Wednesday, September 25, 2013

Global Temperature Measurement

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Reported Temperature Measurements

Average global temperature anomalies (AGT) since temperatures have been measured world wide and with increasing accuracy are reported 1,2,3,4 on the web by three agencies. These reported data are graphed in Figure 1.


Figure 1. Differences in reported average global temperature anomalies are due primarily to differences in reference temperatures. All exhibit trends with similar periodicities.

These all use essentially the same raw temperature measurement database. Each group processes the data slightly differently from the others. Each believes their method is most accurate. To avoid bias, each anomaly trajectory is shifted (reference-temperature change only) so its average is the same as the average for HadCRUT4 over the time period for which both are given and then the average from the available values (as-shifted if not HadCRUT4) for each year is calculated. This normalizes the set to an unbiased single trajectory which is shown in Figure 2.

Figure 2: Normalized average of reported temperature anomaly trajectories. The reported fluctuations are impossibly rapid.

Examination of Figure 2 discloses four approximately linear trends: downtrend 1877-1909, uptrend 1909-1941, downtrend 1941-1973 and uptrend 1973-2005. Although the trend has been flat since 2001, a continuation of history portends a downtrend 2005-2037.

It has been demonstrated 5 that, since AGT have been accurately measured world wide (approximately 1895), the AGT trends are explained (R2=0.9) by the net average natural ocean surface temperature oscillations combined with a proxy factor times the sunspot number time-integral.

Effective Thermal Capacitance

Some ocean surface temperature oscillations have been named according to the particular area of the oceans where they occur. Names such as PDO (Pacific Decadal Oscillation), ENSO (el Nino Southern Oscillation), and AMO (Atlantic Multidecadal Oscillation) may be familiar. They report the temperature of the water surface while the average temperature of the bulk water that is participating in the oscillation (approximate equivalent depth of 110 meters) can not significantly change so quickly because of its high thermal capacitance 6.

A simple check on the 110 meter equivalent depth assessment can be made using only temperature vs. distance-below-the-surface profiles. The rationale uses the realization that the energy increase of a unit of water is equal to the thermal capacitance of the unit times its temperature change. Because the thermal capacitance of a unit is essentially constant, the equivalent depth (the depth that, if all is at the surface temperature, would have the same thermal capacitance as the actual effective thermal capacitance) is equal to the integral of the temperature vs. distance-below-the-surface profile divided by the surface temperature. The temperature typically declines for approximately 1 km below the surface, a bit further for another km and then remains nearly constant at approximately 3 °C on down to the bottom. Thus the temperatures in the profile should be reduced by this constant amount. Actual effective thermal capacitance cannot be greater than this method calculates.

Two temperature profiles were found on line. Applying this method resulted in a calculated effective thermal capacitance equivalent to a depth of 196 meters for one and 225 meters for the other. Given that the effective depth cannot be greater than the actual depth and that much of the ocean is less than 2 km deep, the effective depth of 110 meters for calculating effective thermal capacitance appears reasonable.

Temperature Measurement Uncertainty

The huge effective thermal capacitance absolutely prohibits the reported rapid (year-to-year) AGT fluctuations, such as shown in Figure 2, as a result of any credible forcing. According to one assessment 6, the time constant (time to change 63.2% of the total temperature change that would result from a step change in forcing) is about five years. A possible explanation for the impossibly rapid fluctuations is that the reported rapid fluctuations might be stochastic artifacts of the process that has been used to determine measured AGT. Animations 7,8,9,10 illustrate the continuous fluctuation of local surface temperatures which are measured at discreet points. The uncertainty occurs as a result of the location and timing of the discreet measurements of the continuing fluctuation. Spencer explains similar rapid fluctuations of surface temperature data obtained using meteorological satellites 11.

For the period 1895-2012, the standard deviation (σ) of the reported annual average measurements is approximately ±0.09 K with respect to the trend. The temperature fluctuations of the bulk volume near the surface of the planet are more closely represented by the fluctuations in the trend. The trend is a better indicator of the change in global energy; which is the difference between energy received that is above or below break-even and energy radiated above or below break-even.

Figure 3 shows the approximately Gaussian (normal) distribution of the difference of reported measurements with respect to the calculated trend 5. The average, which is zero as it should be, and standard deviation are also shown. A bin width of 0.025 K was used in generating this distribution of reported measured data. The ordinate is the number of measurements that fell within each of the 21 bins.

Figure 3: Distribution of reported measurements with respect to the trend.

Influence of Natural Ocean Oscillations on Average Global Temperature

There is some average ocean surface temperature oscillation that accounts for all of the oceans considered together of which the named oscillations are participants. Studies 12,13,14,15 of the primary contributor (the PDO) to this planet-wide oscillation have been done which identify the period of this oscillation to be in the range of 50-70 years. One of these studies considered data from as far back as 1000 years.

Future Trends

Complex phase relations between the various local ocean cycles cause the effective over-all surface temperature oscillation to vary in magnitude and period over the centuries. In the present assessment, the period of the planet-wide oscillation, since before 1900, has been found to be approximately 64 years with a magnitude of approximately ± 1/5 K. The most recent calculated trend peak was in 2005.

Average global temperature should, however, continue to correlate with the time-integral of sunspot numbers, as it has ever since sunspots have been regularly recorded (since 1610).

Thus, the prediction of average global temperatures depends primarily on the ability to predict sunspot numbers and secondarily on the oscillation up to about 1/5 K that results from the net effect of the several ocean oscillations above and below the prediction from the time-integral of sunspot numbers. Reported measurements for each year will continue to have an uncertainty equivalent to σ ≈ 0.09 K.


  1. HadCRUT4,
  2. HadCRUT3,
  3.  NOAA,
  4. GISS,
  6. Schwartz, Stephen E., (2007) Heat capacity, time constant, and sensitivity of earth’s climate system, J. Geophys. Res., vol. 113, Issue D15102, doi:10.1029/2007JD009373
  12. MacDonald, Glen M. and Roslyn A. Case (2005), Variations in the Pacific Decadal Oscillation over the past millennium, Geophysical Research Letters, 32, L08703
  13. Mantua, N. J., S. R. Hare, Y. Zhang, J. M. Wallace, and R. C. Francis, A Pacific interdecadal climate oscillation with impacts on salmon production. Bull. Am. Met. Soc. 76, 1069-1079, 1997
  14. Minobe, S., (1999), Resonance in bidecadal and pentadecadal climate oscillations over the North Pacific: Role in climatic regime shifts, Geophys. Res. Lett., 26, 855–858.
  15. Minobe S., (1997) A 50–70 year climatic oscillation over the North Pacific and North America. Geophs. Res. Lett., 24, 683–686.

Key words: Global warming, effective thermal capacitance, uncertainty in reported temperature, natural ocean oscillation

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