Wyatt on Earth
by Marcia Glaze Wyatt Ph.D.

The Stadium-Wave Overview


“Stadium wave” is an allusive term for a hypothesis of multidecadal climate variability. Sequential propagation of an “audience wave” from one section of sports fans to another in a sports arena – i.e. a “stadium wave” - is analogous to the premise of the climate stadium-wave hypothesis. It, too, involves sequential propagation of a signal. In the case of the climate stadium wave, propagation proceeds sequentially through ocean, ice, and atmospheric systems.
Key to signal propagation is network, or collective behavior - a feature ubiquitous throughout natural and man-made systems, a product of time and self-organization.

In the specific case of the climate stadium wave, over time, large-scale processes interact – ocean circulation influences ice cover; ocean processes and ice cover affect atmospheric patterns, and in turn, atmospheric patterns influence ocean and ice. The large-scale processes self-organize into a system of interactive behavior. Positive and negative feedback responses resulting from this collective behavior alternately reinforce and damp the consequent evolving trends and patterns. The end-result is a quasi-periodic, low-frequency oscillatory component of climate variability, with network architecture more significant than individual network members in scripting the large-scale patterns. [See publications page for general understanding of climate-network behavior: specifically 1) Synopsis of Wyatt et al. 2012 and 2) Dissertation Presentation.]

The 'stadium wave' is a hypothesized, multidecadally varying climate signal that propagates across the Northern Hemisphere within a network sequence of synchronized (i.e. matched rhythms) ocean, atmosphere, and sea-ice indices.  All indices vary at the same timescale - ~64 years peak-to-peak throughout 20th century - with one index leading the next in a consistently ordered lead-lag fashion. Hence, the allusive term - 'stadium wave'. (Plot below.)

As the stadium-wave signal courses sequentially through a network of climate systems, it scripts the multidecadal component of the Northern Hemisphere surface average temperature. As the signal propagates, the consequent shifting relationships among indices impact precipitation patterns, drought distribution, hurricane activity, basin-scale wind patterns, sea-ice inventories, ocean-heat storage, and numerous other manifestations of the multidecadal component of climate variability.

Wyatt et al. (2012) first documented the stadium-wave signal in 20th century Northern Hemisphere observational (instrumental) data. Wyatt (2012) subsequently analyzed a variety of proxy networks, several of which could be represented with 300 years of proxy data. All networks showed signal propagation analogous to 20th century results throughout the data records, yet with frequency and amplitude modifications prior to ~1850. Wyatt (2012) and Wyatt and Curry (2014) elucidated a potential mechanism for the signal's propagation, introducing Eurasian Arctic sea ice as a significant network link.  Yet, a conundrum emerges. While numerous and diverse sets of observational data reflect strong presence of propagation, the signal remains elusive in model-generated data. For example, indices constructed from model-generated raw data (CMIP3: Coupled Model Intercomparison Project 3rd version) failed to produce the stadium wave dynamic (Wyatt and Peters (2012)). Similarly, Kravtsov et al. (2014) analyzed models from the more recent version of the CMIP data base (CMIP5). They not only found no signal propagation; they also documented strikingly contrasting spatial patterns between the modeled and observational data sets. Wyatt et al. (2012), Wyatt and Peters, and Kravtsov et al. speculate that dynamics responsible for generating signal propagation in the observed data are not well-represented in the CMIP suites of models. Currently, additional stadium-wave research (by Kravtsov and colleagues) is being done with CMIP5.  And finally, while most stadium-wave research has focused on the data-rich Northern Hemisphere domain, Kravtsov et al. (2014) find evidence for signal propagation in observational data of the Southern Hemisphere. [link to Publications Page]

It is hypothesized that the propagation, itself,  is predominantly internally generated. Wyatt and Curry (2014) argue that West Eurasian Arctic sea-ice is a crucial link in the sequential "baton-passing" within the network. Positive feedbacks give way to negative ones, scripting the propagating signal's quasi-periodic oscillatory signature.  

While the signal's propagation is thought to be mostly internally generated, the stadium wave's multidecadal timescale of  variability is probably only partly so. The source of this timescale of variability is hypothesized by to be the Atlantic Multidecadal Oscillation (AMO), itself thought to be driven, at least in part, by the Atlantic sector of the globally overturning meridional circulation (AMOC). External forcing plausibly nudges the internally set pace of the AMO/AMOC, and by extension, that of the stadium-wave. Assignment of relative contributions to observed timescale stirs controversy. 

Evolution of the multidecadal variability of observed temperature trend:
Climate regimes -- multidecadal intervals of the prevailing surface-average-temperature trend -- evolve in four stages as the hypothesized signal propagates through the climate-index network (Wyatt and Curry 2014). Tempo of variability in North Atlantic Ocean temperatures governs the stadium-wave signal tempo. Perhaps counterintuitive; peak warmth in sea-surface temperatures of the North Atlantic basin (peak +AMO) leads a multiple-decade trend of cooling hemispheric surface average temperatures (NHT). Similarly, maximally cool North Atlantic sea-surface temperatures (maximum negative AMO) coincide with the beginning of a multiple-decade trend of warming hemispheric surface average temperatures. Western Eurasian sea ice and its inventory's impact on atmospheric processes may hold the answer to this observation.

Pivotal Role for West Eurasian Arctic Sea Ice - an abbreviated discussion:
West Eurasian Arctic sea ice plays a key role in converting the initial regional oceanic  signature into an oppositely signed hemispheric one. The West Eurasian shelf sea region is unique. Only here is Arctic sea ice exposed  to the open ocean in winter. Thus, the polarity of the North Atlantic Ocean temperatures strongly influences winter inventory of sea ice. In turn, sea ice inventory regulates escape of ocean heat, which exerts dominant influence on wintertime Arctic surface temperatures, and by extension, on the polar-equatorial temperature gradient (PETG). The PETG dictates equator-to-pole transport of heat, converting the initial regional ocean signal polarity into the oppositely signed atmospheric signature.  As the signal continues to propagate, atmosphere-ice-ocean interactions feed back positively onto the prevailing hemispheric surface-average temperature trend; while Pacific-centered processes negatively feed back onto the North Atlantic's salinity balance. Delayed negative feedback contributions mount within the high latitudes of the Atlantic, compounded by  changes in sea ice and precipitation patterns. Ultimately, cumulative impact of the negative feedback responses  effectively nudges a polarity reversal of Atlantic Ocean temperatures. A climate-regime reversal is set in motion; another cycle begins.

See Publications page: Wyatt and Curry (2014) paper, section 4, for mechanistic details.

See also
the figure
of stadium wave below (Plot of AMO is negatively signed!).
iming of 20thc regime shifts:
~1915 (warming followed),
~1942 (cooling followed),
~1976 (warming followed)
Possible regimes shift ~end of 20th/beginning 21st c

*Note on terms  'regime shifts', 'anomalies',  and 'anomaly trends':
The term regime-shift in climate can foster confusion. Traditionally, a multidecadal regime-shift has been defined by a dominant basin-scale sea-surface-temperature pattern in the North Pacific (the Pacific Decadal Oscillation (PDO)). When the PDO reverses polarity, it is said that a regime-shift has occurred. The dates listed above identify such shifts (either observed directly or inferred from records). Such a shift in PDO anomaly polarity tends to occur with a shift in trend of surface temperature anomalies in the North Atlantic (AMO). Trends of the PDO and AMO are in-quadrature: the oscillating trends, or phases, of each pattern are offset by 90 degrees.

[See plot of stadium wave below (AMO  plotted in its negative polarity.]

Consider the PDO. When it enters positive polarity, as it did in ~1976, the AMO is at its minimum anomaly trend. In ~1976, AMO's trend reversed from decreasing anomalies to increasing anomalies. But, while the trend of anomalies in the latter began increasing around 1976, the AMO anomalies remained negative for approximately 15 years following this reversal. Hence, be alert to shifts in polarity of anomalies versus shifts in trends of anomalies. Anomaly polarity can be identified in real time; anomaly trends can be identified only in retrospect.

One often hears about sea ice in the Arctic. Note how it is reported. Does the information refer to sea ice extent across the entire Arctic or for specific regions of the Arctic? In the stadium-wave hypothesis, only one region of the Arctic is critical. This is the Eurasian Arctic Shelf Sea region. According to the stadium wave's hypothesized hemispheric signal propagation, anomaly trends in Eurasian Arctic sea ice extent begin in the seas furthest to the west (Greenland, Barents, and Kara) and culminate in those to the east (e.g. Laptev and East Siberian seas).

The message here is to keep in mind the difference between reports on anomalies and reports on anomaly trends! And, pay attention to what specific region those reported anomalies and trends involve.

Stadium-wave propagation prior to the 20th century:
Instrumental records for the collection of stadium-wave-network indices are temporally limited to the 20th and early 21st centuries. The signal emerges clearly in this data base, with climate-regime intervals persisting for approximate 30-year stretches. But there are other data that capture traces of the 'wave'. Examples include: multidecadal-scale anomalies in fish populations, Earth's rotational-rate record, isotopic ratios in various media, foraminifera accumulations in sediment, and the like. Records for these data include and pre-date the 20th century, enabling a peek further into the signal's past. Analyses of these data suggest the 'stadium wave', i.e. the signal propagation,  has been in existence for the duration of the data record studied - at least 300 years (Wyatt 2012). Yet what is notable is that the timescale of variability shrinks earlier in the 300-year record, especially prior to the early-mid 1800s. The pace is still multidecadal; yet approximately 40-year quasi-periodic cycles versus 64-year. Amplitudes are inconsistent over this multi-century record, much smaller early in the record. These results could be because of the data; proxy data are inherently noisy and disentangling signals not always reliable. On the other hand, the results could reflect actual stadium-wave signal dynamics, capturing actual modifications of frequency and amplitude. Further research is needed.

Ability of climate models to capture the signal:
And while instrumental and proxy data capture the consistent propagation sequence that characterizes the 'stadium wave'; model-generated data derived from the CMIP3 data base do not (Wyatt and Peters 2012). Reasons for this remain unclear; modeled input parameters used to generate the data set may be one source to consider. For example, ocean-stratosphere-troposphere coupling, geographically shifting atmospheric and oceanic centers-of-action, ocean-atmosphere coupling at western-boundary currents and their extensions, sea-ice dynamics, winter coupling at polar latitudes between stratosphere and troposphere, and network interactions are thought to be fundamental links in the stadium-wave propagation, their collective behaviors difficult to incorporate into large-scale general circulation models. Improved model representation of these features may enhance simulation of the multidecadal natural component of climate variability. Furthermore, network behavior is governed predominantly by network architecture. In other words, the structure of the interactive system is more influential over the evolving dynamics than the "parts" of that structure are. Modeling designs that incorporate network behavior (Van den Berge et al. (2011)) are in their infancy, but hold promise for simulating complex systems such as climate (see Wyatt and Peters (2012)).

Model-based studies and observation-based studies rely on differing views on the low-frequency signal in climate variability. This fundamentally contrasting perspective is further explored next - in the section on competing paradigms.

Competing paradigms:
In addition to overall linearly increasing temperatures, the 20th century Northern Hemisphere surface average temperature (NHT) reflects an undulating low-frequency trend, with an approximate thirty-year interval of stagnating-to-slightly-cooling temperatures mid-century, sandwiched on either end by similarly long intervals of warming temperatures.

Two schools-of-thought hold contrasting ideas of how this low-frequency "wiggle" of the 20th century was generated. One view is the stadium wave. This view holds that on long time scales, climate variability organizes into network behavior, executed through coupled dynamics among ocean, ice, and atmospheric patterns. Collective behavior among indices in a network generates alternating multidecadal intervals of warming and cooling temperatures, and this multidecadal component of climate variability is superimposed upon an upwardly trending longer-timescale trend Observational data support this view.

The contrasting view argues for a temporally non-uniform profile of external forcing (natural and anthropogenic) imposed upon individual climate indices across the globe. According to this view, the observed upwardly trending, multidecadally undulating profile of NHT reflects mostly external forcing, both natural and anthropogenic.  Modeled data support this view.

Is the stadium wave - i.e. signal propagation - an illusion?
In recent years, the competing paradigms described above have pitted modeled data against observational data.
Illustrating this growing debate regarding the fundamental view of multidecadal climate behavior is a recent challenge (Mann et al. (2014)) to the stadium-wave hypothesis. Kravtsov et al. (2014) refuted the challenge. In brief, using modeled data, Mann et al. argue that the stadium wave's propagation signal is not actually a propagation. Instead, they claim it is merely an artifact of methodology. Indeed, if modeled data are used, the propagation (or "phase offsets") is an artifact of methodology. But using observed (instrumental) data, adapted to the Mann et al. methodology, as Kravtsov et al. did, the propagation is statistically significant (>95% confidence level), as determined through phase-offset uncertainties. This observation begs the question; is the difference in results due to the data used (modeled or observed) or due to methodology?

In seeking other ways to test the validity of the propagation of the stadium wave, Kravtsov et al. decomposed a model-generated data set
(GFDL-CM3) and an observation-based data set into their respective 20th century spatiotemporal patterns. They found significant differences in the multidecadal climate components between the two data sets. While a linear trend and a single, stationary multidecadal mode in the simulated indices are reasonably consistent analogues to observed counterparts, a strong second mode of multidecadal variability, offset from the first mode, emerges from the observational data, but not from the modeled data. The significance of this is that two similar multidecadal modes, with phasing offsets, are required for signal propagation.

In summary, Kravtsov et al. found that model-simulated data reflect a stationary, in-phase multidecadal signal, likely reflective of the temporally non-uniform external forcing that is designed into the models. Any phase offsets in the mo
del-simulated data are, indeed, due to random "noise" processes. In contrast, observed multidecadal climate variability requires contributions from two spatial patterns to rationalize the stadium-wave propagation. Two such modes are found in a wide variety of observed geophysical indices (Wyatt 2012; Wyatt and Curry 2014)

[For more detailed and in-depth discussions on this topic, please see Publications Page for Kravtsov et al. paper and for two essays (by M. Wyatt [link to publications page]) further detailing the controversy (Disentangling Forced from Intrinsic Variability) and the Kravtsov et al. paper (Is the Stadium-Wave Propagation an Illusion?).]

Solar variability's potential role in the oscillatory timescale:

A topic ripe for further study is external forcing. What is its role in the stadium-wave ? Solar is suspected as a player (Wyatt 2012) - its tempo and magnitude of variability at the helm.  Exactly how, remains the question.

Relative roles of internally generated dynamics and externally forced behavior:

As discussed above, the current debate regarding climate change focuses on relative roles of external radiative forcing versus internally generated (or intrinsic) variability. Similar debate is worth considering in context of the stadium-wave signal. Is the signal externally forced, intrinsically generated, or a combination of both? While authors of the hypothesis concur that the  propagation of the signal across the Northern Hemisphere is likely tied to internally generated variability (see Wyatt and Curry 2014), the tempo of this propagation is set by variability in the North Atlantic (Atlantic Multidecadal Oscillation (AMO)). The oscillatory frequency of the AMO may, at least in part, be governed by external forcing - natural, anthropogenic, or both. The extent of an externally forced contribution to the observed AMO pattern remains a topic of active research. To recap, intrinsic dynamics (interacting network members) likely are responsible for the stadium-wave's propagation through a hemispherically spanning network of geophysical indices, with Eurasian Arctic sea-ice extent thought to be a major player. On the other hand, external forcing (natural and anthropogenic likely) is suspected to be a probable  contributing factor to the AMO's multidecadal timescale of oscillation, its relative role a topic of debate. In turn, the timescale of AMO variability sets the tempo of the stadium-wave propagation.

Implications for the stadium-wave signal:
The 'stadium wave', if it has been correctly interpreted, illuminates some previously unrecognized details of Earth's machinery. In addition, if the stadium-wave signal, indeed, has captured the multidecadal component of climate variability correctly, and if this signal behavior remains consistent in its propagation sequence, the hypothesis holds potential for: 1) attribution - allowing climate behavior to be better placed in context; 2) for predictive capacity - possibly allowing prediction of decadal-scale trend shifts in  precipitation, drought distribution, wind-regimes, sea ice extent, and temperature; and 3) for facilitating improvements in model design via the identification of critical elements involved in stadium-wave dynamics that may be absent or poorly resolved in computer simulations, assuming these dynamics indeed contribute to the multidecadal component of the overall Northern Hemisphere surface average temperature.

See FAQ page for further discussion.

Figure SW1: The plot above shows the hypothesized stadium-wave propagation through ocean, sea ice, and atmospheric indices. Roman numerals indicate timing of each of four stages  in evolution of a positive, or warming, regime and each of four stages (negative numbers) in a negative, or cooling, regime. Names of selected legend entries are shown in text box  to right of figure. For more complete understanding of the plot and the stadium-wave mechanism, please refer to Wyatt and Curry (2014), section 4. Figure adapted from figure 3 of Wyatt and Curry (2014) paper. 

Additional figures  "Frequently Asked Questions" Sub-Pages. [link to FAQ page]

Selected Legend Entries :

WIE=W.Eurasian sea ice (Greenland, Barents, and Kara Seas)

ngAMO = cool N. Atlantic  SST (negatively signed Atlantic Multidecadal Oscillation) likely linked to the Atlantic sector of the global oceanic 'conveyor belt', the Meridional Overturning Circulation (AMOC)

ArcSib = Siberian Arctic sea ice (Kara Sea dominant)

AT = zonal winds over mid and high latitudes of N. Atlantic and Eurasia

EIE = E. Eurasian sea ice (Laptev, East Siberian, and Chukchi Seas)

PDO = Pacific SST pattern (Pacific Decadal Oscillation)

ArcT = Arctic surface temp

NHT = N. Hemis. surf avg T