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  • Author or Editor: M. Ghil x
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B. Legras
and
M. Ghil

Abstract

We consider regimes of low-frequency variability in large-scale atmospheric dynamics. The model used for the study of these regimes is the fully-nonlinear, equivalent-barotropic vorticity equation on the sphere, with simplified forcing, dissipation and topography. Twenty-five modes are retained in a spherical harmonics expansion of the streamfunction. Solutions are studied as a function of the nondimensional intensity of the forcing and dissipation.

Multiple stationary solutions are obtained as a result of nonlinear interaction between waves, mean flow and orography. The number of modes retained in the analysis permits these multiple equilibria to appear for realistic values of the forcing. The equilibria exhibit blocked and zonal flow patterns bearing a marked resemblance to synoptically defined zonal and blocked Northern Hemisphere midlatitude flows.

Wave-wave interactions influence strongly the stability properties of the equilibria and the time evolution of nonequilibrium solutions. Time-dependent solutions show persistent sequences which occur in the phase-space vicinity of the zonal and blocked equilibria. Composite flow patterns of the persistent sequences are similar to the equilibria nearby, which permits the unambiguous definition of quasi-stationary flow regimes, zonal and blocked, respectively. The number of episodes of blocked or zonal flow decreases monotonically as their duration increases, in agreement with observations.

The statistics of transitions between the two types of planetary flow regimes are computed from the model's deterministic dynamics. These transitional called breaks in statistical-synoptic long-range forecasting, are shown to be influenced by changes in model parameters. This influence is discussed in terms of the effect of anomalous boundary conditions on large-scale midlatitude atmospheric flow and on its predictability.

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D. Kondrashov
,
K. Ide
, and
M. Ghil

Abstract

Multiple flow regimes are reexamined in a global, three-level, quasigeostrophic (QG3) model with realistic topography in spherical geometry. This QG3 model, using a T21 triangular truncation in the horizontal, has a fairly realistic climatology for Northern Hemisphere winter and exhibits multiple regimes that resemble those found in atmospheric observations. Four regimes are robust to changes in the classification method, k-means versus mixture modeling, and its parameters. These regimes correspond roughly to opposite phases of the Arctic Oscillation (AO) and the North Atlantic Oscillation (NAO), respectively.

The Markov chain representation of regime transitions is refined here by finding the preferred transition paths in a three-dimensional (3D) subspace of the model's phase space. Preferred transitions occur from the positive phase of the NAO (NAO+) to that of the AO (AO+), from AO+ to NAO, and from NAO to NAO+, but not directly between opposite phases of the AO. The angular probability density function (PDF) of the regime exits that correspond to these preferred transitions have one or, sometimes, two fairly sharp maxima. These angular PDF maxima are, in most cases, not aligned with the line segments between regime centroids in phase space and might point to heteroclinic or homoclinic connections between unstable equilibria in the model's phase space. Preferred transitions paths are also determined for a stochastically forced Lorenz system to help explain this striking feature of the QG3 model.

The episodic description of the model's low-frequency variability via the Markov chain of multiple regimes is complemented by an oscillatory description. Multichannel singular-spectrum analysis is applied to the trajectory in the same 3D subspace. Two statistically significant oscillations are found and have periods of 19 and 37 days, respectively. Both oscillations have four composites that include NAO+, AO+, and NAO, in this order. The fourth composite occurs between AO+ and NAO; it resembles the Pacific–North American pattern, which is not captured by the model's episodic description. The two oscillations have similar spatial patterns, and are weakly phased locked. They have certain features in common with the westward-propagating Branstator–Kushnir wave, as well as with the standing oscillation that arises from the oscillatory topographic instability of Ghil and associates.

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D. Kondrashov
,
S. Kravtsov
, and
M. Ghil

Abstract

This paper constructs and analyzes a reduced nonlinear stochastic model of extratropical low-frequency variability. To do so, it applies multilevel quadratic regression to the output of a long simulation of a global baroclinic, quasigeostrophic, three-level (QG3) model with topography; the model's phase space has a dimension of O(104).

The reduced model has 45 variables and captures well the non-Gaussian features of the QG3 model's probability density function (PDF). In particular, the reduced model's PDF shares with the QG3 model its four anomalously persistent flow patterns, which correspond to opposite phases of the Arctic Oscillation and the North Atlantic Oscillation, as well as the Markov chain of transitions between these regimes. In addition, multichannel singular spectrum analysis identifies intraseasonal oscillations with a period of 35–37 days and of 20 days in the data generated by both the QG3 model and its low-dimensional analog.

An analytical and numerical study of the reduced model starts with the fixed points and oscillatory eigenmodes of the model's deterministic part and uses systematically an increasing noise parameter to connect these with the behavior of the full, stochastically forced model version. The results of this study point to the origin of the QG3 model's multiple regimes and intraseasonal oscillations and identify the connections between the two types of behavior.

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F-F. Jin
and
M. Ghil

Abstract

A potential vorticity model in a β-channel is used to analyze the resonant response of equivalent-barotropic flow to topography in the presence of a forced zonal jet with arbitrary meridional structure. The nonlinear dynamics near different resonances is studied considering both wave-wave and wave-zonal flow interactions. It is shown that Hopf bifurcations from stationary to periodic flows are possible due to the nonlinear instability of nonzonal, topographically forced flow. Low-frequency, finite-amplitude oscillations arise due to a combination of two factors: (i) nonlinear wave-wave interactions, which tend to reduce the Rossby wave frequency; and (ii) wave-zonal flow interactions, which reflect the importance of wave momentum transport in shifting the westerly jet and of the topographic form drag. The physical mechanism of atmospherically realistic Hopf bifurcations depends crucially on the meridional profile of the mean zonal flow giving rise to a dipole-shaped resonance. The bifurcation phenomena studied here might give some insight into the inherent dynamics of intraseasonal oscillations in the Northern Hemisphere extratropics.

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J-X. Zhao
and
M. Ghil

Abstract

Symmetric inertial instability (SII) is studied here as a mechanism for stratospheric and tropospheric phenomena in the equatorial regions. We investigate the linear and nonlinear dynamics of SII in a two-layer, zonally symmetric model on an equatorial beta plane, in the presence of a basic flow with horizontal and vertical shear, with and without dissipative effects.

Linear symmetric instabilities are, in accordance with previously published results, purely exponential, that is, nonoscillatory. Nonlinear SII, studied here for the first time on a planetary scale, can produce finite-amplitude oscillatory behavior, periodic or chaotic. The period of oscillations in the inviscid case depends on the initial data. In the presence of dissipative effects, all solutions tend to a limit cycle or to a strange attractor. The dominant period in this case, over a wide range of parameters and whether vertical shear is present or not, is in the intraseasonal, 20–30-day range. It appears therefore that nonlinear SII might be a contributing mechanism to low-frequency oscillations in the tropical atmosphere.

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E. Källén
,
C. Crafoord
, and
M. Ghil

Abstract

A study of stable periodic solutions to a simple nonlinear model of the ocean-atmosphere-ice system is presented. The model has two dependent variables: ocean-atmosphere temperature and latitudinal extent of the ice cover. No explicit dependence on latitude is considered in the model. Hence all variables depend only on time and the model consists of a coupled set of nonlinear ordinary differential equations.

The globally averaged ocean-atmosphere temperature in the model is governed by the radiation balance (Budyko, 1969; Sellers, 1969). The reflectivity to incoming solar radiation, i.e., the planetary albedo, includes separate contributions from sea ice and from continental ice sheets. The major physical mechanisms active in the model are 1) albedo-temperature feedback, 2) continental ice-sheet dynamics (Weert-man, 1964, 1976) and 3) precipitation-rate variations.

The model has three equilibrium solutions, two of which are linearly unstable, while one is linearly stable. For some choices of parameters, the stability picture changes and sustained, finite-amplitude oscillations obtain around the previously stable equilibrium solution. The physical interpretation of these oscillations points to the possibility of internal mechanisms playing a role in glaciation cycles.

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A. W. Robertson
,
M. Ghil
, and
M. Latif

Abstract

The response of the Max Planck Institute’s ECHAM3 atmospheric general circulation model to a prescribed decade-long positive anomaly in sea surface temperatures (SSTs) over the North Atlantic is investigated. Two 10-yr realizations of the anomaly experiment are compared against a 100-yr control run of the model with seasonally varying climatological SST using a model spatial resolution of T42. In addition to the time-mean response, particular attention is paid to changes in intraseasonal variability, expressed in terms of North Atlantic–European weather regimes. The model regimes are quite realistic.

Substantial differences are found in the 700-mb geopotential height field response between the two decadal realizations. The time-mean response in the first sample decade is characterized by the positive (zonal) phase of the North Atlantic oscillation (NAO); this response can be identified with changes in the frequency of occurrence of certain weather regimes by about one standard deviation. (Preliminary results of this numerical experiment were reported at the Atlantic Climate Variability Workshop held at the Lamont–Doherty Earth Observatory of Columbia University, Palisades, New York, 24–26 September 1997.) By contrast, the second SST anomaly decade shows a localized trough centered over the British Isles; it projects less strongly onto the model’s intrinsic weather regimes. The control run itself exhibits pronounced decade-to-decade variations in the weather regimes’ frequency of occurrence as well as in its NAO index. The two 10-yr anomaly experiments are insufficient, in length and number, to identify a robust SST response above this level of intrinsic variability.

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S. Kravtsov
,
A. W. Robertson
, and
M. Ghil

Abstract

This paper studies multiple regimes and low-frequency oscillations in the Northern Hemisphere zonal-mean zonal flow in winter, using 55 yr of daily observational data. The probability density function estimated in the phase space spanned by the two leading empirical orthogonal functions exhibits two distinct, statistically significant maxima. The two regimes associated with these maxima describe persistent zonal-flow states that are characterized by meridional displacements of the midlatitude jet, poleward and equatorward of its time-mean position. The geopotential height anomalies of either regime have a pronounced zonally symmetric component, but largest-amplitude anomalies are located over the Atlantic and Pacific Oceans. High-frequency synoptic transients participate in the maintenance of and transitions between these regimes.

Significant oscillatory components with periods of 147 and 72 days are identified by spectral analysis of the zonal-flow time series. These oscillations are described by singular spectrum analysis and the multitaper method. The 147-day oscillation involves zonal-flow anomalies that propagate poleward, while the 72-day oscillation only manifests northward propagation in the Atlantic sector. Both modes mainly describe changes in the midlatitude jet position and intensity. In the horizontal plane though, the two modes exhibit synchronous centers of action located over the Atlantic and Pacific Oceans. The two persistent flow regimes are associated with slow phases of either oscillation.

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S. Kravtsov
,
A. W. Robertson
, and
M. Ghil

Abstract

Atmospheric low-frequency variability (LFV) is studied in a two-layer quasigeostrophic model. The model geometry is a periodic β channel with flat bottom and zonally inhomogeneous thermal forcing. As a result of the idealized land–sea contrast, the model produces a zonally modulated climatological jet with realistic amplitude. The model's LFV is equivalent barotropic; principal component analysis reveals that it consists of (i) dominant stationary patterns with red-noise-like temporal behavior and (ii) propagating waves with periods of 37 and 50 days superimposed on the former.

The vorticity forcing due to synoptic eddies is dominated by self-interaction of high-pass filtered model fields. Applying a phase-randomized, stochastic analog of this forcing to a version of the full model in which fast baroclinic instability and, therefore, synoptic eddies are suppressed, produces a climatology and LFV that are very similar to those in the full model. Synoptic eddies are solely represented in the simplified model version by means of stochastic forcing that is independent of the low-frequency flow. It follows that, while fast synoptic eddies are modulated in the full model by the LFV, this modulation is fairly passive: anomalous generation of the synoptic eddies in the course of the full system's low-frequency evolution, the so-called synoptic-eddy feedback, is not essential in selecting the system's low-frequency modes; the main role of synoptic eddies is to supply energy to these modes.

Further analysis indicates that the LFV in this thermally driven model originates from the barotropic mode's dynamics. The baroclinic mode passively follows, to first order, the low-frequency changes in the barotropic mode. The latter changes are due to stochastically excited, weakly damped linear eigenmodes of the barotropic-mode equation. Two distinct stationary eigenmodes, as well as two pairs of propagating modes with periods of 27 and 36 days, respectively, dominate the low-frequency behavior. The leading empirical orthogonal functions in this model are associated with these six particular eigenmodes. The latter are not well separated, however, from the other eigenmodes in terms of damping time scale, and it is the barotropic nonlinearity that selects the six dynamically important modes over the others. Interactions between these six modes also result in the occurrence of probability density maxima in two-dimensional subspaces of the model's phase space.

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S. Kravtsov
,
A. W. Robertson
, and
M. Ghil

Abstract

The dynamical origin of midlatitude zonal-jet variability is examined in a thermally forced, quasigeostrophic, two-layer channel model on a β plane. The model’s behavior is studied as a function of the bottom-friction strength.

Two distinct zonal-flow states exist at realistic, low, and intermediate values of the bottom drag; these two states are maintained by the eddies and differ mainly in terms of the meridional position of their climatological jets. The system’s low-frequency evolution is characterized by irregular transitions between the two states.

For a given branch of model solutions, the leading stationary and propagating empirical orthogonal functions are related to eigenmodes of the model’s dynamical operator, linearized about the climatological state on this branch. Nonlinear interactions between these modes are instrumental in determining their relative energy level. In particular, the stationary modes’ self-interaction is shown to vanish. Thus, these modes do not exchange energy with the mean flow and, consequently, dominate the lowest-frequency behavior in the model. The leading stationary mode resembles the observed annular mode in the Southern Hemisphere.

The bimodality is due to nonlinear interactions between nearly equivalent barotropic, stationary, and propagating modes, while the synoptic eddies play a modest role in determining the relative persistence of the two states. The role of synoptic eddies is very substantial only at unrealistically high values of the bottom drag, where they give rise to ultralow frequency variability by modifying the jet in a way that reinforces generation of the eddy field. This type of behavior is related to the presence of a homoclinic orbit in the model’s phase space and is not apparent for more realistic, lower values of the bottom drag.

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