Christian Franzke

Is the North Atlantic Oscillation a Breaking Wave

Abstract Given the recent observational evidence that the positive (negative) phase of the North Atlantic Oscillation (NAO) is the remnant of anticyclonic (cyclonic) wave breaking, this study uses a multilevel primitive equation model to investigate important dynamical attributes of the above wave breaking behavior. For this purpose, a hierarchy of different basic states (two- and three-dimensional) and initial perturbations are used. With the three-dimensional climatological flow as the basic state, it is found that initial perturbations located equatorward (poleward) and upstream of the climatological Atlantic jet lead to wave breaking similar to that of the positive (negative) NAO phase. Consistently, analysis of observational data indeed shows that the Pacific storm track is displaced equatorward (poleward) prior the onset of the positive (negative) NAO phase. This result suggests that the latitudinal position of the Pacific storm track plays an important role for determining the phase of the NAO. Sen...

An applied mathematics perspective on stochastic modelling for climate

Systematic strategies from applied mathematics for stochastic modelling in climate are reviewed here. One of the topics discussed is the stochastic modelling of mid-latitude low-frequency variability through a few teleconnection patterns, including the central role and physical mechanisms responsible for multiplicative noise. A new low-dimensional stochastic model is developed here, which mimics key features of atmospheric general circulation models, to test the fidelity of stochastic mode reduction procedures. The second topic discussed here is the systematic design of stochastic lattice models to capture irregular and highly intermittent features that are not resolved by a deterministic parametrization. A recent applied mathematics design principle for stochastic column modelling with intermittency is illustrated in an idealized setting for deep tropical convection; the practical effect of this stochastic model in both slowing down convectively coupled waves and increasing their fluctuations is presented here.

Low-order stochastic mode reduction for a realistic barotropic model climate

Abstract This study applies a systematic strategy for stochastic modeling of atmospheric low-frequency variability to a realistic barotropic model climate. This barotropic model climate has reasonable approximations of the Arctic Oscillation (AO) and Pacific/North America (PNA) teleconnections as its two leading principal patterns of low-frequency variability. 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. 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 unresolve...

Nonlinear Trends, Long-Range Dependence, and Climate Noise Properties of Surface Temperature

This study investigates the significance of trends offourtemperature time series—Central EnglandTemperature (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 gaugethe degree of confidence to havein the significance of trends.

Low-Order Stochastic Mode Reduction for a Prototype Atmospheric GCM

Abstract 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 w...

Are the North Atlantic Oscillation and the Northern Annular Mode Distinguishable

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.

Normal forms for reduced stochastic climate models

The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high-dimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Here techniques from applied mathematics are utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency variables. The use of a few Empirical Orthogonal Functions (EOFs) (also known as Principal Component Analysis, Karhunen–Loéve and Proper Orthogonal Decomposition) depending on observational data to span the low-frequency subspace requires the assessment of dyad interactions besides the more familiar triads in the interaction between the low- and high-frequency subspaces of the dynamics. It is shown below that the dyad and multiplicative triad interactions combine with the climatological linear operator interactions to simultaneously produce both strong nonlinear dissipation and Correlated Additive and Multiplicative (CAM) stochastic noise. For a single low-frequency variable the dyad interactions and climatological linear operator alone produce a normal form with CAM noise from advection of the large scales by the small scales and simultaneously strong cubic damping. These normal forms should prove useful for developing systematic strategies for the estimation of stochastic models from climate data. As an illustrative example the one-dimensional normal form is applied below to low-frequency patterns such as the North Atlantic Oscillation (NAO) in a climate model. The results here also illustrate the short comings of a recent linear scalar CAM noise model proposed elsewhere for low-frequency variability.

Ice core evidence for significant 100‐year regional warming on the Antarctic Peninsula

We present a new 150-year, high-resolution, stable isotope record (delta O-18) from the Gomez ice core, drilled on the data sparse south western Antarctic Peninsula, revealing a similar to 2.7 degrees C rise in surface temperatures since the 1950s. The record is highly correlated with satellite-derived temperature reconstructions and instrumental records from Faraday station on the north west coast, thus making it a robust proxy for local and regional temperatures since the 1850s. We conclude that the exceptional 50-year warming, previously only observed in the northern Peninsula, is not just a local phenomena but part of a statistically significant 100-year regional warming trend that began around 1900. A suite of coupled climate models are employed to demonstrate that the 50 and 100 year temperature trends are outside of the expected range of variability from pre-industrial control runs, indicating that the warming is likely the result of external climate forcing. Citation: Thomas, E. R., P. F. Dennis, T. J. Bracegirdle, and C. Franzke (2009), Ice core evidence for significant 100-year regional warming on the Antarctic Peninsula, Geophys. Res. Lett., 36, L20704, doi: 10.1029/2009GL040104.

Long-Range Dependence and Climate Noise Characteristics of Antarctic Temperature Data

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.

The Continuum and Dynamics of Northern Hemisphere Teleconnection Patterns

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.