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A Zonal Wavenumber-3 Pattern of Northern Hemisphere Wintertime 4

Planetary Wave Variability at High Latitudes 5

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Haiyan Teng and Grant Branstator 8

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National Center for Atmospheric Research, Boulder, Colorado 10

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March 2012 16

Revised 17

Submitted to J. Climate 18

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Corresponding author address: Haiyan Teng, National Center for Atmospheric Research, PO 23

Box 3000, Boulder, CO 80307 24

E-mail: hteng@ucar.edu 25

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ABSTRACT 27

A prominent pattern of variability of the Northern Hemisphere wintertime tropospheric 28

planetary waves, which is referred to here as the Wave3 pattern, is identified based on the 29

NCEP/NCAR reanalysis. It is worthy of attention because its structure is similar to the linear 30

trend pattern as well as the leading pattern of multi-decadal variability of the planetary waves 31

during the past half century. 32

The Wave3 pattern is defined as the second empirical orthogonal function (EOF) of 33

detrended December-February mean 300 hPa meridional wind (V300) and denotes a zonal shift 34

of the ridges and troughs of the climatological flow. Although its interannual variance is 35

roughly comparable to that of EOF1 of V300, which represents the Pacific/North America 36

(PNA) pattern, its multi-decadal variance is nearly twice as large as that of the PNA. Wave3 is 37

not completely structurally or temporally distinct from the Northern Annular Mode (NAM), but 38

for some attributes the linkage of the observed trend, to Wave3 is clearer than to NAM. 39

The prominence of the Wave3 pattern is further supported by attributes of many climate 40

models that participated in phase 3 of the Coupled Model Intercomparison Project (CMIP3). In 41

particular, in the Community Climate System Model version 3 (CCSM3), the Wave3 pattern is 42

present as EOF3 of V300 in both a fully coupled integration and a stand-alone atmospheric 43

integration forced by climatological sea surface temperatures. Its existence in the latter 44

experiment indicates that the pattern can be produced by atmospheric processes alone. 45

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1. Introduction 47

In spite of all the effort that has gone into identifying recurrent patterns of seasonal 48

mean atmospheric circulation anomalies (e.g. the teleconnection patterns of Wallace and 49

Gutzler (1981)), there is still the possibility that there are additional patterns that are worth 50

knowing about. This may be true for several reasons including a) as time goes on the 51

collection of observed states becomes larger, enabling recognition of patterns whose 52

significance could not be established with shorter datasets, b) new patterns may become more 53

prominent if climate changes substantially, c) analysis of new variables and domains may 54

emphasize new characteristics of variability, and d) researchers, by relating patterns to other 55

aspects of climate variability, can bring a new perspective as to which patterns are important. 56

In this paper we present results suggesting the importance of a pattern of interannual 57

variability that has not been widely noted in the literature but whose significance becomes 58

apparent when meridional wind, rather than the more commonly used geopotential height or 59

sea level pressure, is the analyzed variable (reason c, above) and when finding patterns whose 60

structure is similar to observed circulation trends is the goal (reason d). The pattern whose 61

properties we examine is largely confined to the latitudes between 50N and 70N during 62

winter and its signature consists of a distinctive zonal wavenumber-3 disturbance. Previously 63

zonal wavenumber-3 as a prominent pattern of variability has been noticed in the Southern 64

Hemisphere (SH) winter (Mo and White 1985, Cai et al. 1999) but its importance in the 65

Northern Hemisphere (NH) has not been established. We refer to the NH pattern of our study 66

simply as the Wave3 pattern. 67

The reason we have been motivated to learn about the properties of this pattern is that it 68

is similar in structure to the linear tropospheric circulation trend that has occurred in nature 69

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over the last half century. The top row of Fig. 1 shows the NH trends in December-February 70

(DJF) mean surface air temperature (TAS), sea level pressure (SLP), 500 hPa geopotential 71

height (Z500) and 300 hPa meridional wind (V300) during the period of 1958-2011 as given by 72

NCEP/NCAR reanalysis fields (Kalnay et al. 1996). While the hemispheric-wide warming 73

evident in TAS and Z500 is the signature of global warming that has received most attention, 74

we are struck by the three high latitude locations that exhibit a negative Z500 trend, which 75

become even more apparent when the hemispheric mean is removed (bottom row Fig.1). These 76

same three negative anomaly areas are seen in Hoerling et al. (2001)’s depiction of 1950-1999 77

Z500 trends, though in that study their amplitude is even stronger. These lobes are also very 78

apparent in V300 (though they are longitudinally shifted relative to the Z500 negative features 79

as one would expect from the geostrophic relationship) and to a lesser degree in SLP. It is this 80

prominent zonal wavenumber-3 pattern that we believe may be related to the pattern of 81

variability that is the focus of our study. 82

Some previous studies have related the observed trends to other patterns of variability, 83

in particular the Northern Annular Mode/North Atlantic Oscillation (NAM/NAO, Thompson 84

and Wallace 1998, Hurrell 1995). As we discuss in detail later in our paper, the Wave3 pattern 85

we present is not completely structurally or temporally distinct from NAM, but we believe that 86

for certain attributes of the observed trend, the linkage to the Wave3 pattern is clearer than for 87

NAM. 88

If there is a pattern of interannual variability whose structure is similar to the observed 89

trends, presumably the processes that produce it are also important for the generation of the 90

trend. Hence identifying such a linkage should help identify processes that need to be well 91

represented in climate models. Furthermore there are dynamical reasons to expect a similarity 92

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in the structure of the observed circulation trend and prominent interannual patterns. For 93

example there are theories that suggest the response of a dynamical system to a stimulus will 94

tend to have a structure similar to that of prominent intrinsic patterns of the system (Leith 1975, 95

Corti et al. 1999, Branstator and Selten 2009). Hence if the atmospheric trend is externally 96

forced (as in the reaction to greenhouse gas increases) or if it is forced by natural fluctuations 97

of slow components of the climate system (for example oceanic or coupled ocean/atmosphere 98

modes), one would expect such a similarity. 99

To present our results we have organized the paper as follows. Section 2 describes the 100

data sources and analysis methods we have used. This is followed in Section 3 by the 101

definition of the Wave3 pattern and a description of its characteristics as seen in the interannual 102

variability of reanalysis fields, including its relationship to other patterns of variability. In 103

Section 4 we report on the presence of Wave3 in various GCM simulations, including the 20th

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century integrations from the Coupled Model Intercomparison Project phase 3 (CMIP3, Meehl 105

et al. 2007). These results confirm that climate variability at the NH high latitudes tends to 106

favor Wave3-like patterns and that the Wave3 pattern can be produced by processes intrinsic to 107

the atmosphere. In Section 5 we demonstrate, to the degree possible from the observational 108

record, that the Wave3 pattern is more prominent on long time scales and is the leading pattern 109

of multi-decadal variability in the past half century or so. The paper concludes in Section 6 110

with a summary and discussion of results. 111

2. Data, models and methods 112

The primary dataset used in our study is the NCEP/NCAR reanalysis (Kalnay et al. 113

1996) for the period of 1958-2011. In addition to the more reliable 1958-2011 period, in results 114

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not shown here, we have repeated our analysis using data from 1948-2011 and from ERA40 115

(Uppala et al. 2005). Our results are not sensitive to either change. 116

We have used several time-varying indices to represent a number of previously 117

identified patterns of climate variability. The NAM pattern is defined as the first empirical 118

orthogonal function (EOF) of detrended DJF-mean SLP at 20-90N in the period of 1958-119

2011 and the NAM index is the corresponding principal component (PC). The DJF 120

Pacific/North American (PNA) time series is obtained from 121

http://jisao.washington.edu/data/pna/#djf which was constructed following its original 122

definition (Wallace and Gutzler 1981). 123

In addition to the reanalysis data, we have examined the structure of variability in 20th

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century simulations during the period of 1950-1999 performed by 19 CMIP3 models (Meehl et 125

al. 2007). We have also employed two long integrations of one particular CMIP3 model, 126

namely Community Climate System Model version 3 (CCSM3) (Collins et al. 2006). One is a 127

1000-year fully coupled present-day control run, with only the last 700 years analyzed in order 128

to avoid the spin up period. The other is a 12,000-year stand-alone integration of CCSM3’s 129

atmospheric component (CAM3) forced with present-day climatological SSTs that only vary 130

with month of the year. Both runs have a spatial resolution of T42 in the atmospheric model. 131

All results presented here are based on DJF means. In our study we are especially 132

interested in V300 because it has almost no zonal mean and thus emphasizes regional features, 133

and because it is far enough removed from the surface to have structures that are likely to be 134

largely controlled by planetary wave dynamics. Throughout our study we have either analyzed 135

trends or departures from trends and trends are formed simply from least squares fitting a line 136

through seasonal mean values at each grid point north of 20N during the period 1958-2011. 137

http://jisao.washington.edu/data/pna/#djf

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3. Interannual variability 138

a) Latitudinal and hemispheric structure 139

As the first step in investigating whether there is an interannual counterpart to the 140

distinctive high latitude zonal wavenumber-3 pattern in trend fields we have simply determined 141

whether zonal wavenumber-3 is a prominent structure for year-to-year wintertime fluctuations 142

at any latitude. This has been done by decomposing V300 anomalies into zonal harmonics in 143

2.5 latitude bands for DJF means in the NH and June-August means in the SH for each year 144

between 1958 and 2011, and then averaging the amplitude squared of each harmonic (middle 145

panels of Fig.2). For reference, we plot corresponding values derived from the climatological 146

mean and linear trend (m/s per 50 years) in the left and right panels of Fig.2 respectively. 147

Although only NH shows a strong wavenumber-3 trend, the V300 variability is dominated by 148

wavenumber-3 anomalies between approximately 50 and 70 latitude in both hemispheres. 149

For the climatological mean, in both hemispheres wavenumber-3 prevails in latitudes about 10 150

equatorward of this band. Hence, even though factors, including the structure of the 151

subtropical jet, stationary waves and stormtracks, that are thought to contribute to the 152

organization of interannual variability, are markedly different in the two hemispheres, zonal 153

wavenumber 3 is prominent at high latitudes during winter in both domains. 154

b) Definition of the Wave3 pattern 155

Next, to learn about the pattern or patterns that contribute to the NH high latitude 156

wavenumber 3 maximum in interannual variability, we have used EOF analysis. The leading 157

two EOFs of detrended DJF-averaged V300 between 20N and 90N are shown in the bottom 158

panels of Fig.3, and for comparison the climatological mean (contours) and 1958-2011 linear 159

trend (shading) of V300 are displayed in the top panel. EOF1 suggests a wave train spanning 160

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from the subtropical North Pacific to the midlatitudes of North America. By contrast, all six 161

centers of action of EOF2 are largely confined to 50-70N and form a pattern that closely 162

resembles the linear trend (Fig.1, upper right). There is no quadrature pattern of EOF2 among 163

EOFs 3-5, suggesting the wavenumber-3 anomalies tend to be longitudinally phase locked. 164

Compared with the climatological mean, EOF2 in its positive phase indicates an eastward shift 165

of the climatological ridges and troughs, especially in the western hemisphere where the 166

climatological high latitude waves are strongest. Previously, this pattern has not been singled 167

out or named in the scientific literature. We hereafter refer to it as the Wave3 pattern1, and 168

projections of detrended V300 anomalies onto the pattern we refer to as the Wave3 time series. 169

The variance explained by the two leading interannual V300 EOFs is so close (16% for 170

EOF1 and 14% for EOF2) that they cannot be separated by the criterion of North et al. (1982). 171

(On the other hand EOF2 is well separated from EOF3.) This raises the question of whether 172

Wave3 and V300 EOF1 should be considered to be distinct patterns or whether mixtures of 173

Wave3 and V300 EOF1 are just as relevant. But as we show in Section 3d, EOF1 corresponds 174

to the PNA pattern (Wallace and Gutzler 1981), so it and EOF2 are likely to be physically 175

distinct. The separation between EOF1 and EOF2 is also supported by lack of clear indication 176

of dependence between the two time series in scatter plots of concurrent values (not shown), 177

and by their temporal behavior on multi-decadal time scales, as explained in Section 5. 178

c) Vertical structure 179

To investigate the vertical structure of the Wave3 pattern, we have calculated the 180

latitudinal average of detrended meridional wind and air temperature at 50-70N regressed 181

1 If we calculate the EOFs using DJFM instead of DJF means, the resulted EOF2 has similar

wavenumber3 structure except that the amplitude of the positive anomaly over the North

Atlantic and negative anomaly over Europe is much reduced.

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upon the Wave3 time series (Fig. 4 top). The meridional wind anomalies have strongly 182

barotropic structure in the entire troposphere with maxima located at 300 hPa. The air 183

temperature anomalies also have a zonal wavenumber-3 structure from surface to 300 hPa. The 184

locations of the maxima and minima of the regressed air temperature anomalies correspond to 185

the zero-value contours of the meridional wind and are consistent with the thermal wind 186

relationship. 187

To make the comparison of Wave3’s vertical structure to that of the observed trend 188

clear, we use the same format to display the structure of the observed 1958-2011 trend of air 189

temperature and meridional wind at 50-70N (Fig.4 bottom). The air temperature trend 190

generally has the signature of cooling in stratosphere and warming in troposphere seen in many 191

studies. Superimposed on that are local features that closely match the structure of the Wave3 192

pattern as do the placement and patterns of the wind anomalies. 193

d) Teleconnection 194

Centers of action in EOF patterns do not necessary co-vary (Deser 2000, Ambaum et al. 195

2001), but if they do, it is an indication of a pattern that is likely to be a physical mode. In 196

order to examine the co-variability, or “teleconnectivity”, of the Wave3 pattern, we have 197

calculated a correlation matrix that relates detrended V300 at the six centers of action of the 198

Wave3 pattern. We find 12 of the resulting 15 correlation coefficients are significant at the 199

95% level. Moreover, when we use regression to remove the contribution of EOF1 to the year-200

to-year DJF anomalies, all 15 correlation coefficients become significant at the 95% level. 201

These indications of co-variability do suggest that the six lobes of Wave3 are a 202

collection of points at which the meridional wind co-varies to a detectable degree, but 203

meridional wind is an unfamiliar quantity for pattern identification. Because teleconnection 204

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patterns are conventionally defined with Z500 (Wallace and Gutzler 1981), we have 205

determined whether Wave3 also has a noticeable influence on this variable. To this end, we 206

have first regressed detrended DJF mean Z500 upon each of the leading two principal 207

components of V300 (Fig.5 top). The EOF1 regressed pattern appears to strongly resemble the 208

PNA pattern, a conclusion bolstered by the fact that there is a 0.84 correlation coefficient 209

between V300 PC1 and the PNA index. Like the V300 Wave3 pattern, the pattern regressed 210

upon V300 PC2 has six centers of action but the maxima and minima are located about 30 of 211

longitude east of the corresponding centers for V300 EOF2 (Fig.5 top right), as one would 212

expect based on geostrophy. While the Z500 pattern regressed upon V300 EOF1 resembles 213

EOF1 of detrended Z500, the pattern regressed upon V300 EOF2 contains features in both 214

EOF2 and EOF3 of detrended Z500 (figure not shown), so the EOF2s from V300 and Z500 215

correspond to somewhat different characteristics of variability. Quadrelli and Wallace (2004), 216

Branstator (2002) and others have made the point that EOFs of different variables tend to 217

emphasize different aspects of variability. 218

Next we have calculated one-point correlation maps of Z500 with reference to each of 219

the six centers of action of the Z500 rendition of the Wave3 pattern (marked as C1, C2… C6 in 220

Fig.5 top right panel). After using regression to remove the influence of anomalies associated 221

with EOF1 of V300, the six correlation maps formed from the residuals all exhibit Wave3 222

characteristics (Fig.5 bottom two rows), though there are only weak connections between C1 223

and C6, C2 and C5, and C3 and C5, and some small shifts of the centers of action. So 224

Wave3’s influence does carry over to the more familiar Z500. 225

e) Comparison with NAM 226

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Another aspect of the Wave3 pattern that needs to be established is how different it is 227

from the more familiar NAM, a pattern of climate variability that is strongly influenced by the 228

zonal mean. We have found that to a certain degree the Wave3 pattern is indeed related to 229

NAM. This is reflected in their full time series during 1958-2011 (Fig.6) calculated by 230

projecting the V300 and SLP departures from climatology, with the trend retained, onto the 231

corresponding signature pattern defined by an EOF of the detrended data. Especially for longer 232

time scale fluctuations, the time series have notable co-variability resulting in correlation 233

coefficients that are significant at the 90% level. However, for interannual time scale 234

fluctuations, at times Wave3 does not vary in concert with NAM. 235

In order to compare the structure of Wave3 and NAM, we regress detrended DJF-mean 236

SLP, TAS, Z500 and V300 upon the Wave3 and NAM indices (Fig.7). Remarkably, NAM, 237

which is largely characterized by the zonally symmetric component of the SLP field, has a 238

predominantly wavenumber 3 pattern in the high latitude V300 field. In all four examined 239

fields, the two regressed patterns are very similar over the North Atlantic and Europe, which 240

probably results in the significant correlation between the two time series. The major 241

difference is found in the North Pacific and North America. Unlike NAM, the Wave3 pattern in 242

its positive phase has negative SLP anomalies over the North Pacific. This SLP feature is the 243

surface signature of the much stronger zonally asymmetric character of Wave3 throughout the 244

troposphere over East Asia and the North Pacific as seen in the Z500 and V300 regressed 245

fields. Wave3’s in-phase variability between the Aleutian and Icelandic Lows seems to 246

resemble the Cold Ocean Warm Land pattern (COWL, Wallace et al. 1996). However, COWL 247

was not presented as a circulation mode when it was first introduced, and it still remains 248

controversial whether it should be regarded as an intrinsic atmospheric mode (Broccoli et al. 249

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1998, Molteni et al. 2011) or a forced response (Hoerling et al. 2004, Lu et al. 2004, Deser and 250

Phillips 2009). 251

The area weighted pattern correlation coefficient between each pattern in Fig. 7 and the 252

trend is marked at the top right corner of each panel in that figure. They suggest Wave3 can 253

capture the trend slightly better than NAM and are probably a reflection of the good match 254

between the trend and Wave3 in the North Pacific and western North America. One needs to 255

make a linear combination of the leading two EOFs of the SLP in order to replicate the trend 256

structure (Quadrelli and Wallace 2004). None of these regressed patterns can capture the 257

hemispheric distribution of TAS trend which is dominated by Arctic warming, suggesting 258

processes other than those responsible for the Wave3 or NAM variability play an important role 259

in producing the TAS trend. 260

4. Model simulations 261

As a test of the robustness of the Wave3 pattern, we have examined CMIP3 model 262

integrations reasoning that if it is present in these models, in spite of their varying formulations 263

and climates, it will indicate that the existence of the Wave3 pattern is not sensitive to subtle 264

aspects of the climate system nor is its prevalence in the observational record a random 265

statistical event. 266

a) CMIP3 models 267

To provide a characterization of Wave3 in nature that is easily compared to model 268

behavior we have carried out a further analysis of the observational record. This analysis has 269

focused on year-to-year variations of detrended DJF-mean V300 that has been latitudinally 270

averaged between 50N and 70N where the Wave3 pattern prevails in nature. To quantify the 271

prevalence of zonal wavenumber-3 variability we have calculated the percentage variance 272

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explained by each zonal wavenumber, and to investigate whether wavenumber-3 perturbations 273

have a preferred longitudinal phase we have generated a histogram of the phase values which 274

wavenumber-3 anomalies attain. In Fig. 8 these two quantities are plotted for observations 275

during 1958-2011 using thick red lines. Consistent with our earlier results, the dominance of 276

wavenumber 3 is very apparent (left panel), as is its preferred phases of -90 and approximately 277

90. Because of the convention we have used, +90 and -90 correspond to the same 278

longitudinal placement of features in the canonical Wave3 pattern (Fig. 3, bottom right) in its 279

positive and negative phases, respectively. (Note that since the phase is associated with 280

wavenumber-3 anomalies, a 30 difference in phase corresponds to a 10 longitudinal shift in 281

the location of the ridges/troughs of the analyzed waves.) A similar histogram of phase in the 282

SH is flatter than in the NH (figure not shown), suggesting the wavenumber-3 anomalies tend 283

to be more longitudinally phase-locked in the NH. 284

Following the same procedure, we have analyzed detrended V300 for 20th

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simulations during 1950-1999 from nineteen CMIP3 models. In the left panel of Fig.8 the 286

variance percentages of each zonal wavenumber are plotted for each model. For seven of the 287

models wavenumber 3 is not the dominant wavenumber, so the multi-model average of 288

variance percentage as a function of zonal wavenumber (thick blue line) in the left panel has 289

smaller contrast between wavenumber 3 and the neighboring wavenumbers than exists in 290

nature, but the prevalence of wavenumber 3 is still clear. As for histograms of the phase of the 291

wavenumber-3 anomalies, the results are very noisy, but when for each bin we plot the multi-292

model average of histogram values (blue dots) and plus/minus one standard deviation of those 293

values (the vertical blue lines) (Fig.8 right), the existence of two preferred phases in the vicinity 294

of -120 and 90 roughly agrees with the observations. 295

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b) CCSM3 296

The model-to-model differences seen in Fig. 8 may result from differences in model 297

formulation or from sampling fluctuations. To minimize the effect of analyzing short samples, 298

we have looked in more detail at one of the CMIP3 models (CCSM3) and its atmospheric 299

component (CAM3), for which we have long control integrations (cf. Section 2). When we 300

have repeated the V300 variance percentage and phase histogram calculations for CCSM3’s 301

control, we have found the behavior suggested by the short datasets from observations and 302

from the CMIP3 integrations is clearly present (Fig. 9). Zonal wavenumber 3 is the preferred 303

wavenumber with more than 30% of the variance (left panel). For observations wavenumber 3 304

contains somewhat more variance, namely 37%. For the distribution of phases (right panel), the 305

smoothing effect of having a much larger database compared to nature is apparent but the 306

preference for values near -90 and 90 is obvious. 307

As a second test of the presence of Wave3 in the long CCSM3 control run, we have 308

calculated EOFs of DJF averages of V300 between 20N and 90N (Fig. 10, top row). There is 309

a pattern of variability that strongly resembles Wave3, but it is EOF3 rather than EOF2 as in 310

nature. Moreover, it explains 10% rather than 14% of the variance. Owing to the length of the 311

CCSM3 control integration, that all three leading EOFs are well separated from each other and 312

neighboring EOFs can be readily established (North et al. 1982), giving support to the notion 313

that Wave3 is a distinct pattern. 314

Figures 9 and 10 also contain results for CAM3. In most respects removing the 315

interactive ocean has little impact on high latitude DJF variability. Zonal wavenumber 3 is still 316

the preferred scale and it has a preferred phase. The longitudinal position of the troughs and 317

ridges are, however, somewhat different for that preferred phase. As implied by the maxima at 318

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phases of -120 and 60 in Fig. 9 (right), zonal wavenumber 3 variability tends to occur about 319

10 west of where it does in CCSM3. This same shift is visible in the bottom row of Fig.10’s 320

depiction of the leading V300 EOFs of CAM3. 321

An implication of the CAM3 results is that Wave3 can be produced by atmospheric 322

processes alone as the CAM3 experiment is forced by climatological SSTs that are only a 323

function of month of the year. That Wave3 is an intrinsic atmospheric pattern is further 324

suggested when we plot its vertical structure between 50N and 70N in CCSM3 and CAM3 325

using the same regression methodology employed for nature (Fig.4, top) but key on V300 PC3 326

rather than PC2. The plots generated in this way (not shown) are very similar for these two 327

experiments and both resemble the observed vertical structure of Wave3 but with weaker 328

anomalies over the Atlantic sector. 329

Not only is EOF3 similar in the two model experiments but so are EOF1 and EOF2, in 330

terms of both structure and variance explained. As in nature, EOF1 in both runs represents the 331

PNA pattern, but its Asian features are stronger than they are in the observational counterpart 332

(Fig. 3 lower left) and the variance it explains is much higher in the model. EOF2 has a 333

structure that is similar to EOF1, except that longitudinal locations of the centers of action are 334

shifted by about 18° of longitude. Hence these two patterns are in spatial quadrature. 335

Moreover, both EOF1 and EOF2 have a zonal wavenumber-5 structure in the subtropical-to-336

midlatitude region, which is reminiscent of the observed waveguide mode found in nature 337

(Branstator 2002). For our purposes what is noteworthy is that even though wavenumber-5 338

variability is much more prominent in CCSM3 than in nature, there is a high degree of 339

similarity in its Wave3 pattern and the one in nature, a further testament to the robustness of 340

Wave3 as a pattern of variability. 341

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The lengths of the CAM3 and CCSM3 control experiments also have made it possible 342

for us to consider the temporal spectral properties of Wave3 for these models. When we have 343

applied standard power spectrum estimation techniques to DJF averages, we have found CAM3 344

V300 PC3 has a white spectrum. With the air-sea coupling in CCSM3, PC3 reddens, exhibiting 345

several peaks in the interannual to decadal range (however, its multi-decadal variance is weaker 346

than the rough estimate we have made from observations). The total variance associated with 347

the Wave3 pattern increases by 17% relative to Wave3 variance in the CAM3 run, but our 348

significance tests indicate there is a 15% chance that such an increase could be caused by 349

sampling fluctuations. Variance associated with the other two leading EOFs is also enhanced in 350

the fully coupled run; as a result, the Wave3 pattern remains as the third EOF despite the 351

increased variance. However, if we smooth the V300 anomalies with a 20-year running 352

window and recalculate the EOFs, the Wave3 pattern becomes EOF2 in the fully coupled run. 353

Meanwhile, the temporal smoothing does not change the order of the leading three EOFs in the 354

CAM3 run. This suggests that air-sea coupling can advance the prominence of the Wave3 355

pattern on the multi-decadal time scale. 356

5. Predominance of Wave3 on multi-decadal time scales 357

Because observations show a pronounced multi-decadal fluctuation in the Wave3 time 358

series (Fig.6) and because in CCSM3 the Wave3 pattern becomes relatively more prominent 359

when 20-year running means are considered, we have been encouraged to further analyze the 360

role that Wave3 plays in long time scale planetary wave variability. Of course as in all 361

observational studies of decadal and longer time scale variability, results from such an analysis 362

cannot be definitive because the instrumental record is so short. 363

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To determine the structure of multi-decadal variability in nature, we have calculated the 364

leading EOF patterns of detrended TAS, PSL, Z500 and V300 between 20N and 90N from 365

our observational dataset filtered with the same 20-year running mean filter we applied to 366

CCSM3 output. EOF1 from each field is depicted in the top row of Fig. 11. The pattern for 367

V300 is nearly identical to that for Wave3 (Fig.3c), as confirmed by the fact that the pattern 368

correlation for these two is 0.80. Also, as shown in the bottom panel of Fig. 11, when we have 369

projected detrended DJF-mean anomalies onto these four patterns those projections are highly 370

correlated. Indeed TAS, SLP and Z500 are correlated with the V300 time series by values of 371

0.80, 0.85, and 0.85, respectively. Hence for each of these fields the leading pattern of multi-372

decadal variability is strongly related to Wave3. 373

Interestingly, while the V300 EOF2 pattern of interannual variability (i.e., Wave3) 374

becomes the leading pattern for 20 year running mean data, the EOF1 interannual pattern (the 375

PNA) becomes the second leading pattern and explains only about half as much variance as 376

Wave3. This fact demonstrates that Wave3 and the PNA have different temporal 377

characteristics thus serving to further confirm they are individual physical phenomena. A 378

further piece of evidence of the long time scale preference of Wave3 is in the ratio of 10-year 379

low-pass filtered variance to interannual variance for the NAM, PNA, and Wave3 full time 380

series. These ratios are 30%, 29% and 18% for Wave3, NAM and PNA respectively. Wave3 381

becomes even more distinct when we replace the 10-year low-pass filter with 20-year running 382

means. One, however, should not conclude from these facts that Wave3 is primarily a pattern 383

with longer than interannual variations. For when we have removed 20 year running means 384

from interannual V300 and again calculate EOFs, we have found little difference in the leading 385

two patterns or the variance they explain compared to the results in Fig. 3 when all interannual 386

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variability is accounted for. And when we have projected daily data onto the Wave3 pattern, 387

the daily Wave3 time series exhibits significant intraseasonal frequency peaks. 388

6. Concluding remarks 389

In this paper, we have introduced a pattern of NH wintertime planetary wave variability 390

characterized by longitudinally phase-locked zonal wavenumber-3 anomalies between 50N 391

and 70N. It is most prominent in the upper tropospheric meridional wind though it is also seen 392

in other fields throughout the depth of the troposphere. EOF2 of detrended DJF-mean V300 393

during 1958-2011 isolates this pattern well, so we have used this EOF to define the pattern, 394

which we refer to simply as Wave3. Our analysis supports the notion that it is a distinct pattern 395

of variability, and not one of a family of patterns that can be combined arbitrarily. 396

Other studies, including Mo and White (1985) and Cai et al. (1999) have recognized a 397

similar pattern of interannual variability in the SH, but the presence of the NH wavenumber-3 398

pattern has not been recognized before. We believe Wave3 may be important, not only in its 399

own right as a pattern of variability, but because it may shape the structure of trends and/or 400

multi-decadal variability of the wintertime circulation at high latitudes. We have come to this 401

conclusion because our results indicate the Wave3 pattern and associated fields are similar in 402

structure to the circulation trend that has occurred in nature during the last 50 years as well as 403

to the leading pattern of V300 multi-decadal variability during that period. Thus understanding 404

its properties may be a step toward understanding such long time scale features of climate 405

variability and change. 406

Our analysis of climate model simulations has provided additional reasons to believe 407

the Wave3 pattern should be recognized as a prominent pattern of variability. When combined 408

into an aggregate dataset, the CMIP3 models we considered indicate that V300 variability at 409

19

high latitudes favors a zonal wavenumber-3 structure, and that the resulting waves occur at 410

preferred longitudinal positions. We did find considerable model-to-model differences in our 411

results and Wave3 was not prominent in all of them, but this may be a result of sampling 412

fluctuations. For we found that in the model for which we had very long time series, namely 413

CCSM3, the Wave3 pattern clearly stands out. Not only was zonal wavenumber-3 the most 414

important component of high latitude V300 variability, but it had a clear preferred longitudinal 415

phase. As a result the structure of V300 EOF3 in CCSM3 turned out to closely match the 416

observed Wave3 pattern. Also, it is noteworthy that Wave3 is very similar to EOF3 for V300 in 417

a long integration of CAM3, the atmospheric component of CCSM3. Hence the Wave3 pattern 418

is not only a prominent pattern of variability but it can be produced by intrinsic atmospheric 419

processes. 420

Interestingly, Wave3’s prominence in CCSM3 was even more pronounced on multi-421

decadal than interannual time scales. This result adds support to our similar finding for nature, 422

where the short climate record makes the statistical significance of our findings difficult to 423

establish. In the introduction we pointed out that a similarity in structure of trends and an 424

intrinsic atmospheric pattern can occur whether the trends are externally forced or are a 425

manifestation of slow intrinsic climate variability. Because Wave3 may be the atmospheric 426

component of an intrinsic multi-decadal mode, we cannot know whether its trend over the last 427

five decades is forced or intrinsic. After all, during the instrumental record it has undergone a 428

single multi-decadal fluctuation (Fig. 6) and a single cycle of even a pure harmonic oscillation 429

produces a substantial signature in a standard trend analysis. Future work, including 430

examination of the CMIP phase 5 experiments, may help determine which possibility is most 431

likely. 432

20

Future work is also needed to determine the processes that make Wave3 a leading 433

intrinsic mode of atmospheric variability. Simple wave propagation ideas indicate there should 434

be a preference for small zonal wavenumber disturbances near the poles (Hoskins and Karoly 435

1981), and Chang and Fu’s (2002) results indicate that interactions with the synoptic eddies 436

may contribute to an in-phase relationship between variations in the Icelandic and Aleutian 437

Lows, so these two mechanisms are likely to be involved. Perhaps once the key mechanisms 438

are understood other issues regarding the Wave3 pattern will be settled, including why 439

wavenumber 3 is prominent during winter in the very different environments of the two 440

hemispheres and why many CMIP3 models react to greenhouse gas increases with a distinct 441

subtropical wavenumber 5 pattern (Brandefelt and Kornich 2008, Meehl and Teng 2007) rather 442

than with the high latitude wavenumber 3 trend pattern observed in recent decades. 443

444

Acknowledgment 445

This study benefited from comments from the anonymous reviewers. We acknowledge 446

support from DOE Office of Science (BER) under Cooperative Agreement No. DE-FC02-447

97ER62402 (Teng) and contract DE-SC0005355 (Branstator) and by NOAA’s Climate 448

Prediction Program for the Americas Award NA09OAR4310187 (Branstator). NCAR is 449

sponsored by the National Science Foundation. 450

451

21

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(CCSM3). J. Climate, 19, 2122-2143. 469

Corti, S., F. Molteni, and T.N. Palmer, 1999: Signature of recent climate change in frequencies 470

of natural atmospheric circulation regimes. Nature, 398, 799-802. 471

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Climate, 22, 396-413. 476

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510

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Figure captions: 511

Fig.1. (top) Linear trend of DJF-mean surface air temperature (TAS, K/50years), sea level 512

pressure (SLP, hPa/50years), 500hPa geopotential height (Z500, 10m/50years) and 300 hPa 513

meridional wind (V300, ms-1

/50yrs) during the period of 1958-2011 from the NCEP/NCAR 514

reanalysis. (Bottom) Same as the top but with the Northern Hemisphere area weighted averaged 515

trend (0.65 K, 0.27 hPa, 18.6m and -0.06 ms-1

per 50 years for TAS, SLP, Z500 and V300 516

respectively) removed. Stippling indicates the 90% t-test significance level. 517

518

Fig.2. Amplitude squared of zonal harmonic 0-6 of wintertime (DJF for the NH and JJA for 519

the SH) seasonal mean V300 (left) climatology, (middle) interannual anomalies, and (right) 520

fifty-year linear trend during the period of 1958-2011. 521

522

Fig.3. (top) Climatology (ms-1

) in contour and trend (ms-1

per 50 years) in shading of DJF-523

mean V300 during 1958-2011. Stippling indicates the 90% significance level of the trend. 524

(bottom) EOF1 and EOF2 of detrended DJF-mean V300 for 20-90N during the same period. 525

526

Fig.4. (top) DJF-mean meridional wind (contoured with interval 0.5 ms-1

; negative contours are 527

dashed) and air temperature anomalies (shading with units K) regressed upon the Wave3 index 528

and (bottom) their linear trend (wind contoured with interval 0.5 ms-1

per 50 years and 529

temperature shaded with units K per 50 years) during the period of 1958-2011. Stippling 530

indicates the 90% t-test significance level. 531

532

25

Fig.5 (top) DJF-mean Z500 regressed upon the leading two principal components of detrended 533

V300 during 1958-2011. The six centers of action in the EOF2 regressed map are marked as 534

C1, C2, …, and C6. (bottom two rows) One-point correlation maps showing the correlation 535

coefficient between Z500 anomalies at C1, C2, …, C6 (denoted by the cross) and every other 536

grid points. The V300 EOF1 regressed anomalies have been subtracted from the Z500 537

anomalies in construction of bottom two rows. Stippling indicates the 90% significance level. 538

539

Fig.6. Standardized full time series of NAM and the Wave3 pattern during the period of 1958-540

2011. The NAM and Wave3 full time series are calculated by projecting DJF-mean SLP and 541

V300 anomalies containing the linear trend onto the NAM and Wave3 signature patterns, 542

which correspond to EOF1 of detrended SLP and EOF2 of detrended V300 at 20-90N, 543

respectively. 544

545

Fig.7. Detrended DJF-mean TAS, SLP, Z500 and V300 regressed upon (a) Wave3 and (b) 546

NAM index. The NAM index is defined as PC1 of detrended DJF-mean SLP at 20-90N. 547

Stippling indicates the 90% t-test significance level. Unit for TAS, SLP, Z500 and V300 548

anomalies is K, hPa, 10m, and ms-1

, respectively. The number at the top right corner of each 549

panel indicates the pattern correlation between the regressed pattern and the trend of the 550

corresponding field during the period of 1958-2011 (Fig.1). 551

552

Fig.8. (left) Percentage variance of interannual variability of detrended DJF-mean V300 553

averaged for 50-70N explained by each zonal wavenumber. The thick red line represents the 554

NCEP/NCAR reanalysis during 1958-2011, the thick blue line is the average of variance 555

percentages from nineteen CMIP3 models from their 20th

century simulations during 1950-556

26

1999, and the remaining lines correspond to values for each of these models individually. The 557

nineteen models are listed in the legend with the number in the parenthesis indicating the 558

number of realizations included for each model. (right) histogram of phase of zonal 559

wavenumber-3 harmonics of the V300 interannual anomalies for twelve 30 wide bins (the two 560

bins at the two ends of the x-axis are the same). The red line represents the reanalysis and the 561

blue dot denotes the ensemble averaged histogram from 12 models whose V300 variability is 562

dominated by wavenumber 3 according to the left panel. The thin blue vertical line indicates 563

plus/minus one standard deviation of the histogram values among the twelve models. 564

565

Fig.9. Same as Fig.8 but for (left) percentage variance of V300 from a 700-year CCSM3 fully 566

coupled integration (black) and a 12000-year atmosphere stand-alone (CAM3) run (blue). 567

(right) Histogram of phase of the wavenumber-3 harmonics of the two runs (black asterisk for 568

CCSM3 and blue dot for CAM3). Results for the reanalysis are repeated from Fig. 8 with red 569

lines. 570

571

Fig.10. Leading three EOFs of DJF-mean V300 from (top) the 700-year fully coupled CCSM3 572

control integration and (bottom) the 12000-year CCSM3 atmosphere stand-alone integration 573

(CAM3) forced with present-day climatological SSTs. The domain for the EOF analysis is 20-574

90N. 575

576

Fig.11. (top) EOF1 of detrended 20-year running averages of DJF-mean TAS, SLP, Z500 and 577

V300 for 20-90N in the NCEP/NCAR reanalysis during 1958-2011. (bottom) projection of 578

27

the unsmoothed seasonal mean anomalies containing the trend onto the four corresponding 579

EOF1 patterns (top panel). All four time series have been standardized. 580

581

28

582

583

584

585

Fig.1. (top) Linear trend of DJF mean surface air temperature (TAS, K/50years), sea level 586

pressure (SLP, hPa/50years), 500hPa geopotential height (Z500, 10m/50years) and 300 hPa 587

meridional wind (V300, ms-1

/50yrs) during the period of 1958-2011 from the NCEP/NCAR 588

reanalysis. (Bottom) Same as the top but with the Northern Hemisphere area weighted averaged 589

trend (0.65 K, 0.27 hPa, 18.6m and -0.06 ms-1

per 50 years for TAS, SLP, Z500 and V300 590

respectively) removed. Stippling indicates the 90% t-test significance level. 591

29

592 593

594

Fig.2. Amplitude squared of zonal harmonic 0-6 of wintertime (DJF for the NH and JJA for 595

the SH) seasonal mean V300 (left) climatology, (middle) interannual anomalies, and (right) 596

fifty-year linear trend during the period of 1958-2011. 597

30

598

599

600

601

602

Fig.3. (top) Climatology (ms-1

) in contour and trend (ms-1

per 50 years) in shading of DJF-603

mean V300 during 1958-2011. Stippling indicates the 90% significance level of the trend. 604

(bottom) EOF1 and EOF2 of detrended DJF-mean V300 for 20-90N during the same period. 605

606

607

608

31

609

610 611

612

613

Fig.4. (top) DJF-mean meridional wind (contoured with interval 0.5 ms-1

; negative contours are 614

dashed) and air temperature anomalies (shading with units K) regressed upon the Wave3 index 615

and (bottom) their linear trend (wind contoured with interval 0.5 ms-1

per 50 years and 616

temperature shaded with units K per 50 years) during the period of 1958-2011. Stippling 617

indicates the 90% t-test significance level. 618

619

620

32

621

622 623

624

Fig.5 (top) DJF-mean Z500 regressed upon the leading two principal components of detrended 625

V300 during 1958-2011. The six centers of action in the EOF2 regressed map are marked as 626

C1, C2, …, and C6. (bottom two rows) One-point correlation maps showing the correlation 627

coefficient between Z500 anomalies at C1, C2, …, C6 (denoted by the cross) and every other 628

grid points. The V300 EOF1 regressed anomalies have been subtracted from the Z500 629

anomalies in construction of bottom two rows. Stippling indicates the 90% significance level. 630

631

33

632

633 634

635

636

Fig.6. Standardized full time series of NAM and the Wave3 pattern during the period of 1958-637

2011. The NAM and Wave3 full time series are calculated by projecting DJF-mean SLP and 638

V300 anomalies containing the linear trend onto the NAM and Wave3 signature patterns, 639

which correspond to EOF1 of detrended SLP and EOF2 of detrended V300 at 20-90N, 640

respectively. 641

34

642

643 644

645

646

Fig.7. Detrended DJF-mean TAS, SLP, Z500 and V300 regressed upon (a) Wave3 and (b) 647

NAM index. The NAM index is defined as PC1 of detrended DJF-mean SLP at 20-90N. 648

Stippling indicates the 90% t-test significance level. Unit for TAS, SLP, Z500 and V300 649

anomalies is K, hPa, 10m, and ms-1

, respectively. The number at the top right corner of each 650

panel indicates the pattern correlation between the regressed pattern and the trend of the 651

corresponding field during the period of 1958-2011 (Fig.1). 652

653

35

654

655 656

657

658

Fig.8. (left) Percentage variance of interannual variability of detrended DJF-mean V300 659

averaged for 50-70N explained by each zonal wavenumber. The thick red line represents the 660

NCEP/NCAR reanalysis during 1958-2011, the thick blue line is the average of variance 661

percentages from nineteen CMIP3 models from their 20th

century simulations during 1950-662

1999, and the remaining lines correspond to values for each of these models individually. The 663

nineteen models are listed in the legend with the number in the parenthesis indicating the 664

number of realizations included for each model. (right) histogram of phase of zonal 665

wavenumber-3 harmonics of the V300 interannual anomalies for twelve 30 wide bins (the two 666

bins at the two ends of the x-axis are the same). The red line represents the reanalysis and the 667

blue dot denotes the ensemble averaged histogram from 12 models whose V300 variability is 668

dominated by wavenumber 3 according to the left panel. The thin blue vertical line indicates 669

plus/minus one standard deviation of the histogram values among the twelve models. 670

36

671

672 673

674

Fig.9. Same as Fig.8 but for (left) percentage variance of V300 from a 700-year CCSM3 fully 675

coupled integration (black) and a 12000-year atmosphere stand-alone (CAM3) run (blue). 676

(right) Historgram of phase of the wavenumber-3 harmonics of the two runs (black asterisk for 677

CCSM3 and blue dot for CAM3). Results for the reanalysis are repeated from Fig. 8 with red 678

lines. 679

680

681

37

682 683

684

Fig.10. Leading three EOFs of DJF-mean V300 from (top) the 700-year fully coupled CCSM3 685

control integration and (bottom) the 12000-year CCSM3 atmosphere stand-alone integration 686

(CAM3) forced with present-day climatological SSTs. The domain for the EOF analysis is 20-687

90N. 688

689

38

690

691

692 693

694

Fig.11. (top) EOF1 of detrended 20-year running averages of DJF-mean TAS, SLP, Z500 and 695

V300 for 20-90N in the NCEP/NCAR reanalysis during 1958-2011. (bottom) projection of 696

the unsmoothed seasonal mean anomalies containing the trend onto the four corresponding 697

EOF1 patterns (top panel). All four time series have been standardized. 698