New paper tries to disentangle global warming from natural ocean variations

From the paper…
“The first LFP shows a nearly uniform warming pattern, corresponding to a 0.67∘C per century warming of Pacific SSTs throughout the record (Figure 1a) [1900-2016]. The warming of tropical Pacific SSTs is notably uniform, withouta clear El-Niño-like or La-Niña-like warming trend. There is detailed temporal structure to the global tempera-ture rise, with periods of reduced global warming between the mid-1940s and late 1980s and between 1998 and 2013.”
Doesn’t that correspond roughly to what we suspect already and which is not well correlated to the CO2 pattern?

a forerunner article by the same . No paywall
https://www.atmos.washington.edu/~david/Wills_etal_PNAS_submitted_2017.pdf

The answer is that you can’t, at least not easily.
One of the biggest unknowns is the magnitude and persistence of the apparent 1000 year periodicity that shows up in some records such as the ice core data and the Roman Warm Period and Medieval Warm Period. On some estimates, the entire warming since the end of the LIA is independent of the CO2. For people of a skeptical open-minded bent, it is a thorny issue.

Bottom line . What the heck are we spending $trillions of limited resource $$ on the basis of over exaggerating climate models produced from incomplete inputs ?
The problem with overly hyped global warming fear mongering is it sustains itself with unsustainable government debt .

Difficult to believe you can achieve much using just stats and no knowledge of the underlying physics – well apart from deluding yourself.

“Our results give statistical representations of PDO and ENSO that are consistent with their being separate processes”
That would be a problem, since there is a non-trivial amount of science that indicated that the two processes are entangled.

Sometimes the snark only shows that being a smartass doesn’t really distinguish you from a dumbass.
These guys are trying a different approach from modeling. For that alone they deserve cusps. And while it is still statically based – ie subject to mathterbation – their object seems to be worthwhile. As has been remarked on extensively here, we need to understand natural variability before reaching any conclusions about human influences.

A new beautiful statistical method applied to pre-1955 temperature data of the Pacific.
Pray tell, how well do we know these old temperatures?

My criticism is so devastating to Battisti’s study as to make the whole study false . Actually 5 climate scientists demolished Battisti’s study 9 years ago. But before getting to the demolishment, I have some minor housekeeping points.
I got suspicious when I read the words “novel approach” and “novel method” in Battisti’ abstracts of this paper. There are 2 because he has submitted different versions to 2 different climate journals and got both of them published. There are other minor differences in the text except for 2 sub points which are extremely important. The 1st sub point difference is that in the paper published by the Geophysical Research Letters referenced by the WUWT article he stated that “LFCA finds a linear combination of these three EOFs that
eliminates their covariance on decadal time scales” whereas in his paper submitted to the Proceedings of the National Academy of Sciences he states “LFCA finds a linear combination of these three EOFs that
minimizes their covariance on decadal time scales”. The difference between “minimizes” and “eliminates” is important.
The 2nd subpoint is that in the “Geophysical Research Letters” paper he says “We define low-frequency variance as the variance remaining after the pointwise
application of a Lanczos lowpass filter with a 10 year lowpass cutoff.” However in the Proceedings of the National Academy of Sciences paper he states ” “We define low-frequency variance as the variance remaining after the pointwise
application of a Lanczos lowpass filter with a 8 year lowpass cutoff.”
As you can realize; these 2 small changes, means; the papers are effectively different. It is interesting that Battisti had 10 years in his draft version. So he changed his mind twice.
Okay now for the criticism that demolishes his study.
1) There was a paper published in the Journal of Climate Dec 2009 called “Empirical Orthogonal Functions: The Medium is the Message”
https://journals.ametsoc.org/doi/full/10.1175/2009JCLI3062.1
In that paper (there were 2 Canadians of which I am proud to say were the lead authors) they cautioned against the very thing that Battisti did in his “paper(s)”. To understand my demolition you have to understand just what Empirical Orthogonal Functions are. They are a fancy way of pairing values with data points (geographical in nature) so that the values represent something else ( in this case variances).
They said ” Thus, EOF analysis expresses the (discretely sampled) field x as the superposition of N mutually orthogonal spatial patterns modulated by N mutually uncorrelated time series. The spatial patterns and time series occur in matched pairs, which are generally referred to as EOF modes.
We note the following points:
The EOF expansion can be interpreted geometrically as a change of coordinates in 𝗥N through an orthogonal rotation to a basis in which 𝗖 is diagonal. This emphasizes that the EOF expansion is nothing more than another way of describing the time series x in terms of a new basis set in which this description is particularly simple (from the perspective of the distribution of variance).”
But there are mathematical constraints that you have to meet in your data for this to be a valid approach.
They go on to say this about
” EOFs and dynamical modes
The most natural system in which the statistical modes produced by EOF analysis might be expected to have clear individual dynamical significance is one governed by linear dynamics for which the notion of “dynamical modes” as eigenvectors of the linear dynamical operator is straightforward. In fact, North (1984) demonstrated that the correspondence between EOFs and dynamical modes holds only in a very specialized class of linear dynamical systems that are expected to be the exception rather than the rule in the (linearized) dynamics of real geophysical flows.”
“As a first statement about the connection between EOFs and dynamical modes, we can say immediately that the two sets of vectors will not correspond in the case that the linear operator 𝗔 is nonnormal”
Further they say
“Nonnormality of the dynamical matrix is the generic case for the linearized dynamics of geophysical systems, particularly in the presence of shear or coupling between systems with very different time scales (e.g., Farrell and Ioannou 1996; Kleeman 2008). It follows that we can say, as a general rule, that EOFs and dynamical modes will not coincide.
This argument does not rule out the possibility that EOFs correspond to dynamical modes in the special case that the linearized dynamics are governed by a normal operator. In this case, it can be shown (appendix A) that the EOFs will only correspond to the dynamical eigenvectors of 𝗔 if the noise has no spatial structure: that is, if it is spatially uncorrelated. If the driving noise is spatially correlated, then its structure will be imprinted on the covariance matrix of the damped, driven system so that the EOFs of x mix the structure of the noise with the structure of the linearized dynamics. In this case again, the EOFs and dynamical modes will not correspond.”
The only way that Battisti could argue that the noise has no spatial structure is that if the full noise was global warming and nothing else. Indeed that is what Battisti is trying to say in his paper. He is attributing all variance that isnt caused by ENSO or the PDO to the variance caused by global warming caused by CO2. That would be okay if true, but that cannot be the case for 2 reasons. A) There are many causes for SST (the number one being the sun). B) Battisti has not proved any case for global warming caused by CO2. He is simply assuming it.
Furthermore they say
“The correspondence between EOFs and dynamical modes is even less clear in the case of systems governed by nonlinear dynamics, in which the concept of the dynamical mode must be generalized to the more abstract notion of dynamically invariant subspaces (which the system will not leave once having entered). Such subspaces will not in general even be planar, in contrast to the case of subspaces spanned by EOFs or linear dynamical modes. For such systems the EOFs will be of course determined by—but on an individual basis cannot be expected to bear any simple relationship to—the dynamics. ”
Is anybody going to argue that SST is simply a linear system?
The next quote from their study DEMOLISHES ALL GENERAL CIRCULATION CLIMATE MODELS
“4. EOFs and kinematic degrees of freedom
We have seen that EOFs will not generally be of individual dynamical significance. Because statistical properties of a system are descriptions of variability and thus inherently kinematic, we might ask if individual EOF modes will be simply related to natural kinematic descriptors of variability. That this cannot be expected to be the case in general will be illustrated by the example of a simple model of a fluctuating jet in zonal-mean zonal wind, for which the EOF problem is analytically solvable.
In both observations and atmospheric GCMs, the leading EOF of extratropical zonal-mean zonal wind is a dipole with a central zero-crossing at approximately the mean latitude of the eddy-driven jet (e.g., Hartmann and Lo 1998; Codron 2005; Fyfe and Lorenz 2005; Eichelberger and Hartmann 2007). To address the kinematic significance of this EOF mode, we consider a jet in zonal-mean zonal wind with Gaussian profile and fluctuating in strength and position:
where x is a meridional coordinate. In this model, the jet strength U(t) and position xc(t) are the natural kinematic variables of the jet—what we will call the kinematic degrees of freedom. For convenience, we will assume that fluctuations in U(t) and xc(t) are independent and Gaussian. Based on observations of the extratropical zonal-mean eddy-driven jet (in either hemisphere), we will assume that both of l = std(U)/mean(U) and h = std(xc)/σ0 are ≪1. With these assumptions, the covariance matrix of u(x, t) can be computed analytically and expanded as a Taylor series in the small parameters l, h [details of these computations are presented in Monahan and Fyfe (2006)]. From these expansions the leading EOFs can be determined in terms of the normalized basis vectors f1(x), f2(x), and f3(x) (Fig. 4), corresponding respectively to a monopole, a dipole, and a tripole. By symmetry, the dipole is orthogonal to the monopole and tripole, but the monopole and tripole themselves are not mutually orthogonal (and therefore cannot simultaneously be EOFs).
In the case of pure fluctuations in jet strength, the only EOF with nonzero variance is the monopole. For fluctuations in position alone, the leading two EOFs are the dipole and the tripole, respectively. When the jet fluctuates in both strength and position, if fluctuations in position are relatively large compared to those of strength (as is the case in observations) then the leading EOF is the dipole f1(x). The leading PC time series is given by (to leading order in the small parameter h)
That is, while the dipole pattern arises because of the presence of fluctuations in position, the fluctuations in jet strength also project upon it and are therefore mixed into the associated PC time series. The first EOF mode bundles together both kinematic degrees of freedom and cannot be uniquely associated with position fluctuations. Furthermore, the spatial pattern of the second EOF is a monopole/tripole hybrid where the degree of hybridization is determined by the quantity
When δ ≪ 1, e2 is a monopole and when δ ≫ 1 it is a tripole: in between, it is a linear combination of the two. The monopole comes in from strength fluctuations and the tripole from position fluctuations, but because these are not orthogonal they cannot both simultaneously be EOFs. Spatial structures that are EOFs in the case of fluctuations in a single kinematic degree of freedom on its own will not necessarily be EOFs in the presence of multiple fluctuating degrees of freedom as a consequence of the requirement that the EOFs be mutually orthogonal. Not surprisingly, the time series associated with the second EOF, α2(t), also mixes together variability in both strength and position.
The observed extratropical eddy-driven jet fluctuates in strength, position, and width (with the first and third of these correlated as a consequence of momentum conservation). The above arguments can be generalized to include fluctuations in jet width (Monahan and Fyfe 2006), to relax the assumptions of Gaussian jet profile and kinematic parameter probability distributions (Monahan and Fyfe 2009), and to consider the geopotential EOFs associated with the fluctuating jet (Monahan and Fyfe 2008). The central conclusion remains unchanged: despite the fact that they directly reflect the kinematics of variability, the defining constraints on EOFs (orthogonal straight-line axes with uncorrelated time series) prevent them in general from being in simple one-to-one correspondence with kinematic descriptors of the field.”
HAVE YOU HAD ENOUGH? MOST OF YOU WILL HAVE STOPPED READING THIS BY NOW. However there is more.
Dont forget their report was written 8 years before Battist’s paper. So actually the next section demolishes Battisti’s paper 9 years before it was even written. Dont forget that the sample mean variances have to be all Gaussian for Battisti’s method to work correctly. They say
” Another field in which non-Gaussianity is manifest through statistical dependence of EOF modes is tropical Pacific sea surface temperature, as was discussed in Monahan and Dai (2004). Maps of the leading EOF patters of SST as computed from the Hadley Centre Sea Ice and SST dataset (Rayner et al. 2003) are presented in Fig. 7. Also presented are maps of the estimated standard deviation and skewness fields; the latter corresponds to the normalized third-order moment (measuring the asymmetry of a probability distribution around its mean)
skew(@) = eigenvector ((a- eigenvector a)/ std(a))
and vanishes if the distribution is Gaussian. Nonzero values of this statistic are therefore a measure of non-Gaussianity. The skewness field illustrated in Fig. 7 indicates that the SST probability density tilts toward positive anomalies in the eastern equatorial Pacific and toward negative anomalies in a horseshoe-shaped band from the central subtropical South Pacific through the western equatorial Pacific back up to the northern subtropics. The leading SST EOF, which carries the most variance, bears a strong resemblance to the standard deviation field. Also notable is the similarity between e2 and the skewness field, the reason for which becomes evident through an inspection of a scatterplot of α1 with α2 (Fig. 8). From this plot it is evident that strong positive and negative anomalies of α1 (corresponding respectively to El Niño and La Niña events) are both associated with strong positive anomalies of α2. In other words, the second EOF mode makes a positive contribution to the SST field during both extreme phases of ENSO, so on average the strongest positive SST anomalies during El Niño are located farther east than the strongest negative SST anomalies during La Niña. This asymmetry in the SST field between the opposing phases of ENSO is then manifest in the skewness field. Again we see a relationship between non-Gaussianity of the field and statistical dependence of the EOF modes.”