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Bruno Deremble
,
Guillaume Lapeyre
, and
Michael Ghil

Abstract

To understand the atmospheric response to a midlatitude oceanic front, this paper uses a quasigeostrophic (QG) model with moist processes. A well-known, three-level QG model on the sphere has been modified to include such processes in an aquaplanet setting. Its response is analyzed in terms of the upper-level atmospheric jet for sea surface temperature (SST) fronts of different profiles and located at different latitudes.

When the SST front is sufficiently strong, it tends to anchor the mean atmospheric jet, suggesting that the jet’s spatial location and pattern are mainly affected by the latitude of the SST front. Changes in the jet’s pattern are studied, focusing on surface sensible heat flux and on moisture effects through latent heat release. It is found that latent heat release due to moist processes is modified when the SST front is changed, and this is responsible for the meridional displacement of the jet. Moreover, both latent heat release and surface sensible heat flux contribute to the jet’s strengthening. These results highlight the role of SST fronts and moist processes in affecting the characteristics of the midlatitude jet stream and of its associated storm track, particularly their positions.

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Yizhak Feliks
,
Michael Ghil
, and
Eric Simonnet

Abstract

This study examines the flow induced by an east–west-oriented oceanic thermal front in a highly idealized baroclinic model. Previous work showed that thermal fronts could produce energetic midlatitude jets in an equivalent-barotropic atmosphere and that barotropic instabilities of this jet had dominant periods of 25–30 and 65–75 days.

The present study extends this work to a two-mode baroclinic free atmosphere. The baroclinic jet produced in this case is subject to both barotropic and baroclinic instabilities. A barotropic symmetric instability propagates westward with periods of roughly 30 days and is similar to those found in the equivalent-barotropic model. A baroclinic instability results in standing-dipole anomalies and oscillates with a period of 6–8 months. A mixed barotropic–baroclinic instability results in anomalies that propagate northward, perpendicular to the jet, with a period of 2–3 months. The later anomalies are reminiscent of the 70-day oscillation found over the North Atlantic in observed fields.

The atmospheric flow has two distinct states: the flow in the high-energy state exhibits two large gyres and a strong eastward jet; its antisymmetric component is dominant. The low-energy flow is characterized by small gyres and a weak jet.

The model’s dynamics depends on the layer-depth ratio. When the model is nearly equivalent-barotropic, symmetric oscillatory modes dominate. As the two layers become nearly equal, antisymmetric oscillatory modes become significant and the mean energy of the flow increases.

When the oceanic thermal front’s strength T* is weak (T* ≤ 1.5°C), the flow is steady. For intermediate values of the strength (1.5°C < T* < 3°C), several oscillatory instabilities set in. As the frontal strength increases further (T* ≥ 3°C), the flow becomes more turbulent. These results all depend on the atmospheric model’s horizontal resolution being sufficiently high.

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Kingtse C. Mo
and
Michael Ghil

Abstract

Persistent anomalies with recurrent spatial patterns play an important role in the atmosphere's low-frequency variability. We establish a connection between statistical and dynamical methods of description and prediction of persistent anomalies. This is done by computing and analyzing the empirical orthogonal functions (EOFs) in a simple deterministic model, on the one hand, and in Southern Hemisphere geopotential heights, on the other.

The dynamical model is governed by the fully nonlinear, equivalent-barotropic vorticity equation on the sphere, with simplified forcing, dissipation and topography. Model solutions exhibit persistent anomalies identifiable with blocked, zonal and wave-train anomalies in Northern Hemisphere atmospheric data. Flow structures similar to the patterns above occur as high-variance EOFs of this nonlinear model.

The Southern Hemisphere data we analyze consist in gridded daily maps of 500 mb heights from June 1972 to July 1983. Two types of persistent anomalies appear in this time series, both having a strong wavenumber-three component; they differ by the value of the constant phase of this wave and by the strength of the wavenumber-one component. The first two EOFs bear a striking resemblance to these two patterns.

We conclude that the dynamical interpretation of EOFs is their pointing from the time mean to the most populated regions of the system's phase space. Pursuing this interpretation, we introduce a Markov-chain formulation of transitions from one persistent anomaly regime to another, and discuss the implications for long-range forecasting.

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Isabella Bordi
,
Klaus Fraedrich
,
Michael Ghil
, and
Alfonso Sutera

Abstract

The atmospheric general circulation is characterized by both single- and double-jet patterns. The double-jet structure of the zonal mean zonal wind is analyzed in Southern Hemisphere observations for the two calendar months of November and April. The observed features are studied further in an idealized quasigeostrophic and a simplified general circulation model (GCM). Results suggest that capturing the bimodality of the zonal mean flow requires the parameterization of momentum and heat fluxes associated with baroclinic instability of the three-dimensional fields.

The role of eddy heat fluxes in generating the observed double-jet pattern is ascertained by using an analytical Eady model with stratospheric easterlies, in which a single wave disturbance interacts with the mean flow. In this model, the dual jets are generated by the zonal mean flow correction. Sensitivity of the results to the tropospheric vertical wind shear (or, equivalently, the meridional temperature gradient in the basic state’s troposphere) is also studied in the Eady model and compared to related experiments using the simplified GCM.

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Yizhak Feliks
,
Andrew W. Robertson
, and
Michael Ghil

Abstract

This paper addresses the effect of interannual variability in jet stream orientation on weather systems over the North Atlantic basin (NAB). The observational analysis relies on 65 yr of NCEP–NCAR reanalysis (1948–2012). The total daily kinetic energy of the geostrophic wind (GTKE) is taken as a measure of storm activity over the North Atlantic. The NAB is partitioned into four rectangular regions, and the winter average of GTKE is calculated for each quadrant. The spatial GTKE average over all four quadrants shows striking year-to-year variability and is strongly correlated with the North Atlantic Oscillation (NAO).

The GTKE strength in the northeast quadrant is closely related to the diffluence angle of the jet stream in the northwest quadrant. To gain insight into the relationship between the diffluence angle and its downstream impact, a quasigeostrophic baroclinic model is used. The results show that an initially zonal jet persists at its initial latitude over 30 days or longer, while a tilted jet propagates meridionally according to the Rossby wave group velocity, unless kept stationary by external forcing.

A Gulf Stream–like narrow sea surface temperature (SST) front provides the requisite forcing for an analytical steady-state solution to this problem. This SST front influences the atmospheric jet in the northwest quadrant: it both strengthens the jet and tilts it northward at higher levels, while its effect is opposite at lower levels. Reanalysis data confirm these effects, which are consistent with thermal wind balance. The results suggest that the interannual variability found in the GTKE may be caused by intrinsic variability of the thermal Gulf Stream front.

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Matthew Huber
,
James C. McWilliams
, and
Michael Ghil

Abstract

The authors present properties of turbulent, meridional mixing along isentropic surfaces within the troposphere. Twice-daily wind fields analyses from the European Centre for Medium-Range Weather Forecasts numerical weather prediction model for 1992 are used to calculate Lagrangian trajectories of large ensembles of particles. The ensemble-averaged rms growth of the meridional relative dispersion over the first 10 days after particle release is used to quantify mixing properties. These properties are considered as a function of height in the atmosphere, season, and geographic region. Results are characterized by release latitude and flow regime and compared with simple theories.

All three dispersive regimes—exponential, ballistic, and Richardson–Obukhov—that have been documented in previous studies are found to be important. The extratropics are found to display superdiffusive growth of the relative rms dispersion, consistent with the nonlocal character of midlatitude mixing. The Tropics are characterized by exponential growth of the rms dispersion, consistent with locally constant eddy timescales. Some evidence for zonal inhomogeneity in dispersion growth rates is found.

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François Lott
,
Andrew W. Robertson
, and
Michael Ghil

Abstract

The NCEP–NCAR reanalysis dataset for 1958–97 is used to analyze intraseasonal variations in mountain torques and the large-scale atmospheric circulation patterns associated with them. Spectral analysis of the atmospheric angular momentum (AAM) budget shows that the dominant variations of mountain torque have periodicities near 30 days and shorter, while the dominant AAM variations occur in the 40–60-day band. This difference is due to the 40–60-day AAM variations being primarily related to equatorial processes, while mountain torque variations are associated mostly with extratropical processes.

The Northern Hemisphere (NH) mountain torque has enhanced power and significant spectral peaks in the 20–30-day band. The signal in this band accounts for 33% of the NH mountain torque variance, once the seasonal cycle has been removed. Lag composites of the NH 700-hPa geopotential heights based on the 20–30-day mountain torque signal show the latter to be associated with coherent large-scale patterns that resemble low-frequency oscillations identified in this band by previous authors. The composite patterns that are in phase quadrature with the 20–30-day NH mountain torque have a pronounced zonally symmetric component. These patterns are associated with substantial AAM variations, arguably driven by the NH mountain torque in this band.

Principal component (PC) analysis of the NH 700-hPa heights shows that, in the 20–30-day band, the mountain torque is also in phase quadrature with the two leading PCs; the first corresponds to changes in the midlatitude jet intensity near the subtropics, while the second corresponds to the Arctic Oscillation. The relationships with AAM of the latter essentially occurs through the mass term. Mountain torques are, furthermore, nearly in phase with dominant patterns of low-frequency variability that exhibit substantial pressure gradients across the Rockies and the Tibetan Plateau.

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François Lott
,
Andrew W. Robertson
, and
Michael Ghil

Abstract

Important aspects of low-frequency variability (LFV) are regional in character, while the mountain torques of the Rockies and the Himalayas evolve quite independently of each other. The hemispheric analysis of Part I is complemented therefore herein by an analysis of the relationships between individual mountain torques and sectorial LFV patterns in the NCEP–NCAR reanalysis.

In the 20–30-day band, relationships are found between the Rockies (Himalayas) torque and the dominant patterns of LFV over the Pacific (Eurasia). The composites of the atmospheric flow fields that accompany the Rockies (Himalayas) torque in this band exhibit similarities with known low-frequency oscillations that dominate the Pacific and North American (European and North Atlantic) sectors during certain winters. The composites keyed to the 20–30-day Rockies torque affect the persistent North Pacific (PNP) pattern that controls the extension of the midlatitude jet stream over the eastern Pacific. Furthermore, the unfiltered torques for the Northern Hemisphere (NH) and Rockies anticipate the onset of the two dominant winter Pacific circulation regimes that correlate strongly with the PNP pattern. The composites keyed to the 20–30-day Himalayas torque affect the North Atlantic Oscillation (NAO) pattern, which controls the intensity of the North Atlantic jet stream. Furthermore, the unfiltered torques for the NH and the Himalayas anticipate the breaks of the two dominant winter Atlantic circulation regimes, which correlate strongly with the NAO pattern.

These analyses also show that the 20–30-day Rockies (Himalayas) torques produce substantial atmospheric angular momentum (AAM) changes, which are nearly in phase with and larger in amplitude than the AAM changes associated with the midlatitude eastern Pacific (North Atlantic) jet stream variations seen in the composite maps. This result suggests that the Rockies (Himalayas) torque variations drive, at least partially, but actively the changes in the eastern Pacific (North Atlantic) jet stream.

These results are consistent with the Himalayas and the Rockies torques contributing separately to changes in the two leading hemispheric EOFs that were described in Part I; the two are associated with a hemispheric index cycle and the Arctic Oscillation, respectively.

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Robert Vautard
,
Kingtse C. Mo
, and
Michael Ghil

Abstract

Low-frequency variability of large-scale atmospheric dynamics can be represented schematically by a Markov chain of multiple flow regimes. This Markov chain contains useful information for the long-range forecaster, provided that the statistical significance of the associated transition matrix can be reliably tested. Monte Carlo simulation yields a very reliable significance test for the elements of this matrix. The results of this test agree with previously used empirical formulae when each cluster of maps identified as a distinct flow regime is sufficiently large and when they all contain a comparable number of maps. Monte Carlo simulation provides a more reliable way to test the statistical significance of transitions to and from small clusters. It can determine the most likely transitions, as well as the most unlikely ones, with a prescribed level of statistical significance.

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Robert N. Miller
,
Michael Ghil
, and
François Gauthiez

Abstract

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence.

Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided.

Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method—based on an empirical statistical model derived from a Monte Carlo simulation-is formulated, and shown to work very well.

Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

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