For the original analysis posted on WUWT, I only used data from 1900 to the present. The motivation for this was twofold. I had read somewhere that the data prior to 1900 was sketchy and biased cold by the the Krakatoa eruption of 1883. This post by Willis Eschenbach persuaded me that I was being overcautious with respect to the influence of volcanic eruptions so I redid the analysis with the full data set.
The second row of plots shows the main result (slope of the reconstructed signal). Not only do we see the same .6 degC/century change between the 1920s peak and the 1990s peak that we saw before, we see the same .6 degC/century change between the 1850s peak and the 1920s peak! This lends further credence to those who argue that even the .6degC/century change is not attributable to AGW.
Slope Detection Provides First-Order Insensitivity to PDO Amplitude Variations
In the comments to my WUWT post, Willis Eschenbach pointed out that we don’t know how the unaltered climate would have varied over the observation interval. That’s true but the question is how sensitive are we to such variations. I think the answer is not too. Clearly the dominant variant is the quasi-periodic signal whose period is approximately 60 years. In deconstruction we see it is very sinusoidal looking. Let’s pretend to first order we can model this as a sinusoid of approximately constant frequency but whose amplitude varies over the 163 year observation interval. Let’s also assume we have a linear AGW effect . Our model is thus
c(t) = a t+(m b(t)+1) sin(t wo)
where a is the AGW slope, m is the AM modulation index, b(t) is the time function describing the amplitude variation and wo is the frequency of the mode. Since we are detecting the peak slope, we need differentiate c(t) with respect to time.
c'(t) = a + m b'(t) sin(t wo) + wo (m b(t)+1) cos(t wo)
The slope is maximized when c(t) crosses zero or when wo *t = Pi/2. At those points, the cos terms drop out because cos(Pi/2)=0 and the sine term becomes unity. So
c'(t)max = a + m b'(t)
the “a” term is AGW contribution to the temperature slope at the peak. The m b'(t) term is the natural contribution. Note that the values obtained at the peaks are first order insensitive to b(t), the amplitude variation in the mode, and only sensitive to its first derivative, scaled by the mod index (% change in amplitude). This result can be extended via fourier analysis to the general (non-sinusoidal) case: Maximum insensitivity to amplitude variations is obtained by slope detection at the point of maximum deviation. This principle is why FM radios are insensitive to static noise.
We have five samples of maximum slope, three in the positive direction and two in the negative. Note the symmetry in these excursions shown in the figure below where I’ve added two lines of identical slope.
The first three peak excursions (2 positive, 1 negative) occur prior to any significant AGW contribution so the a term above can be assumed negligible over this interval and the peak values are determined by m*b'(t1), m*b'(t1), m*b'(t3).
The figure below shows the data of figure 2 detrended about the central trend, 0.0000588 t – 0.0049.
We see from figure 3 that m*b'(t1) ~ -m*b'(t2) ~ m*b'(t3). Thus an AGW component detectable prior 1965 would show up as a positive offset added to the negative peak excursion of that year. None can be detected and in fact that excursion is slightly more negative. An AGW component detectable prior 1993 would show up as a positive offset added to the positive excursion of that year. Again, no offset is detected and in fact, if we discount the obvious bump attributable to the large el-nino of that year, the peak excursion is probably slightly lower.
This channel has been a reliable predictor of the maximum slope excursion for 150 years, with no discernible effect from exponentially rising CO2 concentrations during the last full cycle. We conclude that the mean rate of increase in the slope of the northern hemisphere sea surface temperature has remained constant over the past 163 years and therefore the null hypothesis (no detectable AGW signal present in the SST data) cannot be rejected.
Rejecting the IPCC Central Tenet
This analysis, while limited to the northern hemisphere sea surface temperature record, finds no support for the IPCC AR5 summary statement that “It is extremely likely that human influence has been the dominant cause of
the observed warming since the mid-20th century.” They also state
Greenhouse gases contributed a global mean surface warming likely to be in the range of 0.5°C to 1.3°C over the period 1951−2010.
We’ve shown above that no detectable AGW signal is present in the SST data so let’s add one in to determine if we could detect a signal producing the IPCC’s lowest estimate, .5°C over the period 1951−2010.
The first thing of note is that to achieve the IPCC low-end estimate only requires a benign .5°C/century component!
Running the detection algorithm with settings unchanged shows that even this minor contribution would be detectable were it there (note the positive offsets at both the negative excursion in 1965 and the positive excursion in 1997).
Most of the data-based conclusions in the IPCC are supported by this analysis. To the extent we can trust the data, it shows the sea surface temperature has indeed warmed over the last century and a half and is warming at a slightly increasing rate. It is in the attribution, where the IPCC switches from data-based conclusions to model-based conclusions, that their confidence becomes unjustifiable.
“Models do not generally reproduce the observed reduction in surface warming trend over the last 10 –15 years.”
That’s because the models cannot reproduce the oscillatory natural variation responsible for both the current “pause” and the rapid warming observed in the 1980s and 1990s and wrongly attributed to GHG.