Atmosphere & climate

Groth, Andreas, and Michael Ghil. “Monte Carlo Singular Spectrum Analysis (SSA) revisited: Detecting oscillator clusters in multivariate datasets.” Journal of Climate 28, no. 19 (2015): 7873–7893. Abstract

Singular spectrum analysis (SSA) along with its multivariate extension (M-SSA) provides an efficient way to identify weak oscillatory behavior in high-dimensional data. To prevent the misinterpretation of stochastic fluctuations in short time series as oscillations, Monte Carlo (MC)–type hypothesis tests provide objective criteria for the statistical significance of the oscillatory behavior. Procrustes target rotation is introduced here as a key method for refining previously available MC tests. The proposed modification helps reduce the risk of type-I errors, and it is shown to improve the test’s discriminating power. The reliability of the proposed methodology is examined in an idealized setting for a cluster of harmonic oscillators immersed in red noise. Furthermore, the common method of data compression into a few leading principal components, prior to M-SSA, is reexamined, and its possibly negative effects are discussed. Finally, the generalized Procrustes test is applied to the analysis of interannual variability in the North Atlantic’s sea surface temperature and sea level pressure fields. The results of this analysis provide further evidence for shared mechanisms of variability between the Gulf Stream and the North Atlantic Oscillation in the interannual frequency band.

Groth, Andreas. “Interannual variability in the North Atlantic SST and wind forcing.” Seminar at International Research Institute for Climate and Society, Columbia, 2014. Abstract

Groth, Andreas. “Oscillatory behavior and oscillatory modes.” SSA workshop Bournemouth, September 2014, 2014. Abstract

Ghil, Michael. “Lecture 2: Toward a Mathematical Theory of Climate Sensitivity.” Workshop on Mathematics of Climate Change, Related Hazards and Risks, CIMAT, Guanajuato, Mexico, 2013. Abstract

Lecture 2: Toward a Mathematical Theory of Climate Sensitivity
Ghil, Michael. “Lecture 3 : The Coupled Dynamics of Climate and Economics.” Workshop on Mathematics of Climate Change, Related Hazards and Risks, CIMAT, Guanajuato, Mexico, 2013. Abstract

Lecture 3 : The Coupled Dynamics of Climate and Economics
de Viron, O., J. O. Dickey, and Michael Ghil. “Global modes of climate variability.” Geophysical Research Letters 40, no. 9 (2013): 1832-1837. Abstract

The atmosphere, hydrosphere and cryosphere form a fully coupled climate system. This system exhibits a number of large-scale phenomena, such as the El Nino Southern Oscillation (ENSO), the Asian Monsoon, the North Atlantic Oscillation (NAO), and the Madden-Julian Oscillation (MJO). While these modes of variability are not exactly periodic, they are oscillatory in character, and their state is monitored using so-called climate indices. Each of these scalar indices is a combination of several climate variables. Here, we use a comprehensive set of 25 climate indices for time intervals that range between 1948 and 2011, and estimate an optimal set of lags between these indices to maximize their correlation. We show that most of the index pairs drawn from this set present a significant correlation on interannual time scales. It is also shown that, on average, about two-thirds of the total variability in each index can be described by using only the four leading principal components of the entire set of lagged indices. Our index set's leading orthogonal modes exhibit several interannual frequencies and capture separately variability associated with the North Atlantic and the North Pacific. These modes are associated, in turn, with large-scale variations of sea surface temperatures.

Kondrashov, Dmitri, Mickaël D. Chekroun, Andrew W. Robertson, and Michael Ghil. “Low-order stochastic model and ``past-noise forecasting" of the Madden-Julian oscillation.” Geophysical Research Letters 40 (2013): 5305–5310.
Feliks, Yizhak, Andreas Groth, Andrew W. Robertson, and Michael Ghil. “Oscillatory Climate Modes in the Indian Monsoon, North Atlantic and Tropical Pacific.” Journal of Climate 26 (2013): 9528-–9544. Abstract

This paper explores the three-way interactions between the Indian monsoon, the North Atlantic and the Tropical Pacific. Four climate records were analyzed: the monsoon rainfall in two Indian regions, the Southern Oscillation Index for the Tropical Pacific, and the NAO index for the North Atlantic. The individual records exhibit highly significant oscillatory modes with spectral peaks at 7–8 yr and in the quasi-biennial and quasi-quadrennial bands. The interactions between the three regions were investigated in the light of the synchronization theory of chaotic oscillators. The theory was applied here by combining multichannel singular-spectrum analysis (M-SSA) with a recently introduced varimax rotation of the M-SSA eigenvectors. A key result is that the 7–8-yr and 2.7-yr oscillatory modes in all three regions are synchronized, at least in part. The energy-ratio analysis, as well as time-lag results, suggest that the NAO plays a leading role in the 7–8-yr mode. It was found therewith that the South Asian monsoon is not slaved to forcing from the equatorial Pacific, although it does interact strongly with it. The time-lag analysis pinpointed this to be the case in particular for the quasi-biennial oscillatory modes. Overall, these results confirm that the approach of synchronized oscillators, combined with varimax-rotated M-SSA, is a powerful tool in studying teleconnections between regional climate modes and that it helps identify the mechanisms that operate in various frequency bands. This approach should be readily applicable to ocean modes of variability and to the problems of air-sea interaction as well.


Ghil, Michael. “The Complex Physics of Climate Change: Nonlinearity and Stochasticity.” Workshop on Critical Transitions in Complex Systems, Imperial College London, United Kingdom, 2012. Conference website Abstract

Deremble, Bruno, Guillaume Lapeyre, and Michael Ghil. “Atmospheric dynamics triggered by an oceanic SST front in a moist quasigeostrophic model.” Journal of the Atmospheric Sciences 69, no. 5 (2012): 1617–1632.
Ghil, Michael. “Toward a Mathematical Theory of Climate Sensitivity.” International Congress on Industrial and Applied Mathematics (ICIAM), Vancouver, 2011. Abstract

SIAM News article

Variability of the Indian summer monsoon is decomposed into an interannually modulated annual cycle (MAC) and a northward-propagating, intraseasonal (30-60-day) oscillation (ISO). To achieve this decomposition, we apply multi-channel singular spectrum analysis (M-SSA) simultaneously to unfiltered daily fields of observed outgoing long-wave radiation (OLR) and to reanalyzed 925-hPa winds over the Indian region, from 1975 to 2008. The MAC is essentially given by the year-to-year changes in the annual and semi-annual components; it displays a slow northward migration of OLR anomalies coupled with an alternation between the northeast winter and southwest summer monsoons. The impact of these oscillatory modes on rainfall is then analyzed using a 1-degree gridded daily data set, focusing on Monsoonal India (north of 17°N and west of 90°E) during the months of June to September. Daily rainfall variability is partitioned into three states using a Hidden Markov Model. Two of these states are shown to agree well with previous classifications of "active" and "break" phases of the monsoon, while the third state exhibits a dipolar east-west pattern with abundant rainfall east of about 77°E and low rainfall to the west. Occurrence of the three rainfall states is found to be an asymmetric function of both the MAC and ISO components. On average, monsoon active phases are favored by large positive anomalies of MAC, and breaks by negative ones. ISO impact is decisive when the MAC is near neutral values during the onset and withdrawal phases of the monsoon. Active monsoon spells are found to require a synergy between the MAC and ISO, while the east-west rainfall dipole is less sensitive to interactions between the two. The driest years, defined from spatially averaged June-September rainfall anomalies, are found to be mostly a result of breaks occurring during the onset and withdrawal stages of the monsoon, e.g., mid-June to mid-July, and during September. These breaks are in turn associated with anomalously late MAC onset or early MAC withdrawal, often together with a large-amplitude, negative ISO event. The occurrence of breaks during the core of the monsoon—from late July to late August—is restricted to a few years when MAC was exceptionally weak, such as 1987 or 2002. Wet years are shown to be mostly associated with more frequent active spells and a stronger MAC than usual, especially at the end of the monsoon season. Taken together, our results suggest that monthly and seasonal precipitation predictability is higher in the early and late stages of the summer monsoon season.

Feliks, Yizhak, Michael Ghil, and Andrew W. Robertson. “Oscillatory Climate Modes in the Eastern Mediterranean and Their Synchronization with the North Atlantic Oscillation.” Journal of Climate 23, no. 15 (2010): 4060–4079. Abstract

Oscillatory climatic modes over the North Atlantic, Ethiopian Plateau, and eastern Mediterranean were examined in instrumental and proxy records from these regions. Aside from the well-known North Atlantic Oscillation (NAO) index and the Nile River water-level records, the authors study for the first time an instrumental rainfall record from Jerusalem and a tree-ring record from the Golan Heights. The teleconnections between the regions were studied in terms of synchronization of chaotic oscillators. Standard methods for studying synchronization among such oscillators are modified by combining them with advanced spectral methods, including singular spectrum analysis. The resulting cross-spectral analysis quantifies the strength of the coupling together with the degree of synchronization. A prominent oscillatory mode with a 7–8-yr period is present in all the climatic indices studied here and is completely synchronized with the North Atlantic Oscillation. An energy analysis of the synchronization raises the possibility that this mode originates in the North Atlantic. Evidence is discussed for this mode being induced by the 7–8-yr oscillation in the position of the Gulf Stream front. A mechanism for the teleconnections between the North Atlantic, Ethiopian Plateau, and eastern Mediterranean is proposed, and implications for interannual-to-decadal climate prediction are discussed.

Kondrashov, Dmitri, Sergey Kravtsov, and Michael Ghil. “Signatures of nonlinear dynamics in an idealized atmospheric model.” Journal of the Atmospheric Sciences 68, no. 1 (2010): 3–12.
Deremble, Bruno, Fabio D'Andrea, and Michael Ghil. “Fixed points, stable manifolds, weather regimes, and their predictability.” Chaos: An Interdisciplinary Journal of Nonlinear Science 19, no. 4 (2009): 043109. Publisher's Version
Zhang, Yunyan, Bjorn Stevens, Brian Medeiros, and Michael Ghil. “Low-cloud fraction, lower-tropospheric stability, and large-scale divergence.” Journal of Climate 22, no. 18 (2009): 4827–4844.
Bordi, Isabella, Klaus Fraedrich, Michael Ghil, and Alfonso Sutera. “Zonal flow regime changes in a GCM and in a simple quasigeostrophic model: The role of stratospheric dynamics.” Journal of the Atmospheric Sciences 66, no. 5 (2009): 1366–1383.
Camargo, Suzana J., Andrew W. Robertson, Anthony G. Barnston, and Michael Ghil. “Clustering of eastern North Pacific tropical cyclone tracks: ENSO and MJO effects.” Geochemistry, Geophysics, Geosystems 9, no. 6 (2008).