Publications by Type: Journal Article

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.
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).
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, 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.
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.

Groth, Andreas, Yizhak Feliks, Dmitri Kondrashov, and Michael Ghil. “Interannual variability in the North Atlantic ocean’s temperature field and its association with the wind stress forcing.” Journal of Climate 30, no. 7 (2017): 2655-2678. Abstract

Spectral 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.

PDF North Atlantic SST 7.7-yr mode
Ghil, Michael. “The wind-driven ocean circulation: Applying dynamical systems theory to a climate problem.” Discrete and Continuous Dynamical Systems - A 37, no. 1 (2017): 189-228. Abstract

The 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.

Hannart, A., A. Carrassi, M. Bocquet, Michael Ghil, P. Naveau, M. Pulido, J. Ruiz, and P. Tandeo. “DADA: data assimilation for the detection and attribution of weather and climate-related events.” Climatic Change 136, no. 2 (2016): 155–174. Publisher's Version Abstract

We 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.

Kondrashov, Dmitri, Mickaël D. Chekroun, and Michael Ghil. “Comment on ``Nonparametric forecasting of low-dimensional dynamical systems''.” Phys. Rev. E 93 (2016): 036201. Publisher's Version
Merkin, V. G., Dmitri Kondrashov, Michael Ghil, and B. J. Anderson. “Data assimilation of low-altitude magnetic perturbations into a global magnetosphere model.” Space Weather 14, no. 2 (2016): 165–184. Publisher's Version