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A. Hannachi

Abstract

Motivated by the need to understand the nature of the remote atmospheric climate signal associated with El Niño–Southern Oscillation (ENSO), the question is addressed of estimating the nonlinear atmospheric response to ENSO using state-of-the-art general circulation models (GCMs). A set of multidecadal integrations of the Hadley Centre GCM model, HadAM1, is considered and the focus is on the variability of the winter 500-mb heights over the North Pacific and North Atlantic basins. The method is based on optimally filtering the signal out given an estimate of the covariance matrices of the ensemble mean and the internal noise, respectively, and requires that the ensemble mean be split into clusters according to the phase of the Southern Oscillation and then the signal in each cluster found. Over the North Pacific, La Niña appears to trigger the negative Pacific–North American (PNA) oscillation while during El Niño the response is degenerate, that is, with more than one response pattern, where the first one has a zonally stretched PNA-like structure with a north–south seesaw signature and the second one is similar to the tropical Northern Hemisphere pattern. None of them is precisely the reverse of the response corresponding to La Niña (−PNA). A similar behavior is observed over the North Atlantic where a tripole pattern emerges during La Niña, whereas the first pattern obtained during El Niño shows a (tilted) dipole structure with a north–south seesaw.

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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

General circulation models (GCMs) can be used to develop diagnostics for identifying weather regimes. The author has looked for three-dimensional (3D) weather regimes associated with a 10-yr run of the U.K. UGAMP GCM with perpetual January boundary conditions; 3D low-pass empirical orthogonal functions (EOFs), using both the 500- and 250-mb streamfunctions (ψ) have been computed. These EOFs provide a low-order phase space in which weather regimes are studied.

The technique here is an extension to 3D of that of . They found, within the 500-mb ψ EOF phase space, two local minima of area-averaged ψ-tendency (based on barotropic vorticity dynamics), which were identified as ±Pacific–North America (PNA). In this work, the author demands that both the flow and its tendency be within the phase space spanned by the 3D EOFs. The streamfunction tendency is computed from the two-level quasigeostrophic potential vorticity equation and projected onto the EOF phase space. This projection produces a finite dynamical system whose singular points are identified as the quasi-stationary states. Two blocking solutions and one zonal solution are found over the Pacific. The first blocking solution is closer to the west coast of North America than the other blocking, which is shifted slightly westward and has a larger scale, rather similar to the +PNA pattern, indicating that blocking over the Pacific may have two phases in the model. Further investigation of the GCM trajectory within the EOF phase space using a mixture analysis shows the existence of realistic three-dimensional weather regimes similar to the singular points. The same solutions were found when the transient eddy contributions to the climatological quasigeostrophic potential vorticity budget were included. It is also shown that this extended technique allows a direct study of the stability of these quasi-stationary states and helps in drawing transition pictures and determining the transition times between them.

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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

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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A. Hannachi

Abstract

A new spectral-based approach is presented to find orthogonal patterns from gridded weather/climate data. The method is based on optimizing the interpolation error variance. The optimally interpolated patterns (OIP) are then given by the eigenvectors of the interpolation error covariance matrix, obtained using the cross-spectral matrix. The formulation of the approach is presented, and the application to low-dimension stochastic toy models and to various reanalyses datasets is performed. In particular, it is found that the lowest-frequency patterns correspond to largest eigenvalues, that is, variances, of the interpolation error matrix. The approach has been applied to the Northern Hemispheric (NH) and tropical sea level pressure (SLP) and to the Indian Ocean sea surface temperature (SST). Two main OIP patterns are found for the NH SLP representing respectively the North Atlantic Oscillation and the North Pacific pattern. The leading tropical SLP OIP represents the Southern Oscillation. For the Indian Ocean SST, the leading OIP pattern shows a tripole-like structure having one sign over the eastern and north- and southwestern parts and an opposite sign in the remaining parts of the basin. The pattern is also found to have a high lagged correlation with the Niño-3 index with 6-months lag.

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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

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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 and N. Trendafilov

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Conventional analysis methods in weather and climate science (e.g., EOF analysis) exhibit a number of drawbacks including scaling and mixing. These methods focus mostly on the bulk of the probability distribution of the system in state space and overlook its tail. This paper explores a different method, the archetypal analysis (AA), which focuses precisely on the extremes. AA seeks to approximate the convex hull of the data in state space by finding “corners” that represent “pure” types or archetypes through computing mixture weight matrices. The method is quite new in climate science, although it has been around for about two decades in pattern recognition. It encompasses, in particular, the virtues of EOFs and clustering. The method is presented along with a new manifold-based optimization algorithm that optimizes for the weights simultaneously, unlike the conventional multistep algorithm based on the alternating constrained least squares. The paper discusses the numerical solution and then applies it to the monthly sea surface temperature (SST) from HadISST and to the Asian summer monsoon (ASM) using sea level pressure (SLP) from ERA-40 over the Asian monsoon region. The application to SST reveals, in particular, three archetypes, namely, El Niño, La Niña, and a third pattern representing the western boundary currents. The latter archetype shows a particular trend in the last few decades. The application to the ASM SLP anomalies yields archetypes that are consistent with the ASM regimes found in the literature. Merits and weaknesses of the method along with possible future development are also discussed.

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S. Pezzulli, D. B. Stephenson, and A. Hannachi

Abstract

Seasons are the complex nonlinear response of the physical climate system to regular annual solar forcing. There is no a priori reason why they should remain fixed/invariant from year to year, as is often assumed in climate studies when extracting the seasonal component. The widely used econometric variant of Census Method II Seasonal Adjustment Program (X-11), which allows for year-to-year variations in seasonal shape, is shown here to have some advantages for diagnosing climate variability. The X-11 procedure is applied to the monthly mean Niño-3.4 sea surface temperature (SST) index and global gridded NCEP–NCAR reanalyses of 2-m surface air temperature. The resulting seasonal component shows statistically significant interannual variations over many parts of the globe. By taking these variations in seasonality into account, it is shown that one can define less ambiguous ENSO indices. Furthermore, using the X-11 seasonal adjustment approach, it is shown that the three cold ENSO episodes after 1998 are due to an increase in amplitude of seasonality rather than being three distinct La Niña events. Globally, variations in the seasonal component represent a substantial fraction of the year-to-year variability in monthly mean temperatures. In addition, strong teleconnections can be discerned between the magnitude of seasonal variations across the globe. It might be possible to exploit such relationships to improve the skill of seasonal climate forecasts.

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