A DYNAMIC COUPLED THERMAL RESERVOIR APPROACH TO...

Roy Clark Null Hypothesis VPM 005.1, Review Draft, Sept 2019

2

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


4

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


6

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.


7

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


8

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.


9

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.


10

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)


11

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


12

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.


13

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.


15

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]


16

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


17

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


18

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.


19

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].


20

Figure 13: Spectral overlap of solar flux sunspot variation, TOA and atmospheric AM 1.0 solar flux and

ocean penetration depth.


21

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.


22

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


23

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


24

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.


25

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.


26

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.


27

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.


28

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.


29

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.


30

Figure 22: a) global evaporation pattern, b) and c) N. and S. winter evaporation patterns.


32

Figure 25: a) Cumulative plot of NAO and b) detrended plot (linear slope subtracted)


33

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.


34

Figure 27: Average temperature rise and heat storage, W m-2 in the world’s oceans, 1969 to 2008.


35

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,


36

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.


37

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


38

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]


39

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.


40

Figure 32: a) AO index from 1950 with linear trend and 13 point moving average. b) Cumulative plot of the

index in Figure 42a.


41

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.


42

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.


43

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.


45

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.


46

Figure 37: Milankovitch cycles and Ice Ages over the last million years and cycle projections for the next

100,000 years.


47

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


48

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.


49

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.


50

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.


51

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.


52

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.


53

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.


55

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


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.

6.0 REFERENCES

Argo, 2019, http://www.argo.ucsd.edu/Marine_Atlas.html

ASTM, 2012, G173-3, Solar reference spectra AM1.5, http://rredc.nrel.gov/solar/spectra/am1.5/

Clark, R. 2019a ‘A Dynamic Coupled Thermal Reservoir Approach to Atmospheric Energy

Transfer Part III: The Surface Temperature’, Ventura Photonics Monograph, VPM 004,

Thousand Oaks, CA, May 2019

http://venturaphotonics.com/files/CoupledThermalReservoir Part III Surface Temperature.pdf

Clark, 2019b, ‘The Greenhouse Effect’, Ventura Photonics Monograph, VPM 003.1, Thousand

Oaks, CA, May 2019

http://venturaphotonics.com/files/The_Greenhouse_Effect.pdf

Clark, R. 2019c, ‘50 years of Climate Fraud’, Ventura Photonics Monograph, VPM 002.1,

Thousand Oaks, CA, May 2019

http://venturaphotonics.com/files/50_Years_of_Climate_Fraud.pdf

Clark, R. 2019d, ‘A Dynamic Coupled Thermal Reservoir Approach to Atmospheric Energy

Transfer Part V: Summary’, Ventura Photonics Monograph, VPM 006, Thousand Oaks, CA, May

2019

http://venturaphotonics.com/files/CoupledThermalReservoir Part V Summary.pdf

Clark, R., 2013a, Energy and Environment 24(3, 4) 319-340 (2013) ‘A dynamic coupled thermal

reservoir approach to atmospheric energy transfer Part I: Concepts’

http://venturaphotonics.com/files/CoupledThermalReservoir_Part_I_E_EDraft.pdf

Clark, R., 2013b, Energy and Environment 24(3, 4) 341-359 (2013) ‘A dynamic coupled thermal

reservoir approach to atmospheric energy transfer Part II: Applications’

http://venturaphotonics.com/files/CoupledThermalReservoir_Part_II__E_EDraft.pdf

Clark, R., 2011, The dynamic greenhouse effect and the climate averaging paradox, Ventura

Photonics Monograph, VPM 001, Thousand Oaks, CA, Amazon, 2011.

http://www.amazon.com/Dynamic-Greenhouse-Climate-Averaging-

Paradox/dp/1466359188/ref=sr 1 1?s=books&ie=UTF8&qid=1318571038&sr=1-1

ENSO, 2019, ftp://www.coaps.fsu.edu/pub/JMA_SST_Index/jmasst1868-today.filter-5

Eschenbach, W., 2010a, Energy and Environment 21(4) 201-200 (2010), ‘The thunderstorm

thermostat hypothesis’


58

Fischer, H.; M. Wahlen, J. Smith, D. Mastroianni and B. Deck, Science 283 1712-1714 (1999),

‘Ice core records of atmospheric CO2 around the last three glacial terminations.’

Goldblatt, C. and K. J. Zahnle, Clim. Past 7 203-220 (2011), ‘Clouds and the faint young sun

paradox’.

HadSST3, 2019, https://crudata.uea.ac.uk/cru/data/temperature/HadSST3-gl.dat

Hale, G. M. and Querry, M. R., Applied Optics, 12(3) 555-563 (1973), ‘Optical constants of

water in the 200 nm to 200 µm region’

Harde, H., Int. J. Atmos. Sci.9251034 (2017), ‘Radiation Transfer Calculations and Assessment of

Global Warming by CO2’ https://doi.org/10.1155/2017/9251034

Harvey, K. L., Proc. 2nd Annual Lowell Observatory Fall Workshop, Oct 5-7, (1997) Ed. J. C.

Hall "Solar analogs: Characteristics and Optimum Candidates", ‘The solar activity cycle and sun-

as-a-star variability in the visible and IR’

Humlum, O.; K. Stordahl and J-E Solheim, Global and Planetary Change 100 51-69 (2013), ‘The

phase relation between atmospheric CO2 and global temperature’

IEEE, IEEE Std 738-1993, IEEE Standard for calculating the current temperature relationship

of bare overhead conductors

IPCC, 2013: Climate Change 2013: The Physical Science Basis. Contribution of Working Group

I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F.,

D. Qin, G-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M.

Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY,

USA, 1535 pp, doi:10.1017/CBO9781107415324.

http://www.climatechange2013.org/report/full-report/

MODTRAN, 2018 http://forecast.uchicago.edu/Projects/modtran.orig.html

Keeling, 2019, https://scripps.ucsd.edu/programs/keelingcurve/

Koll, D. D. B and Cronin, T. W., PNAS, www.PNAS.Org/Cgi/doi/10.1073/pnas.1809868115 pp.

1-6 (2018), ‘Earth’s outgoing longwave radiation linear due to H2O greenhouse effect’.

Lambeck, K., Comptes Rendus Geoscience 336 667-689 (2004), ‘Sea level change through the

last glacial cycle: geophysical, glaciological and paleo-geographic consequences’

Lean, J. Geophys Res. Letts. 27(16) 2425-2428 (2000), ‘Evolution of the sun’s spectral irradiance

since the Maunder minimum’

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2000GL000043

Lean, J. and M. T. DeLand, J. Climate 25(7) 2555-2560 (2012), ‘How does the sun's spectrum

vary?’ https://journals.ametsoc.org/doi/pdf/10.1175/JCLI-D-11-00571.1

Levitus, S. et al, (11 Authors), Geophysical Research Letters, 39 L10603 1-5 (plus auxiliary

material) (2012) ‘World ocean heat content and thermosteric sea level change (0-2000 m), 1955-

2010’

Levitus, S.; J. I. Antonov, T. P. Boyer R. A. Locarini, H. E. Garcia & A. V. Mishinov, Geophysical

Research Letters 36 L07608 1-5 (2009), ‘Global ocean heat content 1955-2008 in light of recently

revealed instrumentation problems.’ , http://www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/


59

Lockwood, M.; M. J. Owens, L. Barnard and I. G. Usoskin, The Astrophysical Journal 824:54,

17pp, June10 (2016) doi:10.3847/0004-637X/824/1/54, ‘An assessment of sunspot number data

composites over 1845-2014,’

http://iopscience.iop.org/article/10.3847/0004-637X/824/1/54/pdf

Milankovitch, M., Théorie Mathématique des Phénomenes Thermiques Produits par la Radiation

Solaire, Gauthier-Villars, Paris (1920); Canon of Insolation and the Ice-Age Problem, Royal

Serbian Acad. Sp. Pub. 132 (1941), Israel Program Sci. Trans., Jerusalem (1969)

Milankovitch Cycles, 2019, https://en.wikipedia.org/wiki/Milankovitch cycles

Muller, R. A.; J. Curry, D. Groom, R. Jacobsen, S. Perlmutter, R. Rohde, A. Rosenfeld, C.

Wickham & J. Wurtele, J. Geophys. Res. 118 5280-5286 (2013), ‘Decadal variations in the global

atmospheric land temperatures,’

http://static.berkeleyearth.org/pdf/berkeley-earth-decadal-variations.pdf

NAO, 2019, https://www.ldeo.columbia.edu/res/pi/NAO/

NAO, UEA, 2019, https://crudata.uea.ac.uk/cru/data/nao/nao.dat

NOAA, 2019, AAO,

https://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily ao index/aao/monthly.aao.index.

b79.current.ascii

NOAA, 2019, AO, https://www.ncdc.noaa.gov/teleconnections/ao/data.csv

NOAA, 2019, AMO, https://www.esrl.noaa.gov/psd/data/correlation/amon.us.long.mean.data

NOAA. 2019, Ocean Gyres, https://oceanservice.noaa.gov/facts/gyre.html

NOAA, 2019, Ocean Heat Content, https://www.ncdc.noaa.gov/cdr/oceanic/ocean-heat-content

NOAA, 2019, Ekman Transport, http://oceanmotion.org/html/background/ocean-in-motion.htm

Ocean-Gyres, 2019, https://oceancurrents.rsmas.miami.edu/ocean-gyres.html

Petit, J. R.; J. Jouzel, D. Raynaud, N. I. Barkov, J.-M. Barnola, I. Basile,M. Bender, J. Chappellaz,

M. Davisk, G. Delaygue, M. Delmotte, V. M. Kotlyakov, M. Legrand, V. Y. Lipenkov, C. Lorius,

L. Pe´ pin, C. Ritz, E. Saltzmank and M. Stievenard, Nature 399 429-436 (1999), ‘Climate and

atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica.’

Shaman, J.; R. M. Samelson and E. Skyllingstad, J. Climate 23 2651-70 (2010) DOI:

10.1175/2010JCLI3269.1, ‘Air–Sea Fluxes over the Gulf Stream Region: Atmospheric Controls

and Trends’, https://journals.ametsoc.org/doi/pdf/10.1175/2010JCLI3269.1

SILSO, 2019, http://www.sidc.be/silso/datafiles

SOI, 2019, ftp://ftp.bom.gov.au/anon/home/ncc/www/sco/soi/soiplaintext.html

Svensmark, H.; T. Bondo & J. Svensmark, Geophys. Res. Letts. 36 L15101 pp1-4 (2009), ‘Cosmic

ray decreases affect atmospheric aerosols and clouds’

Svensmark, H.; M. B. Enghoff, N. J. Shaviv & J. Svensmark, Nature Communications 8:2199

doi:10.1038/s41467-017-02082-2 (2017), Increased ionization supports growth of aerosols into

cloud condensation nuclei’ https://www.nature.com/articles/s41467-017-02082-2

Taylor, F. W., Elementary Climate Physics, Oxford University Press, Oxford, 2006, Chapter 7

UAH, TLT, 2019, https://www.nsstc.uah.edu/data/msu/v6.0/tlt/uahncdc_lt_6.0.txt


60

Varadi, F.; B. Runnegar & M. Ghil, Astrophys. J. 562 620-630 (2003), ‘Successive refinements in

long term integrations of planetary orbits’

VIRGO, 2017, SOHO Satellite VIRO Radiometer Data,

http://www.pmodwrc.ch/pmod.php?topic=tsi/virgo/proj_space_virgo#VIRGO_Radiometry

Wilson, R. C., Astrophys Space Sci DOI 10.1007/s10509-014-1961-4, pp 1-14 (2014), ‘ACRIM3

and the Total Solar Irradiance database’

https://www.researchgate.net/publication/262376602 ACRIM3 and the Total Solar Irradiance

database/download

WWT Paleoclimate, 2018, https://wattsupwiththat.com/paleoclimate/

Yu, L., J. Climate, 20(21) 5376-5390 (2007), ‘Global variations in oceanic evaporation (1958-

2005): The role of the changing wind speed’

Yu, L., Jin, X. and Weller R. A., OAFlux Project Technical Report (OA-2008-01) Jan 2008,

‘Multidecade Global Flux Datasets from the Objectively Analyzed Air-sea Fluxes (OAFlux)

Project: Latent and Sensible Heat Fluxes, Ocean Evaporation, and Related Surface Meteorological

Variables’ http://oaflux.whoi.edu/publications.html

Zachos, J.; M. Pagani, L. Sloan, E. Thomas and K. Billups, Science 292 686-689 (2001),

‘Trends, rhythms and aberrations in the global climate, 65 Ma to present’

A DYNAMIC COUPLED THERMAL RESERVOIR APPROACH TO...

Documents

Transcript of A DYNAMIC COUPLED THERMAL RESERVOIR APPROACH TO...