Abstract
Previously we have used Singular Spectrum Analysis (SSA) to deconstruct the global-mean near-surface temperature observations of the Hadley Centre—Climate Research Unit that extend from 1850 through 2012. While SSA is a very powerful tool, it is rather like a statistical “black box” that gives little intuition about its results. Accordingly, here we use the simplest statistical tool to provide such intuition, the Simple Moving Average (SMA). Firstly we use a 21-year SMA. This reveals a nonlinear trend and an oscillation of about 60 years' length. Secondly we use a 61-year SMA on the raw observations. This yields a nonlinear trend. We subtract this trend from the raw observations and apply a 21-year SMA. This yields a Quasi-periodic Oscillation (QPO) with a period and amplitude of about 62.4 years and 0.11°C. This is the QPO we discovered in our 1994 Nature paper, which has come to be called the Atlantic Multidecadal Oscillation. We then subtract QPO-1 from the detrended observations and apply an 11-year SMA. This yields QPO-2 with a period and amplitude of about 21.0 years and 0.04°C. We subtract QPO-2 from the detrended observations minus QPO-1 and apply a 3-year SMA. This yields QPO-3 with a period and amplitude of about 9.1 years and 0.03°C. QPOs 1, 2 and 3 are sufficiently regular in period and amplitude that we fit them by sine waves, thereby yielding the above periods and amplitudes. We then subtract QPO-3 from the detrended observations minus QPOs 1 and 2. The result is too irregular in period and amplitude to be fit by a sine wave. Accordingly we represent this unpredictable part of the temperature observations by a Gaussian probability distribution (GPD) with a mean of zero and standard deviation of 0.08°C. The sum of QPOs 1, 2 and 3 plus the GPD can be used to project the natural variability of the global-mean near-surface temperature to add to, and be compared with, the continuing temperature trend caused predominantly by humanity’s continuing combustion of fossil fuels.
Highlights
Since 1994 we have published four scientific papers wherein we used Singular Spectrum Analysis (SSA) to analyze up to four observational records of global-mean near-surface temperature
As we do this with each SSA feature, we will subtract it from the observed temperatures and apply another Simple Moving Average (SMA) to reveal the aspect of the observed temperatures
As we showed in Causes, the SSA trend is due to humanity—not nature—as a result of our emissions of greenhouse gases, aerosol precursors, and land-use changes
Summary
Since 1994 we have published four scientific papers wherein we used Singular Spectrum Analysis (SSA) to analyze up to four observational records of global-mean near-surface temperature. In those papers, the SSA results were obtained as if from a statistical “black box”, that is, all at once and not intimately connected to the observed temperatures. In particular we will use Simple Moving Averages (SMAs) of different time periods to reveal an aspect of the observed temperatures. We will compare this aspect to what SSA shows more completely. Here we restrict attention to the HadCRU temperature dataset alone
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