|Global temperatures [pink] correlate to the sunspot time integral [black], a measure of accumulated solar energy [source]
By Dan Pangburn, MSME, reblogged with permission
About 41.8% of reported average global temperature change results from natural ocean surface temperature oscillation and 58.2% results from change in the rate that the planet radiates energy to outer space, as calculated using a proxy, which is the time-integral of sunspot numbers. Using just these two factors explains average global temperatures (least biased values based on HadCRUT4 and other credible measurements) since before 1900 with 89.82% accuracy (R2=0.8982).
If atmospheric carbon dioxide (CO2) is included in the calculation, it might account for about 7.5% of reported average global temperature (AGT) change. If CO2 has that much influence, then the calculated ocean surface temperature effect decreases to about 40.1% and sunspot influence decreases to about 52.4%, but accuracy increases an insignificant amount to 89.91%. This miniscule increase in accuracy indicates that CO2 change probably has substantially less than even 7.5% influence on average global temperature change.
Some ocean cycles 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 can not significantly change so quickly because of its high thermal capacitance 5.
This high thermal capacitance absolutely prohibits the reported rapid (year-to-year) AGT fluctuations as a result of any credible forcing. According to one assessment 5, the time constant is about 5 years. A possible explanation is that the reported rapid fluctuations may be stochastic artifacts of the process that has been used to determine AGT. A simple calculation shows the standard deviation of the reported measurements to be about ±0.1 °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 and energy radiated.
There is some average surface temperature oscillation that accounts for all of the oceans considered together of which the named oscillations are participants. Studies 1,2,3,4 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.
Complex phase relations between the various local cycles cause the effective over-all oscillation to vary in magnitude over the centuries. In the present assessment, the period of the planet-wide oscillation, since before 1900, has been found to be about 64 years with a magnitude of about ± 1/5 °K. The most recent calculated trend peak was in 2005.
Sunspot number time-integral
Sunspots have been suspected as being associated with climate change for a long time. Sunspot numbers are recorded as solar cycles which have been considered by others for magnitude or for time factors with poor success when trying to correlate with AGT trends.
A low but broad solar cycle may have just as much cumulative influence on AGT as a high but brief one. Both magnitude and duration are accounted for by using the time-integral of sunspot numbers. Much of the temperature decline of the Little Ice Age and over half of the AGT rise of the 20th century are accounted for by the time-integral of sunspot numbers with an appropriate proxy factor. Of course, the time-integral of increase must be reduced by the time-integral of energy radiated from the planet; which varies with the fourth power of its absolute temperature. Note that the first law of thermodynamics, conservation of energy, has been applied here.
Atmospheric carbon dioxide
Atmospheric CO2 is called a greenhouse gas (ghg) because it absorbs electromagnetic radiation (EMR) within the range of significant Stephan-Boltzmann (black body) radiation from the planet. The EMR that CO2 absorbs (and emits) is only over a very narrow band of the over-all radiation spectrum from the planet. Most of the EMR that is absorbed is emitted (nearly all of the absorption and emission is actually by water vapor) but about 11.59% is thermalized 8 and appears as sensible heat which warms the atmosphere.
Added increments of CO2 and other ghgs exhibit a logarithmic decline in their influence on AGT. This is accounted for mathematically for each year by taking the logarithm of the ratio of the average CO2 level for the year to the CO2 level in 1895, which was 294.8 ppmv (Law Dome 7). The cumulative effect to a year of interest is the summation of the effects for prior years. The best current source for atmospheric carbon dioxide level 6 is Mauna Loa, Hawaii.
The net effect on AGT of the combination of the above three contributing factors is obtained by their sum in the following physics-based equation.
anom(y) = calculated average global temperature anomaly in year y, in K degrees.
(A,y) = Effective Sea Surface Temperature Anomaly (ESSTA) in year y calculated using a range (peak-to-peak magnitude) of A, °K, and the number of years since the last maximum or minimum. ESSTA is a simple (saw-tooth) surface temperature approximation of the net effect of the Pacific Decadal Oscillation (PDO) and all of the other natural ocean oscillations, named or not. It has a maximum amplitude of about ± 1/5 °K with no intrinsic energy change for the bulk volume at any time between the beginning value and the end value of its estimated 64 year period. The most recent peak was in 2005.
s(i) = average daily Brussels International sunspot number in year i
17 = effective thermal capacitance 5, W Yr m-2 K-1
43.97 = average sunspot number for 1850-1940.
286.8 = global mean surface temperature for 1850-1940, °K.
T(i) = average global absolute temperature of year i, °K,
ppm co2(i) = ppmv CO2 in year i
294.8 = ppmv atmospheric CO2 in 1895
B is a proxy factor in the function that accounts for the solar radiation, W yr m-2.
C is a multiplier in the function that accounts for the influence of atmospheric CO2, W yr m-2
D is merely an offset that shifts the calculated trajectory vertically, without changing its shape, to center it over the measurements, K degrees.
A, B, C, and D are calibration coefficients which have been determined to maximize the coefficient of determination, R2 (which makes the least biased fit of the trajectory that is calculated using the physics-based equation to measurements). Some have mistakenly interpreted these coefficients to indicate mathematical curve fitting, which is something that is entirely different. Instead, the coefficients allow the rational estimation of the amount that each of the two or three major contributors has made to the total temperature change.
It is worth emphasizing that equation (1) provides for a test to determine the influence, or lack thereof, of CO2 to the total contributions to global anomalies by forcing the coefficient, C, to zero and adjusting the other coefficients to maximize R2.
In Figure 1, the anomaly trajectory calculated using Equation (1) is co-plotted with measurements. The excellent match of the up and down trends since before 1900 is displayed and corroborates the usefulness and validity of Equation (1).
Figure 1: Measured average global temperature anomalies with calculated prior and projected trends.
Projections until 2020 use the expected sunspot number trend for the remainder of solar cycle 24 as provided 9 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.
The influence of CO2 can be removed from the equation by setting C to zero. Doing so results in an insignificantly lower coefficient of determination (R2). The coefficients in Equation (1) and resulting R2 are presented in Table 1.
Ocean oscillation, A
Sunspot integral, B
Carbon dioxide influence, C
Table 1. Coefficients in Equation (1) and resulting accuracy.
Complementary theories as to why this calculation works have been described previously10. The most significant theory appears to be: Fewer sunspots; reduced solar magnetic shielding; increased galactic cosmic rays penetrating the atmosphere; increased low-level clouds; lower average cloud altitude; higher average cloud temperature; increased cloud-to-space radiation; declining AGT.
It is easy to show that an increase in average cloud altitude of about 100 meters would account for half of the AGT increase in the 20th century that some have referred to as ‘Global Warming’.
Without human caused Global Warming there can be no human caused climate change.
This assessment demonstrates that the annual average temperatures of the planet, for at least as far back in time as accurate temperatures have been measured world wide, are accurately calculated by considering only natural oscillations and the sunspot numbers, and that credible changes to the levels of non-condensing greenhouse gases [e.g. CO2] have no significant influence on average global temperature.
Equation (1) explains 89.9% of the AGT trajectory since before 1900. All factors that were not explicitly considered must find room in the unexplained 10.1%.
- MacDonald, Glen M. and Roslyn A. Case (2005), Variations in the Pacific Decadal Oscillation over the past millennium, Geophysical Research Letters, 32, L08703
- 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
- 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.
- Minobe S., (1997) A 50–70 year climatic oscillation over the North Pacific and North America. Geophs. Res. Lett., 24, 683–686.
- 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
- Annual average atmospheric carbon dioxide level at Mauna Loaftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_annmean_mlo.txt
- Graphical sunspot number prediction for the remainder of solar cycle 24 http://solarscience.msfc.nasa.gov/predict.shtml