Michael Ghil

Lott, François, Andrew W. Robertson, and Michael Ghil. “Mountain torques and atmospheric oscillations.” Geophys. Res. Lett 28 (2001): 1207–1210.
Ghil, Michael, Tian Ma, and Shouhong Wang. “Structural bifurcation of 2-D incompressible flows.” Indiana University Mathematics Journal 50 (2001): 159–180.
Chang, Kyung-Il, Michael Ghil, Kayo Ide, and Chung-Chieng Aaron Lai. “Transition to aperiodic variability in a wind-driven double-gyre circulation model.” Journal of Physical Oceanography 31, no. 5 (2001): 1260–1286. Abstract

Multiple equilibria as well as periodic and aperiodic solution regimes are obtained in a barotropic model of the midlatitude ocean’s double-gyre circulation. The model circulation is driven by a steady zonal wind profile that is symmetric with respect to the square basin’s zonal axis of north–south symmetry, and dissipated by lateral friction. As the intensity of the wind forcing increases, an antisymmetric double-gyre flow evolves through a pitchfork bifurcation into a pair of steady mirror-symmetric solutions in which either the subtropical or the subpolar gyre dominates. In either one of the two asymmetric solutions, a pair of intense recirculation vortices forms close to and on either side of the point where the two western boundary currents merge to form the eastward jet. To the east of this dipole, a spatially damped stationary wave arises, and an increase in the steady forcing amplifies the meander immediately to the east of the recirculating vortices. During this process, the transport of the weaker gyre remains nearly constant while the transport of the stronger gyre increases. For even stronger forcing, the two steady solution branches undergo Hopf bifurcation, and each asymmetric solution gives rise to an oscillatory mode, whose subannual period is of 3.5–6 months. These two modes are also mirror-symmetric in space. The time-average difference in transport between the stronger and the weaker gyre is reduced as the forcing increases further, while the weaker gyre tends to oscillate with larger amplitude than the stronger gyre. Once the average strength of the weaker gyre on each branch equals the stronger gyre’s, the solution becomes aperiodic. The transition of aperiodic flow occurs through a global bifurcation that involves a homoclinic orbit. The subannual oscillations persist and stay fairly regular in the aperiodic solution regime, but they alternate now with a new and highly energetic, interannual oscillation. The physical causes of these two oscillations—as well as of a third, 19-day oscillation—are discussed. During episodes of the high-amplitude, interannual oscillation, the solution exhibits phases of either the subtropical or subpolar gyre being dominant. Even lower-frequency, interdecadal variability arises due to an irregular alternation between subannual and interannual modes of oscillation.

Chao, Yi, Michael Ghil, and James C. McWilliams. “Pacific interdecadal variability in this century's sea surface temperatures.” Geophysical Research Letters 27, no. 15 (2000): 2261–2264.
Yiou, Pascal, Didier Sornette, and Michael Ghil. “Data-adaptive wavelets and multi-scale singular-spectrum analysis.” Physica D 142, no. 3-4 (2000): 254–290. Abstract

Using multi-scale ideas from wavelet analysis, we extend singular-spectrum analysis (SSA) to the study of nonstationary time series, including the case where intermittency gives rise to the divergence of their variance. The wavelet transform resembles a local Fourier transform within a finite moving window whose width W, proportional to the major period of interest, is varied to explore a broad range of such periods. SSA, on the other hand, relies on the construction of the lag-correlation matrix C on M lagged copies of the time series over a fixed window width W to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components; here W=M[Delta]t with [Delta]t as the time step. The proposed multi-scale SSA is a local SSA analysis within a moving window of width M<=W<=N, where N is the length of the time series. Multi-scale SSA varies W, while keeping a fixed W/M ratio, and uses the eigenvectors of the corresponding lag-correlation matrix C(M) as data-adaptive wavelets; successive eigenvectors of C(M) correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis. Multi-scale SSA thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time-frequency domain by a suitable localization of the signal's correlation matrix. We present several examples of application to synthetic signals with fractal or power-law behavior which mimic selected features of certain climatic or geophysical time series. The method is applied next to the monthly values of the Southern Oscillation Index (SOI) for 1933-1996; the SOI time series is widely believed to capture major features of the El Niño/Southern Oscillation (ENSO) in the Tropical Pacific. Our methodology highlights an abrupt periodicity shift in the SOI near 1960. This abrupt shift between 5 and 3 years supports the Devil's staircase scenario for the ENSO phenomenon (preliminary results of this study were presented at the XXII General Assembly of the European Geophysical Society, Vienna, May 1997, and at the Fall Meeting of the American Geophysical Union, San Francisco, December 1997).

Ghil, Michael. “The essence of data assimilation or why combine data with models.” In Proc. 3rd WMO Intl Symp. Assimilation of Observations in Meteorology & Oceanography, 1–4, 2000, 1–4.
Ghil, Michael, and Andrew W. Robertson. “Solving problems with GCMs: General circulation models and their role in the climate modeling hierarchy.” In General Circulation Model Development: Past, Present and Future, edited by D. Randall, 285–325. Academic Press, San Diego, 2000.
Smyth, Padhraic, Kayo Ide, and Michael Ghil. “Multiple Regimes in Northern Hemisphere Height Fields via Mixture Model Clustering.” Journal of the Atmospheric Sciences 56, no. 21 (1999): 3704–3723.
Ghil, Michael, and Ning Jiang. “Recent Forecast Skill for the El Niño/Southern Oscillation.” Geophysical Research Letters 25 (1998): 171–174. Abstract
We outline a relationship between three slowly varying characteristics of the coupled ocean-atmosphere system in the tropical Pacific: (i) quasi-periodicity, (ii) extended predictability, and (iii) approximate low dimensionality. The Southern Oscillation Index (SOI) and Niño-3 sea surface temperatures characterize climatic variations in the tropical Pacific; these two time series are usually anticorrelated. This low-dimensional characterization suggests that much of the system's seasonal-to-interannual predictability depends on the regular behavior of the two scalar time series under consideration. The predictive skill of two idealized models is studied, showing the strong connection between regularity and predictability. El-Niño/Southern-Oscillation (ENSO) predictability is then assessed for current forecast models. When the periodic component of the ENSO signal is strong, it results in higher forecast skill. This skill decreases when the anti-correlation between SOI and Niño-3 temperature anomalies is lost, as it has been in the first half of this decade.
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.
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.