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Roy Clark Null Hypothesis VPM 005.1, Review Draft, Sept 2019
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ABSTRACT
The prevailing hypothesis in climate science is based on the assumption of radiative convective
equilibrium. Some kind of average equilibrium climate state is assumed to exist in which the
surface temperature is determined by an exact flux balance between the absorbed solar flux and
the emission of long wave IR (LWIR) radiation back to space. When this climate state is perturbed
by the addition of more greenhouse gases such as CO2, the system adjusts to a new state with a
higher surface temperature. This response is amplified by water vapor feedback. Simple
comparison of climate model results with the surface temperature record show that this hypothesis
has failed. In this paper, the null hypothesis for CO2 is introduced. This is based on a description
of the earth’s climate system in terms of dynamically coupled thermal reservoirs. The underlying
principle is that a change in temperature is produced by a change in the heat content or enthalpy
of a thermal reservoir divided by the heat capacity. The change in heat content is produced by the
change in the total, time varying heat flux coupled to the reservoir over a given time period. Any
equilibrium assumption is abandoned. At minimum, there are four thermal reservoirs that are
coupled together to form the tropospheric heat engine. The land and especially the oceans from
the hot reservoirs of the heat engine. The troposphere divides naturally into two separate reservoirs
base on radiative transfer effects related to molecular line broadening. Almost all of the downward
LWIR flux that reaches the surface originates in the lower tropospheric reservoir that extends up
to 2 km from the surface. Above this is, the upper tropospheric reservoir that extend from 2 km to
the tropopause. This forms the cold reservoir of the heat engine. Heat is transported from the
surface by convection. It is then radiated to space, mainly by the water bands in the cold reservoir.
Small increases in the LWIR flux from an increase in atmospheric CO2 concentration have to be
included in the total, time dependent flux terms. They are then too small to cause a measurable
change in surface temperature.
The null hypothesis has 2 parts:
1) It simply impossible for the observed 120 ppm increase in atmospheric CO2 concentration
to have produced any measurable increase in surface temperature.
2) The observed recovery in surface temperature since the Maunder minimum can be
explained in terms of small increases in the solar flux absorbed and accumulated in the
ocean thermal reservoir.
This increase in the solar flux is produced by changes in the flux output of the sun as a result of
changes the sunspot index and other measures of solar activity. The earth’s climate is determined
by a subtle dynamic or time dependent balance between the solar heating and the wind driven
evaporative cooling of the oceans as the ocean water is circulated through the ocean gyres. There
can never be an exact flux balance and the surface temperatures within the gyres must undergo
quasi-periodic oscillations. The penetration depth of the LWIR flux into the oceans is less than
100 micron. Evaporative cooling is also produced by the wind driven removal of water molecules
from the surface. These two processes are mixed together in the surface layer. Any small increase
in the downward LWIR flux at the surface that results from an increase in the atmospheric
Roy Clark Null Hypothesis VPM 005.1, Review Draft, Sept 2019
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1.0 INTRODUCTION
This paper is one of seven papers that describe the research into climate change that has been
conducted at Ventura Photonics since 2009. In the first two papers in this series, , ‘A dynamic
coupled thermal reservoir approach to atmospheric energy transfer Part I: Concepts’ (DTR1) and
‘A dynamic coupled thermal reservoir approach to atmospheric energy transfer Part II:
Applications’ (DTR2) the concept of dynamic coupled thermal reservoirs was introduced and used
to explain climate energy transfer for selected examples. These included the equatorial ocean
warm pool, land surface temperature changes and thermal storage in the lower troposphere [Clark,
2013a, 2013b]. In the third paper, ‘A dynamic coupled thermal reservoir approach to atmospheric
energy transfer Part III: The Surface Temperature’ (DTR3) [Clark, 2019a], the thermal reservoir
approach was used to calculate the surface and surface-air temperatures at the ocean-air and land-
air interfaces. In particular, the role of the dynamic coupled thermal reservoirs in setting the phase
shift or time delay between the peak solar flux and the peak temperature was considered in detail.
These phase shifts provide clear evidence of non-equilibrium thermal storage. Here, in the fourth
paper in this series, the null hypothesis for CO2 is considered in terms of dynamically coupled
thermal reservoirs. Two other papers in this series are ‘The Greenhouse Effect’ and ‘Fifty Years
of Climate Fraud’ [Clark, 2019b and 2019c]. The final paper provides a summary of the research
[Clark, 2019d].
Over the last 200 years, the atmospheric concentration of CO2 has increased by about 120 ppm
from 280 to 400 ppm [Keeling, 2019]. This has produced an increase of approximately 2 W m-2
in the downward LWIR flux from CO2 reaching the surface [Clark, 2013a; 2013b; 2011; Harde.
2017]. Over the oceans, the LWIR flux and the wind driven evaporation are mixed within the first
100 µm surface layer [Hale and Querry, 1973]. The cooler water produced at the surface by the
combined cooling fluxes then sinks and cools the bulk ocean layers below. This is a Rayleigh-
Benard convection process, not simple diffusion. Over land, the LWIR flux is mixed in the surface
layer with both the moist convection and the solar heating. During the day, the surface warms
until the excess absorbed heat is dissipated by moist convection. Heat is also conducted down into
a shallow subsurface layer where it is stored and returned to the surface later in the day after the
subsurface thermal gradient reverses. In both cases, land and ocean, the temperature increase from
the 2 W m-2 increase in LWIR flux from CO2 is too small to be measured. The LWIR flux cannot
be separated and analyzed independently of the other flux terms. Over the ocean, the variation in
the wind speed is so large that the short term changes in evaporation overwhelm any small
increases in LWIR flux from CO2. Over land, the variation in the total flux and the daily change
in the convective transition temperature are also so large that no increase in surface temperature
from the CO2 LWIR flux change can be detected.
The effect of a 2 W m-2 increase in downward LWIR flux on the surface temperature, was
investigated in two different ways. First, the temperature changes produced by running the ocean
and land models with the LWIR cooling flux reduced by 2 W m-2 were investigated. Second,
weather variations were simulated by adding random number generators to vary the ocean wind
Roy Clark Null Hypothesis VPM 005.1, Review Draft, Sept 2019
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2.0 THE EFFECT ON SURFACE TEMPERATURES OF A 120 PPM INCREASE IN
ATMOSPHERIC CO2 CONCENTRATION
The development of the ocean and land surface temperature models and their use to investigate
surface temperature changes and their related phase shifts was described in the previous paper in
this series, DTR3, [Clark, 2019a]. Here, these climate models were used investigate the effect on
surface temperature of an increase in downward LWIR flux of 2 W m-2 at the surface produced by
an increase in atmospheric CO2 concentration of 120 ppm. In Section 2.1, the effect of simply
changing the flux in the model is considered. In Section 2.2 the effect of adding random number
generators to the models to simulate weather variations is described. The results demonstrate the
first part of the null hypothesis for CO2. The observed increase in atmospheric CO2 concentration
of 120 ppm cannot produce any measurable temperature change.
2.1 Model Results for a 2 W m-2 increase in downward LWIR flux
2.1.1 Ocean Model Results
In order to simulate the nominal 2 W m-2 increase in downward flux produced by the observed 120
ppm increase in atmospheric concentration, the ocean surface temperature model used in DTR3
was rerun using an LWIR transmission window flux of 43 W m-2 instead of 45 W m-2. The rest of
the model parameters were kept the same. These are summarized in Table 1. (This is from Table
3 in DTR3). The model was configured to run for 30 years with the temperatures at the end of
each year used as the input start temperatures for the next year. This allowed the model output to
fully stabilize, typically within 10 years. The changes in temperature for a 2 W m-2 increase in
downward flux as a function of ocean temperature at each latitude from a baseline 45 W m-2 LWIR
window flux were determined.
As an additional check, the change in ocean surface temperature needed to compensate for the 2
W m-2 decrease in LWIR cooling flux was also calculated using the LWIR and latent heat
algorithms in the model, for Qirnet and Qlat given by Eqs A6 and A8 from DTR3. The change in
temperature needed to produce a 2 W m-2 increase in blackbody emission over the 0 to 30 C range
was also calculated. The 30 year model run results, the model algorithm calculations and the
blackbody values are plotted in Figure 1. At temperatures above 10 C, the change in temperature
from the ocean response is below the blackbody response. This is because the model adjusts by
changing the rate of evaporation, not the blackbody emission. At lower temperatures where the
evaporation is reduced, the ocean response exceed the blackbody response. There is good
agreement between the ocean response calculated from model algorithms and the 30 year model
output.
Roy Clark Null Hypothesis VPM 005.1, Review Draft, Sept 2019
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Table 1: Ocean surface temperature model input parameters and output summary for an LWIR window
flux of 45 W m-2 (From Table 3, DTR3)
Figure 1: Increase in temperature needed to restore the ocean cooling flux when the downward LWIR
window flux is increased by 2 W m-2. For reference the increase in blackbody temperature need to increase
the flux by 2 W m-2 is also shown (blue line).
As a further check on the model results, the annual average latent heat cooling flux divided by the
annual average wind speed was calculated and compared to the values derived from the long term
zonal averages published by Yu et al [2008]. These are shown in Figure 2. With a fixed value of
45 W m-2 for the LWIR window flux, the model values were approximately double the zonal
averages from 10 to 30° latitude with an additional spike at 0° latitude. To investigate this further,
a linear increase in the LWIR window flux with temperature was added to the model. This is based
on OLR flux measurements described by Koll and Cronin [2018]. The LWIR window flux was
set to:
Qirwin = 45 + 2.2T (Eq. 1)
Where T is the ocean surface temperature in Celsius. This reduced the model evaporation rates
and increased the net LWIR emission at higher ocean surface temperatures. It is also important to
Latitude LWIR Win Flux Solar Fract Level 1 Mix Wnd Sp Wsp Var Wind Coupling T Start Run T Fit Av Evap/Wnd T Mn T max Phase
Deg W m-2 m s-1 m s-1 k C C W m-2/m s-1 C C Days
0 45 1.00 0.00 5 0 4.822 28 28.0003 47.20 27.90 28.84 33; 33
10 45 1.00 0.20 8 2 3.832 26 26.0020 34.25 25.53 28.06 78
20 45 1.00 0.25 7 0.5 4.399 22 22.0011 32.16 21.53 25.28 60
30 45 1.00 0.30 8 2 4.268 20 20.0001 28.47 19.19 24.89 54
40 45 0.85 0.40 10 3 4.209 11 11.0001 16.04 10.10 16.28 54
50 45 0.65 0.50 10 2 3.104 6 6.0003 8.27 5.18 10.50 56
60 45 0.60 0.70 10 3 2.055 4 4.0011 4.60 3.18 7.27 58
Roy Clark Null Hypothesis VPM 005.1, Review Draft, Sept 2019
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note that the data from Yu et al are zonal averages that include evaporation rates at different
temperatures because of ocean gyre circulation. Also, when ocean temperatures approach 30 C,
strong local thunderstorms can occur that create different wind patterns. The model also uses a
simple energy transfer and mixing scheme to illustrate the basic physics of the air ocean interface.
A fixed relative humidity and air-surface temperature difference are used in the evaporation
calculation.
Instead of changing the wind coupling constant, the wind speed was then adjusted to compensate
for the change in LWIR window flux from 45 to 43 W m-2. The increase in wind speed needed to
restore the cooling flux and return the end of model surface temperature to its start value are shown
in Figure 3. Both the fixed LWIR flux and the temperature dependent flux cases were analyzed.
The values increase from 4 to 60 cm s-1 as the latitude increases from 0 to 60°. These changes are
too small to produce a measureable change in surface temperature because of the natural variation
in the wind speed.
Figure 2: Ocean evaporation per unit wind speed, zonal averages from Yu et al [2008] and ocean model
annual average output, 45 W m-2 fixed LWIR window and 45 W m-2+2.2T LWIR window.
Roy Clark Null Hypothesis VPM 005.1, Review Draft, Sept 2019
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Figure 3: Change in wind speed (cm s-1) needed to restore the ocean surface cooling flux when the downward
LWIR flux is increased by 2 W m-2. Both the fixed and the temperature dependent LWIR window flux cases
are shown.
2.1.2 Land Model Results
The effect an increase in the downward LWIR flux of 2 W m-2 on land surface temperatures was
evaluated by changing the LWIR window flux in the land surface temperature model from 40 to
38 W m-2. The model was configured to simulate the 34° latitude Redlands weather station climate
data as described in DTR3 [Clark, 2019a]. The model input parameters were set as follows:
seasonal phase shift, 60 days; transition temperature range and offset, 15 and 2 C, and solar
fraction, 0.85. There was almost no observable change in the daily maximum and minimum
temperature plots as shown in Figure 4a. However, at the beginning and end of the year in the
model run, the minimum surface temperature cooled slightly below the minimum air temperature.
Under these conditions, the model convection term is set to zero and the cooling is determined by
net LWIR emission until the surface warms up during the day. This cross over can be seen in
Figure 4b, where the minimum temperatures are plotted an enlarged scale. Under these conditions,
the 2 W m-2 increase in LWIR flux slows the surface cooling. This can be seen in the increase in
the surface minimum delta temperature in Figure 4c. However, over most of the year, the
difference in surface temperature (38-40 W m-2) is near 0.15 C and the difference in air temperature
is near 0.08 C.
For comparison, the increase in blackbody temperature needed to produce an increase in emission
of 2 W m-2 over the temperature range from 5 to 50 C is shown in Figure 5. At 5 C, an increase
of 0.41 C is needed to reach 2 W m-2. This is larger than the temperature changes shown in Figure
10c. The reason for the small air and surface temperature changes is that the surface responds to
the 2 W m-2 in LWIR flux by increasing the convective cooling. The convection coefficient used
in the model is 25 W m-2 C-1. This means that the surface thermal gradient has to be increased by
approximately 0.08 C to dissipate the additional heat of 2 W m-2.
Roy Clark Null Hypothesis VPM 005.1, Review Draft, Sept 2019
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Figure 4: Effect of changing the LWIR cooling flux by 2 W m-2 from 40 to 38 W m-2: a) temperature plots, b)
temperature with enlarged scale to show cross over points c) delta temperature plots (38 – 40 Wm-2)
Roy Clark Null Hypothesis VPM 005.1, Review Draft, Sept 2019
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Figure 5: Change in blackbody emission temperature needed to produce an increase of 2 Wm-2 in surface
emission for temperatures from 5 to 50 C.
2.2 Random Number Simulations of Weather Variations
The small surface and air temperature changes produced by this dynamic thermal reservoir model
when the LWIR flux is changed by 2 W m-2 clearly demonstrate that the equilibrium atmosphere
assumption is invalid. There can be no ‘climate sensitivity’ to a doubling of the atmospheric CO2
concentration. Nor can there be any ‘water vapor feedback’. In practice, the normal day to day
variations in the surface flux terms are so large that any small increase in the LWIR flux from CO2
cannot produce an observable increase in the measured ocean surface temperature or MSAT. This
was evaluated by adding random number generators to vary selected model parameters. For the
ocean model, the wind speed and LWIR flux were varied. For the land model, the night time
convection transition temperature was changed. The ocean and land model results will now be
considered in turn.
2.2.1 Ocean Model Results for Random Number Simulations
The wind speed was randomly varied daily by up to ±4 m s-1, and in each half hour step by up to
1 m s-1. The LWIR flux was varied in each half hour step by ±10 W m-2. The model was run for
30 years for 3 cases, 1) LWIR window set to 45 W m-2; 2) LWIR window set to 43 W m-2 and 3)
43 W m-2, with wind coupling constant adjusted to return the end temperature to the start
temperature. The latitude was set to 20° and the daily minimum and maximum surface
temperatures were extracted from the output data. The 30 year averages and standard deviations
were calculated for each day. The averages and the ±1 ranges for the minimum and maximum
surface temperatures for the 3 cases are plotted in Figure 6. The plots overlap well within the 1
standard deviation limits. The 30 year runs for the 3 cases with random number generators were
Roy Clark Null Hypothesis VPM 005.1, Review Draft, Sept 2019
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repeated for 40° latitude. The results are shown in Figure 7. Again the plots overlap well within
the 1 standard deviation limits.
Figure 6: 30 year average and 1 standard deviations for cases 1 through 3, 20° latitude, minimum and
maximum temperatures with random number generators to simulate changes in wind speed and LWIR flux.
Roy Clark Null Hypothesis VPM 005.1, Review Draft, Sept 2019
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Figure 7: 30 year average and 1 standard deviations for cases 1 through 3, 40° latitude, minimum and
maximum temperatures with random number generators to simulate changes in wind speed and LWIR flux.
These results clearly demonstrate that the increase in LWIR flux from the observed increase in
atmospheric CO2 concentration cannot couple into the oceans in a way that can cause any
observable increase in surface temperature. The flux changes from the wind speed driven
evaporation overwhelm any small flux increase from the CO2.
Roy Clark Null Hypothesis VPM 005.1, Review Draft, Sept 2019
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3.0 OCEAN WARMING FROM VARIATIONS IN THE SOLAR FLUX
Section 2.0 has demonstrated the first part of the null hypothesis: that the observed increase of 120
ppm in the atmospheric CO2 concentration cannot couple into climate system in a way that can
cause any observable climate change. In this Section, the coupling of the solar flux into the oceans
is considered. In particular, how do small changes in the solar flux cause climate change?
The starting point is to estimate the flux levels need to bring the earth out of an Ice Age and to
warm the earth from the Maunder minimum. These simple calculations indicate that the observed
temperature changes are caused by small flux changes accumulated over time. Next, the solar flux
algorithm in the land and ocean surface temperature models is used to calculate the change in
surface flux produced by a change of 1 W m-2 in the average incoming TOA flux. The changes in
solar flux are produced by two different mechanisms. The variation in the earth’s orbital ellipticity,
obliquity and precession (Milankovitch cycles) produce changes in the TOA flux intensity that do
not alter the spectral distribution. However, the TOA flux changes produced by variations in the
sunspot index and related parameters do change the spectral properties of the solar flux. Almost
of the observed changes occur in the blue and UV parts of the solar spectrum.
The coupling of the solar flux into the oceans is complex. The trade winds produced by the Hadley,
Ferrell and Polar convective cell structure drive five major ocean gyres. In the eastern parts of the
equatorial Atlantic and Pacific Oceans, the wind driven surface evaporation is insufficient to
remove the tropical solar heat and the ocean water transported westwards by the equatorial currents
must heat up. This leads to the formation of the tropical warm pools in the western Atlantic and
Pacific Oceans [Clark, 2019a; b]. The warm water is then transported poleward by the western
boundary currents and recirculated through the gyres. These western currents run fast and deep so
that some of the warmer water is forced below the normal gyre circulation. There is never an exact
balance between the solar heating and the wind driven cooling. This means that the ocean surface
temperatures must oscillate. These are quasi-periodic oscillations that do not have a fixed
frequency. The El Nino Southern Oscillation (ENSO) in the equatorial Pacific Ocean has a period
between 3 and 7 years. The Pacific Decadal oscillation (PDO) and the Atlantic Multi-decadal
Oscillation (AMO) have periods in the 60 to 70 year range.
Changes in the solar flux related to the sunspot cycle have produced climate change over time
scales of a few hundred years including the medieval maximum, the Maunder minimum and the
modern solar maximum. Planetary perturbations of the earth’s orbit, mainly by Jupiter have
produced climate change related to variations in the Earth’s orbital ellipticity, and axial tilt and
precession. These are known as Milankovitch cycles [2019]. Currently, the change in ellipticity
is dominant and cycles the earth through an Ice Age in about 100,000 years. Over longer time
periods, climate change is also caused by variations in ocean circulation as the continental
boundaries change with plate tectonic motion. Major climate shifts were caused by the opening
the Drake Passage to form the Southern Ocean and by the formation of the Isthmus of Panama
[Zachos et al., 2001]
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In much earlier geological times, 2.5 billion years ago, the solar flux was about 80% of its current
level. This leads to the called ‘faint sun paradox’. Using conventional equilibrium greenhouse
effect arguments, the earth should have been much cooler than it was [Goldblatt & Zahnle, 2011].
This may be resolved using the coupled thermal reservoir approach. Ocean temperatures are set
by wind driven evaporation, not by IR thermal equilibrium.
The primary interest here however, is the increase in the temperature of the earth since the Maunder
minimum. In Section 3.1, simple heat transfer arguments are used to estimate the solar flux needed
to produce climate change. The coupling of small changes in the TOA flux to the surface is also
considered. In Section 3.2, the spectral properties of the solar flux and its absorption by the ocean
are described. In Section 3.3, ocean warming since the Maunder minimum is addressed. In Section
3.4, the effects of ocean gyre circulation on the solar heating are considered and in Section 3.5,
longer term climate change is briefly considered.
3.1 Changes in Solar Flux Related to Ice Ages and the Temperature Recovery from the
Maunder Minimum
During the last glacial maximum, sea level was 120 m lower than it is now [Lambeck, 2004]. This
water was stored at higher latitudes as freshwater ice. The amount of heat needed to melt a column
of ice 120 m high with a 1 m2 cross section and heat the melt water from 0 to 15 C is approximately
3.7 x 104 MJ. To melt this ice over a 10,000 years, a 24 hour average flux of 0.12 W m-2 is needed,
coupled directly into the ice sheet.
Since 1850, ocean surface temperatures have warmed by approximately 0.7 C based on a simple
linear fit to the HadSST3 ocean temperature anomaly [HadSST3, 2019]. Assuming a uniform
temperature increase in the first 100 m depth, this requires the addition of 293 MJ of heat per
square meter. Since 1850, this requires a 24 hour average flux of approximately 0.06 W m-2
coupled to the surface.
Using the ‘clean air’ solar flux algorithm from IEEE Standard 378 [IEEE 1993], the change in the
surface flux produced by an increase of 1 W m-2 in TOA flux may be estimated. The calculated
average daily cumulative flux vs. latitude is divided by 1365 to get to the 1 W m-2 TOA flux level.
This is then scaled by a factor of 0.7 to account for cloud attenuation. These flux values can then
be compared to the 0.12 W m-2 needed to bring the earth out of an Ice Age. The flux has to be
reduced by another factor of 0.7 to account for the additional short wavelength atmospheric
attenuation [ASTM, 2012]. These values can then be compared to the 0.06 W m-2 need for the
earth to recover from the Maunder minimum. This is shown in Figure 9. While these are very
approximate estimates, the small changes in flux accumulated over long periods of time are
consistent with the observed warming and provide the justification for further investigation. In
particular, more detailed estimates of the ocean heating, sunspot induced flux changes and other
possible heating and feedback mechanisms are needed. Most of the ocean heating reported by
Levitus et al has occurred since 1985 and is probably caused by warm phase ENSO and related
Roy Clark Null Hypothesis VPM 005.1, Review Draft, Sept 2019
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ocean oscillations [NOAA, Ocean heat content, 2019; Levitus et al, 2012]. The warm surface
water is coupled to lower depths by Ekman transport and Ekman pumping as discussed in Section
3.5.1.
Figure 9: 24 hr average surface flux change produced by a 1 W m-2 change in solar flux estimated from the
IEEE 738 solar algorithm. Blue line with 0.3 albedo added. Orange line with an additional 0.3 atmospheric
transmission reduction included. Dotted lines are estimated Ice Age melt and Maunder minimum warming
flux levels.
3.2 The Spectral Properties of the Solar Flux and Ocean Attenuation
The spectrally resolved solar flux at the top of the atmosphere (TOA) and the flux at the surface
for an air mass of 1.0 (AM 1.0, sun overhead) are shown in Figure 10 for wavelengths from 200
to 2000 nm [ASTM, 2012]. The main absorption peak of O3 is in the 200 to 300 nm region.
Molecular oxygen absorbs below 200 nm. The blue spectral region near 400 nm is attenuated by
Rayleigh scatter. This varies inversely as the fourth power of the wavelength and produces the
blue color of the daylight sky. There are also water vapor overtone bands that absorb the near IR
(NIR) solar flux in the 850, 950 1100, 1400 and 1800 nm regions. These heat the troposphere
through direct absorption of the incident solar flux. The absorbed heat adds to the convection.
The penetration depths for 99% absorption from 300 to 800 nm for pure water and for water with
a 0.02 m-1 scatter term added to simulate ‘pristine’ ocean water are shown in Figure 11 [Hale and
Querry, 1973]. The minimum absorption and therefore maximum penetration depth occurs in the
blue green region near 500 nm. The scatter term reduces the maximum penetration depth to 100
m.
Most sunspot induced changes in the solar flux occur at shorter wavelengths. Figure 12 shows the
estimated average changes in the solar spectrum both during a solar cycle and since the Maunder
minimum on a log-log scale [Lean, 2000]. The upper plot, a) shows the percentage change, the
lower plot b) shows the change in irradiance. The average change in flux during a sunspot cycle
Roy Clark Null Hypothesis VPM 005.1, Review Draft, Sept 2019
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was estimated to be 1.2 W m-2. While the percentage changes are higher at shorter wavelengths,
the irradiances are much lower. Figure 13 shows the solar sunspot spectral change, the
atmospheric solar spectral profile and ocean penetration depth plotted on the same logarithmic
wavelength scale from 100 to 1000 nm (0.1 to 1 µm). Part of the sunspot spectral change is
absorbed by O3 in the stratosphere and part is transmitted through the atmosphere where it may
penetrate to depths up to 50 to 100 m in the ocean. While the flux changes are quite small, they
may accumulate in the oceans over long periods of time. They may also influence stratospheric
temperatures and ozone concentrations.
Figure 10: Top of atmosphere and AM 1.0 solar spectral irradiances from 200 to 2000 nm.
Figure 11: Penetration depth into water and ‘pristine’ ocean from 300 to 800 nm.
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Figure 12: Estimated changes in spectral irradiance from solar cycle minimum (CMIN) to maximum
(CMAX) and from the Maunder Minimum (MMIN) to the mean of the solar cycle, expressed as percentages
in a) and as energy changes in b) [Lean, 2000].
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Figure 13: Spectral overlap of solar flux sunspot variation, TOA and atmospheric AM 1.0 solar flux and
ocean penetration depth.
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3.3 Temperature Recovery Since the Maunder Minimum
Using VIRGO radiometer data from the SOHO satellite, a change in the sunspot index of 100
produces a change in solar flux of approximately 1 W m-2 in the top of atmosphere (TOA) solar
flux [VIRGO, 2017]. It should be noted that the sunspot index was revised in 2015 to Version 2
[SILSO, 2019; Lockwood et al, 2016]. This revision increased the sunspot number values by
approximately 1.6. The analysis here is based on the version 1 index. The VIRGO data and the
corresponding sunspot index are shown in Figure 14. In addition to the change from the sunspot
index, there was an overall increase in brightness in the TOA flux during the recovery from the
maunder minimum. This is shown in Figure 15. The upper trace, Figure 15a shows the TOA
response at all wavelengths. The lower 3 traces, Figures 15b though 15d show the TOA response
in spectral bands at 0.12 to 0.4 µm, 0.4 to 1 µm and 1 to 100 µm. The largest changes are at the
shorter wavelengths.
Figure 14: VIRGO radiometer data and the sunspot index used to estimate the sunspot induced change in the
solar flux. Here, a change in index of 100 is assumed to produce a change of 1 W m-2 in the TOA flux.
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Figure 15: Estimated changes in the total solar irradiance and in selected spectral regions since the Maunder
minimum [Lean, 2000].
Based on Figures 14 and 15, the increase in solar flux from 1850 may be estimated by scaling the
sunspot index and adding an offset. This is illustrated in Figure 16a. Here the index was divided
by 100 and a 0.5 W m-2 offset was added. This provides a simple approximation to the change in
TOA flux that may be used for further analysis. The cumulative TOA flux is shown in Figure 16b.
To start, the cumulative flux derived from the data in Figure 16b was fitted to the HadSTT3 global
ocean surface temperature anomaly series [HadSST3, 2019]. A simple least squares fitting
approach was used with a scale factor and offset. This is shown in Figure 17. The best fit was y
= 0.00384 cum – 0.421. For comparison, the Excel Trendline™ linear fit to the HadSST3 data
gave a slope of 0.0042 or an ocean surface temperature increase of 0.42 C per century. The
conversion factor from a 24 hour average surface flux in W m-2 to the temperature rise for a 100
m x 1 m2 column of water is 0.075 (number of seconds per year/heat capacity). The estimated
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scaling factor for TOA to surface flux conversion with 400 nm atmospheric attenuation from
Figure 9, is 0.08 (From Figure 9 above). When these two numbers are combined, the scale factor
is 0.075*0.08 = 0.006. For the cumulative flux over 150 years, this gives a temperature rise of
1.06 C, which is approximately 1.5 times larger than the observed rise of 0.7 C. Although this is
a rather approximate estimate, the increase in TOA solar flux from sunspots is consistent with the
amount of heat needed to warm the first 100 m of the ocean by 0.7 C over 150 years. This estimate
is based on a static column of water. In the oceans, the solar heat is absorbed and distributed by
the ocean gyre circulation. This will now be considered in more detail.
Figure 16: a) Estimated increase in TOA flux from the Maunder minimum baseline for the period starting
from 1850. b) Cumulative surface flux estimated from a) using a scale factor of 0.08
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Figure 17: HadSST3 global ocean surface temperature index since 1850, linear fit to HadSST3 and best least
squared fit to the scaled cumulative sunspot flux.
3.4 Ocean Gyre Circulation.
The earth’s ocean gyre circulation is illustrated in Figure 18. There are 5 major ocean gyres, the
N. and S. Atlantic gyres, the N. and S. Pacific gyres and the S. Indian gyre [NOAA, Ocean Gures,
2019; Ocean Gyres, 2019]. The southern gyres are coupled to the Southern Ocean. The S. Atlantic
equatorial gyre splits off the coast of Brazil and part feeds into the N. Atlantic gyre. The Pacific
equatorial currents are not centered on the equator, but are shifted approximately 8° north. The
gyres flow on a spherical earth and the surface area of a sphere decreases with increasing latitude.
The gyres are established by the surface winds, particularly the trade winds. In the tropics, the
equatorial currents flow from east to west. The cooler water flowing from the poles along the
eastern continental boundaries is warmed as it turns and flows westwards across the tropical
oceans. The wind driven evaporation is insufficient to balance the tropical solar heating and the
water in the equatorial current must warm up. This leads to the formation of the tropical warm
pools in the equatorial W. Pacific and Atlantic Oceans. The upper limit to the ocean surface
temperature is near 30 C. This is set by an approximate energy balance between the tropical solar
heating and evaporation with an average wind speed near 5 m s-1. If the wind speed drops and the
surface temperature increases above 30 C, strong local thunderstorms are formed that cool the
surface by convection [Eschenbach, 2010]. Changes in wind speed produce changes in the rate of
ocean heating through two effects. As the wind speed decreases, the surface evaporation decreases
and the ocean surface warms faster. The speed of the ocean current also slows and the residence
time of the water along the equatorial current increases. This increases the solar flux that is
absorbed in a local ocean volume. The wind driven evaporation produces cooler water at the
surface that sinks and cools the bulk ocean below. As the surface water sinks, it carries the surface
momentum with it. This drives the ocean current flow at lower depths. Changes in the ocean
warm pools involve changes in the surface area and location rather than increases in the maximum
surface temperature.
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There is never an exact energy balance between the solar heating and the wind driven cooling
within the gyres. This produces characteristic quasi-periodic oscillations such as the El Nino
Southern Oscillation, (ENSO), the Atlantic Multi-decadal Oscillation, (AMO), and the pacific
Decadal Oscillation, (PDO). Changes in the phase of these oscillations have major impacts on the
earth’s climate. The ENSO has a period between 3 and 7 years and the AMO and PDO have
periods in the 60 to 70 year range. The approximate locations of these 3 oscillations is indicated
in Figure 18 and the insets show the oscillation time series. Analysis of the power spectrum of the
AMO and PDO oscillations shows a strong peak near 9 years [Muller et al, 2013]. This means
that caution is needed when attempts are made to link the ocean oscillations to solar, lunar or
planetary cycles.
The wind driven nature of the ENSO can be clearly seen by comparing the ENSO temperature
index with the Southern Oscillation Index (SOI, 2019; ENSO, 2019). This is illustrated in Figure
19. This shows the JMA ENSO index based on the average temperature in the equatorial Pacific
Ocean from 4° N to -4° S and from 90° to 150° W. The SOI is based on the pressure difference
between Darwin, Australia and Tahiti. There is an inverse relationship between temperature and
pressure, since the wind speed increases with the pressure difference. For clarity, SOI index is
plotted with the sign reversed. The indices are both related to changes in flow rate in the tropical
S. Pacific gyre. The cumulative indices from 1880 (the sum over time) are shown in Figure 20.
The cumulative plots have been aligned by adding an offset to the ENSO cum plot using a least
squares fit. The offset was -6 C. The cooling from 1940 to 1980 and the subsequent warming can
be clearly seen.
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Figure 18: The earth’s ocean gyre circulation (schematic). The approximate locations of the ENSO, AMO
and PDO are also indicated and the insets show the oscillation time series.
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Figure 19: ENSO and sign reversed SOI indexes from 1880. There is a clear relationship between
temperature and wind speed.
Figure 20: Cumulative ENSO and SIO indices. The ENSO plot is offset by -6C to align the plots.
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In addition to the ENSO, the AMO is also linked to changes in wind speed, in this case through
the North Atlantic Oscillation, (NAO). This is the pressure difference between Iceland and the
Azores [NAO, 2019; NAO, UEA, 2019]. It is a measure of the wind speed along the northern part
of the subtropical N. Atlantic Gyre. However, a higher wind speed here means a faster transit time
and less cooling, so there is a positive correlation between pressure difference and ocean surface
temperature. In addition, there is a significant increase in wind speed in winter months. As the
Arctic region cools, the air density increases at lower altitudes with the formation of the polar
vortex. As the air descends, conservation of angular momentum leads to an increase in angular
velocity. Figure 21 shows the long term, 1958 to 2006 annual average zonal ocean surface
temperature (a), air temperatures (b), latent heat flux (c), wind speed (d), sensible heat flux (e) and
absolute humidity (f). The monthly values for July and December are also shown [Yu et al, 2008].
From Fig. 21c, the seasonal change in wind speed is 6 m s-1 near 65° N and 4 m s-1 near 65° S.
Figure 22 shows the global and N. winter (December to February) and S. Winter (Jun to Aug)
evaporation patterns and Figure 23 shows the long term average pattern of ocean surface
temperatures [Yu, 2007]. The maximum temperatures (dark red) do not correspond to the
maximum evaporation rates. This is because the evaporation rate is determined by the humidity
gradient and the wind speed, not the surface temperature. Along the western continental boundary
currents, the weather patterns from the land may strongly influence the evaporation rate. For
example, along parts of the Gulf Stream, cold air outbreaks from offshore winds may account for
approximately half of the observed latent and sensible heat flux even though such events occur for
20% of the time [Shaman et al, 2010].
Because of the differences between winter and summer winds and sea level air pressure, the NAO
has its maximum influence during the winter months. Figure 24 shows the NAO index average
for the winter months, December through February. A five year running average is also shown.
Figure 25a shows the cumulative plot from Figure 24 with a straight line fit added. Figure 25b
shows the detrended plot from Fig. 25a. (The straight line has been subtracted). This has a similar
profile to the AMO index. Figure 26 shows the detrended cumulative plot from Figure 25b scaled
to match the annual AMO index [NOAA, AMO, 2019]. The two plots matched more closely from
1930 onwards, so the fit was made using the more limited data set. Over this time period the
correlation coefficient was 0.67. This analysis clearly shows that the winter cooling from the NAO
is a major contributor to the AMO variation. The differences between the two in earlier years is
probably due in part to the sparse ocean temperature data available from ship readings over this
time period.
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Figure 21: Long term, 1958 to 2006 annual average zonal ocean surface temperature (a), air temperature (b),
latent heat flux (c), wind speed (d), sensible heat flux (e) and absolute humidity (f). The monthly values for
July and December are also shown.
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Figure 22: a) global evaporation pattern, b) and c) N. and S. winter evaporation patterns.
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Figure 25: a) Cumulative plot of NAO and b) detrended plot (linear slope subtracted)
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Figure 26: Detrended cumulative NAO plot scaled to match the AMO Index.
3.5 Ocean Heating and Gyre Coupling Below the Surface Mixing Layer
The solar flux is initially absorbed into the first 100 m of the ocean, with the maximum penetration
depth at wavelengths near 500 nm. If it is assumed that the observed increase in ocean surface
temperature of 0.7 C from 1850 observed in the HadSST3 index is accumulated in the first 100 m
layer, this gives a 24 hour average flux of 0.06 W m-2. Starting from estimates of ocean heat
content in the first 700 m ocean layer, Levitus et al provide estimates of the temperature rise and
heat flux accumulated in the various ocean basins from 1969 to 2008 [Levitus et al, 2009]. These
are shown in Figure 27. The world ocean average temperature rise is given as 0.17 C with a heat
flux of 0.36 W m-2. However, each ocean basin has a different value for the temperature rise and
heat flux. The N. Atlantic basin has the highest temperature rise, 0.4 C and the highest heat flux,
0.81 W m-2. The S. Atlantic and S. Pacific ocean basins have lower values than the corresponding
N. basins. These differences show that the ocean heating to 700 m is strongly influenced by the
ocean gyre circulation and is not just a simple accumulation of heat. Part of the S. Atlantic
equatorial current is diverted off the coast of Brazil into the N. Atlantic basin and both the S.
Atlantic and S. Pacific gyres are coupled to the S. Ocean circulation. This is illustrated above in
Figure 18. In addition, most of the heat has accumulated in the Atlantic and Pacific Ocean basins
since 1985. This is shown in Figure 28. The S. Indian Ocean also exhibits similar behavior. The
cumulative ENSO and SIO indices shown above in Figure 20 also show warming trends that
started near 1980. Yu also reports a trend of increasing ocean evaporation starting around 1977-
78 [Yu, 2007]. All of these observations indicate that there is another process that leads to ocean
heating and the transport of heat from the surface to lower depths. This requires a more detailed
examination of the ocean gyre circulation, in particular, the coupling of the earth’s rotation to the
wind driven ocean currents. This involves the Coriolis Effect, although in oceanography this is
known as Ekman transport and Ekman pumping.
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Figure 27: Average temperature rise and heat storage, W m-2 in the world’s oceans, 1969 to 2008.
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Figure 28: Change in heat content, 0 to 700 m depth, for the N. and S. Atlantic and Pacific Ocean basins
from 1955 to 2017. The increase from about 1985 is indicated by the dotted lines.
3.5.1 Ekman Transport and Ekman Pumping
In the oceans, the surface water current flow produced by the wind shear moves at an angle to the
wind direction because of the rotation of the earth [NOAA, Ekman Transport, 2019]. In the N.
hemisphere, the current moves to the right of the wind direction. Below the surface, the shear
continues to drive the current to the right. The direction is reversed in the S. hemisphere. This
produces a spiral flow profile in the first 100 to 150 m layer of the ocean. The net flow is at 90°
to the wind direction. The circular wind pattern around the ocean gyres produces Ekman pumping.
This is illustrated schematically in Figure 29. Within the anticyclonic (high pressure) gyre
circulation, Ekman convergence produces downwelling. The depth of the thermocline increases
and heat can accumulate below the surface. Along the eastern continental boundary currents,
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Ekman divergence produces upwelling. The western continental boundary currents are intensified
by the westward equatorial flow and run deeper and faster than the eastern currents. This is
illustrated in Figure 30.
Figure 29: Ekman pumping a) Ekman transport with a cyclonic wind pattern (low pressure) produces
surface divergence and upwelling. b) Ekman transport with an anticyclonic wind pattern (high pressure)
produces surface convergence and downwelling.
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Figure 30: Eastern and western boundary currents (schematic). The eastern boundary current (Canary
Current) is wide, slow and shallow. The Ekman transport produces upwelling. The western boundary
current (Gulf Stream) is narrow, fast and deep.
Figure 31 shows a set of temperature cross sections of the N. Atlantic Ocean at 10, 20, 30 and 40°
N for February and August 2018. These months generally have the lowest and highest
temperatures. The plot were generated using the Argo Global Marine Atlas [Argo, 2019]. The
color temperature scale changes with the range of temperatures plotted, so the same colors may
indicate different temperatures on different plots. Temperature labels have been added for clarity.
The cross sections at 10° N are through the N. Atlantic Equatorial current. This flows from E to
W towards the W. Atlantic warm pool. Heat accumulates near the surface and the depth of the
warm layer increases as the flow moves west. The depth of the 20° C isotherm increase from
approximately 50 to 120 m. At 20° N, the isotherms are more widely spaced and the western 18°
C isotherm now extends below 300 m. This is the effect of the Ekman convergence within the
gyre. At 30° N, the 18 C isotherm extends below 400 m and some of the features associated with
the Gulf Stream are beginning to emerge. At 40° N, the meanders of the Gulf Stream are fully
developed and the flow is starting to turn eastwards. The Gulf Stream structure extends below 700
m, particularly in February.
The most important point to note however is that wind driven Ekman convergence and the western
continental boundary currents are sufficient to transport the surface ocean heat to lower depths.
Changes in wind patterns explain the ocean heat gain to 700 m shown in Figure 28 and the changes
in cumulative ENSO and SOI indices shown above in Figure 20. None of the heat gain in Figure
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28 can come from the increase in downward LWIR flux from the observed increase in atmospheric
CO2 concentration.
Figure 31: N. Atlantic basin cross sections 0 to 700 m depth at 10, 20, 30 and 40º N showing the isotherms.
For discussion see text [plotted from Argo Global Marine Atlas, 2019]
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3.6 The Winter Increase in Polar Winds
As shown in Figure 21c, there is a significant increase in polar winds as the polar air mass cools
at the start of winter. The cooling shifts the air mass to lower altitudes and the decrease in moment
of inertia leads to an increase in (angular) velocity. However, the details are complex because of
such effects as Rossby waves and Ekman transport. In the Arctic, at the ends of the western
boundary currents, the Gulf Stream and the Kuroshio Current, the increase in ocean-air thermal
gradient leads to an increase in sensible heat loss as shown in Figure 21e. The location and
intensity of the Aleutian and Icelandic lows are important factors in the N. hemisphere winter
weather patterns. Long term changes in the Icelandic low influence the Atlantic Multi-decadal
Oscillation (AMO). However, unlike the equatorial currents, an increase in current velocity along
the northern subtropical gyre leads to warming not cooling. In this case, a shorter transit time
means less cooling. The lower temperatures at higher latitudes significantly reduce the rate of
wind driven evaporative cooling per unit wind speed, as shown in Figure 2 above.
A measure of the long term changes in the high latitude winds are the Arctic and Antarctic
Oscillation Indices [NOAA, AO, 1019; NOAA, AAO, 2019]. These are shown in Figures 32 and
33. Here, a positive index indicated a lower pressure, higher winds and a more constrained polar
vortex. The linear trend and a 13 month running average are also shown. The cumulative plots
are also presented in the lower traces. The AO plot shows no long term trend although the
cumulative plot shows a decrease in index to the mid 1980s followed by a small recovery. The
AAO plot shows a slight increase over the 50 years from 1950. The cumulative plot shows a
decrease from 1950 to 1970 followed by an increase to 2002. This mean that the AAO has been
increasing and the wind speed in the Southern Ocean should therefore by increasing. This
decreases the circulation time which should lead to a warming trend along the S. boundaries of the
S. Atlantic, S. Pacific and S. Indian Ocean gyres.
Figures 32 and 33 show monthly values for the AO and AAO indices over the whole year.
However, most of the cooling occurs in winter. Figure 34 shows the average values of the AO for
just January, February and March. There appears to be a step in the data near the 1990 peak. This
is indicated by the dotted lines.
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Figure 32: a) AO index from 1950 with linear trend and 13 point moving average. b) Cumulative plot of the
index in Figure 42a.
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Figure 33: a) AAO index from 1950 to 2002 with linear trend and 13 point moving average. b) Cumulative
plot of the index in Figure 43a.
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Figure 34: Blue line: AO index average for January, February and March from 1950. Black line: 5 year
running average.
3.7 Cosmic Rays and Cloud Cover
Changes in cloud cover related to cosmic ray seeding have been proposed as a mechanism for
climate change [Svensmark, 2017; 2009]. Cosmic ray seeding increases as sunspot activity
decreases. However, this does not account for the full cloud cycle. Clouds are formed, they can
be transported over long distances by weather systems and they dissipate through deposition and
evaporation. Seeding by cosmic rays increases the initial cloud cover in regions at saturation, but
the effects on cloud lifetime and transport have not been considered. The extra cloud formation
also has to block additional sunlight, so this does not impact regions that already have 100 % cloud
cover. These increases in cloud cover can also increase the downward LWIR flux to the surface
and reduce surface cooling. Any changes in ocean heating may also influence the wind speed.
Further analysis of cosmic ray seeding is needed that includes the full cloud cycle and the detailed
surface energy transfer.
Cosmic ray seeding is associated with climate changes such as the Maunder minimum and the
medieval and modern warming periods. Longer term climate changes such the 100,000 year Ice
Age cycle are produced by planetary perturbations to the earth’s orbital and axial motion as
discussed in Section 4.0 below. These do not involve changes in solar activity and should not be
influenced by cosmic ray seeding.
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3.8 The Coupling of the Solar Sunspot Flux into the Oceans
The increase in solar flux from an increase in sunspot activity is initially coupled into the first 100
m layer of the ocean. From here it is distributed by wind driven ocean currents and accumulates
within the ocean gyre circulation. However, the heat stored in the oceans also involves a subtle
balance between general solar heating and wind driven cooling, including Ekman transport effects.
This balance is not fixed, but is influenced by the various ocean oscillations. The observed 0 to
700 m ocean heating from 1980 shown in Figure 28 is the result of additional heat transport from
the ocean warm pools. However, the earth’s climate is largely determined by ocean surface
temperatures and the transfer of heat from the ocean surface to the troposphere by the latent heat
flux. Figure 35 shows the vertical distribution of the changes in heat content from 1955 to 2010
[Levitus, 2012]. Approximately 25% of the heat is in the first 100 m layer where it can couple to
the surface. Tropospheric heating from the El Nino events indicated in Figure 19 can clearly be
seen in the lower troposphere satellite temperature data shown in Figure 36 [UAH, TLT, 2019].
The El Nino events are indicated with the arrows.
Figure 35: Vertical distribution of the increase in ocean heat content, 1955 to 2010.
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4.0 CLIMATE CHANGE OVER GEOLOGICAL TIME SCALES
Section 3 has considered climate change over relatively short time scales related to the ocean
oscillations and the recovery from the Maunder minimum. In this section, climate change over
longer time scales will be considered, including both the Ice Age cycles and changes in ocean
circulation caused by plate tectonic motion that alters the continental ocean boundaries. Finally,
the young sun paradox is explained in terms of changes in ocean evaporation rates instead of
invalid ‘greenhouse effect’ arguments.
4.1 Ice Ages
Analysis of ocean sediment and ice core data has shown that in the recent geological past, the earth
has cycled through Ice Ages with a period of approximately 100,000 years. This has been
attributed to planetary perturbations of the ellipticity of the earth’s orbit, mainly by Jupiter. The
orbital changes are part of a more general set of perturbations known as Milankovitch cycles that
also include changes to the earth’s axial tilt (obliquity) and precession. This is illustrated in Figure
37 [Milankovitch Cycles, 2019]. Based on ice core data, the increase in temperature produced an
increase in atmospheric CO2 concentration of approximately 80 ppm from 200 to 280 ppm.
However, the change in CO2 concentration followed the change in temperature, it did not cause
it. The oceans had to warm first [Humlum et al, 2013; Fischer et al, 1999; Petit et al, 1999]].
While the various Milakovitch cycle frequencies can be identified in the ocean and ice core data,
the detailed energy transfer mechanisms have not yet been explained. The difference in flux
between perihelion (closest approach) and aphelion (furthest distance) increases with increasing
ellipticity. However, as a result of Kepler’s Second Law, the earth’s velocity increases as the
distance to the sun decreases. The earth sweeps out equal areas in equal time. When the change
in orbital velocity is included, the total solar flux accumulated over time stays constant. The orbital
time between the minor axis points at perihelion is less than that at aphelion. Figure 38 illustrates
the change in orbital geometry with ellipticity. Here, in polar coordinates, r is the distance from
the sun to the earth and is the angle. The axis for = 0 is the perihelion-sun line along the major
axis of the ellipse. As the ellipticity is increased, the focus of the ellipse containing the sun moves
from away from the center of the ellipse, from f to f’. Figure 39 shows the change flux vs orbital
angle at selected ellipticities. The ellipticity of the earth’s orbit has changed from 0.02 at the last
glacial minimum to 0.0167 and will continue to decrease to about 0.003 at the next glacial
maximum. Figure 40 shows the difference in orbital time (days) for each half of the orbit vs.
ellipticity. Figure 41 shows the corresponding change in solar flux. The flux increases by this
amount at perihelion and decreases by the same amount at aphelion. Currently, at an ellipticity of
0.0167, the difference in flux is near 46 Wm-2. This has decreased from a peak of 55 W m-2 at the
last glacial minimum (Holocene optimum) and will continue to decrease to 0.8 W m-2.
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Figure 37: Milankovitch cycles and Ice Ages over the last million years and cycle projections for the next
100,000 years.
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Figure 38: Ellipticity induced changes in the earth’s orbital geometry (not to scale). As the ellipticity
increases, the location of the sun at the focal point moves further away from the center of the ellipse along the
major axis.
Figure 39: Changes in (clear sky) solar flux for selected orbital ellipticity values. The orbital angle in polar
coordinates is defined in Figure 38
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Figure 40: Difference in orbital time vs ellipticity for each half of the orbit (aphelion – perihelion)
Figure 41: Difference in flux vs ellipticity for each half of the orbit, (aphelion – perihelion)/2
In addition to changes in orbital ellipticity, the earth’s axial tilt (obliquity) also changes. As the
tilt angle increases, the amplitude of the solar variation increases at higher latitudes and decreases
neat the equator. This is illustrated in Figure 42. This shows the difference in solar flux vs. latitude
for axial tilts of 24.2 and 22.6° calculated using the IEEE 738 algorithm [IEEE, 1993]. The earth’s
current axial tilt angle is 23.5, and decreasing as shown in Figure 37.
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Figure 42: Change in cumulative daily flux at selected latitudes for a change in axial tilt (obliquity) from 24.2
to 22.6°. These are the maximum and minimum tilt angles for the earth’s current decreasing obliquity cycle
as shown in Figure 37.
During each year, the changes in solar flux related to the Milankovitch cycles are coupled into the
oceans along with the rest of the solar flux. There is no equilibrium flux balance and net heat
transfer depends on the cumulative rates of heating and cooling of the flux coupled into the ocean
gyre circulation. Furthermore, there is a precession between peak orbital flux and the axial tilt that
also has be addressed. Another factor that has not been considered is the seasonal phase shift
between the peak solar flux at equinox and the temperature response. The observed Ice Age cycle
suggests that there is a phase shift or time delay between the rates of heating and cooling associated
with the Milankovitch cycles. When the ellipticity is increasing, the rate of cooling is lower than
the rate of heating as the solar flux increases at perihelion. When the ellipticity is decreasing, the
rate of cooling is higher than the rate of heating at perihelion. There is a similar effect with the
axial tilt. Milankovitch proposed the in change peak summer flux at 65° N as a measure of the
effect of these cycles. However, this did not consider the effect of the ocean gyre circulation.
When the area weighted flux is considered, changes in the heat content of the equatorial warm
pools may be more important.
The earth has been cooling for about the last 6000 years as it has passed though the warm peak of
the (Holocene) glacial cycle and started the next Ice Age cooling cycle. However, superimposed
on this cooling trend are fluctuations produced by long terms variations in the solar flux produced
by the sunspot cycle. This is illustrated in Figure 43 which shows the temperature record for the
last 10,000 years derived from the GISP2 Greenland ice core [WWT, Paleoclimate, 2018]. The
Minoan, Roman and medieval warming periods are indicated along with the Little Ice Age or
Maunder Minimum. The red line indicates the modern warming period.
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Figure 43: Ice core data showing that the earth has been cooling for the last 6000 years.
4.2 Plate Tectonics
The changes in the continental boundaries produced from the breakup of the supercontinent
Pangaea are shown in Figure 44 from 65 million years ago to the present [Zagos et al, 2001]. The
arrows indicate the equatorial ocean flow and the circles highlight the formation of the Southern
Ocean. Initially, ocean circulation near the poles was restricted and the earth was warmer than it
is today. As the continents separated, the formation of the Tasmania-Antarctic Sea and opening
of the Drake Passage established the Southern Ocean. This enabled the ocean water from the S.
Atlantic, S. Pacific and S. Indian gyres to circulate around Antarctica. This led to a major climate
cooling and the formation of the Antarctic ice sheet. Later, the closure of the Isthmus of Panama
also led to further cooling, as more ocean water was diverted to towards the poles. These changes
are illustrated in Figure 45 using plots of the 18O and 13C isotope ratios from deep ocean
sediment cores [Zagos et al, 2001]. The 18O ratio is a proxy for temperature and the 13C ratio is
a proxy for the CO2 concentration. The time scale is from 65 million years ago to the present.
Climatic, tectonic and biotic events are also indicated. This clearly shows that changes in ocean
circulation caused by plate tectonics has had a major effect on the earth’s climate over geological
time.
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Figure 44: Plate tectonics, evolution of the continental boundaries over the last 69 million years. The arrows
indicate the ocean equatorial flow. The circles indicate the formation of the Southern ocean.
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Figure 45: Plots of the 18O and 13C isotope ratios from deep ocean sediment cores [Zagos et al, 2001]. The
18O ratio is a proxy for temperature and the 13C ratio is a proxy for the CO2 concentration. The time scale
is from 65 million years ago to the present.
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4.3 The Young Sun Paradox
During earlier geological times, approximately 2.5 billion years ago, the solar flux was only 80%
of its current value. Using conventional equilibrium greenhouse affect arguments, this reduces the
average outgoing TOA LWIR flux from approximately 240 W m-2 to 192 W m-2. The
corresponding ‘effective emission temperatures’ are 255 and 241 K [Taylor, 2006]. However, the
geological record indicates that the earth was relatively warm at this time with occasional
glaciation. If the average surface temperature stayed at 288 K (15 C) this means that the so called
greenhouse effect temperature had to increase from 33 K to 47 K. This leads to the so called ‘faint
young sun paradox’ [Goldblatt & Zahnle, 2011]. What produced to the increase in greenhouse
effect temperature? In reality, the earth’s climate is determined mainly by ocean evaporation, not
by the LWIR flux.
The ocean response to a 20% reduction in the solar flux may be understood using a simple scaling
argument based on Yu’s formulation of the ocean evaporation [Yu 2007; Yu et al., 2008]. This is
shown in Figure 46. The relative evaporation rate of 1.0 at 30 C indicated by the blue circle is the
ocean warm pool surface temperature for which the cooling flux balances the current tropical solar
flux at an average wind speed of 5 m s-1 and a surface-air temperature difference T of 1 C. The
relative humidity is set to 70%. The evaporative cooling flux is much more sensitive to the wind
speed than the surface–air thermal gradient or the ocean surface temperature. A doubling of the
wind speed from 5 to 10 m s-1 doubles the evaporation rate. Similarly, halving the wind speed
from 5 to 2.5 m s-1 halves the evaporation rate. At 30 C, an increase from 1 to 2 and then to 3 C
in the surface-air temperature difference only increases the evaporation rate by 10 and then 20%.
A reduction in solar flux to 80% of the current value corresponds to a reduction in latent heat flux
to 80% of the current warm pool value. From Figure 46 this corresponds to a reduction in warm
pool temperature of 4 C from 30 to 26 C. From Eq. 1 above, the decrease in net LWIR cooling
flux transmitted through the LWIR atmospheric window is approximately 9 W m-2 [Koll and
Cronin 2018]. This of course assumes similar albedo, ocean and wind circulation patterns to those
of today. While more detailed analysis is required, this simple scaling argument explains the
young sun paradox.
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5.0 CONCLUSIONS
The prevailing radiative convective equilibrium hypothesis in climate science has failed. This
hypothesis greatly oversimplified climate energy transfer processes and created global warming
as a mathematical artifact of the climate modeling assumptions. There can be no climate
equilibrium on any time or spatial scale. The earth’s climate is determined by the time dependent
or dynamic energy transfer between coupled thermal reservoirs. The change in temperature is
determined by the change in heat content or enthalpy of these thermal reservoirs using well defined
thermal properties and time dependent energy transfer processes.
There can be no ‘greenhouse effect temperature’ based on equilibrium temperature arguments.
Instead, the greenhouse effect has to be defined in terms of the surface exchange energy. At the
surface, the downward LWIR flux from the lower troposphere ‘balances’ most of the upward
LWIR flux from the surface. This establishes a non-equilibrium LWIR exchange energy that limits
the net LWIR surface cooling flux to the transmission through the atmospheric LWIR transmission
window. Over land, all of the flux terms are mixed together in a thin surface layer. In order to
dissipate the absorbed solar heat, the surface must warm up during the day until this heat is
dissipated by moist convection. Over the oceans, the surface must warm until the water vapor
pressure is sufficient to support the wind driven evaporation. The penetration depth of the LWIR
flux into the oceans is less than 100 micron. Evaporative cooling is produced by the removal of
water molecules from the surface. These two processes are mixed together in the surface layer.
Any small increase in the downward LWIR flux at the surface that results from an increase in the
atmospheric concentration of CO2 is too small to produce a measurable increase in surface
temperature. It is overwhelmed by the magnitude and variation of the wind driven evaporative
cooling flux.
Over the last 200 years, the observed increase of 120 ppm in the atmospheric CO2 concentration
has produced an increase in downward LWIR flux at the surface of approximately 2 W m-2. This
has to be combined with the other surface flux terms and coupled to the thermal reservoirs. It
cannot be separated and analyzed independently. In this paper, the null hypothesis for CO2 has
been introduced and demonstrated using simple surface energy transfer models for the ocean-air
and land-air interfaces. The surface responds to the additional CO2 flux by adjusting the
convection and evaporation terms, not just the net LWIR cooling flux as predicted using the
conventional equilibrium greenhouse effect approach. Furthermore, there is no ‘water vapor
feedback’ that can be used to amplify the surface heating effect. It is simply impossible for the
observed 120 ppm increase in atmospheric CO2 concentration to have produced any measurable
increase in surface temperature.
Instead, climate change can be explained in terms of small changes in the solar flux absorbed and
accumulated in the ocean thermal reservoir. The earth’s climate is determined by a subtle dynamic,
or time dependent balance between the solar heating and the wind driven evaporative cooling of
the oceans as the water is circulated through the ocean gyres. There can never be an exact flux
Roy Clark Null Hypothesis VPM 005.1, Review Draft, Sept 2019
57
ACKNOWLEDGEMENT
This work was performed as independent research by the author. It was not supported by any grant
awards and none of the work was conducted as a part of employment duties for any employer. The
views expressed are those of the author.
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