Ghil, Michael. “Natural climate variability.” In Encyclopedia of Global Environmental Change, edited by M. MacCracken and J. Perry, 1:544–549. Wiley & Sons, Chichester/New York, 2002.
Gildor, Hezi, and Michael Ghil. “Phase relations between climate proxy records: Potential effect of seasonal precipitation changes.” Geophysical Research Letters 29, no. 2 (2002).
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Kao, C.-Y. J., D. I. Cooper, J. M. Reisner, W. E. Eichinger, and Michael Ghil. “Probing near-surface atmospheric turbulence with high-resolution lidar measurements and models.” Journal of Geophysical Research: Atmospheres 107, no. D10 (2002).
Koo, Seongjoon, and Michael Ghil. “Successive bifurcations in a simple model of atmospheric zonal-flow vacillation.” Chaos: An Interdisciplinary Journal of Nonlinear Science 12, no. 2 (2002): 300–309.
Ghil, Michael, and Andrew W. Robertson. “``Waves'' vs. ``particles'' in the atmosphere's phase space: A pathway to long-range forecasting?Proceedings of the National Academy of Sciences 99 (2002): 2493–2500. Abstract

Thirty years ago, E. N. Lorenz provided some approximate limits to atmospheric predictability. The details—in space and time—of atmospheric flow fields are lost after about 10 days. Certain gross flow features recur, however, after times of the order of 10–50 days, giving hope for their prediction. Over the last two decades, numerous attempts have been made to predict these recurrent features. The attempts have involved, on the one hand, systematic improvements in numerical weather prediction by increasing the spatial resolution and physical faithfulness in the detailed models used for this prediction. On the other hand, theoretical attempts motivated by the same goal have involved the study of the large-scale atmospheric motions’ phase space and the inhomoge- neities therein. These ‘‘coarse-graining’’ studies have addressed observed as well as simulated atmospheric data sets. Two distinct approaches have been used in these studies: the episodic or intermittent and the oscillatory or periodic. The intermittency approach describes multiple-flow (or weather) regimes, their per- sistence and recurrence, and the Markov chain of transitions among them. The periodicity approach studies intraseasonal oscil- lations, with periods of 15–70 days, and their predictability. We review these two approaches, ‘‘particles’’ vs. ‘‘waves,’’ in the quantum physics analogy alluded to in the title of this article, discuss their complementarity, and outline unsolved problems.

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Ide, Kayo, H. Le Treut, Z.-X. Li, and Michael Ghil. “Atmospheric radiative equilibria. Part II: bimodal solutions for atmospheric optical properties.” Climate Dynamics 18, no. 1-2 (2001): 29–49.
Saunders, Amira, and Michael Ghil. “A Boolean delay equation model of ENSO variability.” Physica D: Nonlinear Phenomena 160, no. 1 (2001): 54–78.
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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.
Ghil, Michael. “Hilbert problems for the geosciences in the 21st century.” Nonlinear Processes in Geophysics 8, no. 4/5 (2001): 211–211.
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.
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-Alfvénic) 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-β 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–physical 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.
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.