1

Role for Eurasian Arctic shelf sea ice in a secularly varying hemispheric 1

climate signal during the 20th

century 2

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By Marcia Glaze Wyatt1 and Judith A. Curry

2 4

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6 16 September 2013 7

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Accepted by Climate Dynamics 10 11

Abstract: A hypothesized low-frequency climate signal propagating across the Northern 12

Hemisphere through a network of synchronized climate indices was identified in previous 13

analyses of instrumental and proxy data. The tempo of signal propagation is rationalized in terms 14

of the multidecadal component of Atlantic Ocean variability – the Atlantic Multidecadal 15

Oscillation. Through multivariate statistical analysis of an expanded database, we further 16

investigate this hypothesized signal to elucidate propagation dynamics. The Eurasian Arctic 17

Shelf-Sea Region, where sea ice is uniquely exposed to open ocean in the Northern Hemisphere, 18

emerges as a strong contender for generating and sustaining propagation of the hemispheric 19

signal. Ocean-ice-atmosphere coupling spawns a sequence of positive and negative feedbacks 20

that convey persistence and quasi-oscillatory features to the signal. Further stabilizing the system 21

are anomalies of co-varying Pacific-centered atmospheric circulations. Indirectly related to 22

dynamics in the Eurasian Arctic, these anomalies appear to negatively feed back onto the 23

Atlantic‘s freshwater balance. Earth’s rotational rate and other proxies encode traces of this 24

signal as it makes its way across the Northern Hemisphere. 25

26

Keywords: synchronized network · Arctic sea ice· multidecadal variability · climate regime 27

1 Department of Geologic Sciences, CIRES/INSTAAR, Benson Earth Sciences Building, University of Colorado-

Boulder, Boulder, CO 80309, USA e-mail: marciawyatt@earthlink.net

2 School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia, USA.

2

1. Introduction 28

Behavior of numerous and diverse geophysical indices – from fish populations to cosmic 29

nuclides – fluctuate at a quasi-periodic 50-to-80 year tempo (e.g. Ogurtsov et al. 2002; Patterson 30

et al. 2004; Klyashtorin and Lyubushin 2007). Motivated by this ubiquity of tempo, Wyatt et al. 31

(2012; hereafter WKT) analyzed 20th

-century indices in the context of a hemispherically 32

spanning climate network through which a signal propagates. WKT termed this propagating 33

signal the ‘stadium-wave’ – an allusion to sections of sports fans seated in a stadium, standing 34

and sitting as a ‘wave’ propagates through the audience. In like manner, a signal ‘wave’ appears 35

to propagate through a hemispheric climate network. 36

Wyatt (2012) further explored the ‘stadium-wave’ signal, both spatially and temporally 37

expanding the network. A 300-year proxy record revealed a hemispherically propagating signal, 38

albeit with modifications of amplitude and tempo prior to the late 1700s. Wyatt and Peters (2012; 39

hereafter WP) analyzed networks of indices reconstructed from model-simulated data generated 40

by a suite of models in the third Coupled Model Intercomparison Project (CMIP3) using 20th

41

century and pre-industrial forcings. No secularly varying, hemispherically propagating signal 42

was found in the model simulations. 43

The stadium-wave signature identified in instrumental and proxy data is characterized by 44

two leading modes of variability that together capture the spatio-temporal nature of the 45

hemispherically spanning signal. WKT invoked numerous observational and model-based 46

studies to support suggested physical dynamics potentially conveying connectivity within the 47

stadium-wave network. Candidate mechanisms include low-frequency geographical shifts in 48

oceanic and atmospheric mid-latitude centers-of-action and meridional displacements of ocean-49

gyre frontal boundaries (western-boundary-current extensions), from which ocean-heat flux to 50

3

the atmosphere has the potential to influence overlying jet-stream behavior at decadal timescales. 51

While modeling of interactions between individual components provides insight into potential 52

localized coupling within the climate network, interaction between individual components is not 53

the same as collective interaction, where a change in one network component or interaction 54

promotes changes in all other network members and interactions among them. Recognizing this 55

fundamental trait of network behavior (Pikovsky et al. 2001), WP hypothesized that failure to 56

find the signal in any of the CMIP-model simulations might reflect the absence or poor 57

representation of network dynamics fundamental to signal propagation. WP also discussed 58

CMIP-modeling deficiencies in representing magnitude, configuration, and geographical 59

displacements of the rather complex Arctic high-pressure system, a significant factor in 60

simulating sea ice growth, extent and related dynamics (Gudkovich et al. 2008; Kwok 2011). 61

This paper extends WKT by investigating the underlying physical mechanisms associated 62

with the stadium wave through analysis of an expanded network of geophysical indices, with 63

particular focus on the Arctic region. Proxy indices are introduced to provide further insight into 64

the multiple dynamics related to hemispheric signal propagation, such as migration of the 65

Intertropical Convergence Zone, basin-scale wind patterns, western-boundary-current dynamics, 66

and Arctic sea ice processes. Establishing proxy-process relationships connotes their potential 67

use in extending the record prior to the 20th

century. The expanded index collection provides 68

insight and perspective on attribution and potential predictive capacity of the stadium wave. 69

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2 Data and Methods 74

2.1 Data 75

We evaluate network (collective) behavior of geophysical indices, following WKT and WP. All 76

newly added indices are discussed below and summarized details and index references are listed 77

in Table 1. See WKT for descriptions of and references for original indices. 78

79

Original indices: Indices used in the original WKT stadium-wave analysis are also used in the 80

present study. These indices include 20th

-century instrumental values of well-known indices, 81

such as the Northern Hemisphere area-averaged surface temperature (NHT), the Atlantic 82

Multidecadal Oscillation (AMO), the North Atlantic Oscillation (NAO), an index representative 83

of the El Nino-Southern Oscillation (NINO3.4), the North Pacific Oscillation (NPO), the Pacific 84

Decadal Oscillation (PDO), the Aleutian Low Pressure Index (ALPI), and the less well-known 85

index of Atmospheric-Mass-Transfer anomalies (AT: Vangenheim (1940); Girs (1971a)). 86

Long used in Russian studies, AT reflects atmospheric-pressure ‘topography’ that is used 87

to assess whether the general direction of large-scale wind-flow patterns at mid-to-high latitudes 88

(30ºN to 80ºN) of the Atlantic-Eurasian sector is zonal or meridional. Direction of cyclonic and 89

anticyclonic air-mass transfers between 45ºE and 75ºE is evaluated daily from atmospheric-90

pressure maps. Anomalies relative to a long-term annual mean number-of-days that are 91

characterized by dominantly zonal or meridional flow are tabulated for the year. The resulting 92

AT time series, available since 1891, reflects negative meridional values, whereby positive 93

values of AT indicate anomalous zonal flow (see Klyashtorin and Lyubushin 2007). 94

5

Indices of the original WKT index network were annually sampled. When available, 95

boreal winter values were used - December, January, February, and March (DJFM) – when 96

atmospheric variability is most intense and atmospheric modes are most pronounced. 97

Arctic indices: We have added the winter Arctic Oscillation (AO; Thompson and 98

Wallace 2000) to our data set to augment our insight into the stratospheric-tropospheric coupling 99

that occurs within the polar vortex during winter months. Variations in latitudinal distribution of 100

atmospheric mass are associated with the AO, which represents the dominant pattern of non-101

seasonal sea-level-pressure (SLP) variations north of 20ºN. SLP and the associated atmospheric-102

mass shifts give insight into anomalies of cyclonicity or anti-cyclonicity at high latitudes – 103

features that impact dynamics of atmosphere, sea ice, and ocean. 104

Arctic processes, particularly those in the Eurasian Arctic Shelf Seas, exhibit variability 105

on timescales analogous to that of the stadium-wave signal. To examine whether there is a low-106

frequency relationship between Arctic processes and the propagating signal, we incorporate into 107

our expanded network the annual mean Arctic surface air temperature (ArcT (70ºN to 85ºN) 108

Frolov et al. 2009) and August mean values of the Eurasian Arctic sea ice extent (1900-2008: 109

Frolov et al. 2009). These data are based on Russian sea ice charts (1933 to 2006: Arctic and 110

Antarctic Research Institute (AARI)) and archival records, both compiled by the AARI. These 111

data, digitized and available since 2006 (see Frolov et al. 2009 for full discussion and references 112

within), have complete records for at least the 20th

century for all the Eurasian Shelf Seas for the 113

month of August, when seasonal ice is close to its annual minimum. The region considered here 114

lies between 15ºW eastward to 155ºW. From west-to-east these seas are: the Greenland, Barents, 115

Kara, Laptev, East Siberian, and Chukchi Seas (Figure 1). 116

6

Russian terminology groups these six seas into two categories according to shared 117

seasonal characteristics: i) the North European Basin (NEB), comprised of the Greenland and 118

Barents Seas, is distinguished by the fact that portions of the region remain ice free during winter 119

and interannual variability of ice extent is not confined to summer; ii) the Arctic Seas of Siberia 120

(ArcSib), which includes the Kara, Laptev, East Siberian, and Chukchi Seas, typically remains 121

mostly ice-covered throughout the winter, interannually varying only in the summer. Summer 122

melt strongly influences sea-ice thickness the following winter, and by extension, governs extent 123

of ocean-heat flux through the ice cover to the overlying atmosphere during those months when 124

ocean’s influence on the atmosphere at high latitudes is greatest. 125

We further sort these seas according to dominant frequency of variability to elucidate 126

impact of timescale: i) the West Eurasian Seas (West Ice Extent (WIE)) exhibit a pronounced 127

50-to-80-year tempo of sea-ice-extent variability and include the Greenland, Barents, and Kara 128

Seas; while ii) the East Eurasian Seas (East Ice Extent (EIE)), which include the Laptev, East 129

Siberian, and Chukchi Seas, are dominated by interannual-to-interdecadal timescales of 130

variability: 20-to-30 years and eight-to-ten years. These higher frequencies are superimposed 131

upon a weak multidecadal component in EIE. Combined normalized values of WIE and EIE 132

equal the total ice extent (TIE) of the Eurasian Arctic Seas (Table 2). 133

Atlantic-Eurasian and Pacific circulation indices: Decadal-scale anomaly trends of 134

Atlantic-Eurasian atmospheric circulation (i.e. AT), are captured in the Atmospheric Circulation 135

Index (ACI (aka Vangenheim-Girs Index): Girs 1971a; Beamish 1998). ACI is the time-integral 136

curve of AT anomalies (aka cumulative-sum of AT (csAT)). Trend reversals of the anomaly 137

trends, or change points, have been linked to decadal-scale changes in temperature, precipitation 138

(Girs 1971b), and rotation of the solid Earth (Sidorenko and Svirenko 1988, 1991). 139

7

Similarly, an index representing decadal-scale anomaly trends of large-scale atmospheric 140

circulation over the North Pacific Ocean and North American continent is known as the Pacific 141

Circulation Index (PCI: King et al. 1998). As with ACI, PCI reflects the dominant direction – 142

zonal versus meridional - of large-scale wind patterns. PCI is derived in much the same way as 143

ACI. Information is gleaned from analysis of daily sea-surface-pressure fields over the North 144

Pacific and North American region and used to construct synoptic maps whose ‘topography’ is 145

used to classify atmospheric circulation patterns according to the Girs (1971) classification 146

scheme. Winter-month averages are computed, anomalies generated, and cumulative sums 147

calculated. The PCI record is available for the full 20th

century. 148

King et al. (1998) compared PCI to the time-integral of the Aleutian Low Pressure Index 149

(csALPI). Strong correspondence exists between their records of variability, despite the fact that 150

the two indices are derived using different metrics (see WKT table 1). They conclude that the 151

winter PCI provides a single-index representation of the multiple influences and sub-processes 152

associated with anomaly trends of ALPI. In a similar manner, we use both ACI and PCI to gain 153

insight into cumulative forcings of wind-flow patterns and their associated sub-processes on 154

dynamics within the stadium wave. 155

Proxy indices: Motivated by observations of secular-scale variability in a variety of 156

proxy indices and by their apparent relationships to either temperature or sub-processes within 157

the stadium-wave network, we have added several proxies to our expanded index collection. The 158

proxy indices used here include: 159

i) An 825-year sub-decadally resolved (annual resolution available for the portion used in 160

this study) record of Globigerina bulloides abundance, available through 2009 (GB: Black et al. 161

1999; personal communication), as measured from marine sediment in the Cariaco Basin off the 162

8

coast of Venezuela – a proxy associated with latitudinal migrations of the Atlantic mean 163

Intertropical Convergence Zone (ITCZ). 164

ii) Monthly resolved records of Sr/Ca isotope ratios in corals from Palmyra Island 165

(Nurhati et al. 2011) that capture a century-long record of sea-surface-temperatures (SST) of the 166

central Pacific tropics (162ºW, 6ºN) - a region that on decadal time scales is linked with 167

extratropical climate variability related to the North Pacific Gyre Oscillation (NPGO: Di Lorenzo 168

et al. 2008). The NPGO affects dynamics of the Kuroshio-Oyashio western-boundary-current 169

and its extension, the North Pacific Current (Ceballos et al. 2009; Di Lorenzo et al. 2010). 170

iii) Japanese Sardines (JS: Klyashtorin 1998; Noto and Yasuda 1999, 2003), whose 171

population outbursts off the Japanese coast are spatially related to the meridional migrations of 172

the western-boundary current (Kuroshio Current) and its extension (Oyashio Front) and 173

temporally associated with positive polarities of Pacific ocean-atmospheric circulation patterns 174

(PDO, NPO, NINO, ALPI). Annually resolved commercial statistics are available since 1920. 175

Japanese chronicles extend the record to 1640 (Kawasaki 1994). 176

iv) Earth’s rotational-rate anomalies, whose fluctuations have been systematically 177

documented via telescope since ~1623 and are measured in terms of the negative length-of-day 178

index (ngLOD: Stephenson and Morrison 1984), represent the difference between an actual 179

(astronomical) day and the mean length-of-day (86,400 seconds). Rotational-rate anomalies, 180

measured in milliseconds (ms), are physically linked to a variety of geophysical processes, their 181

associated impacts on Earth’s axial angular momentum and moment of inertia invoked to 182

rationalize observed correlations (Lambeck and Cazenave 1976; Dickey et al. 2011). At high-183

frequency timescales, with variations of ~0.2 to 0.4 ms, atmospheric circulation accounts for the 184

majority of ngLOD variability (Dickey et al. 2007). At low-frequency timescales, with 185

9

multidecadal variations of 4 to 8 ms, atmospheric circulation and related sub-processes of 186

precipitation and global redistribution of water account for ~14% of the magnitude of ngLOD 187

variability (Gross 2005); the remainder attributed to interactions within the Earth’s interior (Jault 188

et al. 1988), suggesting a mechanism common to both factors (Sidorenkov et al. 2005; 189

Sidorenkov 2005, 2009; Dickey and Marcus 2011). 190

Dickey and Marcus investigated a hypothesized relationship between ngLOD and the 191

global surface average temperature in their 2011 paper (hereafter DM; 2011). Examination of a 192

140-year record of observed and modeled temperature data revealed strong correlation between 193

the two indices until the 1930s, after which the surface temperature trend increased much more 194

than that of ngLOD. DM removed the estimated anthropogenic footprint from the surface 195

average temperature to generate a ‘corrected’ temperature, one assumed to reflect only natural 196

variability. Correlation between ngLOD and the ‘corrected’ temperature was strong. 197

We use annually resolved ngLOD as a proxy for patterns of long-period variability in 198

large-scale wind flow, which are related to the multidecadal components of surface average 199

temperatures, in particular, Arctic temperature (Klyashtorin et al. 1998). 200

v) The Atlantic SST Dipole (Dipole: Latif et al. (2006); Keenlyside et al. (2008)) is based 201

on sea-surface-temperatures (SST: Rayner et al. 2003; 20063) between mid-latitudes of the North 202

and South Atlantic Oceans. The Dipole index isolates SST variability related to variations in the 203

Atlantic sector of the meridionally overturning circulation (AMOC). We use the Dipole as a 204

proxy for meridional migrations of the ITCZ, which studies suggest is ‘pushed’ northward 205

(southward) with intensification (weakening) of the AMOC, the consequent atmospheric heat 206

transports effectively compensating for the northerly directed, cross-equatorial ocean heat 207

3 Rayner et al. 2003 record 1871-2000; Rayner et al. 2006 record 1850-2004.

10

transport related to dynamics of the AMOC (Zhang and Delworth 2005; Kang et al. 2008; 208

Frierson and Hwang 2012; Donohoe et al. 2013; Marshall et al. 2013). 209

Note: indices plotted in their negative polarity are indicated by the prefix, ‘ng’. The 210

prefix is chosen over the negative sign as it is easier to see on charts and figure legends. If the 211

index has no prefix, it represents positive polarity. 212

213

2.2 Methods 214

Prior to analysis, all raw indices were linearly detrended (least squares method), resulting in a 215

mean of zero. Our intent in removing the linear trend was to remove the centennial scale trend to 216

highlight multidecadal variability. After the data are linearly detrended, the values are 217

normalized to unit variance, thereby facilitating intercomparison of index behavior. 218

The cornerstone of our analysis is the Multichannel Singular Spectrum Analysis (M-SSA: 219

Broomhead and King 1986; Elsner and Tsonis 1996; Ghil et al. 2002). M-SSA is used to extract 220

and characterize dominant spatio-temporal patterns of variability shared by indices within a 221

network. The technique is particularly skillful in identifying signals from relatively short, noisy 222

data sets and in identifying non-zero-lag, or propagating, relationships (Ghil et al. 2002). Both 223

high-frequency oscillatory signals and secularly varying trends can be extracted using M-SSA. 224

Mean values of these M-SSA-extracted patterns, or modes of index co-variability, are plotted on 225

an M-SSA spectrum and error bars (based on North et al. 1982 criterion) appended. 226

To estimate the error bars, the variance of the mode is multiplied by the square root of 227

2/N*, where N* = the number of degrees of freedom. N*=N(1-r2)/(1+r

2), where N is the length of 228

each time series in the index set. One-hundred-year time series for each index were auto-229

correlated. The auto-correlation plots showed that the maximum autocorrelation after one year 230

11

among the eight indices was r~0.65. Using this auto-correlation value in the Bretherton formula 231

(Bretherton et al. 1999), the effective number of degrees of freedom was estimated to be 40. 232

From this, the projected decorrelation time is N/N* = 100/40 = 2.5 years. This is considered the 233

amount of time after which each data point can be considered independent from the ones 234

preceding and following it. 235

In the original stadium-wave study (WKT), M-SSA extracted two leading modes of 236

variability. Together, the two leading modes captured the complex spatial and temporal 237

characteristics of a secularly varying, hemispherically propagating signal. The likelihood that a 238

low-frequency signal, characterized by a delayed alignment of spatially and dynamically diverse 239

indices, i.e. a hemispherically propagating signal, could be due to mere random chance was 240

found to be less than 5%. This is the signal we further explore through the expanded database. 241

There is a risk of adding too many indices when applying M-SSA, which can lead to 242

overfitting, distorting the results. Additional spatial information must be introduced to avoid this 243

caveat. We do this by appending regions heretofore unexplored: e.g. the Arctic and tropical 244

Atlantic latitudes. We evaluate numerous subsets of the expanded data base, network sizes 245

ranging from four to 20 members, all combinations hemispherically representative. 246

To visualize this signal as it is expressed in each index, M-SSA modes are represented in 247

their original index space by reconstructed components (RCs). A reconstructed component is 248

effectively the narrow-band filtered version of an original index time series. RCs of the identified 249

leading modes, summed and normalized, generate the stadium-wave filter for index networks. 250

A second method applied to our raw-data sets, and done independently from the M-SSA 251

exercise, is correlation analysis. Correlated indices, considered along with M-SSA results, 252

potentially add further insight into dynamics associated with the signal’s propagation. Prior to 253

12

computing correlations between pairs of linearly detrended, normalized raw time series, values 254

were smoothed with a 13-year running mean filter to sort out shorter-term fluctuations in order to 255

highlight longer-term behavior of indices. We also experimented with a variety of filter sizes, 256

from five years to 20; results were virtually unchanged. 257

We also introduce transformed time series to convey insight into forcings and responses 258

among indices whose behaviors are interconnected within a network. Transformed time series 259

include two types: time-integrated, such as ACI and PCI, and time-differentiated values. The 260

former yields anomaly trends of an index’s time series; while the latter converts time series of 261

indices into incremental values – an approximation of the time-derivative of a trend (e.g. AT is 262

the approximate time-derivative of ACI). Transformed indices are useful in detecting potential 263

cause-and-effect relationships. We focus on the time-integrated transformation in this study. 264

To transform a raw time series into its anomaly trend, or time integral (Hurst 1951; Outcalt et 265

al. 1997), one computes a cumulative sum from a time series of anomalies (raw time series 266

linearly detrended via least-squares method and normalized to unit variance). Cumulative sum 267

(cs) of a time series of anomalies, X, is obtained via equation (1): 268

X(cs)(n) = X(n) + Xcs(n-1) (1) 269

where X(cs)(n) is the cumulative-sum value at time n; X(n) is the anomaly time-series value at 270

time n; and X(cs)(n-1) is the cumulative-sum value at n-1. 271

We use a red-noise model to test the statistical significance of spatial and propagation 272

properties of the M-SSA-identified low-frequency signal and also of the correlation analysis 273

results. The red-noise model, used to generate surrogate time series, is fitted independently to 274

each index time series of raw values previously detrended and normalized and has the form: 275

xn +1

= axn

+ σw , (2) 276

13

where xn is the simulated value of a given index at time n; x

n +1 is its value at time n+1; w is a 277

random number drawn from the standard normal distribution with zero mean and unit variance, 278

while parameters a and σ are computed by linear regression. 279

Resulting surrogate time series are subject to the same analyses, M-SSA and correlation 280

analysis, as are the ‘real data’ time series. Analyses on the surrogate values are repeated 1000 281

times and the 95th

percentile of results is computed (see WKT and WP for details). 282

283

3 Stadium-wave relationships 284

The stadium-wave signal propagation sequence through the network of eight original indices is 285

shown in Figure 2a. Low-frequency behavior is evident, although the random occurrence of a 286

multidecadal tempo in a time series of only 100 years cannot be ruled out. WKT therefore did 287

not assign an exact period to the signal; rather, the signal is described as secularly varying, with 288

an apparent 64-year period during the 20th

century. Despite limitations of a short time series, its 289

short length does not prevent assigning strong statistical significance to patterns of variability 290

that are shared by all indices in the network. Regional diversity of indices made this finding 291

more significant, adding a spatial signature to the signal. Phasing-offsets among the indices, 292

repeating in an orderly fashion, indicate the signal’s propagating nature. Figure 2b shows the 293

leading two modes of the WKT signal plotted on an M-SSA spectrum; p < 5%. 294

Figure 3 shows a plot of normalized reconstructed components of the stadium-wave 295

signal in one of the 20th

-century expanded networks analyzed. In Figure 4, mean variances of the 296

modes are plotted on an M-SSA spectrum including error bars and the red-noise envelope. The 297

leading two modes are well-separated from all others, with overlapping error bars, reflecting 298

similar variances of the two modes. This statistically significant signal (p < 5%) is essentially the 299

14

same signal identified in WKT and was repeatedly identified in other hemispherically 300

representative index combinations, ranging in network size from four members to 20. 301

The spatially expanded networks reveal dynamical links not apparent in WKT. In 302

addition to the role of the Atlantic Ocean identified by WKT, our results elucidate roles played 303

by the atmosphere and Arctic sea ice. As this signal propagates, distinct regimes of warming or 304

cooling hemispheric temperature trends prevail. Based on this analysis, we propose that there are 305

four stages of a climate regime, which are indicated in the annotation of Figure 3. Each stage is 306

dominated by a particular type of behavior, with a particular geographical focus. Each stage 307

features a subset of indices within the broader network whose behaviors reach peaks and valleys 308

at similar times. We term these four co-varying index clusters ‘Temporal Groups’ (I-IV). 309

Not all indices express the signal equally. The amount of variability due to the stadium-310

wave signal in each index is captured in a channel fraction variance plot (Figure 5). The circled 311

regions indicate channel fraction variance values for index clusters of the four Temporal Groups. 312

Indices in Groups I and IV express the signal strongly. Expression of the signal is less in Group 313

II indices. Group III indices have a large range of fractional variances. Channel fraction variance 314

is tied to an index’s dominant time scale of variability. Indices with long ‘memories’ 315

(persistence), which fluctuate at low-frequency tempos, manifest the stadium-wave signal the 316

most strongly. These indices tend to integrate into their ‘memory’ incremental direct or indirect 317

forcings of higher frequency indices, such as incremental changes in wind or ice cover. We 318

suggest that long-memory indices in Groups I and IV tend to represent the ‘cumulative’ effect of 319

interacting processes related to higher frequency dynamics. AMO is an example of an index that 320

integrates incremental forcings of higher frequency sub-processes. We will show that it is the 321

long-memory indices that set the signal tempo, while the higher frequency atmospheric indices 322

15

carry the signal hemispherically and reinforce the low frequency tempo via accumulated sub-323

process-related forcings incorporated into the ocean memory. Sea ice appears to link the lower 324

and higher frequency indices. 325

Maximum values of indices characterizing Groups I, II, III, and IV represent the timing 326

of trend reversals of Group clusters as the wave propagates through the four stages of a warming 327

climate regime. Similarly, minimum values of these Group indices represent the timing of 328

oppositely signed trend reversals that occur in sequence as a cooling regime unfolds. In the 329

discussion to follow, we focus on evolution of a warming regime, but it is implicit that a cooling 330

regime evolves similarly but with opposite sign4. 331

332

3.1 Temporal Groups 333

A Temporal Group’s indices tend to reflect a dominant geographic region exhibiting a dominant 334

set of sub-processes. This is especially apparent in Groups I through III. Group IV differs 335

slightly. Instead of representing specific sub-processes of a region, Group IV indices reflect a 336

culmination of influences of anomalies of sub-processes. 337

Peak activity within each of the four Groups represents stages of climate regime 338

development as the signal propagates through the network. To obtain plots of these Groups, 339

reconstructed components (RCs) of indices whose peak values represent each stage of regime 340

development are extracted from an expanded network (e.g. Figure 3) to which M-SSA was 341

applied. Representative RCs then are plotted according to Group. Tables 3 through 6 reflect 342

correlation values between raw time series (detrended, normalized, and smoothed with a 13-year 343

filter) of index pairs. Significance levels = p<5% are shown in blue; p<1% are shown in red. 344

4 Terminology: We refer to stages of a cooling either as the minima of Groups I through IV, or as peak values of

Groups –I, -II, -III, and –IV.

16

345

3.1.1 Temporal Group I: Ocean-ice interactions in the North Atlantic sector of the Arctic 346

predominate in this Group. Cool Atlantic sea-surface temperatures (ngAMO) correlate strongly 347

with positive sea ice extent of the Greenland and Barents Seas (NEB) - and by extension, with 348

sea ice of the West Eurasian Arctic (WIE) (Table 3a). 349

Negative PCI co-varies with Group I (Table 3b), which may reflect the remote and 350

cumulative teleconnected influence of Pacific circulations on the Atlantic’s freshwater balance. 351

An atmospheric bridge, of sorts, conveys Pacific influence on Atlantic precipitation patterns. 352

Through modified atmospheric patterns, associated Pacific sea-surface-temperature anomalies 353

are linked to surface salinity anomalies of the Atlantic, ultimately providing negative feedback to 354

the Atlantic Meridional Overturning Circulation (AMOC) (Latif et al. 2000; Schmittner et al. 355

2000; Latif et al. 2001), and by extension, the AMO (Knight et al. 2005; Latif et al. 2006; 356

Msadek et al. 2010a), setting the stage for the AMO’s subsequent influence on ice inventory. 357

Plotted raw indices in Figure 6 reflect the relationships among ngAMO, the negatively signed 358

cumulative sum of PDO, and ngPCI – an index related to decadal-scale trends of Pacific 359

circulation patterns. 360

Globigerina bulloides and the Atlantic SST Dipole correlate strongly with Group I 361

indices. Positive values of G. bulloides suggest enhanced upwelling of cold water off the coast of 362

Venezuela (Black et al. 1999), which may be associated with a southward displacement of the 363

Atlantic sector of the Intertropical Convergence Zone (ITCZ). The negative polarity of the 364

Atlantic SST Dipole suggests the same. A south shifted ITCZ is linked to a weakened Atlantic 365

meridional overturning circulation (AMOC) (Latif et al. 2006; Donohoe et al. 2013, Kang et al. 366

2012; Marshall et al. 2013). These dynamics co-occur with the shifting Arctic Front in response 367

17

to the migrating sea-ice edge (e.g. Zakharov 1997, 2013), related to phase of AMO. Figure 7 and 368

Table 3c reflect these relationships: as sea ice increases with a cool AMO and a weak AMOC, 369

the sea ice edge advances equatorward, and the ITCZ shifts southward (section 2.1), as indicated 370

by positive anomaly values of GB and ngDipole. (See WKT on AMOC-AMO link.) Peaks of 371

index plots occur near ~1918 and 1976, with a minimum at ~1942. These are timings of 372

previously identified climate-regime shifts (Tsonis et al. 2007; Van Loon et al. 2007). 373

374

3.1.2 Temporal Group II: Atmospheric response to an ice-induced polar-equatorial meridional 375

temperature gradient, particularly pronounced in the Siberian sector of the Eurasian Arctic, 376

characterizes Temporal Group II (Figure 8). Indices peak ~1923 and ~1982 and minimum 377

values center on ~1950. Co-varying indices in Group II include the ice index of ArcSib north of 378

Siberia and AT, a measure of the zonal component of large-scale wind flow. The SST-based 379

proxy representing NPGO also co-varies with this Group. NPGO is a wind-driven ocean-gyre 380

index in the North Pacific, related to both extratropical atmospheric dynamics and to meridional 381

migrations of the Pacific ITCZ. Positive co-variance among these sea ice and wind related 382

indices (Table 4) is consistent with a basin-scale wind response to the polar-equatorial 383

meridional temperature gradient (Honda et al. 2009; Petoukhov and Semenov 2010; Outten and 384

Esau 2011): increased sea ice extent inhibits ocean-heat flux to the atmosphere, thus cooling 385

Arctic temperatures, augmenting a meridional atmospheric temperature gradient, and thereby 386

intensifying large-scale wind flow with an enhanced zonal component. Boreal winter indices, 387

NAO and AO5, also co-vary with Group II. 388

389

5 Winter indices of NAO and AO behave differently from their annual counterparts. In table and figure legends used

in this paper, we emphasize the use of winter indices by adding the letter ‘w’: e.g. NAOw and AOw.

18

3.1.3 Temporal Group III: North Pacific activity and ice-influenced atmospheric dynamics 390

dominate Temporal Group III (Figure 9). Continued sea ice attrition west of the Pacific sector 391

and the subsequent increase of ocean-heat flux to the atmosphere in that region remotely 392

influence Pacific circulations by shifting air mass away from the high latitudes, displacing it to 393

mid-latitudes. Latitudinal redistribution of atmospheric mass weakens the Arctic High, effects of 394

which extend to the Pacific as the anomalous low-pressure system expands (e.g. Overland et al. 395

1999; van Loon et al. 2007), intensifying the Aleutian Low. These processes are reflected in the 396

strong connections between the Pacific centered circulations (NPO, ALPI, and PDO) and 397

anomaly trends (cumulative-sums (cs)) of WIE, TIE, and Kara Sea ice (Table 5a). We 398

hypothesize that these relationships reflect the incremental influence of sea ice extent 399

fluctuations on the atmosphere that are consistent with observed dynamics (e.g. Zakharov 1997; 400

Bengtsson 2004; Frolov et al. 2009): incremental reductions in ice cover (particularly in the 401

Atlantic sector) lead to increased ocean-heat flux to atmosphere, promoting a decrease in sea-402

level-pressure of the Arctic High, the influence of which ultimately extends into the Pacific (e.g. 403

Overland et al. 1999; van Loon et al. 2007). Group III indices peak ~1929-1933 and ~1985-1990. 404

The multidecadal component of EIE – sea ice of the Laptev, East Siberian, and Chukchi 405

Seas – positively co-varies with Pacific centered circulations. The sea ice edge in the Pacific 406

shifts southward with increasing trends in this stage (Asmus et al. 2005; see Frolov et al. 2009), 407

coinciding with a weakening Arctic High, displacement of atmospheric mass equatorward, and 408

an increased number of cyclones co-varying with an intensified Aleutian Low. 409

Centuries-long records reveal decadal-scale variability of Japanese sardine outbursts in 410

the Kuroshio-Oyashio western-boundary-current extension. Japanese sardine outbursts co-vary 411

positively with Pacific circulations - PDO, in particular (Table 5b). Fueling these outbursts is an 412

19

increased supply of nutrients – a product of a deepened mixed-layer depth (Polovina et al. 1995). 413

Yasuda (2003) demonstrate a relationship between Japanese sardine outbursts and a deepened 414

mixed-layer-depth to ‘Oyashio Intrusions’ - southward shifts of the Kuroshio-Oyashio boundary 415

– the ocean-gyre boundary that separates the Oyashio Current of the subpolar region from the 416

Kuroshio Current of the subtropical zone. The Kuroshio-Oyashio front shifts southward as the 417

sea ice edge in the Pacific sector of the Arctic advances and as PDO increases (Miller and 418

Schneider 2000). Between the mid-1960s to the mid-late 1980s EIE and Pacific circulations 419

increased. Japanese sardine populations also increased. The mixed-layer depth was unusually 420

deep (Yasuda et al. 2000). Similar trends occurred between ~ 1905 and the early 1930s as Group 421

III indices were increasing. 422

423

3.1.4 Temporal Group IV: High latitudes of the Northern Hemisphere are the focus in Temporal 424

Group IV. The culmination of anomaly trends of the various large-scale wind and wind-related 425

patterns, particularly those related to Group II, are featured (Figure 10). They co-vary with the 426

Arctic temperature and NHT, perhaps indicating a relationship between intervals of anomalies 427

(in sea ice extent, corresponding ocean-heat flux, and associated winds and wind-related 428

dynamics) and the overlying temperature. Correlations among these indices are listed in Table 6a 429

and further discussed in section 4. The anomaly trend of ArcSib leads indices of this Group by 430

~3 years. Also co-varying with this Group is Earth’s rotational rate (ngLOD). It is strongly 431

correlated to the anomaly trend of large-scale wind patterns (csAT) and by extension, the Arctic 432

temperature and NHT (section 2.1 and Table 6b). 433

Maxima of Group IV indices occur around 1938 and 1998. At these times of peak Arctic 434

temperature and NHT, AMO is nearing maximum warmth, sea ice in NEB and WIE continues to 435

20

shrink (Table 6c), and the poleward retreated sea ice edge in the Atlantic sector displaces the 436

Arctic Front far northward. The Atlantic ITCZ is similarly displaced. Minima center on ~1910 437

and 1971 and host the same dynamics, yet of opposite sign. 438

439

3.2 Changing Index Relationships as a Regime Evolves 440

Index relationships appear complex as the regimes evolve. Figure 11 simplifies the pattern: 441

trends of successive Group-indices systematically and sequentially reverse as the signal 442

propagates through stages of a regime. Stages, which coincide with peaks of each Group, are 443

indicated by vertical lines. Each Temporal Group is represented by one index (e.g. AMO, AT, 444

PDO, and Arctic T) for the sake of simplicity, and all indices are shown as positively signed6 in 445

order to illustrate our point. Ice indices are not included in this discussion; only ocean, 446

atmosphere, and temperature indices are considered. The chart begins in 1910 (peak of Group –447

IV) with a transition from a cooling regime to a warming one. In ~ 1910, prior to the beginning 448

of the warming regime that began ~1918, indices representing Groups II through IV are trending 449

together (red lines). Their values are increasing, while AMO of Group I is trending out-of-phase 450

(blue line). An AMO trend in opposition to other indices marks the transition between regimes. 451

Once the AMO reverses trend, as it did in ~1918 at the peak of Group I when the Atlantic 452

was at its coolest, all indices of all Groups are increasing. This shared uni-directional upward 453

trend among indices distinguishes an incipient warm regime – i.e. stage I. As the wave 454

progresses through the network sequence, passing through successive stages, indices begin to 455

reverse trend direction, one-by-one. 456

After the peak of Group II, all indices continue to increase except for AT and its co-457

varying Group II indices. After the peak of Group III, AT and PDO, and related indices have 458

6 This is in contrast to AMO in all stadium-wave figures, where AMO is plotted in its negative polarity (ngAMO).

21

reversed trend, now decreasing. AMO and surface temperatures continue an upward trend until 459

the peak of Group IV. After the peak of Group IV, AT, PDO, and ArcT are all decreasing; while 460

only AMO continues to increase. This continued upward trend of AMO, co-occurring with all 461

other indices in decline, marks the transition at the end of the warming regime, leading into a 462

cooling regime. After a several year transitional interval, the ensuing cooling regime begins with 463

AMO reversing trend ~ 1942. All indices decrease during this initial stage of a cooling regime. 464

Stages one through four of the cooling regime, indicated by peaks of Groups –I through –IV, 465

lead to the next regime transition in ~1971. A new regime of warming begins ~1976. 466

467

4 Stadium-Wave Mechanisms 468

WKT hypothesized that the stadium-wave signal propagates through a hemispheric network of 469

synchronized climate indices. We have argued that through this propagation, climate regimes 470

evolve in four stages. Low-frequency variability of sea ice extent in the Eurasian Arctic Seas is a 471

critical component underpinning the hypothesized signal and multi-decadal scale evolution of 472

climate regimes. 473

What makes sea ice in this particular region so fundamental to the wave’s existence? Sea 474

ice in the Northern Hemisphere is uniquely exposed to open ocean (the North Atlantic) in the 475

Eurasian Arctic. This juxtaposition governs sea ice growth by giving the Atlantic Ocean 476

dominant constructive or destructive influence over the feature mostly responsible for wintertime 477

sea ice cover, the halocline. The halocline is a subsurface zone, approximately 150 meters thick, 478

where salinity concentration changes rapidly with depth; in the North Atlantic sector of the 479

Arctic, salinity values decrease with depth. Formation of the halocline relies upon the interaction 480

between layers of water with contrasting properties: Overlying cool, desalinated Arctic surface 481

22

water mixes with warm, saline water below. The halocline’s resulting vertical density structure, 482

in turn, maintains separation between the two water masses and prevents ocean heat at depth 483

from reaching the surface. Where a strong halocline exists, sea ice growth is promoted (Zakharov 484

1997; Frolov et al. 2009 and references within). Ice extent influences large-scale wind patterns, 485

which influence long-term temperature trends (e.g. Outten and Esau 2011). Thus dynamics that 486

either build or destroy the halocline in the North Atlantic sector of the Arctic have a marked 487

influence on climate-regime evolution as the stadium-wave propagates through the network. 488

The schematic of Figure 12 and sections 4.1 through 4.5 summarize the stadium-wave’s 489

propagation through the four stages of climate regime evolution. We discuss only stages I 490

through IV of the evolution of a warming regime. (Stages –I through –IV of the cooling regime 491

are simply opposite.) 492

493

4.1 Processes and Trends Relate to Stage I 494

A regime of warming temperature commences with maximum cool sea-surface temperatures in 495

the North Atlantic. Sea ice extent in the West Eurasian Arctic (WIE) is at maximum values. 496

ITCZ is displaced to its most southerly position. For a decade-plus prior to these index maxima, 497

conditions conducive to sea ice growth in the Atlantic sector of the Arctic have been building. 498

These include high sea-level-pressure anomalies in the Arctic High. Associated with the high 499

sea-level-pressure anomalies are anticyclonic-wind anomalies that govern sea ice export patterns 500

within the WIE region. Their net effect is to bolster halocline development through freshening of 501

the Greenland, Barents, and Kara Seas (Bengtsson et al. 2004; Frolov et al. 2009 and references 502

within). The atmospheric Arctic Front shifts southward with the advancing ice edge (Zakharov 503

1997). Precipitation zones shift southward, gradually reducing freshwater delivery to the Arctic – 504

23

a negative feedback sowing future reversal of the regime against a backdrop of dominantly 505

positive feedbacks reinforcing sea ice growth. This stage ends with AMO, WIE, and ITCZ 506

having reversed their trends. 507

508

4.2 Processes and Trends Related to Stage II 509

Sea ice of WIE dominates, despite its recently reversed trend. Even though AMO is slowly 510

warming, ocean heat flux is inhibited by the ice cover and the atmosphere at high latitudes chills. 511

Simultaneously, yet in quadrature offset, EIE in the Laptev, East Siberian, and Chukchi Seas is 512

growing. Group II indices respond to the increasing, albeit eastward shifting, distributions of 513

total ice cover – a region dominated by the Kara Sea. Total ice cover, specifically ArcSib, co-514

varies with a strong meridional temperature gradient that simultaneously develops between the 515

ice and snow covered surfaces of high latitudes and the warm surfaces of lower latitudes in the 516

Eurasian region. In atmospheric response, large-scale winds (AT) strengthen; their zonal 517

component advecting heat and moisture from the lower latitudes of the Atlantic Ocean to the 518

mid-to-high latitudes of the Eurasian landmass downwind, disrupting previously stable surface 519

conditions and increasing high cloudiness, both changes leading to increasing continental 520

temperatures, in particular those at low altitudes and higher latitudes (e.g. Van Loon et al. 2007). 521

Cyclonic (negative sea-level-pressure) anomalies weaken the Arctic High; westerly winds 522

increase in intensity, further advecting atmospheric heat and moisture eastward. WIE from 523

Group I is now decreasing, in part due to changing sea ice export patterns. The cyclonic winds 524

altering the ice export pattern that previously augmented the WIE inventory now are restricting 525

the freshwater supply to the western marginal seas (Gudkovich and Nikolayeva 1963; see Frolov 526

et al. 2009). The Arctic Front’s southward displacement continues to deprive the Arctic of 527

24

precipitation and related runoff. The anomalous cyclonic winds dynamically impact the ice, 528

leading to open cracks in the ice surface through which heat from the ocean escapes, heating the 529

overlying atmosphere. Winds increase influx of warm Atlantic water into the Arctic. The initial 530

cold signal converts to a warming one. Initially, ice scripted the atmospheric response. The 531

atmosphere now begins directly and indirectly to modify the ice cover. The Atlantic sea ice edge 532

retreats, its progress traced by similar northward migrations of the Arctic Front and the ITCZ. 533

Ocean-heat flux to the atmosphere increases. Surface temperatures increase. The regime thus far 534

built by processes reflecting the stadium-wave propagation through Group I and II indices 535

continues to mature. The halocline is now deteriorating, inhibiting sea ice growth. ArcSib has 536

reached peak values and WIE is in decline. 537

538

4.3 Processes and Trends Related to Stage III 539

As the ArcSib and resulting winds related to AT and NPGO begin to wane, WIE continues to 540

decrease and AMO continues to warm along with surface air temperatures. Westerlies continue 541

to dominate, albeit more shifted toward the North Pacific. Atmospheric (NPO, ALPI) and related 542

oceanic patterns (PDO) are increasing as an indirect result of the sea ice attrition in WIE. 543

Enhanced ocean-heat flux leads to lower SLP anomalies in the Arctic High. The deepened 544

center-of-action extends well into the North Pacific, intensifying the Aleutian Low, which shifts 545

its center south and east. East Eurasian sea-ice (EIE) governed by complex and competing ice-546

atmosphere-ocean interactions, increases with strengthening Pacific circulations, tracking in-547

quadrature with AMO and WIE. Wind-flow patterns in the Atlantic sector of the Arctic are 548

decreasing the freshness of the shelf seas in the western Eurasian region, via modified sea ice 549

export patterns between the Arctic Basin and marginal seas (Subbotin 1988; Frolov et al. 2009). 550

25

This overarching process coincides with a second, more localized wind pattern that is generated 551

by a sea-level-pressure anomaly, the source of which lies near the Barents-Kara border. These 552

winds, confined to the lower troposphere, now coax an influx of saline water from the warming 553

Atlantic into the Barents and Kara Seas (Bengtsson et al. 2004). Both wind-related patterns 554

reduce the halocline. WIE continues to diminish and ArcSib is in decline. As the signal continues 555

its propagation, this penultimate stage of climate-regime development begins to weaken and all 556

of sea ice indices now are decreasing: WIE, ArcSib, TIE, and EIE. The sea ice edge in the 557

western Eurasian Arctic continues its poleward retreat. 558

559

4.4 Processes and Trends Related to Stage IV 560

By the time Group IV indices begin to peak, positive anomalies of ArcSib and its associated 561

winds cease. The Arctic temperature and NHT reach maximum values. Unlike at other stages of 562

regime development, no sub-processes of our expanded network peak at stage IV. Instead, 563

anomaly trends peak, representing the conclusion of a multidecadal stretch of anomalies of sub-564

processes related to Group II. These anomaly trends represent the culmination of impacts related 565

to interlinked changes in sea ice extent, ocean-heat flux, sea-level-pressure, large-scale wind and 566

sea-ice-export patterns, position of Arctic Front, and consequent atmospheric heat and moisture 567

influx into the Arctic (Zakharov 1997; Francis and Hunter 2007) - their collective interaction 568

coinciding with an increased influx of Atlantic Intermediate Water into the Arctic, the 569

temperature anomalies of which closely co-vary with Arctic temperatures (Bengtsson et al. 2004; 570

Polyakov et al. 2004, 2005, 2010). In effect, incremental forcings resulting from a cascade of 571

feedbacks reducing sea ice extent appear to be integrated into the system. The product of their 572

collective impact is expressed in peak values of Arc T. NHT lags by about a year or two. 573

26

Simultaneous with the culmination of anomalies that have been collectively destroying 574

ice and delivering heat to the Arctic are processes that counter this trend. One example is the 575

poleward displacement of the Arctic Front due to the retreating sea ice edge. Precipitation and 576

associated runoff are similarly displaced poleward. They are major supplies of freshwater for the 577

subsequent regime’s ice growth. But for now, only decreasing ice, increasing Atlantic sea-578

surface temperatures, and warming surface-air temperatures are apparent. 579

580

4.5 Transition: After temperatures peak, surface temperatures begin to decrease, while AMO 581

continues to warm and sea-ice extent continues to wane. This short duration of seemingly 582

incongruent index trends marks regime transition, indicated by dashed line on Figure 12, from 583

the peak of Group IV to the regime reversal at the peak of Group –I. Once the peak of Group –I 584

is reached, a maximally warm AMO reverses trend; WIE begins to rebound. A new regime of 585

cooling begins - punctuation on a continuum of an ever evolving, quasi-oscillatory system. 586

587

5 Summary and Discussion 588

We used multivariate statistical analysis to extend the WKT hypothesis of a secularly varying 589

signal hemispherically propagating through a network of synchronized climate indices during the 590

20th

century. We expanded the original database with the incorporation of Arctic sea ice and a 591

variety of other parameters, including proxy data reflecting sub-processes within the wave. Sea 592

ice in the shelf seas of the Eurasian Arctic region emerged in this study as playing the pivotal 593

role in propagating and sustaining the 20th

century stadium-wave signal, with interaction of 594

positive and negative feedbacks governing the ice coverage and related atmospheric/oceanic 595

responses. 596

27

We found that the stadium-wave signal propagates through four different stages of 597

climate regime evolution. Each stage reflects a particular behavior or a particular set of sub-598

process interactions. And at each stage, activity is heightened in a particular geographic region. 599

At all stages, seeds of regime reversal are embedded within the collection of sub-processes 600

regulating the Arctic freshwater balance, thereby subtly and incrementally imposing ‘curbs’ on 601

the prevailing trend of sea ice coverage, assuring an inevitable regime reversal years in the 602

future. These negative feedbacks modify the Arctic freshwater balance through: i) sea ice related 603

shifts in the Arctic Front and associated zones of precipitation and continental runoff; ii) ice-604

cover associated sea-level-pressure changes that reorganize winds and thereby direction of 605

freshwater and sea ice export between the Arctic Basin and marginal seas; iii) modified influx of 606

warm, saline water into the marginal seas, particularly in the Atlantic sector; iv) and Pacific 607

atmospheric circulation anomalies negatively feeding back onto the Atlantic freshwater balance 608

through remote modification of precipitation regimes. 609

A robust halocline and extensive ice cover introduce a warm regime and promote 610

processes that lead to their destruction. Overshadowed are the accruing embedded ‘curbs’ that 611

ultimately moderate the destruction and bring a warm regime to its close. Reduced ice cover and 612

a weak halocline at the end of a warming interval initiate a cooling regime whose dynamics 613

collectively rebuild the halocline and ice cover, accompanied by an accumulating influence of 614

embedded ‘curbs’ that ultimately reverse the trend. Our results for this multidecadal component 615

of Eurasian Arctic dynamics are consistent with the ideas of Zakharov (1997) who describes the 616

oscillatory nature of the ice-ocean-atmosphere system in terms of ‘braking’ – the idea that 617

positive and negative feedbacks interact in such a way as to limit trends of sea ice growth and sea 618

ice destruction. 619

28

Sub-processes that interact to impose this blueprint of positive and negative feedbacks 620

and the consequent temperature trends are schematically summarized in Figure 13. This 621

stadium-wave ‘wheel’ cartoon representation combines components involved in stadium-wave 622

propagation with the co-varying proxy indices. The wheel is divided into eight segments, each 623

representing a Temporal Group of co-varying indices: four positive-polarity Groups and four 624

negative-polarity Groups. Roman numerals designating the Temporal Group number are 625

positioned at the narrow end of its associated segment. Indices of each Temporal Group populate 626

the designated wheel segment. Dates on the perimeter indicate dates around which the indices 627

peaked (or are projected to peak); these dates represent stages of regime development: four 628

stages for a warming regime (dates in red) supplanted by four stages of a cooling regime (dates 629

in blue). Differently colored rings host indices belonging to shared process or medium, e.g. WKT 630

indices in the inner grey ring; ice indices in the yellow ring; wind related ones in the blue; and 631

co-varying proxy indices in the outer green ring. Read clockwise to follow the propagating wave 632

as it moves through each of the three systems – ocean, ice, and wind – divided among the 633

Temporal Groups, the peaks of which represent stages of climate-regime evolution, the processes 634

of which leave traces etched into the co-varying proxy indices. 635

By framing regime evolution in context of stadium-wave propagation, we gain insight 636

into behaviors resulting from the temporal alignment of the different stages. For example, 637

McCabe et al. (2004) document drought patterns of the western United States, finding their 638

occurrences increase with warm AMO phases. North-south distribution of drought patterns is 639

further scripted by which phase of PDO co-occurs with AMO. The stadium wave also provides 640

perspective on seemingly discordant observations. Examples can be found in the previously 641

discussed out-of-phase alignment of surface air temperature with AMO that occur during 642

29

hypothesized transitions between regimes; and in changing trends of sea ice among the various 643

seas during intervals of dominantly positive or negative surface temperature anomalies. 644

We suggest that the stadium-wave hypothesis holds promise in putting in perspective the 645

numerous observations of climate behavior; offers potential attribution and predictive capacity; 646

and that through use of its associated proxies, may facilitate investigation of past behavior that 647

may better inform our view of future behavior. 648

In recent decades, rapid changes in the Arctic have been documented (e.g. Alkire et al. 649

2007). Most interpretations of the recent decline in Arctic sea ice extent have focused on the role 650

of anthropogenic forcing (e.g. Johannessen et al. 2004), with some allowance for natural 651

variability (e.g. Zhang el al. 2010). How can we interpret the recent decline of Arctic Sea ice 652

extent in context of the stadium wave? Alexeev et al (2013) observe pronounced low ice 653

coverage between 2004 and 2008 and conclude it is primarily linked to the temperature of the 654

influx of the Atlantic Intermediate Water (AIW; Polyakov et al. 2004, 2010) into the Barents 655

Sea. Data values of the Eurasian region in 2008, not included in our analysis, indicate maximum 656

summer ice-cover destruction in the ArcSib region east of the Barents Sea, accompanied by late-657

onset of sea ice growth the following winter months. And further to the east, influx of warm 658

Pacific water through the Bering Strait has been identified (Shimada et al. 2006; Wang et al. 659

2009; Alexeev et al. 2013) as one factor contributing to the Arctic sea ice decline there. None of 660

these observations are inconsistent with the stadium wave, which if extrapolated beyond the 20th

661

century, reflects low ice in all three regions cited: the WIE, ArcSib, and EIE (see Figure 3). But 662

according to stadium-wave projections, and according to our interpretation of stadium-wave 663

evolution, this trend should reverse, under the condition that the stadium-wave hypothesis 664

30

captures 20th

century dynamics correctly. Rebound in WIE, followed by ArcSib should occur 665

after the estimated 2006 minimum of WIE and maximum of AMO (e.g. Figures 3, 10, and 13). 666

Timmermans et al. (2011) measured a notable increase in surface freshening of the region 667

of the Greenland Sea, between the North Pole and the Fram Strait in 2010 that was not due to 668

summer melt. Using models to interpret their observations, they concluded that relatively abrupt 669

changes documented to have occurred in 2009 in large-scale wind patterns could account for 670

freshening via re-distribution of freshwater within the Arctic and an increase in river runoff. 671

Timmermans et al. concede that they cannot speculate on duration of this observed freshening 672

and wind shift, but note that the upper-ocean salinity changes are not of seasonal origin. 673

While evidence strongly supports our hypothesis of a secularly varying climate signal 674

propagating through a hemispheric network of synchronized ocean, atmosphere, and ice indices 675

during the 20th

century, we cannot know if this variability, tempo, and sequential chronology will 676

continue into the future. How changes in external forcing might affect the Eurasian Arctic sea ice 677

in context of an apparent quasi-oscillatory ocean-ice-atmosphere system is a burning question. 678

Modeled results are often invoked to guide projected climate trends, yet WP found no 679

decadal to multidecadal-scale hemispherically propagating signal in networks of indices 680

simulated from data generated by runs of the CMIP3 suite of models, leading to the inference 681

that 21st-century model simulations may not accurately capture dynamics necessary to 682

reconstruct stadium-wave behavior. 683

Understanding how stadium-wave behavior might respond to changing external forces 684

may be facilitated by extending the record prior to the 20th

century via proxy data. Evaluation of 685

300-year records of proxies by Wyatt (2012) suggests that changes occurred in tempo and 686

amplitude prior to the 1800s, perhaps in response to changes in external forcing. Proxy-process 687

31

relationships established throughout the paper, representing the proposed four stages of climate-688

regime evolution, suggest a means of extending the stadium-wave signal’s record, providing 689

potential insight into attribution of behavior past, present, and future. 690

691

Acknowledgments We thank S. Kravtsov for helpful guidance on statistical aspects of this 692

study; Vasily M. Smolyanitsky, who provided data and helpful feedback on our work; and two 693

anonymous reviewers for comments on an earlier version of the manuscript, which helped clarify 694

the presentation. Judith Curry’s contributions to this paper were supported by a DOE STTR 695

grant. 696

697

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936

937

938

42

Table Captions 939

Table 1. Index descriptions for indices appended to original stadium-wave network 940

Table 2. Ice Categories: Correlations of sea ice-extent in shelf seas of the Eurasian Arctic. Seas 941

are grouped in several ways. Each group plays a specific role in the generation and/or 942

transmission of climate signal. Raw data smoothed 13-y. Significance levels: in 943

red=p<1%; in blue =p< 5%. 944

Table 3a. Temporal Group I: correlations reflecting ocean-ice coupling. Raw data smoothed 13-945

y. Significance levels: in red=p<1%; in blue = p<5%. 946

Table 3b. Temporal Group I: correlations reflecting relationship between anomalies of Pacific-947

centered circulations and Group I indices. Raw data smoothed 13-y. Significance levels: 948

in red=p<1%; in blue = p<5%. 949

Table 3c. Temporal Group I: correlations of Proxies with Group I indices. Raw data smoothed 950

13-y. Significance levels: in red=p<1%; in blue = p<5%. 951

Table 4. Temporal Group II: correlations reflecting ice-atmosphere coupling. Significance 952

levels: in red=p<1%; in blue = p<5%. 953

Table 5a. Temporal Group III: Correlations between anomaly trends of sea ice extent and 954

associated wind patterns with Pacific-centered ocean/atmosphere circulations. 955

Significance level: in red=p<1%. 956

Table 5b. Temporal Group III: Japanese Sardine Proxy with Pacific-centered circulation-pattern 957

indices. Significance level: in red=p<1%. 958

Table 6a. Temporal Group IV: anomaly trends of sea ice extent and related circulation patterns 959

correlate with temperature. Significance levels for correlations: in red=p<1%; in blue = 960

p<5%. 961

43

Table 6b. Temporal Group IV: ngLOD proxy with wind anomaly and Arctic T. Significance 962

levels: in red=p<1%; in blue =p< 5%. 963

Table 6c. Temporal Group IV: correlation shows relationship of Arctic temperature with sea ice 964

in WIE. Significance Levels: in red=p<1%; in blue = p<5%. 965

966

967

968

969

970

971

972

973

974

975

976

977

978

979

980

981

982

983

984

44

Figure Captions 985

Fig. 1. Arctic Ocean and marginal seas used in this study (1-6 in this study (shaded in gray)): 1) 986

Greenland Sea, 2) Barents Sea, 3) Kara Sea, 4) Laptev Sea, 5) East Siberian Sea, 6) 987

Chukchi Sea. Categories of Seas include: NEB = 1&2; ArcSib = 3-6; WIE = 1-3; EIE = 988

4-6; and TIE = 1-6. [Also shown: 7) Beaufort Seas, 8) Baffin Bay, 9) Hudson Bay, and 989

10) the Norwegian Sea.] Adapted with permission from: Frolov et al. 2009. 990

Fig. 2. a) Plot of MSSA normalized RCs 1&2 of Original 20th

-century Stadium-Wave (adapted 991

from Wyatt et al. 2011 (WKT)). Note: NHT and AMO are negative; b) M-SSA spectrum 992

of a. Error bars in b are based on North et al. (1982) criterion, with the number of 993

degrees-of-freedom set to 40, based on decorrelation time of ~2.5 years. Red-dashed lines 994

in panel (b) represent the 95% spread of M-SSA eigenvalues based on 100 simulations of 995

the 8-valued red-noise model (1), which assumes zero true correlations between the 996

members of the eight-index set. 997

Fig. 3. Annotated Expanded ‘Stadium Wave’ shows 20th

-century signal propagation through a 998

15-index-member network. Selected indices are a sub-set of a broader network. Four 999

clusters of indices are highlighted (+/- I through IV). Each cluster is termed a “Temporal 1000

Group”. Peak values of Group indices represent stages of climate-regime evolution. Each 1001

is discussed individually (see text) and plotted (Figures 7-10). Plotted indices are 1002

normalized reconstructed components of M-SSA modes 1&2. 1003

Fig. 4. M-SSA spectrum of expanded stadium-wave network shown in Figure 3. Error bars are 1004

based on North et al. (1982) criterion, with the number of degrees-of-freedom set to 40, 1005

based on decorrelation time of ~2.5 years. Red-dashed lines in panel represent the 95% 1006

spread of M-SSA eigenvalues based on 1000 simulations of the 15-valued red-noise 1007

45

model (1), which assumes zero true correlations between the members of the 15-index 1008

set. 1009

Fig. 5. Channel-fraction variance due to M-SSA leading modes 1&2. Values indicate the amount 1010

of an index’s variability that is due to the stadium-wave signal. Indices represent Groups: 1011

I [WIE, AMO, GB]; II [ArcSib, AT, NAOw, NPGO]; III [EIE, NINO, JS, PDO, ALPI]; 1012

IV [ArcticT, ngLOD, and NHT]. 1013

Fig. 6. Raw data plots: 20th

-century relationships among anomaly trends of negatively signed 1014

Pacific circulations (e.g. ngPCI and -csPDO) and the trend of ngAMO. “Change-points” 1015

of anomaly trends indicate endings of intervals dominated by either positive or negative 1016

anomalies. Change-points of Pacific anomaly trends co-occur with extrema of the AMO 1017

curve. Plotted indices: raw data. AMO smoothed 13y; ngPCI and-csPDO are not 1018

smoothed. 1019

Fig. 7. Temporal Group I: characterized by ocean-ice coupling, with focus of activity in the 1020

Atlantic sector. Peak values center on ~1918 and 1976; minimum values in the 20th

1021

century center on ~1942. Associated proxies are the G. bulloides and ngDipole. Plotted 1022

indices are normalized reconstructed components of M-SSA modes 1&2. 1023

Fig. 8. Temporal Group II: characterized by ice-atmosphere coupling. Sea ice extent in Russian 1024

Arctic (ArcSib) and related large-scale wind patterns co-vary with peak values centered 1025

on ~1923 and ~1982; minimum values center on ~1950. Associated proxy is the NPGO 1026

proxy. Plotted indices are normalized reconstructed components of M-SSA modes 1&2. 1027

Fig. 9. Temporal Group III: Pacific centered atmospheric, oceanic, and ice indices. Indices reach 1028

maximum values ~1930 and 1990 and minimum values ~1904 and ~1964. Associated 1029

46

proxy is the Japanese Sardine index. Plotted indices are normalized reconstructed 1030

components of M-SSA modes 1&2. 1031

Fig. 10. Temporal Group IV: culmination of anomaly trends of sea ice extent, associated basin-1032

scale winds, and temperature extrema. Maximum values center on ~1938 and ~1998; 1033

minima ~1910 and ~1971. Note: csArcSib leads other indices ~3y. Associated proxy is 1034

ngLOD. Plotted indices are normalized reconstructed components of M-SSA modes 1&2. 1035

Fig. 11. Schematic reflects index relationships at each stage of climate-regime evolution. 1036

Vertical lines represent peak values of indices for each Temporal Group (refer to Figures 1037

7-10). Dates for these maxima are indicated along the bottom. Four Temporal Groups are 1038

represented, each by one index. They are listed in the left column. Arrows indicate index 1039

trends between ‘stages’ (or peaks of Temporal-Group indices). Red arrows indicate an 1040

increasing trend. Blue arrows a decreasing one. Note: AMO sign is positive in chart. See 1041

text for explanation. 1042

Fig. 12. Stadium-Wave ‘Mechanism’: schematic of simplified version of stadium-wave-signal 1043

propagation through the ocean-ice-atmospheric network and its influence on climate-1044

regime evolution. Roman numerals indicate processes related to Temporal Groups I 1045

through IV. Numbers in red (blue) indicate increasing (decreasing) Arctic and Northern 1046

Hemisphere temperatures. (MTG = meridional temperature gradient; WAA = warm air 1047

advection) 1048

Fig. 13. Stadium-Wave ‘Wheel’: Temporal Group indices are displayed in ‘wheel’ segments. 1049

Rings contain indices according to system: WKT indices are in the grey ring; ice indices 1050

fill the yellow ring; wind and wind-related indices, the blue-green ring; and proxies 1051

populate the outer green ring. Refer to text on how to read ‘the wheel’. 1052

47

Table 1. Index descriptions for indices appended to original stadium-wave network 1053

1054

Index/Acronym Reference/Data source Description/General

Information

(AO) Arctic Oscillation Thompson and Wallace 2000 www.atmos.colostate.edu or

http://jisao.washington.edu/ao#data

Leading EOF of SLP

poleward 20N

(GB) Globigerina.bulloides

Black et al. 1999 (record updated to 2009 (personal

communication)

G. bulloides Cariaco Basin

(ITCZ proxy)

(JS) Japanese Sardine

Klyashtorin and Lyubushin (2007); Kawasaki 1994;Klyashtorin

1998 (and personal communication)

Outbursts off coast of

Japan. Related to +PDO

(ngLOD) Earth’s Rotational-Rate

Sidorenkov (2005; 2009) and personal communication

http://hpiers.obspm.fr/eop-pc/earthor/ut1lod/lod-1623.html

low-frequency-variability

of negative length-of-day

(NPGO) SST proxy

Nurhati et al. (2011):

+NPGO ~ -SSTs of coral-based Sr/Ca proxy (R = -0.85)

Coral Sr/Ca SST proxy

162ºW, 6ºN

(Arctic T) Arctic surface

temperature anomalies

Frolov et al. (2009) personal communication Smolyanitsky

http://wdc.aari.ru/datasets/d0005/txt

Mean annual surface air

temperature (SAT): 70 to

85ºN for 1900-2007

(Grnlnd) Greenland sea-ice extent

Frolov et al. (2009) also available at:

http://wdc.aari.ru/datasets/d0005/txt

Mean August values

~15ºW-15ºE

(Barents) Barents sea-ice extent

Frolov et al. (2009) also available at:

http://wdc.aari.ru/datasets/d0005/txt

Mean August values

~15ºE-60ºE

(NEB) North European

Basin

Frolov et al (2009) Mean August values:

(Greenland + Barents ice)

(Kara) Kara sea-ice extent

Frolov et al. (2009) also available at:

http://wdc.aari.ru/datasets/d0005/txt

Mean August values

~60ºE-100ºE

(WIE) [Grn, Bar, Kara]

West Ice Extent

Frolov et al. (2009) Mean August values:

~15ºW~100ºE

(Laptv) Laptev sea-ice extent

Frolov et al. (2009) also available at:

http://wdc.aari.ru/datasets/d0005/txt

Mean August values:

~100ºE-140ºE

(E.Sib) East Siberian SIE

Frolov et al. (2009) also available at:

http://wdc.aari.ru/datasets/d0005/txt

Mean August values:

~140ºE-~180º

(Chuk) Chukchi sea-ice extent

Frolov et al. (2009) also available at:

http://wdc.aari.ru/datasets/d0005/txt

Mean August values:

~180-155ºW

(EIE) [Lap,ESib, Chuk]

East Ice Extent

Frolov et al. (2009) Mean August values:100ºE

-~155ºW

(ArcSib) Arctic Seas of

Siberia [Kara EIE]

Frolov et al. (2009) Mean August values: Kara

+ EIE

(TIE) WIE + EIE

Total Ice Extent :

Frolov et al. (2009) Mean August values: 15ºW

- 155ºW

(PCI) Pacific Circulation Indx

Beamish et al. 1998; King et al. 1998 Anomaly trend of Pacific

atmospheric circulation

(Dipole) proxy A-ITCZ

Atlantic SST Dipole

Keenlyside et al. 2008

SSTavg (60 to 10W, 40to

60N)-(50to0W, 40to60S );

1055

1056

1057

48

Table 2. Ice Categories: Correlations of sea ice-extent in shelf seas of the Eurasian Arctic. Seas 1058

are grouped in several ways. Each group plays a specific role in the generation and/or 1059

transmission of climate signal. Raw data smoothed 13-y. Significance levels: in 1060

red=p<1%; in blue =p< 5%. 1061

1062

Indices NEB WIE TIE Arc_Sib EIE

Greenland 0.95 0.90 0.65

Barents 0.98 0.94 0.66

Kara 0.70 0.87 0.94 0.87

WIE 0.96 1.0 0.84 0.57

TIE 0.68 0.84 1.0 0.91

Laptev 0.70 0.85

East_Sib 0.55 0.91

Chukchi 0.63 0.91

EIE 0.69 1.0

1063

1064

1065

1066

Table 3a. Temporal Group I: correlations reflecting ocean-ice coupling. Raw data smoothed 13-1067

y. Significance levels: in red=p<1%; in blue = p<5%. 1068

1069

Indices NEB WIE

ngAMO 0.88 0.89

1070

1071

1072

1073

1074

Table 3b. Temporal Group I: correlations reflecting relationship between anomalies of Pacific-1075

centered circulations and Group I indices. Raw data smoothed 13-y. Significance levels: 1076

in red=p<1%; in blue = p<5%. 1077

1078

Indices NEB WIE ngAMO ngPCI

ngPCI 0.84 0.92 0.93 1.0

cs(ng)NPO 0.82 0.89 0.93 0.96

cs(ng)PDO 0.73 0.83 0.86 0.95

cs(ng)ALPI 0.72 0.84 0.83 0.95

1079

49

Table 3c. Temporal Group I: correlations of Proxies with Group I indices. Raw data smoothed 1080

13-y. Significance levels: in red=p<1%; in blue = p<5%. 1081

1082

Indices GB ngDipole

Greenland 0.78 0.79

Barents 0.72 0.70

NEB 0.77 0.76

WIE 0.78 0.75

ngAMO 0.88 0.90

ngPCI 0.80 0.79

Ng_csPDO 0.85 0.83

Ng_csNPO 0.83 0.81

1083

1084

1085

Table 4. Temporal Group II: correlations reflecting ice-atmosphere coupling. Significance 1086

levels: in red=p<1%; in blue = p<5%. 1087

1088

Indices TIE ArcSib Kara ice Chukchi ice Laptev ice

AT 0.75 0.76 0.70 0.57

NPGO 0.56 0.69 0.62 0.60

1089

1090

1091

Table 5a. Temporal Group III: Correlations between anomaly trends of sea ice extent and 1092

associated wind patterns with Pacific-centered ocean/atmosphere circulations. 1093

Significance level: in red=p<1%. 1094

1095

Indices csWIE csTIE csNEB csArc_Sib csKara csAT

NPO 0.83 0.86 0.77 0.81 0.87 0.77

ALPI 0.79 0.81 0.77 0.76

PDO 0.83 0.82 0.81

1096

1097

1098

1099

1100

1101

1102

50

Table 5b. Temporal Group III: Japanese Sardine Proxy with Pacific-centered circulation-pattern 1103

indices. Significance level: in red=p<1%. 1104

1105

Indices JS

NPO 0.69

PDO 0.80

ALPI 0.70

1106

Table 6a. Temporal Group IV: anomaly trends of sea ice extent and related circulation patterns 1107

correlate with temperature. Significance levels for correlations: in red=p<1%; in blue = 1108

p<5%. 1109

1110

Indices Arctic Temperature NHT csArcSib

csNAOw 0.81

csAOw 0.86

csNPGO 0.79

csAT (aka ACI) 0.92 0.81 0.88

csNINO 0.85 0.83

csArcSib 0.77

1111

1112

Table 6b. Temporal Group IV: ngLOD proxy with wind anomaly and Arctic T. Significance 1113

levels: in red=p<1%; in blue =p< 5%. 1114

1115

Indices ngLOD

csAT (aka ACI) 0.83

ArcticT 0.76

1116

1117

1118

1119 Table 6c. Temporal Group IV: correlation shows relationship of Arctic temperature with sea ice 1120

in WIE. Significance Levels: in red=p<1%; in blue = p<5%. 1121

1122

Indices Arctic Temperature

NEB -0.78

WIE -0.76

1123

1124

1125

51

1126

1127

1128

1129

1130

1131

1132

1133

1134

1135

1136

1137

1138

1139

1140

1141 Fig. 1. Arctic Ocean and marginal seas used in this study (1-6 in this study (shaded in gray)): 1) 1142

Greenland Sea, 2) Barents Sea, 3) Kara Sea, 4) Laptev Sea, 5) East Siberian Sea, 6) 1143

Chukchi Sea. Categories of Seas include: NEB = 1&2; ArcSib = 3-6; WIE = 1-3; EIE = 1144

4-6; and TIE = 1-6. [Also shown: 7) Beaufort Seas, 8) Baffin Bay, 9) Hudson Bay, and 1145

10) the Norwegian Sea.] Adapted with permission from: Frolov et al. 2009. 1146

1147

1148

1149

1150

1151

1152

1153

52

1154

1155

1156

1157

1158

1159

1160

1161

1162

1163

1164

1165

1166

1167

1168

1169

1170

1171

1172 Fig. 2. a) Plot of MSSA normalized RCs 1&2 of Original 20

th-century Stadium-Wave (adapted 1173

from Wyatt et al. 2011 (WKT)). Note: NHT and AMO are negative; b) M-SSA spectrum 1174

of a. Error bars in b are based on North et al. (1982) criterion, with the number of 1175

degrees-of-freedom set to 40, based on decorrelation time of ~2.5 years. Red-dashed lines 1176

in panel (b) represent the 95% spread of M-SSA eigenvalues based on 100 simulations of 1177

the 8-valued red-noise model (1), which assumes zero true correlations between the 1178

members of the eight-index set. 1179

1180

1181

1182

1183

1184

1185

1186

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time (yr)

std

indic

es

Original 20thc Stadium Wave

-NHT

-AMO

AT

NAO

NINO3.4

NPO

PDO

ALPI

a)

b)

Eight-member Network

M-SSA Spectra

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 00

2

4

6

8

1 0

1 2

1 4

1 6

1 8

M - S S A f o r T e le c o n n e c t io n N e tw o rkF r a c t io n o f v a r ia n c e ( % ) M = 2 0

M - S S A m o d e

53

1187

1188

1189

1190

1191

1192

1193

1194

1195

1196

1197

1198

1199

1200

1201

1202

1203

1204

1205

1206

1207

1208

1209 Fig. 3. Annotated Expanded ‘Stadium Wave’ shows 20

th-century signal propagation through a 1210

15-index-member network. Selected indices are a sub-set of a broader network. Four 1211

clusters of indices are highlighted (+/- I through IV). Each cluster is termed a “Temporal 1212

Group”. Peak values of Group indices represent stages of climate-regime evolution. Each 1213

is discussed individually (see text) and plotted (Figures 7-10). Plotted indices are 1214

normalized reconstructed components of M-SSA modes 1&2. 1215

1216

1217

1218

1219

1220

1221

1222

1223

Expanded Stadium Wave

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

T im e (yr)

Indic

es

N o rmalized reconstructed components leading modes 1& 2 S tadium W ave

W IE

ngA M O

GB

A rcS ib

A T

N A Ow

N P GO

E IE

N INO

JS

P D O

A LP I

A rcT

ngLO D

N HT

I II III IV

I

II

III

IV

I II III IV

-I -II -III -IV

54

1224

1225

1226

1227

1228

1229

1230

1231

1232

1233

Fig. 4. M-SSA spectrum of expanded stadium-wave network shown in Figure 3. Error bars are 1234

based on North et al. (1982) criterion, with the number of degrees-of-freedom set to 40, 1235

based on decorrelation time of ~2.5 years. Red-dashed lines in panel represent the 95% 1236

spread of M-SSA eigenvalues based on 1000 simulations of the 15-valued red-noise 1237

model (1), which assumes zero true correlations between the members of the 15-index 1238

set. 1239

1240

1241

1242

1243

1244

1245

1246

1247

1248

1249

M-SSA Expanded Network15 indices

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

M-SSA of Expanded Stadium Wave15 indices

Fraction of variance (%) M=20

M-SSA mode

55

1250

1251

1252

1253

1254

1255

1256

1257

1258

1259

1260

Fig. 5. Channel-fraction variance due to M-SSA leading modes 1&2. Values indicate the amount 1261

of an index’s variability that is due to the stadium-wave signal. Indices represent Groups: 1262

I [WIE, AMO, GB]; II [ArcSib, AT, NAOw, NPGO]; III [EIE, NINO, JS, PDO, ALPI]; 1263

IV [ArcticT, ngLOD, and NHT]. 1264

1265

1266

1267

1268

1269

1270

1271

1272

1273

1274

Channel-Fraction Variance of Expanded

Index Network

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 50

1 0

2 0

3 0

4 0

5 0

6 0

Channe l-va ria n c e fra c tio ns d u e to M -SSA 1 a n d 2Fraction (%

)

WIE AMO GB ArcS ib AT NAOw NPGO EIE NINO JS PDO ALP I ArcT ngLOD NHT

I II III IV

56

1275

1276

1277

1278

1279

1280

1281

1282

1283

Fig. 6. Raw data plots: 20th

-century relationships among anomaly trends of negatively signed 1284

Pacific circulations (e.g. ngPCI and -csPDO) and the trend of ngAMO. “Change-points” 1285

of anomaly trends indicate endings of intervals dominated by either positive or negative 1286

anomalies. Change-points of Pacific anomaly trends co-occur with extrema of the AMO 1287

curve. Plotted indices: raw data. AMO smoothed 13y; ngPCI and-csPDO are not 1288

smoothed. 1289

1290

1291

1292

1293

1294

1295

1296

1297

1298

1299

1300

Relationship between Time-Integral & Raw Indices(Group I plotted with cs of negative Group III)

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000-3

-2

-1

0

1

2

3

t im e(yr)

indic

es

Raw Indic es

ng csP D O

ngA MO

ngP C I

57

1301

1302

1303

1304

1305

1306

1307

1308

1309

1310

1311

1312 Fig. 7. Temporal Group I: characterized by ocean-ice coupling, with focus of activity in the 1313

Atlantic sector. Peak values center on ~1918 and 1976; minimum values in the 20th

1314

century center on ~1942. Associated proxies are the G. bulloides and ngDipole. Plotted 1315

indices are normalized reconstructed components of M-SSA modes 1&2. 1316

1317

1318

1319

1320

1321

1322

1323

1324

1325

1326

1327

1328

1329

1330

1331

1332

1333

1334

1335

1336

1337

1338

Temporal Group I

1 9 0 0 1 9 1 0 1 9 2 0 1 9 3 0 1 9 4 0 1 9 5 0 19 6 0 1 9 7 0 1 9 8 0 1 9 9 0 2 0 0 0-2

-1 .5

-1

-0 .5

0

0 .5

1

1 .5

2

t im e (y r)

indic

es

Te m po ra l G ro up I R e co ns truc te d C o m p o ne nts o f M -S S A m o d e s 1 & 2

ng D ip o le

G B

W IE

ng A MO

ng P C I

58

1339

1340

1341

1342

1343

1344

1345

1346

1347

1348

1349

1350

1351

1352

1353

1354

1355

1356

1357

1358

1359

1360 Fig. 8. Temporal Group II: characterized by ice-atmosphere coupling. Sea ice extent in Russian 1361

Arctic (ArcSib) and related large-scale wind patterns co-vary with peak values centered 1362

on ~1923 and ~1982; minimum values center on ~1950. Associated proxy is the NPGO 1363

proxy. Plotted indices are normalized reconstructed components of M-SSA modes 1&2. 1364

1365

1366

1367

1368

1369

1370

1371

1372

1373

1374

Temporal Group II

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000-2

-1 .5

-1

-0 .5

0

0 .5

1

1 .5

t im e (y r)

ind

ices

Tem poral Group II Reconstruc ted C om ponents o f M -S S A m odes 1& 2

A rcS ib

A T

NP G O

A O w

NA O w

59

1375

1376

1377

1378

1379

1380

1381

1382

1383

1384

1385

1386

1387

1388

1389

1390

1391 Fig. 9. Temporal Group III: Pacific centered atmospheric, oceanic, and ice indices. Indices reach 1392

maximum values ~1930 and 1990 and minimum values ~1904 and ~1964. Associated 1393

proxy is the Japanese Sardine index. Plotted indices are normalized reconstructed 1394

components of M-SSA modes 1&2. 1395

1396

1397

1398

1399

1400

1401

1402

1403

1404

1405

1406

1407

1408

1409

1410

1411

1412

1413

1414

1415

1416

Temporal Group III

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

tim e (y r)

ind

ices

Tem poral G roup III Rec ons truc ted C om ponents of M -S S A m odes 1& 2

E IE

J S

P D O

NP O

c sT IE

A L P I

60

1417

1418

1419

1420

1421

1422

1423

1424

1425

1426

1427

1428

1429

1430

1431

1432

1433

1434

1435 Fig. 10. Temporal Group IV: culmination of anomaly trends of sea ice extent, associated basin-1436

scale winds, and temperature extrema. Maximum values center on ~1938 and ~1998; 1437

minima ~1910 and ~1971. Note: csArcSib leads other indices ~3y. Associated proxy is 1438

ngLOD. Plotted indices are normalized reconstructed components of M-SSA modes 1&2. 1439

1440

1441

1442

1443

1444

1445

1446

1447

1448

1449

1450

1451

Temporal Group IV

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

time (yr)

indic

es

Temporal Group IV Reconstruc ted Components of M-S SA modes 1&2

csArcSib

csAT

ngLOD

ArcT

NHT

61

1452

1453

1454

1455

1456

1457

1458

1459

1460

1461

1462

1463

Fig. 11. Schematic reflects index relationships at each stage of climate-regime evolution. 1464

Vertical lines represent peak values of indices for each Temporal Group (refer to Figures 1465

7-10). Dates for these maxima are indicated along the bottom. Four Temporal Groups are 1466

represented, each by one index. They are listed in the left column. Arrows indicate index 1467

trends between ‘stages’ (or peaks of Temporal-Group indices). Red arrows indicate an 1468

increasing trend. Blue arrows a decreasing one. Note: AMO sign is positive in chart. See 1469

text for explanation. 1470

1471

1472

1473

1474

1475

1476

1477

1478

AMO

AT

PDO

ArcticT

TR

AN

SIT

ION

OC-ATM-T indices

Groups I - IV

After Peak

Group I

After Peak

Group II

After Peak

Group III

> P

ea

k IV

TR

AN

SIT

ION After

Peak Group -I

TR

AN

SIT

IONAfter

Peak Group -II

After Peak

Group -III

WARMING REGIME

> P

eak

-IV

COOLING REGIME

Index Relationships at Peaks of Each Stage of Regime Development

~1910 ~1918 ~1923 ~1930 ~1938 ~1942 ~1954 ~1968 ~1973

Pea

k G

roup

I

Pe

ak G

roup

II

Pea

k G

roup

III

Pea

k G

roup

IV

Pe

ak G

roup

-I

Pea

k G

roup

-II

Pea

k G

roup

-II

I

Pe

ak G

rou

p -

IV

~1976

Pe

ak G

rou

p I

After Peak

Group I

> P

ea

k -

IV

Pea

k G

roup

-IV

62

1479

1480

1481

1482

1483

1484

1485

1486

1487

1488

1489

1490

1491

Fig. 12. Stadium-Wave ‘Mechanism’: schematic of simplified version of stadium-wave-signal 1492

propagation through the ocean-ice-atmospheric network and its influence on climate-1493

regime evolution. Roman numerals indicate processes related to Temporal Groups I 1494

through IV. Numbers in red (blue) indicate increasing (decreasing) Arctic and Northern 1495

Hemisphere temperatures. (MTG = meridional temperature gradient; WAA = warm air 1496

advection) 1497

1498

1499

1500

1501

1502

1503

1504

Cold Atlantic

↑ MTG

↑ zonal Winds

↑ WAA

Accumulating Sum

of Positive

Anomalies of

Ice & Wind

End positive

anomalies ice,

wind, WAA

related to

Atlantic

↑ Arctic T

Positive Polarity

Pacific Circulation

End positive

anomalies in

Pacific

↑ NHT

Warm

Atlantic

TIE begins↑

↓MTG

↓ zonal Winds

↓ WAA

Accumulating Sum of

Negative Anomalies of

Ice & Wind

End negative

anomalies ice,

wind, WAA

related to

Atlantic

↓ Arctic T

Negative Polarity

Pacific Circulation

End

negative

anomalies

in Pacific

↓ NHT

High regional SLP in Arctic: related anticyclonic anomalies set stage for strong halocline and increased sea-ice-growthD

ecre

asin

g S

LP

; incre

ase

d c

yclo

nic

an

om

alie

s

Low regional SLP in Arctic: related cyclonic anomalies set stage for weak halocline and decreased sea-ice-growth

Incre

asin

g S

LP

; in

cre

ase

d a

nti-c

yclo

nic

an

om

alie

s

↓ ArcSib

↑ ArcSib

TIE begins ↓

WIE begins ↓

WIE minimum →

WIE maximum →

WIE begins↑

TIE continues ↓TIE minimum

TIE maximumTIE continues ↑

↑ Arctic T &

NHT

↓Arctic T &

NHT

IVIV

II

IIIIII

IIII

--IVIV

--IIIIII

--IIII

--II

Arctic Front S ↓ ppt

Arctic Front N ↑ ppt

Regime Regime

ReversesReverses

Regime Regime

ReversesReverses

Increased horizontal extent of halocline

Decreased horizontal extent of halocline

Sh

rinkin

g h

alo

clin

eExp

and

ing

ha

loclin

e

63

1505

1506

1507

1508

1509

1510

1511

1512

1513

1514

1515

1516

1517

1518

1519

1520

1521

1522 Fig. 13. Stadium-Wave ‘Wheel’: Temporal Group indices are displayed in ‘wheel’ segments. 1523

Rings contain indices according to system: WKT indices are in the grey ring; ice indices 1524

fill the yellow ring; wind and wind-related indices, the blue-green ring; and proxies 1525

populate the outer green ring. Refer to text on how to read ‘the wheel’. 1526

1527

IIIIII

IIIIII

IVIV--II

--IIII

--IIIIII

--IVIV

ngDIPOLE

+GB

+NEB +WIE

ngPCI

ngAMO

+AMO

ngNEB ngWIE

+PCI

-GB+DIPOLE

1915 / 1976 / (2036?)1915 / 1976 / (2036?)

19441944 / / (2006?)(2006?)

AT

ngAT

+ArcSib

ngArcSib

+TIE

ngTIE

+AT

+NAO

+AO

ngAT

ngNAO

ngAO

ngNPGO

+NPGO

ngNPGO (proxy)

NPGO (proxy)

19231923

19821982

(1895?)(1895?)

19541954

(2014?)(2014?)

ngEIE

ngNPO

ngALPI

+ALPI

+NPO

+EIE+PDO

ngPDO

+NINO

ngNINOngJS

+JS

19041904

19641964

(2024?)(2024?) 19301930

19901990

+NHT

ngNHT

+csTIE

ng_csTIE

+Arc T

ng_Arc T

ng_csArcSib

+ csArcSib

ng_csAT

+csAT

+LOD

ngLOD

19381938

19981998

19101910

19711971

(2031?)(2031?)