THE MECHANISMS OF CLIMATE CHANGE



Ventura Photonics Climate Post 008.1 Feb. 27, 2022


Roy Clark





PREFACE



Simple inspection of the climate record and time dependent thermal engineering calculations of the earth’s surface temperature both demonstrate that the observed increases in atmospheric CO2 concentration over the last 200 years have had no effect on the earth’s climate. There is no ‘equilibrium climate state’ that can be perturbed by an increase in atmospheric CO2 concentration. The whole equilibrium argument based on forcings, feedbacks and a ‘climate sensitivity’ to CO2 is pseudoscientific nonsense. There is no ‘climate emergency’. Eisenhower’s warning about the corruption of science by government funding has come true. Our so called climate ‘scientists’ are trapped in a web of lies of their own making. They have abandoned the Law of Physics and become Prophets of the Imperial Cult of the Global Warming Apocalypse. Irrational belief in the results of completely fraudulent climate models has replaced scientific observation and reason.


The troposphere is an open cycle heat engine that transports absorbed solar heat from the surface to the middle troposphere by moist convection. This is a mass transport process that is coupled to both the gravitational field and the rotation of the earth. These interactions produce the earth’s weather patterns. The long wave IR (LWIR) flux in the troposphere is fully coupled to this mass transport and cannot be separated and analyzed independently of the other energy transfer processes. Climate change is caused by subtle changes in the rates of heating and cooling of the surface thermal reservoirs, particularly the oceans. The role of the wind speed, both in ocean evaporation and the determination of the ocean gyre velocity cannot be neglected. Similarly, the penetration depth of the solar insolation into the oceans is wavelength dependent. This must also be included in any realistic analysis of climate change.


The earth is a sphere that is illuminated by an almost collimated beam of electromagnetic radiation from the sun. Maximum solar insolation occurs at low latitudes in the tropics. The rate of heating exceeds the rate of cooling. The heat that is absorbed by the tropical oceans accumulates in the equatorial warm pools. From here it is circulated through the rest of the ocean gyres. At higher latitudes, the rate of cooling exceeds the rate of heating. Changes in zonal surface heating and cooling rates of the order of 0.15 W m-2 are sufficient to cycle the earth through an Ice Age. In this post, at least some of the mechanisms related to these longer term climate changes are examined. The main focus is on two areas that have been overlooked in equilibrium climate analysis. The first is the wavelength dependence of the coupling of the solar flux to the oceans. The second is the role of changing wind speed on the ocean surface cooling and the ocean gyre circulation. It is hoped that this discussion will help to re-establish the process of scientific observation and analysis in climate science and suggest areas for further study.



SUMMARY



The earth’s climate is always changing. Different change mechanisms operate on different time scales. Over geological time scales, 1 to 100 million years or more, climate change is produced by plate tectonics. The ocean circulation changes as the continents move and the ocean boundaries shift. The climate cools as more ocean water is circulated near the poles. Over the 10,000 to 100,000 year time scale, planetary perturbations, mainly by Jupiter and Saturn alter the orbital eccentricity, axial tilt and precession of the earth. These are known as Milankovitch cycles. At present, the dominant term is the change in eccentricity which cycles the earth through an Ice Age in about 100,000 years. The Milankovitch cycles do not change the average annual solar flux reaching the earth. The axial tilt variation changes the solar flux intensity at different latitudes. The eccentricity changes the solar intensity by changing the sun-earth distance along the minor axis of the orbit. However, the orbital velocity increases as the earth moves closer to the sun according to Kepler’s laws. This compensates for the change in intensity. Precession changes the time of perihelion relative to the seasons. This is caused by a ‘wobble’ in the earth’s rotation axis. The sun is also a slightly variable star over time scales near 1000 years. Small changes in solar insolation as measured by sunspot activity and other solar parameters have produced the climate changes known as the Minoan, Roman, Medieval and Modern warming periods and the Maunder minimum or Little Ice Age.


On shorter time scales, climate change is caused by quasi-periodic variations in ocean surface temperatures known as ocean oscillations. The downward LWIR flux from the lower troposphere interacts with the upward LWIR flux from the surface to produce a partial LWIR exchange energy. In order to dissipate the absorbed solar flux, the surface warms up so that the excess heat is removed by moist convection. This is the real cause of the so called ‘greenhouse effect’. Over the oceans, the bulk ocean temperature increases until wind driven evaporation at the surface removes the excess heat. There is no requirement for an exact flux balance between the solar heating and the wind driven cooling. This produces quasi-periodic ocean oscillations on different time scales. The Atlantic Multi-decadal Oscillation (AMO) and the Pacific Decadal oscillation (PDO) have periods in the 60 to 70 year range. There are also changes on the 15 to 25 year time scale. The El Nino Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) are short period oscillations in the 3 to 7 year range. In signal processing terms, the ocean oscillations produce a ‘noise floor’ of quasi-random temperature fluctuations.


In the early 1860’s, Tyndall speculated that Ice Ages could be caused by changes in atmospheric CO2 concentration. This led to the scientific dogma that increases in the atmospheric concentration of CO2 produced by fossil fuel combustion could cause climate warming. This argument is based on the invalid assumption of an equilibrium average climate. Simple inspection of the climate record shows that there is no relationship the surface temperature and the CO2 concentration. A thermal engineering calculation of the change in surface temperature produced by the increase in the CO2 related downward LWIR flux from the lower troposphere to the surface requires a time dependent thermal analysis. There are four main flux terms, the absorbed solar flux, the net LWIR flux, the moist convection or evapotranspiration and the subsurface thermal transport. These terms are interactive and any increase in the downward LWIR flux to the surface cannot be separated and analyzed independently of the other flux terms. The increase in surface temperature produced by the increase the downward LWIR flux from CO2 is too small to measure. Within the troposphere, the temperature variations from convection, including air compression from downslope winds and ‘blocking’ high pressure systems overwhelm any change in temperature produced by increased absorption from CO2. Similarly, over the oceans, the normal variation in wind driven latent heat flux overwhelms any change in surface temperature from CO2 induced LWIR flux changes. Over land, the normal variation in the diurnal transition temperature is too large for any change in surface temperature from CO2 to be detected. The concepts of radiative forcing, water vapor feedbacks and climate sensitivity to CO2 incorporated into the equilibrium climate models are pseudoscientific nonsense. In particular, the latest warming phase of the AMO has been misinterpreted as a CO2 induced warming signal.


The issue therefore is how do small changes in solar flux intensity and distribution produce the observed climate changes?



1.0 INTRODUCTION



The earth reached its maximum climate temperature or glacial minimum in the current Ice Age cycle about 6000 years ago and is now cooling. However, this has been a ‘roller coaster ride’ with a series of peaks superimposed on top of the temperature decrease. These peaks have coincided with changes in human civilization related to the Minoan, Roman and Medieval warming periods [Alley, 2000, AMO, 2020]. This is illustrated in Figure 1. The cause of these changes is small variations in the solar insolation related to sunspot activity and other measures of the solar flux reaching the earth. The atmospheric concentration of CO2 did not increase significantly until after the start of the industrial revolution about 200 years ago [EPICA, 2008, Keeling, 2020]. There is no reason to expect that CO2 suddenly became a major driver of the earth’s climate. Instead, recent climate warming can be explained by variations in the solar flux combined with changes in ocean surface temperatures related to ocean oscillations. However, the climate energy transfer processes involved are complex and include the effects of changes in wind speed on ocean evaporation and the ocean gyre circulation. Unfortunately, these processes have been ignored or oversimplified through the continued use of the invalid equilibrium climate assumption and related concepts. This creates CO2 induced global warming, by definition as a mathematical artifact in the equilibrium climate models. The climate modeling fraud is discussed in detail in other posts on this site [See Research Pages 1 through 7]. Since it is clear that changes in the atmospheric CO2 concentration cannot cause the observed climate changes, the question that needs to be addressed is: how do rather small changes in the solar flux and flux distribution influence the earth’s climate?





Figure 1: 6000 years of climate cooling, a) Ruins of Hvalsey Church, Greenland. This region was inhabited by Norse farmers during the medieval warm period from approximately 900 to 1400 AD [Shepherd, 2016]. b) Ice fair on the River Thames near London Bridge, 1677. c) Temperature proxy data from the GISP ice core, Greenland [Alley, 2000], with AMO anomaly data set added [AMO, 2020]. d) Atmospheric CO2 concentration from EPICA ice core data, Antarctica [EPICA, 2020] with the modern Keeling data added for reference [Keeling, 2020].



The earth is not in thermal equilibrium. The surface temperature does not respond immediately to the change in solar flux. There are diurnal and seasonal time delays or phase shifts between the peak solar flux and the temperature response of the various thermal reservoirs in the climate system that are characteristic of non-equilibrium thermal transfer. The absorbed solar heat is stored and released over a wide range of time scales. Over the oceans, approximately half of the solar flux is absorbed within the first meter layer of the ocean and 90% is absorbed within the first 10 m layer [Hale and Querry, 1973]. The ocean surface is almost transparent to the solar flux. The oceans are cooled at the surface by a combination of net long wave IR (LWIR) emission, wind driven evaporation (latent heat flux) and sensible heat flux (dry convection). In order to dissipate the absorbed solar heat, the bulk ocean temperature increases until the water vapor pressure is sufficient for the excess heat to be removed by wind driven evaporation. The cooler water produced at the surface sinks and is replaced by warmer water from the bulk ocean below. This establishes a Rayleigh-Benard type of convection with columns of warm and cool water moving in opposite directions. In addition, ocean water is circulated through the ocean basins by the wind driven ocean gyre circulation. These energy transfer processes are illustrated in Figure 2. There is no requirement for an exact flux balance on any time scale. A local change in ocean surface temperature requires a change in the local rates of heating and/or cooling. Natural variations in wind speed produce quasi-periodic oscillations within the ocean gyre circulation. These include the Atlantic Multi-decadal Oscillation (AMO) with a period in the 60 to 70 year range, the Pacific Decadal Oscillation (PDO) with periods in the 50 to 70 and 15 to 25 year range. There are also short term oscillations in the 3 to 7 year range including the El Nino Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD). The ocean gyre circulation and the four main ocean oscillations are shown in Figure 3 [AMO, 2020, PDO, 2020, ENSO, 2020, IOD, 2020].





Figure 2: Ocean surface energy transfer (schematic)



The small changes in solar flux produced by variations in solar activity related to sunspots and other solar parameters occur mainly in the blue and UV regions of the solar spectrum, [Harvey, 1997, Lean, 2000, Lean and DeLand, 2012]. The shorter wavelength UV radiation is absorbed by ozone in the stratosphere [Huffman, 1985]. The UV flux at wavelengths below 300 nm does not reach the surface. The ‘pristine’ ocean has maximum transmission in the blue green region of the spectrum near 475 nm [Hale and Querry, 1973]. This means that the increase in solar flux that reaches the ocean surface can be absorbed and the solar heat can accumulate below the ocean surface. In addition, changes in ocean surface temperature produce changes in evaporation. Water vapor in the troposphere absorbs near IR (NIR) solar radiation and this can both heat the troposphere and reduce the solar flux reaching the ocean surface, (see Figure 7, below) [ASTM, 2012, Collins et al, 2006]. Furthermore, almost all of the solar flux in the 700 to 2000 nm region is absorbed close to the ocean surface where it is coupled to the wind driven evaporation. The ocean heating effects produced by small changes in the solar flux are therefore complex.


The Milankovitch cycles also produce changes in the rates of heating and cooling of the oceans. As the axial tilt increases, the rate of solar heating near the equator decreases slightly and the rate of heating increases at high latitudes. An increase in eccentricity produces an increase in the solar flux near perihelion (closest approach to the sun) and a decrease in the solar near aphelion (furthest distance from the sun). However, there also changes in orbital velocity related to Kepler’s laws that alter the lengths of the seasons so that the total solar flux at TOA over the year does not change. At present the eccentricity is near 0.0167 and the difference in the solar flux at TOA between perihelion and aphelion is near ±45 W m-2. The precession or ‘wobble’ of the earth’s rotation axis means that the timing of perihelion relative to the seasons changes. At present, the earth reaches perihelion on January 5. This is close to summer solstice in the S. hemisphere [Milankovitch, 1920, Milankovitch cycles, 2021.





Figure 3: The ocean gyre circulation and the four main ocean oscillations (schematic).



In order to understand how the change in solar activity and the Milankovitch cycles change the earth’s climate it is necessary to consider the coupling of the solar flux to the oceans in some detail, including the wavelength dependence. In addition to changes to the solar heating, it is also necessary to consider changes to the wind driven rates of evaporation. These include indirect contributions from changes to ozone heating by UV absorption and the effects of near IR absorption of the solar flux in the troposphere. The rates of heating and cooling at the ocean surface are then simulated using a simple parametric approach that can be used to investigate the effects of changes in ocean heating and cooling on ocean temperatures.


In Section 2 of this post, the solar illumination of the earth and the changes in solar flux related to both solar activity and the Milankovitch cycles are described. In Section 3, the observed changes in ocean temperatures are presented. First, the seasonal and diurnal changes in ocean are illustrated using selected Argo float and TRITON buoy data. Second, the observed changes in ocean surface temperature since 1900 are considered, including the variation in the ENSO and AMO. In Section 4, the coupling of the solar flux into the oceans and the changes in the wind driven latent heat flux are considered in more detail. The results from a simple ocean energy transfer model at 5 latitudes, 0°, 15°, 30°, 45° and 60° are presented, including the phase shifts. To start, a baseline model with a circular orbit and an axial tilt of 23.5° is used. The effects of changes in axial tilt and eccentricity/precession are then considered as modifications to the baseline model. The resulting changes in ocean temperatures and energy transfer are considered, including the phase shift. Other mechanisms of climate change, cosmic ray cloud seeding and the faint young sun paradox are briefly considered in Section 5. Conclusions and references follow.



2.0 THE SOLAR ILLUMINATION OF THE EARTH



The earth is in an almost circular orbit around a rather ordinary, slightly variable G2 type star, the sun. At present, the orbital eccentricity is 0.0167 and the axial tilt is 23.44°. The eccentricity changes the solar flux at the top of the atmosphere (TOA) by approximately ±45 W m-2. The peak intensity at perihelion (closest approach) occurs in early January. The orbital and axial parameters are perturbed by other planets, mainly Jupiter. The eccentricity varies from 0.00055 to 0.0679 and the tilt varies from 22.1 and 24.5°. The variations with time are known as Milankovitch cycles. In the recent geological past, for about the last million years, the change in eccentricity has produced an Ice Age with a period of approximately 100,000 years. Prior to this, the Ice Age period followed the 41,000 year obliquity or tilt cycle [Lisiecki and Raymo, 2005].


2.1 The Seasonal Variation in the Solar Flux


The seasonal variation in the total cumulative daily ‘clear sky’ solar flux (MJ m-2 day-1) produced by the axial tilt is shown in Figure 4 for selected latitudes in the N. Hemisphere [IEEE, 1993]. Near the equator, the peak solar flux is reached at the equinox points. At higher latitudes the peak occurs at summer solstice. Although the peak solar flux at noon is lower higher latitudes, the length of the day at summer solstice is longer, so the daily cumulative flux remains high. The total annual cumulative ‘clear sky’ flux (MJ m-2 yr-1) vs. latitude is shown in Figure 5. This decreases from approximately 9000 MJ m-2 yr-1 near the equator to 3000 MJ m-2 yr-1 at 75° latitude. Approximately half of the total solar flux is contained within the ±30° latitude bands. This is illustrated in Figure 6a. The solar flux is illuminating a sphere, so the surface area also decreases with latitude. Half of the surface area is contained within the ±30° latitude bands and 70% of the surface area falls within the ±45° latitude bands. This is illustrated in Figure 6b. This simple ‘clear sky’ illumination analysis shows that any small increase in the solar flux from solar activity should accumulate initially in the tropics. However, the warm water in the equatorial warm pools is coupled to the ocean gyre circulation and some is transported to higher latitudes along the western continental boundary currents. Climate change has to be analyzed by considering the effects of the changes in solar insolation at all latitudes, not just at 65 N as considered by Milankovitch.





Figure 4: The seasonal variation in the total cumulative daily ‘clear sky’ solar flux at selected latitudes. For reference, a daily flux of 25 MJ m-2 day-1 corresponds to a 24 hour average solar flux of 289.4 W m-2.





Figure 5: The total annual cumulative ‘clear sky’ flux vs. latitude





Figure 6: a) The total annual cumulative ‘clear sky’ flux fraction vs. latitude and b) the cumulative surface area fraction of the earth vs. latitude.



2.1 The Spectral Distribution and Ocean Absorption of the Solar Flux


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 7 for wavelengths from 300 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 spectral regions. These heat the troposphere through direct absorption of the incident solar flux [Collins et al, 2006]. 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 8 [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.





Figure 7: Top of atmosphere and AM 1.0 solar spectral irradiances from 200 to 2000 nm.





Figure 8: Penetration depth into water and ‘pristine’ ocean from 300 to 800 nm.



2.2 The Change in Solar Flux Produced by the Sunspot Cycle


Most sunspot induced changes in the solar flux occur at shorter wavelengths. Figure 9 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 was estimated to be 1.2 W m-2. While the percentage changes are higher at shorter UV wavelengths, the irradiances are much lower. Figure 10 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 ocean depths in the 50 to 100 m range. While the flux changes are quite small, they can accumulate in the oceans over long periods of time. They may also influence stratospheric temperatures and ozone concentrations.





Figure 9: 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].





Figure 10: Spectral overlap of a) solar flux sunspot variation, from Figure 9b, b) TOA and atmospheric AM 1.0 solar flux, and c) ocean penetration depth.



2.3 The Change in Total Solar Flux at TOA produced by the Sunspot Cycle.


Based on VIRGO satellite radiometer data, the change in total solar insolation (TSI) at TOA may be estimated by dividing the original (Version 1) annual sunspot numbers by 100. This is illustrated in Figure 11 for solar cycles 23 and 24 [VIRGO, 2021]. A new Version 2 sunspot index has been introduced that is approximately 1.6 times larger than the original one [SILSO, 2020]. This has increased the scale factor from 100 to 160 for the new index. The SILSO index from 1700 is shown in Figure 12. The estimated change in TSI is shown in Figure 13a and the cumulative change is shown in Figure 13b.





Figure 11: a) VIRGO radiometer data and b) the V1 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.





Figure 12: SILSO annual sunspot index from 1700





Figure 13: a) change in TSI from 1850 estimated from Figure 12 and b) cumulative change in flux from a).



2.4 The Change in Solar Flux at the Earth’s Surface and the Ocean Temperature Rise


Figure 13 gives the change in TSI at TOA. This has to be converted to an estimate of the change in solar flux at the earth’s surface. The change in annual solar flux at the earth’s surface for a 1 W m-2 change in TSI at TOA may be estimated for ‘clear sky’ conditions by dividing the total annual cumulative flux from Figure 5 at each latitude by the solar ‘constant’, 1365 W m-2. This gives the change in annual cumulative flux at the surface in MJ m-2 produced by a 1 W m-2 increment in the solar flux at TOA. This scale factor may then be used to convert the flux estimates from Figure 13a to annual changes in surface flux. These values for each year may then be added to give the total cumulative surface flux vs. latitude due to the sunspot TSI changes from 1850. This is shown in Figure 14a. This is still for clear sky conditions. These values have to be reduced to account for the earth’s albedo or reflectivity near 0.3 and the additional attenuation of the short wavelength radiation compares to the TSI. This was estimated to be near 0.5 based on the ASTM solar data. The total reduction factor is 0.7 x 0.5 = 0.35. It is then assumed that the flux is coupled into an ocean depth of 100 m with a heat capacity of 420 MJ K-1 for a 1 m2 water column. The estimated ocean temperature increase from 1850 vs. latitude is shown in Figure 14b. These values are rather approximate, but they show that the increase in TSI flux from the observed sunspot activity is sufficient to produce an observable increase in ocean temperature.





Figure 14: a) estimated increase in total cumulative ‘clear sky’ solar flux at the surface from 1850 scaled from the change in the sunspot index and b) estimated increase in ocean surface temperature produce by the flux shown in a).



The change in solar flux produced by the sunspot index and other measures of solar activity is an area of active research and a wide range of values have been published. Connolley et al [2021] provide 8 ‘low’ and 8 ‘high’ sets of estimates. However, ocean temperatures are the result of the interaction of all of the flux terms at the surface, not just the solar heating. In particular changes in wind driven evaporation are also an important factor in setting ocean temperatures. As shown above in Figure 3, changes in ocean temperatures caused by ocean oscillations are ocean basin specific. In particular, for the AMO, part of the S. Atlantic equatorial current is diverted northwards off the coast of Brazil and is coupled to the N. Atlantic gyre circulation.


2.5 Milankovitch Cycles and Ice Ages


The orbital and axial parameters of the earth are perturbed by motions of the other planets, mainly Jupiter. There are three perturbations. These are the changes to the eccentricity of the earth’s orbit around the sun, and changes to the axial tilt (obliquity) and orientation (precession) of the earth’s rotation. They are known as Milankovitch cycles [Milankovitch, 1920, Milankovitch Cycles, 2020, Laskar et al, 2010, La2020, 2021]. These change the distribution of the solar insolation reaching the earth at different times and latitudes during the year, but they do not significantly change the total cumulative annual solar flux reaching the earth at the top of the atmosphere. Figure 15 shows the various cycles from 800,000 years ago to 800,000 years ahead. Ice age cycles as indicated by delta 18O2 isotope ratios from ocean sediments and the Vostok ice core are also shown. The obliquity or axial tilt varies between 22.1 and 24.5° with a cycle of approximately 41,000 years. The current value is 23.44°. The eccentricity, e is the departure of the earth’s orbital shape from a circle. This varies with periods of 413,000, 95,000 and 125,000 years. The combination gives an approximate variation of 100,000 years. The values vary from 0.00055 (almost circular) to 0.0679. The earth’s orbital eccentricity is currently 0.0167. The major axis of the ellipse stays fixed. As the minor axis decreases, the intensity of the solar flux reaching the earth increases, but the orbital velocity also increases with decreasing distance. There is almost no overall change in the annual average solar flux reaching the earth. The precession is a ‘wobble’ of the earth’s rotation axis. It is given as the sine of the angle omega between the tilt orientation and the position of the vernal equinox on the tilt circle. This is then multiplied by the eccentricity to give the climatic precession. The period of the precession is near 26,000 years.





Figure 15: Milankovitch cycles for the last 800,000 years and projections for the next 800,000 years. The solar insolation at 65° N and Ice Age cycles based on isotope ratio proxies from ocean sediment and ice core data are also shown.



In the recent geological past, over the last million years, the dominant Ice Age term has been the 100,000 year eccentricity cycle. Before this, the Ice Ages followed the 41, 000 year obliquity cycle. This transition is shown in Figure 16 [Lisiecki and Raymo, 2005]. A major change in ocean circulation occurred approximately 3 million years ago with the formation of the Isthmus of Panama. This stopped the warm water equatorial flow from the Atlantic to the Pacific Oceans and diverted it to the Arctic along the E. Coast of N. America as part of the N. Atlantic Ocean gyre. This produced a significant climate cooling.





Figure 16: Ice Age cycles for the last 5 million years based on delta 18O2 isotope ratios from benthic formanifera in deep drilled ocean sediment cores.



The combination of the Milankovitch cycles changes the solar insolation at different latitudes and over the seasons. Usually the change in solar insolation at 65° N is considered as an indicator of the Ice Age cycles. This is an oversimplification of the complex interactions between the changes in solar flux and the ocean gyre circulation. Figure 17 shows the changes in total ‘clear sky’ solar flux at selected latitudes as the obliquity or axial tilt is increased from 22.6° to 24.2°. Figure 18 shows the changes in total ‘clear sky’ solar flux at selected latitudes for the current value of the eccentricity, 0.0167 relative to a circular orbit, e = 0.00. The maximum increase in flux is adjusted to January 5, to match the current date of perihelion or closest approach. The maximum increase in flux is nearly coincident with the S. hemisphere summer solstice. The changes for the two hemispheres are shown separately.





Figure 17: Changes in cumulative daily ‘clear sky’ solar flux at selected northern latitudes as the obliquity or axial tilt is increased from 22.6° to 24.2°. The changes are the same in both hemispheres although the seasons are reversed in the S. Hemisphere.





Figure 18: Changes in cumulative daily ‘clear sky’ solar flux at selected latitudes produced by the current eccentricity and precession values. The N. and S. hemispheres are shown separately. The eccentricity is 0.0167 and perihelion or closest approach is January 5 th.



The Ice Age cycle involves some rather subtle changes to the rates of heating and cooling of the oceans over tens of thousands of years. At the last glacial maximum, sea level was approximately 120 meters lower than it is now and the water was stored as fresh water ice in sheets over 2 km thick at higher latitudes [Lambeck, 2004]. The amount of heat required to melt a 120 m column of ice, with a cross section of 1 m2 and then heat the meltwater to 15 C is approximately 4.8x104 MJ m-2. Over 10,000 years, this requires an increase in global flux coupled into the oceans of approximately 0.15 W m-2. In order to even begin to understand the changes in heating and cooling rates involved, it is necessary to examine the spectrally resolved energy transfer processes in more detail. The absorption of the solar flux at different depths is shown in Figure 19. Almost all of the NIR flux is absorbed close to the surface, within the first 1m layer. Only 20% of the shorter wavelength solar flux is absorbed in this layer. This means that the NIR solar flux dominates the near surface ocean heating and the heat produced here is removed first by the cooling processes that occur at the surface. It is only the shorter wavelengths that can penetrate to lower depths where the heat can accumulate.





Figure 19: Absorbed fraction of the solar flux vs wavelength at selected depths.



3.0 OBSERVED OCEAN TEMPERATURE CHANGES



Ocean surface temperatures are dynamic. They depend on the local balance between the solar heating and the surface cooling. There is no requirement for an exact local flux balance between ocean heating and cooling on any time scale. The dominant cooling term is usually the wind driven evaporation or latent heat flux. Outside of the tropics, during spring and summer, the solar heating exceeds the wind driven cooling. The lower subsurface layers are not coupled to the surface by convective mixing and a stable thermal gradient is established. During the fall and winter, the wind driven evaporation exceeds the solar heating and the surface temperatures cool and establish a uniform temperature layer down to 100 m or lower. There is a significant time delay or phase shift of 4 to 8 weeks between the solstice and the ocean max/min temperature response. At low latitudes near the equator, in the eastern Atlantic and Pacific Oceans, the diurnal and seasonal temperature variations are not sufficient to mix the subsurface layers below the 25 to 50 m levels and heat can accumulate at these depths for extended periods. Heat continues to accumulate as the ocean water travels westwards with the Atlantic and Pacific equatorial currents. This leads to the formation of the equatorial ocean warm pool in the western Atlantic Ocean/Gulf of Mexico and the western Pacific Ocean. The ocean surface temperature increases until the wind driven evaporation balances the tropical solar heating. In the Pacific warm pool this occurs at a surface temperature near 30 C and an average wind speed near 5 m s-1. The seasonal changes in N. Atlantic Ocean temperatures are considered in more detail in Section 3.1.


In addition to the seasonal changes in ocean temperatures, wind speed variations also influence the diurnal temperature rise and phase shift. This is illustrated in Section 3.2 using TRITON buoy data at 156° E on the equator. Changes in wind speed also drive the ocean oscillations such as the ENSO and the AMO. This is considered as part of the changes in ocean surface temperatures from 1900 presented in Section 3.3. Additional mechanisms related to the Brewer Dobson flow that may also influence wind speed are described briefly in Section 3.4.


3.1 N. Atlantic Ocean Seasonal Ocean Temperatures from Argo Float Data


Figure 20 shows ocean temperatures from 2.5 to 200 m along the 20° W transect in the N. Atlantic Ocean from 60° to the equator at 10° latitude intervals. Monthly ocean temperature data for 2018 were downloaded from the Argo ocean atlas for 5° x 1° (latitude x longitude) strips centered at the selected locations. A map of the locations is also shown [Argo, 2020]. A summary of the maximum and minimum 2.5 m surface temperatures and the delta T, (max – min) for each latitude are shown in Figure 21.





Figure 20: Argo float data from 60° N to the equator along the 20° W transect.





Figure 21: Maximum, minimum and delta temperatures from Figure 20.



For latitudes from 20° to 60° N, the data show a winter surface temperature minimum in March or April. Summer solar heating then produces a stable stratified thermal layer structure with a surface temperature peak in August or September. The peak temperatures increase from 10 C at 60° N to 25 C at 20° N. The subsurface thermal layer structure collapses as the wind driven evaporative cooling in winter exceeds the solar heating. In addition, there is a significant time delay or phase shift between the peak solar flux and the peak surface temperature response.


At low latitudes, 0° and 10° N, there is no obvious summer temperature peak. These locations are influenced by the S. Atlantic equatorial current. The cooler water from the Benguela Current that that flows northwards along the west coast of Africa changes direction and flows westwards towards S. America. For 0° N, the surface temperature increases from approximately 27 to 29 C for the first 5 months of the year. It then decreases to approximately 24 C over the next 3 months and gradually warms up during the rest of the year. The May peak is produced by the summer solar heating in the S. Hemisphere.


3.2 Diurnal Temperature Changes in the Pacific Warm Pool at 156 E on the Equator.


The upper ocean layers are heated by the solar flux during the day and cooled continuously by the wind driven evaporation. The net LWIR and SH flux terms also add to the cooling. Figure 22 shows the air and 1.5 m surface temperature, 25 m temperature, relative humidity (%) scaled by 1/10, the wind speed, m s-1 and the solar flux (MJ m-2 hr-1) measured by the TRITON buoy located on the equator in the Pacific warm pool at 156° E for the 4 day period from July 10 to 14 th, 2010 [Clark, 2013].


During the 4 day period shown here, the wind speed increased from less than 1 m s-1 to over 7 m s-1. The diurnal temperature rise decreased from 1.1 C on July 10 th to 0.3 C on July 13 th. The phase shift or time delay between the peak solar flux and peak temperature response decreased from approximately 5 hours to 3. The latent heat flux was estimated from the wind speed assuming a sensitivity of 25 W m-2/m s-1 of the latent heat flux to the wind speed. This is based on long term TRITON buoy data [TRITON, 2021]. The estimated magnitude of the latent heat flux increased from 20 to over 150 W m-2. The negative sign indicates cooling. The daily flux terms are shown in Figure 23.





Figure 22: TRITON buoy data from the mooring at 156° E on the equator. Hourly data, for July 10 to 14, 2010 are shown. The upper plot gives the air temperature and ocean temperatures at 1.5 and 25 m depth. The middle trace shows the latent heat flux calculated from the latent heat flux term in Eqn. 3. The lower plot shows the relative humidity (%divided by 10), the wind speed, m s-1 and the solar flux MJ m-2 hr-1.





Figure 23: Average daily heat flux terms estimated from the data shown in Figure 22.



3.3 Trends in Ocean Surface Temperatures from 1900


Figure 24 shows the global, hemispheric and selected regional sea surface temperature (SST) anomaly changes from 1900 to 2006 for six different ocean SST databases from Kennedy et al, [2011], prepared as part of the analysis of the HadSST3 ocean surface temperature data series. The right panel shows the decadal temperature increases over selected time periods. The long term global and some of the regional decadal trends for 1900 to 1999 are near 0.06 C per decade. This is assumed to be the effect of the increase in solar flux due to sunspot related activity combined with other flux changes related to ocean oscillations and wind driven evaporation. For reference, 0.06 C per decade with a 100 m depth corresponds to an increase in heat flux of 0.08 W m-2 coupled into the oceans. The two regional data sets of interest here are the Nino 3.4 and the N. Atlantic basin. The surface temperature in the Nino 3.4 region is one of the data sets used to define the ENSO and the average surface temperature of the N. Atlantic basin is used to define the AMO. These will now be considered in more detail.







Figure 24: Global- and regional-average marine temperature anomalies 1900-2006 (relative to 1961-1990) from the ERSSTv3 analysis (green), HadSST2 (blue), MOHMAT (orange), Kaplan SST (purple), COBE (pink), ICOADS summaries (1941-2006 only, black) and HadSST3 (grey area). All data sets have been reduced to have the same coverage as HadSST3. The panels on the right show trends (°C/decade) for the periods: 1900-1999, 1940-1999, 1960-1999, 1970-1999 and 1980-1999 from the same data sets.



3.3.1 The El Nino Southern Oscillation (ENSO)


The ENSO is the change in ocean surface temperature in the Nino 3.4 region in the equatorial Pacific Ocean between 120° and 170° W and between 5° N and 5° S. Other definitions of the ENSO index are also used [Hanley et al, 2003]. There is a strong negative correlation between the ENSO and the Southern Oscillation Index (SOI). This is the surface air pressure difference between Tahiti and Darwin Australia. The SOI is a measure of the wind speed. As the wind speed increases, the equatorial current velocity increases and so does the wind driven evaporation or latent heat flux. Both effects produce ocean cooling. As the equatorial current velocity increases, the dwell time of a parcel of ocean water crossing the Pacific Ocean decreases. This decreases the amount of time available for solar heating during transit. The 13 month rolling average of the monthly ENSO data and the inverted, scaled (-0.086) SOI index are shown in Figure 25. The linear trend over the entire data set is 0.02 C per decade. The peak to peak ENSO temperature variation is near 3 C. The upper limit to the temperature of the equatorial Pacific warm pool is near 30 C. When the wind speed drops and the surface temperature starts to increase above 30 C, strong local thunderstorms are formed that reduce the SST [Eschenbach, 2010]. As the wind speed changes, the extent and location of the Pacific warm pool changes. The ENSO has a major impact on the Earth’s climate, mainly because of the changes in evaporation and rainfall. The ENSO (scaled) and the lower tropospheric temperature in the tropical region from UAH satellite microwave sounder data are shown in Figure 26 [UAH, 2021]. There is a time delay of approximately 6 months between the ENSO peak and the tropospheric temperature response.







Figure 25: 13 month rolling averages of the monthly ENSO index and the scaled SOI (-0.086). The temperature trend is 0.02 C per decade. The inset above shows the location of the Nino 3.4 region.





Figure 26: Scaled ENSO anomaly and the UAH tropical ocean lower troposphere temperature from satellite microwave sounders.



3.3.2 The Atlantic Multi-Decadal Oscillation (AMO)


The AMO is defined as the change in average surface temperature of the N. Atlantic basin. The annual average from 1856 is shown in Figure 27 [AMO, 2020]. There is an approximate linear increase in temperature of 0.03 C per decade. The oscillation based on a least squares fit from 1900 has an amplitude of 0.2 C and a period of 62 years. The AMO is associated with variations in the interaction between the Icelandic low and Azores high pressure systems. These interactions are complex. A tri-modal explanation has been proposed [Francombe et al, 2010]. The Azores high drives the equatorial current. The locations and the pressure difference between the high and low pressure systems determines the wind speed therefore the velocity of the easterly flow across the northern leg of the gyre. The interactions between the low pressure system and the Arctic circulation determines the coupling between the cooler Arctic Ocean (N. Atlantic subpolar gyre) and the N. Atlantic gyre. In addition, part of the S. Atlantic equatorial current is diverted northwards off the coast of Brazil and is coupled to the N. Atlantic Gyre. This is illustrated above in Figure 3.





Figure 27: The annual average of the AMO from 1856. The linear slope and the fit to the oscillation from 1900 are also shown.



3.3.3 The Effect of Wind Speed on the AMO


The effect of wind speed may be investigated by comparing the AMO to the North Atlantic Oscillation, (NAO) measured during the winter months. 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, cooling part of the 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. Conservation of angular momentum leads to an increase in angular velocity. Figure 28 shows the long term, 1958 to 2006 annual average zonal ocean surface temperatures (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. 28c, the seasonal change in wind speed is 6 m s-1 near 65° N and 4 m s-1 near 65° S. Figure 29 shows the global and N. winter (December to February) and S. Winter (Jun to Aug) evaporation patterns and Figure 30 shows the long term average pattern of ocean surface temperatures [Yu, 2007, Yu et al, 2008]. 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. The western boundary currents, the Gulf Stream and the Japan Current transport water from the equatorial warm pools to higher latitudes. Here the water cools as it is circulated through the northern legs of the gyre circulation. 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, the NAO has its maximum influence during the winter months. Figure 31 shows the NAO index average for the winter months, December through February. A five year average is also shown. Figure 32a shows the cumulative plot from Figure 31 with a straight line fit added. Figure 32b shows the detrended plot from Fig. 32a. (The straight line has been subtracted). This has a similar profile to the AMO index. Figure 33 shows the detrended cumulative plot from Figure 32b scaled to match the annual AMO index [AMO, 2020]. The two plots matched more closely from 1930 onwards, so the fit was made using the more limited data set. The correlation coefficient was 0.6. This analysis shows that the winter cooling from the wind speed related to NAO is a major contributor to the AMO variation. Other, shorter term oscillations related to the subpolar gyre and the equatorial current also contribute to the AMO.





Figure 28: 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 [Yu et al, 2008].





Figure 29: a) global evaporation pattern, b) and c) N. and S. winter evaporation patterns. An evaporation rate of 100 cm per year corresponds to a latent heat flux of 78 W m-2.





Figure 30: Long term average (1958 to 2006) ocean surface temperatures.





Figure 31: NAO index from 1826, with 5 year average and linear trend added.





Figure 32: a) Cumulative plot of NAO and b) detrended plot (linear slope subtracted)





Figure 33: Detrended cumulative NAO plot scaled to match the 5 year average AMO Index.



3.4 Atmospheric Heating and Transport Effects (Brewer-Dobson Flow)


Part of the increase in UV flux from sunspot related solar activity is absorbed by ozone in the stratosphere. In addition, an increase ocean surface temperature produces an increase in evaporation and therefore an increase in tropospheric water vapor concentration. This in turn produces an increase in tropospheric heating and convection through the near IR (NIR) absorption of the solar flux by water vapor, especially at lower latitudes. This absorption is shown above in Figure 7. These factors can lead to an increase in stratospheric poleward transport known as the Brewer-Dobson circulation [Butchart, 2014]. In addition, the altitude of the flow may increase. Since the AMO is at least in part driven by the change in high latitude winter wind speed, this suggests that there may also be a general longer term increase in this wind speed related to an enhanced Brewer-Dobson circulation. This provides a plausible mechanism for an additional heating effect related to the increase in solar sunspot activity. As the polar air mass cools in winter the increase in air mass at higher altitudes descends to lower altitudes. Conservation of angular momentum with a reduced moment of inertia leads to a higher angular velocity and an increase in wind speed.


There may also be changes in the location of the various permanent or semi-permanent high and low pressure systems such as the Azores high. In addition, the equatorial counter currents that form the boundary between the N. and S. ocean basins are not located at the equator. At present this boundary is several degrees north. This may also change. Further study of these processes is needed.



4.0 OCEAN SURFACE ENERGY TRANSFER



The analysis of climate change requires the simulation of small and subtle variations in the rates of ocean heating and cooling over very long periods of time. The current Ice Age cycle is approximately 100,000 years. The starting point is that the changes in the solar flux distribution at TOA are well defined by the Milankovitch cycles. However, the energy transfer processes at the ocean surface are complex and there is no requirement for an exact balance between ocean heating and cooling on any time scale. The ocean-air interface is a turbulent boundary between two fluids that is difficult, or even impossible to analyze using a detailed fluid dynamics approach. The solutions to the non-linear equations are inherently unstable over the time scales involved [Lorenz, 1963]. In addition, there are quasi periodic ocean surface temperature changes or oscillations associated with specific ocean basins. These are produced by natural variations in wind driven surface evaporation (See Figure 3 above). For example, the ENSO is linked to the Southern Oscillation Index (SOI) and changes in wind speed of 2 meters per second that produce variations in latent flux of approximately 40 W m-2. These are at least two orders of magnitude larger than the long term flux distribution changes needed to cycle the earth through an Ice Age.


Unfortunately, climate ‘science’ has been dominated by the pseudoscientific dogma of radiative forcing in a fictional equilibrium average climate [Ramaswamy et al, 2019, IPCC, 2021, IPCC 2013]. The idea that changes in the atmospheric concentration of ‘greenhouse gases’ such as CO2 can cause climate change has now reached the status of a quasi-religious cult. Irrational belief in the results from invalid climate computer models has replaced scientific observation and reason. Ice ages are not caused by global changes in the atmospheric LWIR flux. Instead, they are caused by small changes in the relative distribution of the solar flux coupled into the oceans at different latitudes. The total annual solar flux at the top of the atmosphere does not change. In order to even begin to define the energy processes associated with long term climate change it is necessary to start over with a more realistic, latitude and time dependent description of the basic rates of heating and cooling involved. This is simply a return to the normal process of scientific hypothesis and iteration based on observation.


4.1 A Simple Ocean Energy Transfer Model


To start, a parametric energy transfer model was constructed that captured the coupling of the flux terms to the ocean with a basic thermal mixing algorithm. Ocean currents and effects such as ice melt were not included. The results from this model may be used to identify areas for further study including both measurements and model algorithms. The flux terms and mixing algorithms used in the model will now be described, followed by the results at selected latitudes.


4.1.1. The Solar Flux


The ‘clear sky’ solar flux reaching the surface was calculated using the algorithm from the IEEE Standard 738 for the solar heating of electrical power lines [IEEE, 1993, Clark, 2013]. This algorithm includes the solar declination angle or axial tilt as one of the inputs. The effects of orbital eccentricity were added as the fractional daily change in solar intensity determined from a calculation of the variation in solar-earth distance with eccentricity using the inverse square law and Keppler’s second law. The eccentricity was set to its current value of 0.0167 with perihelion on January 5 th. Solar intensity was also determined for perihelion on April 5 th, July 5th and October 5 th. The coupling of the solar flux into the ocean was determined from the spectral distribution of the solar flux at the surface for normal incidence using the AM0 spectral irradiance from Figure 7 and the ocean absorption vs. depth from Figure 8 (ASTM, 2012, Hale and Querry, 1973). The attenuation of the total solar intensity vs. depth is shown in Figure 34. The solar flux absorbed by the Nth ocean layer is given by:





Here, AN is the attenuation of the Nth layer with thickness XN and the incident solar flux at the surface is Qsun.


4.1.2 The Net LWIR and Sensible Heat Fluxes


The net LWIR flux, Qirnet, was calculated from Stefan’s law with a fixed term, Qirwin, added to describe the LWIR window transmission. The sensible heat flux, Qsh, was fixed at 5 W m-2.





4.1.3 The Latent Heat Flux


The wind driven evaporation is determined from the equation given by Yu et al [2008].


Qlat = klat(PTws – RhPTwa)U (Eqn. 3)


Here, klat is an empirical coupling coefficient, PTws is the saturated water vapor concentration at the surface temperature Ts, PTwa is the saturated water vapor concentration at the surface air temperature Ta, Rh is the relative humidity and U is the wind speed.


4.1.4 Ocean Layer Mixing


The warmer water produced by the solar heating and the cooler water produced at the surface are mixed by the Rayleigh-Benard convection. This is a complex fluid dynamic process that is difficult to simulate. A simple parametric mixing process was used in the model. The solar heating was calculated for each 1 m ocean layer. The cooling terms were coupled to the top 1 m layer. The ocean layers were mixed at the end of each 0.5 hour time step iteration. A 10 layer exponential diffusion mixing was first used to blend the layers. The layers were then mixed using a simple layer temperature algorithm. The cooler surface layers were mixed downward sequentially until the uniform mixed layer matched the temperature of the layer below. Since most of the solar flux was absorbed in the first layer, additional mixing of this layer was simulated by adjusting the solar absorption coefficients. This was needed to reduce the summer surface temperature rise, especially at higher latitudes. A fraction of the flux absorbed was removed from the first layer and distributed over the next 100 layers.


The long term zonal averages of ocean surface and air temperatures, latent heat flux, wind speed and sensible heat flux from Yu et al [2008] and the Argo data shown in Figures 20 and 28 above were used as guide to set the model parameters. The axial tilt was set to its current value of 23.5°. The model was adjusted to simulate, approximately the ocean surface temperatures at 0, 15, 30, 45 and 60° latitude. At each latitude, the model was adjusted so that the surface temperature after a 1 year model run returned to the starting value. The parameters used are summarized in Table 1. The model simulated diurnal and seasonal temperature changes and phase shifts. The mixing also simulated the summer stratification at higher latitudes. The baseline model at each latitude was then used as a probe to investigate the changes in temperature and flux terms produced by the variations in solar flux related to the Milankovitch cycles.


The axial declination was changed from 23.5° to 22.6° and 24.2°. An eccentricity of 0.0167 was then added to the model for four different precession cases. The solar intensity peak at perihelion was adjusted to occur at Jan. 5 th, April th, July 5th and October 5 th.





Table 1: Baseline model input parameters at the selected wavelengths



4.2 Baseline Ocean Model Results


The model ocean temperature results for the five selected latitudes at 1, 20, 30, 40 60 and 100 m depths are shown in Figures 34a through 34e. The time step is 0.5 hours. The insets show the diurnal temperature changes at higher resolution over a 10 day interval near the summer (or equinox) temperature peak. The daily average surface temperatures and flux terms are shown in Figures 35a through 35e. The flux terms are scaled to fit on the same plot as the temperature. The phase shift between the peak solar flux and the peak surface temperature is also indicated. The diurnal temperature cycle for day 81 is shown in Figures 36a through 36e. The peak of the solar flux and the latent heat flux are also shown, scaled to fit the temperature plot. The diurnal phase shift is indicated. The model results from these figures will now be discussed for each latitude in turn.









Figure 34: The model ocean temperature results for the five selected latitudes at 1, 20, 30, 40 60 and 100 m depths. The insets show the temperature detail on an enlarged time scale for a 10 day period as indicated. The time step is 0.5 hours.





Figure 35: Daily average temperatures and flux terms for the 365 day model runs at the five selected latitudes. The flux terms are scaled to fit the plots. The scale factors are shown on the plot legends. The seasonal phase shifts are also indicated.





Figure 36: The diurnal temperature cycles at the five latitudes for day 81 (vernal equinox). The latent heat flux and the phase shift are also shown. The flux terms are scale to fit the plot and the scale factors are indicate in the plot legends.



4.2.1 0° Latitude Results


At 0° latitude, the annual temperature changes are small. The maximum and minimum temperatures in the 0.5 hour data are 30.4 C and 29.9 C. There are two temperature peaks related to the maximum solar flux as the sun crosses the equator at the equinox points on days 81 and 264. The temperature peaks occur on days 118 and 302. The corresponding seasonal phase shifts are 37 and 38 days. Temperatures stay the same to 40 m depth. There is no seasonal stratification. The latent heat flux tracks the surface temperature. The diurnal temperature rise for day 81 is 0.36 C and the phase shift is 4 hours.


The model temperature variations are smaller than those observed in the equatorial warm pools. This is because the wind speed in the model is fixed at 6 m s-1. In the Pacific equatorial warm pool, the 1 sigma standard deviation of the wind speed is 2 m s-1. In addition, the model does not include the heating effects observed in the equatorial currents. Cooler ocean water from the eastern continental boundary currents in the Atlantic and Pacific Oceans turn westwards and become the N. and S. equatorial currents. In the eastern section of the equatorial currents, the wind driven evaporation is insufficient to remove the solar heat and the ocean water warms as it travels west. The seasonal variations from higher latitudes are reduced as the ocean water moves west and approaches the western equatorial warm pools.


4.2.2 15° Latitude Results


At 15° latitude there is a broad, almost flat solar flux peak because of the transition from the dual equatorial equinox peaks to the higher latitude single solstice peak. There are still 2 flux peaks at days 150 and 195 but the daily average solar flux at summer solstice only decreases by 0.15 W m-2. The peak daily average ocean surface temperature of 29.8 C occurs on day 247. The seasonal phase shift is 52 days from the second solar peak. The maximum and minimum temperatures in the 0.5 hour data are 30.1 C and 26.7 C. The seasonal stratification reaches a depth of 48 m. The latent heat flux tracks the surface temperature. The diurnal temperature rise for day 81 is 0.5 C and the phase shift is 3.8 hours.


4.2.3 30° Latitude Results


At 30° latitude there is a single peak in the solar flux at solstice. The maximum daily average ocean surface temperature of 29.8 C occurs on day 231. The seasonal phase shift is 59 days. The maximum and minimum temperatures in the 0.5 hour data are 25.9 C and 19.3 C. The seasonal stratification reaches a depth of 80 m. The diurnal temperature rise for day 81 is 0.34 C and the phase shift is 3.3 hours. At this latitude, based on Figure 28c, the wind speed was varied from 8 m s-1 on day 1 to a minimum of 6 m s-1 at summer solstice, day 172 and back to 8 m s-1 on day 365. A sine function based on the day of the year was used to vary the wind speed. This also changed the phase of the latent heat flux, so the peak LH flux was not reached until 21 days after the temperature peak.


4.2.4 45° Latitude Results


At 45° latitude the temperature profile is similar to the 30° latitude results except that the temperatures are reduced. The maximum daily average ocean surface temperature of 16.6 C occurs on day 230. The seasonal phase shift is 58 days. The maximum and minimum temperatures in the 0.5 hour data are 16.8 C and 10.0 C. The seasonal stratification reaches a depth of 85 m. The diurnal temperature rise for day 81 is 0.12 C and the phase shift is 4 hours. The starting wind speed was set to 10 m s-1 with a sinusoidal 3 m s-1 reduction to 7 m s-1 at summer solstice, increasing back to 10 m s-1 at the end of the year. Because of the variation in wind speed, the peak latent heat flux was reached 22 days after the temperature peak.


4.2.4 60° Latitude Results


At 60° latitude the temperature profile is again similar to the 30° and 45° latitude results except that the temperatures are reduced. The maximum daily average ocean surface temperature of 13.6 C occurs on day 228. The seasonal phase shift is 56 days. The maximum and minimum temperatures in the 0.5 hour data are 13.7 C and 6.9 C. The seasonal stratification reaches a depth of 82 m. The diurnal temperature rise for day 81 is 0.03 C and the phase shift is 3.5 hours. The starting wind speed was set to 10 m s-1 with a sinusoidal 3 m s-1 reduction to 7 m s-1 at summer solstice, increasing back to 10 m s-1 at the end of the year. Because of the variation in wind speed, the peak latent heat flux was reached 22 days after the temperature peak.



4.3 Changes in Axial Tilt (Obliquity)


The baseline models at the 5 latitudes with an axial tilt of 23.5° were rerun using tilts of 22.6° (t1) and 24.2° (t2). As the axial tilt is increased, the seasonal solar illumination time decreases slightly near the equator and increases at higher latitudes. Figure 37a through 37e show the annual daily average temperatures for the baseline and tilt runs (left) and the temperature differences, delta T (right). When the tilt angle is increased, there is an increase in the peak temperature at higher latitudes, 30° and above. There is also a slight cooling at low latitudes near the equator. Milankovitch, in his original analysis used the change in solar flux at 65° N as a measure of the effect of the change in axial tilt. However, there are changes in the solar flux distribution at all latitudes. In addition, the absorbed solar heat is also removed by the wind driven evaporation. Changes in the rates of both heating and cooling within the ocean gyre circulation have to be considered in any quantitative analysis of the effect of changes in axial tilt on the temperature of the earth. The simple model used here does not include any coupling to the polar ice sheet and the ocean gyre circulation is not considered.







Figure 37: Effect of changing the axial tilt angle from 22.6° (t1) to 24.2° (t2). The daily average temperatures at the five selected latitudes are shown on the left and the temperature differences relative to the 23.5° tilt baseline are shown on the right.



4.4 Changes in Precession


The baseline models at the 5 latitudes with an axial tilt of 23.5° were rerun with an eccentricity of 0.0167 added. This changed the solar flux at the surface by approximately ±3%. Four precession cases were run with the peak flux at perihelion (closest approach) set to Jan 5th, April 5th, July 5th and Oct 5th. These are labelled e1 through e4. The scale factors used to change the solar flux in the model are shown in Figure 39. Figure 40a through 40e show the annual daily average temperatures for the baseline and precession runs (left) and the temperature differences, delta T (right).


At the equator, the maximum temperature changes are near 0.2 C and occur in the e2 and e4 runs when the precession is aligned with the equinox points. At higher latitudes, this shifts to the e1 and e4 runs where the precession is aligned with the solstice points. The maximum temperature changes increase to 0.6 C. The pattern of the temperature changes is complex and will not be considered in detail. In general, interglacial or warm periods in the Ice Ages are associated with higher values of axial tilt and eccentricity and a precession alignment with the solstice [Best, 2016a, 2016b].





Figure 38: The scale factors used to change the solar flux for the eccentricity calculations.







Figure 39: The effect on daily average surface temperature of an ellipticity of 0.0167 with perihelions at Jan 5 th, Apr 5 th, July 5 th and Oct 5 th for the 5 selected latitudes. The temperatures, including the circular orbit baseline (e = 0.000) are shown on the left. The changes in temperature relative to the baseline are shown on the right.



5.0 OTHER CAUSES OF CLIMATE CHANGE



5.1 Cosmic Ray Cloud Seeding


Changes in cloud cover related to cosmic ray seeding have been proposed as a mechanism for climate change [Svensmark et al, 2021, 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/sublimation. 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 Sections 2.0 and 4.0 above. These do not involve changes in solar activity and should not be influenced by cosmic ray seeding.


5.2 The Faint Young Sun Paradox


During earlier geological times, approximately 2.5 billion years ago, the solar flux was only 80% of its current value. However, the geological record indicates that the earth was relatively warm at this time with occasional glaciation. This leads to the so called ‘faint young sun paradox’ [Goldblatt & Zahnle, 2011]. Using conventional equilibrium climate arguments, the earth should have been much cooler. In reality, the earth’s climate is determined mainly by ocean evaporation, not by the LWIR flux. If the wind speed is assumed to be the same, a simple scaling argument indicates that temperature of the equatorial warm pool would decrease from 30 to approximately 26 C. The climate would also depend on the location of the continents and the ocean circulation.



6.0 CONCLUSIONS



Some of the mechanisms of climate change related to variations solar activity and the Milankovitch cycles have been identified. In particular, the wavelength dependence of the solar flux coupled into the oceans and the effects of axial tilt, eccentricity and precession on the latitude and seasonal solar flux distribution have been considered. An increase in sunspot activity increases the solar flux in the blue and UV spectral regions. The oceans reach maximum transmission in the blue green region, so the increase in solar flux can be absorbed and accumulate below the ocean surface.


Some of the increase in UV flux, particularly at shorter wavelengths is absorbed by stratospheric ozone. The heating produced may increase the atmospheric Dobson flow to higher latitudes. As the Polar Regions cool in winter, this can lead to an increase in winter wind speed which in turn decreases the transit time of the ocean flow across the high latitude cooling section of the ocean gyres. This is just conservation of angular momentum. A shorter transit time reduces the cooling and may increase the ocean surface temperature within the gyre circulation. Changes in winter wind speed related to the NAO have been identified as a possible cause of the observed temperature changes in the AMO. In addition, the S. Atlantic equatorial current divides off the coast of Brazil and part of the flow is diverted northwards where it adds to the N. Atlantic warming.


The Milankovitch cycles involve changes in the axial tilt (obliquity) and eccentricity and precession of the earth’s orbital and axial rotation. These do not change the total annual solar flux reaching the earth. The variations in axial tilt change the latitude distribution of the solar flux. A higher axial tilt increase the summer ocean temperatures at higher latitudes. An increase in eccentricity increases the difference in solar insolation between perihelion and aphelion. The effects on ocean temperatures also depend on the precession or the relationship between perihelion and the seasonal temperature changes defined by the solstice and equinox points.


A simple ocean heating model was used to illustrate the basic properties of the ocean surface energy transfer including the effects of wind speed and the phase shifts between the peak solar flux and the temperature response. Historically, Milankovitch cycles have been evaluated using the change in solar insolation at 65° N. However, even the simple ocean model used here shows that the changes in flux produce changes in ocean temperatures at all latitudes. The accumulation of heat in the equatorial warm pools, the transfer of this heat to higher latitudes through the ocean gyre system and the cooling at higher latitudes are all part of the energy transfer processes that contribute to climate change. The effects of wind driven evaporation and the phase shift between the peak solar flux and the ocean temperature response are important parameters that should be included in the analysis.


At the last glacial maximum, sea level was approximately 120 m lower than it is today. The ocean water was stored as fresh water ice sheets at higher latitudes. A simple calculation of the amount of heat needed to melt this ice and warm the meltwater to 15 C shows that a change in flux to the oceans of 0.15 W m-2 over 10,000 years is sufficient to cycle the earth through an Ice Age.


The small changes in LWIR flux related to changes in the atmospheric CO2 concentration are fully coupled to the wind driven evaporation or latent heat flux. Any changes in ocean surface temperature from CO2 are too small to measure. The observed phase shifts are clear evidence of non-equilibrium thermal energy transfer. There are no radiative forcings or feedbacks, nor is there any ‘climate sensitivity’ to CO2.



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. He hopes that you will agree with them.



REFERENCES



Normally, the references given in an article of this nature would be almost exclusively to the peer reviewed literature, with limited references to websites that provide access to climate data. Unfortunately, climate science has been thoroughly corrupted by the global warming fraud. The peer review process has collapsed and been replaced by blatant cronyism. Many of the publications in ‘prestigious’ journals such as Nature, Science, PNAS and others that relate to climate modeling predictions of global warming are fraudulent and should never have been published. Consequently many of the important references given here are to website publications. This should not detract from the integrity of the information provided. Many of these website publications have received a more thorough review than they might have received through the traditional peer review process.


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