In part 1 we used auto-correlation to adjust the hadcrut4v2 global temperature data to remove the influence of the ADO that are assumed to be not germane to the climate sensitivity to CO2. The result was the adjusted dataset plotted below.

Hadcrutv2 adjusted to remove ADO effects

Hadcrutv2 adjusted to remove ADO effects

If we look at the auto-correlation of this data, we see evidence of a remaining periodicity.

ACF of adjusted data

ACF of adjusted data

Power spectral density of the adjusted data

Power spectral density of the adjusted data

Sine fit to residual

Sine fit (T ~ 88 years) to residual

Proceeding as before, we remove this periodicity resulting in the the doubly adjusted data shown below.

Hadcrut4v2 with 65 and 89 year periodicities removed

Hadcrut4v2 with 63 and 89 year periodicities removed

ACF of doubly-adjusted data

ACF of doubly-adjusted data

PSD of doubly-corrected data

PSD of doubly-corrected data

The remaining spectral peaks are statistically insignificant. We’ll test the significance of the periodicity removed thus far in part 3. The plot below shows A1 and A2 plotted with the uncorrected data with Gaussian filtering (r=6) applied for de-noising.

Hadcrut4v2 with ADO (A1), ADO+87 year cycle (A2) removed vs uncorrected data

Hadcrut4v2 with ADO (A1), ADO+87 year cycle (A2) removed vs uncorrected data

Comparing A1 to the uncorrected plot, it is evident that the ADO accounts for the cooling evident in the late nineteenth century,  the rapid rise in temperatures in the first 40 years if the twentieth century, and the cooling era between 1940 -1975. It also accounts for the rapidity of the rise in temperatures of the last 25 year of the twentieth century when global warming became a concern as well as the recent flattening of temperatures experienced during the so called “pause”.

The scattergrams below compare the raw, adjusted (A1), and double adjusted (A2) to the CO2 data obtained from here, which concatenates the data  from the Law Dome ice core reconstruction with the direct observations from the Mauna Loa observatory plotted in the lower right panel.

Scattergrams of Temperature vs. CO2 (Law Dome + Mauna Loa)

Scattergrams of Temperature vs. CO2 (Law Dome + Mauna Loa)

The three datasets show a similar pattern- little correlation until the CO2 concentration exceeds 300 ppm, then the expected roughly logarithmic relationship. Comparing the A1 and A2 plots, it appears the final adjustment removed some low concentration correlation. If we examine the PSD of the de-trended CO2 plot we can see why.

PSD of p=3 residual of CO2 time series

PSD of p=3 residual of CO2 time series

The spectral peak the same frequency detected in the final adjustment above. Thus the 88 year “periodicity” is actually a response of the climate to the variation in CO2. We reject A2 in favor of A1.

In order to avoid biasing the estimation of climate sensitivity, we must avoid the zero-slope segment where no correlation is exhibited (i.e concentrations below 295 ppm) and add a positive offset to the temperature data such that all points are well above zero. We remove this offset from the fit equation after performing the OLE regression. This only effects the reference concentration corresponding to the  zero anomaly temperature and does not impact the sensitivity. The OLE logarithmic fit to the data (Ta=2.83ln(x/246.278)-0.809 where x is the Co2 concentration in ppm) is shown in the plot below.

Logarithmic regression of temperature anomally

Logarithmic regression of temperature anomaly

The transient sensitivity to 2x CO2 is then calculated as 2.83*ln(2)= 1.96 degrees C .

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