Publications by Author: Ghil, Michael

2007
Kravtsov, Sergey, William K. Dewar, Pavel S. Berloff, James C. McWilliams, and Michael Ghil. “A highly nonlinear coupled mode of decadal variability in a mid-latitude ocean–atmosphere model.” Dynamics of Atmospheres and Oceans 43, no. 3 (2007): 123–150.
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Kondrashov, Dmitri, Y. Shprits, Michael Ghil, and R. Thorne. “A Kalman filter technique to estimate relativistic electron lifetimes in the outer radiation belt.” Journal of Geophysical Research: Space Physics 112, no. A10 (2007).
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Feliks, Yizhak, Michael Ghil, and Eric Simonnet. “Low-frequency variability in the midlatitude baroclinic atmosphere induced by an oceanic thermal front.” Journal of the Atmospheric Sciences 64, no. 1 (2007): 97–116.
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Kondrashov, Dmitri, Jie Shen, Richard Berk, Fabio D'Andrea, and Michael Ghil. “Predicting weather regime transitions in Northern Hemisphere datasets.” Climate Dynamics 29, no. 5 (2007): 535–551.
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Gaffney, Scott J., Andrew W. Robertson, Padhraic Smyth, Suzana J. Camargo, and Michael Ghil. “Probabilistic clustering of extratropical cyclones using regression mixture models.” Climate Dynamics 29, no. 4 (2007): 423–440.
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Shprits, Yuri, Dmitri Kondrashov, Yue Chen, Richard Thorne, Michael Ghil, Reiner Friedel, and Geoff Reeves. “Reanalysis of relativistic radiation belt electron fluxes using CRRES satellite data, a radial diffusion model, and a Kalman filter.” Journal of Geophysical Research: Space Physics 112, no. A12 (2007).
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Kondrashov, Dmitri, and Michael Ghil. “Reply to T. Schneider's comment on "Spatio-temporal filling of missing points in geophysical data sets".” Nonlinear Processes in Geophysics 14, no. 1 (2007): 3–4.
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Sushama, L., Michael Ghil, and K. Ide. “Spatio-temporal variability in a mid-latitude ocean basin subject to periodic wind forcing.” Atmosphere-ocean 45, no. 4 (2007): 227–250. Abstract

The mid-latitude ocean's response to time-dependent zonal wind-stress forcing is studied using a reduced-gravity, 1.5-layer, shallow-water model in two rectangular ocean basins of different sizes. The small basin is 1000 km $\times$ 2000 km and the larger one is 3000 km $\times$ 2010 km; the aspect ratio of the larger basin is quite similar to that of the North Atlantic between 20$\deg$N and 60$\deg$N. The parameter dependence of the model solutions and their spatio-temporal variability subject to time-independent wind stress forcing serve as the reference against which the results for time-dependent forcing are compared. For the time-dependent forcing case, three zonal-wind profiles that mimic the seasonal cycle are considered in this study: (1) a fixed-profile wind-stress forcing with periodically varying intensity; (2) a wind-stress profile with fixed intensity, but north–south migration of the mid-latitude westerly wind maximum; and (3) a north–south migrating profile with periodically varying intensity. Results of the small-basin simulations show the intrinsic variability found for time-independent forcing to persist when the intensity of the wind forcing varies periodically. It thus appears that the physics behind the upper ocean's variability is mainly controlled by internal dynamics, although the solutions’ spatial patterns are now more complex, due to the interaction between the external and internal modes of variability. The north–south migration of wind forcing, however, does inhibit the inertial recirculation; its suppression increases with the amplitude of north–south migration in the wind-stress forcing. Model solutions in the larger rectangular basin and at smaller viscosity exhibit more realistic recirculation gyres, with a small meridional-to-zonal aspect ratio, and an elongated eastward jet; the low-frequency variability of these solutions is dominated by periodicities of 14 and 6–7 years. Simulations performed in this setting with a wind-stress profile that involves seasonal variations of realistic amplitude in both the intensity and the position of the atmospheric jet show the seven-year periodicity in the oceanic circulation to be robust. The intrinsic variability is reinforced by the periodic variations in the jet's intensity and weakened by periodic variations in the meridional position; the two effects cancel, roughly speaking, thus preserving the overall characteristics of the seven-year mode.

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Deloncle, Axel, Richard Berk, Fabio D'Andrea, and Michael Ghil. “Weather regime prediction using statistical learning.” Journal of the Atmospheric Sciences 64, no. 5 (2007): 1619–1635.
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2006
Kao, Jim, Dawn Flicker, Kayo Ide, and Michael Ghil. “Estimating model parameters for an impact-produced shock-wave simulation: Optimal use of partial data with the extended Kalman filter.” Journal of Computational Physics 214, no. 2 (2006): 725–737.
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Feliks, Yizhak, Michael Ghil, Israel Ziona, and Météorologie Dynamique. “Long-range forecasting and the scientific background in Joseph's interpretation to Pharaoh’s dreams.” In Proc. 16th Conf. Research Judaea & Samaria. in press, 2006. Abstract

Long-range forecasting is today a major area of climate research. Such forecasts affect socioeconomic planning in many fields of activity. There are essentially two approaches to longrange forecasting: one is based on solving the equations that govern atmospheric and ocean dynamics, the other on the statistical properties of past climate records. The present talk is based on the latter, statistical approach. Joseph’s interpretation of Pharaoh’s dreams provides a striking example of long-range planning based on a climate forecast. Joseph interpreted the two dreams as a forecast for seven years of plenty, followed by seven of famine. Based on this forecast, he proposed to Pharaoh a plan for running the agriculture and economy of Egypt. It is not clear from the Biblical story why Pharaoh trusted Joseph’s forecast and appointed him to implement the plan. Our answer to this question is based on ancient and medieval Egypt’s being entirely dependent on the Nile River’s seasonal flooding: when the highest water levels did not cover the arable areas of the river valley, crops were insufficient to feed the population. When successive years of hunger weakened the economy and the state, change of rulers could, and sometimes did ensue. Extreme examples were the fall of the Old Kingdom in 2185 B.C. and the Fatimid conquest of Egypt in 969 A.D. Hence the Egyptians measured the high-water mark of the Nile River for over 5000 years, using different tools. The most advanced of these tools was the nilometer; typical nilometers appear in several mosaics from the Roman and Byzantine period around the Mediterranean, such as the “Nile Festival” mosaic in Zippori (Upper Galilee), Fig. 1. The measurements had a twofold purpose: first to set the annual taxes, which were a function of the high-water mark, for obvious reasons; and second, to provide information for water management, with a view to reduce drought damage. Our analysis of high- and low-water levels for 622–1922 A.D. shows that oscillations with a period of several years occur, with a 7-year oscillation being dominant. We suspect that the origin of this 7-year swing lies in the same periodicity being present in the North Atlantic’s sea-surface temperatures and sea-level pressures. This North Atlantic Oscillation affects the climate of Europe, North America and the Middle East, and might be the ultimate reason for Joseph’s successful climate forecast.

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Kravtsov, S., Andrew W. Robertson, and Michael Ghil. “Multiple regimes and low-frequency oscillations in the Northern Hemisphere's zonal-mean flow.” Journal of the Atmospheric Sciences 63, no. 3 (2006): 840–860.
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Bellon, G., Michael Ghil, and H. Le Treut. “Scale separation for moisture-laden regions in the tropical atmosphere.” Geophysical Research Letters 33, no. 1 (2006).
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Kondrashov, Dmitri, and Michael Ghil. “Spatio-temporal filling of missing points in geophysical data sets.” Nonlinear Processes in Geophysics 13, no. 2 (2006): 151–159. Abstract

The majority of data sets in the geosciences are obtained from observations and measurements of natural systems, rather than in the laboratory. These data sets are often full of gaps, due to to the conditions under which the measurements are made. Missing data give rise to various problems, for example in spectral estimation or in specifying boundary conditions for numerical models. Here we use Singular Spectrum Analysis (SSA) to fill the gaps in several types of data sets. For a univariate record, our procedure uses only temporal correlations in the data to fill in the missing points. For a multivariate record, multi-channel SSA (M-SSA) takes advantage of both spatial and temporal correlations. We iteratively produce estimates of missing data points, which are then used to compute a self-consistent lag-covariance matrix; cross-validation allows us to optimize the window width and number of dominant SSA or M-SSA modes to fill the gaps. The optimal parameters of our procedure depend on the distribution in time (and space) of the missing data, as well as on the variance distribution between oscillatory modes and noise. The algorithm is demonstrated on synthetic examples, as well as on data sets from oceanography, hydrology, atmospheric sciences, and space physics: global sea-surface temperature, flood-water records of the Nile River, the Southern Oscillation Index (SOI), and satellite observations of relativistic electrons.

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Ghil, Michael, and Ilya Zaliapin. “Une Nouvelle source de Fractales: Les Equations Booléennes avec Retard, et leurs Applications aux Sciences de la Planete.” In L'irruption Des Géométries Fractales Dans Les Sciences,une Apologie De L'oeuvre De Benoît Mandelbrot, 161–187. Paris: Editions de l'Académie Européenne Interdisciplinaire des Sciences, 2006.
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2005
Kravtsov, S., Andrew W. Robertson, and Michael Ghil. “Bimodal behavior in the zonal mean flow of a baroclinic beta-channel model.” Journal of the Atmospheric Sciences 62, no. 6 (2005): 1746–1769.
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Zhang, Yunyan, Bjorn Stevens, and Michael Ghil. “On the diurnal cycle and susceptibility to aerosol concentration in a stratocumulus-topped mixed layer.” Quarterly Journal of the Royal Meteorological Society 131, no. 608 (2005): 1567–1583.
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Kondrashov, Dmitri, S Kravtsov, Andrew W. Robertson, and Michael Ghil. “A hierarchy of data-based ENSO models.” Journal of climate 18, no. 21 (2005): 4425–4444. Abstract

Global sea surface temperature (SST) evolution is analyzed by constructing predictive models that best describe the dataset’s statistics. These inverse models assume that the system’s variability is driven by spatially coherent, additive noise that is white in time and are constructed in the phase space of the dataset’s leading empirical orthogonal functions. Multiple linear regression has been widely used to obtain inverse stochastic models; it is generalized here in two ways. First, the dynamics is allowed to be nonlinear by using polynomial regression. Second, a multilevel extension of classic regression allows the additive noise to be correlated in time; to do so, the residual stochastic forcing at a given level is modeled as a function of variables at this level and the preceding ones. The number of variables, as well as the order of nonlinearity, is determined by optimizing model performance. The two-level linear and quadratic models have a better El Niño–Southern Oscillation (ENSO) hindcast skill than their one-level counterparts. Estimates of skewness and kurtosis of the models’ simulated Niño-3 index reveal that the quadratic model reproduces better the observed asymmetry between the positive El Niño and negative La Niña events. The benefits of the quadratic model are less clear in terms of its overall, cross-validated hindcast skill; this model outperforms, however, the linear one in predicting the magnitude of extreme SST anomalies. Seasonal ENSO dependence is captured by incorporating additive, as well as multiplicative forcing with a 12-month period into the first level of each model. The quasi-quadrennial ENSO oscillatory mode is robustly simulated by all models. The “spring barrier” of ENSO forecast skill is explained by Floquet and singular vector analysis, which show that the leading ENSO mode becomes strongly damped in summer, while nonnormal optimum growth has a strong peak in December.

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Simonnet, Eric, Michael Ghil, and Henk Dijkstra. “Homoclinic bifurcations in the quasi-geostrophic double-gyre circulation.” Journal of Marine Research 63, no. 5 (2005): 931–956. Abstract

The wind-driven double-gyre circulation in a rectangular basin goes through several dynamical regimes as the amount of lateral friction is decreased. This paper studies the transition to irregular flow in the double-gyre circulation by applying dynamical systems methodology to a quasi-geostrophic, equivalent-barotropic model with a 10-km resolution. The origin of the irregularities, in space and time, is the occurrence of homoclinic bifurcations that involve phase-space behavior far from stationary solutions. The connection between these homoclinic bifurcations and earlier transitions, which occur at larger lateral friction, is explained. The earlier transitions, such as pitchfork and asymmetric Hopf bifurcation, only involve the nonlinear saturation of linear instabilities, while the homoclinic bifurcations are associated with genuinely nonlinear behavior. The sequence of bifurcations—pitchfork, Hopf, and homoclinic—is independent of the lateral friction and may be described as the unfolding of a singularity that occurs in the frictionless, Hamiltonian limit of the governing equations. Two distinct chaotic regimes are identified: Lorenz chaos at relatively large lateral friction versus Shilnikov chaos at relatively small lateral friction. Both types of homoclinic bifurcations induce chaotic behavior of the recirculation gyres that is dominated by relaxation oscillations with a well-defined period. The relevance of these results to the mid-latitude oceans' observed low-frequency variations is discussed. A previously documented 7-year peak in observed North-Atlantic variability is shown to exist across a hierarchy of models that share the gyre modes and homoclinic bifurcations discussed herein.

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Dijkstra, Henk A., and Michael Ghil. “Low-frequency variability of the large-scale ocean circulation: a dynamical systems approach.” Reviews of Geophysics 43 (2005). Abstract

Oceanic variability on interannual, interdecadal, and longer timescales plays a key role in climate variability and climate change. Paleoclimatic records suggest major changes in the location and rate of deepwater formation in the Atlantic and Southern oceans on timescales from millennia to millions of years. Instrumental records of increasing duration and spatial coverage document substantial variability in the path and intensity of ocean surface currents on timescales of months to decades. We review recent theoretical and numerical results that help explain the physical processes governing the large-scale ocean circulation and its intrinsic variability. To do so, we apply systematically the methods of dynamical systems theory. The dynamical systems approach is proving successful for more and more detailed and realistic models, up to and including oceanic and coupled ocean-atmosphere general circulation models. In this approach one follows the road from simple, highly symmetric model solutions, through a “bifurcation tree,” toward the observed, complex behavior of the system under investigation. The observed variability can be shown to have its roots in simple transitions from a circulation with high symmetry in space and regularity in time to circulations with successively lower symmetry in space and less regularity in time. This road of successive bifurcations leads through multiple equilibria to oscillatory and eventually chaotic solutions. Key features of this approach are illustrated in detail for simplified models of two basic problems of the ocean circulation. First, a barotropic model is used to capture major features of the wind-driven ocean circulation and of the changes in its behavior as wind stress increases. Second, a zonally averaged model is used to show how the thermohaline ocean circulation changes as buoyancy fluxes at the surface increase. For the wind-driven circulation, multiple separation patterns of a “Gulf-Stream like” eastward jet are obtained. These multiple equilibria are followed by subannual and interannual oscillations of the jet and of the entire basin's circulation. The multiple equilibria of the thermohaline circulation include deepwater formation near the equator, near either pole or both, as well as intermediate possibilities that bear some degree of resemblance to the currently observed Atlantic overturning pattern. Some of these multiple equilibria are subject, in turn, to oscillatory instabilities with timescales of decades, centuries, and millennia. Interdecadal and centennial oscillations are the ones of greatest interest in the current debate on global warming and on the relative roles of natural and anthropogenic variability in it. They involve the physics of the truly three-dimensional coupling between the wind-driven and thermohaline circulation. To arrive at this three-dimensional picture, the bifurcation tree is sketched out for increasingly complex models for both the wind-driven and the thermohaline circulation.

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