Robert Vautard

Singular-spectrum analysis: a toolkit for short, noisy chaotic signals

Abstract Singular-spectrum analysis (SSA) is developed further, based on experience with applications to geophysical time series. It is shown that SSA provides a crude but robust approximation of strange attractors by tori, in the presence of noise. The method works well for short, noisy time series. The lagged-covariance matrix of the processes studied is the basis of SSA. We select subsets of eigenelements and associated principal components (PCs) in order to provide (i) a noise-reduction algorithm, (ii) a detrending algorithm, and (iii) an algorithm for the identification of oscillatory components. Reconstructed components (RCs) are developed to provide optimal reconstruction of a dynamic process at precise epochs, rather than averaged over the window length of the analysis. SSA is combined with advanced spectral-analysis methods - the maximum entropy method (MEM) and the multi-taper method (MTM) - to refine the interpretation of oscillatory behavior. A combined SSA-MEM method is also used for the prediction of selected subsets of RCs. The entire toolkit is validated against a set of four prescribed time series generated by known processes, quasi-periodic or chaotic. It is also applied to a time series of global surface air temperatures, 130 years long, which has attracted considerable attention in the context of the global warming issue and provides a severe test for noise reduction and prediction.

Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series

We distinguish between two dimensions of a dynamical system given by experimental time series. Statistical dimension gives a theoretical upper bound for the minimal number of degrees of freedom required to describe tje attractor up to the accuracy of the data, taking into account sampling and noise problems. The dynamical dimension is the intrinsic dimension of the attractor and does not depend on the quality of the data. Singular Spectrum Analysis (SSA) provides estimates of the statistical dimension. SSA also describes the main physical phenomena reflected by the data. It gives adaptive spectral filters associated with the dominant oscillations of the system and clarifies the noise characteristics of the data. We apply SSA to four paleoclimatic records. The principal climatic oscillations, and the regime changes in their amplitude are detected. About 10 degrees of freedom are statistically significant in the data. Large noise and insufficient sample length do not allow reliable estimates of the dynamical dimension.

Weather Regimes: Recurrence and Quasi Stationarity

Abstract Two different definitions of midlatitude weather regimes are compared. The first seeks recurrent atmospheric patterns. The second seeks quasi-stationary patterns, whose average tendency vanishes. Recurrent patterns are identified by cluster analysis, and quasi-stationary patterns are identified by solving a nonlinear equilibration equation. Both methods are applied on the same dataset: the NMC final analyses of 700-hPa geopotential heights covering 44 winters. The analysis is performed separately over the Atlantic and Pacific sectors. The two methods give the same number of weather regimes—four over the Atlantic sector and three over the Pacific sector. However, the patterns differ significantly. The investigation of the tendency, or drift, of the clusters shows that recurrent flows have a systematic slow evolution, explaining this difference. The patterns are in agreement with the ones obtained from previous studies, but their number differs. The cluster analysis algorithm used here is a partiti...

Spells of Low-Frequency Oscillations and Weather Regimes in the Northern Hemisphere

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,...

Hot European Summers and the Role of Soil Moisture in the Propagation of Mediterranean Drought

Abstract Drought in spring and early summer has been shown to precede anomalous hot summer temperature. In particular, drought in the Mediterranean region has been recently shown to precede and to contribute to the development of extreme heat in continental Europe. In this paper, this mechanism is investigated by performing integrations of a regional mesoscale model at the scale of the European continent in order to reproduce hot summer inception, starting with different initial values of soil moisture south of 46°N. The mesoscale model is driven by the large-scale atmospheric conditions corresponding to the 10 hottest summers on record from the European Climate Assessment dataset. A northward progression of heat and drought from late spring to summer is observed from the Mediterranean regions, which leads to a further increase of temperature during summer in temperate continental Europe. Dry air formed over dry soils in the Mediterranean region induces less convection and diminished cloudiness, which get...

The European climate under a 2 °C global warming

A global warming of 2 C relative to pre-industrial climate has been considered as a threshold which society should endeavor to remain below, in order to limit the dangerous effects of anthropogenic climate change. The possible changes in regional climate under this target level of global warming have so far not been investigated in detail. Using an ensemble of 15 regional climate simulations downscaling six transient global climate simulations, we identify the respective time periods corresponding to 2 C global warming, describe the range of projected changes for the European climate for this level of global warming, and investigate the uncertainty across the multi-model ensemble. Robust changes in mean and extreme temperature, precipitation, winds and surface energy budgets are found based on the ensemble of simulations. The results indicate that most of Europe will experience higher warming than the global average. They also reveal strong distributional patterns across Europe, which will be important in subsequent impact assessments and adaptation responses in different countries and regions. For instance, a North‐South (West‐East) warming gradient is found for summer (winter) along with a general increase in heavy precipitation and summer extreme temperatures. Tying the ensemble analysis to time periods with a prescribed global temperature change rather than fixed time periods allows for the identification of more robust regional patterns of temperature changes due to removal of some of the uncertainty related to the global models’ climate sensitivity.

On the Source of Midlatitude Low-Frequency Variability. Part II: Nonlinear Equilibration of Weather Regimes

Abstract We present a new statistical-dynamical approach to the concept of weather regimes, including the effect of tralisients, without any assumption other than scale separation. The method is applied to a quasi-geostrophic channel model without topography and forced by a local baroclinic jet. Baroclinic perturbations grow and decay along a storm track which is linked with a maximum of low-frequency variability towards its exit, in agreement with the observations. The weather regimes are searched within the subspace spanned by the large scales only. They are identified through the resolution of a stationary problem in which the feedback of the transients is included as an ensemble average over analogs of the large-scale flow. In this way, the feedback is a continuous function of the large-scale flow only, and the system of equations is closed, taking into account the whole coupling. The solution is obtained using a nonlinear optimization technique. Several regimes are identified corresponding to zonal a...

Attribution of extreme weather and climate‐related events

Extreme weather and climate‐related events occur in a particular place, by definition, infrequently. It is therefore challenging to detect systematic changes in their occurrence given the relative shortness of observational records. However, there is a clear interest from outside the climate science community in the extent to which recent damaging extreme events can be linked to human‐induced climate change or natural climate variability. Event attribution studies seek to determine to what extent anthropogenic climate change has altered the probability or magnitude of particular events. They have shown clear evidence for human influence having increased the probability of many extremely warm seasonal temperatures and reduced the probability of extremely cold seasonal temperatures in many parts of the world. The evidence for human influence on the probability of extreme precipitation events, droughts, and storms is more mixed. Although the science of event attribution has developed rapidly in recent years, geographical coverage of events remains patchy and based on the interests and capabilities of individual research groups. The development of operational event attribution would allow a more timely and methodical production of attribution assessments than currently obtained on an ad hoc basis. For event attribution assessments to be most useful, remaining scientific uncertainties need to be robustly assessed and the results clearly communicated. This requires the continuing development of methodologies to assess the reliability of event attribution results and further work to understand the potential utility of event attribution for stakeholder groups and decision makers. WIREs Clim Change 2016, 7:23–41. doi: 10.1002/wcc.380 For further resources related to this article, please visit the WIREs website.

On the Source of Midlatitude Low-Frequency Variability. Part I: A Statistical Approach to Persistence

Abstract The forcing of low-frequency variability by synoptic transient traveling perturbations is investigated within a quasi-geostrophic channel forced by a localized baroclinic jet. Spontaneously generated baroclinic perturbations grow and decay along a storm track; at the end of the track a maximum of low-frequency variability is obtained, in agreement with atmospheric observations. The structure of low-frequency variability is studied with a combination of statistical methods, using a multivariate red noise model as a random reference. We show that the anomalies are preferentially linked with local stationary structures or long-wave vacillations according to their location and their sign. A systematic study of persistence is conducted with a criterion based on rms of the streamfunction variations. The interesting quantity is the probability of persistence which shows a very inhomogeneous distribution in phase space and several separated maxima. The composites based on these maxima exhibit the charact...

Nonlinear variability of the climatic system from singular and power spectra of Late Quaternary records

Stable-isotope records from seven marine cores and one ice core provide invaluable information on the intricate behavior of the climatic system over time scales of 104 to 105 years. These records, in conjunction with a simple coupled climate model, help us understand major mechanisms of paleoclimatic variability. The time intervals covered by the records include the last glacial-interglacial cycle. In spite of the difference in the nature of the records, common features are revealed by advanced spectral-analysis tools. The dominant features are the presence of orbital frequencies, on the one hand, and a low number of internal degrees of freedom, on the other. The climatic system appears therefore to act on the Quaternary time scales considered as a forced nonlinear oscillator. The internal mechanisms giving rise to the aperiodic oscillations include ice-albedo feedback, precipitation-temperature feedback, and interactions between the ice sheets and the bedrock.