by Judith Curry
Our new stadium wave paper is now published.
Our new paper was motivated by Mann’s recent paper characterizing the AMO, which was critiqued by Nic Lewis: Critique of Mann’s new paper characterizing the AMO. In the Mann et al. paper, they wrote:
“Claims of multidecadal ‘stadium wave’ patterns across multiple climate indices are also shown to be likely an artifact of this flawed procedure for isolating putative climate oscillations.”
So, do Mann et al. have a valid point re the stadium wave? We immediately started discussing a response, although Geophysical Research Letters does not allow replies, notes or correspondence regarding its published papers, a policy that I personally don’t like. So, led by Sergey Kravtsov, we decided to write a stand alone paper that takes a broader perspective on the issues raised by Mann et al. and also conducts a deeper statistical analysis of the stadium wave.
Two contrasting views of multidecadal climate variability in the 20th century
Sergey Kravtsov, Marcia Wyatt, Judith Curry, and Anastasios Tsonis
Abstract. The bulk of our knowledge about causes of 20th century climate change comes from simulations using numerical models. In particular, these models seemingly reproduce the observed nonuniform global warming, with periods of faster warming in 1910–1940 and 1970–2000, and a pause in between. However, closer inspection reveals some differences between the observations and model simulations. Here we show that observed multidecadal variations of surface climate exhibited a coherent global-scale signal characterized by a pair of patterns, one of which evolved in sync with multidecadal swings of the global temperature, and the other in quadrature with them. In contrast, model simulations are dominated by the stationary — single pattern — forced signal somewhat reminiscent of the observed “in-sync” pattern most pronounced in the Pacific. While simulating well the amplitude of the largest-scale — Pacific and hemispheric — multidecadal variability in surface temperature, the model underestimates variability in the North Atlantic and atmospheric indices.
- An objective filtering method identifies a global mode of climate variability
- Space–time structure of climate in historic simulations reflects forced signal
- Modeled multidecadal climate variations are too weak, especially in atmosphere
Marcia Wyatt’s post
Marcia Wyatt has an extensive post on her website describing the paper [link]. Here are some excerpts:
Mann et al. claim that flawed methodology has generated an apparent, or false, propagation in the [stadium wave] signal. The contended flawed methodology is linear detrending, a statistical step once innocent in its ability to highlight lower frequency behavior within a time series – a signal often associated with the AMO – but today, a source of controversy, a portion of which has been aimed at the stadium wave.
Kravtsov et al. (2014) consider the challenge, adopting a strategy that evaluates phase uncertainties of the propagation, as well as spatio-temporal patterns of the signal in modeled and observed databases. Findings show: i) The propagation of the “stadium wave” is highly unlikely to be due random occurrence or flawed methodology; and ii) pronounced and fundamental differences occur between analyses using observation-based data and analyses using model-generated data. Differences involve spatial patterns of the signals: ocean indices of the Atlantic and Pacific and atmospheric indices across the hemisphere play significant roles in the observed stadium wave; while only the Pacific appears significant in model generated data. Differences also involve temporal patterns: the model-based signals are in-phase, stationary ones, requiring only one mode of variability to explain its profile; while observation-based signals are not in-phase, requiring two modes of variability to explain their alignment.
To better “see” these undulations [e.g. AMO], researchers traditionally have removed the long-term linear trend of a time series so as to highlight the higher-frequency fluctuations, the multidecadal ones among them. Yet, with the attribution issue (i.e. forced versus intrinsic) unresolved, appropriateness of this technique has come into question. The argument against it contends that linear detrending assumes removal of the forced signal. Thus, it is argued that if a linear trend is removed, a vestige of the forced wiggle is imprinted upon the remaining signal. In that case, if one interprets that detrended product to be of intrinsic character, the role assigned to it will be overestimated.
Linear detrending is implicated as a fatal flaw in a relatively new hypothesis regarding multidecadal-scale climate variability – the stadium-wave hypothesis. The stadium-wave hypothesis of multidecadal-scale climate variability assumes that synchronized network behavior governs the low-frequency quasi-periodic oscillatory component shared among a collection of interacting ocean, ice, and atmosphere indices. Phasing-offset among the synchronized network members reflects hemispheric propagation of the signal, the pace of which appears to be governed by variability in the AMO.
If AMO is linearly detrended, is there, or is there not, a vestige forced signature imprinted upon the residual, thereby exaggerating the perceived role of internal processes? We arrive back at the impasse. Yet this impasse is not to be conflated with fundamentals of the stadium-wave signal. Stadium-wave propagation is hypothesized to have an intimate connection with AMO – the latter being its pace setter. Perhaps not immediately intuited, this association says nothing about the driver of AMO. Propagation of the stadium wave proceeds, so the hypothesis goes, irrespective of the source of AMO oscillatory energy, be it external forcing, internally generated variability, or a combination of both.
Mann et al. (2014) contend that the propagation – the distinguishing signature of the stadium-wave hypothesis – is no more than a statistical artifact of flawed methodology – i.e. of linear detrending. Linear detrending is a step in the analysis used to document the stadium wave, the intended purpose to remove the centennial-scale trend to highlight multidecadal variability. But, regardless of intended use of the method, it is worth taking into account the findings of Mann et al.
Kravtsov et al. (2014) considered Mann et al.’s contention that the stadium-wave propagation is no more than an artifact of methodology. Mann et al. illustrated that a random realization of interannual variability (white noise), superimposed upon their artificial climate indices – an in-phase forced signal common to each – would, once linearly detrended and smoothed, produce a false appearance of propagation. Choice of noise realization would dictate propagation sequence and phase offsets. Thus, one could generate a variety of different “stadium waves” according to the nature of the white noise imprint, an outcome implying that the propagating stadium-wave signal identified by Wyatt and collaborators was illusory, and any apparent stadium-wave lags were statistically insignificant.
Kravtsov et al. concede that a collection of indices constructed from a commonly shared, in-phase, forced signal, whose only differences are those imposed by regional noise 4 processes, do generate false “stadium waves”, once linearly detrended and smoothed – as was done in Mann et al. In methodological contrast, Wyatt and collaborators, in their stadium-wave analyses, have sought to identify timescales of co-variability among network indices. Their use of Multi-channel Singular Spectrum Analysis (M-SSA) — a generalized application of the more commonly known Empirical Orthogonal Function (EOF) analysis, adept at identifying propagating signals and shared variability among indices — has documented multidecadal-scale stadium-wave propagation (a structure of M-SSA-generated phase-shifted signals) in a variety of geophysical index collections. The phase shifts between the “real” stadium-wave indices are, of course, subject to uncertainty, just as are the indices in the synthetic example of Mann et al. (2014). However, the real question is whether these uncertainties are so large as to render the stadium-wave propagation statistically insignificant. That is the point Kravtsov et al. first investigate.
Merging this view of M-SSA generated phase-shifted signals plus noise with the strategy of Mann et al. in constructing surrogate networks, Kravtsov et al. show that the phase uncertainties of each index are significantly smaller than the actual phase lags (lag time in years between propagating indices) among those indices in the “real” stadium wave. This finding supports the Kravtsov et al. counterargument to Mann et al’s contention that artificial propagation is a product of sampling associated with climate noise. According to Kravtsov et al., such sampling variations are unlikely to explain the propagation observed in the “real” stadium wave; thus weakening Mann et al.’s challenge.
The reviews on this paper were thorough (see here for previous versions of the paper, the reviews and our responses) – three rounds of reviews involving four reviewers. The reviewer comments weren’t particularly substantive with regards to the actual analysis, but did help clarify the paper.
If you check the reference list, you will see that Mann’s papers figure prominently – a natural editorial decision would be to invite Mann to review the paper. We specifically requested that Mann not be involved in the review process, owing to public statements that he has made about me. I frequently make such a request when submitting a paper (related to public statements made by people that I regard as too conflicted to review a paper of mine). As far as I can tell, the editors have always honored this request. In the absence of blind peer reviewing, I regard this to be a very useful strategy to help support fair peer review.
The insights from the stadium wave relate to the propagation of the multi-decadal signal; per se the stadium wave does not directly provide insights into the the issues of 20th century attribution or transient climate sensitivity. The point raised by Mann and the alternative perspective provided by our paper does raise the broader issues of whether you can separate forced from intrinsic variability, and if so, how to do this. The big unresolved question remains as to the effect of multidecadal internal variability on our estimates of climate sensitivity and 20th century attribution of warming.