Atmosphere & climate

Legras B, Ghil M. Persistent anomalies, blocking and variations in atmospheric predictability. Journal of the Atmospheric Sciences. 1985;42 (5) :433–471.Abstract

We consider regimes of low-frequency variability in large-scale atmospheric dynamics. The model used for the study of these regimes is the fully-nonlinear, equivalent-barotropic vorticity equation on the sphere, with simplified forcing, dissipation and topography. Twenty-five modes are retained in a spherical harmonics expansion of the streamfunction. Solutions are studied as a function of the nondimensional intensity of the forcing and dissipation.Multiple stationary solutions are obtained as a result of nonlinear interaction between waves, mean flow and orography. The number of modes retained in the analysis permits these multiple equilibria to appear for realistic values of the forcing. The equilibria exhibit blocked and zonal flow patterns bearing a marked resemblance to synoptically defined zonal and blocked Northern Hemisphere midlatitude flows.Wave-wave interactions influence strongly the stability properties of the equilibria and the time evolution of nonequilibrium solutions. Time-dependent solutions show persistent sequences which occur in the phase-space vicinity of the zonal and blocked equilibria. Composite flow patterns of the persistent sequences are similar to the equilibria nearby, which permits the unambiguous definition of quasi-stationary flow regimes, zonal and blocked, respectively. The number of episodes of blocked or zonal flow decreases monotonically as their duration increases, in agreement with observations.The statistics of transitions between the two types of planetary flow regimes are computed from the model's deterministic dynamics. These transitional called breaks in statistical-synoptic long-range forecasting, are shown to be influenced by changes in model parameters. This influence is discussed in terms of the effect of anomalous boundary conditions on large-scale midlatitude atmospheric flow and on its predictability.

Ghil M, Vautard R. Interdecadal oscillations and the warming trend in global temperature time series. Nature. 1991;350 (6316) :324–327.Abstract

The ability to distinguish a warming trend from natural variability is critical for an understanding of the climatic response to increasing greenhouse-gas concentrations. Here we use singular spectrum analysis1 to analyse the time series of global surface air tem-peratures for the past 135 years2, allowing a secular warming trend and a small number of oscillatory modes to be separated from the noise. The trend is flat until 1910, with an increase of 0.4 °C since then. The oscillations exhibit interdecadal periods of 21 and 16 years, and interannual periods of 6 and 5 years. The interannual oscillations are probably related to global aspects of the El Niño-Southern Oscillation (ENSO) phenomenon3. The interdecadal oscillations could be associated with changes in the extratropical ocean circulation4. The oscillatory components have combined (peak-to-peak) amplitudes of >0.2 °C, and therefore limit our ability to predict whether the inferred secular warming trend of 0.005 °Cyr-1 will continue. This could postpone incontrovertible detection of the greenhouse warming signal for one or two decades.

Moron V, Vautard R, Ghil M. Trends, interdecadal and interannual oscillations in global sea-surface temperatures. Climate Dynamics. 1998;14 (7) :545–569.Abstract

This study aims at a global description of climatic phenomena that exhibit some regularity during the twentieth century. Multi-channel singular spectrum analysis is used to extract long-term trends and quasi-regular oscillations of global sea-surface temperature (SST) fields since 1901. Regional analyses are also performed on the Pacific, (Northern and Southern) Atlantic, and Indian Ocean basins. The strongest climatic signal is the irregular long-term trend, characterized by overall warming during 1910–1940 and since 1975, with cooling (especially of the Northern Hemisphere) between these two warming intervals. Substantial cooling prevailed in the North Pacific between 1950 and 1980, and continues in the North Atlantic today. Both cooling and warming are preceded by SST anomalies of the same sign in the subpolar North Atlantic. Near-decadal oscillations are present primarily over the North Atlantic, but also over the South Atlantic and the Indian Ocean. A 13–15-y oscillation exhibits a seesaw pattern between the Gulf-Stream region and the North-Atlantic Drift and affects also the tropical Atlantic. Another 7–8-y oscillation involves the entire double-gyre circulation of the North Atlantic, being mostly of one sign across the basin, with a minor maximum of opposite sign in the subpolar gyre and the major maximum in the northwestern part of the subtropical gyre. Three distinct interannual signals are found, with periods of about 60–65, 45 and 24–30 months. All three are strongest in the tropical Eastern Pacific. The first two extend throughout the whole Pacific and still exhibit some consistent, albeit weak, patterns in other ocean basins. The latter is weaker overall and has no consistent signature outside the Pacific. The 60-month oscillation obtains primarily before the 1960s and the 45-month oscillation afterwards.

Groth A, Ghil M. Monte Carlo Singular Spectrum Analysis (SSA) revisited: Detecting oscillator clusters in multivariate datasets. Journal of Climate. 2015;28 (19) :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.