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Christian Franzke

Abstract

The dynamics of low-frequency variability is investigated in terms of sensitivity to the dependence of its relative zonal position of a single storm track in a simplified global circulation model. A streamfunction tendency equation is derived that explicitly distinguishes between barotropic and baroclinic components. One of the two low-frequency patterns located in the center of the storm track grows barotropically, and its decay is accomplished by low-frequency eddy vorticity fluxes and the baroclinic contribution to the divergence term. The growth and decay of the second pattern, located at the downstream end of the storm track, is dominated by nonlinear processes. This indicates that the dynamical processes leading to growth and decay of low-frequency patterns depend on the zonal position of the low-frequency pattern relative to a storm track.

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Christian Franzke

Abstract

This study examines the long-range dependency, climate noise characteristics, and nonlinear temperature trends of eight Antarctic stations from the Reference Antarctic Data for Environmental Research (READER) dataset. Evidence is shown that Antarctic temperatures are long-range dependent. To identify possible nonlinear trends, the ensemble empirical mode decomposition (EEMD) method is used, and then the question of whether the observed trends can arise from internal atmospheric fluctuations is examined. To answer this question, surrogate data are generated from two paradigmatic null models: a standard first-order autoregressive process representing a short-range dependent process and a fractional integrated process representing a long-range dependent process. It is found that three of the eight stations show statistically significant trends when tested against the short-range dependent process while only the Faraday–Vernadsky station temperature time series shows a significant trend when tested against the long-range dependent null model. All other considered stations show no trends that are statistically significant against the two null models, and thus they can be explained by internal atmospheric variability. These results imply that more attention should be given to assessing the correlation structure of climate time series.

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Christian Franzke

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This study investigates the significance of trends of four temperature time series—Central England Temperature (CET), Stockholm, Faraday-Vernadsky, and Alert. First the robustness and accuracy of various trend detection methods are examined: ordinary least squares, robust and generalized linear model regression, Ensemble Empirical Mode Decomposition (EEMD), and wavelets. It is found in tests with surrogate data that these trend detection methods are robust for nonlinear trends, superposed autocorrelated fluctuations, and non-Gaussian fluctuations. An analysis of the four temperature time series reveals evidence of long-range dependence (LRD) and nonlinear warming trends. The significance of these trends is tested against climate noise. Three different methods are used to generate climate noise: (i) a short-range-dependent autoregressive process of first order [AR(1)], (ii) an LRD model, and (iii) phase scrambling. It is found that the ability to distinguish the observed warming trend from stochastic trends depends on the model representing the background climate variability. Strong evidence is found of a significant warming trend at Faraday-Vernadsky that cannot be explained by any of the three null models. The authors find moderate evidence of warming trends for the Stockholm and CET time series that are significant against AR(1) and phase scrambling but not the LRD model. This suggests that the degree of significance of climate trends depends on the null model used to represent intrinsic climate variability. This study highlights that in statistical trend tests, more than just one simple null model of intrinsic climate variability should be used. This allows one to better gauge the degree of confidence to have in the significance of trends.

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Christian Franzke and Tim Woollings

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The persistence and climate noise properties of North Atlantic climate variability are of importance for trend identification and assessing predictability on all time scales from several days to many decades. Here, the authors analyze these properties by applying empirical mode decomposition to a time series of the latitude of the North Atlantic eddy-driven jet stream. In previous studies, it has been argued that a slow decay of the autocorrelation function at large lags suggests potential extended-range predictability during the winter season. The authors show that the increased autocorrelation time scale does not necessarily lead to enhanced intraseasonal predictive skill. They estimate the fraction of interannual variability that likely arises due to climate noise as 43%–48% in winter and 70%–71% in summer. The analysis also indentifies a significant poleward trend of the jet stream that cannot be explained as arising from climate noise. These findings have important implications for the predictability of North Atlantic climate variability.

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Christian Franzke and Steven B. Feldstein

Abstract

This study presents an alternative interpretation for Northern Hemisphere teleconnection patterns. Rather than comprising several different recurrent regimes, this study suggests that there is a continuum of teleconnection patterns. This interpretation indicates either that 1) all members of the continuum can be expressed in terms of a linear combination of a small number of real physical modes that correspond to basis functions or 2) that most low-frequency patterns within the continuum are real physical patterns, each having its own spatial structure and frequency of occurrence.

Daily NCEP–NCAR reanalysis data are used that cover the boreal winters of 1958–97. A set of nonorthogonal basis functions that span the continuum is derived. The leading basis functions correspond to well-known patterns such as the Pacific–North American teleconnection and North Atlantic Oscillation. Evidence for the continuum perspective is based on the finding that 1) most members of the continuum tend to have similar variance and autocorrelation time scales and 2) that members of the continuum show dynamical characteristics that are intermediate between those of the surrounding basis functions. The latter finding is obtained by examining the streamfunction tendency equation both for the basis functions and some members of the continuum.

The streamfunction tendency equation analysis suggests that North Pacific patterns (basis functions and continuum) are primarily driven by their interaction with the climatological stationary eddies and that North Atlantic patterns are primarily driven by transient eddy vorticity fluxes. The decay mechanism for all patterns is similar, being due to the impact of low-frequency (period greater than 10 days) transient eddies and horizontal divergence. Analysis with outgoing longwave radiation shows that tropical convection is found to play a much greater role in exciting North Pacific patterns. A plausible explanation for these differences between the North Atlantic and North Pacific patterns is presented.

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Christian Franzke and Andrew J. Majda

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This study applies a systematic strategy for stochastic modeling of atmospheric low-frequency variability to a three-layer quasigeostrophic model. This model climate has reasonable approximations of the North Atlantic Oscillation (NAO) and Pacific–North America (PNA) patterns. The systematic strategy consists first of the identification of slowly evolving climate modes and faster evolving nonclimate modes by use of an empirical orthogonal function (EOF) decomposition in the total energy metric. The low-order stochastic climate model predicts the evolution of these climate modes a priori without any regression fitting of the resolved modes. The systematic stochastic mode reduction strategy determines all correction terms and noises with minimal regression fitting of the variances and correlation times of the unresolved modes. These correction terms and noises account for the neglected interactions between the resolved climate modes and the unresolved nonclimate modes. Low-order stochastic models with 10 or less resolved modes capture the statistics of the original model very well, including the variances and temporal correlations with high pattern correlations of the transient eddy fluxes. A budget analysis establishes that the low-order stochastic models are highly nonlinear with significant contributions from both additive and multiplicative noise. This is in contrast to previous stochastic modeling studies. These studies a priori assume a linear model with additive noise and regression fit the resolved modes. The multiplicative noise comes from the advection of the resolved modes by the unresolved modes. The most straightforward low-order stochastic climate models experience climate drift that stems from the bare truncation dynamics. Even though the geographic correlation of the transient eddy fluxes is high, they are underestimated by a factor of about 2 in the a priori procedure and thus cannot completely overcome the large climate drift in the bare truncation. Also, variants of the reduced stochastic modeling procedure that experience no climate drift with good predictions of both the variances and time correlations are discussed. These reduced models without climate drift are developed by slowing down the dynamics of the bare truncation compared with the interactions with the unresolved modes and yield a minimal two-parameter regression fitting strategy for the climate modes. This study points to the need for better optimal basis functions that optimally capture the essential slow dynamics of the system to obtain further improvements for the reduced stochastic modeling procedure.

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Steven B. Feldstein and Christian Franzke

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This study addresses the question of whether persistent events of the North Atlantic Oscillation (NAO) and the Northern Annular Mode (NAM) teleconnection patterns are distinguishable from each other. Standard daily index time series are used to specify the amplitude of the NAO and NAM patterns. The above question is examined with composites of sea level pressure, and 300- and 40-hPa streamfunction, along with tests of field significance.

A null hypothesis is specified that the NAO and NAM persistent events are indistinguishable. This null hypothesis is evaluated by calculating the difference between time-averaged NAO and NAM composites. It is found that the null hypothesis cannot be rejected even at the 80% confidence level. The wave-breaking characteristics during the NAM life cycle are also examined. Both the positive and negative NAM phases yield the same wave-breaking properties as those for the NAO.

The results suggest that not only are the NAO and NAM persistent events indistinguishable, but that the NAO/NAM events are neither confined to the North Atlantic, nor are they annular.

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Christian Franzke, Tim Woollings, and Olivia Martius

Abstract

The persistent regime behavior of the eddy-driven jet stream over the North Atlantic is investigated. The North Atlantic jet stream variability is characterized by the latitude of the maximum lower tropospheric wind speed of the 40-yr ECMWF Re-Analysis (ERA-40) data for the period 1 December 1957–28 February 2002. A hidden Markov model (HMM) analysis reveals that the jet stream exhibits three persistent regimes that correspond to northern, southern, and central jet states. The regime states are closely related to the North Atlantic Oscillation and the eastern Atlantic teleconnection pattern. The regime states are associated with distinct changes in the storm tracks and the frequency of occurrence of cyclonic and anticyclonic Rossby wave breaking. Three preferred regime transitions are identified, namely, southern to central jet, northern to southern jet, and central to northern jet. The preferred transitions can be interpreted as a preference for poleward propagation of the jet, but with the southern jet state entered via a dramatic shift from the northern state. Evidence is found that wave breaking is involved in two of the three preferred transitions (northern to southern jet and central to northern jet transitions). The predictability characteristics and the interannual variability in the frequency of occurrence of regimes are also discussed.

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Christian Franzke, Andrew J. Majda, and Grant Branstator

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Mean phase space tendencies are investigated to systematically identify the origin of nonlinear signatures and the dynamical significance of small deviations from Gaussianity of planetary low-frequency waves. A general framework for the systematic investigation of mean phase space tendencies in complex geophysical systems is derived. In the special case of purely Gaussian statistics, this theory predicts that the interactions among the planetary waves themselves are the source of the nonlinear signatures in phase space, whereas the unresolved waves contribute only an amplitude-independent forcing, and cannot contribute to any nonlinear signature.

The predictions of the general framework are studied for a simple stochastic climate model. This toy model has statistics that are very close to being Gaussian and a strong nonlinear signature in the form of a double swirl in the mean phase space tendencies of its low-frequency variables, much like recently identified signatures of nonlinear planetary wave dynamics in prototype and comprehensive atmospheric general circulation models (GCMs). As predicted by the general framework for the Gaussian case, the double swirl results from nonlinear interactions of the low-frequency variables. Mean phase space tendencies in a reduced space of a prototype atmospheric GCM are also investigated. Analysis of the dynamics producing nonlinear signatures in these mean tendencies shows a complex interplay between waves resolved in the subspace and unresolved waves. The interactions among the resolved planetary waves themselves do not produce the nonlinear signature. It is the interaction with the unresolved waves that is responsible for the nonlinear dynamics. Comparing this result with the predictions of the general framework for the Gaussian case shows that the impact of the unresolved waves is due to their small deviations from Gaussianity. This suggests that the observed deviations from Gaussianity, even though small, are dynamically relevant.

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Meng Gao and Christian L. E. Franzke

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In this study, temporal trends and spatial patterns of extreme temperature change are investigated at 352 meteorological stations in China over the period 1956–2013. The temperature series are first examined for evidence of long-range dependence at daily and monthly time scales. At most stations there is evidence of significant long-range dependence. Noncrossing quantile regression has been used for trend analysis of temperature series. For low quantiles of daily mean temperature and monthly minimum value of daily minimum temperature (TNn) in January, there is an increasing trend at most stations. A decrease is also observed in a zone ranging from northeastern China to central China for higher quantiles of daily mean temperature and monthly maximum value of daily maximum temperature (TXx) in July. Changes of the large-scale atmospheric circulation partly explain the trends of temperature extremes. To reveal the spatial pattern of temperature changes, a density-based spatial clustering algorithm is used to cluster the quantile trends of daily temperature series for 19 quantile levels (0.05, 0.1, …, 0.95). Spatial cluster analysis identifies a few large clusters showing different warming patterns in different parts of China. Finally, quantile regression reveals the connections between temperature extremes and two large-scale climate patterns: El Niño–Southern Oscillation (ENSO) and the Arctic Oscillation (AO). The influence of ENSO on cold extremes is significant at most stations, but its influence on warm extremes is only weakly significant. The AO not only affects the cold extremes in northern and eastern China, but also affects warm extremes in northeastern and southern China.

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