Publications by Type: Journal Article

2004
Kondrashov, Dmitri, K. Ide, and Michael Ghil. “Weather regimes and preferred transition paths in a three-level quasigeostrophic model.” Journal of the Atmospheric Sciences 61, no. 5 (2004): 568–587.
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2003
Zaliapin, Ilya, Vladimir Keilis-Borok, and Michael Ghil. “A Boolean delay equation model of colliding cascades. Part I: Multiple seismic regimes.” Journal of Statistical Physics 111, no. 3-4 (2003): 815–837.
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Zaliapin, Ilya, Vladimir Keilis-Borok, and Michael Ghil. “A Boolean delay equation model of colliding cascades. Part II: Prediction of critical transitions.” Journal of Statistical Physics 111, no. 3-4 (2003): 839–861.
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Ghil, Michael. “Did celestial chaos kill the dinosaurs?The Observatory 123, no. 1177 (2003): 328–333.
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Simonnet, Eric, Michael Ghil, Shouhong Wang, and Zhi-Min Chen. “Hopf Bifurcation in Quasi-geostrophic Channel Flow.” SIAM J. Appl. Math. 64, no. 1 (2003): 343–368.
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Bellon, G., H. Le Treut, and Michael Ghil. “Large-scale and evaporation-wind feedbacks in a box model of the tropical climate.” Geophysical Research Letters 30, no. 22 (2003).
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Kravtsov, S., Andrew W. Robertson, and Michael Ghil. “Low-Frequency Variability in a Baroclinic Beta-Channel with Land-Sea Contrast*.” Journal of the Atmospheric Sciences 60, no. 18 (2003): 2267–2293.
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Simonnet, Eric, Michael Ghil, Kayo Ide, Roger Temam, and Shouhong Wang. “Low-frequency variability in shallow-water models of the wind-driven ocean circulation. Part II: Time-dependent solutions.” Journal of Physical Oceanography 33, no. 4 (2003). 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.

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Simonnet, Eric, Michael Ghil, Kayo Ide, Roger Temam, and Shouhong Wang. “Low-Frequency Variability in Shallow-Water Models of the Wind-Driven Ocean Circulation. Part I: Steady-State Solution.” Journal of Physical Oceanography 33, no. 4 (2003). Abstract

Successive bifurcations—from steady states through periodic to aperiodic solutions—are studied in a shallow- water, reduced-gravity, 2 ½ -layer model of the midlatitude ocean circulation subject to time-independent wind stress. The bifurcation sequence is studied in detail for a rectangular basin with an idealized spatial pattern of wind stress. The aperiodic behavior is studied also in a North Atlantic–shaped basin with realistic continental contours. The bifurcation sequence in the rectangular basin is studied in Part I, the present article. It follows essentially the one reported for single-layer quasigeostrophic and 1 ½ -layer shallow-water models. As the intensity of the north– south-symmetric, zonal wind stress is increased, the nearly symmetric double-gyre circulation is destabilized through a perturbed pitchfork bifurcation. The low-stress steady solution, with its nearly equal subtropical and subpolar gyres, is replaced by an approximately mirror-symmetric pair of stable equilibria. The two solution branches so obtained are named after the inertial recirculation cell that is stronger, subtropical or subpolar, respectively. This perturbed pitchfork bifurcation and the associated Hopf bifurcations are robust to changes in the interface friction between the two active layers and the thickness H 2 of the lower active layer. They persist in the presence of asymmetries in the wind stress and of changes in the model’s spatial resolution and finite- difference scheme. Time-dependent model behavior in the rectangular basin, as well as in the more realistic, North Atlantic–shaped one, is studied in Part II.

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Varadi, F., B. Runnegar, and Michael Ghil. “Successive refinements in long-term integrations of planetary orbits.” The Astrophysical Journal 592, no. 1 (2003): 620.
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2002
Ghil, Michael, M. R. Allen, M. D. Dettinger, Kayo Ide, Dmitri Kondrashov, M. E. Mann, Andrew W. Robertson, et al.Advanced spectral methods for climatic time series.” Reviews of Geophysics 40, no. 1 (2002): 1–41.
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Ghil, M, Y Feliks, and L. U. Sushama. “Baroclinic and barotropic aspects of the wind-driven ocean circulation.” Physica D: Nonlinear Phenomena 167, no. 1 (2002): 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.

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Sun, Chaojiao, Zheng Hao, Michael Ghil, and J. David Neelin. “Data assimilation for a coupled ocean-atmosphere model. Part I: Sequential state estimation.” Monthly Weather Review 130, no. 5 (2002): 1073–1099.
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Kravtsov, Sergey, and A. Robertson. “Midlatitude ocean-atmosphere interaction in an idealized coupled model.” Climate Dynamics 19, no. 8 (2002): 693–711.
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Koo, Seongjoon, Andrew W. Robertson, and Michael Ghil. “Multiple regimes and low-frequency oscillations in the Southern Hemisphere's zonal-mean flow.” Journal of Geophysical Research: Atmospheres 107, no. D21 (2002).
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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).
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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.
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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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2001
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.
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