Michael Ghil

Kondrashov, Dmitri, Mickaël D. Chekroun, Xiaojun Yuan, and Michael Ghil. 2018. “Data-Adaptive Harmonic Decomposition and Stochastic Modeling of Arctic Sea Ice.” Advances in Nonlinear Geosciences, edited by Anastasios Tsonis. Springer. 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, Mickaël D. Chekroun, and Michael Ghil. 2018. “Data-adaptive harmonic decomposition and prediction of Arctic sea ice extent.” Dynamics and Statistics of the Climate System 3 (1): 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.
Sainte Fare Garnot, Vivien, Andreas Groth, and Michael Ghil. 2018. “Coupled Climate-Economic Modes in the Sahel's Interannual Variability.” Ecological Economics 153. Elsevier BV: 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.
Ghil, Michael, Andreas Groth, Dmitri Kondrashov, and Andrew W. Robertson. 2018. “Extratropical sub-seasonal–to–seasonal oscillations and multiple regimes: The dynamical systems view.” The Gap between Weather and Climate Forecasting: Sub-Seasonal to Seasonal Prediction, edited by Andrew W. Robertson and Frederic Vitart, 1st ed., 119-142. Elsevier. 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.

Groth, Andreas, and Michael Ghil. 2017. “Synchronization of world economic activity.” Chaos 27 (12): 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, and Michael Ghil. 2017. Synchronization of world economic activity. Paris: Chair Energy & Prosperity. 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.

Ghil, Michael. 2017. “The Mathematics of Climate Change and of its Impacts.” Workshop on "Mathematical Approaches to Climate Change Impacts - MAC2I" at the Istituto Nazionale di Alta Matematica "Francesco Severi" (INdAM), Italy. Workshop website Abstract

Ghil, Michael. 2017. “Circulation Regimes for the Hitchhiker Through the Galaxy.” Physics school on Diversity of Planetary Circulation Regimes, in our Solar System and beyond, Les Houches, France, March 2017. Conference website Abstract

Ghil, Michael. 2017. “The atmosphere and oceans as unsteady flows: Intrinsic variability and time-dependent forcing.” BIRS Workshop 17w5048 - Transport in Unsteady Flows: from Deterministic Structures to Stochastic Models and Back Again. Workshop website Abstract
PDF Video
Groth, Andreas, Yizhak Feliks, Dmitri Kondrashov, and Michael Ghil. 2017. “Interannual variability in the North Atlantic ocean’s temperature field and its association with the wind stress forcing.” Journal of Climate 30 (7): 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. 2017. “The wind-driven ocean circulation: Applying dynamical systems theory to a climate problem.” Discrete and Continuous Dynamical Systems - A 37 (1): 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. 2016. “DADA: data assimilation for the detection and attribution of weather and climate-related events.” Climatic Change 136 (2): 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. 2016. “Comment on ``Nonparametric forecasting of low-dimensional dynamical systems''.” Phys. Rev. E 93. American Physical Society: 036201. Publisher's Version
Merkin, V. G., Dmitri Kondrashov, Michael Ghil, and B. J. Anderson. 2016. “Data assimilation of low-altitude magnetic perturbations into a global magnetosphere model.” Space Weather 14 (2): 165–184. Publisher's Version
Greco, G, Dmitri Kondrashov, S Kobayashi, Michael Ghil, M Branchesi, C Guidorzi, G Stratta, M Ciszak, F Marino, and A Ortolan. 2016. “Singular Spectrum Analysis for astronomical time series: constructing a parsimonious hypothesis test.” The Universe of Digital Sky Surveys, 105–107. Springer. Publisher's Version
Ghil, Michael. 2016. “A Mathematical Theory of Climate Sensitivity: A Tale of Deterministic & Stochastic Dynamical Systems.” 11th AIMS Conf. on Dynamical Systems, Differential Equations & Applications, Honoring Peter Lax’s 90th Birthday, Orlando, FL, July 2016. Abstract

Sella, Lisa, Gianna Vivaldo, Andreas Groth, and Michael Ghil. 2016. “Economic Cycles and Their Synchronization: A Comparison of Cyclic Modes in Three European Countries.” Journal of Business Cycle Research 12 (1). Springer: 25-48. Publisher's Version Abstract

The 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.

Feliks, Yizhak, Andrew W. Robertson, and Michael Ghil. 2016. “Interannual Variability in North Atlantic Weather: Data Analysis and a Quasigeostrophic Model.” Journal of the Atmospheric Sciences 73 (8): 3227-3248. Abstract

This 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.

Walwer, Damian, Eric Calais, and Michael Ghil. 2016. “Data-Adaptive Detection of Transient Deformation in Geodetic Networks.” Journal of Geophysical Research: Solid Earth 121 (3). Wiley Online Library: 2129-2152 . Abstract

The 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.

Pierini, S., Michael Ghil, and Mickaël D. Chekroun. 2016. “Exploring the pullback attractors of a low-order quasigeostrophic ocean model: The deterministic case.” Journal of Climate 29 (11): 4185-4202. Abstract

A 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.