# Publications by Type: Journal Article

2003
Simonnet, Eric, Michael Ghil, Kayo Ide, Roger Temam, and Shouhong Wang. 2003. “Low-frequency variability in shallow-water models of the wind-driven ocean circulation. Part II: Time-dependent solutions.” Journal of Physical Oceanography 33 (4). Abstract

The time-dependent wind-driven ocean circulation is investigated for both a rectangular and a North Atlantic– shaped basin. Multiple steady states in a 2 ½ -layer shallow-water model and their dependence on various pa- rameters and other model properties were studied in Part I for the rectangular basin. As the wind stress on the rectangular basin is increased, each steady-state branch is destabilized by a Hopf bifurcation. The periodic solutions that arise off the subpolar branch have a robust subannual periodicity of 4–5 months. For the subtropical branch, the period varies between sub- and interannual, depending on the inverse Froude number F 2 defined with respect to the lower active layer’s thickness H 2 . As F 2 is lowered, the perturbed-symmetric branch is destabilized baroclinically, before the perturbed pitchfork bifurcation examined in detail in Part I occurs. Transition to aperiodic behavior arises at first by a homoclinic explosion off the isolated branch that exists only for sufficiently high wind stress. Subsequent global and local bifurcations all involve the subpolar branch, which alone exists in the limit of vanishing wind stress. Purely subpolar solutions vary on an interannual scale, whereas combined subpolar and subtropical solutions exhibit complex transitions affected by a second, subpolar homoclinic orbit. In the latter case, the timescale of the variability is interdecadal. The role of the global bifurcations in the interdecadal variability is investigated. Numerical simulations were carried out for the North Atlantic with earth topography- 5 minute (ETOPO-5) coastline geometry in the presence of realistic, as well as idealized, wind stress forcing. The simulations exhibit a realistic Gulf Stream at 20-km resolution and with realistic wind stress. The variability at 12-km resolution exhibits spectral peaks at 6 months, 16 months, and 6–7 years. The subannual mode is strongest in the subtropical gyre; the interannual modes are both strongest in the subpolar gyre.

Varadi, F., B. Runnegar, and Michael Ghil. 2003. “Successive refinements in long-term integrations of planetary orbits.” The Astrophysical Journal 592 (1). IOP Publishing: 620.
2002
Ghil, Michael, M. R. Allen, M. D. Dettinger, Kayo Ide, Dmitri Kondrashov, M. E. Mann, Andrew W. Robertson, et al. 2002. “Advanced spectral methods for climatic time series.” Reviews of Geophysics 40 (1): 1–41.
Ghil, M, Y Feliks, and L. U. Sushama. 2002. “Baroclinic and barotropic aspects of the wind-driven ocean circulation.” Physica D: Nonlinear Phenomena 167 (1). Elsevier: 1–35. Abstract

The double-gyre circulation induced by a symmetric wind-stress pattern in a quasi-geostrophic model of the mid-latitude ocean is studied analytically and numerically. The model is discretized vertically by projection onto normal modes of the mean stratification. Within its horizontally rectangular domain, the numerical model captures the wind-driven circulation’s three dynamic regimes: (1) a basin-scale double-gyre circulation, cyclonic in the basin’s northern part and anticyclonic in the south, which is dominated by Sverdrup balance; (2) a swift western boundary current in either gyre, with dissipation most important near the coast and inertial balance further out; and (3) a strong recirculating dipole near the intersection of the western boundary with the symmetry line of zero wind-stress curl. The flow inside this stationary dipole is highly nonlinear, and equivalent-barotropic. An analytical solution to the potential vorticity equation with variable stratification describes the dipole, and fits well the full numerical model’s steady-state solutions. Changes in the numerical model’s solutions are investigated systematically as a function of changes in the strength of the wind stress $\tau$ and the Rossby radius of deformation LR. The main changes occur in the recirculation region, while the basin-scale gyres and the western boundary currents are affected but little. A unique symmetric dipole is observed for small $\tau$, and agrees in its properties with the analytical solution. As $\tau$ increases, multiple asymmetric equilibria arise due to pitchfork bifurcation and are stable for large enough LR. The numerically obtained asymmetric equilibria also agree in their main properties with the analytical ones, as well as with the corresponding solutions of a shallow-water model. Increasing $\tau$ further results in two successive Hopf bifurcations, that lead to limit cycles with periods near 10 and 1 years, respectively. Both oscillatory instabilities have a strong baroclinic component. Above a certain threshold in $\tau$ the solutions become chaotic. Flow pattern evolution in this chaotic regime resembles qualitatively the circulation found in the Gulf Stream and Kuroshio current systems after their separation from the continent.

Sun, Chaojiao, Zheng Hao, Michael Ghil, and J. David Neelin. 2002. “Data assimilation for a coupled ocean-atmosphere model. Part I: Sequential state estimation.” Monthly Weather Review 130 (5): 1073–1099.
Kravtsov, Sergey, and A. Robertson. 2002. “Midlatitude ocean-atmosphere interaction in an idealized coupled model.” Climate Dynamics 19 (8). Springer: 693–711.
Koo, Seongjoon, Andrew W. Robertson, and Michael Ghil. 2002. “Multiple regimes and low-frequency oscillations in the Southern Hemisphere's zonal-mean flow.” Journal of Geophysical Research: Atmospheres 107 (D21). Wiley Online Library.
Gildor, Hezi, and Michael Ghil. 2002. “Phase relations between climate proxy records: Potential effect of seasonal precipitation changes.” Geophysical Research Letters 29 (2). Wiley Online Library.
Kao, C.-Y. J., D. I. Cooper, J. M. Reisner, W. E. Eichinger, and Michael Ghil. 2002. “Probing near-surface atmospheric turbulence with high-resolution lidar measurements and models.” Journal of Geophysical Research: Atmospheres 107 (D10). Wiley Online Library.
Koo, Seongjoon, and Michael Ghil. 2002. “Successive bifurcations in a simple model of atmospheric zonal-flow vacillation.” Chaos: An Interdisciplinary Journal of Nonlinear Science 12 (2). AIP Publishing: 300–309.
Ghil, Michael, and Andrew W. Robertson. 2002. “Waves'' vs. particles'' in the atmosphere's phase space: A pathway to long-range forecasting?” Proceedings of the National Academy of Sciences 99. National Acad Sciences: 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.

2001
Ide, Kayo, H. Le Treut, Z.-X. Li, and Michael Ghil. 2001. “Atmospheric radiative equilibria. Part II: bimodal solutions for atmospheric optical properties.” Climate Dynamics 18 (1-2). Springer: 29–49.
Saunders, Amira, and Michael Ghil. 2001. “A Boolean delay equation model of ENSO variability.” Physica D: Nonlinear Phenomena 160 (1). Elsevier: 54–78.
Tian, Yudong, Eric R. Weeks, Kayo Ide, J. S. Urbach, Charles N. Baroud, Michael Ghil, and Harry L. Swinney. 2001. “Experimental and numerical studies of an eastward jet over topography.” Journal of Fluid Mechanics 438. Cambridge Univ Press: 129–157.
Ghil, Michael. 2001. “Hilbert problems for the geosciences in the 21st century.” Nonlinear Processes in Geophysics 8 (4/5): 211–211.
Lott, François, Andrew W. Robertson, and Michael Ghil. 2001. “Mountain torques and atmospheric oscillations.” Geophys. Res. Lett 28: 1207–1210.
Ghil, Michael, Tian Ma, and Shouhong Wang. 2001. “Structural bifurcation of 2-D incompressible flows.” Indiana University Mathematics Journal 50: 159–180.
Chang, Kyung-Il, Michael Ghil, Kayo Ide, and Chung-Chieng Aaron Lai. 2001. “Transition to aperiodic variability in a wind-driven double-gyre circulation model.” Journal of Physical Oceanography 31 (5): 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. 2000. “Pacific interdecadal variability in this century's sea surface temperatures.” Geophysical Research Letters 27 (15). Wiley Online Library: 2261–2264.
Yiou, Pascal, Didier Sornette, and Michael Ghil. 2000. “Data-adaptive wavelets and multi-scale singular-spectrum analysis.” Physica D 142 (3-4): 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).