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Zheng Hao and Michael Ghil

Abstract

A major error source in the numerical simulation of tropical oceans is the uncertainty in wind stress forcing. A reduced-gravity shallow-water model has been used to test how assimilated ocean data correct simulation errors caused by erroneous wind stress in the tropics. The geometry of the basin is rectangular and symmetric about the equator, and the long-wave approximation is applied. All experiments are of the identical-twin type: the “observations” are generated by sampling the desired reference solution, and the data are assimilated by optimal interpolation into the same model, with wind stress forcing different from that in the reference case.

In this paper, three types of wind stress errors are considered: errors of timing only, as well as persistent errors, systematic or stochastic. The relative usefulness of thermocline depth and current observations, and the effect of data distribution on state estimation are examined. The role of equatorial ocean waves in the process of data assimilation is also studied.

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Shi Jiang and Michael Ghil

Abstract

Numerical ocean diagnoses and predictions rely on two types of information: model information and data information. Sequential estimation theory shows that the most probable state is a linear combination of the two, weighted according to their error statistics. A Kalman filter technique is applied to a one-layer reduced-gravity linear ocean model in a rectangular midlatitude basin. The model reproduces the main features of the subtropical wind-driven gyre; the filter is used to study the dynamical behavior of the error statistics.

On a midlatitude f plane, the error-correlation patterns among the state variables revealed by the Kalman filter are isotropic and homogeneous and satisfy a geostrophic relation. Introducing the β effect breaks the isotropy and homogeneity of the correlations, inducing behavior that is in agreement with two observational facts: 1) the latitudinal dependence of horizontal correlations and 2) the elliptic correlation shape of the mass field, elongated along the southwest–northeast orientation in the Northern Hemisphere. When a meridional line of observations is assimilated intermittently, the correlation patterns are dynamically adjusted to be wider to the east of the observing line than to the west. This is due to the westward propagation of errors by the model's Rossby wave dynamics.

The influence function of observations, based on the gain matrix of the Kalman filter, is subjected to polar decomposition into an amplitude part and a vector normalized by the amplitude—that is, a solid angle. The amplitude part contains the current observational information and determines the absolute weight given to an observation. The angular part is related to the previous observations only and reflects the structure of relative weights, whose behavior is similar to that of error correlations.

A criterion measuring the relative importance of different types of observations is defined, using Kalman filter techniques and geostrophic-error assumptions. The results from numerical experiments to examine the correctness of this criterion resolve apparent contradictions among the recent results of R. Daley, M. Ghil, and N. A. Phillips.

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Cécile Penland and Michael Ghil

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.

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Andreas Groth and Michael Ghil

Abstract

Singular spectrum analysis (SSA) along with its multivariate extension (M-SSA) provides an efficient way to identify weak oscillatory behavior in high-dimensional data. To prevent the misinterpretation of stochastic fluctuations in short time series as oscillations, Monte Carlo (MC)–type hypothesis tests provide objective criteria for the statistical significance of the oscillatory behavior. Procrustes target rotation is introduced here as a key method for refining previously available MC tests. The proposed modification helps reduce the risk of type-I errors, and it is shown to improve the test’s discriminating power. The reliability of the proposed methodology is examined in an idealized setting for a cluster of harmonic oscillators immersed in red noise. Furthermore, the common method of data compression into a few leading principal components, prior to M-SSA, is reexamined, and its possibly negative effects are discussed. Finally, the generalized Procrustes test is applied to the analysis of interannual variability in the North Atlantic’s sea surface temperature and sea level pressure fields. The results of this analysis provide further evidence for shared mechanisms of variability between the Gulf Stream and the North Atlantic Oscillation in the interannual frequency band.

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Fei Chen and Michael Ghil

Abstract

A hybrid coupled ocean–atmosphere model is used to investigate low-frequency variability in the climate system. The model's atmospheric component is a Budyko-Sellers-North, two-dimensional energy-balance model; the oceanic component is a simplified general circulation model. The coupled model is confined to an idealized, rectangular North Atlantic basin. In the present model version, the ocean density depends exclusively on temperature.

An interdecadal oscillation with a period of 40–50 years is found in the hybrid coupled model when model parameters are within the climatological range, even though density does not depend on salinity. This interdecadal oscillation is characterized by a pair of vortices of opposite signs, that grow and decay in quadrature with each other in the ocean's upper layer; their centers follow each other anticlockwise through the northwestern quadrant of the model domain.

The interdecadal oscillation's physical mechanism resembles that of the interdecadal oscillation analyzed in an earlier, uncoupled model by the same authors. Central to the mechanism is the prescribed component in the surface heat fluxes. In this coupled model, the prescribed forcing component comes from solar radiation. Surface-density variations in high latitudes drive the oscillation and are due to the cooling effect of atmospheric forcing there.

Sensitivity studies are performed by adjusting two free parameters in the model: the atmospheric thermal diffusion coefficient and air-sea coupling coefficient. The 40–50 year oscillation arises, by Hopf bifurcation as the model parameters cross the neutral stability curve. The resulting limit cycle is fairly robust, exists in a wide parameter range, and responds more to the diffusion parameter than the coupling parameter. Larger values of both parameters reduce the amplitude of the interdecadal oscillation, but neither affects crucially its period.

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Masahide Kimoto and Michael Ghil

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This paper presents an observational analysis of recurrent flow patterns in the Northern Hemisphere (NH) winter, based on a 37-year series of daily 700-mb height anomalies. Large-scale anomaly patterns that appear repeatedly and persist beyond synoptic time scales are identified by searching for local maxima of probability density in a phase subspace, which is spanned by the leading empirical orthogenal functions (EOFs).

By using an angular probability density function (PDF), we focus on the shape, not magnitude, of the anomaly patterns. The PDF estimate is nonparametric; that is, our algorithm makes no a priori assumption on symmetry with respect to the climatological mean as in one-point correlation and rotated EOF analyses. The local density maxima are searched by iterative bump hunting.

Based on observed partial decoupling between the Pacific (PAC) and the Atlantic-Eurasian (ATL) sectors, the classification algorithm is applied separately to each of the two. Seven PAC and six ATL patterns are obtained. Anomaly maps that belong to the neighborhood of each PDF peak are associated with distinct flow regimes. These include regional blocked and zonal flows, and wave train-like anomaly patterns, some of them well known from previous studies, others revealed by our analysis for the first time.

Successive appearances of flow regimes are generally separated by unclassifiable, transient periods. A Markov chain describes transitions between different flow regimes; highly likely, as well as unlikely routes of transition exist. Chains of preferred transitions may be related to the existence of oscillatory modes in the NH extratropics.

A synoptic characterization of onsets and breaks for the flow regimes obtained is given by compositing. In situ evolutions of anomaly patterns, slow westward shifts of high-latitude anomaly centers, and successive down-stream increase of anomaly magnitudes are the typical signatures of such events.

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Nathan Paldor and Michael Ghil

Abstract

The linear instability of a zonal geostrophic jet with a cosh−2 meridional profile on an f plane is investigated in a reduced-gravity, shallow-water model. The stability theory developed here extends classic quasigeostrophic theory to cases where the change of active-layer depth across the jet is not necessarily small. A shooting method is used to integrate the equations describing the cross-stream structure of the alongstream wave perturbations. The phase speeds of these waves are determined by the boundary conditions of regularity at infinity. Regions exist in parameter space where the waves that propagate along the jet will grow exponentially with time. The wavelength of the most unstable waves is 2π R, where R is the internal deformation radius on the deep side, and their e-folding time is about 25 days.

The upper-layer thickness of the basic state in the system has a spatial structure resembling that of the isopycnals across the Gulf Stream. The unstable waves obtained in the present analysis have a wavelength that is in agreement with some recent observations—based on infrared imaging of the sea surface temperature field—of the fastest- growing meanders’ wavelength. Calculated growth rates fall toward the low end of the range of values obtained from these infrared observations on the temporal evolution of Gulf Stream meanders.

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Hisanori Itoh and Michael Ghil

Abstract

Numerical experiments are performed to clarify the excitation mechanism of mixed Rossby-gravity waves (Yanai waves) in the tropical troposphere, as well as the selection of zonal wavenumbers 4–5 and of the five-day period. The model used is governed by the primitive equations on an equatorial β-plane. Moisture budgets are calculated explicitly.

A nonlinear wave-CISK mechanism produces Yanai waves with the same spectral peaks in wavenumber and frequency as observed. In the absence of antisymmetric lateral forcing, these peaks do not appear distinctly, because the symmetric equatorially trapped modes, i.e., Kelvin-like waves having different spectral peaks, are dominant. It is the lateral antisymmetric forcing which puts the peaks characterizing the antisymmetric Yanai waves in evidence.

It appears that Yanai waves of very small wavenumbers (1–3) cannot have large amplitudes because their frequencies are too large for moisture to be effectively supplied for the convection associated with these waves. Symmetric Kelvin modes are dominant in the absence of forcing asymmetries due at least in part to the difference in the nature of heating between symmetric and antisymmetric modes: precipitation, and hence heating, is not normally distributed. Given a strongly skewed distribution of heating, it can be shown that symmetric modes are excited more effectively. Finally, our results indicate that the vertical wavenumber, and hence the period of Yanai waves are selected by the height of cumulus convection, while the lateral forcing selects the horizontal wavenumber within a certain band provided by the nonlinear wave-CISK mechanism.

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Michael Ghil and Kingtse Mo

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.

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Andrew W. Robertson and Michael Ghil

Abstract

Weather regimes are used to determine changes in the statistical distribution of winter precipitation and temperature at eight locations within the western United States. Six regimes are identified from daily 700-mb heights during 46 winters (1949–95) over the North Pacific sector applying cluster analysis; these include the Pacific–North American (PNA) pattern, reverse-PNA, a tropical–Northern Hemisphere (TNH) regime, and a Pacific Ω block. Most of the regimes have a statistically significant effect on the local median temperature, as well as daily temperature extremes; differences between locations are secondary to the large-scale effects. Local precipitation frequency is also conditioned significantly by certain weather regimes, but differences between groups of locations are larger. Precipitation extremes are dispersed and hard to classify. The dependence of local temperature statistics on the warm- or cold-air advection associated with particular weather regimes is discussed, as is the dependence of precipitation anomalies on the regimes’ displaced storm tracks.

The extent to which the El Niño–Southern Oscillation modulates the probability of occurrence of each of the six weather regimes is then investigated. Warm event (El Niño) winters are found to be associated with a significant increase in prevalence of a TNH regime, in which negative height anomalies exhibit a northwest–southeast tilt over the North Pacific. During La Niña winters, this TNH regime occurs significantly less frequently, while a regime characterized by a ridge over southwestern North America becomes more prevalent. These two regimes are associated with regional precipitation-frequency anomalies of opposite sign, that contribute to a north–south contrast in precipitation anomalies over the western United States during El Niño and La Niña winters. On interdecadal timescales, the frequency-of-occurrence of the PNA pattern is found to be notably higher during the 1970s and early 1980s.

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