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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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Padhraic Smyth, Kayo Ide, and Michael Ghil

Abstract

A mixture model is a flexible probability density estimation technique, consisting of a linear combination of k component densities. Such a model is applied to estimate clustering in Northern Hemisphere (NH) 700-mb geopotential height anomalies. A key feature of this approach is its ability to estimate a posterior probability distribution for k, the number of clusters, given the data and the model. The number of clusters that is most likely to fit the data is thus determined objectively.

A dataset of 44 winters of NH 700-mb fields is projected onto its two leading empirical orthogonal functions (EOFs) and analyzed using mixtures of Gaussian components. Cross-validated likelihood is used to determine the best value of k, the number of clusters. The posterior probability so determined peaks at k = 3 and thus yields clear evidence for three clusters in the NH 700-mb data. The three-cluster result is found to be robust with respect to variations in data preprocessing and data analysis parameters. The spatial patterns of the three clusters’ centroids bear a high degree of qualitative similarity to the three clusters obtained independently by Cheng and Wallace, using hierarchical clustering on 500-mb NH winter data: the Gulf of Alaska ridge, the high over southern Greenland, and the enhanced climatological ridge over the Rockies.

Separating the 700-mb data into Pacific (PAC) and Atlantic (ATL) sector maps reveals that the optimal k value is 2 for both the PAC and ATL sectors. The respective clusters consist of Kimoto and Ghil’s Pacific–North American (PNA) and reverse PNA regimes, as well as the zonal and blocked phases of the North Atlantic oscillation. The connections between our sectorial and hemispheric results are discussed from the perspective of large-scale atmospheric dynamics.

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Christopher Strong, Fei-fei Jin, and Michael Ghil

Abstract

Observational and modeling studies have shown that intraseasonal, 40-day oscillations over the Northern Hemisphere extratropics are strongest around the winter season. To explore intraseasonal variability in the presence of the annual cycle, an eigenanalysis method based on Floquet theory is used. This approach helps us determine the stability of the large-scale, midlatitude atmospheric flow's periodic basic state. It gives information about the growth rate of the unstable, intraseasonal eigenmode and confirms the atmosphere's preference for intraseasonal activity during the winter months, as the annual cycle modulates the eigenvector field.

This eigenmode solution, furthermore, provides a basis for making extended-range (40-day) streamfunction-anomaly forecasts on a set of intraseasonal oscillations whose amplitude and phase depend on the season. A simple autoregressive model is developed to shed light on the seasonal dependence of predictive skill for the intraseasonal signal.

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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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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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Yizhak Feliks, Michael Ghil, and Eric Simonnet

Abstract

This study examines the flow induced in a highly idealized atmospheric model by an east–west-oriented oceanic thermal front. The model has a linear marine boundary layer coupled to a quasigeostrophic, equivalent- barotropic free atmosphere. The vertical velocity at the top of the boundary layer drives the flow in the free atmosphere and produces an eastward jet, parallel to the oceanic front's isotherms. A large gyre develops on either side of this jet, cyclonic to the north and anticyclonic to the south of it. As the jet intensifies during spinup from rest, it becomes unstable. The most unstable wave has a length of about 500 km, it evolves into a meander, and eddies detach from the eastern edge of each gyre.

The dependence of the atmospheric dynamics on the strength T∗ of the oceanic front is studied. The Gulf Stream and Kuroshio fronts correspond roughly, in the scaling used here, to T∗ ≅ 7°C. For weak fronts, T∗ ≤ 4°C, the circulation is steady and exhibits two large, antisymmetric gyres separated by a westerly zonal jet. As the front strengthens, 4 < T∗ < 5, the solution undergoes Hopf bifurcation to become periodic in time, with a period of 30 days, and spatially asymmetric. The bifurcation is due to the westerly jet's barotropic instability, which has a symmetric spatial pattern. The addition of this pattern to the antisymmetric mean results in the overall asymmetry of the full solution. The spatial scale and amplitude of the symmetric, internally generated, and antisymmetric, forced mode increase with the strength T∗ of the oceanic front. For T∗ ≥ 5°C, the solution becomes chaotic, but a dominant period still stands out above the broadband noise. This dominant period increases with T∗ overall, but the increase is not monotonic.

The oceanic front's intensity dictates the mean speed of the atmospheric jet. Two energy regimes are obtained. 1) In the low-energy regime, the SST front, and hence the atmospheric jet, are weak; in this regime, small meanders develop along the jet axis, and the dominant period is about 25 days. 2) In the high-energy regime, the SST front and the jet are strong; in it, large meanders and eddies develop along the jet, and the dominant oscillation has a period of about 70 days. The physical nature of the two types of oscillations is discussed, as are possible transitions between them when T∗ changes on very long time scales. The results are placed in the context of previous theories of ocean front effects on atmospheric flows, in which baroclinic phenomena are dominant.

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Michael Ghil, Boris Shkoller, and Victor Yangarber

Abstract

We derive a system of diagnostic equations for the velocity field, or “wind laws,” for a barotropic primitive-equation model of large-scale atmospheric flow. The derivation is mathematically exact and does not involve any physical assumptions, such as nondivergence or vanishing of derivatives of the divergence, which are not already present in the prognostic equations. Therefore, initial states computed by solving these diagnostic equations should be compatible with the type of motion described by the prognostic equations of the model, and should not generate initialization shocks when inserted into the prognostic model.

Based on the diagnostic system obtained, we are able to give precise meaning to the question whether the wind field is determined by the mass field and by its time history. The answer to this important question is affirmative, in the precise formulation we provide.

The diagnostic system corresponding to the chosen barotropic model is a generalization of the classical balance equation. The ellipticity condition for this system is derived and given a physical interpretation. Numerical solutions of the diagnostic system are exhibited, including cases in-which the system is of mixed elliptic-hyperbolic type.

Such diagnostic systems can be obtained for other primitive equation models. They are valid for all atmospheric scales and regions for which the prognostic models from which they are derived hold. Some problems concerning the possibility of implementing such a system in operational numerical weather prediction are discussed.

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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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Yizhak Feliks, Michael Ghil, and Andrew W. Robertson

Abstract

Oscillatory climatic modes over the North Atlantic, Ethiopian Plateau, and eastern Mediterranean were examined in instrumental and proxy records from these regions. Aside from the well-known North Atlantic Oscillation (NAO) index and the Nile River water-level records, the authors study for the first time an instrumental rainfall record from Jerusalem and a tree-ring record from the Golan Heights.

The teleconnections between the regions were studied in terms of synchronization of chaotic oscillators. Standard methods for studying synchronization among such oscillators are modified by combining them with advanced spectral methods, including singular spectrum analysis. The resulting cross-spectral analysis quantifies the strength of the coupling together with the degree of synchronization.

A prominent oscillatory mode with a 7–8-yr period is present in all the climatic indices studied here and is completely synchronized with the North Atlantic Oscillation. An energy analysis of the synchronization raises the possibility that this mode originates in the North Atlantic. Evidence is discussed for this mode being induced by the 7–8-yr oscillation in the position of the Gulf Stream front. A mechanism for the teleconnections between the North Atlantic, Ethiopian Plateau, and eastern Mediterranean is proposed, and implications for interannual-to-decadal climate prediction are discussed.

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