Much of the alarm about man’s influence on the climate is due to the observed rapid rise in temperatures over the two decade period starting in the late 1970s. The rise was coincident with a exponential rise in the concentration of CO2 in the atmosphere, which, while still a piddling .04% of the atmospheric volume, was assumed to have an impact greater than its mass through feedback. The clarion call was sounded and 100 of billions of dollars in direct and indirect costs have been spent since trying to ameliorate the perceived environmental threat.

HAdcrut3 Temperature anomaly, box-care averaged (P=12) and decimated (D=12)

Hadcrut3 Temperature anomaly, boxcar averaged (P=12) and decimated (D=12)

Parts 1 and 2 of this series and the original post on WUWT examined the temperature record through two different means of spectral decomposition. Both showed the strong likelihood of a significant periodic signal in the climate record with a repeating period of about 60 years. The phase stability of this cycle and the presence of smaller, harmonically related signals, points to a celestial origin – natural, emergent cycles simply do not exhibit this type of stable behavior. But for this analysis, we are going to assume only that it is a natural phenomenon, unrelated to any human activity.

Singular spectrum analysis (SSA) provides the means to decompose a time series into components which when summed together, reconstruct the original signal with precision. Some of these components correspond to (at least locally) periodic signals present in the data, while some are just noise. There are statistical means to tell one from the other. SSA then allows us to reconstruct the record in various ways, depending on the time frame of interest, and whether we want to filter off the noisy signals.

The 60 year signal is the second strongest mode (after the trend, which may or may not actually be another periodic low-frequency signal harmonically related to the 60 year cycle). As mentioned above, we are going proceed under the assumption that the second mode is a natural (and perhaps temporary) phenomenon, and ask the question, what would the temperature record have looked like had this natural cycle not been present?

SSA allows us to answer this question, because by definition, all of the trend information is contained in the first mode. The other modes represent trendless fluctuations about the main trend. We can adjust the window length (L) to maximize the amplitude difference between the trend and the second mode, and reconstruct the signal, leaving out the contribution of the 60-year (second) mode. The result in shown below (purple line) along with the original timeseries (blue) and a linear fit to the reconstructed record (red dashed).

Hadcrut3 SSA recontruction (L=35,k=1,3,4) without the 60-year mode

The slope of the best-fit line is a benign .5 degreeC per century, remarkably constant over the entire 113-year record. Had the 60-year signal not been present, no discernible acceleration in warming would have been observed, no conclusions as to cause would have been jumped to and the ensuing damage to the world’s economy would have been avoided.

What about all the other modes we’ve filtered out (by using a low k-value). The higher modes correspond to noise at various bandwidths. We can add them back as shown below.

Hadcrut3 SSA  recontruction (L=35,k=1,3-35) without the 60-year mode

Hadcrut3 SSA recontruction (L=35,k=1,3-35) without the 60-year mode

With the high-frequency noise added back in, the slope is virtually unchanged (insignificantly smaller at .49 degsC / century).

This truly is the cycle that changed history. Only time will tell if Climatology will admit they fell victim to the fallacy we all learned in our first day of college – never confuse correlation with causation, and end their global warming hysteria. I’m not holding my breath.

Part IV – Global warming a la mode