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Feliks Y, Robertson AW, Ghil M. Interannual Variability in North Atlantic Weather: Data Analysis and a Quasigeostrophic Model. Journal of the Atmospheric Sciences. 2016;73 (8) :3227-3248.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.

Plaut G, Vautard R. Spells of Low-Frequency Oscillations and Weather Regimes in the Northern Hemisphere. Journal of the Atmospheric Sciences. 1994;51 (2) :210–236.Abstract
The low-frequency variability in the midlatitudes is described through an analysis of the oscillatory phenomena. In order to isolate nearly periodic components of the atmospheric flow, the multichannel version of the singular spectrum analysis (M-SSA) is developed and applied to an NMC 32-year long set of 700-hPa geopotential heights. In the same way that principal component analysis identifies the spatial patterns dominating the variability, M-SSA identifies dynamically relevant space?time patterns and provides an adaptive filtering technique. Three major low-frequency oscillations (LFOs) are found, with periods of 70 days, 40?45 days, and 30?35 days. The 70-day oscillation consists of fluctuations in both position and amplitude of the Atlantic jet, with a poleward-propagating anomaly pattern. The 40?45-day oscillation is specific to the Pacific sector and has a pronounced Pacific/North American (PNA) structure in its high-amplitude phase. The 30?35-day mode is confined over the Atlantic region, and consists of the retrogression of a dipole pattern. All these oscillations are shown to be intermittently excited, and M-SSA allows the localization of their spells. The two Atlantic oscillations turn out to be frequently phase locked, so that the 30?35-day mode is likely to be a harmonic of the 70-day mode. The phase locking of the Pacific 40?45-day with the Atlantic 30?35-day oscillations is also studied. Next, the relationships between LFOs and weather regimes are studied. It is shown in particular that the occurrence of the Euro-Atlantic blocking regime is strongly favored, although not systematically caused, by particular phases of the 30?35-day mode. The LFOs themselves are able to produce high-amplitude persistent anomalies by interfering with each other. The transition from a zonal regime to a blocking regime is also shown to be highly connected to the life cycle of the 30?35-day mode, indicating that regime transitions do not result only from the random occurrence of particular transient eddy forcing. There are preferred paths between weather regimes. This result leaves us with the hope that at least the large-scale environment-favoring weather regimes may be forecast in the long range. Conditional probability of occurrence of blocking, 30 days ahead, is enhanced, relative to climatological probability, by a factor of 2 if the phase of the 30?35-day oscillation is known. This also emphasizes the necessity of operational models to represent correctly the extratropical LFOs in order to produce skillful long-range and even medium-range forecasts of weather regimes.
Penland C, Ghil M. Forecasting Northern Hemisphere 700\mbox-mb geopotential height anomalies using empirical normal modes. Monthly Weather Review. 1993;121 (8) :2355–2372.Abstract
Multivariate linear prediction based on single-lag inverse modeling is developed further and critically examined. The method is applied to the National Meteorological Center analyses of Northern Hemisphere 700-mb geopotential height anomalies, which have been filtered to eliminate periods shorter than 10 days. Empirically derived normal modes of the randomly forced linear system are usually correlated, even at zero lag, suggesting that combinations of modes should be used in predictions. Due to nonlinearities in the dynamics and the neglect of interactions with other pressure levels, the lag at which the analysis is performed is crucial; best predictions obtain when the autocovariances involved in the analysis are calculated at a lag comparable to the exponential decay times of the modes. Errors in prediction have a significant seasonal dependence, indicating that the annual cycle affects the higher-order statistics of the field. Optimized linear predictions using this method are useful for about half a day longer than predictions made by persistence. Conditional probabilities are much more efficiently calculated using normal-mode parameters than from histograms, and yield similar results. Maps of the model's Fourier spectra—integrated over specified frequency intervals and consistent with the assumptions made in a linear analysis—agree with maps obtained from fast Fourier transforms of the data.
Kimoto M, Ghil M. Multiple flow regimes in the Northern Hemisphere winter. Part I: Methodology and hemispheric regimes. Journal of the Atmospheric Sciences. 1993;50 (16) :2625–2644.Abstract
Recurrent and persistent flow patterns are identified by examining multivariate probability density functions (PDFs) in the phase space of large-scale atmospheric motions. This idea is pursued systematically here in the hope of clarifying the extent to which intraseasonal variability can be described and understood in terms of multiple flow regimes. Bivariate PDFs of the Northern Hemisphere (NH) wintertime anomaly heights at 700 mb are examined in the present paper, using a 37-year dataset. The two-dimensional phase plane is defined by the two leading empirical orthogonal functions (EOFs) of the anomaly fields. PDFs on this plane exhibit synoptically intriguing and statistically significant inhomogeneities on the periphery of the distribution. It is shown that these inhomogeneities are due to the existence of persistent and recurrent anomaly patterns, well-known as dominant teleconnection patterns; that is, the Pacific/North American (PNA) pattern, its reverse, and zonal and blocked phases of the North Atlantic Oscillation (NAO). It is argued that the inhomogeneities are obscured when PDFs are examined in a smaller-dimensional subspace than dynamically desired.
Ghil M, Mo K. Intraseasonal Oscillations in the Global Atmosphere. Part I: Northern Hemisphere and Tropics. Journal of the Atmospheric Sciences. 1991;48 (5) :752–779.Abstract
We have examined systematically oscillatory modes in the Northern Hemisphere and in the tropics. The 700 mb heights were used to analyze extratropical oscillations, and the outgoing longwave radiation to study tropical oscillations in convection. All datasets were band-pass filtered to focus on the intraseasonal (IS) band of 10-120 days. Leading spatial patterns of variability were obtained by applying EOF analysis to these IS data. The leading principal components (PCs) were subjected to singular spectrum analysis (SSA). SSA is a statistical technique related to EOF analysis, but in the time domain, rather than the spatial domain. It helps identify nonlinear oscillations in short and noisy time series.In the Northern Hemisphere, there are two important modes of oscillation with periods near 48 and 23 days, respectively. The 48-day mode is the most important of the two. It has both traveling and standing components, and is dominated by a zonal wavenumber two. The 23-day mode has the spatial structure and propagation properties described by Branstator and by Kushnir.In the tropics, the 40-50 day oscillation documented by Madden and Julian, Weickmann, Lau, their colleagues, and many other authors dominates the Indian and Pacific oceans from 60°E to the date line. From 170°W to 90°W, however, a 24-28 day oscillation is equally strong. The extratropical modes are often independent of, and sometimes lead, the tropical modes.
Ghil M, Mo K. Intraseasonal Oscillations in the Global Atmosphere. Part II: Southern Hemisphere. Journal of the Atmospheric Sciences. 1991;48 :780–792.Abstract
In Part II of this two-part article, we complete the systematic examination of oscillatory modes in the global atmosphere by studying 12 years of 500 mb geopotential heights in the Southern Hemisphere. As in Part I, for the tropics and Northern Hemisphere extratropics, the data were band-pass filtered to focus on intraseasonal (IS) phenomena, and spatial EOFs were obtained. The leading principal components were subjected to singular spectrum analysis (SSA), in order to identify nonlinear IS oscillations with high statistical confidence.In the Southern Hemisphere, the dominant mode has a period of 23 days, with spatial patterns carried by the second and third winter EOF of the IS band. It has a zonal wavenumber-four structure. The 40-day mode is second, and dominated by wavenumbers three and four, while a 16-day mode is too weak to separate its spatial behavior from the previous two. The IS dynamics in the Southern Hemisphere is more complex and dominated by shorter wavenumbers than the Northern Hemisphere. No statistically significant correlations between the Southern Hemisphere and the tropics or the Northern Hemisphere are apparent in the IS band.
Moron V, Robertson AW, Ghil M. Impact of the modulated annual cycle and intraseasonal oscillation on daily-to-interannual rainfall variability across monsoonal India. Climate Dynamics. 2011 :666.Abstract
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Variability of the Indian summer monsoon is decomposed into an interannually modulated annual cycle (MAC) and a northward-propagating, intraseasonal (30-60-day) oscillation (ISO). To achieve this decomposition, we apply multi-channel singular spectrum analysis (M-SSA) simultaneously to unfiltered daily fields of observed outgoing long-wave radiation (OLR) and to reanalyzed 925-hPa winds over the Indian region, from 1975 to 2008. The MAC is essentially given by the year-to-year changes in the annual and semi-annual components; it displays a slow northward migration of OLR anomalies coupled with an alternation between the northeast winter and southwest summer monsoons. The impact of these oscillatory modes on rainfall is then analyzed using a 1-degree gridded daily data set, focusing on Monsoonal India (north of 17°N and west of 90°E) during the months of June to September. Daily rainfall variability is partitioned into three states using a Hidden Markov Model. Two of these states are shown to agree well with previous classifications of "active" and "break" phases of the monsoon, while the third state exhibits a dipolar east-west pattern with abundant rainfall east of about 77°E and low rainfall to the west. Occurrence of the three rainfall states is found to be an asymmetric function of both the MAC and ISO components. On average, monsoon active phases are favored by large positive anomalies of MAC, and breaks by negative ones. ISO impact is decisive when the MAC is near neutral values during the onset and withdrawal phases of the monsoon. Active monsoon spells are found to require a synergy between the MAC and ISO, while the east-west rainfall dipole is less sensitive to interactions between the two. The driest years, defined from spatially averaged June-September rainfall anomalies, are found to be mostly a result of breaks occurring during the onset and withdrawal stages of the monsoon, e.g., mid-June to mid-July, and during September. These breaks are in turn associated with anomalously late MAC onset or early MAC withdrawal, often together with a large-amplitude, negative ISO event. The occurrence of breaks during the core of the monsoon—from late July to late August—is restricted to a few years when MAC was exceptionally weak, such as 1987 or 2002. Wet years are shown to be mostly associated with more frequent active spells and a stronger MAC than usual, especially at the end of the monsoon season. Taken together, our results suggest that monthly and seasonal precipitation predictability is higher in the early and late stages of the summer monsoon season.

Chekroun MD, Ghil M, Liu H, Wang S. Low-dimensional Galerkin approximations of nonlinear delay differential equations. Discrete and Continuous Dynamical Systems - Series S. 2016;36 (8) :4133-4177.Abstract

This article revisits the approximation problem of systems of nonlinear delay differential equations (DDEs) by a set of ordinary differential equations (ODEs). We work in Hilbert spaces endowed with a natural inner product including a point mass, and introduce polynomials orthogonal with respect to such an inner product that live in the domain of the linear operator associated with the underlying DDE. These polynomials are then used to design a general Galerkin scheme for which we derive rigorous convergence results and show that it can be numerically implemented via simple analytic formulas. The scheme so obtained is applied to three nonlinear DDEs, two autonomous and one forced: (i) a simple DDE with distributed delays whose solutions recall Brownian motion; (ii) a DDE with a discrete delay that exhibits bimodal and chaotic dynamics; and (iii) a periodically forced DDE with two discrete delays arising in climate dynamics. In all three cases, the Galerkin scheme introduced in this article provides a good approximation by low-dimensional ODE systems of the DDE's strange attractor, as well as of the statistical features that characterize its nonlinear dynamics.

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