Moron, Vincent, Robert Vautard, and Michael Ghil. “Trends, interdecadal and interannual oscillations in global sea-surface temperatures.” Climate Dynamics 14, no. 7 (1998): 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.

Jiang, Shi, and Michael Ghil. “Tracking Nonlinear Solutions with Simulated Altimetric Data in a Shallow-Water Model.” Journal of Physical Oceanography 27, no. 1 (1997): 72–95. Abstract
Low-frequency variability of western boundary currents (WBCs) is pervasive in both observations and numerical models of the oceans. Because advection is of the essence in WBCs, nonlinearities are thought to be important in causing their variability. In numerical models, this variability can be distorted by our incomplete knowledge of the system’s dynamics, manifested in model errors. A reduced-gravity shallow-water model is used to study the interaction of model error with nonlinearity. Here our focus is on a purely periodic solution and a weakly aperiodic one. For the periodic case, the noise-corrupted system loses its periodicity due to nonlinear processes. For the aperiodic case, the intermittent occurrences of two relatively persistent states—a straight jet with high total energy and a meandering one with low total energy—in the perturbed model are almost out of phase with the unperturbed one. For both cases, the simulation errors are trapped in the WBC region, where the nonlinear dynamics is most vigorous. Satellite altimeters measure sea surface height globally in space and almost synoptically in time. They provide an opportunity to track WBC variability through its pronounced sea surface signature. By assimilating simulated Geosat data into the stochastically perturbed model with the improved optimal interpolation method, the authors can faithfully track the periodic behavior that had been lost and capture the correct occurrences of two relatively persistent patterns for the aperiodic case. The simulation errors accumulating in the WBC region are suppressed, thus improving the system’s predictability. The domain-averaged rms errors reach a statistical equilibrium below the observational error level. Comparison experiments using simulated Geosat and TOPEX/POSEIDON tracks show that spatially dense sampling yields lower rms errors than temporally frequent sampling for the present model. A criterion defining spatial oversampling—that is, diminishing returns—is also addressed.
Ghil, Michael. “Advances in Sequential Estimation for Atmospheric and Oceanic Flows.” Journal of the Meteorological Society of Japan 75, no. 1B (1997): 289–304.
Ide, Kay, Phillippe Courtier, Michael Ghil, and Andrew C. Lorenz. “Unified Notation for Data Assimilation: Operational, Sequential and Variational.” Journal of Meteorological Society of Japan 75, no. 1B (1997): 181–189.
Jin, F.-F., J. David Neelin, and Michael Ghil. “El Niño Southern Oscillation and the annual cycle: Subharmonic frequency-locking and aperiodicity.” Physica D 98 (1996): 442–465.
Ghil, Michael, and Pascal Yiou. “Spectral methods: What they can and cannot do for climatic time series.” In Decadal Climate Variability: Dynamics and Predictability, edited by D. Anderson and J. Willebrand, 446–482. Springer-Verlag, Berlin/Heidelberg, 1996.
Strong, Christopher, Fei-fei Jin, and Michael Ghil. “Intraseasonal Oscillations in a Barotropic Model with Annual Cycle, and Their Predictability.” Journal of the Atmospheric Sciences 52, no. 15 (1995): 2627–2642. Abstract
Observational and modeling studies have shown that intraseasonal, 40-day oscillations over the Northern Hemisphere extratropics are strongest around the winter season. To explore intraseasonal variability in the presence of the annual cycle, an eigenanalysis method based on Floquet theory is used. This approach helps us determine the stability of the large-scale, midlatitude atmospheric flow's periodic basic state. It gives information about the growth rate of the unstable, intraseasonal eigenmode and confirms the atmosphere's preference for intraseasonal activity during the winter months, as the annual cycle modulates the eigenvector field. This eigenmode solution, furthermore, provides a basis for making extended-range (40-day) streamfunction-anomaly forecasts on a set of intraseasonal oscillations whose amplitude and phase depend on the season. A simple autoregressive model is developed to shed light on the seasonal dependence of predictive skill for the intraseasonal signal.
Speich, S, H Dijkstra, and M Ghil. “Successive bifurcations in a shallow-water model applied to the wind-driven ocean circulation.” Nonlinear Processes in Geophysics 2 (1995): 241–268. Abstract
Climate - the "coarse-gridded" state of the coupled ocean - atmosphere system - varies on many time and space scales. The challenge is to relate such variation to specific mechanisms and to produce verifiable quantitative explanations. In this paper, we study the oceanic component of the climate system and, in particular, the different circulation regimes of the mid-latitude win driven ocean on the interannual time scale. These circulations are dominated by two counterrotating, basis scale gyres: subtropical and subpolar. Numerical techniques of bifurcation theory are used to stud the multiplicity and stability of the steady-state solution of a wind-driven, double-gyre, reduced-gravity, shallow water model. Branches of stationary solutions and their linear stability are calculated systematically as parameter are varied. This is one of the first geophysical studies i which such techniques are applied to a dynamical system with tens of thousands of degrees of freedom. Multiple stationary solutions obtain as a result of nonlinear interactions between the two main recirculating cell (cyclonic and anticyclonic) of the large- scale double-gyre flow. These equilibria appear for realistic values of the forcing and dissipation parameters. They undergo Hop bifurcation and transition to aperiodic solutions eventually occurs. The periodic and chaotic behaviour is probably related to an increased number of vorticity cells interaction with each other. A preliminary comparison with observations of the Gulf Stream and Kuroshio Extensions suggests that the intern variability of our simulated mid-latitude ocean is a important factor in the observed interannual variability o these two current systems.
Jiang, Shi, Fei-fei Jin, and Michael Ghil. “Multiple Equilibria, Periodic, and Aperiodic Solutions in a Wind-Driven, Double-Gyre, Shallow-Water Model.” Journal of Physical Oceanography 25, no. 5 (1995): 764–786. Abstract
A reduced-gravity shallow-water (SW) model is used to study the nonlinear behavior of western boundary currents (WBCs), with particular emphasis on multiple equilibria and low-frequency variations. When the meridionally symmetric wind stress is sufficiently strong, two steady solutions–nearly antisymmetric about the x axis–are achieved from different initial states. These results imply that 1) the inertial WBCs could overshoot either southward or northward along the western boundary, depending on their initial states; and thus, 2) the WBC separation and eastward jet could occur either north or south of the maximum wind stress line. The two equilibria arise via a perturbed pitchfork bifurcation, as the wind stress increases. A low-order, double-gyre, quasigeostrophic (QG) model is studied analytically to provide further insight into the physical nature of this bifurcation. In this model, the basic state is exactly antisymmetric when the wind stress is symmetric. The perturbations destroying the symmetry of the pitchfork bifurcation can arise, therefore. in the QG model only from the asymmetric components of the wind stress. In the SW model, the antisymmetry of the system's basic response to the symmetric forcing is destroyed already at arbitrarily low wind stress. The pitchfork bifurcation from this basic state to more complex states at high wind stress is accordingly perturbed in the absence of any forcing asymmetry. Periodic solutions arise by Hopf bifurcation from either steady-state branch of the SW model. A purely periodic solution is studied in detail. The subtropical and subpolar recirculations, separation, and eastward jet exhibit a perfectly periodic oscillation with a period of about 2.8 years. Outside the recirculation zones, the solutions are nearly steady. The alternating anomalies of the upper-layer thickness are periodically generated adjacent to the ridge of the first and strongest downstream meander and are then propagated and advected into the two WBC zones, by Rossby waves and the recirculating currents, respectively. These anomalies periodically change the pressure gradient field near the WBCs and maintain the periodic oscillation. Aperiodic solutions are also studied by either increasing wind forcing or decreasing the viscosity.
Dettinger, Michael D, Michael Ghil, and Christian L Keppenne. “Interannual and interdecadal variability in United States surface-air temperatures, 1910-87.” Climatic Change 31, no. 1 (1995): 35–66. Abstract
Monthly mean surface-air temperatures at 870 sites in the contiguous United States were analyzed for interannual and interdecadal variability over the time interval 1910-87. The temperatures were analyzed spatially by empirical-orthogonal-function analysis and temporally by singularspectrum analysis (SSA). The dominant modes of spatio-temporal variability are trends and nonperiodic variations with time scales longer than 15 years, decadal-scale oscillations with periods of roughly 7 and 10 years, and interannual oscillations of 2.2 and 3.3 years. Together, these modes contribute about 18% of the slower-than-annual United States temperature variance. Two leading components roughly capture the mean hemispheric temperature trend and represent a long-term warming, largest in the southwest, accompanied by cooling of the domain's southeastern quadrant. The extremes of the 2.2-year interannual oscillation characterize temperature differences between the Northeastern and Southwestern States, whereas the 3.3-year cycle is present mostly in the Western States. The 7- to 10-year oscillations are much less regular and persistent than the interannual oscillations and characterize temperature differences between the western and interior sectors of the United States. These continental- or regional-scale temperature variations may be related to climatic variations with similar periodicities, either global or centered in other regions; such variations include quasi-biennial oscillations over the tropical Pacific or North Atlantic and quasi-triennial oscillations of North Pacific sea-surface temperatures.
Unal, Yurdanur Sezginer, and Michael Ghil. “Interannual and interdecadal oscillation patterns in sea level.” Climate Dynamics 11, no. 5 (1995): 255–278. Abstract

Relative sea-level height (RSLH) data at 213 tide-gauge stations have been analyzed on a monthly and an annual basis to study interannual and interdecadal oscillations, respectively. The main tools of the study are singular spectrum analysis (SSA) and multi-channel SSA (M-SSA). Very-low-frequency variability of RSLH was filtered by SSA to estimate the linear trend at each station. Global sea-level rise, after postglacial rebound corrections, has been found to equal 1.62±0.38 mm/y, by averaging over 175 stations which have a trend consistent with the neighboring ones. We have identified two dominant time scales of El Niño-Southern Oscillation (ENSO) variability, quasi-biennial and low-frequency, in the RSLH data at almost all stations. However, the amplitudes of both ENSO signals are higher in the equatorial Pacific and along the west coast of North America. RSLH data were interpolated along ocean coasts by latitudinal intervals of 5 or 10 degrees, depending on station density. Interannual variability was then examined by M-SSA in five regions: eastern Pacific (25°S–55°N at 10° resolution), western Pacific (35°S–45°N at 10°), equatorial Pacific (123°E–169°W, 6 stations), eastern Atlantic (30°S, 0°, and 30°N–70°N at 5°) and western Atlantic (50°S–50°N at 10°). Throughout the Pacific, we have found three dominant spatio-temporal oscillatory patterns, associated with time scales of ENSO variability; their periods are 2, 2.5–3 and 4–6 y. In the eastern Pacific, the biennial mode and the 6-y low-frequency mode propagate poleward. There is a southward propagation of low-frequency modes in the western Pacific RSLH, between 35°N and 5°S, but no clear propagation in the latitudes further south. However, equatorward propagation of the biennial signal is very clear in the Southern Hemisphere. In the equatorial Pacific, both the quasi-quadrennial and quasi-biennial modes at 10°N propagate westward. Strong and weak El Niño years are evident in the sea-level time series reconstructed from the quasi-biennial and low-frequency modes. Interannual variability with periods of 3 and 4–8 y is detected in the Atlantic RSLH data. In the eastern Atlantic region, we have found slow propagation of both modes northward and southward, away from 40–45°N. Interdecadal oscillations were studied using 81 stations with sufficiently long and continuous records. Most of these have variability at 9–13 and some at 18 y. Two significant eigenmode pairs, corresponding to periods of 11.6 and 12.8 y, are found in the eastern and western Atlantic ocean at latitudes 40°N–70°N and 10°N–50°N, respectively.

Plaut, Guy, Michael Ghil, and Robert Vautard. “Interannual and Interdecadal Variability in 335 Years of Central England Temperatures.” Science 268, no. 5211 (1995): 710–713. Abstract

Understanding the natural variability of climate is important for predicting its near-term evolution. Models of the oceans' thermohaline and wind-driven circulation show low-frequency oscillations. Long instrumental records can help validate the oscillatory behavior of these models. Singular spectrum analysis applied to the 335-year-long central England temperature (CET) record has identified climate oscillations with interannual (7- to 8-year) and interdecadal (15- and 25-year) periods, probably related to the North Atlantic's wind-driven and thermohaline circulation, respectively. Statistical prediction of oscillatory variability shows CETs decreasing toward the end of this decade and rising again into the middle of the next.

Jiang, N., J. David Neelin, and Michael Ghil. “Quasi-quadrennial and quasi-biennial variability in the equatorial Pacific.” Climate Dynamics 12 (1995): 101–112. Abstract

Evaluation of competing El Niño/Southern Oscillation (ENSO) theories requires one to identify separate spectral peaks in equatorial wind and sea-surface temperature (SST) time series. To sharpen this identification, we examine the seasonal-to-interannual variability of these fields by the data-adaptive method of multi-channel singular spectrum analysis (M-SSA). M-SSA is applied to the equatorial band (4°N-4°S), using 1950 1990 data from the Comprehensive Ocean and Atmosphere Data Set. Two major interannual oscillations are found in the equatorial SST and surface zonal wind fields, U. The main peak is centered at about 52-months; we refer to it as the quasi-quadrennial (QQ) mode. Quasi-biennial (QB) variability is split between two modes, with periods near 28 months and 24 months. A faster, 15-month oscillation has smaller amplitude. The QQ mode dominates the variance and has the most distinct spectral peak. In time-longitude reconstructions of this mode, the SST has the form of a standing oscillation in the eastern equatorial Pacific, while the U-field is dominated by a standing oscillation pattern in the western Pacific and exhibits also slight eastward propagation in the central and western Pacific. The locations of maximum anomalies in both QB modes are similar to those of the QQ mode. Slight westward migration in SST, across the eastern and central, and eastward propagation of U, across the western and central Pacific, are found. The significant wind anomaly covers a smaller region than for the QQ. The QQ and QB modes together represent the ENSO variability well and interfere constructively during major events. The sharper definition of the QQ spectral peak and its dominance are consistent with the “devil's staircase” interaction mechanism between the annual cycle and ENSO.

Plaut, Guy, and Robert Vautard. “Spells of Low-Frequency Oscillations and Weather Regimes in the Northern Hemisphere.” Journal of the Atmospheric Sciences 51, no. 2 (1994): 210–236. Abstract
The low-frequency variability in the midlatitudes is described through an analysis of the oscillatory phenomena. In order to isolate nearly periodic components of the atmospheric flow, the multichannel version of the singular spectrum analysis (M-SSA) is developed and applied to an NMC 32-year long set of 700-hPa geopotential heights. In the same way that principal component analysis identifies the spatial patterns dominating the variability, M-SSA identifies dynamically relevant space?time patterns and provides an adaptive filtering technique. Three major low-frequency oscillations (LFOs) are found, with periods of 70 days, 40?45 days, and 30?35 days. The 70-day oscillation consists of fluctuations in both position and amplitude of the Atlantic jet, with a poleward-propagating anomaly pattern. The 40?45-day oscillation is specific to the Pacific sector and has a pronounced Pacific/North American (PNA) structure in its high-amplitude phase. The 30?35-day mode is confined over the Atlantic region, and consists of the retrogression of a dipole pattern. All these oscillations are shown to be intermittently excited, and M-SSA allows the localization of their spells. The two Atlantic oscillations turn out to be frequently phase locked, so that the 30?35-day mode is likely to be a harmonic of the 70-day mode. The phase locking of the Pacific 40?45-day with the Atlantic 30?35-day oscillations is also studied. Next, the relationships between LFOs and weather regimes are studied. It is shown in particular that the occurrence of the Euro-Atlantic blocking regime is strongly favored, although not systematically caused, by particular phases of the 30?35-day mode. The LFOs themselves are able to produce high-amplitude persistent anomalies by interfering with each other. The transition from a zonal regime to a blocking regime is also shown to be highly connected to the life cycle of the 30?35-day mode, indicating that regime transitions do not result only from the random occurrence of particular transient eddy forcing. There are preferred paths between weather regimes. This result leaves us with the hope that at least the large-scale environment-favoring weather regimes may be forecast in the long range. Conditional probability of occurrence of blocking, 30 days ahead, is enhanced, relative to climatological probability, by a factor of 2 if the phase of the 30?35-day oscillation is known. This also emphasizes the necessity of operational models to represent correctly the extratropical LFOs in order to produce skillful long-range and even medium-range forecasts of weather regimes.
Miller, Robert N., Michael Ghil, and François Gauthiez. “Advanced Data Assimilation in Strongly Nonlinear Dynamical Systems.” Journal of Atmospheric Sciences 51 (1994): 1037–1056.
Ghil, Michael. “Cryothermodynamics: the chaotic dynamics of paleoclimate.” Physica D 77, no. 1-3 (1994): 130–159.
Jin, F.-F., J. David Neelin, and Michael Ghil. “El Niño on the Devil's Staircase: Annual subharmonic steps to chaos.” Science 264 (1994): 70–72.
Penland, Cécile, and Michael Ghil. “Forecasting Northern Hemisphere 700\mbox-mb geopotential height anomalies using empirical normal modes.” Monthly Weather Review 121, no. 8 (1993): 2355–2372. Abstract
Multivariate linear prediction based on single-lag inverse modeling is developed further and critically examined. The method is applied to the National Meteorological Center analyses of Northern Hemisphere 700-mb geopotential height anomalies, which have been filtered to eliminate periods shorter than 10 days. Empirically derived normal modes of the randomly forced linear system are usually correlated, even at zero lag, suggesting that combinations of modes should be used in predictions. Due to nonlinearities in the dynamics and the neglect of interactions with other pressure levels, the lag at which the analysis is performed is crucial; best predictions obtain when the autocovariances involved in the analysis are calculated at a lag comparable to the exponential decay times of the modes. Errors in prediction have a significant seasonal dependence, indicating that the annual cycle affects the higher-order statistics of the field. Optimized linear predictions using this method are useful for about half a day longer than predictions made by persistence. Conditional probabilities are much more efficiently calculated using normal-mode parameters than from histograms, and yield similar results. Maps of the model's Fourier spectra—integrated over specified frequency intervals and consistent with the assumptions made in a linear analysis—agree with maps obtained from fast Fourier transforms of the data.
Kimoto, Masahide, and Michael Ghil. “Multiple flow regimes in the Northern Hemisphere winter. Part I: Methodology and hemispheric regimes.” Journal of the Atmospheric Sciences 50, no. 16 (1993): 2625–2644. Abstract
Recurrent and persistent flow patterns are identified by examining multivariate probability density functions (PDFs) in the phase space of large-scale atmospheric motions. This idea is pursued systematically here in the hope of clarifying the extent to which intraseasonal variability can be described and understood in terms of multiple flow regimes. Bivariate PDFs of the Northern Hemisphere (NH) wintertime anomaly heights at 700 mb are examined in the present paper, using a 37-year dataset. The two-dimensional phase plane is defined by the two leading empirical orthogonal functions (EOFs) of the anomaly fields. PDFs on this plane exhibit synoptically intriguing and statistically significant inhomogeneities on the periphery of the distribution. It is shown that these inhomogeneities are due to the existence of persistent and recurrent anomaly patterns, well-known as dominant teleconnection patterns; that is, the Pacific/North American (PNA) pattern, its reverse, and zonal and blocked phases of the North Atlantic Oscillation (NAO). It is argued that the inhomogeneities are obscured when PDFs are examined in a smaller-dimensional subspace than dynamically desired.
Feliks, Yizhak, and Michael Ghil. “Downwelling-front instability and eddy formation in the Eastern Mediterranean.” Journal of physical oceanography 23, no. 1 (1993): 61–78. Abstract
The instability of the downwelling front along the southern coast of Asia Minor is studied with a multimode quasigeostrophic model. Linear analysis shows that the most unstable wave has a length of about 100 km, The wavelength depends only very weakly on the transversal scale of the front. The wave period is larger by an order of magnitude than the e-folding time; that is, rapid local growth occurs with little propagation. The growth rate is proportional to the maximum of the speed of the downwelling westward jet. The evolution of the frontal waves can be divided into three stages. At first, the evolution is mainly due to linear instability; the second stage is characterized by closed eddy formation; and finally, isolated eddies separate from the front and penetrate into the open sea. The largest amount of available potential energy is transferred to kinetic energy and into the barotropic mode during the second, eddy-forming stage, when several dipoles develop in this mode. The formation of anticyclonic eddies is due to advection of the ridges of the unstable wave's first baroclinic mode by the barotropic dipole. The baroclinic eddies ride on the barotropic dipoles. The propagation of such dipole-rider systems is determined mainly by the evolution of the corresponding barotropic dipole. These results suggest that the warm- and salty-core eddies observed in the Eastern Mediterranean are due, at least in part, to the instability of the downwelling front along the basin's northeastern coastline. There is both qualitative and quantitative similarity between the observed and calculated eddies in their radius (35–50 km), thermal structure, and distribution along the coast.