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 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 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 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 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 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 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 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 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 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 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 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 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 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