Calculated Mean Global Temperatures 1610-2012
Guest post by Dan Pangburn
Introduction
This monograph is a clarification and further refinement of Reference 10 which also considers only average global temperature. It does not discuss weather, which is a complex study of energy moving about the planet. It does not even address local climate, which includes precipitation. It does, however, consider the issue of Global Warming and the mistaken perception that human activity has a significant influence on it.
The word ‘trend’ is used here for measured temperatures in two different contexts. To differentiate, α-trend applies to averaging-out the uncertainties in reported average global temperature measurements to produce the average global temperature oscillation resulting from the net ocean surface oscillation. The term β-trend applies to averaging-out the average global temperature oscillation to produce the slower average temperature change of the planet which is associated with change to the temperature of the bulk volume of the water involved.
The first paper to suggest the hypothesis that the sunspot number time-integral is a proxy for a substantial driver of average global temperature change was made public 6/1/2009. The discovery started with application of the first law of thermodynamics, conservation of energy, and the hypothesis that the energy acquired, above or below breakeven (appropriately accounting for energy radiated from the planet), is proportional to the time-integral of sunspot numbers. The derived equation revealed a rapid and sustained global energy rise starting in about 1941. The average global temperature anomaly change β-trend is proportional to global energy change.
Measured temperature anomaly α-trends oscillate above and below the temperature anomaly trend calculated using only the sunspot number time-integral. The existence of ocean oscillations, especially the Pacific Decadal Oscillation, led to the perception that there must be an effective net surface temperature oscillation with all named and unnamed ocean oscillations as participants. Plots of measured average global temperatures indicate that the net surface temperature oscillation must have a period of 64 years with the most recent maximum in 2005.
Combination of the effects results in the effect of the ocean surface temperature oscillation (α-trend) decline 1941-1973 being slightly stronger than the effect of the rapid rise from sunspots (β-trend) resulting in a slight decline of the trend of reported average global temperatures. The steep rise 1973-2005 occurred because the effects added. A high coefficient of determination, R2, demonstrates that the hypothesis is true.
Several refinements to this work slightly improved the accuracy and led to the equations and figures in this paper.
Prior work
The law of conservation of energy is applied as described in Reference 1 in the development of the equations that calculate temperature anomalies.
Change to the level of atmospheric carbon dioxide has no significant effect on average global temperature. This was demonstrated in 2008 at Reference 6 and is corroborated at Reference 2.
As determined in Reference 3, reported average global temperature anomaly measurements have a random uncertainty with equivalent standard deviation ≈ 0.09 K.
Global Warming ended more than a decade ago as shown in Reference 4 and Reference 2.
Average global temperature is very sensitive to cloud change as shown in Reference 5.
The parameter for average sunspot number was 43.97 (average 1850-1940) in Ref. 1, 42 (average 1895-1940) in Ref. 9, and 40 (average 1610-2012) in Ref. 10. It is set at 34 (average 1610-1940) in this paper. The procession of values for average sunspot number produces slight but steady improvement in R2 for the period of measured temperatures and progressively greater credibility of average global temperature estimates for the period prior to direct measurements becoming available. A graph of R2 vs. average sunspot number indicates that further lowering of the number would not significantly increase R2 and might even reduce it.
Initial work is presented at http://climaterealists.com/index.php?tid=145&linkbox=true
The sunspot number time-integral drives the temperature anomaly trend
It is axiomatic that change to the average temperature trend of the planet is due to change from break-even to the net energy retained by the planet.
Table 1 in reference 2 shows the influence of atmospheric CO2 to be insignificant (tiny change in R2 if considering CO2 or not) so it can be removed from the equation by setting coefficient ‘C’ to zero. With ‘C’ set to zero, Equation 1 in Reference 2 calculates average global temperature anomalies (AGT) since 1895 with 89.82% accuracy (R2 = 0.898220).
The current analysis determined that 34, the approximate average of sunspot numbers from 1610-1940, provides a slightly better fit to the measured temperature data than did 43.97 and other values 9,10. The approximate AGT during 1610-1940 is 286.2 K. With these refinements to Equation (1) in Reference 1 the coefficients become A = 0.3596, B = 0.003503 and D = ‑ 0.4475. R2 increases slightly to 0.904839 and the calculated anomaly in 2005 is 0.5046 K. Also with these refinements the equation calculates lower early anomalies and projects slightly higher future anomalies. The excellent match of the up and down trends since before 1900 of calculated and measured anomalies, shown here in Figure 1, corroborates the usefulness and validity of the calculations.
Projections until 2020 use the expected sunspot number trend for the remainder of solar cycle 24 as provided 11 by NASA. After 2020 the limiting cases are either assuming sunspots like from 1925 to 1941 or for the case of no sunspots which is similar to the Maunder Minimum.
Some noteworthy volcanos and the year they occurred are also shown on Figure 1. No consistent AGT response is observed to be associated with these. Any global temperature perturbation that might have been caused by volcanos of this size is lost in the temperature measurement uncertainty. Much larger volcanoes can cause significant temporary global cooling from the added reflectivity of aerosols and airborne particulates. The Tambora eruption, which started on April 10, 1815 and continued to erupt for at least 6 months, was approximately ten times the magnitude of the next largest in recorded history and led to 1816 which has been referred to as ‘the year without a summer’. The cooling effect of that volcano exacerbated the already cool temperatures associated with the Dalton Minimum.
(Click on image or equation to enlarge)
Figure 1: Measured average global temperature anomalies with calculated prior and future trends using 34 as the average daily sunspot number.
As discussed in Reference 2, ocean oscillations produce oscillations of the surface temperature with no significant change to the average temperature of the bulk volume of water involved. The effect on AGT of the full range of surface temperature oscillation is given by the coefficient ‘A’.
The influence of ocean surface temperature oscillations can be removed from the equation by setting ‘A’ to zero. To use all regularly recorded sunspot numbers, the integration starts in 1610. The offset, ‘D’ must be changed to -0.2223 to account for the different integration start point and setting ‘A’ to zero. Setting ‘A’ to zero requires that the anomaly in 2005 be 0.5046 - 0.3596/2 = 0.3248 K. The result, Equation (1) here, then calculates the trend 1610-2012 resulting from just the sunspot number time-integral.
(1)
Where:
Trend3anom(y) = calculated temperature anomaly trend in year y, K degrees.
0.003503 = the proxy factor, B, W yr m-2.
17 = effective thermal capacitance of the planet, W Yr m-2 K-1
s(i) = average daily Brussels International sunspot number in year i
34 ≈ average sunspot number for 1610-1940.
286.2 ≈ global mean surface temperature for 1610-1940, K.
T(i) = average global absolute temperature of year i, K,
-0.2223 is merely an offset that shifts the calculated trajectory vertically on the graph, without changing its shape, so that the calculated temperature anomaly in 2005 is 0.3248 K which is the calculated anomaly for 2005 if the ocean oscillation is not included.
Sunspot numbers back to 1610 are shown in Reference 1 Figure 2.
Applying Equation (1) to the sunspot numbers of Reference 1 Figure 2, produces the trace shown in Figure 2 below.
Figure 2: Anomaly trend from just the sunspot number time-integral using Equation (1).
Combined Sunspot Effect and Ocean Oscillation Effect
Average global temperatures were not directly measured in 1610 (thermometers had not been invented yet) or even estimated very accurately using proxies. The anomaly trend that Equation (1) calculates for that time is roughly consistent with other estimates but cannot be verified. Also, there is no way to determine for sure how much and which way the ocean surface temperature cycles would influence the values.
As a possibility, the period and amplitude of oscillations attributed to ocean cycles demonstrated to be valid after 1895 are assumed to maintain back to 1610. Equation (1) is modified as shown in Equation (2) to account for including the effects of ocean oscillations. Since the expression for the oscillations calculates values from zero to the full range but oscillations must be centered on zero, it must be reduced by half the oscillation range.
(2)
The ocean oscillation factor, (0.3596,y) – 0.1798, is applied prior to the start of temperature measurements as a possibility.
Applying Equation (2) to the sunspot numbers from Figure 2 of Reference 1 produces the trend shown in Figure 3 next below. Available measured average global temperatures from Reference 3 are superimposed on the calculated values.
Figure 3: Trend from the sunspot number time-integral plus ocean oscillation using Equation (2) with superimposed available measured data.
Figure 3 shows that temperature anomalies calculated using Equation (2) estimate possible trends since 1610 and actual trends of reported temperatures since they have been accurately measured world wide. The match from 1895 on has R2 = 0.9048 which means that 90.48% of average global temperature anomaly measurements are explained. All factors not explicitly considered must find room in that unexplained 9.52%. Note that a coefficient of determination, R2 = 0.9048 means a correlation coefficient of 0.95.
Calculated anomalies look reasonable back to 1700 but indicate higher temps prior to that than most proxy estimates. They qualitatively agree with Vostok, Antarctica ice core data but decidedly differ from Sargasso Sea estimates during that time (see the graph for the last 1000 years in Reference 6). Credible accurate assessments of average global temperature that far back were not found. Perhaps solar output was a bit lower for a period prior to 1700 which would allow lower average global temperatures in spite of more sunspots. Ocean oscillations might also have been different from assumed.
Other assessments
Other assessments are discussed in Reference 1.
Conclusions
Others that have looked at only amplitude or only time factors for solar cycles got poor correlations with average global temperature. The good correlation comes by combining the two, which is what the time-integral of sunspot numbers does. As shown in Figure 2, the anomaly trend determined using the sunspot number time-integral has experienced substantial change over the recorded period. Prediction of future sunspot numbers more than a decade or so into the future has not yet been confidently done although assessments using planetary synodic periods appear to be relevant 7,8.
If the temperature of the bulk volume of water participating in the ocean oscillation is used in place of the surface temperature of the water, the time-integral of sunspot numbers alone appears to correlate with the estimated true average global temperature trend after approximately 1700.
The net effect of ocean oscillations is to cause the surface temperature trend to oscillate above and below the trend calculated using only the sunspot number time-integral. Equation (2) accounts for both and also, since it matches measurements so well, shows that rational change to the level of atmospheric carbon dioxide can have no significant influence.
References:
1. http://conenssti.blogspot.com/
2. http://climatechange90.blogspot.com/2013/05/natural-climate-change-has-been.html
3. http://globaltem.blogspot.com/
4. http://endofgw.blogspot.com/
5. http://lowaltitudeclouds.blogspot.com
6. http://www.middlebury.net/op-ed/pangburn.html
7. http://tallbloke.wordpress.com/2011/08/05/jackpot-jupiter-and-saturn-solar-cycle-link-confirmed/
8. http://digital.library.okstate.edu/oas/oas_pdf/v35/p156_157.pdf
9. http://danpangburn.blogspot.com/
10. http://averageglobaltemperature.blogspot.com/
Graphical sunspot number prediction for the remainder of solar cycle 24 http://solarscience.msfc.nasa.gov/predict.shtml
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