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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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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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Stefano Pierini, Michael Ghil, and Mickael D. Chekroun

Abstract

A low-order quasigeostrophic double-gyre ocean model is subjected to an aperiodic forcing that mimics time dependence dominated by interdecadal variability. This model is used as a prototype of an unstable and nonlinear dynamical system with time-dependent forcing to explore basic features of climate change in the presence of natural variability. The study relies on the theoretical framework of nonautonomous dynamical systems and of their pullback attractors (PBAs), that is, of the time-dependent invariant sets attracting all trajectories initialized in the remote past. The existence of a global PBA is rigorously demonstrated for this weakly dissipative nonlinear model. Ensemble simulations are carried out and the convergence to PBAs is assessed by computing the probability density function (PDF) of localization of the trajectories. A sensitivity analysis with respect to forcing amplitude shows that the PBAs experience large modifications if the underlying autonomous system is dominated by small-amplitude limit cycles, while less dramatic changes occur in a regime characterized by large-amplitude relaxation oscillations. The dependence of the attracting sets on the choice of the ensemble of initial states is then analyzed. Two types of basins of attraction coexist for certain parameter ranges; they contain chaotic and nonchaotic trajectories, respectively. The statistics of the former does not depend on the initial states whereas the trajectories in the latter converge to small portions of the global PBA. This complex scenario requires separate PDFs for chaotic and nonchaotic trajectories. General implications for climate predictability are finally discussed.

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Yizhak Feliks, Michael Ghil, and Andrew W. Robertson

Abstract

Spectral analyses of the sea surface temperature (SST) in the Simple Ocean Data Analysis (SODA) reanalysis for the past half-century identify prominent and statistically significant interannual oscillations in two regions along the Gulf Stream front over the North Atlantic. A model of the atmospheric marine boundary layer coupled to a baroclinic quasigeostrophic model of the free atmosphere is then forced with the SST history from the SODA reanalysis. Two extreme states are found in the atmospheric simulations: 1) an eastward extension of the westerly jet associated with the front, which occurs mainly during boreal winter, and 2) a quiescent state of very weak flow found predominantly in the summer. This vacillation of the oceanic-front-induced jet in the model is found to exhibit periodicities similar to those identified in the observed Gulf Stream SST front itself. In addition, a close correspondence is found between interannual spectral peaks in the observed North Atlantic Oscillation (NAO) index and the SODA-induced oscillations in the atmospheric model. In particular, significant oscillatory modes with periods of 8.5, 4.2, and 2.8 yr are found in both observed and simulated indices and are shown to be highly synchronized and of similar energy in both time series. These oscillatory modes in the simulations are shown to be suppressed when either (i) the Gulf Stream front or (ii) its interannual oscillations are omitted from the SST field. Moreover, these modes also disappear when (iii) the SST front is spatially smoothed, thus confirming that they are indeed induced by the oceanic front.

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Yizhak Feliks, Michael Ghil, and Andrew W. Robertson

Abstract

Oscillatory climatic modes over the North Atlantic, Ethiopian Plateau, and eastern Mediterranean were examined in instrumental and proxy records from these regions. Aside from the well-known North Atlantic Oscillation (NAO) index and the Nile River water-level records, the authors study for the first time an instrumental rainfall record from Jerusalem and a tree-ring record from the Golan Heights.

The teleconnections between the regions were studied in terms of synchronization of chaotic oscillators. Standard methods for studying synchronization among such oscillators are modified by combining them with advanced spectral methods, including singular spectrum analysis. The resulting cross-spectral analysis quantifies the strength of the coupling together with the degree of synchronization.

A prominent oscillatory mode with a 7–8-yr period is present in all the climatic indices studied here and is completely synchronized with the North Atlantic Oscillation. An energy analysis of the synchronization raises the possibility that this mode originates in the North Atlantic. Evidence is discussed for this mode being induced by the 7–8-yr oscillation in the position of the Gulf Stream front. A mechanism for the teleconnections between the North Atlantic, Ethiopian Plateau, and eastern Mediterranean is proposed, and implications for interannual-to-decadal climate prediction are discussed.

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Blandine L’Hévéder, Francis Codron, and Michael Ghil

Abstract

This paper explores the impact of anomalous northward oceanic heat transport on global climate in a slab ocean setting. To that end, the GCM LMDZ5A of the Laboratoire de Météorologie Dynamique is coupled to a slab ocean, with realistic zonal asymmetries and seasonal cycle. Two simulations with different anomalous surface heating are imposed: 1) uniform heating over the North Atlantic basin and 2) concentrated heating in the Gulf Stream region, with a compensating uniform cooling in the Southern Ocean in both cases. The magnitudes of the heating and of the implied northward interhemispheric heat transport are within the range of current natural variability. Both simulations show global effects that are particularly strong in the tropics, with a northward shift of the intertropical convergence zone (ITCZ) toward the heating anomalies. This shift is accompanied by a northward shift of the storm tracks in both hemispheres. From the comparison between the two simulations with different anomalous surface heating in the North Atlantic, it emerges that the global climate response is nearly insensitive to the spatial distribution of the heating. The cloud response acts as a large positive feedback on the oceanic forcing, mainly because of the low-cloud-induced shortwave anomalies in the extratropics. While previous literature has speculated that the extratropical Q flux may impact the tropics by the way of the transient eddy fluxes, it is explicitly demonstrated here. In the midlatitudes, the authors find a systematic northward shift of the jets, as well as of the associated Ferrel cells, storm tracks, and precipitation bands.

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Yizhak Feliks, Andreas Groth, Andrew W. Robertson, and Michael Ghil

Abstract

This paper explores the three-way interactions between the Indian monsoon, the North Atlantic, and the tropical Pacific. Four climate records were analyzed: the monsoon rainfall in two Indian regions, the Southern Oscillation index for the tropical Pacific, and the NAO index for the North Atlantic. The individual records exhibit highly significant oscillatory modes with spectral peaks at 7–8 yr and in the quasi-biennial and quasi-quadrennial bands.

The interactions between the three regions were investigated in the light of the synchronization theory of chaotic oscillators. The theory was applied here by combining multichannel singular-spectrum analysis (M-SSA) with a recently introduced varimax rotation of the M-SSA eigenvectors.

A key result is that the 7–8-yr and 2.7-yr oscillatory modes in all three regions are synchronized, at least in part. The energy-ratio analysis, as well as time-lag results, suggests that the NAO plays a leading role in the 7–8-yr mode. It was found therewith that the South Asian monsoon is not slaved to forcing from the equatorial Pacific, although it does interact strongly with it. The time-lag analysis pinpointed this to be the case in particular for the quasi-biennial oscillatory modes.

Overall, these results confirm that the approach of synchronized oscillators, combined with varimax-rotated M-SSA, is a powerful tool in studying teleconnections between regional climate modes and that it helps identify the mechanisms that operate in various frequency bands. This approach should be readily applicable to ocean modes of variability and to the problems of air–sea interaction as well.

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Yunyan Zhang, Bjorn Stevens, Brian Medeiros, and Michael Ghil

Abstract

This paper explores the capability of the mixed-layer model (MLM) to represent the observed relationship between low-cloud fraction and lower-tropospheric stability; it also investigates the influence of large-scale meteorological fields and their variability on this relationship. The MLM’s local equilibrium solutions are examined subject to realistic boundary forcings that are derived from data of the 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40). The MLM is successful in reproducing the positive correlation between low-cloud fraction and lower-tropospheric stability. The most accurate relationship emerges when the forcings capture synoptic variability, in particular, the daily varying large-scale divergence is a leading factor in improving the regression slope.

The feature of the results is mainly attributed to the model cloud fraction’s intrinsic nonlinear response to the divergence field. Given this nonlinearity, the full range of divergence must be accounted for since a broad distribution of divergences will give a better cloud fraction overall, although model biases might still affect individual MLM results. The model cloud fraction responds rather linearly to lower-tropospheric stability, and the distribution of the latter is less sensitive to sampling at different time scales than divergence. The strongest relationship between cloud fraction and stability emerges in the range of intermediate stability values. This conditional dependence is evident in both model results and observations. The observed correlation between cloud fraction and stability may thus depend on the underlying distribution of weather noise, and hence may not be appropriate in situations where such statistics can be expected to change.

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Andreas Groth, Yizhak Feliks, Dmitri Kondrashov, and Michael Ghil

Abstract

Spectral analyses of the North Atlantic temperature field in the Simple Ocean Data Analysis (SODA) reanalysis identify prominent and statistically significant interannual oscillations along the Gulf Stream front and in large regions of the North Atlantic. A 7–8-yr oscillatory mode is characterized by a basinwide southwest-to-northeast–oriented propagation pattern in the sea surface temperature (SST) field. This pattern is found to be linked to a seesaw in the meridional dipole structure of the zonal wind stress forcing (TAUX). In the subpolar gyre, the SST and TAUX fields of this mode are shown to be in phase opposition, which suggests a cooling effect of the wind stress on the upper ocean layer. Over all, this mode’s temperature field is characterized by a strong equivalent-barotropic component, as shown by covariations in SSTs and sea surface heights, and by phase-coherent behavior of temperature layers at depth with the SST field. Recent improvements of multivariate singular spectrum analysis (M-SSA) help separate spatiotemporal patterns. This methodology is developed further and applied to studying the ocean’s response to variability in the atmospheric forcing. Statistical evidence is shown to exist for other mechanisms generating oceanic variability of similar 7–8-yr periodicity in the Gulf Stream region; the latter variability is likewise characterized by a strongly equivalent-barotropic component. Two other modes of biennial variability in the Gulf Stream region are also identified, and it is shown that interannual variability in this region cannot be explained by the ocean’s response to similar variability in the atmospheric forcing alone.

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Brian H. Kahn, Annmarie Eldering, Michael Ghil, Simona Bordoni, and Shepard A. Clough

Abstract

A set of simulated high-resolution infrared (IR) emission spectra of synthetic cirrus clouds is used to perform a sensitivity analysis of top-of-atmosphere (TOA) radiance to cloud parameters. Principal component analysis (PCA) is applied to assess the variability of radiance across the spectrum with respect to microphysical and bulk cloud quantities. These quantities include particle shape, effective radius (r eff), ice water path (IWP), cloud height Z cld and thickness ΔZ cld, and vertical profiles of temperature T(z) and water vapor mixing ratio w(z). It is shown that IWP variations in simulated cloud cover dominate TOA radiance variability. Cloud height and thickness, as well as T(z) variations, also contribute to considerable TOA radiance variability.

The empirical orthogonal functions (EOFs) of radiance variability show both similarities and differences in spectral shape and magnitude of variability when one physical quantity or another is being modified. In certain cases, it is possible to identify the EOF that represents variability with respect to one or more physical quantities. In other instances, similar EOFs result from different sets of physical quantities, emphasizing the need for multiple, independent data sources to retrieve cloud parameters. When analyzing a set of simulated spectra that include joint variations of IWP, r eff, and w(z) across a realistic range of values, the first two EOFs capture approximately 92%–97% and 2%–6% of the total variance, respectively; they reflect the combined effect of IWP and r eff. The third EOF accounts for only 1%–2% of the variance and resembles the EOF from analysis of spectra where only w(z) changes. Sensitivity with respect to particle size increases significantly for r eff several tens of microns or less. For small-particle r eff, the sensitivity with respect to the joint variation of IWP, r eff, and w(z) is well approximated by the sum of the sensitivities with respect to variations in each of three quantities separately.

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