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Christopher Torrence and Gilbert P. Compo

A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Niño–Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes and using these to establish significance levels and confidence intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmöller, cross-wavelet spectra, and coherence are described.

The statistical significance tests are used to give a quantitative measure of changes in ENSO variance on interdecadal timescales. Using new datasets that extend back to 1871, the Niño3 sea surface temperature and the Southern Oscillation index show significantly higher power during 1880–1920 and 1960–90, and lower power during 1920–60, as well as a possible 15-yr modulation of variance. The power Hovmöller of sea level pressure shows significant variations in 2–8-yr wavelet power in both longitude and time.

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Gilbert P. Compo and Prashant D. Sardeshmukh

Abstract

This paper is concerned with estimating the predictable variation of extratropical daily weather statistics (“storm tracks”) associated with global sea surface temperature (SST) changes on interannual to interdecadal scales, and its magnitude relative to the unpredictable noise. The SST-forced storm track signal in each northern winter in 1950–99 is estimated as the mean storm track anomaly in an ensemble of atmospheric general circulation model (AGCM) integrations for that winter with prescribed observed SSTs. Two sets of ensembles available from two modeling centers, with anomalous SSTs prescribed either globally or only in the Tropics, are used. Since the storm track signals cannot be derived directly from the archived monthly AGCM output, they are diagnosed from the SST-forced winter-mean 200-mb height signals using an empirical linear storm track model (STM). For two particular winters, the El Niño of January–February–March (JFM) 1987 and the La Niña of JFM 1989, the storm track signals and noise are estimated directly, and more accurately, from additional large ensembles of AGCM integrations. The linear STM is remarkably successful at capturing the AGCM's storm track signal in these two winters, and is thus also suitable for estimating the signal in other winters.

The principal conclusions from this analysis are as follows. A predictable SST-forced storm track signal exists in many winters, but its strength and pattern can change substantially from winter to winter. The correlation of the SST-forced and observed storm track anomalies is high enough in the Pacific–North America (PNA) sector to be of practical use. Most of the SST-forced signal is associated with tropical Pacific SST forcing; the central Pacific (Niño-4) is somewhat more important than the eastern Pacific (Niño-3) in this regard. Variations of the pattern correlation of the SST-forced and observed storm track anomaly fields from winter to winter, and among five-winter averages, are generally consistent with variations of the signal strength, and to that extent are identifiable a priori. Larger pattern correlations for the five-winter averages found in the second half of the 50-yr record are consistent with the stronger El Niño SST forcing in the second half. None of these conclusions, however, apply in the Euro-Atlantic sector, where the correlations of the SST-forced and observed storm track anomalies are found to be much smaller. Given also that they are inconsistent with the estimated signal-to-noise ratios in this region, substantial AGCM error in representing the regional response to tropical SST forcing, rather than intrinsically lower Euro-Atlantic storm track predictability, is argued to be behind these lower correlations.

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Gilbert P. Compo and Prashant D. Sardeshmukh
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Gilbert P. Compo and Prashant D. Sardeshmukh

Abstract

An important question in assessing twentieth-century climate change is to what extent have ENSO-related variations contributed to the observed trends. Isolating such contributions is challenging for several reasons, including ambiguities arising from how ENSO itself is defined. In particular, defining ENSO in terms of a single index and ENSO-related variations in terms of regressions on that index, as done in many previous studies, can lead to wrong conclusions. This paper argues that ENSO is best viewed not as a number but as an evolving dynamical process for this purpose. Specifically, ENSO is identified with the four dynamical eigenvectors of tropical SST evolution that are most important in the observed evolution of ENSO events. This definition is used to isolate the ENSO-related component of global SST variations on a month-by-month basis in the 136-yr (1871–2006) Hadley Centre Sea Ice and Sea Surface Temperature dataset (HadISST). The analysis shows that previously identified multidecadal variations in the Pacific, Indian, and Atlantic Oceans all have substantial ENSO components. The long-term warming trends over these oceans are also found to have appreciable ENSO components, in some instances up to 40% of the total trend. The ENSO-unrelated component of 5-yr average SST variations, obtained by removing the ENSO-related component, is interpreted as a combination of anthropogenic, naturally forced, and internally generated coherent multidecadal variations. The following two surprising aspects of these ENSO-unrelated variations are emphasized: 1) a strong cooling trend in the eastern equatorial Pacific Ocean and 2) a nearly zonally symmetric multidecadal tropical–extratropical seesaw that has amplified in recent decades. The latter has played a major role in modulating SSTs over the Indian Ocean.

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Jeffrey S. Whitaker, Gilbert P. Compo, and Jean-Noël Thépaut

Abstract

An observing system experiment, simulating a surface-only observing network representative of the 1930s, is carried out with three- and four-dimensional variational data assimilation systems (3D-VAR and 4D-VAR) and an ensemble-based data assimilation system (EnsDA). It is found that 4D-VAR and EnsDA systems produce analyses of comparable quality and that both are much more accurate than the analyses produced by the 3D-VAR system. The EnsDA system also produces useful estimates of analysis error, which are not directly available from the variational systems.

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Prashant D. Sardeshmukh, Gilbert P. Compo, and Cécile Penland

Abstract

Away from the tropical Pacific Ocean, an ENSO event is associated with relatively minor changes of the probability distributions of atmospheric variables. It is nonetheless important to estimate the changes accurately for each ENSO event, because even small changes of means and variances can imply large changes of the likelihood of extreme values. The mean signals are not strictly symmetric with respect to El Niño and La Niña. They also depend upon the unique aspects of the SST anomaly patterns for each event. As for changes of variance and higher moments, little is known at present. This is a concern especially for precipitation, whose distribution is strongly skewed in areas of mean tropospheric descent.

These issues are examined here in observations and GCM simulations of the northern winter (January–March, JFM). For the observational analysis, the 42-yr (1958–99) reanalysis data generated at NCEP are stratified into neutral, El Niño, and La Niña winters. The GCM analysis is based on NCEP atmospheric GCM runs made with prescribed seasonally evolving SSTs for neutral, warm, and cold ENSO conditions. A large number (180) of seasonal integrations, differing only in initial atmospheric states, are made each for observed climatological mean JFM SSTs, the SSTs for an observed warm event (JFM 1987), and the SSTs for an observed cold event (JFM 1989). With such a large ensemble, the changes of probability even in regions not usually associated with strong ENSO signals are ascertained.

The results suggest a substantial asymmetry in the remote response to El Niño and La Niña, not only in the mean but also the variability. In general the remote seasonal mean geopotential height response in the El Niño experiment is stronger, but also more variable, than in the La Niña experiment. One implication of this result is that seasonal extratropical anomalies may not necessarily be more predictable during El Niño than La Niña. The stronger seasonal extratropical variability during El Niño is suggested to arise partly in response to stronger variability of rainfall over the central equatorial Pacific Ocean. The changes of extratropical variability in these experiments are large enough to affect substantially the risks of extreme seasonal anomalies in many regions. These and other results confirm that the remote impacts of individual tropical ENSO events can deviate substantially from historical composite El Niño and La Niña signals. They also highlight the necessity of generating much larger GCM ensembles than has traditionally been done to estimate reliably the changes to the full probability distribution, and especially the altered risks of extreme anomalies, during those events.

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Prashant D. Sardeshmukh, Gilbert P. Compo, and Cécile Penland

Abstract

Given the reality of anthropogenic global warming, it is tempting to seek an anthropogenic component in any recent change in the statistics of extreme weather. This paper cautions that such efforts may, however, lead to wrong conclusions if the distinctively skewed and heavy-tailed aspects of the probability distributions of daily weather anomalies are ignored or misrepresented. Departures of several standard deviations from the mean, although rare, are far more common in such a distinctively non-Gaussian world than they are in a Gaussian world. This further complicates the problem of detecting changes in tail probabilities from historical records of limited length and accuracy.

A possible solution is to exploit the fact that the salient non-Gaussian features of the observed distributions are captured by so-called stochastically generated skewed (SGS) distributions that include Gaussian distributions as special cases. SGS distributions are associated with damped linear Markov processes perturbed by asymmetric stochastic noise and as such represent the simplest physically based prototypes of the observed distributions. The tails of SGS distributions can also be directly linked to generalized extreme value (GEV) and generalized Pareto (GP) distributions. The Markov process model can be used to provide rigorous confidence intervals and to investigate temporal persistence statistics. The procedure is illustrated for assessing changes in the observed distributions of daily wintertime indices of large-scale atmospheric variability in the North Atlantic and North Pacific sectors over the period 1872–2011. No significant changes in these indices are found from the first to the second half of the period.

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Matthew Newman, Gilbert P. Compo, and Michael A. Alexander

Abstract

Variability of the Pacific decadal oscillation (PDO), on both interannual and decadal timescales, is well modeled as the sum of direct forcing by El Niño–Southern Oscillation (ENSO), the “reemergence” of North Pacific sea surface temperature anomalies in subsequent winters, and white noise atmospheric forcing. This simple model may be taken as a null hypothesis for the PDO, and may also be relevant for other climate integrators that have been previously related to the PDO.

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Catherine A. Smith, Gilbert P. Compo, and Don K. Hooper

While atmospheric reanalysis datasets are widely used in climate science, many technical issues hinder comparing them to each other and to observations. The reanalysis fields are stored in diverse file architectures, data formats, and resolutions. Their metadata, such as variable name and units, can also differ. Individual users have to download the fields, convert them to a common format, store them locally, change variable names, regrid if needed, and convert units. Even if a dataset can be read via the Open-Source Project for a Network Data Access Protocol (commonly known as OPeNDAP) or a similar protocol, most of this work is still needed. All of these tasks take time, effort, and money. Our group at the Cooperative Institute for Research in the Environmental Sciences at the University of Colorado and affiliated colleagues at the NOAA's Earth System Research Laboratory Physical Sciences Division have expertise both in making reanalysis datasets available and in creating web-based climate analysis tools that have been widely used throughout the meteorological community. To overcome some of the obstacles in reanalysis intercomparison, we have created a set of web-based Reanalysis Intercomparison Tools (WRIT) at www.esrl.noaa.gov/psd/data/writ/. WRIT allows users to easily plot and compare reanalysis datasets, and to test hypotheses. For standard pressure-level and surface variables there are tools to plot trajectories, monthly mean maps and vertical cross sections, and monthly mean time series. Some observational datasets are also included. Users can refine date, statistics, and plotting options. WRIT also facilitates the mission of the Reanalyses.org website as a convenient toolkit for studying the reanalysis datasets.

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Gilbert P. Compo, Prashant D. Sardeshmukh, and Cécile Penland

Abstract

This paper is concerned with assessing the impact of the El Niño–Southern Oscillation (ENSO) on atmospheric variability on synoptic, intraseasonal, monthly, and seasonal timescales. Global reanalysis data as well as atmospheric general circulation model (AGCM) simulations are used for this purpose. For the observational analysis, 53 yr of NCEP reanalyses are stratified into El Niño, La Niña, and neutral winters [Jan–Feb–Mar (JFM)]. The AGCM analysis is based on three sets of 180 seasonal integrations made with prescribed global sea surface temperatures corresponding to an observed El Niño event (JFM 1987), an observed La Niña event (JFM 1989), and climatological mean JFM conditions. These ensembles are large enough to estimate the ENSO-induced changes of variability even in regions not usually associated with an ENSO effect. The focus is on the anomalous variability of precipitation and 500-mb heights.

The most important result from this analysis is that the patterns of the anomalous extratropical height variability change sharply from the synoptic to the intraseasonal to monthly timescales, but are similar thereafter. In contrast, the patterns of the anomalous tropical rainfall variability are nearly identical across these timescales. On the synoptic and monthly scales, the anomalous extratropical height variability is generally opposite for El Niño and La Niña, and is also roughly symmetric about the equator. On the intraseasonal scale, however, the anomalous height variability is of the same sign for El Niño and La Niña in the Atlantic sector, and is antisymmetric about the equator in the Pacific sector. In the North Pacific, these intraseasonal variance anomalies (which are consistent with a decrease of blocking activity during El Niño and an increase during La Niña) are of opposite sign to the monthly and seasonal variance anomalies.

The sharp differences across timescales in the ENSO-induced changes of extratropical variability suggest that different dynamical mechanisms dominate on different timescales. They also have implications for the predictability of extreme events on those timescales. Finally, there is evidence here that these impacts on extratropical variability may differ substantially from ENSO event to event, especially in the northern Atlantic and over Europe.

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