Atmosphere & climate

In Press
Ghil, Michael, and Valerio Lucarini. “The Physics of Climate Variability and Climate Change” (In Press). 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.
Ghil, Michael, and Eric Simonnet. “Geophysical Fluid Dynamics, Nonautonomous Dynamical Systems, and the Climate Sciences.” In Mathematical Approach to Climate Change and its Impacts: MAC2I, edited by Piermarco Cannarsa, Daniela Mansutti, and Antonello Provenzale, 3–81. Springer International Publishing, 2020. Abstract
This contribution introduces the dynamics of shallow and rotating flows that characterizes large-scale motions of the atmosphere and oceans. It then focuses on an important aspect of climate dynamics on interannual and interdecadal scales, namely the wind-driven ocean circulation. Studying the variability of this circulation and slow changes therein is treated as an application of the theory of nonautonomous dynamical systems. The contribution concludes by discussing the relevance of these mathematical concepts and methods for the highly topical issues of climate change and climate sensitivity.
Ghil, Michael. “Coupled Climate–Economics Modeling and Data Analysis: EnBCs and Fluctuation–Dissipation Theory.” CliMathParis 2019, Course IV: Coupled Climate–Ecology–Economy Modeling, Institut Henri Poincaré, Paris, France, 2019. CliMathParis 2019 Abstract

Groth, Andreas. “Impact of interannual climate variability on the agricultural sector in the Sahel region.” CliMathParis 2019, Workshop 3: Coupled climate-ecology-economy modeling and model hierarchies, Institut Henri Poincaré, Paris, France, 2019. Workshop website Abstract

Ghil, Michael. “Low-Frequency Climate Variability: Markov Chains and Nonlinear Oscillations.” CliMathParis 2019, Associated Workshop I: The 9th International Workshop on Climate Informatics, Ecole Normale Supérieure & Institut Henri Poincaré, Paris, France, 2019. Workshop website Abstract

Ghil, Michael. “Data Assimilation: Interesting Past, Bright Future.” CliMathParis 2019, Workshop 2: Big data, data assimilation, and uncertainty quantification, Institut Henri Poincaré, Paris, France, 2019. Workshop website Abstract

Ghil, Michael. “Nonautonomous and Random Dynamical Systems in the Climate Sciences.” CliMathParis 2019, Workshop 1: Nonlinear and stochastic methods in climate and geophysical fluid dynamics, Institut Henri Poincaré, Paris, France, 2019. Workshop website Abstract

Walwer, Damian, Michael Ghil, and Eric Calais. “Oscillatory nature of the Okmok volcano's deformation.” Earth and Planetary Science Letters 506 (2019): 76–86.
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.
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, 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.
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.

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.
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, 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). 

Ghil, Michael. “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, 2017. Workshop website Abstract

Ghil, Michael. “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, 2017. Conference website Abstract

Ghil, Michael. “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, 2017. Workshop website Abstract
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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