This is an example of pulling out the signature of CO2 controlled greenhouse gas warming from global mean surface ttemperature records such as GISS, HadCrut, and BEST.

The temperature records as provided show noise at the yearly, decadal, and multi-decadal level due to natural variation. Many factors contribute to noise. When all these factors are small and of the same order of magnitude in their impact, it may no longer make sense to deconstruct the individual contributions. At that point statistical characterization of the noise makes sense.

A typical application of signal-to-noise reduction is in situations where one of the contributors to the noise dynamics starts starts to rise above the background din. In the case of the changing climate, the signal emerging is that of AGW due to atmospheric CO2 growth and the noise is captured by various inferred measures.

So the obvious approach is to remove these fluctuations from the global temperature time-series so that the Signal-to-Noise Ratio (SNR) is further improved. The set of measures that we consider include:

• Southern Oscillation Index (SOI) representing pressure changes
• Aerosols from volcanic eruptions
• Length-of-Day (LOD) adjustments reflecting multidecadal energy
• Total Solar Irradiance (TSI)

As an example of one measure, the SOI essentially isolates one of the significant noise sources. This source is still much smaller than the AGW signal : The model uses a variational approach to esentially minimize the free energy changes

dG = Vdp - SdT

This is an active research area [1][2]. [1]J. L. Lean and D. H. Rind, "How natural and anthropogenic influences alter global and regional surface temperatures: 1889 to 2006," Geophysical Research Letters, vol. 35, no. 18, 2008.

[2]Y. Kosaka and S.-P. Xie, "Recent global-warming hiatus tied to equatorial Pacific surface cooling," Nature, vol. 501, no. 7467, pp. 403–407, 2013.