We analyzed networks of reconstructed indices from model-generated data from the third Coupled Model Intercomparison Project (CMIP3). Our goal in so doing was to determine if a hemispherically propagating climate signal, previously detected at secularly varying time scales in analogous index networks reconstructed from 20th-century instrumental data, could be identified. That secular-scale signal found in 20th century instrumental data, termed the ‘stadium wave’, was characterized by two leading modes of low-frequency variability, whose normalized sum of RCs documented a spatiotemporally complex signature propagating across the Northern Hemisphere. Subsequent to identification of stadium-wave behavior in 20th-century instrumental data (Wyatt et al. 2011), analogous stadium-wave behavior was found in a companion study, which was based on a variety of spatially and dynamically diverse instrumental-data sets, and temporally expanded proxy-data sets (Wyatt (2012); submitted manuscript (2013)).
In the present model-data based study, we adapted methods identical to those used in two prior companion studies. And in this study, we were unable to identify a ‘wave’ analogous to the original stadium wave detected in observations. While results of some model experiments hinted at signal propagation, none of these signals were found to be statistically significant or stationary. Furthermore, none were spatially or temporally analogous to the “wave” found in observational and proxy data.
As a whole, co-variability among indices of seven-member networks assembled from data generated by models of the CMIP3-ensemble simulations appears to be dominated by high-frequency fluctuations, with the most dominant ones at biannual to sub-decadal periodicities. These are often marked by non-stationarity across the time interval evaluated. Radiative-forcing signatures (in the NHT, in particular) are apparent at the secular-scale in some runs. These signatures are characterized by a long, non-periodic variation with at most only one full cycle in a one-hundred-year span. Statistically significant signal propagation is absent among the model sets analyzed. These features stand in contrast to those of the observed stadium wave. Furthermore, consistency of results from model to model, or even model-run to model-run of the same model was not an outstanding feature in our analysis; while in previous stadium-wave studies, the same secularly varying, hemispherically propagating, spatio-temporal signal emerged consistently, time-after-time, in one index set after another.
Negative results from a study such as this are not capable of definitively claiming the existence of deficiencies in model design. We conducted this experiment not to evaluate model design, nor to support or refute the stadium-wave signal detected in other data sets in previous studies. This research was conducted simply to answer the question, ‘is the hemispherically propagating climate signal found in observational and proxy data sets also found in model-simulated data sets of the CMIP3 ensemble?’ The answer is ‘no’. With this unexpected result, we are left to question, why not. We submit this question invites curiosity.
Our methods used in this study to generate data sets may be the culprit. Were our index reconstructions sound? Or did the omission of the index, AT (atmospheric-mass transfer anomalies), from our reconstructed networks negatively affect the modeled outcome? Perhaps these possible deficiencies deserve closer scrutiny. As far as the former, we did test each reconstruction code designed for the model data. We did so by substituting “real” data for the modeled data. Our results were good. But this does not rule out the possibility of undetected small errors that grew when combined with other small index errors. As far as the latter caveat, as discussed in section 2.2.2, the ‘stadium-wave’ signal emerged as statistically significant in data sets with the AT index omitted; yet that statistical significance was not as robust as with AT’s inclusion. This may have made a difference when using the model-simulated indices. Perhaps we performed too few analyses. Or perhaps our studies suffer from deficiencies we have yet to recognize.
But we also posit that these results - the failure of the model-generated data to yield a propagating signal – might speak to a missing ingredient in modeling design. We offer that this missing ingredient includes dynamics that play significant roles in hemispheric signal propagation, in linking one regional circulation pattern with another.
For example, in observation-based studies, geographical positioning of large-scale oceanic and atmospheric centers-of-action (COA)f has been found to be critical to connectivity among regional circulations, establishing communication links that help make sense of intra-hemispheric signal propagation (Kirov and Georgieva 2002; Polonsky et al. 2004; Dima and Lohmann 2007, Wang et al. 2007; Msadek et al. 2010 for examples). For instance, the Icelandic and Aleutian Lows shift longitudinally and latitudinally (Dima and Lohmann 2007; Georgieva et al. 2007) on decadal-plus timescales, influencing, among other things, dominant basin-scale wind flow. Inter-basin connectivity modifies accordingly.
One related example is drawn from research by (Wang et al. 2007). They find that COA migrations generate intervals when climate patterns over the North Pacific and over the Eurasian continent upstream are linked. Likewise, regions downstream are linked. These linkages can be traced to an enhanced Pacific North American (PNA) pattern and to an eastwardly extended jet stream. These nuanced factors influence El Nino’s relationship with the Aleutian Low Pressure system.
Another example can be found in works by (Sugimoto and Hanawa 2009) and (Frankignoul et al. 2011). These works suggest that low-frequency latitudinal shifts in atmospheric COAs, influence migrations of western-boundary currents and their extensions (ocean-gyre frontal boundaries), with consequent impact on western-boundary dynamics and air-sea interaction (Kwon et al. 2010; Frankignoul et al. 2011). Ocean-atmospheric dynamics related to western-boundary currents are not typically well modeled, spatial resolution and representation of heat flux out of the ocean being among the limiting factors (Dong and Kelly 2004; Kelly and Dong 2004; Kelly et al. 2010). We offer this limitation may play a role in the contrasting results of the stadium-wave studies, observation-based versus model-based.
Geographical placement of the Arctic High (Kwok 2011) presents another illustration of this theme. Mean and shifting geographical placements of the polar high-pressure system play strong roles in Arctic sea-ice dynamics, freshwater balance, and by extension, in climate response Wyatt (2012); submitted manuscript (2013). Most models inadequately simulate the Northern Hemisphere’s polar-high placement. (Kwok 2011) evaluated simulations of Arctic sea-ice motion in the CMIP3 collection. Sea-ice motion is largely wind-driven. The impacts of these winds are a function of, among other things, the geographical placement of the polar-high. This placement indirectly scripts regional sea-ice inventory, distribution, spatial pattern of ice thickness, and sea-ice export. Kwok examined groups of models. He found the overall CMIP3 simulations of sea-ice dynamics and related features to be poor, with some models performing better than others. He suggests the culprit is the significant displacement of the mean high-pressure pattern in the southern Beaufort region. Its modeled position tends to be skewed toward the central Arctic Basin rather than its observed mean position in the southern Beaufort Sea. Misplacement of related large-scale mean features of the circulation pattern follows. Other influences on the Arctic freshwater balance derive from sea-ice extent north of the Bering Strait. This, too, has been linked to non-static geographical placement of the Aleutian Low (Niebauer 1998). And according to (Jun et al. 2008), errors related to sea-ice north of the Bering Strait are common among models: GFDL, GISS, NCAR, and UKMO.
Geographical placement of centers-of-action and dynamics of western-boundary currents are but two identified features that appear to determine whether a regional circulation pattern’s reach remains regional or extends beyond, via direct or indirect means. These features are examples of small variations begetting disproportionately large results. The classic work on network theory by sociologist Mark Granovetter (1973) points to such small links yielding profound consequences. In his seminal work, he describes the crucial role of weak ties in enlarging and stabilizing a network. He describes the phenomenon in terms of societal behavior; yet this concept applies to any network. We suggest the “weak-tie” details of inter-connectivity within the climate network may be a necessary ingredient for hemispheric signal propagation. It may be that regional patterns are well modeled. But is their connectivity equally well modeled, be that through geographical positioning of oceanic and atmospheric centers-of-action; western-boundary currents, their extensions, and their relationship to overlying jet-stream tracks; or other such “small-scale” features?
And finally, along that same vein, (Van den Berge et al. 2011) have considered connectivity among nodes when modeling climate. They invoke the influential work done by (Pecora and Carroll 1990) on non-linear systems, applying principles of synchronized theory to modeling climate. In essence, they have found that with a limited amount of information exchanged, a system’s behavior can be reconstructed. This information exchange is accomplished by connecting each variable of a model to each variable of two other models. By linking chaotic systems, synchronization of the network of systems follows (Pecora and Carroll 1990). Here, consistent with what we see in stadium-wave dynamics, links between nodes are critical to capturing the full spatio-temporal signature of the climate network.