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Stefano Pierini
,
Michael Ghil
, and
Mickael D. Chekroun

Abstract

A low-order quasigeostrophic double-gyre ocean model is subjected to an aperiodic forcing that mimics time dependence dominated by interdecadal variability. This model is used as a prototype of an unstable and nonlinear dynamical system with time-dependent forcing to explore basic features of climate change in the presence of natural variability. The study relies on the theoretical framework of nonautonomous dynamical systems and of their pullback attractors (PBAs), that is, of the time-dependent invariant sets attracting all trajectories initialized in the remote past. The existence of a global PBA is rigorously demonstrated for this weakly dissipative nonlinear model. Ensemble simulations are carried out and the convergence to PBAs is assessed by computing the probability density function (PDF) of localization of the trajectories. A sensitivity analysis with respect to forcing amplitude shows that the PBAs experience large modifications if the underlying autonomous system is dominated by small-amplitude limit cycles, while less dramatic changes occur in a regime characterized by large-amplitude relaxation oscillations. The dependence of the attracting sets on the choice of the ensemble of initial states is then analyzed. Two types of basins of attraction coexist for certain parameter ranges; they contain chaotic and nonchaotic trajectories, respectively. The statistics of the former does not depend on the initial states whereas the trajectories in the latter converge to small portions of the global PBA. This complex scenario requires separate PDFs for chaotic and nonchaotic trajectories. General implications for climate predictability are finally discussed.

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Shi Jiang
,
Fei-fei Jin
, and
Michael Ghil

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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Chaojiao Sun
,
Zheng Hao
,
Michael Ghil
, and
J. David Neelin

Abstract

The assimilation problem for the coupled ocean–atmosphere system in the tropical Pacific is investigated using an advanced sequential estimator, the extended Kalman filter (EKF). The intermediate coupled model used in this study consists of an upper-ocean model and a steady-state atmospheric response to it. Model errors arise from the uncertainty in atmospheric wind stress. Data assimilation is applied in this idealized context to produce a time-continuous, dynamically consistent description of the model's El Niño–Southern Oscillation, based on incomplete and inaccurate observations. This study has two parts: Part I (the present paper) deals with state estimation for the coupled system, assuming that model parameters are correct, while Part II will deal with simultaneous state and parameter estimation.

The dynamical structure of forecast errors is estimated sequentially using a linearized Kalman filter and compared with that of an uncoupled ocean model. The coupling produces large changes in the structure of the error-correlation field. For example, error correlations with opposite signs in the western and eastern part of the model basin are caused by wind stress feedbacks.

The full EKF method is used to assimilate various model-generated synthetic oceanic datasets into the coupled model in an identical-twin framework. The assimilated datasets include the sea surface temperature and a combination of wave velocities and thermocline depth anomaly. With the EKF, the model's forecast-assimilation cycle is able to estimate correctly the phase and amplitude of the basic ENSO oscillation while using very few observations. This includes a set of observations that only cover a single meridional section of the ocean, preferably in the eastern basin.

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Christian L. Keppenne
,
Steven L. Marcus
,
Masahide Kimoto
, and
Michael Ghil

Abstract

A two-layer shallow-water model with R15 truncation and topographic forcing is used to study intraseasonal variability in the Northern Hemisphere’s (NH’s) extratropical atmosphere. The model’s variability is dominated by oscillations with average periods near 65–70 and 40–50 days. These periods are also found in 13.5 years of daily upper-air data from January 1980 to July 1993.

The spatial variability associated with these oscillations is examined by compositing the streamfunction-anomaly fields of the model and the observations. The model’s 70-day oscillation is strongest in the Euro-Atlantic sector, where it bears a close resemblance to observed streamfunction composites of the North Atlantic oscillation. The observed 70-day mode exhibits similar features in the Euro-Atlantic sector, accompanied by a north–south “seesaw” over the Pacific and Eurasia. Previous authors, in their analyses of geopotential height observations, also found these features to be present in an empirical orthogonal function that contains aspects of both the North Pacific and North Atlantic oscillations.

The 40-day oscillation is characterized, in both the model simulations and observed data, by a zonal wavenumber-2 pattern anchored over the NH topography. This pattern undergoes a tilted-trough vacillation in both the model and observations. This midlatitude vacillation is strongest in the Pacific–North American sector, where it resembles a 40-day oscillation in the University of California, Los Angeles, general circulation model that is largely driven by mountain torques over the Rockies. Comparisons with observational data show a clear separation between a tropical 50-day oscillation, not present in the authors’ model results, and a 40-day NH extratropical oscillation, which resembles the topographically induced oscillation that arises in their two-layer model.

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Yizhak Feliks
,
Andreas Groth
,
Andrew W. Robertson
, and
Michael Ghil

Abstract

This paper explores the three-way interactions between the Indian monsoon, the North Atlantic, and the tropical Pacific. Four climate records were analyzed: the monsoon rainfall in two Indian regions, the Southern Oscillation index for the tropical Pacific, and the NAO index for the North Atlantic. The individual records exhibit highly significant oscillatory modes with spectral peaks at 7–8 yr and in the quasi-biennial and quasi-quadrennial bands.

The interactions between the three regions were investigated in the light of the synchronization theory of chaotic oscillators. The theory was applied here by combining multichannel singular-spectrum analysis (M-SSA) with a recently introduced varimax rotation of the M-SSA eigenvectors.

A key result is that the 7–8-yr and 2.7-yr oscillatory modes in all three regions are synchronized, at least in part. The energy-ratio analysis, as well as time-lag results, suggests that the NAO plays a leading role in the 7–8-yr mode. It was found therewith that the South Asian monsoon is not slaved to forcing from the equatorial Pacific, although it does interact strongly with it. The time-lag analysis pinpointed this to be the case in particular for the quasi-biennial oscillatory modes.

Overall, these results confirm that the approach of synchronized oscillators, combined with varimax-rotated M-SSA, is a powerful tool in studying teleconnections between regional climate modes and that it helps identify the mechanisms that operate in various frequency bands. This approach should be readily applicable to ocean modes of variability and to the problems of air–sea interaction as well.

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Carlos R. Mechoso
,
John D. Farrara
, and
Michael Ghil

Abstract

The intraseasonal variability of the Southern Hemisphere stratosphere and troposphere is studied using multilevel geopotential height data for nine winters (1979–87). The study uses empirical orthogonal function (EOF) analysis of unfiltered data at five tropospheric and five stratospheric levels.

The four leading EOFs at all tropospheric levels exhibit the patterns previously detected at 500 mb. Study of the corresponding principal components (PCs) at each level shows that the quasi-stationary anomalies associated with the leading EOFs are equivalent barotropic and exhibit no preference for early, middle or late winter.

The five leading EOFs in the stratosphere fall into two classes. The first three EOFs at all levels form the first class. This class represents anomalies that are dominated by zonal wavenumber one (wave 1), exhibit strong westward tilt with height and travel slowly eastward or remain stationary. Most cases of large, persistent PC values for this class occur in early winter. The fourth and fifth EOFs form the other class. This class represents anomalies that are dominated by wavenumber two, and tilt noticeably, but less strongly than the first class, westward with height. These anomalies tend to develop mostly in late winter and to travel eastward more rapidly. The intraseasonal variability in the stratosphere resides therewith, as expected, in structures dominated by the longest planetary waves.

No systematic connections between tropospheric and stratospheric persistent anomalies are apparent in the dataset.

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Nathan Paldor
,
Ching-Hwang Liu
,
Michael Ghil
, and
Roger M. Wakimoto

Abstract

A short-wave instability theory is applied to secondary waves on a narrow cold-front rainband observed during the Experiment on Rapidly Intensifying Cyclones over the Atlantic (ERICA). The basic mean state is approximated by the parabolic, geostrophically balanced interface between two layers of homogeneous density. The observed wavelength of perturbations along the ERICA cold front is about 20–30 km and their doubling time is about 2 hours. The observed wavelength is well within the short-wave regime of the theory, which yields a growth rate in good agreement with the ERICA observations. The spatial patterns of both the horizontal and vertical velocity components observed during ERICA are consistent with the model-derived patterns.

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Christopher M. Strong
,
Fei-Fei Jin
, and
Michael Ghil

Abstract

It has recently been suggested that oscillatory topographic instability could contribute to low-frequency variability over the Northern Hemisphere midlatitudes. A barotropic potential vorticity model, with a hierarchy of forcing and topography configurations on the sphere, is used to investigate the nature of low-frequency oscillations induced by such instabilities. Steady-state solutions of the model include multiple unstable equilibria that sustain oscillatory instabilities with periods of 10–15 days, 35–50 days, and 150–180 days, for a realistic forcing pattern.

Time-dependent solutions exhibit chaotic behavior with episodic oscillations, featuring both the intraseasonal (35–50 day) and biweekly (10–15 day) modes. The former is dominated by standing spatial patterns, the latter by traveling wave patterns. The phases of the intraseasonal oscillation are robust for all cases, exhibiting a clear oscillatory exchange of atmospheric angular momentum with the solid earth via mountain torque. It is demonstrated, through linear stability analysis on the sphere, that the intraseasonal oscillations are induced by topographic instabilities.

The role of the seasonal cycle is studied by prescribing an annual cycle in the forcing. In this case, the winter forcing is more favorable than the summer for the occurrence of episodic intraseasonal oscillations. Recent observations are consistent with this model result.

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Andreas Groth
,
Yizhak Feliks
,
Dmitri Kondrashov
, and
Michael Ghil

Abstract

Spectral analyses of the North Atlantic temperature field in the Simple Ocean Data Analysis (SODA) reanalysis identify prominent and statistically significant interannual oscillations along the Gulf Stream front and in large regions of the North Atlantic. A 7–8-yr oscillatory mode is characterized by a basinwide southwest-to-northeast–oriented propagation pattern in the sea surface temperature (SST) field. This pattern is found to be linked to a seesaw in the meridional dipole structure of the zonal wind stress forcing (TAUX). In the subpolar gyre, the SST and TAUX fields of this mode are shown to be in phase opposition, which suggests a cooling effect of the wind stress on the upper ocean layer. Over all, this mode’s temperature field is characterized by a strong equivalent-barotropic component, as shown by covariations in SSTs and sea surface heights, and by phase-coherent behavior of temperature layers at depth with the SST field. Recent improvements of multivariate singular spectrum analysis (M-SSA) help separate spatiotemporal patterns. This methodology is developed further and applied to studying the ocean’s response to variability in the atmospheric forcing. Statistical evidence is shown to exist for other mechanisms generating oceanic variability of similar 7–8-yr periodicity in the Gulf Stream region; the latter variability is likewise characterized by a strongly equivalent-barotropic component. Two other modes of biennial variability in the Gulf Stream region are also identified, and it is shown that interannual variability in this region cannot be explained by the ocean’s response to similar variability in the atmospheric forcing alone.

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Eric Simonnet
,
Michael Ghil
,
Kayo Ide
,
Roger Temam
, and
Shouhong Wang

Abstract

Successive bifurcations—from steady states through periodic to aperiodic solutions—are studied in a shallow-water, reduced-gravity, 2½-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 1½-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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