with fractal boundaries. The positivity constraint on the solutions’ components replaces here the quadratic-energy–preserving constraint of fluid-flow problems and it successfully prevents blow-up.

%B Physica D: Nonlinear Phenomena %I Elsevier %V 297 %P 33–55 %G eng %R 10.1016/j.physd.2014.12.005 %0 Book %B Geophysical Monographs %D 2015 %T Extreme Events: Observations, Modeling and Economics %E M. Chavez %E Ghil, Michael %E J. Urrutia-Fucugauchi %XThe monograph covers the fundamentals and the consequences of extreme geophysical phenomena like asteroid impacts, climatic change, earthquakes, tsunamis, hurricanes, landslides, volcanic eruptions, flooding, and space weather. This monograph also addresses their associated, local and worldwide socio-economic impacts. The understanding and modeling of these phenomena is critical to the development of timely worldwide strategies for the prediction of natural and anthropogenic extreme events, in order to mitigate their adverse consequences. This monograph is unique in as much as it is dedicated to recent theoretical, numerical and empirical developments that aim to improve: (i) the understanding, modeling and prediction of extreme events in the geosciences, and, (ii) the quantitative evaluation of their economic consequences. The emphasis is on coupled, integrative assessment of the physical phenomena and their socio-economic impacts. With its overarching theme, Extreme Events: Observations, Modeling and Economics will be relevant to and become an important tool for researchers and practitioners in the fields of hazard and risk analysis in general, as well as to those with a special interest in climate change, atmospheric and oceanic sciences, seismo-tectonics, hydrology, and space weather.

%B Geophysical Monographs %I American Geophysical Union & Wiley %C Washington, DC %V 214 %G eng %U http://www.wiley.com/WileyCDA/WileyTitle/productCd-1119157013.html %0 Journal Article %J Acta Applicandae Mathematicae %D 2015 %T Finite-horizon parameterizing manifolds, and applications to suboptimal control of nonlinear parabolic PDEs %A Chekroun, Mickaël D. %A Liu, Honghu %B Acta Applicandae Mathematicae %V 135 %P 81–144 %G eng %N 1 %R 10.1007/s10440-014-9949-1 %0 Book Section %B Extreme Events : Observations, Modeling, and Economics %D 2015 %T Impacts of natural disasters on a dynamic economy %A Groth, Andreas %A Dumas, Patrice %A Ghil, Michael %A Hallegatte, Stéphane %E Eric Chavez %E Ghil, Michael %E Jaime Urrutia-Fucugauchi %XThis chapter 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 phe nomena. The challenge is to describe the interfaces between human activities and the functioning of the earth system. We examine the way in which this interface works in the presence of endogenous business cycle dynam ics, based on a nonequilibrium 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 expan sions 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 demon strate that the behavior of the U.S. economy changes significantly between intervals of growth and recession, with higher volatility during expansions.

%B Extreme Events : Observations, Modeling, and Economics %I American Geophysical Union and Wiley-Blackwell %P 343–360 %@ 978-1-119-15701-4 %G eng %0 Book Section %B Climate Change: Multidecadal and Beyond %D 2015 %T A mathematical theory of climate sensitivity or, How to deal with both anthropogenic forcing and natural variability? %A Ghil, Michael %E C. P. Chang %E Ghil, Michael %E Latif, Mojib %E J. M. Wallace %XRecent estimates of climate evolution over the coming century still differ by several degrees. This uncertainty motivates the work presented here. There are two basic approaches to apprehend the complexity of climate change: deterministically nonlinear and stochastically linear, i.e., the Lorenz and the Hasselmann approach. The grand unification of these two approaches relies on the theory of random dynamical systems. We apply this theory to study the random attractors of nonlinear, stochastically perturbed climate models. Doing so allows one to examine the interaction of internal climate variability with the forcing, whether natural or anthropogenic, and to take into account the climate system's non-equilibrium behavior in determining climate sensitivity. This non-equilibrium behavior is due to a combination of nonlinear and random effects. We give here a unified treatment of such effects from the point of view of the theory of dynamical systems and of their bifurcations. Energy balance models are used to illustrate multiple equilibria, while multi-decadal oscillations in the thermohaline circulation illustrate the transition from steady states to periodic behavior. Random effects are introduced in the setting of random dynamical systems, which permit a unified treatment of both nonlinearity and stochasticity. The combined treatment of nonlinear and random effects is applied to a stochastically perturbed version of the classical Lorenz convection model. Climate sensitivity is then defined mathematically as the derivative of an appropriate functional or other function of the system’s state with respect to the bifurcation parameter. This definition is illustrated by using numerical results for a model of the El Niño–Southern Oscillation. The concept of a hierarchy of models is the thread that runs across this chapter, and the robustness of elementary bifurcations across such a hierarchy is emphasized.

%B Climate Change: Multidecadal and Beyond %I World Scientific Publ. Co./Imperial College Press %P 31–51 %G eng %R 10.1142/9789814579933_0002 %0 Journal Article %J Journal of Climate %D 2015 %T Monte Carlo Singular Spectrum Analysis (SSA) revisited: Detecting oscillator clusters in multivariate datasets %A Groth, Andreas %A Ghil, Michael %XSingular spectrum analysis (SSA) along with its multivariate extension (M-SSA) provides an efficient way to identify weak oscillatory behavior in high-dimensional data. To prevent the misinterpretation of stochastic fluctuations in short time series as oscillations, Monte Carlo (MC)–type hypothesis tests provide objective criteria for the statistical significance of the oscillatory behavior. Procrustes target rotation is introduced here as a key method for refining previously available MC tests. The proposed modification helps reduce the risk of type-I errors, and it is shown to improve the test’s discriminating power. The reliability of the proposed methodology is examined in an idealized setting for a cluster of harmonic oscillators immersed in red noise. Furthermore, the common method of data compression into a few leading principal components, prior to M-SSA, is reexamined, and its possibly negative effects are discussed. Finally, the generalized Procrustes test is applied to the analysis of interannual variability in the North Atlantic’s sea surface temperature and sea level pressure fields. The results of this analysis provide further evidence for shared mechanisms of variability between the Gulf Stream and the North Atlantic Oscillation in the interannual frequency band.

%B Journal of Climate %V 28 %P 7873–7893 %G eng %N 19 %R 10.1175/JCLI-D-15-0100.1 %0 Journal Article %J OECD Journal: Journal of Business Cycle Measurement and Analysis %D 2015 %T The Role of Oscillatory Modes in U.S. Business Cycles %A Groth, Andreas %A Ghil, Michael %A Hallegatte, Stéphane %A Dumas, Patrice %XWe apply multivariate singular spectrum analysis to the study of U.S. business cycle dynamics. This method provides a robust way to identify and reconstruct oscillations, whether intermittent or modulated. We show such oscillations to be associated with comovements across the entire economy. The problem of spurious cycles generated by the use of detrending filters is addressed and we present a Monte Carlo test to extract significant oscillations. The behavior of the U.S. economy is shown to change significantly from one phase of the business cycle to another: the recession phase is dominated by a five-year mode, while the expansion phase exhibits more complex dynamics, with higher-frequency modes coming into play. We show that the variations so identified cannot be generated by random shocks alone, as assumed in ‘real’ business-cycle models, and that endogenous, deterministically generated variability has to be involved.

%B OECD Journal: Journal of Business Cycle Measurement and Analysis %P 63–81 %8 Oct %G eng %N 2015/1 %R 10.1787/jbcma-2015-5jrs0lv715wl %0 Journal Article %J Geophysical Research Letters %D 2015 %T Stochastic modeling of decadal variability in ocean gyres %A Kondrashov, Dmitri %A Berloff, Pavel S. %B Geophysical Research Letters %V 42 %P 1543–1553 %G eng %R 10.1002/2014gl062871 %0 Book %D 2015 %T Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations: Stochastic Manifolds for Nonlinear SPDEs II %A Chekroun, Mickaël D. %A Liu, Honghu %A Wang, S. %X[[{"fid":"281","view_mode":"default","type":"media","attributes":{"height":"293","width":"210","style":"float: right;","class":"media-element file-default"}}]]

In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.

%I Springer Briefs in Mathematics, Springer %C New York %G eng %U http://link.springer.com/book/10.1007/978-3-319-12520-6/page/1 %0 Book Section %B Extreme Events: Observations, Modeling and Economics %D 2015 %T Understanding ENSO variability and its extrema: A delay differential equation approach %A Ghil, Michael %A Zaliapin, I. %E M. Chavez %E Ghil, Michael %E J. Urrutia-Fucugauchi %XThe El-Nino/Southern-Oscillation (ENSO) phenomenon is the most prominent signal of seasonal-to-interannual climate variability. The past 30 years of research have shown that ENSO dynamics is governed, by and large, by the interplay of the nonlinear mechanisms, and that their simplest version can be studied in autonomous or forced delay differential equation (DDE) models. This chapter briefly reviews the results of Ghil et al., Zaliapin and Ghil, and Ghil and Zaliapin and pursues their DDE model analysis by focusing on multiple model solutions for the same parameter values and the dynamics of local extrema. It first introduces the DDE model of ENSO variability, reviews the main theoretical results concerning its solutions, and comments on the appropriate numerical integration methods. Novel results on multiple solutions and their extrema are reported and illustrated. After discussing the model's pullback attractor, the chapter explores parameter dependence in the model over its entire 3D parameter space.

%B Extreme Events: Observations, Modeling and Economics %S Geophysical Monographs %I American Geophysical Union & Wiley %P 63–78 %G eng %N 214 %R 10.1002/9781119157052.ch6 %0 Journal Article %J Journal of Geophysical Research: Space Physics %D 2014 %T Noise statistics identification for Kalman filtering of the electron radiation belt observations I: Model errors %A Podladchikova, T. V. %A Shprits, Y. Y. %A Kondrashov, Dmitri %A Kellerman, A. C. %K Data assimilation %K Instruments and techniques %K Kalman filter %K model error identification %K Modeling and forecasting %K Prediction %K Radiation belts %K Space weather %B Journal of Geophysical Research: Space Physics %V 119 %P 5700–5724 %G eng %U http://dx.doi.org/10.1002/2014JA019897 %N 7 %R 10.1002/2014JA019897 %0 Journal Article %J Journal of Geophysical Research: Space Physics %D 2014 %T Noise statistics identification for Kalman filtering of the electron radiation belt observations: 2. Filtration and smoothing %A Podladchikova, T. V. %A Shprits, Y. Y. %A Kellerman, A. C. %A Kondrashov, Dmitri %K Data assimilation %K Instruments and techniques %K Kalman filter %K Modeling and forecasting %K observation error identification %K optimal smoothing %K Prediction %K Radiation belts %K Space weather %B Journal of Geophysical Research: Space Physics %V 119 %P 5725–5743 %G eng %U http://dx.doi.org/10.1002/2014JA019898 %N 7 %R 10.1002/2014JA019898 %0 Journal Article %J Geophysical Research Letters %D 2014 %T Reconstruction of gaps in the past history of solar wind parameters %A Kondrashov, Dmitri %A Denton, R. %A Shprits, Y. Y. %A Singer, H. J. %K gaps %K reconstruction %K singular spectrum analysis %K solar wind %K Solar wind plasma %K Time series analysis %B Geophysical Research Letters %V 41 %P 2702–2707 %G eng %U http://dx.doi.org/10.1002/2014GL059741 %N 8 %R 10.1002/2014GL059741 %0 Journal Article %J Journal of Geophysical Research: Space Physics %D 2014 %T Three-dimensional data assimilation and reanalysis of radiation belt electrons: Observations of a four-zone structure using five spacecraft and the VERB code %A Kellerman, A. C. %A Shprits, Y. Y. %A Kondrashov, Dmitri %A Subbotin, D. %A Makarevich, R. A. %A Donovan, E. %A Nagai, T. %K 3-D %K Data assimilation %K Magnetosphere: inner %K Models %K Numerical modeling %K Radiation belts %K Space radiation environment %K storm %B Journal of Geophysical Research: Space Physics %V 119 %P 8764–8783 %G eng %U http://dx.doi.org/10.1002/2014JA020171 %N 11 %R 10.1002/2014JA020171 %0 Journal Article %J Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences %D 2014 %T Parameter estimation for energy balance models with memory %A Roques, Lionel %A Chekroun, Mickaël D. %A Cristofol, Michel %A Soubeyrand, Samuel %A Ghil, Michael %X We study parameter estimation for one-dimensional energy balance models with memory (EBMMs) given localized and noisy temperature measurements. Our results apply to a wide range of nonlinear, parabolic partial differential equations with integral memory terms. First, we show that a space-dependent parameter can be determined uniquely everywhere in the PDE’s domain of definition D, using only temperature information in a small subdomain E⊂D. This result is valid only when the data correspond to exact measurements of the temperature. We propose a method for estimating a model parameter of the EBMM using more realistic, error-contaminated temperature data derived, for example, from ice cores or marine-sediment cores. Our approach is based on a so-called mechanistic-statistical model that combines a deterministic EBMM with a statistical model of the observation process. Estimating a parameter in this setting is especially challenging, because the observation process induces a strong loss of information. Aside from the noise contained in past temperature measurements, an additional error is induced by the age-dating method, whose accuracy tends to decrease with a sample’s remoteness in time. Using a Bayesian approach, we show that obtaining an accurate parameter estimate is still possible in certain cases. %B Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences %I The Royal Society %V 470 %G eng %U http://rspa.royalsocietypublishing.org/content/470/2169/20140349 %N 2169 %R 10.1098/rspa.2014.0349 %0 Journal Article %J Proceedings of the National Academy of Sciences %D 2014 %T Rough parameter dependence in climate models and the role of Ruelle-Pollicott resonances %A Chekroun, Mickaël D. %A Neelin, J. David %A Kondrashov, Dmitri %A McWilliams, James C. %A Ghil, Michael %XDespite the importance of uncertainties encountered in climate model simulations, the fundamental mechanisms at the origin of sensitive behavior of long-term model statistics remain unclear. Variability of turbulent flows in the atmosphere and oceans exhibits recurrent large-scale patterns. These patterns, while evolving irregularly in time, manifest characteristic frequencies across a large range of time scales, from intraseasonal through interdecadal. Based on modern spectral theory of chaotic and dissipative dynamical systems, the associated low-frequency variability may be formulated in terms of Ruelle-Pollicott (RP) resonances. RP resonances encode information on the nonlinear dynamics of the system, and an approach for estimating them—as filtered through an observable of the system—is proposed. This approach relies on an appropriate Markov representation of the dynamics associated with a given observable. It is shown that, within this representation, the spectral gap—defined as the distance between the subdominant RP resonance and the unit circle—plays a major role in the roughness of parameter dependences. The model statistics are the most sensitive for the smallest spectral gaps; such small gaps turn out to correspond to regimes where the low-frequency variability is more pronounced, whereas autocorrelations decay more slowly. The present approach is applied to analyze the rough parameter dependence encountered in key statistics of an El-Niño–Southern Oscillation model of intermediate complexity. Theoretical arguments, however, strongly suggest that such links between model sensitivity and the decay of correlation properties are not limited to this particular model and could hold much more generally.

%B Proceedings of the National Academy of Sciences %V 111 %P 1684-1690 %G eng %N 5 %R 10.1073/pnas.1321816111 %0 Journal Article %J Geophysical Research Letters %D 2013 %T Application of a new data operator-splitting data assimilation technique to the 3-D VERB diffusion code and CRRES measurements %A Shprits, Yuri %A Kellerman, Adam %A Kondrashov, Dmitri %A Subbotin, Dmitriy %K Data assimilation %K modeling %K Modeling and forecasting %K Particle acceleration %K Radiation belts %K Wave/particle interactions %B Geophysical Research Letters %V 40 %P 4998–5002 %G eng %U http://dx.doi.org/10.1002/grl.50969 %N 19 %R 10.1002/grl.50969 %0 Journal Article %J Fondazione Eni Enrico Mattei (FEEM) %D 2013 %T Economic Cycles and their Synchronization: A spectral survey %A Lisa Sella %A Gianna Vivaldo %A Groth, Andreas %A Ghil, Michael %XThe present work applies several advanced spectral methods to the analysis of macroeconomic fluctuations in three countries of the European Union: Italy, The Netherlands, and the United Kingdom. We focus here in particular on singular-spectrum analysis (SSA), which provides valuable spatial and frequency information of multivariate data and that goes far beyond a pure analysis in the time domain. The spectral methods discussed here are well established in the geosciences and life sciences, but not yet widespread in quantitative economics. In particular, they enable one to identify and describe nonlinear trends and dominant cycles –- including seasonal and interannual components –- that characterize the deterministic behavior of each time series. These tools have already proven their robustness in the application on short and noisy data, and we demonstrate their usefulness in the analysis of the macroeconomic indicators of these three countries. We explore several fundamental indicators of the countries' real aggregate economy in a univariate, as well as a multivariate setting. Starting with individual single-channel analysis, we are able to identify similar spectral components among the analyzed indicators. Next, we consider combinations of indicators and countries, in order to take different effects of comovements into account. Since business cycles are cross-national phenomena, which show common characteristics across countries, our aim is to uncover hidden global behavior across the European economies. Results are compared with previous findings on the U.S. indicators \citepGroth.ea.FEEM.2012. Finally, the analysis is extended to include several indicators from the U.S. economy, in order to examine its influence on the European market.

%B Fondazione Eni Enrico Mattei (FEEM) %I Fondazione Eni Enrico Mattei (FEEM) %V 105 %P 1 %G eng %U http://www.feem.it/getpage.aspx?id=6017&sez=Publications&padre=73 %N 105 %9 working paper %0 Journal Article %J Geophysical Research Letters %D 2013 %T Global modes of climate variability %A de Viron, O. %A Dickey, J. O. %A Ghil, Michael %XThe atmosphere, hydrosphere and cryosphere form a fully coupled climate system. This system exhibits a number of large-scale phenomena, such as the El Nino Southern Oscillation (ENSO), the Asian Monsoon, the North Atlantic Oscillation (NAO), and the Madden-Julian Oscillation (MJO). While these modes of variability are not exactly periodic, they are oscillatory in character, and their state is monitored using so-called climate indices. Each of these scalar indices is a combination of several climate variables. Here, we use a comprehensive set of 25 climate indices for time intervals that range between 1948 and 2011, and estimate an optimal set of lags between these indices to maximize their correlation. We show that most of the index pairs drawn from this set present a significant correlation on interannual time scales. It is also shown that, on average, about two-thirds of the total variability in each index can be described by using only the four leading principal components of the entire set of lagged indices. Our index set's leading orthogonal modes exhibit several interannual frequencies and capture separately variability associated with the North Atlantic and the North Pacific. These modes are associated, in turn, with large-scale variations of sea surface temperatures.

%B Geophysical Research Letters %V 40 %P 1832-1837 %G eng %N 9 %R 10.1002/grl.50386 %0 Journal Article %J Geophysical Research Letters %D 2013 %T Low-order stochastic model and ``past-noise forecasting" of the Madden-Julian oscillation %A Kondrashov, Dmitri %A Chekroun, Mickaël D. %A Robertson, Andrew W. %A Ghil, Michael %B Geophysical Research Letters %V 40 %P 5305–5310 %G eng %R 10.1002/grl.50991 %0 Journal Article %J Climate of the Past %D 2013 %T Major dust events in Europe during marine isotope stage 5 (130–74 ka): a climatic interpretation of the" markers" %A Rousseau, D.-D. %A Ghil, Michael %A Kukla, G. %A Sima, A. %A Antoine, P. %A Fuchs, M. %A Hatté, C. %A Lagroix, F. %A Debret, M. %A Moine, O. %B Climate of the Past %I Copernicus GmbH %V 9 %P 2213–2230 %G eng %N 5 %0 Journal Article %J Journal of Climate %D 2013 %T Oscillatory Climate Modes in the Indian Monsoon, North Atlantic and Tropical Pacific %A Feliks, Yizhak %A Groth, Andreas %A Robertson, Andrew W. %A Ghil, Michael %XThis paper explores the three-way interactions between the Indian monsoon, the North Atlantic and the Tropical Pacific. Four climate records were analyzed: the monsoon rainfall in two Indian regions, the Southern Oscillation Index for the Tropical Pacific, and the NAO index for the North Atlantic. The individual records exhibit highly significant oscillatory modes with spectral peaks at 7–8 yr and in the quasi-biennial and quasi-quadrennial bands. The interactions between the three regions were investigated in the light of the synchronization theory of chaotic oscillators. The theory was applied here by combining multichannel singular-spectrum analysis (M-SSA) with a recently introduced varimax rotation of the M-SSA eigenvectors. A key result is that the 7–8-yr and 2.7-yr oscillatory modes in all three regions are synchronized, at least in part. The energy-ratio analysis, as well as time-lag results, suggest that the NAO plays a leading role in the 7–8-yr mode. It was found therewith that the South Asian monsoon is not slaved to forcing from the equatorial Pacific, although it does interact strongly with it. The time-lag analysis pinpointed this to be the case in particular for the quasi-biennial oscillatory modes. Overall, these results confirm that the approach of synchronized oscillators, combined with varimax-rotated M-SSA, is a powerful tool in studying teleconnections between regional climate modes and that it helps identify the mechanisms that operate in various frequency bands. This approach should be readily applicable to ocean modes of variability and to the problems of air-sea interaction as well.

%B Journal of Climate %V 26 %P 9528-–9544 %G eng %R 10.1175/JCLI-D-13-00105.1 %0 Journal Article %J Climate Dynamics %D 2012 %T Impact of the modulated annual cycle and intraseasonal oscillation on daily-to-interannual rainfall variability across monsoonal India %A Moron, Vincent %A Robertson, Andrew W. %A Ghil, Michael %B Climate Dynamics %I Springer %V 38 %P 2409–2435 %G eng %N 11-12 %0 Journal Article %J Journal of Climate %D 2012 %T Atmospheric circulations induced by a midlatitude SST front: A GCM study %A Brachet, Sidonie %A Codron, Francis %A Feliks, Yizhak %A Ghil, Michael %A Le Treut, Hervé %A Simonnet, Eric %XThe atmospheric effects of sea surface temperature (SST) anomalies over and near western boundary currents are a matter of renewed interest. The general circulation model (GCM) of the Laboratoire de Météorologie Dynamique (LMD-Z) has a zooming capability that allows a regionally increased resolution. This GCM is used to analyze the impact of a sharp SST front in the North Atlantic Ocean: two simulations are compared, one with climatological SSTs and the other with an enhanced Gulf Stream front. The results corroborate the theory developed previously by the present team to explain the impact of oceanic fronts. In this theory, the vertical velocity at the top of the atmospheric boundary layer has two components: mechanical and thermal. It is the latter that is dominant in the tropics, while in midlatitudes both play a role in determining the wind convergence above the boundary layer. The strengthened SST front does generate the previously predicted stronger ascent above the warmer water south of the front and stronger descent above the colder waters to the north. In the GCM simulations, the ascent over the warm anomalies is deeper and more intense than the descent.

%B Journal of Climate %V 25 %P 1847–1853 %G eng %N 6 %0 Journal Article %J Journal of the Atmospheric Sciences %D 2012 %T Atmospheric dynamics triggered by an oceanic SST front in a moist quasigeostrophic model %A Deremble, Bruno %A Lapeyre, Guillaume %A Ghil, Michael %B Journal of the Atmospheric Sciences %V 69 %P 1617–1632 %G eng %N 5 %0 Journal Article %J Encyclopedia of Atmospheric Sciences. Elsevier %D 2012 %T Climate variability: nonlinear and random effects %A Ghil, Michael %B Encyclopedia of Atmospheric Sciences. Elsevier %P 1–6 %G eng %0 Journal Article %J Discrete and Continuous Dynamical Systems - Series A %D 2012 %T Homeomorphisms group of normed vector space: Conjugacy problems and the Koopman operator %A Chekroun, Mickaël D. %A Jean Roux %B Discrete and Continuous Dynamical Systems - Series A %V 33 %P 3957–3980 %G eng %R 10.3934/dcds.2013.33.3957 %0 Journal Article %J Communications in Mathematical Physics %D 2012 %T Invariant measures for dissipative dynamical systems: Abstract results and applications %A Chekroun, Mickaël D. %A Glatt-Holtz, N. E. %B Communications in Mathematical Physics %V 316 %P 723–761 %G eng %R 10.1007/s00220-012-1515-y %0 Journal Article %J Nonlinear Processes in Geophysics %D 2012 %T Multiple equilibria and oscillatory modes in a mid-latitude ocean-forced atmospheric model %A Deremble, B. %A Simonnet, E. %A Ghil, Michael %B Nonlinear Processes in Geophysics %V 19 %P 479–499 %G eng %N 5 %R 10.5194/npg-19-479-2012 %0 Journal Article %J Climate of the Past %D 2012 %T Natural variability and anthropogenic effects in a Central Mediterranean core %A Alessio, Silvia %A Gianna Vivaldo %A Taricco, Carla %A Ghil, Michael %B Climate of the Past %V 8 %P 831–839 %G eng %N 2 %R 10.5194/cp-8-831-2012 %0 Journal Article %J Fondazione Eni Enrico Mattei (FEEM) %D 2012 %T The Role of Oscillatory Modes in U.S. Business Cycles %A Groth, Andreas %A Ghil, Michael %A Hallegatte, Stéphane %A Dumas, Patrice %XWe apply the advanced time-and-frequency-domain method of singular spectrum analysis to study business cycle dynamics in a set of nine U.S. macroeconomic indicators. This method provides a robust way to identify and reconstruct shared oscillations, whether intermittent or modulated. We address the problem of spurious cycles generated by the use of detrending filters and present a Monte Carlo test to extract significant oscillations. Finally, we demonstrate that the behavior of the U.S. economy changes significantly between episodes of growth and recession; these variations cannot be generated by random shocks alone, in the absence of endogenous variability.

%B Fondazione Eni Enrico Mattei (FEEM) %I Fondazione Eni Enrico Mattei (FEEM) %V 26 %P 1 %G eng %U http://www.feem.it/getpage.aspx?id=4820&sez=Publications&padre=73 %9 working paper %0 Journal Article %J Geophysical Research Letters %D 2012 %T The uncertain future of climate uncertainty %A Hannart, A. %A Ghil, Michael %A Dufresne, J. L. %A Naveau, P. %B Geophysical Research Letters %G eng %0 Journal Article %J Advances in Space Research %D 2011 %T Reanalysis of radiation belt electron phase space density using various boundary conditions and loss models %A M. Daae %A Shprits, Y. Y. %A B. Ni %A J. Koller %A Kondrashov, Dmitri %A Y. Chen %B Advances in Space Research %V 48 %P 1327 - 1334 %G eng %U http://www.sciencedirect.com/science/article/pii/S0273117711004741 %N 8 %R http://dx.doi.org/10.1016/j.asr.2011.07.001 %0 Magazine Article %D 2011 %T Toward a Mathematical Theory of Climate Sensitivity %B SIAM News %G eng %0 Journal Article %J Physica D %D 2011 %T Stochastic climate dynamics: Random attractors and time-dependent invariant measures %A Chekroun, Mickaël D. %A Simonnet, Eric %A Ghil, Michael %X This article attempts a unification of the two approaches that have dominated theoretical climate dynamics since its inception in the 1960s: the nonlinear deterministic and the linear stochastic one. This unification, via the theory of random dynamical systems (RDS), allows one to consider the detailed geometric structure of the random attractors associated with nonlinear, stochastically perturbed systems. We report on high-resolution numerical studies of two idealized models of fundamental interest for climate dynamics. The first of the two is a stochastically forced version of the classical Lorenz model. The second one is a low-dimensional, nonlinear stochastic model of the El Niño-Southern Oscillation (ENSO). These studies provide a good approximation of the two models' global random attractors, as well as of the time-dependent invariant measures supported by these attractors; the latter are shown to have an intuitive physical interpretation as random versions of Sina\"ı-Ruelle-Bowen (SRB) measures. %B Physica D %V 240 %P 1685-–1700 %G eng %N 21 %R 10.1016/j.physd.2011.06.005 %0 Journal Article %J Discrete and Continuous Dynamical Systems - Series S %D 2011 %T Asymptotics of the Coleman-Gurtin model %A Chekroun, Mickaël D. %A Di Plinio, F. %A Glatt-Holtz, N. E. %A Pata, V. %B Discrete and Continuous Dynamical Systems - Series S %V 4 %P 351–369 %G eng %N 2 %R 10.3934/dcdss.2011.4.351 %0 Journal Article %J Journal of Climate %D 2011 %T The atmospheric circulation over the North Atlantic as induced by the SST field %A Feliks, Yizhak %A Ghil, Michael %A Robertson, Andrew W. %XSpectral analyses of the sea surface temperature (SST) in the Simple Ocean Data Analysis (SODA) reanalysis for the past half-century identify prominent and statistically significant interannual oscillations in two regions along the Gulf Stream front over the North Atlantic. A model of the atmospheric marine boundary layer coupled to a baroclinic quasi-geostrophic model of the free atmosphere is then forced with the SST history from the SODA reanalysis. Two extreme states are found in the atmospheric simulations: they consist of (1) an eastward extension of the westerly jet associated with the front, which occurs mainly during boreal winter; and (2) a quiescent state of very weak flow found predominantly in the summer. This vacillation of the oceanic-front–induced jet in the model is found to exhibit periodicities similar to those identified in the observed Gulf Stream SST front itself. In addition, a close correspondence is found between interannual spectral peaks in the observed North Atlantic Oscillation (NAO) index, and the SODA-induced oscillations in the atmospheric model. In particular, significant oscillatory modes with periods of 8.5, 4.2 and 2.8 years are found in both the observed and simulated indices, and shown to be highly synchronized and of similar energy in both time series. These oscillatory modes in the simulations are shown to be suppressed when either (a) the Gulf Stream front or (b) its interannual oscillations are omitted from the SST field. Moreover, these modes also disappear when (c) the SST front is spatially smoothed, thus confirming that they are indeed induced by the oceanic front.

%B Journal of Climate %V 24 %P 522–542 %G eng %R 10.1175/2010JCLI3859.1 %0 Journal Article %J International Journal of Bifurcation and Chaos %D 2011 %T Boolean delay equations on networks in economics and the geosciences %A Coluzzi, Barbara %A Ghil, Michael %A Hallegatte, Stéphane %A Weisbuch, Gérard %B International Journal of Bifurcation and Chaos %I World Scientific %V 21 %P 3511–3548 %G eng %N 12 %R 10.1142/s0218127411030702 %0 Journal Article %J Math. & Sci. hum. / Mathematics and Social Sciences %D 2011 %T Dynamic coupling of the climate and macroeconomic systems %A Dumas, Patrice %A Ghil, Michael %A Groth, Andreas %A Hallegatte, Stéphane %XThis review paper presents a modeling framework for macroeco- nomic growth dynamics that is motivated by recent attempts to formulate and study “integrated models” of the coupling between natural and socio-economic phenomena. The challenge is to describe the interfaces between human acti- vities 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, and review the macroeconomic response to natural disasters. Our model exhibits a larger response to natural disasters during expansions than during recessions, and we raise questions about the as- sessment of climate change damages or natural disaster losses that are based purely on long-term growth models. In order to compare the theoretical fin- dings with observational data, we present a new method for extracting cyclic behavior from the latter, based on multivariate singular spectral analysis.

%B Math. & Sci. hum. / Mathematics and Social Sciences %G eng %0 Journal Article %J Ocean Science %D 2011 %T An empirical stochastic model of sea-surface temperatures and surface winds over the Southern Ocean %A Kravtsov, Sergey %A Kondrashov, Dmitri %A Kamenkovich, I. %A Ghil, Michael %XThis study employs NASA's recent satellite measurements of sea-surface temperatures (SSTs) and sea-level winds (SLWs) with missing data filled-in by Singular Spectrum Analysis (SSA), to construct empirical models that capture both intrinsic and SST-dependent aspects of SLW variability. The model construction methodology uses a number of algorithmic innovations that are essential in providing stable estimates of the model's propagator. The best model tested herein is able to faithfully represent the time scales and spatial patterns of anomalies associated with a number of distinct processes. These processes range from the daily synoptic variability to interannual signals presumably associated with oceanic or coupled dynamics. Comparing the simulations of an SLW model forced by the observed SST anomalies with the simulations of an SLW-only model provides preliminary evidence for the ocean driving the atmosphere in the Southern Ocean region.

%B Ocean Science %V 7 %P 755–770 %G eng %U http://www.ocean-sci.net/7/755/2011/ %N 6 %R 10.5194/os-7-755-2011 %0 Journal Article %J Nonlinear Processes in Geophysics %D 2011 %T Extreme events: dynamics, statistics and prediction %A Ghil, Michael %A P. Yiou %A Hallegatte, S. %A Malamud, B. D. %A Naveau, P. %A Soloviev, A. %A Friederichs, P. %A Keilis-Borok, V. %A Kondrashov, Dmitri %A Kossobokov, V. %A Mestre, O. %A Nicolis, C. %A Rust, H. W. %A Shebalin, P. %A Vrac, M. %A Witt, A. %A Zaliapin, I. %XWe review work on extreme events, their causes and consequences, by a group of Euro- pean and American researchers involved in a three-year project on these topics. The review covers theoretical aspects of time series analysis and of extreme value theory, as well as of the deteministic modeling of extreme events, via continuous and discrete dynamic models. The applications include climatic, seismic and socio-economic events, along with their prediction.

%B Nonlinear Processes in Geophysics %V 18 %P 295–350 %G eng %N 3 %R 10.5194/npg-18-295-2011 %0 Journal Article %J Climate Dynamics %D 2011 %T Impact of the modulated annual cycle and intraseasonal oscillation on daily-to-interannual rainfall variability across monsoonal India %A Moron, Vincent %A Robertson, Andrew W. %A Ghil, Michael %XVariability of the Indian summer monsoon is decomposed into an interannually modulated annual cycle (MAC) and a northward-propagating, intraseasonal (30-60-day) oscillation (ISO). To achieve this decomposition, we apply multi-channel singular spectrum analysis (M-SSA) simultaneously to unfiltered daily fields of observed outgoing long-wave radiation (OLR) and to reanalyzed 925-hPa winds over the Indian region, from 1975 to 2008. The MAC is essentially given by the year-to-year changes in the annual and semi-annual components; it displays a slow northward migration of OLR anomalies coupled with an alternation between the northeast winter and southwest summer monsoons. The impact of these oscillatory modes on rainfall is then analyzed using a 1-degree gridded daily data set, focusing on Monsoonal India (north of 17°N and west of 90°E) during the months of June to September. Daily rainfall variability is partitioned into three states using a Hidden Markov Model. Two of these states are shown to agree well with previous classifications of "active" and "break" phases of the monsoon, while the third state exhibits a dipolar east-west pattern with abundant rainfall east of about 77°E and low rainfall to the west. Occurrence of the three rainfall states is found to be an asymmetric function of both the MAC and ISO components. On average, monsoon active phases are favored by large positive anomalies of MAC, and breaks by negative ones. ISO impact is decisive when the MAC is near neutral values during the onset and withdrawal phases of the monsoon. Active monsoon spells are found to require a synergy between the MAC and ISO, while the east-west rainfall dipole is less sensitive to interactions between the two. The driest years, defined from spatially averaged June-September rainfall anomalies, are found to be mostly a result of breaks occurring during the onset and withdrawal stages of the monsoon, e.g., mid-June to mid-July, and during September. These breaks are in turn associated with anomalously late MAC onset or early MAC withdrawal, often together with a large-amplitude, negative ISO event. The occurrence of breaks during the core of the monsoon—from late July to late August—is restricted to a few years when MAC was exceptionally weak, such as 1987 or 2002. Wet years are shown to be mostly associated with more frequent active spells and a stronger MAC than usual, especially at the end of the monsoon season. Taken together, our results suggest that monthly and seasonal precipitation predictability is higher in the early and late stages of the summer monsoon season.

%B Climate Dynamics %P 666 %8 dec %G eng %R 10.1007/s00382-011-1253-4 %0 Journal Article %J Space Weather %D 2011 %T Lognormal Kalman filter for assimilating phase space density data in the radiation belts %A Kondrashov, Dmitri %A Ghil, Michael %A Y. Shprits %B Space Weather %I Wiley Online Library %V 9 %G eng %N 11 %R 10.1029/2011sw000726 %0 Journal Article %J Physical Review E %D 2011 %T Multivariate singular spectrum analysis and the road to phase synchronization %A Groth, Andreas %A Ghil, Michael %XWe show that multivariate singular spectrum analysis (M-SSA) greatly helps study phase synchronization in a large system of coupled oscillators and in the presence of high observational noise levels. With no need for detailed knowledge of individual subsystems nor any a priori phase de?nition for each of them, we demonstrate that M-SSA can automatically identify multiple oscillatory modes and detect whether these modes are shared by clusters of phase- and frequency-locked oscillators. As an essential modi?cation of M-SSA, here we introduce variance-maximization (varimax) rotation of the M-SSA eigenvectors to optimally identify synchronized-oscillator clustering.

%B Physical Review E %V 84 %P 036206 %G eng %R 10.1103/PhysRevE.84.036206 %0 Journal Article %J Proceedings of the National Academy of Sciences %D 2011 %T Predicting stochastic systems by noise sampling, and application to the El Niño-Southern Oscillation %A Chekroun, Mickaël D. %A Kondrashov, Dmitri %A Ghil, Michael %XInterannual and interdecadal prediction are major challenges of climate dynamics. In this article we develop a prediction method for climate processes that exhibit low-frequency variability (LFV). The method constructs a nonlinear stochastic model from past observations and estimates a path of the “weather” noise that drives this model over previous finite-time windows. The method has two steps: (i) select noise samples—or “snippets”—from the past noise, which have forced the system during short-time intervals that resemble the LFV phase just preceding the currently observed state; and (ii) use these snippets to drive the system from the current state into the future. The method is placed in the framework of pathwise linear-response theory and is then applied to an El Niño–Southern Oscillation (ENSO) model derived by the empirical model reduction (EMR) methodology; this nonlinear model has 40 coupled, slow, and fast variables. The domain of validity of this forecasting procedure depends on the nature of the system’s pathwise response; it is shown numerically that the ENSO model’s response is linear on interannual time scales. As a result, the method’s skill at a 6- to 16-month lead is highly competitive when compared with currently used dynamic and statistic prediction methods for the Niño-3 index and the global sea surface temperature field.

%B Proceedings of the National Academy of Sciences %V 108 %P 11766–11771 %G eng %N 29 %R 10.1073/pnas.1015753108 %0 Journal Article %J Nonlinear Processes in Geophysics %D 2011 %T Reply to G.H. Roe's and M.B. Baker's comment on "Another look at climate sensitivity" %A Zaliapin, Ilya %A Ghil, Michael %B Nonlinear Processes in Geophysics %I Copernicus GmbH %V 18 %P 129–131 %8 feb %G eng %N 1 %R 10.5194/npg-18-129-2011 %0 Book Section %B Stochastic physics and climate modeling. Cambridge University Press, Cambridge %D 2010 %T Empirical model reduction and the modelling hierarchy in climate dynamics and the geosciences %A Kravtsov, Sergey %A Kondrashov, Dmitri %A Ghil, Michael %E P. Williams %E T. Palmer %B Stochastic physics and climate modeling. Cambridge University Press, Cambridge %I Cambridge University Press %P 35–72 %G eng %0 Journal Article %J Nonlinear Processes in Geophysics %D 2010 %T A delay differential model of ENSO variability, Part 2: Phase locking, multiple solutions, and dynamics of extrema %A Zaliapin, Ilya %A Ghil, Michael %B Nonlinear Processes in Geophysics %V 17 %P 123–135 %8 mar %G eng %N 2 %R 10.5194/npg-17-123-2010 %0 Book %D 2010 %T Mathématiques Appliquées aux sciences de la Vie et de la Planète Cours et exercices corrigés %A Ghil, Michael %A Jean Roux %X Ce manuel s'adresse aux étudiants en L3, M1. Il présente les outils théoriques et les méthodes numériques utiles en sciences de la vie ou de la Terre. Des exercices corrigés en fin de chapitre permettent de verifier que le cours a bien été assimilé. %I Sciences Sup, Dunod %P 400 %G eng %0 Journal Article %J Nonlinear Processes in Geophysics %D 2010 %T Another look at climate sensitivity %A Zaliapin, Ilya %A Ghil, Michael %XWe revisit a recent claim that the Earth's climate system is characterized by sensitive dependence to parameters; in particular, that the system exhibits an asymmetric, large-amplitude response to normally distributed feedback forcing. Such a response would imply irreducible uncertainty in climate change predictions and thus have notable implications for climate science and climate-related policy making. We show that equilibrium climate sensitivity in all generality does not support such an intrinsic indeterminacy; the latter appears only in essentially linear systems. The main flaw in the analysis that led to this claim is inappropriate linearization of an intrinsically nonlinear model; there is no room for physical interpretations or policy conclusions based on this mathematical error. Sensitive dependence nonetheless does exist in the climate system, as well as in climate models – albeit in a very different sense from the one claimed in the linear work under scrutiny – and we illustrate it using a classical energy balance model (EBM) with nonlinear feedbacks. EBMs exhibit two saddle-node bifurcations, more recently called "tipping points," which give rise to three distinct steady-state climates, two of which are stable. Such bistable behavior is, furthermore, supported by results from more realistic, nonequilibrium climate models. In a truly nonlinear setting, indeterminacy in the size of the response is observed only in the vicinity of tipping points. We show, in fact, that small disturbances cannot result in a large-amplitude response, unless the system is at or near such a point. We discuss briefly how the distance to the bifurcation may be related to the strength of Earth's ice-albedo feedback.

%B Nonlinear Processes in Geophysics %V 17 %P 113–122 %G eng %N 2 %R 10.5194/npg-17-113-2010 %0 Journal Article %J Discrete and Continuous Dynamical Systems %D 2010 %T Averaging of time-periodic systems without a small parameter %A Chekroun, Mickaël D. %A Ghil, Michael %A Jean Roux %A Varadi, Ferenc %B Discrete and Continuous Dynamical Systems %I American Institute of Mathematical Sciences (AIMS) %V 14 %P 753–782 %8 jan %G eng %N 4 %R 10.3934/dcds.2006.14.753 %0 Journal Article %J Ecological Complexity %D 2010 %T Does reaction-diffusion support the duality of fragmentation effect? %A Roques, Lionel %A Chekroun, Mickaël D. %B Ecological Complexity %I Elsevier %V 7 %P 100–106 %G eng %N 1 %R 10.1016/j.ecocom.2009.07.003 %0 Journal Article %J Geophysical Research Letters %D 2010 %T Gap Filling of Solar Wind Data by Singular Spectrum Analysis %A Kondrashov, Dmitri %A Shprits, Yuri %A Ghil, Michael %XObservational data sets in space physics often contain instrumental and sampling errors, as well as large gaps. This is both an obstacle and an incentive for research, since continuous data sets are typically needed for model formulation and validation. For example, the latest global empirical models of Earth's magnetic field are crucial for many space weather applications, and require time continuous solar wind and interplanetary magnetic field (IMF) data; both of these data sets have large gaps before 1994. Singular spectrum analysis (SSA) reconstructs missing data by using an iteratively inferred, smooth “signal” that captures coherent modes, while “noise” is discarded. In this study, we apply SSA to fill in large gaps in solar wind and IMF data, by combining it with geomagnetic indices that are time continuous, and generalizing it to multivariate geophysical data consisting of gappy “driver” and continuous “response” records. The reconstruction error estimates provide information on the physics of co variability between particular solar wind parameters and geomagnetic indices.

%B Geophysical Research Letters %I CiteSeerX - Scientific Literature Digital Library and Search Engine [http://citeseerx.ist.psu.edu/oai2] (United States) %V 37 %P L15101 %G eng %R 10.1029/2010GL044138 %0 Journal Article %J Astronomy & Geophysics %D 2010 %T Geophysical flows as dynamical systems: the influence of Hide's experiments %A Ghil, Michael %A Read, Peter %A Smith, Leonard %B Astronomy & Geophysics %I Oxford University Press %V 51 %P 4–28 %G eng %N 4 %0 Journal Article %J Journal of Climate %D 2010 %T Oscillatory Climate Modes in the Eastern Mediterranean and Their Synchronization with the North Atlantic Oscillation %A Feliks, Yizhak %A Ghil, Michael %A Robertson, Andrew W. %XOscillatory climatic modes over the North Atlantic, Ethiopian Plateau, and eastern Mediterranean were examined in instrumental and proxy records from these regions. Aside from the well-known North Atlantic Oscillation (NAO) index and the Nile River water-level records, the authors study for the first time an instrumental rainfall record from Jerusalem and a tree-ring record from the Golan Heights. The teleconnections between the regions were studied in terms of synchronization of chaotic oscillators. Standard methods for studying synchronization among such oscillators are modified by combining them with advanced spectral methods, including singular spectrum analysis. The resulting cross-spectral analysis quantifies the strength of the coupling together with the degree of synchronization. A prominent oscillatory mode with a 7–8-yr period is present in all the climatic indices studied here and is completely synchronized with the North Atlantic Oscillation. An energy analysis of the synchronization raises the possibility that this mode originates in the North Atlantic. Evidence is discussed for this mode being induced by the 7–8-yr oscillation in the position of the Gulf Stream front. A mechanism for the teleconnections between the North Atlantic, Ethiopian Plateau, and eastern Mediterranean is proposed, and implications for interannual-to-decadal climate prediction are discussed.

%B Journal of Climate %V 23 %P 4060–4079 %G eng %N 15 %R 10.1175/2010JCLI3181.1 %0 Journal Article %J Physica D: Nonlinear Phenomena %D 2010 %T Reduced models of atmospheric low-frequency variability: Parameter estimation and comparative performance %A Strounine, K. %A Kravtsov, Sergey %A Kondrashov, Dmitri %A Ghil, Michael %XLow-frequency variability (LFV) of the atmosphere refers to its behavior on time scales of 10–100 days, longer than the life cycle of a mid-latitude cyclone but shorter than a season. This behavior is still poorly understood and hard to predict. The present study compares various model reduction strategies that help in deriving simplified models of LFV. Three distinct strategies are applied here to reduce a fairly realistic, high-dimensional, quasi-geostrophic, 3-level (QG3) atmospheric model to lower dimensions: (i) an empirical–dynamical method, which retains only a few components in the projection of the full QG3 model equations onto a specified basis, and finds the linear deterministic and the stochastic corrections empirically as in Selten (1995) [5]; (ii) a purely dynamics-based technique, employing the stochastic mode reduction strategy of Majda et al. (2001) [62]; and (iii) a purely empirical, multi-level regression procedure, which specifies the functional form of the reduced model and finds the model coefficients by multiple polynomial regression as in Kravtsov et al. (2005) [3]. The empirical–dynamical and dynamical reduced models were further improved by sequential parameter estimation and benchmarked against multi-level regression models; the extended Kalman filter was used for the parameter estimation. Overall, the reduced models perform better when more statistical information is used in the model construction. Thus, the purely empirical stochastic models with quadratic nonlinearity and additive noise reproduce very well the linear properties of the full QG3 model’s LFV, i.e. its autocorrelations and spectra, as well as the nonlinear properties, i.e. the persistent flow regimes that induce non-Gaussian features in the model’s probability density function. The empirical–dynamical models capture the basic statistical properties of the full model’s LFV, such as the variance and integral correlation time scales of the leading LFV modes, as well as some of the regime behavior features, but fail to reproduce the detailed structure of autocorrelations and distort the statistics of the regimes. Dynamical models that use data assimilation corrections do capture the linear statistics to a degree comparable with that of empirical–dynamical models, but do much less well on the full QG3 model’s nonlinear dynamics. These results are discussed in terms of their implications for a better understanding and prediction of LFV.

%B Physica D: Nonlinear Phenomena %I Elsevier %V 239 %P 145–166 %G eng %N 3 %R 10.1016/j.physd.2009.10.013 %0 Journal Article %J Journal of the Atmospheric Sciences %D 2010 %T Signatures of nonlinear dynamics in an idealized atmospheric model %A Kondrashov, Dmitri %A Kravtsov, Sergey %A Ghil, Michael %B Journal of the Atmospheric Sciences %V 68 %P 3–12 %G eng %N 1 %R 10.1175/2010jas3524.1 %0 Journal Article %J Journal of Geophysical Research: Earth Surface %D 2010 %T Transport on river networks: A dynamic tree approach %A Zaliapin, Ilya %A Foufoula-Georgiou, Efi %A Ghil, Michael %B Journal of Geophysical Research: Earth Surface %I Wiley Online Library %V 115 %G eng %N F2 %R 10.1029/2009jf001281 %0 Journal Article %J Journal of Geophysical Research: Space Physics %D 2009 %T Reanalyses of the radiation belt electron phase space density using nearly equatorial CRRES and polar-orbiting Akebono satellite observations %A Ni, Binbin %A Shprits, Yuri %A Nagai, Tsugunobu %A Thorne, Richard %A Chen, Yue %A Kondrashov, Dmitri %A Kim, Hee-jeong %K Charged particle motion and acceleration %K Data assimilation %K data assimilation technique %K Magnetic storms and substorms %K phase space density %K radiation belt electrons %K Radiation belts %K Space radiation environment %B Journal of Geophysical Research: Space Physics %V 114 %P n/a–n/a %G eng %U http://dx.doi.org/10.1029/2008JA013933 %N A5 %R 10.1029/2008JA013933 %0 Journal Article %J Stochastic physics and climate modelling. Cambridge University Press, Cambridge %D 2009 %T Empirical model reduction and the modelling hierarchy in climate dynamics and the geosciences %A Kravtsov, Sergey %A Kondrashov, Dmitri %A Ghil, Michael %X Modern climate dynamics uses a two-fisted approach in attacking and solving the problems of atmospheric and oceanic flows. The two fists are: (i) observational analyses; and (ii) simulations of the geofluids, including the coupled atmosphere–ocean system, using a hierarchy of dynamical models. These models represent interactions between many processes that act on a broad range of spatial and time scales, from a few to tens of thousands of kilometers, and from diurnal to multidecadal, respectively. The evolution of virtual climates simulated by the most detailed and realistic models in the hierarchy is typically as difficult to interpret as that of the actual climate system, based on the available observations thereof. Highly simplified models of weather and climate, though, help gain a deeper understanding of a few isolated processes, as well as giving clues on how the interaction between these processes and the rest of the climate system may participate in shaping climate variability. Finally, models of intermediate complexity, which resolve well a subset of the climate system and parameterise the remainder of the processes or scales of motion, serve as a conduit between the models at the two ends of the hierarchy. We present here a methodology for constructing intermediate mod- els based almost entirely on the observed evolution of selected climate fields, without reference to dynamical equations that may govern this evolution; these models parameterise unresolved processes as multi- variate stochastic forcing. This methodology may be applied with equal success to actual observational data sets, as well as to data sets resulting from a high-end model simulation. We illustrate this methodology by its applications to: (i) observed and simulated low-frequency variability of atmospheric flows in the Northern Hemisphere; (ii) observed evo- lution of tropical sea-surface temperatures; and (iii) observed air–sea interaction in the Southern Ocean. Similar results have been obtained for (iv) radial-diffusion model simulations of Earth’s radiation belts, but are not included here because of space restrictions. In each case, the reduced stochastic model represents surprisingly well a variety of linear and nonlinear statistical properties of the resolved fields. Our methodology thus provides an efficient means of constructing reduced, numerically inexpensive climate models. These models can be thought of as stochastic–dynamic prototypes of more complex deterministic models, as in examples (i) and (iv), but work just as well in the situation when the actual governing equations are poorly known, as in (ii) and (iii). These models can serve as competitive prediction tools, as in (ii), or be included as stochastic parameterisations of certain processes within more complex climate models, as in (iii). Finally, the methodology can be applied, with some modifications, to geophysical problems outside climate dynamics, as illustrated by (iv). %B Stochastic physics and climate modelling. Cambridge University Press, Cambridge %P 35–72 %G eng %0 Journal Article %J PAGES News %D 2009 %T Accurate dating of the Gallipoli Terrace (Ionian Sea) sediments as a basis for reliable climate proxy series %A Gianna Vivaldo %A Taricco, Carla %A Alessio, Silvia %A Ghil, Michael %B PAGES News %I PAGES International Project Office %V 17 %P 8–9 %G eng %N 1 %0 Book Section %B Handbook of numerical analysis %D 2009 %T Bifurcation analysis of ocean, atmosphere, and climate models %A Simonnet, Eric %A Dijkstra, Henk A. %A Ghil, Michael %E R. Temam %E J. Tribbia %B Handbook of numerical analysis %I Elsevier %V 14 %P 187–229 %G eng %0 Journal Article %J Chaos: An Interdisciplinary Journal of Nonlinear Science %D 2009 %T Fixed points, stable manifolds, weather regimes, and their predictability %A Deremble, Bruno %A D'Andrea, Fabio %A Ghil, Michael %B Chaos: An Interdisciplinary Journal of Nonlinear Science %I AIP Publishing %V 19 %P 043109 %G eng %U http://link.aip.org/link/?CHA/19/043109 %N 4 %0 Journal Article %J Journal of Climate %D 2009 %T Low-cloud fraction, lower-tropospheric stability, and large-scale divergence %A Zhang, Yunyan %A Stevens, Bjorn %A Medeiros, Brian %A Ghil, Michael %B Journal of Climate %V 22 %P 4827–4844 %G eng %N 18 %R 10.1175/2009jcli2891.1 %0 Journal Article %J Climate of the Past %D 2009 %T Two millennia of climate variability in the Central Mediterranean %A Taricco, Carla %A Ghil, Michael %A Alessio, Silvia %A Gianna Vivaldo %XThis experimental work addresses the need for high-resolution, long and homogeneous climatic time series that facilitate the study of climate variability over time scales of decades to millennia. We present a high-resolution record of foraminiferal d18O from a Central-Mediterranean sediment core that covers the last two millennia. The record was analyzed using advanced spectral methods and shows highly significant oscillatory components with periods of roughly 600, 350, 200, 125 and 11 years. Over the last millennium, our data show several features related to known climatic periods, such as the Medieval Optimum, the Little Ice Age and a recent steep variation since the beginning of the Industrial Era. During the preceding millennium, the d18O series also reveals a surprising maximum at about 0 AD, suggesting low temperatures at that time. This feature contradicts widely held ideas about the Roman Classical Period; it is, therefore, discussed at some length, by reviewing the somewhat contradictory evidence about this period. We compare the d18O record with an alkenone-derived sea surface temperature time series, obtained from cores extracted in the same Central-Mediterranean area (Gallipoli Terrace, Ionian Sea), as well as with Italian and other European temperature reconstructions over the last centuries. Based on this comparison, we show that the long-term trend and the 200-y oscillation in the records are temperature driven and have a dominant role in describing temperature variations over the last two millennia.

%B Climate of the Past %I European Geosciences Union %V 5 %P 171–181 %G eng %N 5 %R 10.5194/cp-5-171-2009 %0 Journal Article %J Journal of the Atmospheric Sciences %D 2009 %T Zonal flow regime changes in a GCM and in a simple quasigeostrophic model: The role of stratospheric dynamics %A Bordi, Isabella %A Fraedrich, Klaus %A Ghil, Michael %A Sutera, Alfonso %B Journal of the Atmospheric Sciences %V 66 %P 1366–1383 %G eng %N 5 %0 Journal Article %J Physica D %D 2008 %T Anthropogenic climate change: Scientific uncertainties and moral dilemmas %A Rafaela Hillerbrand %A Ghil, Michael %XThis paper considers the role of scientific expertise and moral reasoning in the decision making process involved in climate-change issues. It points to an unresolved moral dilemma that lies at the heart of this decision making, namely how to balance duties towards future generations against duties towards our contemporaries. At present, the prevailing moral and political discourses shy away from addressing this dilemma and evade responsibility by falsely drawing normative conclusions from the predictions of climate models alone. We argue that such moral dilemmas are best addressed in the framework of Expected Utility Theory. A crucial issue is to adequately incorporate into this framework the uncertainties associated with the predicted consequences of climate change on the well-being of future generations. The uncertainties that need to be considered include those usually associated with climate modeling and prediction, but also moral and general epistemic ones. This paper suggests a way to correctly incorporate all the relevant uncertainties into the decision making process.

%B Physica D %V 237 %P 2132–2138 %G eng %N 14-17 %R DOI: 10.1016/j.physd.2008.02.015 %0 Journal Article %J Physica D: Nonlinear Phenomena %D 2008 %T Boolean delay equations: A simple way of looking at complex systems %A Ghil, Michael %A Zaliapin, Ilya %A Coluzzi, Barbara %B Physica D: Nonlinear Phenomena %I Elsevier %V 237 %P 2967–2986 %G eng %N 23 %0 Journal Article %J Journal of Economic Behavior & Organization %D 2008 %T Business cycles, bifurcations and chaos in a neo-classical model with investment dynamics %A Hallegatte, Stéphane %A Ghil, Michael %A Dumas, Patrice %A Hourcade, Jean-Charles %XThis paper presents a non-equilibrium dynamic model (NEDyM) that introduces investment dynamics and non-equilibrium effects into a Solow growth model. NEDyM can reproduce several typical economic regimes and, for certain ranges of parameter values, exhibits endogenous business cycles with realistic characteristics. The cycles arise from the investment-profit instability and are constrained by the increase in labor costs and the inertia of production capacity. For other parameter ranges, the model exhibits chaotic behavior. These results show that complex variability in the economic system may be due to deterministic, intrinsic factors, even if the long-term equilibrium is neo-classical in nature.

%B Journal of Economic Behavior & Organization %V 67 %P 57–77 %G eng %N 1 %R doi:10.1016/j.jebo.2007.05.001 %0 Journal Article %J Physica D %D 2008 %T Climate dynamics and fluid mechanics: Natural variability and related uncertainties %A Ghil, Michael %A Chekroun, Mickaël D. %A Simonnet, Eric %B Physica D %V 237 %P 2111–2126 %G eng %R 10.1016/j.physd.2008.03.036 %0 Journal Article %J Geochemistry, Geophysics, Geosystems %D 2008 %T Clustering of eastern North Pacific tropical cyclone tracks: ENSO and MJO effects %A Camargo, Suzana J. %A Robertson, Andrew W. %A Barnston, Anthony G. %A Ghil, Michael %B Geochemistry, Geophysics, Geosystems %I Wiley Online Library %V 9 %G eng %N 6 %R 10.1029/2007gc001861 %0 Journal Article %J Chaos %D 2008 %T Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system %A Alberto Carrassi %A Ghil, Michael %A Anna Trevisan %A Francesco Uboldi %XWe study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system leads to the uniqueness of its sequentially estimated solutions and is required for the convergence of these solutions to the system's true, chaotic evolution. The key ideas of our approach are illustrated for a linearized Lorenz system. Stability of two nonlinear prediction-assimilation systems from dynamic meteorology is studied next via the complete spectrum of their Lyapunov exponents; these two systems are governed by a large set of ordinary and of partial differential equations, respectively. The degree of data-induced stabilization is crucial for the performance of such a system. This degree, in turn, depends on two key ingredients: (i) the observational network, either fixed or data-adaptive, and (ii) the assimilation method.

%B Chaos %I AIP %V 18 %P 023112 %G eng %N 2 %R 10.1063/1.2909862 %0 Journal Article %J Monthly Weather Review %D 2008 %T Data Assimilation for a Coupled Ocean–Atmosphere Model. Part II: Parameter Estimation %A Kondrashov, Dmitri %A Sun, Chaojiao %A Ghil, Michael %XThe parameter estimation problem for the coupled ocean–atmosphere system in the tropical Pacific Ocean is investigated using an advanced sequential estimator [i.e., the extended Kalman filter (EKF)]. The intermediate coupled model (ICM) used in this paper consists of a prognostic upper-ocean model and a diagnostic atmospheric model. Model errors arise from the uncertainty in atmospheric wind stress. First, the state and parameters are estimated in an identical-twin framework, based on incomplete and inaccurate observations of the model state. Two parameters are estimated by including them into an augmented state vector. Model-generated oceanic datasets are assimilated to produce a time-continuous, dynamically consistent description of the model’s El Niño–Southern Oscillation (ENSO). State estimation without correcting erroneous parameter values still permits recovering the true state to a certain extent, depending on the quality and accuracy of the observations and the size of the discrepancy in the parameters. Estimating both state and parameter values simultaneously, though, produces much better results. Next, real sea surface temperatures observations from the tropical Pacific are assimilated for a 30-yr period (1975–2004). Estimating both the state and parameters by the EKF method helps to track the observations better, even when the ICM is not capable of simulating all the details of the observed state. Furthermore, unobserved ocean variables, such as zonal currents, are improved when model parameters are estimated. A key advantage of using this augmented-state approach is that the incremental cost of applying the EKF to joint state and parameter estimation is small relative to the cost of state estimation alone. A similar approach generalizes various reduced-state approximations of the EKF and could improve simulations and forecasts using large, realistic models.

%B Monthly Weather Review %V 136 %P 5062–5076 %G eng %R 10.1175/2008MWR2544.1 %0 Journal Article %J Physica D %D 2008 %T A mechanistic model of mid-latitude decadal climate variability %A Kravtsov, Sergey %A Dewar, W. K. %A Ghil, Michael %A J. C. McWilliams %A Berloff, Pavel S. %B Physica D %V 237 %P 584–599 %G eng %R 10.1016/j.physd.2007.09.025 %0 Journal Article %J Ecological Economics %D 2008 %T Natural disasters impacting a macroeconomic model with endogenous dynamics %A Hallegatte, Stéphane %A Ghil, Michael %XWe investigate the macroeconomic response to natural disasters by using an endogenous business cycle (EnBC) model in which cyclical behavior arises from the investment-profit instability. Our model exhibits a larger response to natural disasters during expansions than during recessions. This apparently paradoxical result can be traced to the disasters amplifying pre-existing disequilibria during expansions, while the existence of unused resources during recessions damps the exogenous shocks. It thus appears that high-growth periods are also highly vulnerable to supply-side shocks. In our EnBC model, the average production loss due to a set of disasters distributed at random in time is highly sensitive to the dynamical characteristics of the impacted economy. Larger economic flexibility allows for a more efficient and rapid response to supply-side shocks and reduces production losses. On the other hand, too high a flexibility can lead to vulnerability phases that cause average production losses to soar. These results raise questions about the assessment of climate change damages or natural disaster losses that are based purely on long-term growth models.

%B Ecological Economics %V 68 %P 582–592 %G eng %N 1-2 %R 10.1016/j.ecolecon.2008.05.022 %0 Journal Article %J Nonlinear Processes in Geophysics %D 2008 %T North Atlantic climate variability in coupled models and data %A Kravtsov, Sergey %A Dewar, W. K. %A Berloff, P. %A J. C. McWilliams %A Ghil, Michael %B Nonlinear Processes in Geophysics %V 15 %P 13–24 %G eng %R 10.5194/npg-15-13-2008 %0 Journal Article %J Proceedings of the National Academy of Sciences %D 2007 %T Development at the wildland urban interface and the mitigation of forest-fire risk %A V. Spyratos %A P. S. Bourgeron %A Ghil, Michael %XThis work addresses the impacts of development at the wildland-urban interface on forest fires that spread to human habitats. Catastrophic fires in the western United States and elsewhere make these impacts a matter of urgency for decision makers, scientists, and the general public. Using a simple fire-spread model, along with housing and vegetation data, we show that fire size probability distributions can be strongly modified by the density and flammability of houses. We highlight a sharp transition zone in the parameter space of vegetation flammability and house density. Many actual fire landscapes in the United States appear to have spreading properties close to this transition. Thus, the density and flammability of buildings should be taken into account when assessing fire risk at the wildland-urban interface. Moreover, our results highlight ways for regulation at this interface to help mitigate fire risk.

%B Proceedings of the National Academy of Sciences %I Proceedings of the National Academy of Sciences %V 104 %P 14272–14276 %G eng %N 36 %R 10.1073/pnas.0704488104 %0 Journal Article %J Nonlinear Processes in Geophysics %D 2007 %T Comment on "Spatio-temporal filling of missing points in geophysical data sets" by D. Kondrashov and M. Ghil, Nonlin. Processes Geophys., 13, 151–159, 2006 %A Schneider, T. %B Nonlinear Processes in Geophysics %V 14 %P 1–2 %G eng %N 1 %R 10.5194/npg-14-1-2007 %0 Journal Article %J Journal of Climate %D 2007 %T Cluster analysis of typhoon tracks. Part I: General properties %A Camargo, Suzana J. %A Robertson, Andrew W. %A Gaffney, Scott J. %A Smyth, Padhraic %A Ghil, Michael %B Journal of Climate %V 20 %P 3635–3653 %G eng %N 14 %R 10.1175/jcli4188.1 %0 Journal Article %J Journal of Climate %D 2007 %T Cluster analysis of typhoon tracks. Part II: Large-scale circulation and ENSO %A Camargo, Suzana J. %A Robertson, Andrew W. %A Gaffney, Scott J. %A Smyth, Padhraic %A Ghil, Michael %B Journal of Climate %V 20 %P 3654–3676 %G eng %N 14 %R 10.1175/jcli4203.1 %0 Journal Article %J Monthly Weather Review %D 2007 %T An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems %A T. M. Chin %A M. J. Turmon %A J. B. Jewell %A Ghil, Michael %XMonte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.

%B Monthly Weather Review %V 135 %P 186–202 %G eng %R 10.1175/MWR3353.1 %0 Journal Article %J Physica D: Nonlinear Phenomena %D 2007 %T Graphical models for statistical inference and data assimilation %A Ihler, Alexander T. %A Kirshner, Sergey %A Ghil, Michael %A Robertson, Andrew W. %A Smyth, Padhraic %B Physica D: Nonlinear Phenomena %I Elsevier %V 230 %P 72–87 %G eng %N 1 %R 10.1016/j.physd.2006.08.023 %0 Journal Article %J Dynamics of Atmospheres and Oceans %D 2007 %T A highly nonlinear coupled mode of decadal variability in a mid-latitude ocean–atmosphere model %A Kravtsov, Sergey %A Dewar, William K. %A Berloff, Pavel S. %A McWilliams, James C. %A Ghil, Michael %B Dynamics of Atmospheres and Oceans %I Elsevier %V 43 %P 123–150 %G eng %N 3 %R 10.1016/j.dynatmoce.2006.08.001 %0 Journal Article %J Journal of Geophysical Research: Space Physics %D 2007 %T A Kalman filter technique to estimate relativistic electron lifetimes in the outer radiation belt %A Kondrashov, Dmitri %A Y. Shprits %A Ghil, Michael %A Thorne, R. %B Journal of Geophysical Research: Space Physics %I Wiley Online Library %V 112 %G eng %N A10 %R 10.1029/2007ja012583 %0 Journal Article %J Journal of the Atmospheric Sciences %D 2007 %T Low-frequency variability in the midlatitude baroclinic atmosphere induced by an oceanic thermal front %A Feliks, Yizhak %A Ghil, Michael %A Simonnet, Eric %B Journal of the Atmospheric Sciences %V 64 %P 97–116 %G eng %N 1 %R 10.1175/jas3780.1 %0 Journal Article %J Climate Dynamics %D 2007 %T Predicting weather regime transitions in Northern Hemisphere datasets %A Kondrashov, Dmitri %A Shen, Jie %A Berk, Richard %A D'Andrea, Fabio %A Ghil, Michael %B Climate Dynamics %I Springer %V 29 %P 535–551 %G eng %N 5 %R 10.1007/s00382-007-0293-2 %0 Journal Article %J Climate Dynamics %D 2007 %T Probabilistic clustering of extratropical cyclones using regression mixture models %A Gaffney, Scott J. %A Robertson, Andrew W. %A Smyth, Padhraic %A Camargo, Suzana J. %A Ghil, Michael %B Climate Dynamics %I Springer %V 29 %P 423–440 %G eng %N 4 %R 10.1007/s00382-007-0235-z %0 Journal Article %J Journal of Geophysical Research: Space Physics %D 2007 %T Reanalysis of relativistic radiation belt electron fluxes using CRRES satellite data, a radial diffusion model, and a Kalman filter %A Shprits, Yuri %A Kondrashov, Dmitri %A Chen, Yue %A Thorne, Richard %A Ghil, Michael %A Friedel, Reiner %A Reeves, Geoff %B Journal of Geophysical Research: Space Physics %I Wiley Online Library %V 112 %G eng %N A12 %R 10.1029/2007ja012579 %0 Journal Article %J Nonlinear Processes in Geophysics %D 2007 %T Reply to T. Schneider's comment on "Spatio-temporal filling of missing points in geophysical data sets" %A Kondrashov, Dmitri %A Ghil, Michael %B Nonlinear Processes in Geophysics %V 14 %P 3–4 %G eng %N 1 %R 10.5194/npg-14-3-2007 %0 Journal Article %J Atmosphere-ocean %D 2007 %T Spatio-temporal variability in a mid-latitude ocean basin subject to periodic wind forcing %A Sushama, L. %A Ghil, Michael %A Ide, K. %XThe mid-latitude ocean's response to time-dependent zonal wind-stress forcing is studied using a reduced-gravity, 1.5-layer, shallow-water model in two rectangular ocean basins of different sizes. The small basin is 1000 km $\times$ 2000 km and the larger one is 3000 km $\times$ 2010 km; the aspect ratio of the larger basin is quite similar to that of the North Atlantic between 20$\deg$N and 60$\deg$N. The parameter dependence of the model solutions and their spatio-temporal variability subject to time-independent wind stress forcing serve as the reference against which the results for time-dependent forcing are compared. For the time-dependent forcing case, three zonal-wind profiles that mimic the seasonal cycle are considered in this study: (1) a fixed-profile wind-stress forcing with periodically varying intensity; (2) a wind-stress profile with fixed intensity, but north–south migration of the mid-latitude westerly wind maximum; and (3) a north–south migrating profile with periodically varying intensity. Results of the small-basin simulations show the intrinsic variability found for time-independent forcing to persist when the intensity of the wind forcing varies periodically. It thus appears that the physics behind the upper ocean's variability is mainly controlled by internal dynamics, although the solutions’ spatial patterns are now more complex, due to the interaction between the external and internal modes of variability. The north–south migration of wind forcing, however, does inhibit the inertial recirculation; its suppression increases with the amplitude of north–south migration in the wind-stress forcing. Model solutions in the larger rectangular basin and at smaller viscosity exhibit more realistic recirculation gyres, with a small meridional-to-zonal aspect ratio, and an elongated eastward jet; the low-frequency variability of these solutions is dominated by periodicities of 14 and 6–7 years. Simulations performed in this setting with a wind-stress profile that involves seasonal variations of realistic amplitude in both the intensity and the position of the atmospheric jet show the seven-year periodicity in the oceanic circulation to be robust. The intrinsic variability is reinforced by the periodic variations in the jet's intensity and weakened by periodic variations in the meridional position; the two effects cancel, roughly speaking, thus preserving the overall characteristics of the seven-year mode.

%B Atmosphere-ocean %I Taylor & Francis %V 45 %P 227–250 %G eng %N 4 %R 10.3137/ao.450404 %0 Journal Article %J Journal of the Atmospheric Sciences %D 2007 %T Weather regime prediction using statistical learning %A Deloncle, Axel %A Berk, Richard %A D'Andrea, Fabio %A Ghil, Michael %B Journal of the Atmospheric Sciences %V 64 %P 1619–1635 %G eng %N 5 %R 10.1175/jas3918.1 %0 Journal Article %J Journal of the Atmospheric Sciences %D 2006 %T Empirical Mode Reduction in a Model of Extratropical Low-Frequency Variability %A Kondrashov, Dmitri %A Kravtsov, S. %A M. Ghil %B Journal of the Atmospheric Sciences %V 63 %P 1859-1877 %G eng %U http://dx.doi.org/10.1175/JAS3719.1 %N 7 %R 10.1175/JAS3719.1 %0 Journal Article %J Journal of Climate %D 2006 %T Dynamical origin of low-frequency variability in a highly nonlinear midlatitude coupled model. %A Kravtsov, S %A Berloff, P %A Dewar, William K. %A Ghil, M %A McWilliams, James C. %XA novel mechanism of decadal midlatitude coupled variability, which crucially depends on the nonlinear dynamics of both the atmosphere and the ocean, is presented. The coupled model studied involves quasigeostrophic atmospheric and oceanic components, which communicate with each other via a constant-depth oceanic mixed layer. A series of coupled and uncoupled experiments show that the decadal coupled mode is active across parameter ranges that allow the bimodality of the atmospheric zonal flow to coexist with oceanic turbulence. The latter is most intense in the regions of inertial recirculation (IR). Bimodality is associated with the existence of two distinct anomalously persistent zonal-flow modes, which are characterized by different latitudes of the atmospheric jet stream. The IR reorganizations caused by transitions of the atmosphere from its high- to low-latitude state and vice versa create sea surface temperature anomalies that tend to induce transition to the opposite atmospheric state. The decadal–interdecadal time scale of the resulting oscillation is set by the IR adjustment; the latter depends most sensitively on the oceanic bottom drag. The period T of the nonlinear oscillation is 7–25 yr for the range of parameters explored, with the most realistic parameter values yielding T \approx 20 yr. Aside from this nonlinear oscillation, an interannual Rossby wave mode is present in all coupled experiments. This coupled mode depends neither on atmospheric bimodality, nor on ocean eddy dynamics; it is analogous to the mode found previously in a channel configuration. Its time scale in the model with a closed ocean basin is set by cross-basin wave propagation and equals 3–5 yr for a basin width comparable with the North Atlantic.

%B Journal of Climate %V 19 %G eng %N 24 %R 10.1175/JCLI3976.1 %0 Journal Article %J Journal of the Atmospheric Sciences %D 2006 %T Empirical mode reduction in a model of extratropical low-frequency variability %A Kondrashov, Dmitri %A Kravtsov, S %A Ghil, M %XThis paper constructs and analyzes a reduced nonlinear stochastic model of extratropical low-frequency variability. To do so, it applies multilevel quadratic regression to the output of a long simulation of a global baroclinic, quasigeostrophic, three-level (QG3) model with topography; the model's phase space has a dimension of O(104). The reduced model has 45 variables and captures well the non-Gaussian features of the QG3 model's probability density function (PDF). In particular, the reduced model's PDF shares with the QG3 model its four anomalously persistent flow patterns, which correspond to opposite phases of the Arctic Oscillation and the North Atlantic Oscillation, as well as the Markov chain of transitions between these regimes. In addition, multichannel singular spectrum analysis identifies intraseasonal oscillations with a period of 35–37 days and of 20 days in the data generated by both the QG3 model and its low-dimensional analog. An analytical and numerical study of the reduced model starts with the fixed points and oscillatory eigenmodes of the model's deterministic part and uses systematically an increasing noise parameter to connect these with the behavior of the full, stochastically forced model version. The results of this study point to the origin of the QG3 model's multiple regimes and intraseasonal oscillations and identify the connections between the two types of behavior.

%B Journal of the Atmospheric Sciences %V 63 %P 1859–1877 %G eng %N 7 %R 10.1175/JAS3719.1 %0 Journal Article %J Journal of Computational Physics %D 2006 %T Estimating model parameters for an impact-produced shock-wave simulation: Optimal use of partial data with the extended Kalman filter %A Kao, Jim %A Flicker, Dawn %A Ide, Kayo %A Ghil, Michael %B Journal of Computational Physics %I Elsevier %V 214 %P 725–737 %G eng %N 2 %R 10.1016/j.jcp.2005.10.022 %0 Conference Paper %B Proc. 16th Conf. Research Judaea & Samaria %D 2006 %T Long-range forecasting and the scientific background in Joseph's interpretation to Pharaohs dreams %A Feliks, Yizhak %A Ghil, Michael %A Ziona, Israel %A Dynamique, Météorologie %XLong-range forecasting is today a major area of climate research. Such forecasts affect socioeconomic planning in many fields of activity. There are essentially two approaches to longrange forecasting: one is based on solving the equations that govern atmospheric and ocean dynamics, the other on the statistical properties of past climate records. The present talk is based on the latter, statistical approach. Joseph’s interpretation of Pharaoh’s dreams provides a striking example of long-range planning based on a climate forecast. Joseph interpreted the two dreams as a forecast for seven years of plenty, followed by seven of famine. Based on this forecast, he proposed to Pharaoh a plan for running the agriculture and economy of Egypt. It is not clear from the Biblical story why Pharaoh trusted Joseph’s forecast and appointed him to implement the plan. Our answer to this question is based on ancient and medieval Egypt’s being entirely dependent on the Nile River’s seasonal flooding: when the highest water levels did not cover the arable areas of the river valley, crops were insufficient to feed the population. When successive years of hunger weakened the economy and the state, change of rulers could, and sometimes did ensue. Extreme examples were the fall of the Old Kingdom in 2185 B.C. and the Fatimid conquest of Egypt in 969 A.D. Hence the Egyptians measured the high-water mark of the Nile River for over 5000 years, using different tools. The most advanced of these tools was the nilometer; typical nilometers appear in several mosaics from the Roman and Byzantine period around the Mediterranean, such as the “Nile Festival” mosaic in Zippori (Upper Galilee), Fig. 1. The measurements had a twofold purpose: first to set the annual taxes, which were a function of the high-water mark, for obvious reasons; and second, to provide information for water management, with a view to reduce drought damage. Our analysis of high- and low-water levels for 622–1922 A.D. shows that oscillations with a period of several years occur, with a 7-year oscillation being dominant. We suspect that the origin of this 7-year swing lies in the same periodicity being present in the North Atlantic’s sea-surface temperatures and sea-level pressures. This North Atlantic Oscillation affects the climate of Europe, North America and the Middle East, and might be the ultimate reason for Joseph’s successful climate forecast.

%B Proc. 16th Conf. Research Judaea & Samaria %I in press %G eng %0 Journal Article %J Journal of the Atmospheric Sciences %D 2006 %T Multiple regimes and low-frequency oscillations in the Northern Hemisphere's zonal-mean flow %A Kravtsov, S. %A Robertson, Andrew W. %A Ghil, Michael %B Journal of the Atmospheric Sciences %V 63 %P 840–860 %G eng %N 3 %0 Journal Article %J Geophysical Research Letters %D 2006 %T Scale separation for moisture-laden regions in the tropical atmosphere %A Bellon, G. %A Ghil, Michael %A Treut, H. Le %B Geophysical Research Letters %I Wiley Online Library %V 33 %G eng %N 1 %R 10.1029/2005gl024578 %0 Journal Article %J Nonlinear Processes in Geophysics %D 2006 %T Spatio-temporal filling of missing points in geophysical data sets %A Kondrashov, Dmitri %A Ghil, Michael %XThe majority of data sets in the geosciences are obtained from observations and measurements of natural systems, rather than in the laboratory. These data sets are often full of gaps, due to to the conditions under which the measurements are made. Missing data give rise to various problems, for example in spectral estimation or in specifying boundary conditions for numerical models. Here we use Singular Spectrum Analysis (SSA) to fill the gaps in several types of data sets. For a univariate record, our procedure uses only temporal correlations in the data to fill in the missing points. For a multivariate record, multi-channel SSA (M-SSA) takes advantage of both spatial and temporal correlations. We iteratively produce estimates of missing data points, which are then used to compute a self-consistent lag-covariance matrix; cross-validation allows us to optimize the window width and number of dominant SSA or M-SSA modes to fill the gaps. The optimal parameters of our procedure depend on the distribution in time (and space) of the missing data, as well as on the variance distribution between oscillatory modes and noise. The algorithm is demonstrated on synthetic examples, as well as on data sets from oceanography, hydrology, atmospheric sciences, and space physics: global sea-surface temperature, flood-water records of the Nile River, the Southern Oscillation Index (SOI), and satellite observations of relativistic electrons.

%B Nonlinear Processes in Geophysics %V 13 %P 151–159 %G eng %N 2 %R 10.5194/npg-13-151-2006 %0 Book Section %B L'irruption Des Géométries Fractales Dans Les Sciences,une Apologie De L'oeuvre De Benoît Mandelbrot %D 2006 %T Une Nouvelle source de Fractales: Les Equations Booléennes avec Retard, et leurs Applications aux Sciences de la Planete %A Ghil, Michael %A Zaliapin, Ilya %B L'irruption Des Géométries Fractales Dans Les Sciences,une Apologie De L'oeuvre De Benoît Mandelbrot %I Editions de l'Académie Européenne Interdisciplinaire des Sciences %C Paris %P 161–187 %G eng %0 Journal Article %J Eos, Transactions American Geophysical Union %D 2005 %T New tools for analyzing time series relationships and trends %A Moore, JC %A Grinsted, Aslak %A Jevrejeva, S %X Geophysical studies are plagued by short and noisy time series. These time series are typically nonstationary contain various long-period quasi-periodic components, and have rather low signal-to-noise ratios and/or poor spatial sampling. Classic examples of these time series are tide gauge records, which are influenced by ocean and atmospheric circulation patterns, twentieth-century warming, and other long-term variability. Remarkable progress recently has been made in the statistical analysis of time series. Ghil et al. [2002] presented a general review of several advanced statistical methods with a solid theoretical foundation. This present article highlights several new approaches that are easy to use and that may be of general interest. %B Eos, Transactions American Geophysical Union %I Wiley Online Library %V 86 %P 226–232 %G eng %N 24 %R 10.1029/2005EO240003 %0 Journal Article %J Journal of the Atmospheric Sciences %D 2005 %T Bimodal behavior in the zonal mean flow of a baroclinic beta-channel model %A Kravtsov, S. %A Robertson, Andrew W. %A Ghil, Michael %B Journal of the Atmospheric Sciences %V 62 %P 1746–1769 %G eng %N 6 %0 Journal Article %J Quarterly Journal of the Royal Meteorological Society %D 2005 %T On the diurnal cycle and susceptibility to aerosol concentration in a stratocumulus-topped mixed layer %A Zhang, Yunyan %A Stevens, Bjorn %A Ghil, Michael %B Quarterly Journal of the Royal Meteorological Society %I Wiley Online Library %V 131 %P 1567–1583 %G eng %N 608 %R 10.1256/qj.04.103 %0 Journal Article %J Journal of climate %D 2005 %T A hierarchy of data-based ENSO models %A Kondrashov, Dmitri %A Kravtsov, S %A Robertson, Andrew W. %A Ghil, Michael %XGlobal sea surface temperature (SST) evolution is analyzed by constructing predictive models that best describe the dataset’s statistics. These inverse models assume that the system’s variability is driven by spatially coherent, additive noise that is white in time and are constructed in the phase space of the dataset’s leading empirical orthogonal functions. Multiple linear regression has been widely used to obtain inverse stochastic models; it is generalized here in two ways. First, the dynamics is allowed to be nonlinear by using polynomial regression. Second, a multilevel extension of classic regression allows the additive noise to be correlated in time; to do so, the residual stochastic forcing at a given level is modeled as a function of variables at this level and the preceding ones. The number of variables, as well as the order of nonlinearity, is determined by optimizing model performance. The two-level linear and quadratic models have a better El Niño–Southern Oscillation (ENSO) hindcast skill than their one-level counterparts. Estimates of skewness and kurtosis of the models’ simulated Niño-3 index reveal that the quadratic model reproduces better the observed asymmetry between the positive El Niño and negative La Niña events. The benefits of the quadratic model are less clear in terms of its overall, cross-validated hindcast skill; this model outperforms, however, the linear one in predicting the magnitude of extreme SST anomalies. Seasonal ENSO dependence is captured by incorporating additive, as well as multiplicative forcing with a 12-month period into the first level of each model. The quasi-quadrennial ENSO oscillatory mode is robustly simulated by all models. The “spring barrier” of ENSO forecast skill is explained by Floquet and singular vector analysis, which show that the leading ENSO mode becomes strongly damped in summer, while nonnormal optimum growth has a strong peak in December.

%B Journal of climate %V 18 %P 4425–4444 %G eng %N 21 %R 10.1175/JCLI3567.1 %0 Journal Article %J Journal of Marine Research %D 2005 %T Homoclinic bifurcations in the quasi-geostrophic double-gyre circulation %A Simonnet, Eric %A Ghil, Michael %A Dijkstra, Henk %XThe wind-driven double-gyre circulation in a rectangular basin goes through several dynamical regimes as the amount of lateral friction is decreased. This paper studies the transition to irregular flow in the double-gyre circulation by applying dynamical systems methodology to a quasi-geostrophic, equivalent-barotropic model with a 10-km resolution. The origin of the irregularities, in space and time, is the occurrence of homoclinic bifurcations that involve phase-space behavior far from stationary solutions. The connection between these homoclinic bifurcations and earlier transitions, which occur at larger lateral friction, is explained. The earlier transitions, such as pitchfork and asymmetric Hopf bifurcation, only involve the nonlinear saturation of linear instabilities, while the homoclinic bifurcations are associated with genuinely nonlinear behavior. The sequence of bifurcations—pitchfork, Hopf, and homoclinic—is independent of the lateral friction and may be described as the unfolding of a singularity that occurs in the frictionless, Hamiltonian limit of the governing equations. Two distinct chaotic regimes are identified: Lorenz chaos at relatively large lateral friction versus Shilnikov chaos at relatively small lateral friction. Both types of homoclinic bifurcations induce chaotic behavior of the recirculation gyres that is dominated by relaxation oscillations with a well-defined period. The relevance of these results to the mid-latitude oceans' observed low-frequency variations is discussed. A previously documented 7-year peak in observed North-Atlantic variability is shown to exist across a hierarchy of models that share the gyre modes and homoclinic bifurcations discussed herein.

%B Journal of Marine Research %I Sears Foundation for Marine Research %V 63 %P 931–956 %G eng %N 5 %R 10.1357/002224005774464210 %0 Journal Article %J Reviews of Geophysics %D 2005 %T Low-frequency variability of the large-scale ocean circulation: a dynamical systems approach %A Dijkstra, Henk A. %A Ghil, Michael %XOceanic variability on interannual, interdecadal, and longer timescales plays a key role in climate variability and climate change. Paleoclimatic records suggest major changes in the location and rate of deepwater formation in the Atlantic and Southern oceans on timescales from millennia to millions of years. Instrumental records of increasing duration and spatial coverage document substantial variability in the path and intensity of ocean surface currents on timescales of months to decades. We review recent theoretical and numerical results that help explain the physical processes governing the large-scale ocean circulation and its intrinsic variability. To do so, we apply systematically the methods of dynamical systems theory. The dynamical systems approach is proving successful for more and more detailed and realistic models, up to and including oceanic and coupled ocean-atmosphere general circulation models. In this approach one follows the road from simple, highly symmetric model solutions, through a “bifurcation tree,” toward the observed, complex behavior of the system under investigation. The observed variability can be shown to have its roots in simple transitions from a circulation with high symmetry in space and regularity in time to circulations with successively lower symmetry in space and less regularity in time. This road of successive bifurcations leads through multiple equilibria to oscillatory and eventually chaotic solutions. Key features of this approach are illustrated in detail for simplified models of two basic problems of the ocean circulation. First, a barotropic model is used to capture major features of the wind-driven ocean circulation and of the changes in its behavior as wind stress increases. Second, a zonally averaged model is used to show how the thermohaline ocean circulation changes as buoyancy fluxes at the surface increase. For the wind-driven circulation, multiple separation patterns of a “Gulf-Stream like” eastward jet are obtained. These multiple equilibria are followed by subannual and interannual oscillations of the jet and of the entire basin's circulation. The multiple equilibria of the thermohaline circulation include deepwater formation near the equator, near either pole or both, as well as intermediate possibilities that bear some degree of resemblance to the currently observed Atlantic overturning pattern. Some of these multiple equilibria are subject, in turn, to oscillatory instabilities with timescales of decades, centuries, and millennia. Interdecadal and centennial oscillations are the ones of greatest interest in the current debate on global warming and on the relative roles of natural and anthropogenic variability in it. They involve the physics of the truly three-dimensional coupling between the wind-driven and thermohaline circulation. To arrive at this three-dimensional picture, the bifurcation tree is sketched out for increasingly complex models for both the wind-driven and the thermohaline circulation.

%B Reviews of Geophysics %V 43 %G eng %R 10.1029/2002RG000122 %0 Journal Article %J Journal of Climate %D 2005 %T Multilevel regression modeling of nonlinear processes: Derivation and applications to climatic variability %A Kravtsov, S %A Kondrashov, Dmitri %A Ghil, M %XPredictive models are constructed to best describe an observed field’s statistics within a given class of nonlinear dynamics driven by a spatially coherent noise that is white in time. For linear dynamics, such inverse stochastic models are obtained by multiple linear regression (MLR). Nonlinear dynamics, when more appropriate, is accommodated by applying multiple polynomial regression (MPR) instead; the resulting model uses polynomial predictors, but the dependence on the regression parameters is linear in both MPR and MLR. The basic concepts are illustrated using the Lorenz convection model, the classical double-well problem, and a three-well problem in two space dimensions. Given a data sample that is long enough, MPR successfully reconstructs the model coefficients in the former two cases, while the resulting inverse model captures the three-regime structure of the system’s probability density function (PDF) in the latter case. A novel multilevel generalization of the classic regression procedure is introduced next. In this generalization, the residual stochastic forcing at a given level is subsequently modeled as a function of variables at this level and all the preceding ones. The number of levels is determined so that the lag-0 covariance of the residual forcing converges to a constant matrix, while its lag-1 covariance vanishes. This method has been applied to the output of a three-layer, quasigeostrophic model and to the analysis of Northern Hemisphere wintertime geopotential height anomalies. In both cases, the inverse model simulations reproduce well the multiregime structure of the PDF constructed in the subspace spanned by the dataset’s leading empirical orthogonal functions, as well as the detailed spectrum of the dataset’s temporal evolution. These encouraging results are interpreted in terms of the modeled low-frequency flow’s feedback on the statistics of the subgrid-scale processes.

%B Journal of Climate %V 18 %P 4404–4424 %G eng %N 21 %R 10.1175/JCLI3544.1 %0 Journal Article %D 2005 %T A Multiple-Regime Approach to Atmospheric Zonal-Flow Vacillation %A Koo, Seongjoon %A Robertson, Andrew W. %A Ghil, Michael %G eng %0 Journal Article %J Geophysical Research Letters %D 2005 %T Oscillatory modes of extended Nile River records (A.D. 622–1922) %A Kondrashov, Dmitri %A Feliks, Yizhak %A Ghil, Michael %XThe historical records of the low- and high-water levels of the Nile River are among the longest climatic records that have near-annual resolution. There are few gaps in the first part of the records (A.D. 622-1470) and larger gaps later (A.D. 1471-1922). We apply advanced spectral methods, Singular-Spectrum Analysis (SSA) and the Multi-Taper Method (MTM), to fill the gaps and to locate interannual and interdecadal periodicities. The gap filling uses a novel, iterative version of SSA. Our analysis reveals several statistically significant features of the records: a nonlinear, data-adaptive trend that includes a 256-year cycle, a quasi-quadriennial (4.2-year) and a quasi-biennial (2.2-year) mode, as well as additional periodicities of 64, 19, 12, and, most strikingly, 7 years. The quasi-quadriennial and quasi-biennial modes support the long-established connection between the Nile River discharge and the El-Niño/Southern Oscillation (ENSO) phenomenon in the Indo-Pacific Ocean. The longest periods might be of astronomical origin. The 7-year periodicity, possibly related to the biblical cycle of lean and fat years, seems to be due to North Atlantic influences.

%B Geophysical Research Letters %I AGU %V 32 %P L10702 %8 may %G eng %N 10 %R 10.1029/2004GL022156 %0 Conference Paper %B Proc. ECMWF Workshop on Representation of Sub-grid Processes Using Stochastic-Dynamic Models %D 2005 %T Stochastic effects in the representation of stratocumulus-topped mixed layers %A Stevens, Bjorn %A Zhang, Yunyan %A Ghil, Michael %B Proc. ECMWF Workshop on Representation of Sub-grid Processes Using Stochastic-Dynamic Models %I Shinfield Park, Reading, UK %P 79–90 %G eng %0 Journal Article %J SIAM J. Appl. Math. %D 2005 %T Structural Bifurcation of 2-D Nondivergent Flows with Dirichlet Boundary Conditions: Applications to Boundary-Layer Separation %A Ghil, Michael %A Tian Ma %A Wang, Shouhong %B SIAM J. Appl. Math. %I Society for Industrial & Applied Mathematics (SIAM) %V 65 %P 1576–1596 %8 jan %G eng %N 5 %R 10.1137/s0036139903438818 %0 Journal Article %J Journal of the atmospheric sciences %D 2004 %T Low-frequency variability in the midlatitude atmosphere induced by an oceanic thermal front %A Feliks, Yizhak %A Ghil, Michael %A Simonnet, Eric %B Journal of the atmospheric sciences %V 61 %P 961–981 %G eng %N 9 %0 Journal Article %J Journal of the Atmospheric Sciences %D 2004 %T Low-frequency variability in the midlatitude atmosphere induced by an oceanic thermal front %A Feliks, Yizhak %A Ghil, Michael %A Simonnet, Eric %X This study examines the flow induced in a highly idealized atmospheric model by an east–west-oriented oceanic thermal front. The model has a linear marine boundary layer coupled to a quasigeostrophic, equivalent- barotropic free atmosphere. The vertical velocity at the top of the boundary layer drives the flow in the free atmosphere and produces an eastward jet, parallel to the oceanic front's isotherms. A large gyre develops on either side of this jet, cyclonic to the north and anticyclonic to the south of it. As the jet intensifies during spinup from rest, it becomes unstable. The most unstable wave has a length of about 500 km, it evolves into a meander, and eddies detach from the eastern edge of each gyre. The dependence of the atmospheric dynamics on the strength T of the oceanic front is studied. The Gulf Stream and Kuroshio fronts correspond roughly, in the scaling used here, to T 7°C. For weak fronts, T < 4°C, the circulation is steady and exhibits two large, antisymmetric gyres separated by a westerly zonal jet. As the front strengthens, 4 < T < 5, the solution undergoes Hopf bifurcation to become periodic in time, with a period of 30 days, and spatially asymmetric. The bifurcation is due to the westerly jet's barotropic instability, which has a symmetric spatial pattern. The addition of this pattern to the antisymmetric mean results in the overall asymmetry of the full solution. The spatial scale and amplitude of the symmetric, internally generated, and antisymmetric, forced mode increase with the strength T of the oceanic front. For T > 5°C, the solution becomes chaotic, but a dominant period still stands out above the broadband noise. This dominant period increases with T overall, but the increase is not monotonic. The oceanic front's intensity dictates the mean speed of the atmospheric jet. Two energy regimes are obtained. 1) In the low-energy regime, the SST front, and hence the atmospheric jet, are weak; in this regime, small meanders develop along the jet axis, and the dominant period is about 25 days. 2) In the high-energy regime, the SST front and the jet are strong; in it, large meanders and eddies develop along the jet, and the dominant oscillation has a period of about 70 days. The physical nature of the two types of oscillations is discussed, as are possible transitions between them when T changes on very long time scales. The results are placed in the context of previous theories of ocean front effects on atmospheric flows, in which baroclinic phenomena are dominant. %B Journal of the Atmospheric Sciences %V 61 %P 961–981 %G eng %N 9 %R 10.1175/1520-0469(2004)061%3C0961%3ALVITMA%3E2.0.CO%3B2 %0 Journal Article %J Physica D: Nonlinear Phenomena %D 2004 %T Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow %A Ghil, Michael %A Liu, Jian-Guo %A Wang, Cheng %A Wang, Shouhong %B Physica D: Nonlinear Phenomena %I Elsevier BV %V 197 %P 149–173 %8 oct %G eng %N 1-2 %R 10.1016/j.physd.2004.06.012 %0 Journal Article %J Journal of Computational Physics %D 2004 %T Data assimilation with an extended Kalman filter for impact-produced shock-wave dynamics %A Kao, Jim %A Flicker, Dawn %A Henninger, Rudy %A Frey, Sarah %A Ghil, Michael %A Ide, Kayo %B Journal of Computational Physics %I Elsevier %V 196 %P 705–723 %G eng %N 2 %R 10.1016/j.jcp.2003.11.028 %0 Journal Article %J Journal of Physical Oceanography %D 2004 %T Interdecadal variability in a hybrid coupled ocean-atmosphere-sea ice model %A Kravtsov, Sergey %A Ghil, Michael %B Journal of Physical Oceanography %V 34 %P 1756–1775 %G eng %N 7 %R 10.1175/1520-0485(2004)034<1756:iviahc>2.0.co;2 %0 Journal Article %J BMC Ecology %D 2004 %T Intrinsic and climatic factors in North-American animal population dynamics %A Loeuille, Nicolas %A Ghil, Michael %B BMC Ecology %I BioMed Central %V 4 %P 1 %G eng %U http://www.biomedcentral.com/1472-6785/4/6 %N 1 %0 Journal Article %J Journal of the Atmospheric Sciences %D 2004 %T Mountain torques and Northern Hemisphere low-frequency variability. Part II: Regional aspects %A Lott, François %A Robertson, Andrew W. %A Ghil, Michael %B Journal of the Atmospheric Sciences %V 61 %P 1272–1283 %G eng %N 11 %0 Journal Article %J Journal of the Atmospheric Sciences %D 2004 %T Mountain torques and Northern Hemisphere low-frequency variability. Part I: Hemispheric aspects %A Lott, François %A Robertson, Andrew W. %A Ghil, Michael %B Journal of the Atmospheric Sciences %V 61 %P 1259–1271 %G eng %N 11 %R 10.1175/1520-0469(2004)061<1259:mtanhl>2.0.co;2 %0 Journal Article %J Paleoceanography %D 2004 %T Rapid switch-like sea ice growth and land ice–sea ice hysteresis %A Sayag, Roiy %A Tziperman, Eli %A Ghil, Michael %B Paleoceanography %I Wiley Online Library %V 19 %G eng %N 1 %R 10.1029/2003pa000946 %0 Journal Article %J Journal of Climate %D 2004 %T Sensitivity analysis of cirrus cloud properties from high-resolution infrared spectra. Part I: Methodology and synthetic cirrus %A Kahn, Brian H. %A Eldering, Annmarie %A Ghil, Michael %A Bordoni, Simona %A Clough, Shepard A. %B Journal of Climate %V 17 %P 4856–4870 %G eng %N 24 %R 10.1175/jcli-3220.1 %0 Journal Article %J Journal of the Atmospheric Sciences %D 2004 %T Weather regimes and preferred transition paths in a three-level quasigeostrophic model %A Kondrashov, Dmitri %A Ide, K. %A Ghil, Michael %B Journal of the Atmospheric Sciences %V 61 %P 568–587 %G eng %N 5 %R 10.1175/1520-0469(2004)061<0568:wraptp>2.0.co;2 %0 Journal Article %J Journal of Statistical Physics %D 2003 %T A Boolean delay equation model of colliding cascades. Part I: Multiple seismic regimes %A Zaliapin, Ilya %A Keilis-Borok, Vladimir %A Ghil, Michael %B Journal of Statistical Physics %I Springer %V 111 %P 815–837 %G eng %N 3-4 %0 Journal Article %J Journal of Statistical Physics %D 2003 %T A Boolean delay equation model of colliding cascades. Part II: Prediction of critical transitions %A Zaliapin, Ilya %A Keilis-Borok, Vladimir %A Ghil, Michael %B Journal of Statistical Physics %I Springer %V 111 %P 839–861 %G eng %N 3-4 %0 Journal Article %J The Observatory %D 2003 %T Did celestial chaos kill the dinosaurs? %A Ghil, Michael %B The Observatory %V 123 %P 328–333 %G eng %N 1177 %0 Journal Article %J SIAM J. Appl. Math. %D 2003 %T Hopf Bifurcation in Quasi-geostrophic Channel Flow %A Simonnet, Eric %A Ghil, Michael %A Wang, Shouhong %A Chen, Zhi-Min %B SIAM J. Appl. Math. %I Society for Industrial & Applied Mathematics (SIAM) %V 64 %P 343–368 %G eng %N 1 %R 10.1137/s0036139902406164 %0 Conference Paper %B Proceedings ECMWF/CLIVAR Workshop on Simulation and Prediction of Intra-Seasonal Variability with Emphasis on the MJO %D 2003 %T Intraseasonal oscillations in the mid-latitudes: observations, theory, and GCM results %A Ghil, Michael %A Kondrashov, Dmitri %A Lott, F. %A Robertson, Andrew W. %B Proceedings ECMWF/CLIVAR Workshop on Simulation and Prediction of Intra-Seasonal Variability with Emphasis on the MJO %P 3–6 %G eng %0 Journal Article %J Geophysical Research Letters %D 2003 %T Large-scale and evaporation-wind feedbacks in a box model of the tropical climate %A Bellon, G. %A Treut, H. Le %A Ghil, Michael %B Geophysical Research Letters %I Wiley Online Library %V 30 %G eng %N 22 %R 10.1029/2003gl017895 %0 Journal Article %J Journal of the Atmospheric Sciences %D 2003 %T Low-Frequency Variability in a Baroclinic Beta-Channel with Land-Sea Contrast* %A Kravtsov, S. %A Robertson, Andrew W. %A Ghil, Michael %B Journal of the Atmospheric Sciences %V 60 %P 2267–2293 %G eng %N 18 %R 10.1175/1520-0469(2003)060<2267:lviabc>2.0.co;2 %0 Journal Article %J Journal of Physical Oceanography %D 2003 %T Low-frequency variability in shallow-water models of the wind-driven ocean circulation. Part II: Time-dependent solutions %A Simonnet, Eric %A Ghil, Michael %A Ide, Kayo %A Temam, Roger %A Wang, Shouhong %XThe time-dependent wind-driven ocean circulation is investigated for both a rectangular and a North Atlantic– shaped basin. Multiple steady states in a 2 ½ -layer shallow-water model and their dependence on various pa- rameters and other model properties were studied in Part I for the rectangular basin. As the wind stress on the rectangular basin is increased, each steady-state branch is destabilized by a Hopf bifurcation. The periodic solutions that arise off the subpolar branch have a robust subannual periodicity of 4–5 months. For the subtropical branch, the period varies between sub- and interannual, depending on the inverse Froude number F 2 defined with respect to the lower active layer’s thickness H 2 . As F 2 is lowered, the perturbed-symmetric branch is destabilized baroclinically, before the perturbed pitchfork bifurcation examined in detail in Part I occurs. Transition to aperiodic behavior arises at first by a homoclinic explosion off the isolated branch that exists only for sufficiently high wind stress. Subsequent global and local bifurcations all involve the subpolar branch, which alone exists in the limit of vanishing wind stress. Purely subpolar solutions vary on an interannual scale, whereas combined subpolar and subtropical solutions exhibit complex transitions affected by a second, subpolar homoclinic orbit. In the latter case, the timescale of the variability is interdecadal. The role of the global bifurcations in the interdecadal variability is investigated. Numerical simulations were carried out for the North Atlantic with earth topography- 5 minute (ETOPO-5) coastline geometry in the presence of realistic, as well as idealized, wind stress forcing. The simulations exhibit a realistic Gulf Stream at 20-km resolution and with realistic wind stress. The variability at 12-km resolution exhibits spectral peaks at 6 months, 16 months, and 6–7 years. The subannual mode is strongest in the subtropical gyre; the interannual modes are both strongest in the subpolar gyre.

%B Journal of Physical Oceanography %V 33 %G eng %N 4 %0 Journal Article %J Journal of Physical Oceanography %D 2003 %T Low-Frequency Variability in Shallow-Water Models of the Wind-Driven Ocean Circulation. Part I: Steady-State Solution %A Simonnet, Eric %A Ghil, Michael %A Ide, Kayo %A Temam, Roger %A Wang, Shouhong %XSuccessive bifurcations—from steady states through periodic to aperiodic solutions—are studied in a shallow- water, reduced-gravity, 2 ½ -layer model of the midlatitude ocean circulation subject to time-independent wind stress. The bifurcation sequence is studied in detail for a rectangular basin with an idealized spatial pattern of wind stress. The aperiodic behavior is studied also in a North Atlantic–shaped basin with realistic continental contours. The bifurcation sequence in the rectangular basin is studied in Part I, the present article. It follows essentially the one reported for single-layer quasigeostrophic and 1 ½ -layer shallow-water models. As the intensity of the north– south-symmetric, zonal wind stress is increased, the nearly symmetric double-gyre circulation is destabilized through a perturbed pitchfork bifurcation. The low-stress steady solution, with its nearly equal subtropical and subpolar gyres, is replaced by an approximately mirror-symmetric pair of stable equilibria. The two solution branches so obtained are named after the inertial recirculation cell that is stronger, subtropical or subpolar, respectively. This perturbed pitchfork bifurcation and the associated Hopf bifurcations are robust to changes in the interface friction between the two active layers and the thickness H 2 of the lower active layer. They persist in the presence of asymmetries in the wind stress and of changes in the model’s spatial resolution and finite- difference scheme. Time-dependent model behavior in the rectangular basin, as well as in the more realistic, North Atlantic–shaped one, is studied in Part II.

%B Journal of Physical Oceanography %V 33 %G eng %N 4 %0 Journal Article %J The Astrophysical Journal %D 2003 %T Successive refinements in long-term integrations of planetary orbits %A F. Varadi %A Runnegar, B. %A Ghil, Michael %B The Astrophysical Journal %I IOP Publishing %V 592 %P 620 %G eng %N 1 %R 10.1086/375560 %0 Conference Paper %B Uncertainty Modeling and Analysis, 2003. ISUMA 2003. Fourth International Symposium on %D 2003 %T Using extended Kalman filter for data assimilation and uncertainty quantification in shock-wave dynamics %A Kao, J. %A Flicker, D. %A Henninger, R. %A Ghil, Michael %A Ide, K. %B Uncertainty Modeling and Analysis, 2003. ISUMA 2003. Fourth International Symposium on %I IEEE %P 398–407 %G eng %R 10.1109/isuma.2003.1236192 %0 Journal Article %J Reviews of Geophysics %D 2002 %T Advanced spectral methods for climatic time series %A Ghil, Michael %A M. R. Allen %A M. D. Dettinger %A Ide, Kayo %A Kondrashov, Dmitri %A M. E. Mann %A Robertson, Andrew W. %A A. Saunders %A Y. Tian %A Varadi, Ferenc %A Yiou, Pascal %B Reviews of Geophysics %V 40 %P 1–41 %G eng %N 1 %R 10.1029/2000RG000092 %0 Journal Article %J Physica D: Nonlinear Phenomena %D 2002 %T Baroclinic and barotropic aspects of the wind-driven ocean circulation %A Ghil, M %A Feliks, Y %A Sushama, L. U. %XThe double-gyre circulation induced by a symmetric wind-stress pattern in a quasi-geostrophic model of the mid-latitude ocean is studied analytically and numerically. The model is discretized vertically by projection onto normal modes of the mean stratification. Within its horizontally rectangular domain, the numerical model captures the wind-driven circulation’s three dynamic regimes: (1) a basin-scale double-gyre circulation, cyclonic in the basin’s northern part and anticyclonic in the south, which is dominated by Sverdrup balance; (2) a swift western boundary current in either gyre, with dissipation most important near the coast and inertial balance further out; and (3) a strong recirculating dipole near the intersection of the western boundary with the symmetry line of zero wind-stress curl. The flow inside this stationary dipole is highly nonlinear, and equivalent-barotropic. An analytical solution to the potential vorticity equation with variable stratification describes the dipole, and fits well the full numerical model’s steady-state solutions. Changes in the numerical model’s solutions are investigated systematically as a function of changes in the strength of the wind stress $\tau$ and the Rossby radius of deformation LR. The main changes occur in the recirculation region, while the basin-scale gyres and the western boundary currents are affected but little. A unique symmetric dipole is observed for small $\tau$, and agrees in its properties with the analytical solution. As $\tau$ increases, multiple asymmetric equilibria arise due to pitchfork bifurcation and are stable for large enough LR. The numerically obtained asymmetric equilibria also agree in their main properties with the analytical ones, as well as with the corresponding solutions of a shallow-water model. Increasing $\tau$ further results in two successive Hopf bifurcations, that lead to limit cycles with periods near 10 and 1 years, respectively. Both oscillatory instabilities have a strong baroclinic component. Above a certain threshold in $\tau$ the solutions become chaotic. Flow pattern evolution in this chaotic regime resembles qualitatively the circulation found in the Gulf Stream and Kuroshio current systems after their separation from the continent.

%B Physica D: Nonlinear Phenomena %I Elsevier %V 167 %P 1–35 %G eng %N 1 %R 10.1016/S0167-2789(02)00392-5 %0 Book Section %B Encyclopedia of Atmospheric Sciences %D 2002 %T Climate variability: Nonlinear aspects %A Ghil, Michael %E J. R. Holton %E J. Pyle %E J. A. Curry %B Encyclopedia of Atmospheric Sciences %I Academic Press %P 432–438 %G eng %0 Conference Paper %B AMS Symposium on Observations, Data Assimilation, and Probabilistic Prediction %D 2002 %T Data Assimilation and Weather Regimes in a Three-Level Quasi-Geostrophic Model %A Kondrashov, Dmitri %A Ghil, Michael %A Ide, K. %A Todling, R. %B AMS Symposium on Observations, Data Assimilation, and Probabilistic Prediction %G eng %0 Journal Article %J Monthly Weather Review %D 2002 %T Data assimilation for a coupled ocean-atmosphere model. Part I: Sequential state estimation %A Sun, Chaojiao %A Hao, Zheng %A Ghil, Michael %A Neelin, J. David %B Monthly Weather Review %V 130 %P 1073–1099 %G eng %N 5 %R 10.1175/1520-0493(2002)130<1073:dafaco>2.0.co;2 %0 Journal Article %J Climate Dynamics %D 2002 %T Midlatitude ocean-atmosphere interaction in an idealized coupled model %A Kravtsov, Sergey %A Robertson, A. %B Climate Dynamics %I Springer %V 19 %P 693–711 %G eng %N 8 %R 10.1007/s00382-002-0256-6 %0 Journal Article %J Journal of Geophysical Research: Atmospheres %D 2002 %T Multiple regimes and low-frequency oscillations in the Southern Hemisphere's zonal-mean flow %A Koo, Seongjoon %A Robertson, Andrew W. %A Ghil, Michael %B Journal of Geophysical Research: Atmospheres %I Wiley Online Library %V 107 %G eng %N D21 %R 10.1029/2001jd001353 %0 Book Section %B Encyclopedia of Global Environmental Change %D 2002 %T Natural climate variability %A Ghil, Michael %E M. MacCracken %E J. Perry %B Encyclopedia of Global Environmental Change %I Wiley & Sons, Chichester/New York %V 1 %P 544–549 %G eng %0 Journal Article %J Geophysical Research Letters %D 2002 %T Phase relations between climate proxy records: Potential effect of seasonal precipitation changes %A Gildor, Hezi %A Ghil, Michael %B Geophysical Research Letters %I Wiley Online Library %V 29 %G eng %N 2 %R 10.1029/2001gl013781 %0 Journal Article %J Journal of Geophysical Research: Atmospheres %D 2002 %T Probing near-surface atmospheric turbulence with high-resolution lidar measurements and models %A Kao, C.-Y. J. %A Cooper, D. I. %A Reisner, J. M. %A Eichinger, W. E. %A Ghil, Michael %B Journal of Geophysical Research: Atmospheres %I Wiley Online Library %V 107 %G eng %N D10 %R 10.1029/2001jd000746 %0 Journal Article %J Chaos: An Interdisciplinary Journal of Nonlinear Science %D 2002 %T Successive bifurcations in a simple model of atmospheric zonal-flow vacillation %A Koo, Seongjoon %A Ghil, Michael %B Chaos: An Interdisciplinary Journal of Nonlinear Science %I AIP Publishing %V 12 %P 300–309 %G eng %N 2 %R 10.1063/1.1468249 %0 Journal Article %J Proceedings of the National Academy of Sciences %D 2002 %T ``Waves'' vs. ``particles'' in the atmosphere's phase space: A pathway to long-range forecasting? %A Ghil, Michael %A Robertson, Andrew W. %XThirty years ago, E. N. Lorenz provided some approximate limits to atmospheric predictability. The details—in space and time—of atmospheric flow fields are lost after about 10 days. Certain gross flow features recur, however, after times of the order of 10–50 days, giving hope for their prediction. Over the last two decades, numerous attempts have been made to predict these recurrent features. The attempts have involved, on the one hand, systematic improvements in numerical weather prediction by increasing the spatial resolution and physical faithfulness in the detailed models used for this prediction. On the other hand, theoretical attempts motivated by the same goal have involved the study of the large-scale atmospheric motions’ phase space and the inhomoge- neities therein. These ‘‘coarse-graining’’ studies have addressed observed as well as simulated atmospheric data sets. Two distinct approaches have been used in these studies: the episodic or intermittent and the oscillatory or periodic. The intermittency approach describes multiple-flow (or weather) regimes, their per- sistence and recurrence, and the Markov chain of transitions among them. The periodicity approach studies intraseasonal oscil- lations, with periods of 15–70 days, and their predictability. We review these two approaches, ‘‘particles’’ vs. ‘‘waves,’’ in the quantum physics analogy alluded to in the title of this article, discuss their complementarity, and outline unsolved problems.

%B Proceedings of the National Academy of Sciences %I National Acad Sciences %V 99 %P 2493–2500 %G eng %R 10.1073/pnas.012580899 %0 Journal Article %J Climate Dynamics %D 2001 %T Atmospheric radiative equilibria. Part II: bimodal solutions for atmospheric optical properties %A Ide, Kayo %A Treut, H. Le %A Li, Z.-X. %A Ghil, Michael %B Climate Dynamics %I Springer %V 18 %P 29–49 %G eng %N 1-2 %R 10.1007/s003820100168 %0 Journal Article %J Physica D: Nonlinear Phenomena %D 2001 %T A Boolean delay equation model of ENSO variability %A Saunders, Amira %A Ghil, Michael %B Physica D: Nonlinear Phenomena %I Elsevier %V 160 %P 54–78 %G eng %N 1 %0 Journal Article %J Journal of Fluid Mechanics %D 2001 %T Experimental and numerical studies of an eastward jet over topography %A Tian, Yudong %A Weeks, Eric R. %A Ide, Kayo %A Urbach, J. S. %A Baroud, Charles N. %A Ghil, Michael %A Swinney, Harry L. %B Journal of Fluid Mechanics %I Cambridge Univ Press %V 438 %P 129–157 %G eng %R 10.1017/s0022112001004372 %0 Journal Article %J Nonlinear Processes in Geophysics %D 2001 %T Hilbert problems for the geosciences in the 21st century %A Ghil, Michael %B Nonlinear Processes in Geophysics %V 8 %P 211–211 %G eng %N 4/5 %R 10.5194/npg-8-211-2001 %0 Journal Article %J Geophys. Res. Lett %D 2001 %T Mountain torques and atmospheric oscillations %A Lott, François %A Robertson, Andrew W. %A Ghil, Michael %B Geophys. Res. Lett %V 28 %P 1207–1210 %G eng %R 10.1029/2000gl011829 %0 Journal Article %J Indiana University Mathematics Journal %D 2001 %T Structural bifurcation of 2-D incompressible flows %A Ghil, Michael %A Tian Ma %A Wang, Shouhong %B Indiana University Mathematics Journal %V 50 %P 159–180 %G eng %0 Journal Article %J Journal of Physical Oceanography %D 2001 %T Transition to aperiodic variability in a wind-driven double-gyre circulation model %A Chang, Kyung-Il %A Ghil, Michael %A Ide, Kayo %A Lai, Chung-Chieng Aaron %XMultiple equilibria as well as periodic and aperiodic solution regimes are obtained in a barotropic model of the midlatitude ocean’s double-gyre circulation. The model circulation is driven by a steady zonal wind profile that is symmetric with respect to the square basin’s zonal axis of north–south symmetry, and dissipated by lateral friction. As the intensity of the wind forcing increases, an antisymmetric double-gyre flow evolves through a pitchfork bifurcation into a pair of steady mirror-symmetric solutions in which either the subtropical or the subpolar gyre dominates. In either one of the two asymmetric solutions, a pair of intense recirculation vortices forms close to and on either side of the point where the two western boundary currents merge to form the eastward jet. To the east of this dipole, a spatially damped stationary wave arises, and an increase in the steady forcing amplifies the meander immediately to the east of the recirculating vortices. During this process, the transport of the weaker gyre remains nearly constant while the transport of the stronger gyre increases. For even stronger forcing, the two steady solution branches undergo Hopf bifurcation, and each asymmetric solution gives rise to an oscillatory mode, whose subannual period is of 3.5–6 months. These two modes are also mirror-symmetric in space. The time-average difference in transport between the stronger and the weaker gyre is reduced as the forcing increases further, while the weaker gyre tends to oscillate with larger amplitude than the stronger gyre. Once the average strength of the weaker gyre on each branch equals the stronger gyre’s, the solution becomes aperiodic. The transition of aperiodic flow occurs through a global bifurcation that involves a homoclinic orbit. The subannual oscillations persist and stay fairly regular in the aperiodic solution regime, but they alternate now with a new and highly energetic, interannual oscillation. The physical causes of these two oscillations—as well as of a third, 19-day oscillation—are discussed. During episodes of the high-amplitude, interannual oscillation, the solution exhibits phases of either the subtropical or subpolar gyre being dominant. Even lower-frequency, interdecadal variability arises due to an irregular alternation between subannual and interannual modes of oscillation.

%B Journal of Physical Oceanography %V 31 %P 1260–1286 %G eng %N 5 %R 10.1175/1520-0485(2001)031<1260:TTAVIA>2.0.CO;2 %0 Journal Article %J Geophysical Research Letters %D 2000 %T Pacific interdecadal variability in this century's sea surface temperatures %A Chao, Yi %A Ghil, Michael %A McWilliams, James C. %B Geophysical Research Letters %I Wiley Online Library %V 27 %P 2261–2264 %G eng %N 15 %R 10.1029/1999gl011324 %0 Journal Article %J Physica D %D 2000 %T Data-adaptive wavelets and multi-scale singular-spectrum analysis %A Yiou, Pascal %A Sornette, Didier %A Ghil, Michael %XUsing multi-scale ideas from wavelet analysis, we extend singular-spectrum analysis (SSA) to the study of nonstationary time series, including the case where intermittency gives rise to the divergence of their variance. The wavelet transform resembles a local Fourier transform within a finite moving window whose width W, proportional to the major period of interest, is varied to explore a broad range of such periods. SSA, on the other hand, relies on the construction of the lag-correlation matrix C on M lagged copies of the time series over a fixed window width W to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components; here W=M[Delta]t with [Delta]t as the time step. The proposed multi-scale SSA is a local SSA analysis within a moving window of width M<=W<=N, where N is the length of the time series. Multi-scale SSA varies W, while keeping a fixed W/M ratio, and uses the eigenvectors of the corresponding lag-correlation matrix C(M) as data-adaptive wavelets; successive eigenvectors of C(M) correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis. Multi-scale SSA thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time-frequency domain by a suitable localization of the signal's correlation matrix. We present several examples of application to synthetic signals with fractal or power-law behavior which mimic selected features of certain climatic or geophysical time series. The method is applied next to the monthly values of the Southern Oscillation Index (SOI) for 1933-1996; the SOI time series is widely believed to capture major features of the El Niño/Southern Oscillation (ENSO) in the Tropical Pacific. Our methodology highlights an abrupt periodicity shift in the SOI near 1960. This abrupt shift between 5 and 3 years supports the Devil's staircase scenario for the ENSO phenomenon (preliminary results of this study were presented at the XXII General Assembly of the European Geophysical Society, Vienna, May 1997, and at the Fall Meeting of the American Geophysical Union, San Francisco, December 1997).

%B Physica D %V 142 %P 254–290 %G eng %N 3-4 %R 10.1016/S0167-2789(00)00045-2 %0 Conference Paper %B Proc. 3rd WMO Intl Symp. Assimilation of Observations in Meteorology & Oceanography %D 2000 %T The essence of data assimilation or why combine data with models %A Ghil, Michael %B Proc. 3rd WMO Intl Symp. Assimilation of Observations in Meteorology & Oceanography %P 1–4 %G eng %0 Book Section %B General Circulation Model Development: Past, Present and Future %D 2000 %T Solving problems with GCMs: General circulation models and their role in the climate modeling hierarchy %A Ghil, Michael %A Robertson, Andrew W. %E D. Randall %B General Circulation Model Development: Past, Present and Future %I Academic Press, San Diego %P 285–325 %G eng %R 10.1016/s0074-6142(00)80058-3 %0 Journal Article %J The Astrophysical Journal %D 1999 %T Three-dimensional Magnetohydrodynamic Simulationsof the Interaction of Magnetic Flux Tubes %A Kondrashov, D. %A J. Feynman %A P. C. LIEWER %A A. Ruzmaikin %X We use a three-dimensional Cartesian resistive MHD code to investigate three-dimensional aspects of the interaction of magnetic flux tubes as observed in the solar atmosphere and studied in laboratory experiments. We present here the first results from modeling the reconnection of two Gold-Hoyle magnetic flux tubes that follow the system evolution to a final steady state. The energy evolution and reconnection rate for flux tubes with both parallel and antiparallel axial fields and with equal and nonequal strengths are studied. For the first time, we calculate a gauge-invariant relative magnetic helicity of the system and compare its evolution for all the above cases. We observed that the rate at which helicity is dissipated may vary significantly for different cases, and it may be comparable with the energy dissipation rate. The footpoints of the interacting flux tubes were held fixed or allowed to move to simulate different conditions in the solar photosphere. The cases with fixed footpoints had lower magnetic energy release and reached a steady state faster than cases with moving footpoints. For all computed cases the magnetic energy was released mostly through work done on the plasma by the electromagnetic forces rather than through resistive dissipation. The reconnection rate of the poloidal magnetic field is faster for the case with antiparallel flux tubes than for the case with parallel flux tubes, consistent with laboratory experiments. We find that during reconnection supersonic (but sub-Alfv√©nic) flows develop, and it may take a considerably longer time for the system to reach a steady state than for magnetic flux to reconnect. It is necessary to retain the pressure gradient in the momentum equation; the plasma pressure may be significant for the final equilibrium steady state even with low-Œ≤ initial conditions, and the work done on the plasma by compression is important in energy exchange. %B The Astrophysical Journal %V 519 %P 884 %G eng %U http://stacks.iop.org/0004-637X/519/i=2/a=884 %N 2 %0 Journal Article %J Journal of Plasma Physics %D 1999 %T Three-dimensional deformable-grid electromagnetic particle-in-cell for parallel computers %A J. WANG %A Kondrashov, Dmitri %A P. C. LIEWER %A S. R. KARMESIN %XWe describe a new parallel, non-orthogonal-grid, three-dimensional electromagnetic particle-in-cell (EMPIC) code based on a finite-volume formulation. This code uses a logically Cartesian grid of deformable hexahedral cells, a discrete surface integral (DSI) algorithm to calculate the electromagnetic field, and a hybrid logical‚Äìphysical space algorithm to push particles. We investigate the numerical instability of the DSI algorithm for non-orthogonal grids, analyse the accuracy for EMPIC simulations on non-orthogonal grids, and present performance benchmarks of this code on a parallel supercomputer. While the hybrid particle push algorithm has a second-order accuracy in space, the accuracy of the DSI field solve algorithm is between first and second order for non-orthogonal grids. The parallel implementation of this code, which is almost identical to that of a Cartesian-grid EMPIC code using domain decomposition, achieved a high parallel efficiency of over 96% for large-scal" # "e simulations.

%B Journal of Plasma Physics %I Cambridge University Press %V 61 %P 367-389 %8 04 %G eng %U https://www.cambridge.org/core/article/three-dimensional-deformable-grid-electromagnetic-particle-in-cell-for-parallel-computers/162F88C631B4741CB569FA2BE4BBD14A %N 3 %0 Journal Article %J Journal of the Atmospheric Sciences %D 1999 %T Multiple Regimes in Northern Hemisphere Height Fields via Mixture Model Clustering %A Smyth, Padhraic %A Ide, Kayo %A Ghil, Michael %B Journal of the Atmospheric Sciences %V 56 %P 3704–3723 %G eng %N 21 %R 10.1175/1520-0469(1999)056<3704:mrinhh>2.0.co;2 %0 Journal Article %J Geophysical Research Letters %D 1998 %T Recent Forecast Skill for the El Niño/Southern Oscillation %A Ghil, Michael %A Jiang, Ning %X We outline a relationship between three slowly varying characteristics of the coupled ocean-atmosphere system in the tropical Pacific: (i) quasi-periodicity, (ii) extended predictability, and (iii) approximate low dimensionality. The Southern Oscillation Index (SOI) and NiÃ±o-3 sea surface temperatures characterize climatic variations in the tropical Pacific; these two time series are usually anticorrelated. This low-dimensional characterization suggests that much of the system's seasonal-to-interannual predictability depends on the regular behavior of the two scalar time series under consideration. The predictive skill of two idealized models is studied, showing the strong connection between regularity and predictability. El-NiÃ±o/Southern-Oscillation (ENSO) predictability is then assessed for current forecast models. When the periodic component of the ENSO signal is strong, it results in higher forecast skill. This skill decreases when the anti-correlation between SOI and NiÃ±o-3 temperature anomalies is lost, as it has been in the first half of this decade. %B Geophysical Research Letters %I American Geophysical Union %V 25 %P 171–174 %G eng %R 10.1029/97GL03635 %0 Journal Article %J Climate Dynamics %D 1998 %T Trends, interdecadal and interannual oscillations in global sea-surface temperatures %A Moron, Vincent %A Vautard, Robert %A Ghil, Michael %XThis study aims at a global description of climatic phenomena that exhibit some regularity during the twentieth century. Multi-channel singular spectrum analysis is used to extract long-term trends and quasi-regular oscillations of global sea-surface temperature (SST) fields since 1901. Regional analyses are also performed on the Pacific, (Northern and Southern) Atlantic, and Indian Ocean basins. The strongest climatic signal is the irregular long-term trend, characterized by overall warming during 1910–1940 and since 1975, with cooling (especially of the Northern Hemisphere) between these two warming intervals. Substantial cooling prevailed in the North Pacific between 1950 and 1980, and continues in the North Atlantic today. Both cooling and warming are preceded by SST anomalies of the same sign in the subpolar North Atlantic. Near-decadal oscillations are present primarily over the North Atlantic, but also over the South Atlantic and the Indian Ocean. A 13–15-y oscillation exhibits a seesaw pattern between the Gulf-Stream region and the North-Atlantic Drift and affects also the tropical Atlantic. Another 7–8-y oscillation involves the entire double-gyre circulation of the North Atlantic, being mostly of one sign across the basin, with a minor maximum of opposite sign in the subpolar gyre and the major maximum in the northwestern part of the subtropical gyre. Three distinct interannual signals are found, with periods of about 60–65, 45 and 24–30 months. All three are strongest in the tropical Eastern Pacific. The first two extend throughout the whole Pacific and still exhibit some consistent, albeit weak, patterns in other ocean basins. The latter is weaker overall and has no consistent signature outside the Pacific. The 60-month oscillation obtains primarily before the 1960s and the 45-month oscillation afterwards.

%B Climate Dynamics %V 14 %P 545–569 %G eng %N 7 %R 10.1007/s003820050241 %0 Journal Article %J Journal of Physical Oceanography %D 1997 %T Tracking Nonlinear Solutions with Simulated Altimetric Data in a Shallow-Water Model %A Jiang, Shi %A Ghil, Michael %X Low-frequency variability of western boundary currents (WBCs) is pervasive in both observations and numerical models of the oceans. Because advection is of the essence in WBCs, nonlinearities are thought to be important in causing their variability. In numerical models, this variability can be distorted by our incomplete knowledge of the system’s dynamics, manifested in model errors. A reduced-gravity shallow-water model is used to study the interaction of model error with nonlinearity. Here our focus is on a purely periodic solution and a weakly aperiodic one. For the periodic case, the noise-corrupted system loses its periodicity due to nonlinear processes. For the aperiodic case, the intermittent occurrences of two relatively persistent states—a straight jet with high total energy and a meandering one with low total energy—in the perturbed model are almost out of phase with the unperturbed one. For both cases, the simulation errors are trapped in the WBC region, where the nonlinear dynamics is most vigorous. Satellite altimeters measure sea surface height globally in space and almost synoptically in time. They provide an opportunity to track WBC variability through its pronounced sea surface signature. By assimilating simulated Geosat data into the stochastically perturbed model with the improved optimal interpolation method, the authors can faithfully track the periodic behavior that had been lost and capture the correct occurrences of two relatively persistent patterns for the aperiodic case. The simulation errors accumulating in the WBC region are suppressed, thus improving the system’s predictability. The domain-averaged rms errors reach a statistical equilibrium below the observational error level. Comparison experiments using simulated Geosat and TOPEX/POSEIDON tracks show that spatially dense sampling yields lower rms errors than temporally frequent sampling for the present model. A criterion defining spatial oversampling—that is, diminishing returns—is also addressed. %B Journal of Physical Oceanography %V 27 %P 72–95 %G eng %N 1 %0 Journal Article %J Journal of the Meteorological Society of Japan %D 1997 %T Advances in Sequential Estimation for Atmospheric and Oceanic Flows %A Ghil, Michael %B Journal of the Meteorological Society of Japan %V 75 %P 289–304 %G eng %N 1B %0 Journal Article %J Journal of Meteorological Society of Japan %D 1997 %T Unified Notation for Data Assimilation: Operational, Sequential and Variational %A Kay Ide %A Phillippe Courtier %A Ghil, Michael %A Andrew C. Lorenz %B Journal of Meteorological Society of Japan %V 75 %P 181–189 %G eng %N 1B %0 Journal Article %J Physica D %D 1996 %T El Niño Southern Oscillation and the annual cycle: Subharmonic frequency-locking and aperiodicity %A Jin, F.-F. %A Neelin, J. David %A Ghil, Michael %B Physica D %V 98 %P 442–465 %G eng %R 10.1016/0167-2789(96)00111-x %0 Book Section %B Decadal Climate Variability: Dynamics and Predictability %D 1996 %T Spectral methods: What they can and cannot do for climatic time series %A Ghil, Michael %A Yiou, Pascal %E D. Anderson %E J. Willebrand %B Decadal Climate Variability: Dynamics and Predictability %I Springer-Verlag, Berlin/Heidelberg %P 446–482 %G eng %0 Journal Article %J Journal of the Atmospheric Sciences %D 1995 %T Intraseasonal Oscillations in a Barotropic Model with Annual Cycle, and Their Predictability %A Strong, Christopher %A Jin, Fei-fei %A Ghil, Michael %X Observational and modeling studies have shown that intraseasonal, 40-day oscillations over the Northern Hemisphere extratropics are strongest around the winter season. To explore intraseasonal variability in the presence of the annual cycle, an eigenanalysis method based on Floquet theory is used. This approach helps us determine the stability of the large-scale, midlatitude atmospheric flow's periodic basic state. It gives information about the growth rate of the unstable, intraseasonal eigenmode and confirms the atmosphere's preference for intraseasonal activity during the winter months, as the annual cycle modulates the eigenvector field. This eigenmode solution, furthermore, provides a basis for making extended-range (40-day) streamfunction-anomaly forecasts on a set of intraseasonal oscillations whose amplitude and phase depend on the season. A simple autoregressive model is developed to shed light on the seasonal dependence of predictive skill for the intraseasonal signal. %B Journal of the Atmospheric Sciences %V 52 %P 2627–2642 %G eng %N 15 %R 10.1175/1520-0469(1995)052<2627:IOIABM>2.0.CO;2 %0 Journal Article %J Nonlinear Processes in Geophysics %D 1995 %T Successive bifurcations in a shallow-water model applied to the wind-driven ocean circulation %A Speich, S %A Dijkstra, H %A Ghil, M %X Climate - the "coarse-gridded" state of the coupled ocean - atmosphere system - varies on many time and space scales. The challenge is to relate such variation to specific mechanisms and to produce verifiable quantitative explanations. In this paper, we study the oceanic component of the climate system and, in particular, the different circulation regimes of the mid-latitude win driven ocean on the interannual time scale. These circulations are dominated by two counterrotating, basis scale gyres: subtropical and subpolar. Numerical techniques of bifurcation theory are used to stud the multiplicity and stability of the steady-state solution of a wind-driven, double-gyre, reduced-gravity, shallow water model. Branches of stationary solutions and their linear stability are calculated systematically as parameter are varied. This is one of the first geophysical studies i which such techniques are applied to a dynamical system with tens of thousands of degrees of freedom. Multiple stationary solutions obtain as a result of nonlinear interactions between the two main recirculating cell (cyclonic and anticyclonic) of the large- scale double-gyre flow. These equilibria appear for realistic values of the forcing and dissipation parameters. They undergo Hop bifurcation and transition to aperiodic solutions eventually occurs. The periodic and chaotic behaviour is probably related to an increased number of vorticity cells interaction with each other. A preliminary comparison with observations of the Gulf Stream and Kuroshio Extensions suggests that the intern variability of our simulated mid-latitude ocean is a important factor in the observed interannual variability o these two current systems. %B Nonlinear Processes in Geophysics %V 2 %P 241–268 %G eng %R 10.5194/npg-2-241-1995 %0 Journal Article %J Journal of Physical Oceanography %D 1995 %T Multiple Equilibria, Periodic, and Aperiodic Solutions in a Wind-Driven, Double-Gyre, Shallow-Water Model %A Jiang, Shi %A Jin, Fei-fei %A Ghil, Michael %X A reduced-gravity shallow-water (SW) model is used to study the nonlinear behavior of western boundary currents (WBCs), with particular emphasis on multiple equilibria and low-frequency variations. When the meridionally symmetric wind stress is sufficiently strong, two steady solutions–nearly antisymmetric about the x axis–are achieved from different initial states. These results imply that 1) the inertial WBCs could overshoot either southward or northward along the western boundary, depending on their initial states; and thus, 2) the WBC separation and eastward jet could occur either north or south of the maximum wind stress line. The two equilibria arise via a perturbed pitchfork bifurcation, as the wind stress increases. A low-order, double-gyre, quasigeostrophic (QG) model is studied analytically to provide further insight into the physical nature of this bifurcation. In this model, the basic state is exactly antisymmetric when the wind stress is symmetric. The perturbations destroying the symmetry of the pitchfork bifurcation can arise, therefore. in the QG model only from the asymmetric components of the wind stress. In the SW model, the antisymmetry of the system's basic response to the symmetric forcing is destroyed already at arbitrarily low wind stress. The pitchfork bifurcation from this basic state to more complex states at high wind stress is accordingly perturbed in the absence of any forcing asymmetry. Periodic solutions arise by Hopf bifurcation from either steady-state branch of the SW model. A purely periodic solution is studied in detail. The subtropical and subpolar recirculations, separation, and eastward jet exhibit a perfectly periodic oscillation with a period of about 2.8 years. Outside the recirculation zones, the solutions are nearly steady. The alternating anomalies of the upper-layer thickness are periodically generated adjacent to the ridge of the first and strongest downstream meander and are then propagated and advected into the two WBC zones, by Rossby waves and the recirculating currents, respectively. These anomalies periodically change the pressure gradient field near the WBCs and maintain the periodic oscillation. Aperiodic solutions are also studied by either increasing wind forcing or decreasing the viscosity. %B Journal of Physical Oceanography %I American Meteorological Society %V 25 %P 764–786 %G eng %N 5 %R 10.1175/1520-0485(1995)025<0764:MEPAAS>2.0.CO;2 %0 Journal Article %J Climatic Change %D 1995 %T Interannual and interdecadal variability in United States surface-air temperatures, 1910-87 %A Dettinger, Michael D %A Ghil, Michael %A Keppenne, Christian L %X Monthly mean surface-air temperatures at 870 sites in the contiguous United States were analyzed for interannual and interdecadal variability over the time interval 1910-87. The temperatures were analyzed spatially by empirical-orthogonal-function analysis and temporally by singularspectrum analysis (SSA). The dominant modes of spatio-temporal variability are trends and nonperiodic variations with time scales longer than 15 years, decadal-scale oscillations with periods of roughly 7 and 10 years, and interannual oscillations of 2.2 and 3.3 years. Together, these modes contribute about 18% of the slower-than-annual United States temperature variance. Two leading components roughly capture the mean hemispheric temperature trend and represent a long-term warming, largest in the southwest, accompanied by cooling of the domain's southeastern quadrant. The extremes of the 2.2-year interannual oscillation characterize temperature differences between the Northeastern and Southwestern States, whereas the 3.3-year cycle is present mostly in the Western States. The 7- to 10-year oscillations are much less regular and persistent than the interannual oscillations and characterize temperature differences between the western and interior sectors of the United States. These continental- or regional-scale temperature variations may be related to climatic variations with similar periodicities, either global or centered in other regions; such variations include quasi-biennial oscillations over the tropical Pacific or North Atlantic and quasi-triennial oscillations of North Pacific sea-surface temperatures. %B Climatic Change %I Springer %V 31 %P 35–66 %G eng %N 1 %R 10.1007/BF01092980 %0 Journal Article %J Climate Dynamics %D 1995 %T Interannual and interdecadal oscillation patterns in sea level %A Unal, Yurdanur Sezginer %A Ghil, Michael %XRelative sea-level height (RSLH) data at 213 tide-gauge stations have been analyzed on a monthly and an annual basis to study interannual and interdecadal oscillations, respectively. The main tools of the study are singular spectrum analysis (SSA) and multi-channel SSA (M-SSA). Very-low-frequency variability of RSLH was filtered by SSA to estimate the linear trend at each station. Global sea-level rise, after postglacial rebound corrections, has been found to equal 1.62±0.38 mm/y, by averaging over 175 stations which have a trend consistent with the neighboring ones. We have identified two dominant time scales of El Niño-Southern Oscillation (ENSO) variability, quasi-biennial and low-frequency, in the RSLH data at almost all stations. However, the amplitudes of both ENSO signals are higher in the equatorial Pacific and along the west coast of North America. RSLH data were interpolated along ocean coasts by latitudinal intervals of 5 or 10 degrees, depending on station density. Interannual variability was then examined by M-SSA in five regions: eastern Pacific (25°S–55°N at 10° resolution), western Pacific (35°S–45°N at 10°), equatorial Pacific (123°E–169°W, 6 stations), eastern Atlantic (30°S, 0°, and 30°N–70°N at 5°) and western Atlantic (50°S–50°N at 10°). Throughout the Pacific, we have found three dominant spatio-temporal oscillatory patterns, associated with time scales of ENSO variability; their periods are 2, 2.5–3 and 4–6 y. In the eastern Pacific, the biennial mode and the 6-y low-frequency mode propagate poleward. There is a southward propagation of low-frequency modes in the western Pacific RSLH, between 35°N and 5°S, but no clear propagation in the latitudes further south. However, equatorward propagation of the biennial signal is very clear in the Southern Hemisphere. In the equatorial Pacific, both the quasi-quadrennial and quasi-biennial modes at 10°N propagate westward. Strong and weak El Niño years are evident in the sea-level time series reconstructed from the quasi-biennial and low-frequency modes. Interannual variability with periods of 3 and 4–8 y is detected in the Atlantic RSLH data. In the eastern Atlantic region, we have found slow propagation of both modes northward and southward, away from 40–45°N. Interdecadal oscillations were studied using 81 stations with sufficiently long and continuous records. Most of these have variability at 9–13 and some at 18 y. Two significant eigenmode pairs, corresponding to periods of 11.6 and 12.8 y, are found in the eastern and western Atlantic ocean at latitudes 40°N–70°N and 10°N–50°N, respectively.

%B Climate Dynamics %V 11 %P 255–278 %G eng %N 5 %R 10.1007/BF00211679 %0 Journal Article %J Science %D 1995 %T Interannual and Interdecadal Variability in 335 Years of Central England Temperatures %A Plaut, Guy %A Ghil, Michael %A Vautard, Robert %XUnderstanding the natural variability of climate is important for predicting its near-term evolution. Models of the oceans' thermohaline and wind-driven circulation show low-frequency oscillations. Long instrumental records can help validate the oscillatory behavior of these models. Singular spectrum analysis applied to the 335-year-long central England temperature (CET) record has identified climate oscillations with interannual (7- to 8-year) and interdecadal (15- and 25-year) periods, probably related to the North Atlantic's wind-driven and thermohaline circulation, respectively. Statistical prediction of oscillatory variability shows CETs decreasing toward the end of this decade and rising again into the middle of the next.

%B Science %V 268 %P 710–713 %G eng %N 5211 %R 10.1126/science.268.5211.710 %0 Journal Article %J Climate Dynamics %D 1995 %T Quasi-quadrennial and quasi-biennial variability in the equatorial Pacific %A Jiang, N. %A Neelin, J. David %A Ghil, Michael %XEvaluation of competing El Niño/Southern Oscillation (ENSO) theories requires one to identify separate spectral peaks in equatorial wind and sea-surface temperature (SST) time series. To sharpen this identification, we examine the seasonal-to-interannual variability of these fields by the data-adaptive method of multi-channel singular spectrum analysis (M-SSA). M-SSA is applied to the equatorial band (4°N-4°S), using 1950 1990 data from the Comprehensive Ocean and Atmosphere Data Set. Two major interannual oscillations are found in the equatorial SST and surface zonal wind fields, U. The main peak is centered at about 52-months; we refer to it as the quasi-quadrennial (QQ) mode. Quasi-biennial (QB) variability is split between two modes, with periods near 28 months and 24 months. A faster, 15-month oscillation has smaller amplitude. The QQ mode dominates the variance and has the most distinct spectral peak. In time-longitude reconstructions of this mode, the SST has the form of a standing oscillation in the eastern equatorial Pacific, while the U-field is dominated by a standing oscillation pattern in the western Pacific and exhibits also slight eastward propagation in the central and western Pacific. The locations of maximum anomalies in both QB modes are similar to those of the QQ mode. Slight westward migration in SST, across the eastern and central, and eastward propagation of U, across the western and central Pacific, are found. The significant wind anomaly covers a smaller region than for the QQ. The QQ and QB modes together represent the ENSO variability well and interfere constructively during major events. The sharper definition of the QQ spectral peak and its dominance are consistent with the “devil's staircase” interaction mechanism between the annual cycle and ENSO.

%B Climate Dynamics %V 12 %P 101–112 %G eng %R 10.1007/BF00223723 %0 Journal Article %J Journal of the Atmospheric Sciences %D 1994 %T Spells of Low-Frequency Oscillations and Weather Regimes in the Northern Hemisphere %A Plaut, Guy %A Vautard, Robert %K Climate %K MSSA %X The low-frequency variability in the midlatitudes is described through an analysis of the oscillatory phenomena. In order to isolate nearly periodic components of the atmospheric flow, the multichannel version of the singular spectrum analysis (M-SSA) is developed and applied to an NMC 32-year long set of 700-hPa geopotential heights. In the same way that principal component analysis identifies the spatial patterns dominating the variability, M-SSA identifies dynamically relevant space?time patterns and provides an adaptive filtering technique. Three major low-frequency oscillations (LFOs) are found, with periods of 70 days, 40?45 days, and 30?35 days. The 70-day oscillation consists of fluctuations in both position and amplitude of the Atlantic jet, with a poleward-propagating anomaly pattern. The 40?45-day oscillation is specific to the Pacific sector and has a pronounced Pacific/North American (PNA) structure in its high-amplitude phase. The 30?35-day mode is confined over the Atlantic region, and consists of the retrogression of a dipole pattern. All these oscillations are shown to be intermittently excited, and M-SSA allows the localization of their spells. The two Atlantic oscillations turn out to be frequently phase locked, so that the 30?35-day mode is likely to be a harmonic of the 70-day mode. The phase locking of the Pacific 40?45-day with the Atlantic 30?35-day oscillations is also studied. Next, the relationships between LFOs and weather regimes are studied. It is shown in particular that the occurrence of the Euro-Atlantic blocking regime is strongly favored, although not systematically caused, by particular phases of the 30?35-day mode. The LFOs themselves are able to produce high-amplitude persistent anomalies by interfering with each other. The transition from a zonal regime to a blocking regime is also shown to be highly connected to the life cycle of the 30?35-day mode, indicating that regime transitions do not result only from the random occurrence of particular transient eddy forcing. There are preferred paths between weather regimes. This result leaves us with the hope that at least the large-scale environment-favoring weather regimes may be forecast in the long range. Conditional probability of occurrence of blocking, 30 days ahead, is enhanced, relative to climatological probability, by a factor of 2 if the phase of the 30?35-day oscillation is known. This also emphasizes the necessity of operational models to represent correctly the extratropical LFOs in order to produce skillful long-range and even medium-range forecasts of weather regimes. %B Journal of the Atmospheric Sciences %V 51 %P 210–236 %G eng %N 2 %R 10.1175/1520-0469(1994)051<0210:SOLFOA>2.0.CO;2 %0 Journal Article %J Journal of Atmospheric Sciences %D 1994 %T Advanced Data Assimilation in Strongly Nonlinear Dynamical Systems %A Miller, Robert N. %A Ghil, Michael %A Gauthiez, François %B Journal of Atmospheric Sciences %V 51 %P 1037–1056 %G eng %R 10.1175/1520-0469(1994)051 %0 Journal Article %J Physica D %D 1994 %T Cryothermodynamics: the chaotic dynamics of paleoclimate %A Ghil, Michael %B Physica D %I Elsevier Science Publishers B. V. %C Amsterdam, The Netherlands, The Netherlands %V 77 %P 130–159 %G eng %N 1-3 %R 10.1016/0167-2789(94)90131-7 %0 Journal Article %J Science %D 1994 %T El Niño on the Devil's Staircase: Annual subharmonic steps to chaos %A Jin, F.-F. %A Neelin, J. David %A Ghil, Michael %B Science %V 264 %P 70–72 %G eng %R 10.1126/science.264.5155.70 %0 Journal Article %J Monthly Weather Review %D 1993 %T Forecasting Northern Hemisphere 700\mbox-mb geopotential height anomalies using empirical normal modes %A Penland, Cécile %A Ghil, Michael %X Multivariate linear prediction based on single-lag inverse modeling is developed further and critically examined. The method is applied to the National Meteorological Center analyses of Northern Hemisphere 700-mb geopotential height anomalies, which have been filtered to eliminate periods shorter than 10 days. Empirically derived normal modes of the randomly forced linear system are usually correlated, even at zero lag, suggesting that combinations of modes should be used in predictions. Due to nonlinearities in the dynamics and the neglect of interactions with other pressure levels, the lag at which the analysis is performed is crucial; best predictions obtain when the autocovariances involved in the analysis are calculated at a lag comparable to the exponential decay times of the modes. Errors in prediction have a significant seasonal dependence, indicating that the annual cycle affects the higher-order statistics of the field. Optimized linear predictions using this method are useful for about half a day longer than predictions made by persistence. Conditional probabilities are much more efficiently calculated using normal-mode parameters than from histograms, and yield similar results. Maps of the model's Fourier spectra—integrated over specified frequency intervals and consistent with the assumptions made in a linear analysis—agree with maps obtained from fast Fourier transforms of the data. %B Monthly Weather Review %V 121 %P 2355–2372 %G eng %N 8 %R 10.1175/1520-0493(1993)121%3C2355%3AFNHMGH%3E2.0.CO%3B2 %0 Journal Article %J Journal of the Atmospheric Sciences %D 1993 %T Multiple flow regimes in the Northern Hemisphere winter. Part I: Methodology and hemispheric regimes %A Kimoto, Masahide %A Ghil, Michael %X Recurrent and persistent flow patterns are identified by examining multivariate probability density functions (PDFs) in the phase space of large-scale atmospheric motions. This idea is pursued systematically here in the hope of clarifying the extent to which intraseasonal variability can be described and understood in terms of multiple flow regimes. Bivariate PDFs of the Northern Hemisphere (NH) wintertime anomaly heights at 700 mb are examined in the present paper, using a 37-year dataset. The two-dimensional phase plane is defined by the two leading empirical orthogonal functions (EOFs) of the anomaly fields. PDFs on this plane exhibit synoptically intriguing and statistically significant inhomogeneities on the periphery of the distribution. It is shown that these inhomogeneities are due to the existence of persistent and recurrent anomaly patterns, well-known as dominant teleconnection patterns; that is, the Pacific/North American (PNA) pattern, its reverse, and zonal and blocked phases of the North Atlantic Oscillation (NAO). It is argued that the inhomogeneities are obscured when PDFs are examined in a smaller-dimensional subspace than dynamically desired. %B Journal of the Atmospheric Sciences %V 50 %P 2625–2644 %G eng %N 16 %R 10.1175/1520-0469(1993)050<2625:MFRITN>2.0.CO;2 %0 Journal Article %J Journal of physical oceanography %D 1993 %T Downwelling-front instability and eddy formation in the Eastern Mediterranean %A Feliks, Yizhak %A Ghil, Michael %X The instability of the downwelling front along the southern coast of Asia Minor is studied with a multimode quasigeostrophic model. Linear analysis shows that the most unstable wave has a length of about 100 km, The wavelength depends only very weakly on the transversal scale of the front. The wave period is larger by an order of magnitude than the e-folding time; that is, rapid local growth occurs with little propagation. The growth rate is proportional to the maximum of the speed of the downwelling westward jet. The evolution of the frontal waves can be divided into three stages. At first, the evolution is mainly due to linear instability; the second stage is characterized by closed eddy formation; and finally, isolated eddies separate from the front and penetrate into the open sea. The largest amount of available potential energy is transferred to kinetic energy and into the barotropic mode during the second, eddy-forming stage, when several dipoles develop in this mode. The formation of anticyclonic eddies is due to advection of the ridges of the unstable wave's first baroclinic mode by the barotropic dipole. The baroclinic eddies ride on the barotropic dipoles. The propagation of such dipole-rider systems is determined mainly by the evolution of the corresponding barotropic dipole. These results suggest that the warm- and salty-core eddies observed in the Eastern Mediterranean are due, at least in part, to the instability of the downwelling front along the basin's northeastern coastline. There is both qualitative and quantitative similarity between the observed and calculated eddies in their radius (35–50 km), thermal structure, and distribution along the coast. %B Journal of physical oceanography %V 23 %P 61–78 %G eng %N 1 %R 10.1175/1520-0485(1993)023%3C0061:DFIAEF%3E2.0.CO;2 %0 Journal Article %J International Journal of Bifurcation and Chaos %D 1993 %T Adaptive filtering and prediction of noisy multivariate signals: an application to subannual variability in atmospheric angular momentum %A Christian L. Keppenne %A Ghil, Michael %XPrincipal component analysis (PCA) in the space and time domains is applied to filter adaptively the dominant modes of subannual (SA) variability of a 12-year long multivariate time series of Northern Hemisphere atmospheric angular momentum (AAM); AAM is computed in 23 latitude bands of equal area from operational analyses of the U.S. National Meteorological Center. PCA isolates the leading empirical orthogonal functions (EOFs) of spatial dependence, while multivariate singular spectrum analysis (M-SSA) yields filtered time series that capture the dominant low-frequency modes of SA variability. The time series prefiltered by M-SSA lend themselves to prediction by the maximum entropy method (MEM). Whole-field predictions are made by combining the forecasts so obtained with the leading spatial EOFs obtained by PCA. The combination of M-SSA and MEM has predictive ability up to about a month. These methods are essentially linear but data-adaptive. They seem to perform well for short, noisy, multivariate time series, to which purely nonlinear, deterministically based methods are difficult to apply.

%B International Journal of Bifurcation and Chaos %V 3 %P 625–634 %G eng %R 10.1142/S0218127493000520 %0 Journal Article %J Journal of Geophysical Research: Atmospheres %D 1992 %T Adaptive filtering and prediction of the Southern Oscillation index %A Christian L. Keppenne %A Ghil, Michael %B Journal of Geophysical Research: Atmospheres %I Wiley Online Library %V 97 %P 20449–20454 %G eng %N D18 %0 Journal Article %J Physica D %D 1992 %T Singular-spectrum analysis: A toolkit for short, noisy chaotic signals %A Vautard, Robert %A Yiou, Pascal %A Ghil, Michael %X Singular-spectrum analysis (SSA) is developed further, based on experience with applications to geophysical time series. It is shown that SSA provides a crude but robust approximation of strange attractors by tori, in the presence of noise. The method works well for short, noisy time series. The lagged-covariance matrix of the processes studied is the basis of SSA. We select subsets of eigenelements and associated principal components (PCs) in order to provide (i) a noise-reduction algorithm, (ii) a detrending algorithm, and (iii) an algorithm for the identification of oscillatory components. Reconstructed components (RCs) are developed to provide optimal reconstruction of a dynamic process at precise epochs, rather than averaged over the window length of the analysis. SSA is combined with advanced spectral-analysis methods - the maximum entropy method (MEM) and the multi-taper method (MTM) - to refine the interpretation of oscillatory behavior. A combined SSA-MEM method is also used for the prediction of selected subsets of RCs. The entire toolkit is validated against a set of four prescribed time series generated by known processes, quasi-periodic or chaotic. It is also applied to a time series of global surface air temperatures, 130 years long, which has attracted considerable attention in the context of the global warming issue and provides a severe test for noise reduction and prediction. %B Physica D %V 58 %P 95–126 %G eng %N 1–4 %R 10.1016/0167-2789(92)90103-T %0 Journal Article %J Journal of geophysical research %D 1991 %T Adaptive filtering and maximum entropy spectra with application to changes in atmospheric angular momentum %A Penland, Cecile %A Ghil, Michael %A Weickmann, Klaus M. %X The spectral resolution and statistical significance of a harmonic analysis obtained by low-order maximum entropy methods (MEM) can be improved by subjecting the data to an adaptive filter. This adaptive filter consists of projecting the data onto the leading temporal empirical orthogonal functions obtained from singular spectrum analysis (SSA). The combined SSA-MEM method is applied both to a synthetic time series and a time series of atmospheric angular momentum (AAM) data. The procedure is very effective when the background noise is white and less so when the background noise is red. The latter case obtains in the AAM data. Nevertheless, we detect reliable evidence for intraseasonal and interannual oscillations in AAM. The interannual periods include a quasi-biennial one and low-frequency one of 5 years, both related to the El Niño/Southern Oscillation. In the intraseaonal band, separate oscillations of about 48..5 and 51 days are ascertained. %B Journal of geophysical research %V 96 %P 22659–22671 %G eng %N D12 %R 10.1029/91JD02107 %0 Journal Article %J Journal of the Atmospheric Sciences %D 1991 %T Intraseasonal Oscillations in the Global Atmosphere. Part I: Northern Hemisphere and Tropics %A Ghil, Michael %A Mo, Kingtse %X We have examined systematically oscillatory modes in the Northern Hemisphere and in the tropics. The 700 mb heights were used to analyze extratropical oscillations, and the outgoing longwave radiation to study tropical oscillations in convection. All datasets were band-pass filtered to focus on the intraseasonal (IS) band of 10-120 days. Leading spatial patterns of variability were obtained by applying EOF analysis to these IS data. The leading principal components (PCs) were subjected to singular spectrum analysis (SSA). SSA is a statistical technique related to EOF analysis, but in the time domain, rather than the spatial domain. It helps identify nonlinear oscillations in short and noisy time series.In the Northern Hemisphere, there are two important modes of oscillation with periods near 48 and 23 days, respectively. The 48-day mode is the most important of the two. It has both traveling and standing components, and is dominated by a zonal wavenumber two. The 23-day mode has the spatial structure and propagation properties described by Branstator and by Kushnir.In the tropics, the 40-50 day oscillation documented by Madden and Julian, Weickmann, Lau, their colleagues, and many other authors dominates the Indian and Pacific oceans from 60°E to the date line. From 170°W to 90°W, however, a 24-28 day oscillation is equally strong. The extratropical modes are often independent of, and sometimes lead, the tropical modes. %B Journal of the Atmospheric Sciences %V 48 %P 752–779 %G eng %N 5 %R 10.1175/1520-0469(1991)048<0752:IOITGA>2.0.CO;2 %0 Journal Article %J Journal of the Atmospheric Sciences %D 1991 %T Intraseasonal Oscillations in the Global Atmosphere. Part II: Southern Hemisphere. %A Ghil, Michael %A Mo, Kingtse %X In Part II of this two-part article, we complete the systematic examination of oscillatory modes in the global atmosphere by studying 12 years of 500 mb geopotential heights in the Southern Hemisphere. As in Part I, for the tropics and Northern Hemisphere extratropics, the data were band-pass filtered to focus on intraseasonal (IS) phenomena, and spatial EOFs were obtained. The leading principal components were subjected to singular spectrum analysis (SSA), in order to identify nonlinear IS oscillations with high statistical confidence.In the Southern Hemisphere, the dominant mode has a period of 23 days, with spatial patterns carried by the second and third winter EOF of the IS band. It has a zonal wavenumber-four structure. The 40-day mode is second, and dominated by wavenumbers three and four, while a 16-day mode is too weak to separate its spatial behavior from the previous two. The IS dynamics in the Southern Hemisphere is more complex and dominated by shorter wavenumbers than the Northern Hemisphere. No statistically significant correlations between the Southern Hemisphere and the tropics or the Northern Hemisphere are apparent in the IS band. %B Journal of the Atmospheric Sciences %V 48 %P 780–792 %G eng %R 10.1175/1520-0469(1991)048<0780:IOITGA>2.0.CO;2 %0 Journal Article %J Advances in Geophysics %D 1991 %T Data assimilation in meteorology and oceanography %A Ghil, Michael %A Malanotte-Rizzoli, Paola %B Advances in Geophysics %I Elsevier %V 33 %P 141–266 %G eng %R 10.1016/s0065-2687(08)60442-2 %0 Journal Article %J Nature %D 1991 %T Interdecadal oscillations and the warming trend in global temperature time series %A Ghil, Michael %A Vautard, Robert %XThe ability to distinguish a warming trend from natural variability is critical for an understanding of the climatic response to increasing greenhouse-gas concentrations. Here we use singular spectrum analysis1 to analyse the time series of global surface air tem-peratures for the past 135 years2, allowing a secular warming trend and a small number of oscillatory modes to be separated from the noise. The trend is flat until 1910, with an increase of 0.4 °C since then. The oscillations exhibit interdecadal periods of 21 and 16 years, and interannual periods of 6 and 5 years. The interannual oscillations are probably related to global aspects of the El Niño-Southern Oscillation (ENSO) phenomenon3. The interdecadal oscillations could be associated with changes in the extratropical ocean circulation4. The oscillatory components have combined (peak-to-peak) amplitudes of >0.2 °C, and therefore limit our ability to predict whether the inferred secular warming trend of 0.005 °Cyr-1 will continue. This could postpone incontrovertible detection of the greenhouse warming signal for one or two decades.

%B Nature %V 350 %P 324–327 %G eng %N 6316 %R 10.1038/350324a0 %0 Journal Article %J Dynamics of Atmospheres and Oceans %D 1989 %T Meteorological data assimilation for oceanographers. Part I: Description and theoretical framework %A Ghil, Michael %B Dynamics of Atmospheres and Oceans %I Elsevier %V 13 %P 171–218 %G eng %N 3-4 %R 10.1016/0377-0265(89)90040-7 %0 Journal Article %J Physica D %D 1989 %T Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series %A Vautard, Robert %A Ghil, Michael %XWe distinguish between two dimensions of a dynamical system given by experimental time series. Statistical dimension gives a theoretical upper bound for the minimal number of degrees of freedom required to describe tje attractor up to the accuracy of the data, taking into account sampling and noise problems. The dynamical dimension is the intrinsic dimension of the attractor and does not depend on the quality of the data. Singular Spectrum Analysis (SSA) provides estimates of the statistical dimension. SSA also describes the main physical phenomena reflected by the data. It gives adaptive spectral filters associated with the dominant oscillations of the system and clarifies the noise characteristics of the data. We apply SSA to four paleoclimatic records. The principal climatic oscillations, and the regime changes in their amplitude are detected. About 10 degrees of freedom are statistically significant in the data. Large noise and insufficient sample length do not allow reliable estimates of the dynamical dimension.

%B Physica D %V 35 %P 395–424 %8 may %G eng %N 3 %R 10.1016/0167-2789(89)90077-8 %0 Book %D 1987 %T Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory and Climate Dynamics %A Ghil, Michael %A Childress, S. %I Springer-Verlag, New York/Berlin %P 485 %G eng %0 Journal Article %J Journal of the Atmospheric Sciences %D 1985 %T Persistent anomalies, blocking and variations in atmospheric predictability %A Legras, B. %A Ghil, Michael %XWe consider regimes of low-frequency variability in large-scale atmospheric dynamics. The model used for the study of these regimes is the fully-nonlinear, equivalent-barotropic vorticity equation on the sphere, with simplified forcing, dissipation and topography. Twenty-five modes are retained in a spherical harmonics expansion of the streamfunction. Solutions are studied as a function of the nondimensional intensity of the forcing and dissipation.Multiple stationary solutions are obtained as a result of nonlinear interaction between waves, mean flow and orography. The number of modes retained in the analysis permits these multiple equilibria to appear for realistic values of the forcing. The equilibria exhibit blocked and zonal flow patterns bearing a marked resemblance to synoptically defined zonal and blocked Northern Hemisphere midlatitude flows.Wave-wave interactions influence strongly the stability properties of the equilibria and the time evolution of nonequilibrium solutions. Time-dependent solutions show persistent sequences which occur in the phase-space vicinity of the zonal and blocked equilibria. Composite flow patterns of the persistent sequences are similar to the equilibria nearby, which permits the unambiguous definition of quasi-stationary flow regimes, zonal and blocked, respectively. The number of episodes of blocked or zonal flow decreases monotonically as their duration increases, in agreement with observations.The statistics of transitions between the two types of planetary flow regimes are computed from the model's deterministic dynamics. These transitional called breaks in statistical-synoptic long-range forecasting, are shown to be influenced by changes in model parameters. This influence is discussed in terms of the effect of anomalous boundary conditions on large-scale midlatitude atmospheric flow and on its predictability.

%B Journal of the Atmospheric Sciences %V 42 %P 433–471 %G eng %N 5 %R 10.1175/1520-0469(1985)042<0433:PABAVI>2.0.CO;2 %0 Book %D 1985 %T Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics %E Ghil, Michael %E Benzi, R. %E Parisi, G. %I North-Holland Publ. Co., Amsterdam/New York %P 449 %G eng %0 Journal Article %J Siam Journal on Applied Mathematics %D 1983 %T Global Hopf Bifurcation in a Simple Climate Model %A Ghil, Michael %A Tavantzis, John %X The mathematical structure of a simple climate model is investigated. The model is governed by a system of two nonlinear, autonomous differential equations for the evolution in time of global temperature $T$ and meridional ice-sheet extent $L$. The system's solutions are studied by a combination of qualitative reasoning with explicit calculations, both analytical and numerical. For plausible values of the physical parameters, a branch of periodic solutions obtains, which is both orbitally and structurally stable. The amplitude of the stable periodic solutions in $T$ and $L$ correspond roughly to that obtained from proxy records of Quaternary glaciation cycles. The period of these solutions increases along the branch, until it becomes infinite, while the amplitude of the limiting solution is finite. The limiting solution is a homoclinic orbit formed by the reconnecting separatrix of a saddle. The exchange of stability between the branch of periodic solutions and the steady solution from which it arises is studied by a slight simplification of known methods [20], [21]. %B Siam Journal on Applied Mathematics %I Society for Industrial and Applied Mathematics %V 43 %P 1019–1041 %G eng %U http://links.jstor.org/sici?sici=0036-1399%28198310%2943%3A5%3C1019%3AGHBIAS%3E2.0.CO%3B2-P %N 5 %0 Book Section %B Dynamic meteorology: Data assimilation methods %D 1981 %T Applications of estimation theory to numerical weather prediction %A Ghil, Michael %A Cohn, S. %A Tavantzis, John %A K. Bube %A Isaacson, Eugene %B Dynamic meteorology: Data assimilation methods %I Springer %P 139–224 %G eng %R 10.1007/978-1-4612-5970-1_5 %0 Journal Article %J Journal of Geophysical Research %D 1981 %T A climate model with cryodynamics and geodynamics %A Ghil, Michael %A Le Treut, H. %B Journal of Geophysical Research %V 86 %P 5262–5270 %G eng %U http://adsabs.harvard.edu/abs/1981JGR....86.5262G %0 Book Section %B Applied Mathematical Sciences %D 1981 %T Dynamic Meteorology: Data Assimilation Methods %A Ghil, Michael %A S. Coho, J. Tavantzis %A K. Bube %A E. Isaacson %E L. Bengtsson %E Ghil, Michael %E E. Källén %B Applied Mathematical Sciences %7 Dynamic Meteorology - Data Assimilation Methods %I Springer-Verlag %V 36 %P 139–224 %G eng %& Applications of Estimation Theory to Numerical Weather Prediction