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A. Hannachi

Abstract

Investigation of preferred structures of planetary wave dynamics is addressed using multivariate Gaussian mixture models. The number of components in the mixture is obtained using order statistics of the mixing proportions, hence avoiding previous difficulties related to sample sizes and independence issues. The method is first applied to a few low-order stochastic dynamical systems and data from a general circulation model. The method is next applied to winter daily 500-hPa heights from 1949 to 2003 over the Northern Hemisphere. A spatial clustering algorithm is first applied to the leading two principal components (PCs) and shows significant clustering. The clustering is particularly robust for the first half of the record and less for the second half. The mixture model is then used to identify the clusters. Two highly significant extratropical planetary-scale preferred structures are obtained within the first two to four EOF state space. The first pattern shows a Pacific–North American (PNA) pattern and a negative North Atlantic Oscillation (NAO), and the second pattern is nearly opposite to the first one. It is also observed that some subspaces show multivariate Gaussianity, compatible with linearity, whereas others show multivariate non-Gaussianity. The same analysis is also applied to two subperiods, before and after 1978, and shows a similar regime behavior, with a slight stronger support for the first subperiod. In addition a significant regime shift is also observed between the two periods as well as a change in the shape of the distribution. The patterns associated with the regime shifts reflect essentially a PNA pattern and an NAO pattern consistent with the observed global warming effect on climate and the observed shift in sea surface temperature around the mid-1970s.

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A. Hannachi

Abstract

Sectorial and planetary-scale winter circulation regimes are studied and the relationship between them is investigated in order to find how much the simultaneous occurrence of sectorial regimes contributes to the occurrence of hemispheric regimes. The strategy is based on the multivariate Gaussian mixture model. The number of components in the model is estimated using two approaches. The first one is based on arguments from order statistics of the mixture proportions and the second uses a more severe test based on reproducibility. The procedure is applied next to the 500-hPa height field over the North Pacific, the North Atlantic, and the Northern Hemisphere using the empirical orthogonal function state space. Two highly significant regimes are found in each case, namely, the Pacific–North America (pattern) (±PNA)–North Atlantic Oscillation (±NAO) for the hemisphere—±PNA for the Pacific sector and ±NAO for the Atlantic sector. The sectorial regimes reflect mainly blocking and no-blocking flows. The results are tested further by applying a spatial clustering algorithm and are found to be consistent, particularly along the regime axes in the system state space. The relationship between hemispheric and sectorial circulation regimes is investigated. The data in each sector are first classified and then the times of simultaneous occurrence of sectorial regimes are identified. A new hemispheric dataset is then obtained by discarding maps corresponding to those co-occurrence times, and a new regime analysis is conducted. The results show that the hemispheric regime behavior has significantly decreased, suggesting that synchronization between sectorial circulation regimes could play an important role in the occurrence of planetary circulation regimes. The interannual variability of regime events is also discussed.

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A. Hannachi

Abstract

The Pacific weather regimes found by Haines and Hannachi from a GCM perpetual January 10-year run, identified as ±Pacific–North American (PNA), are examined for stability both within a model-derived EOF phase space and the full phase space for the 500-mb flow level. The authors also examine the behavior of the 500-mb streamfunction tendency based on the barotropic vorticity equation model projected onto the EOF phase space. Normal mode and nonnormal mode analysis of these regimes are performed. It is shown in particular that the +PNA state is less stable than the −PNA, which can explain previous results concerning the greater robustness in finding the −PNA state as a fixed point in the attractor. Of particular interest is the local character of the +PNA regime, which indicates fast growth rates within the EOF phase space of the order 3–4 days.

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K. Haines
and
A. Hannachi

Abstract

Weather regimes have been sought by examining the 500-mb streamfunction of the UGAMP GCM run for 10 yr at T42 resolution with perpetual January forcing. Five-day low-pass EOFs provide a low-order phase space in which to study dynamical aspects of the variability. The PNA pattern shows up as the first EOF over the Northern Hemisphere representing 12% of the variance, rising to 18.5% for Pacific-area-only EOFs.

Within the phase space of three to five EOFs, two local minima of the area-averaged ψ tendency (based on rotational velocity advection) are found. These two flow patterns both have a smaller implied tendency than the climatology and lie in the ±PNA regions of the phase space. It is suggested that these patterns may be acting as “fixed points” within the atmospheric attractor, encouraging persistent flows and the formation of weather regimes. These dynamical attracting points are compared with a more conventional means of identifying weather regimes using a statistical maximum likelihood analysis of all model states during the 10-yr GCM run. This analysis also indicates two preferred classes, separate from the climatology, in the ±PNA regions of phase space. These classes tend to be nearer the climatology than the dynamical states but have similar appearance otherwise.

Finally the role of low-frequency transients are examined to improve the dynamical interpretation of the regime centers. The method is first demonstrated for the extended Lorenz model of Molteni et al. The fixed points of the GCM attractor are assumed to be steady solutions to the 500-mb vorticity equation in the absence of contributions from transient eddies. The eddy contributions to the climatological vorticity budget are first determined, and then the deviations from the climatology that could provide similar contributions to the budget are found. Again two states in the ±PNA regions of phase space are found to satisfy the above conditions. The authors speculate that the attractors themselves are determined by the large-scale steady effects of topography and land-sea contrasts.

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A. Hannachi
and
W. Iqbal

Abstract

Nonlinearity in the Northern Hemisphere’s wintertime atmospheric flow is investigated from both an intermediate-complexity model of the extratropics and reanalyses. A long simulation is obtained using a three-level quasigeostrophic model on the sphere. Kernel empirical orthogonal functions (EOFs), which help delineate complex structures, are used along with the local flow tendencies. Two fixed points are obtained, which are associated with strong bimodality in two-dimensional kernel principal component (PC) space, consistent with conceptual low-order dynamics. The regimes reflect zonal and blocked flows. The analysis is then extended to ERA-40 and JRA-55 using daily sea level pressure (SLP) and geopotential heights in the stratosphere (20 hPa) and troposphere (500 hPa). In the stratosphere, trimodality is obtained, representing disturbed, displaced, and undisturbed states of the winter polar vortex. In the troposphere, the probability density functions (PDFs), for both fields, within the two-dimensional (2D) kernel EOF space are strongly bimodal. The modes correspond broadly to opposite phases of the Arctic Oscillation with a signature of the negative North Atlantic Oscillation (NAO). Over the North Atlantic–European sector, a trimodal PDF is also obtained with two strong and one weak modes. The strong modes are associated, respectively, with the north (or +NAO) and south (or −NAO) positions of the eddy-driven jet stream. The third weak mode is interpreted as a transition path between the two positions. A climate change signal is also observed in the troposphere of the winter hemisphere, resulting in an increase (a decrease) in the frequency of the polar high (low), consistent with an increase of zonal flow frequency.

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A. Hannachi
,
D. Mitchell
,
L. Gray
, and
A. Charlton-Perez

Abstract

The polar winter stratospheric vortex is a coherent structure that undergoes different types of deformation that can be revealed by the geometric invariant moments. Three moments are used—the aspect ratio, the centroid latitude, and the area of the vortex based on stratospheric data from the 40-yr ECMWF Re-Analysis (ERA-40) project—to study sudden stratospheric warmings. Hierarchical clustering combined with data image visualization techniques is used as well. Using the gap statistic, three optimal clusters are obtained based on the three geometric moments considered here. The 850-K potential vorticity field, as well as the vertical profiles of polar temperature and zonal wind, provides evidence that the clusters represent, respectively, the undisturbed (U), displaced (D), and split (S) states of the polar vortex. This systematic method for identifying and characterizing the state of the polar vortex using objective methods is useful as a tool for analyzing observations and as a test for climate models to simulate the observations. The method correctly identifies all previously identified major warmings and also identifies significant minor warmings where the atmosphere is substantially disturbed but does not quite meet the criteria to qualify as a major stratospheric warming.

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