2001

Saunders, Amira, and Michael Ghil. “A Boolean delay equation model of ENSO variability.” Physica D: Nonlinear Phenomena 160, no. 1 (2001): 54–78.

PDF PDF (figures)Tian, Yudong, Eric R. Weeks, Kayo Ide, J. S. Urbach, Charles N. Baroud, Michael Ghil, and Harry L. Swinney. “Experimental and numerical studies of an eastward jet over topography.” Journal of Fluid Mechanics 438 (2001): 129–157.

PDFGhil, Michael. “Hilbert problems for the geosciences in the 21st century.” Nonlinear Processes in Geophysics 8, no. 4/5 (2001): 211–211.

PDFLott, François, Andrew W. Robertson, and Michael Ghil. “Mountain torques and atmospheric oscillations.” Geophys. Res. Lett 28 (2001): 1207–1210.

PDFGhil, Michael, Tian Ma, and Shouhong Wang. “Structural bifurcation of 2-D incompressible flows.” Indiana University Mathematics Journal 50 (2001): 159–180.

PDFChang, 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.

2000

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).

1999

Kondrashov, D., J. Feynman, P. C. LIEWER, and A. Ruzmaikin. “Three-dimensional Magnetohydrodynamic Simulationsof the Interaction of Magnetic Flux Tubes.” The Astrophysical Journal 519, no. 2 (1999): 884. Publisher's Version Abstract

We use a three-dimensional Cartesian resistive MHD code to investigate three-dimensional aspects of the interaction of magnetic flux tubes as observed in the solar atmosphere and studied in laboratory experiments. We present here the first results from modeling the reconnection of two Gold-Hoyle magnetic flux tubes that follow the system evolution to a final steady state. The energy evolution and reconnection rate for flux tubes with both parallel and antiparallel axial fields and with equal and nonequal strengths are studied. For the first time, we calculate a gauge-invariant relative magnetic helicity of the system and compare its evolution for all the above cases. We observed that the rate at which helicity is dissipated may vary significantly for different cases, and it may be comparable with the energy dissipation rate. The footpoints of the interacting flux tubes were held fixed or allowed to move to simulate different conditions in the solar photosphere. The cases with fixed footpoints had lower magnetic energy release and reached a steady state faster than cases with moving footpoints. For all computed cases the magnetic energy was released mostly through work done on the plasma by the electromagnetic forces rather than through resistive dissipation. The reconnection rate of the poloidal magnetic field is faster for the case with antiparallel flux tubes than for the case with parallel flux tubes, consistent with laboratory experiments. We find that during reconnection supersonic (but sub-Alfv√©nic) flows develop, and it may take a considerably longer time for the system to reach a steady state than for magnetic flux to reconnect. It is necessary to retain the pressure gradient in the momentum equation; the plasma pressure may be significant for the final equilibrium steady state even with low-Œ≤ initial conditions, and the work done on the plasma by compression is important in energy exchange.

WANG, J., Dmitri Kondrashov, P. C. LIEWER, and S. R. KARMESIN. “Three-dimensional deformable-grid electromagnetic particle-in-cell for parallel computers.” Journal of Plasma Physics 61, no. 3 (1999): 367-389. Publisher's Version Abstract

We describe a new parallel, non-orthogonal-grid, three-dimensional electromagnetic particle-in-cell (EMPIC) code based on a finite-volume formulation. This code uses a logically Cartesian grid of deformable hexahedral cells, a discrete surface integral (DSI) algorithm to calculate the electromagnetic field, and a hybrid logical‚Äìphysical space algorithm to push particles. We investigate the numerical instability of the DSI algorithm for non-orthogonal grids, analyse the accuracy for EMPIC simulations on non-orthogonal grids, and present performance benchmarks of this code on a parallel supercomputer. While the hybrid particle push algorithm has a second-order accuracy in space, the accuracy of the DSI field solve algorithm is between first and second order for non-orthogonal grids. The parallel implementation of this code, which is almost identical to that of a Cartesian-grid EMPIC code using domain decomposition, achieved a high parallel efficiency of over 96% for large-scal" # "e simulations.

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.

1998

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 NiÃ±o-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-NiÃ±o/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 NiÃ±o-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.

1997

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.

PDF1996

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.

1995

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.

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