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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

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

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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A. Hannachi
and
N. Trendafilov

Abstract

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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A. Hannachi
,
S. Unkel
,
N. T. Trendafilov
, and
I. T. Jolliffe

Abstract

The complexity inherent in climate data makes it necessary to introduce more than one statistical tool to the researcher to gain insight into the climate system. Empirical orthogonal function (EOF) analysis is one of the most widely used methods to analyze weather/climate modes of variability and to reduce the dimensionality of the system. Simple structure rotation of EOFs can enhance interpretability of the obtained patterns but cannot provide anything more than temporal uncorrelatedness. In this paper, an alternative rotation method based on independent component analysis (ICA) is considered. The ICA is viewed here as a method of EOF rotation. Starting from an initial EOF solution rather than rotating the loadings toward simplicity, ICA seeks a rotation matrix that maximizes the independence between the components in the time domain. If the underlying climate signals have an independent forcing, one can expect to find loadings with interpretable patterns whose time coefficients have properties that go beyond simple noncorrelation observed in EOFs. The methodology is presented and an application to monthly means sea level pressure (SLP) field is discussed. Among the rotated (to independence) EOFs, the North Atlantic Oscillation (NAO) pattern, an Arctic Oscillation–like pattern, and a Scandinavian-like pattern have been identified. There is the suggestion that the NAO is an intrinsic mode of variability independent of the Pacific.

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Christopher A. T. Ferro
,
Abdelwaheb Hannachi
, and
David B. Stephenson

Abstract

Anthropogenic influences are expected to cause the probability distribution of weather variables to change in nontrivial ways. This study presents simple nonparametric methods for exploring and comparing differences in pairs of probability distribution functions. The methods are based on quantiles and allow changes in all parts of the probability distribution to be investigated, including the extreme tails. Adjusted quantiles are used to investigate whether changes are simply due to shifts in location (e.g., mean) and/or scale (e.g., variance). Sampling uncertainty in the quantile differences is assessed using simultaneous confidence intervals calculated using a bootstrap resampling method that takes account of serial (intraseasonal) dependency. The methods are simple enough to be used on large gridded datasets. They are demonstrated here by exploring the changes between European regional climate model simulations of daily minimum temperature and precipitation totals for winters in 1961–90 and 2071–2100. Projected changes in daily precipitation are generally found to be well described by simple increases in scale, whereas minimum temperature exhibits changes in both location and scale.

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