Natural Climate Change has been Hiding in Plain Sight
See refined assessment 16102012 at http://agwunveiled.blogspot.com/
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 and/or reflects it, as
calculated using a proxy, which is the timeintegral 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 (R^{2}=0.8982). [Refined assessment: 37.8% from ocean cycles, 62.2% from sunspots, R^2 = 0.9049 and credible estimate back to 1610]
If atmospheric carbon dioxide (CO_{2}) is included
in the calculation, it might account for as much as 17.6% of reported average global
temperature (AGT) change during the period 19092005. If CO_{2} has that much influence, then the calculated
ocean surface temperature effect decreases to about 37.8% and sunspot influence
decreases to about 44.6%, but accuracy increases an insignificant amount to
90.06%. This miniscule increase in accuracy indicates that CO_{2}
change probably has substantially less than 17.6% influence on average
global temperature change.
Ocean oscillations
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) might 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 (yeartoyear) 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 annual average 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 that is above or below breakeven and energy radiated above or below breakeven.
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 planetwide oscillation have been done which
identify the period of this oscillation to be in the range of 5070 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 overall oscillation to vary in magnitude and period over the centuries. In
the present assessment, the period of the planetwide 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
timeintegral
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 timeintegral of sunspot numbers. The temperature trend rise from the
Little Ice Age and over half of the AGT rise of the 20^{th} century are
accounted for by the timeintegral of sunspot numbers with an appropriate proxy
factor. Of course, the timeintegral of increase above or below
breakeven must be reduced by the timeintegral of energy radiated from
the planet above or below breakeven; which varies with the fourth power of its
absolute temperature.
The
first law of thermodynamics, conservation of energy, is applied to evaluate the
hypothesis that the temperature trend is influenced by sunspot numbers. Average
global temperature has not changed much over the centuries so on average, over
the centuries, energyin equals energyout. In any one year, the energyin is
given by
E_{in} = B * S(i) (a)
where
‘B’ is the proxy factor. If the AGT never changed, the energyout is given by
E_{const AGT} = B * S_{avg}
To
account for the yearly variation in energyout it is multiplied by the fourth
power of the temperature ratio which gives
E_{i out} = B * S_{avg} * [T(i)/T_{avg}]^{4} (b)
Subtracting
(b) from (a) results in the energy change for any year. Also, factor out B
E_{chg} = B * {S(i) – S_{avg} *
[T(i)/T_{avg}]^{4}} (c)
Dividing
the energy change by the thermal capacitance gives the temperature change from
the previous year. Summation of changes for previous years obtains the total
change from the start of the summation.
T_{chng} = B/C_{effective} * Σ^{y}_{initial} {S(i) – S_{avg}
* [T(i)/T_{avg}]^{4}} (d)
With
appropriate offset this becomes the sunspot number contribution to the temperature
anomaly. The high coefficient of correlation demonstrates that the hypothesis is
true.
Atmospheric carbon
dioxide
Atmospheric CO_{2} is called a greenhouse gas (ghg)
because it absorbs electromagnetic radiation (EMR) within the range of
significant StephanBoltzmann (black body) radiation from the planet. The EMR
that CO_{2}^{ }absorbs (and emits) is only over a very narrow
band of the overall radiation spectrum from the planet (never mind that the ghg effect is an insignificant factor in how greenhouses work). 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 CO_{2} 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
CO_{2} level for the year to the CO_{2} 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 plus the effect for the current year. The best current
source for atmospheric carbon dioxide level ^{6} is Mauna Loa, Hawaii.
Combined equation
The net effect on AGT of the combination of the above three
contributing factors is obtained by their sum. The word equation is: anomaly = ocean oscillation effect + net sunspot & thermal radiation effect + CO_{2} effect + offset. This is expressed in the following physicsbased
equation.
(1)
Where:
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 (peaktopeak magnitude) of A, °K, and the number of years since the
last maximum or minimum. ESSTA is a simple (sawtooth) 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 18501940.
286.8 = global mean surface temperature for 18501940, °K.
T(i) = average global absolute temperature of year i, °K,
ppm co2(i) = ppmv CO_{2} in year i
294.8 = ppmv atmospheric CO_{2} 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 CO_{2}, 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. This offset is equivalent to having selected slightly different reference temperatures for the measured anomalies.
A, B,
C, and D are calibration
coefficients which have been determined to maximize the coefficient of
determination, R^{2} (which makes the least biased fit of the trajectory,
that is calculated using the physicsbased 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 CO_{2} to the
total contributions to global anomalies by forcing the coefficient, C, to zero
and adjusting the other coefficients to maximize R^{2}.
In Figure 1, the anomaly trajectory calculated using
Equation (1) is coplotted 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.
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 CO_{2} can be removed from the
equation by setting C to zero. Doing
so results in an insignificantly lower coefficient of determination (R^{2}).
The coefficients in Equation (1) and resulting R^{2} are presented in
Table 1.
Ocean oscillation, A

Sunspot integral, B

Carbon dioxide influence, C

Offset, D

Accuracy, R^{2}

0.3593

0.003731

0.3112

–0.3903

0.900641

0.400

0.004894

0.0

–0.3892

0.898220

Table 1. Coefficients in Equation (1) and resulting
accuracy.
Complementary theories as to why this calculation works have
been described previously^{10}. The most significant theory appears to
be: Fewer sunspots; reduced solar magnetic shielding; increased galactic cosmic
rays penetrating the atmosphere; increased lowlevel clouds; lower average
cloud altitude; higher average cloud temperature; increased cloudtospace
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
20^{th} century that some have referred to as ‘Global Warming’. Increased low level clouds also means increased overall cloud cover with attendant increased albedo. This also leads to declining AGT ^{11}.
Without human caused Global Warming there can be no human
caused climate change.
Climate science appears to have missed the above and other factors ^{12}.
Climate science appears to have missed the above and other factors ^{12}.
Conclusions
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 ocean oscillations and the sunspot numbers, and that
credible changes to the levels of noncondensing greenhouse gases have no significant
influence on average global temperature.
Equation (1) explains approximately 90% of the AGT trajectory since
before 1900. All factors that were not explicitly considered must find room in
the unexplained 10%.
References:
 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, 10691079, 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 Loa ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_annmean_mlo.txt
 http://climaterealists.com/attachments/ftp/Cloudaltitudevsglobaltemperature.pdf
 Graphical sunspot number
prediction for the remainder of solar cycle 24 http://solarscience.msfc.nasa.gov/predict.shtml
 http://climaterealists.com/attachments/ftp/Verification%20Dan%20P.pdf
 http://endofgw.blogspot.com/

Obsolete graph