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.
Cite this paper
M. Schlesinger, D. Lindner, M. Ring and E. Cross, "A Simple Deconstruction of the HadCRU Global-Mean Near-Surface Temperature Observations," Atmospheric and Climate Sciences, Vol. 3 No. 3, 2013, pp. 348-354. doi: 10.4236/acs.2013.33036.
 M. J. Ring, D. Lindner, E. F. Cross and M. E. Schlesinger, “Causes of the Global Warming Observed Since the 19th Century,” Atmospheric and Climate Sciences, Vol. 2, No. 3, 2012, pp. 401-415. doi:10.4236/acs.2012.24035
 M. E. Schlesinger, D. Lindner, M. J. Ring and E. F. Cross, “A Fair Plan to Safeguard Earth’s Climate. 3: Outlook for Global Temperature Change throughout the 21st Century,” Journal of Environmental Protection, Vol. 4, No. 6, 2013, pp. 653-664. doi:10.4236/jep.2013.46075
 C. P. Morice, J. J. Kennedy, N. A. Rayner and P. D. Jones, “Quantifying Uncertainties in Global and Regional Temperature Change Using an Ensemble of Observational Estimates: The HadCRUT4 Dataset,” Journal of Geophysical Research, Vol. 117, No. D8, 2012, pp. 1984-2012.
 T. M. Smith, R. W. Reynolds, T. C. Peterson and J. H. Lawrimore, “Improvements to NOAA’s Historical Merged Land-Ocean Surface Temperature Analysis,” Journal of Climate, Vol. 21, No. 10, 2008, pp. 2283-2296.
 J. Hansen, R. Ruedy, M. Sato and K. Lo, “Global Surface Temperature Change,” Reviews of Geophysics, Vol. 48, No. 4, 2010, Article ID: RG4004.
 K. Ishihara, “Calculation of Global Surface Temperature Anomalies with COBE-SST,” (Japanese) Weather Service Bulletin, Vol. 73, 2006, pp. S19-S25.
 K. Ishihara, “Estimation of Standard Errors in Global Average Surface Temperature,” (Japanese) Weather Service Bulletin, Vol. 74, 2007, pp. 19-26.
 S. W. Smith, “Moving Average Filters,” The Scientist and Engineer’s Guide to Digital Signal Processing, 1999, pp. 277-284.
 M. E. Schlesinger and N. Ramankutty, “An Oscillation in the Global Climate System of Period 65 -70 years,” Nature, Vol. 367, No. 6465, 1994, pp. 723-726.
 T. Delworth, S. Manabe, R. S. Stouffer, N. G. Andronova and M. E. Schlesinger, “Interdecadal Variations of the Thermohaline Circulation in a Coupled Ocean-Atmosphere Model,” Journal of Climate, Vol. 6, No. 11, 1993, pp. 1993-2011.
 M. Ghil and R. Vautard, “Interdecadal Oscillations and the Warming Trend in the Global Temperature Time Series,” Nature, Vol. 350, No. 6316, 1991, pp. 324-327.
 D. Lindner, “Quasi-Periodic Oscillations in Observed and Simulated Temperatures and Implications for the Future,” Ph.D. Thesis, University of Illinois, Urbana-Champaign, 2013, 135p.
 N. G. Andronova and M. E. Schlesinger, “Causes of Temperature Changes during the 19th and 20th Centuries,” Geophysical Research Letters, Vol. 27, No. 14, 2000, pp. 2137-2140. doi:10.1029/2000GL006109