Publications

Submitted
Ghil, Michael, and Valerio Lucarini. “The Physics of Climate Variability and Climate Change” (Submitted). arxiv Abstract
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject to various external forcings, natural as well as anthropogenic. This paper reviews the observational evidence on climate phenomena and the governing equations of planetary-scale flow, as well as presenting the key concept of a hierarchy of models as used in the climate sciences. Recent advances in the application of dynamical systems theory, on the one hand, and of nonequilibrium statistical physics, on the other, are brought together for the first time and shown to complement each other in helping understand and predict the system's behavior. These complementary points of view permit a self-consistent handling of subgrid-scale phenomena as stochastic processes, as well as a unified handling of natural climate variability and forced climate change, along with a treatment of the crucial issues of climate sensitivity, response, and predictability.
2019
Marangio, L., J. Sedro, S. Galatolo, A. Di Garbo, and Michael Ghil. “Arnold Maps with Noise: Differentiability and Non-monotonicity of the Rotation Number.” Journal of Statistical Physics (2019).
Metref, Sammy, Alexis Hannart, Juan Ruiz, M. Bocquet, Alberto Carrassi, and Michael Ghil. “Estimating model evidence using ensemble-based data assimilation with localization - The model selection problem.” Quarterly Journal of the Royal Meteorological Society (2019).
Walwer, Damian, Michael Ghil, and Eric Calais. “Oscillatory nature of the Okmok volcano's deformation.” Earth and Planetary Science Letters 506 (2019): 76–86.
Ghil, Michael. “A Century of Nonlinearity in the Geosciences.” Earth and Space Science 6, no. 7 (2019): 1007–1042. Publisher's Version
Prevost, Paoline, Kristel Chanard, Luce Fleitout, Eric Calais, Damian Walwer, Tonie van Dam, and Michael Ghil. “Data-adaptive spatio-temporal filtering of GRACE data.” Geophysical Journal International 219, no. 3 (2019): 2034–2055.
Rousseau, Denis-Didier, Pierre Antoine, Niklas Boers, France Lagroix, Michael Ghil, Johanna Lomax, Markus Fuchs, et al.DO-like events of the penultimate climate cycle: the loess point of view.” Clim. Past Discuss. (2019).
2018
Pierini, Stefano, Mickaël D. Chekroun, and Michael Ghil. “The onset of chaos in nonautonomous dissipative dynamical systems: a low-order ocean-model case study.” Nonlinear Processes in Geophysics 25, no. 3 (2018): 671–692.
Boers, Niklas, Michael Ghil, and Denis-Didier Rousseau. “Ocean circulation, ice shelf, and sea ice interactions explain Dansgaard-Oeschger cycles.” Proceedings of the National Academy of Sciences 115, no. 47 (2018): E11005–E11014.
Kondrashov, Dmitri, Mickaël D. Chekroun, Xiaojun Yuan, and Michael Ghil. “Data-Adaptive Harmonic Decomposition and Stochastic Modeling of Arctic Sea Ice.” In Advances in Nonlinear Geosciences, edited by Anastasios Tsonis. Springer, 2018. Publisher's Version Abstract

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. 

Kondrashov, Dmitri, and Mickaël D Chekroun. “Data-adaptive harmonic analysis and modeling of solar wind-magnetosphere coupling.” Journal of Atmospheric and Solar-Terrestrial Physics, 177 (2018): 179-189. Publisher's Version Abstract
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.
Kondrashov, Dmitri, Mickaël D. Chekroun, and Michael Ghil. “Data-adaptive harmonic decomposition and prediction of Arctic sea ice extent.” Dynamics and Statistics of the Climate System 3, no. 1 (2018): dzy001. Publisher's Version Abstract
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, 27 for the description, modeling and prediction of the Multisensor Analyzed Sea Ice Extent (MASIE, 2006–2016) data set. The DAH decomposition of MASIE identifies narrowband, spatio-temporal data-adaptive modes over four key Arctic regions. The time evolution of the DAH coefficients of these modes can be modelled and predicted by using a set of coupled Stuart–Landau stochastic differential equations that capture the modes’ frequencies and amplitude modulation in time. Retrospective forecasts show that our resulting multilayer Stuart–Landau model (MSLM) is quite skilful in predicting September SIE compared to year-to-year persistence; moreover, the DAH–MSLM approach provided accurate real-time prediction that was highly competitive for the 2016–2017 Sea Ice Outlook.
Kondrashov, Dmitri, Mickaël D. Chekroun, and Pavel Berloff. “Multiscale Stuart-Landau Emulators: Application to Wind-Driven Ocean Gyres.” Fluids 3, no. 1 (2018): 21. Publisher's Version Abstract

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. 

Sainte Fare Garnot, Vivien, Andreas Groth, and Michael Ghil. “Coupled Climate-Economic Modes in the Sahel's Interannual Variability.” Ecological Economics 153 (2018): 111–123. Abstract
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.
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Ghil, Michael, Andreas Groth, Dmitri Kondrashov, and Andrew W. Robertson. “Extratropical sub-seasonal–to–seasonal oscillations and multiple regimes: The dynamical systems view.” In The Gap between Weather and Climate Forecasting: Sub-Seasonal to Seasonal Prediction, edited by Andrew W. Robertson and Frederic Vitart, 119-142. 1st ed. Elsevier, 2018. Publisher's Version Abstract

This 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.

2017
Duane, G. S., C. Grabow, F. Selten, and Michael Ghil, ed. Synchronization in Large Networks and Continuous Media – Data, Models, and Supermodels. Focus Issue in Chaos. 27th ed. American Institute of Physics, Melville, NY, 2017.
Chekroun, Mickaël D., and Dmitri Kondrashov. “Data-adaptive harmonic spectra and multilayer Stuart-Landau models.” Chaos 27 (2017): 093110. Publisher's Version Abstract

Harmonic 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. 

Groth, Andreas, and Michael Ghil. “Synchronization of world economic activity.” Chaos 27, no. 12 (2017): 127002. Abstract

Common 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.

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Groth, Andreas, and Michael Ghil. Synchronization of world economic activity. Paris: Chair Energy & Prosperity, 2017. Publisher's version Abstract

Common 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.

Kondrashov, Dmitri. “Data-adaptive Harmonic Decomposition and Real-time Prediction of 2016 September Arctic Sea Ice Extent.” 4th Polar Prediction Workshop, 27-30 March 2017, Bremerhaven, Germany, 2017. Workshop Website Abstract

Decline in the Arctic sea ice extent (SIE) has profound socio-economic implications and is a focus of active scientific research. Of particular interest is prediction of SIE on subseasonal time scales, i.e.~from early summer into fall, when sea ice coverage in Arctic reaches its minimum. However, subseasonal forecasting of SIE is very challenging due to the high variability of ocean and atmosphere over Arctic in summer, as well as shortness of observational data and inadequacies of the physics-based models to simulate sea-ice dynamics. The Sea Ice Outlook (SIO) by Sea Ice Prediction Network (SIPN, http://www.arcus.org/sipn) is a collaborative effort to facilitate and improve subseasonal prediction of September SIE by physics-based and data-driven statistical models.

Data-adaptive Harmonic Decomposition (DAH) and Multilayer Stuart-Landau Models (MSLM) techniques [Chekroun and Kondrashov, 2017], have been successfully applied to the nonlinear stochastic modeling, as well as retrospective and real-time forecasting of Multisensor Analyzed Sea Ice Extent (MASIE) dataset in key four Arctic regions. In particular, the real-time DAH-MSLM predictions outperformed most statistical models and physics-based models in 2016 SIO submissions. The key success factors are associated with DAH ability to disentangle complex regional dynamics of MASIE by data-adaptive harmonic spatio-temporal patterns that reduce the data-driven modeling effort to elemental MSLMs stacked per frequency with fixed and small number of model coefficients to estimate.

This is a joint work with Mickael Chekroun (UCLA) and Michael Ghil (UCLA,ENS). 

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