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This book starts from first principles and examines the energy transfer processes that determine the surface temperature at the land-air and ocean-air interfaces. The book is divided into 9 chapters with a total of 232 pages and 143 figures. An extensive index is also included.

Chapter 1, Introduction explains climate change over time including plate tectonics, Milankovitch cycles, sunspot cycle fluctuations and ocean oscillations. The concept of a control mechanism built into the diurnal cycle that limits the surface temperature change over a single day is then introduced.

Chapter 2, Climate Energy Transfer provides an overview of climate energy transfer. This starts with a discussion of climate equilibrium, climate energy balance and a comparison of the surface temperatures on the moon and the earth. The various climate energy transfer processes, the solar flux, the longwave IR (LWIR) radiation field in the atmosphere, the subsurface thermal transport and the evapotranspiration (moist convection) are then described. The convection transition temperature over land is introduced. This is the evening temperature at which the surface and surface air temperatures equalize. Convection stops and the surface then cools more slowly by net LWIR emission. The transition temperature is reset each day by the local weather system passing through. The dual role of water vapor in both heating and cooling the climate system is then explained. Finally, the meaning of the term ‘greenhouse effect’ is considered in the context of a time dependent non-equilibrium climate system. There can be no ‘greenhouse effect temperature’ of 33 K. The spectral distribution of the LWIR emitted to space at the top of the atmosphere does not define an ‘effective emission temperature’ of 255 K.

Chapter 3, Complexity Theory introduces the Lorenz equations and explains the diurnal cycle as a drifting attractor. State diagrams of the temperature and the LWIR vs. the solar flux are presented and the concept of a ‘restoring force’ within the dynamic equilibrium cycle is explained.

Chapter 4, A Quantitative Description of the Diurnal Cycle explains the surface flux balance equations needed to quantify the diurnal cycle over land and over the oceans. This includes the solar flux, the downward LWIR flux to the surface, the evapotranspiration (moist convection) and the subsurface thermal transport. The application of these equations to a series of data sets that illustrate various aspects of the energy transfer processes that determine the surface temperature is then introduced.

Chapter 5, Land Surface Temperatures applies the flux balance equations to four data sets that illustrate various aspects of the energy transfer processes at the land-air interface. First, the energy transfer processes related to a single diurnal cycle are considered using data from O’Neill, Neb. recorded August 13-14, 1953 as part of the Great Plains Turbulence Field Program. Second, seasonal changes in the diurnal cycles for arid desert conditions are analyzed using data from Desert Rock, Nevada recorded as part of the SURFRAD (Surface Radiation Budget) Network. Third, the onshore/offshore transition in S. California is analyzed using part of the 2008 data set recorded at a US DOE AmeriFlux monitoring site located in Limestone Canyon Regional Park near Irvine, California. Finally, two warming events produced by blocking high pressure systems over Woomera, S. Australia during December 2018 and 2019 are compared. The record high temperatures in 2019 were produced by the combination of a high IOD (Indian Ocean Dipole) index and a longer residence time over the Australian Bight.

Chapter 6, Ocean Surface Temperatures applies the flux balance equations to a data set containing monthly temperatures along the 20° W longitude transect in the N. Atlantic Ocean. Data are given at 13 depths from 2.5 to 200 m from 60° N to the equator, 0° N recorded at 10° intervals. The data are taken from the Argo Ocean Atlas. For reference, the data at 0° N are also compared with measurements from the PIRATA buoy at 0° N, 23° W. In order to account for the subsurface solar heating, a second thermal reservoir is added to the thermal analysis. Ocean flow effects are also considered. In addition, the 20 year (2000 to 2019) averages of daily solar, latent heat, net IR, sensible heat and net heat flux terms are discussed. These are derived from TRITON buoy data for 10 buoys moored along the equator in the S. Pacific equatorial current.

Chapter 7, The Coupling of Ocean Temperatures to the Diurnal Cycle over Land explains the mechanism that couples variations in ocean temperatures to the weather station record through changes to the convection transition temperature. Almost all of the absorbed solar heat over land is dissipated in the same diurnal cycle in which it is produced. The observed seasonal phase shifts and the longer term changes related to ocean oscillations are considered. Thirty year daily climate averages are used to show the seasonal phase shifts in selected US weather station data in California and in the continental US near 35°, 40° and 45° latitudes. The coupling of the Pacific Decadal Oscillation (PDO) to selected California weather stations and the coupling of the Atlantic Multi-decadal Oscillation (AMO) to selected UK weather stations is explained. Such ocean oscillations may be used, with caution, as a reference baseline to detect urban heat island (UHI) effects and other biases in the weather station data. The coupling of the AMO to the global mean temperature record accounts for most of the warming found in the HadCRUT4 data set. The role of other bias effects including UHI, changes to the urban/rural station mix and ‘homogenization’ require further investigation.

Chapter 8, The Effect of an Increase in the Atmospheric Concentration of Carbon Dioxide on the Diurnal Cycle considers the possible influence of CO₂ on the surface temperature. The decrease in long wave IR (LWIR) flux at the top of the atmosphere (TOA) or ‘radiative forcing’ produced by a doubling of the CO₂ concentration does not couple to the surface and cannot cause any measurable change in surface temperature. The decrease in LWIR flux at TOA is produced by small changes in absorption at many different levels in the atmosphere. The maximum change in the local rate of cooling in the troposphere is a slight warming of +0.08 K per day. At an average lapse rate of -6.5 K km^-1, an increase of +0.08 K is produced by a decrease in altitude of about 12 meters. This is equivalent to riding an elevator down four floors. The slight heating of the troposphere is dissipated by wideband LWIR emission to space. The ‘radiative forcing’ produced by an increase in ‘greenhouse gas concentration’ does not change the energy balance of the earth. There is also a small increase in the downward LWIR flux to the surface. Over the oceans the penetration depth of the LWIR flux into the surface layer is less than 100 micron (0.004 inches). Here it is fully coupled to the wind driven ocean evaporation. Within the ±30° latitude bands, the sensitivity of the latent heat flux to the wind speed is at least 15 W m^-2/m s^-1. The increase in downward LWIR flux to the surface produced by the observed 140 ppm increase in atmospheric CO₂ concentration is approximately 2 W m^-2. Within the ±30° latitude bands, this is dissipated by an increase in wind speed near 13 cm s^-1. The average increase in CO₂ concentration at present is near 2.4 ppm. This corresponds to an annual increase of 0.034 W m^-2 in the downward LWIR flux to the surface which is dissipated by an increase in wind speed near 2 millimeters per second. Any change in ocean temperature produced by the current annual increase in the atmospheric CO₂ concentration is too small to measure. Furthermore, the increase in CO₂ concentration has had no effect on ‘extreme weather events’. When the 2 W m^-2 increase in downward LWIR flux to the surface from CO₂ is coupled to the land thermal reservoir, for example using the ‘grasslands’ data set, the calculated increase in surface temperature is again ‘too small to measure’.

Chapter 9, Conclusions and Suggestions for Further Research summarizes the results of the analysis and discussion presented in the previous chapters. The oversimplified paradigm of a planetary energy balance has been changed by addressing the question ‘What determines the energy flow at the surface of the earth?’ The concepts of complexity theory are applied to the four main time dependent flux terms that determine the diurnal energy flow. This leads to a different view of climate energy transfer and climate change in which the evapotranspiration plays a major role in setting the surface temperature. Three main areas for future research are identified. First, more detailed measurements of the surface energy transfer are needed, especially for the oceans. Second, the study of the time dependence of the diurnal cycle and the seasonal changes allows more information to be collected on the time delays or phase shifts between the peak solar flux and the temperature response. This is a potentially rich vein of study that may provide deeper insight into the energy flows and the mechanisms of climate change. Third, the simple models of the surface energy flow used in this book need to be expanded and incorporated into larger scale climate models that can simulate the mechanisms of climate change, particularly those related to the oceans oscillations. This may require a very different approach that does not rely on large scale global circulation models.

2.3 Energy Balance and the Temperature of the Earth

2.9 What is meant by the Greenhouse Effect?

The downward LWIR flux from the lower troposphere to the surface establishes an exchange energy that limits the net LWIR cooling flux. The surface temperature increases until the thermal/humidity gradient at the surface-air interface is sufficient to remove the excess heat by evapotranspiration (moist convection). The troposphere functions as an open cycle heat engine that transports part of the surface heat to the middle to upper troposphere. From here it is radiated back to space, mainly by the water bands. The surface must be warmer than the cold reservoir of the tropospheric heat engine.

7.4 The Influence of the AMO on the Global Temperature Change Record

When the climate anomaly record, such as the HadCRUT4 data set is evaluated, the dominant term is found to be the Atlantic Multi-decadal Oscillation (AMO). There is a 0.3 °C offset between the AMO and the HadCRUT data after 1970. This requires further investigation of the ‘homogenization’ process and bias effects related to changes in the number and location of the weather stations used to generate the HadCRUT averages. There can be no CO₂ signal in the global temperature change record.

8.1 The Decrease in LWIR Flux at TOA Produced by CO2 Absorption

The decrease in LWIR flux at the top pf the atmosphere (TOA) is produced by an increase in absorption by CO₂ at lower levels in the atmosphere. In order to evaluate the effect on temperature, the change in absorption has to be converted to changes in the local rate of heating or cooling. In addition, it is necessary to consider molecular line broadening effects in the lower troposphere and the coupling of the LWIR flux to the mass transport (convection) in the troposphere. The maximum increase in the tropospheric heating rate produced by a 'CO₂ doubling' is +0.08 K per day at an altitude near 2 km. At a lapse rate of -6.5 K km^-1, an increase in tropospheric temperature of 0.08 K corresponds to a decrease in altitude of approximately 12 meters. This is equivalent to riding an elevator down four floors.

8.3 The Effect of an Increase in CO2 Concentration on the Ocean Surface Temperature

In order to determine if the change in temperature produced by the increase in downward LWIR flux from CO₂ can be detected, we first examine the changes in wind speed, latent heat flux, temperature and ocean heat content related to the 2016 ENSO peak using TRITON buoy data. Over a 6 month period, the change in temperature to 75 m depth was 2.5 °C and change in heat content was 800 MJ m^-2. This change in heat content is 3000 times larger than cumulative the increase in downward LWIR flux to the surface produced by the increase in CO₂ concentration over the same time period.

Over the ±30° latitude bands, the sensitivity of the latent heat flux to the wind speed is is at least 15 W m^-2/m s^-1. The increase in downward LWIR flux to the surface produced by the observed 140 ppm increase in atmospheric CO2 concentration is approximately 2 W m^-2. Within the ±30° latitude bands, this is dissipated by an increase in wind speed near 13 cm s^-1. Any change in ocean temperature produced by the observed 140 ppm increase in atmospheric CO₂ concentration is too small to measure.

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2.3 Energy Balance and the Temperature of the Earth

The surface temperature of the earth is usually explained by the ‘greenhouse effect’. The average surface temperature of the earth is 33 K higher than the ‘effective emission temperature’ of 255 K (-18 °C). This is attributed to the absorption and emission of LWIR radiation in the atmosphere. However, the greenhouse effect argument is based on an oversimplified description of the surface energy transfer and the LWIR emission to space. In particular, evapotranspiration and the role of the oceans in stabilizing the climate have been neglected (see Section 2.9).

Conservation of energy applied to the solar illumination of a rotating sphere with an albedo near 0.3 indicates that the planetary average LWIR flux emitted at the top of the atmosphere (TOA) should be near 240 W m^-2. Using the Stefan Boltzmann Law, the ‘effective emission temperature’ is near 255 K. This is illustrated in Figure 2.4. Satellite observations give values near 240 ±100 W m^-2. An IR image of the earth recorded by the CERES radiometer on the NASA Aqua satellite is shown in Figure 2.5.^[1] The LWIR emission at TOA is the cumulative emission from many different levels in the atmosphere at different temperatures. The upward LWIR emission from each level is modified by the LWIR absorption and emission of the levels above. The spectral distribution of the LWIR flux at TOA is not that of a blackbody (see Figure 2.16). Therefore, like the moon, the average planetary LWIR flux should not be used to define an ‘effective emission temperature’, T_eff of 255 K. Furthermore, this should not be subtracted from an ‘average surface temperature’, T_surfav of 288 K to give a ‘greenhouse effect temperature’ of 33 K.^[2] The LWIR flux at TOA is just a planetary cooling flux. It should be interpreted in terms of rates of cooling at different levels in the atmosphere. The net LWIR emission at each level is divided by the heat capacity of the local air parcel to give a local cooling rate. For the tropical atmosphere, the tropospheric LWIR cooling rate is near 2 K per day.^[3] The LWIR cooling rate is discussed in more detail in Section 8.1.

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(Reference numbers are not the same as the footnote numbers in the book)

[1] Parkinson, C. L. (2013), “Summarizing the first 10 years of NASA's Aqua Mission”, IEEE Journal of Selected Topics in Applied Earth observations and Remote Sensing, 6(3) pp. 1179-1188. [https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6423809]

[2] Taylor, F. W. (2006), Elementary Climate Physics, Oxford University Press, Oxford, Chapter 7.

[3] Feldman D.R., K. N. Liou, R. L. Shia and Y. L. Yung (2008), “On the information content of the thermal IR cooling rate profile from satellite instrument measurements” J. Geophys. Res. 113 D1118 pp. 1-14. [https://doi.org/10.1029/2007JD009041]

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2.9 What is meant by the ‘Greenhouse Effect’?

The energy transfer processes that determine the ‘temperature of the earth’ are often simplified and explained in terms of a ‘greenhouse effect’. The ‘average surface temperature’ of the earth is warmer than a hypothetical ‘effective emission temperature’ at TOA. The troposphere functions as an open cycle heat engine. The surface thermal reservoirs are the hot reservoirs and the upper tropospheric thermal reservoir is the cold reservoir of this heat engine. The ‘greenhouse effect’ therefore may be understood in terms of the energy transfer processes that determine the temperatures of these thermal reservoirs. Our primary focus is the control mechanism that resides in the diurnal cycle of the surface temperature. This leads to an opposite view of the ‘greenhouse effect’. The Second Law of Thermodynamics requires that surface must be warmer than the cold reservoir of the tropospheric heat engine. Here we provide a brief overview of the ‘greenhouse’ effect’ including some history and the role of evapotranspiration (moist convection) in setting the reservoir temperatures.

The earth is an isolated planet that is heated by absorbed electromagnetic radiation from the sun and cooled by LWIR emission to space from the top of the atmosphere (TOA). There is no thermal equilibrium. The absorbed solar heat is stored and released over a wide range of time scales. The various flux terms define rates of heating and cooling of the thermal reservoirs. There are well known time delays or phase shifts between the peak solar flux and the diurnal and seasonal temperature response (see Figures 2.21, 2.23b, 2.24 and 2.26). These are clear evidence of a non-equilibrium thermal system. Conservation of energy for a stable climate requires that the long term planetary average of the absorbed solar flux should be equal to the average planetary LWIR flux returned to space at TOA. A simple calculation based on the illumination of a sphere by a collimated disk of solar radiation gives an average planetary LWIR flux at TOA of approximately 240 W m^-2 (see Figure 2.4). Satellite observations give a range of approximately 240 ±100 W m^-2 (see Figure 2.5). It is often assumed that the earth’s average surface temperature is near 288 K (15 °C). From the Stefan Boltzmann Law, a blackbody surface at 288 K is emitting approximately 390 W m^-2 of thermal radiation. Similarly, a flux of 240 W m^-2 gives an ‘effective emission temperature’ near 255 K (-18 °C). This raises an apparent issue with the First Law of Thermodynamics. How can a planet that is absorbing an average solar flux of 240 W m^-2 have a surface temperature that is 33 K higher than its ‘effective emission temperature’ of 255 K? The historical explanation has relied on a poorly defined ‘greenhouse effect’.

Fourier recognized the warming effects of the atmosphere and the oceans in memoires of 1824 and 1827.^[4],[5] He also described a solar calorimeter with glass windows. However, the term ‘greenhouse effect’ was not used until much later. Arrhenius incorrectly cited Fourier by stating “Fourier maintained that the atmosphere acts like the glass of a hothouse”.^[6] The words ‘greenhouse effect’ were first introduced by Poynting in 1907.^[7] The history of the ‘greenhouse effect’ has been discussed by Easterbrook,^[8] Fleming^[9] and Mudge.^[10]

Taylor (2006), Chapter 7^[2] states: “The presence of an atmosphere [with an IR radiation field] raises the mean temperature of the surface of the earth considerably over what it would be on an airless sphere with the same size, albedo and distance from the sun”

An ‘average surface temperature’ and an ‘effective emission temperature’ are both mathematical constructs that have no real physical meaning. A detailed discussion of the greenhouse effect is given by Gerlich and Tscheuschner^[11] and average temperatures are considered by Essex et al.^[12] A discussion of the ‘average temperature’ of the earth with and without ‘greenhouse gases’ is pointless.

The spectral distribution of the LWIR flux emitted at TOA is not that of a blackbody emitter at 255 K (see Figure 2.16). It is simply a cumulative cooling flux emitted from many different levels in the atmosphere at different temperatures. It should not be used to define an ‘effective emission temperature’. The LWIR emission from each level in the atmosphere is modified by the absorption and emission of the layers above. In order to understand cooling effects of the LWIR flux, the net cooling flux at each level has to be converted to a cooling rate by dividing by the local heat capacity (see Figure 8.2). The effect of changes in the LWIR flux in the atmosphere produced by changes in ‘greenhouse gas’ concentration, for example an increase in CO₂ concentration, can then be understood in terms of changes in the local LWIR cooling rate (see Figure 8.3). The rates of cooling produced by the LWIR flux may also be compared to the rates of cooling produced by mass transport (moist convection) in the troposphere (see Section 8.1).

In order to understand the energy transfer processes that determine the surface temperature it is necessary to consider the Second Law of Thermodynamics, not just the First. To remove the stored solar heat from the surface thermal reservoir, there has to be a thermal and/or a humidity gradient. The downward LWIR flux from the lower troposphere to the surface reduces the net LWIR flux that can cool the surface. Some of the IR photons are exchanged between the surface and the lower troposphere without any significant transfer of thermal energy. The surface temperature increases until the thermal/humidity gradient at the surface-air interface is sufficient to remove the excess heat by evapotranspiration (moist convection). The troposphere functions as an open cycle heat engine that transports part of the surface heat by convection to the middle to upper troposphere (see Figure 2.1). Here it is radiated to space, mainly by the water bands. As the surface temperature increases above the air temperature, the net LWIR cooling flux also increases. Part of this increase is transmitted into the LWIR window and part is absorbed by the lower troposphere. The air that is heated by LWIR absorption becomes part of the turbulent mixing layer near the surface as warm air rises from the surface and is replaced by cooler air from above (see Figures 2.17, 2.18 and 2.27).

As the warm air rises through the troposphere, it expands and cools. Part of the internal (molecular) energy of the rising air parcel is converted to gravitational potential energy. For dry air, the tropospheric temperature profile or lapse rate is -9.8 K km^-1. If the air is moist, water vapor can condense above the saturation level with the release of latent heat. This reduces the lapse rate. The US Standard Atmosphere uses an average moist lapse rate of -6.5 K km^-1. The LWIR emission from the water bands above the saturation level is mainly determined by the local air temperature. The peak emission occurs in a broad temperature band centered near -13 °C.^[13],[14] The ‘greenhouse effect temperature’ may be understood as the temperature difference between the surface and the cold reservoir of the tropospheric heat engine. It is determined by the thermodynamic properties of the atmosphere. This is discussed in more detail by Holmes^[15] and by Jelbring.^[16]

The thermal properties of the air-ocean and air-land interfaces are different and have to be considered separately. The ocean surface is almost transparent to the solar flux. The solar heat is initially absorbed and stored in the ocean thermal reservoir that may extend to 100 m or more in depth. Because of the large volume and heat capacity of the ocean thermal reservoir, the diurnal surface temperature rise is small, typically 1 to 2 °C or less. In order to dissipate the absorbed solar heat, the ocean surface must warm up until the excess heat is removed by wind driven evaporation (latent heat flux). Maximum ocean temperatures near 30 °C are reached in the equatorial warm pools (see Section 6.7). The minimum ocean surface temperature is near -1.8 °C, the freezing point of sea ice. The annual variation in ocean surface temperatures is typically near 6 °C (see Figure 2.23). At the ocean surface, the penetration depth of the LWIR flux is 100 micron or less (see Figure 2.28). Here it is fully coupled to the wind driven evaporation or latent heat flux.

There is no requirement for an exact flux balance on any time scale between the ocean solar heating and the surface cooling. Natural variations in wind speed lead to quasi-periodic oscillations in ocean surface temperatures and these provide a ‘noise floor’ for climate temperature changes (see Figures 2.29 through 2.32). The ENSO does not change the maximum ocean surface temperature. Instead, changes in the wind speed in the central equatorial Pacific Ocean alter the location and area of the warm pool. If the wind speed drops and the local ocean surface temperature starts to increase above 30 °C, strong local thunderstorms form that reduce the surface temperature.^[17]

Over land, the minimum daily temperature is normally set by the bulk air temperature of the local weather system passing through. As the absorbed solar flux warms the surface during the day, a temperature gradient is established both between the surface and the air layer above and between the surface and the subsurface layers below. The surface-air gradient drives the evapotranspiration (moist convection). Heat is also conducted below the surface as the surface warms. The subsurface gradient then reverses as the surface cools and almost all of the stored heat is returned to the surface later in the day. In the evening, there is a convection transition temperature at which the surface and air temperatures equalize and the surface cools more slowly overnight by net LWIR emission. The convection transition temperature is reset each day by the local weather system passing through. There may also be local heating produced by air compression related to downslope winds or the downward airflow within a high pressure dome (see Sections 5.4 and 5.5). In many parts of the world, the prevailing weather systems are formed over the oceans and move overland. This couples both the seasonal ocean phase shifts and the ocean oscillations to the weather station temperatures (see Chapter 7).

Based on this discussion, the surface temperature of the earth may be explained by considering the coupling of the four main flux terms, the solar flux, the net LWIR flux, the evapotranspiration and the subsurface thermal transport to the surface thermal reservoirs. The net LWIR flux is insufficient to remove the absorbed solar flux and the surface warms up so that the excess heat is removed by evapotranspiration (moist convection). This is a mass transport process. As the warm air rises from the surface it is coupled to the gravitational potential and rotation of the earth. This establishes the earth’s basic weather patterns. The troposphere functions as an open cycle heat engine that transports part of the surface heat to the middle to upper troposphere. From here it is radiated back to space, mainly by the water bands. As the temperature, pressure and water vapor concentration decrease with altitude, there is a transition from LWIR absorption and emission to a free photon flux. The peak of the water band emission occurs near 260 K (-13 °C). The altitude of this temperature level is determined by the local lapse rate, not by the LWIR flux. In addition, the release of latent heat from water vapor condensation is reduced so that it no longer drives the convection. The climate is stabilized by the large heat capacity of the ocean thermal reservoir. Air and water are also fluids that redistribute the absorbed solar heat from the equator towards the poles. The LWIR flux cannot be separated from the mass transport. The surface must be warmer than the cold reservoir of the tropospheric heat engine.

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[4] Fourier, J.-B.-J. (1824), “Remarques générales sur les températures du globe terrestre et des espaces planétaires” Annales de Chimie et de Physique 27 pp. 136–167. [https://gallica.bnf.fr/ark:/12148/bpt6k65708960/f142.image#] English translation: [http://fourier1824.geologist-1011.mobi/]

[5] Fourier, B.-J.-B. (1827), “Mémoire sur les températures du globe terrestre et des espaces planétaires” Mém. Acad. R. Sci. Inst. Fr., 7 pp. 527-604. [https://www.academie-sciences.fr/pdf/dossiers/Fourier/Fourier_pdf/Mem1827_p569_604.pdf] English translation: [http://www.wmconnolley.org.uk/sci/fourier_1827/]

[6] Arrhenius, S. (1896), “On the influence of carbonic acid in the air upon the temperature of the ground” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 41 pp. 237-276. [https://doi.org/10.1080/14786449608620846]

[7] Poynting, J. H. (1907), “On Prof. Lowell's method for evaluating the surface-temperatures of the planets, with an attempt to represent the effect of day and night on the temperature of the earth” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 14(84) pp. 749-760, [http://dx.doi.org/10.1080/14786440709463737]

[8] Easterbrook, S. (2015), “Who first coined the term 'Greenhouse Effect'?” [https://www.easterbrook.ca/steve/2015/08/who-first-coined-the-term-greenhouse-effect/]

[9] Fleming, J. R. (1999), “Joseph Fourier, the ‘greenhouse effect’ and the quest for a universal theory of terrestrial temperatures” Endeavour 23(2) pp. 72-75. [https://doi.org/10.1016/S0160-9327(99)01210-7]

[10] Mudge, F. B. (1997), “The development of the ‘greenhouse’ theory of global climate change from Victorian times” Weather 52(1) pp. 13–17. [https://doi.org/10.1002/j.1477-8696.1997.tb06243.x]

[11] Gerlich, G. and R. D. Tscheuschner (2009), “Falsification of the atmospheric CO₂ greenhouse effects within the frame of physics” Int. J. Mod. Phys. B. 23(3) pp. 274-394. [https://www.worldscientific.com/doi/abs/10.1142/S021797920904984X]

[12] Essex, C., R. McKitrick and B. Andresen (2006), “Does a global temperature exist?” J. Non-Equilibrium Thermodynamics 31(1) pp. 1-27. [https://doi.org/10.1515/JNETDY.2007.001]

[13] Clark, R. (2013), “A dynamic, coupled thermal reservoir approach to atmospheric energy transfer Part I: Concepts” Energy and Environment 24(3, 4) pp. 319-340. [https://doi.org/10.1260/0958-305X.24.3-4.319]

[14] Koll, D. D. B and T. W. Cronin (2018), “Earth’s outgoing longwave radiation linear due to H2O greenhouse effect” PNAS, 115(41) pp. 10293-10298. [https://www.pnas.org/doi/10.1073/pnas.1809868115]

[15] Holmes, R. I. (2017), “Molar Mass Version of the Ideal Gas Law Points to a Very Low Climate Sensitivity” Earth Sciences 6(6) pp. 157-163. [http://article.sciencepublishinggroup.com/pdf/10.11648.j.earth.20170606.18.pdf]

[16] Jelbring, H. (2003), “The greenhouse effect as a function of atmospheric mass” Energy and Environment 14(2) pp. 351-356. [https://doi.org/10.1260/095830503765184655]

[17] Eschenbach, W. (2010), “The thunderstorm thermostat hypothesis” Energy and Environment 21(4) pp. 201-224. [https://doi.org/10.1260/0958-305X.21.4.201]

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7.4 The influence of the AMO on the Global Temperature Change Record

The global temperature change record is an area weighted average of the weather station data after it has been extensively processed or ‘homogenized’ and the mean has been subtracted. When the climate anomaly record, such as the HadCRUT4 data set is evaluated, the dominant term is found to be the Atlantic Multi-decadal Oscillation (AMO). The correlation coefficient between the two data sets is 0.8. This is illustrated in Figure 7.15.^[18],[19] The AMO consists of a quasi-periodic oscillation superimposed on an underlying linear trend. A least squares fit to the data from 1900 gives a sinusoidal oscillation with an amplitude of 0.2 °C and a period of 61 years with a long term linear trend near 0.3 °C per century. The linear trend is attributed to the temperature recovery from the Maunder minimum or Little Ice Age.^[20] Both the period and the slope may change with time. There is a 0.3 °C offset between the AMO and the HadCRUT data after 1970. This requires further investigation of the ‘homogenization’ process and bias effects related to changes in the number and location of the weather stations used to generate the HadCRUT averages.

The influence of the AMO extends over large areas of N. America, Western Europe and parts of Africa. The weather systems that form over the oceans and move overland couple the ocean surface temperature to the weather station data through the diurnal convection transition temperature. The contributions of the other ocean oscillations to the global temperature anomaly are smaller. The IOD and the PDO are dipoles that tend to cancel and the ENSO is limited to a relatively small area of the tropical Pacific Ocean. However, small surface temperature variations in the tropical oceans have a major impact on ocean evaporation and rainfall. Figure 7.16 shows a tree ring construction of the AMO from 1567.^[21],[22] The modern instrument record is also indicated in green.

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[18] AMO (2022), [https://www.esrl.noaa.gov/psd/data/correlation/amon.us.long.mean.data]

[19] HadCRUT4 (2022), [https://www.metoffice.gov.uk/hadobs/hadcrut4/data/current/time_series/HadCRUT.4.6.0.0.annual_ns_avg.txt]

[20] Akasofu, S.-I. (2010), “On the recovery from the Little Ice Age” Natural Science 2(11) pp. 1211-1224. [http://dx.doi.org/10.4236/ns.2010.211149]

[21] Gray, S. T., L. J. Graumlich, J. L. Betancourt and G. T. Pederson (2004), “A tree-ring based reconstruction of the Atlantic Multi-decadal Oscillation since 1567 A.D.” Geophys. Res. Letts, 31 L12205, pp. 1-4. [https://doi.org/10.1029/2004GL019932]

[22] Gray, S. T., et al. (2004), Atlantic Multi-decadal Oscillation (AMO) Index Reconstruction, IGBP PAGES/World Data, Center for Paleoclimatology, Data Contribution Series #2004-062, NOAA/NGDC Paleoclimatology Program, Boulder CO, USA. [https://www.ncei.noaa.gov/pub/data/paleo/treering/reconstructions/amo-gray2004.txt]

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8.1 The Decrease in LWIR Flux at TOA Produced by CO₂ Absorption

The decrease in LWIR flux at the top of the atmosphere (TOA) is produced by an increase in absorption by CO₂ at lower levels in the atmosphere. In order to evaluate the effect on temperature, the change in absorption has to be converted to changes in the local rate of heating or cooling. This involves the calculation of the absorbed LWIR flux at each level in the atmosphere and dividing by the local heat capacity. In addition, it is necessary to consider molecular line broadening effects in the lower troposphere and the coupling of the LWIR flux to the mass transport (convection) in the troposphere. Most of the initial absorption occurs in the P and R branches of the ν₂ CO₂ band near 640 and 700 cm^-1. There is also some weaker absorption by the CO₂ overtone bands near 950 and 1050 cm^-1. The slight warming produced by these absorptions is then dissipated by a combination of wideband LWIR emission across all of the atmospheric emission bands and coupling to the convection. Some of the thermal energy is converted to gravitational potential energy followed by LWIR emission at a later time. This is illustrated schematically in Figure 8.1. The total and band averaged cooling rate profiles for the tropical model atmosphere are shown in Figure 8.2. In the lower and middle troposphere the total cooling rate is near 2 K per day.^[23],[24] The changes in atmospheric heating rates for a ‘doubling’ of the CO₂ concentration, in this case from 287 to 574 ppm at mid latitude are shown in Figure 8.3.^[25] In the troposphere, as shown in Figure 8.3a, the maximum increase in the heating rate is +0.08 K per day at an altitude near 2 km. In the stratosphere, as shown in Figure 8.3b, there is a maximum increase in the cooling rate near 50 km of -3 K per day. At a lapse rate of -6.5 K km^-1, an increase in tropospheric temperature of 0.08 K corresponds to a decrease in altitude of approximately 12 meters. This is equivalent to riding an elevator down four floors.

The troposphere functions as an open cycle heat engine that transports heat from the surface to higher altitudes in the troposphere by moist convection. From here it is radiated back to space, mainly by the water bands. The local temperature profile of the troposphere is set by the local lapse rate, which depends on the surface temperature, the relative humidity and the convection. The stratosphere is heated mainly by the absorption of UV solar flux by ozone and cools by LWIR emission from CO₂ and ozone. The local solar heating changes on a daily and a seasonal time scale. The downward flux from the LWIR emission in the stratosphere and upper troposphere is absorbed in the lower troposphere and does not reach the surface. This is discussed above in Section 2.5 (see Figure 2.15).

The local temperature of an air parcel in the troposphere depends on the local LWIR flux balance and the vertical motion. Within the plane-parallel atmosphere approximation there are four contributing LWIR flux terms. The air parcel absorbs part of the LWIR flux from above and below. It is also emitting LWIR radiation upwards and downwards. This emission depends on the local temperature and IR species concentrations. There may also be some direct heating of the air parcel produced by the near IR (NIR) absorption of the solar flux by the water NIR overtone bands (see Figure 2.6). As the air parcel changes altitude, particularly during convective ascent, the temperature change from expansion/compression is generally much larger than the LWIR cooling rate. As an air parcel rises and cools, internal molecular energy is converted to gravitational potential energy. For an ascent rate of 1 km per hour at a lapse rate of -6.5 K km^-1, the cooling rate is 6.5 K per hour. From Figure 8.1, the tropospheric cooling rate from LWIR emission is near 2 K per day or 0.08 K per hour. The rate of cooling during convective ascent may easily be 100 times larger than that produced by the net LWIR emission. The energy transfer processes for an air parcel in the troposphere are illustrated schematically in Figure 8.4.

During the day, the turbulent mixing processes within the boundary layer can be complex. There is both upward and downward motion related to convective plumes. The vertical velocity may be investigated using heterodyne LIDAR (laser ranging) techniques. Variations in velocity of ±2 m s^-1 in the surface boundary layer up to 2 km in altitude were reported by Gibert et al.^[26] This was based on measurements recorded over 10 hours at the École Polytechnique, south of Paris, July 10th 2005. At 2 m s^-1, a 1 km change in altitude occurs in approximately 10 minutes. The change in temperature depends on the local lapse. The upper limit is set by the lapse rate for dry air, -9.8 K km^-1.

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[23] Feldman, D. R., K. N. Liou, R.L. Shia and Y. L. Yung (2008), “On the information content of the thermal IR cooling rate profile from satellite instrument measurements” J. Geophys. Res. 113 D1118 pp. 1-14. [https://doi.org/10.1029/2007JD009041]

[24] Lacis, A. A. and V. Oinas (1991), “A description of the correlated k distributing method for modeling non gray gaseous absorption, thermal emission and multiple scattering in vertically inhomogeneous atmospheres”, J. Geophys. Res. 96(D5) pp. 9027-9063. [https://doi.org/10.1029/90JD01945]

[25] Iacono, M. J., J. S. Delamere, E. J. Mlawer, M. W. Shephard, S. A. Clough, and W. D. Collins (2008), “Radiative forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models” J. Geophys. Res., 113, D13103 pp. 1-8. [https://doi.org/10.1029/2008JD009944]

[26] Gibert, F. J. Cuesta, J.-I. Yano, N. Arnault and P. H. Flamant (2007), “On the Correlation between Convective Plume Updrafts and Downdrafts, Lidar Reflectivity and Depolarization Ratio” Boundary Layer Meteorology 125 pp. 553-573. [https://doi.org/10.1007/s10546-007-9205-6]

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8.3 The Effect of an Increase in CO₂ Concentration on the Ocean Surface Temperature

Using our simple two reservoir thermal model for ocean energy transfer, we found that the dominant cooling term was the wind driven evaporation. There was also a weak, slowly drifting attractor that worked to restore the small diurnal temperature rise to its initial dynamic equilibrium state. There was no requirement for an exact flux balance between the solar heating and the various cooling flux terms. This leads to the formation of natural, quasi-periodic oscillations in the ocean surface temperature. These are illustrated above in Figure 2.29. The wind driven nature of the ENSO is shown in Figure 2.30. In order to determine if the change in temperature produced by the increase in downward LWIR flux from CO₂ can be detected, we start by examining the changes in wind speed, latent heat flux, temperature and ocean heat content related to the 2016 ENSO peak using TRITON buoy data.

The average monthly wind speeds from 2014 through 2017 recorded by the TRITON buoys at 155° W, 0°, 2°, 5° and 8° S are shown in Figure 8.6a. These buoys are located in the S. Pacific equatorial current gyre circulation. The average wind speed over the four years was 5.6 m s^-1. There was a decrease in wind speed of approximately 2 m s^-1 towards the end of 2015 and in early 2016. The ocean temperatures at 1, 25, 50, 75 and 100 m recorded by the buoy at 155° W, 5° S are shown in Figure 8.6b. There was an increase of 2.5 °C in the 1 m and 25 m ocean temperatures over a 1 year period starting in the fall of 2014. The 1 m and 25 m temperatures then decreased by 2.5 °C as the wind speed recovered after the start of 2016. Similar temperature changes occurred down to 75 m depth. The change in ocean heat content down to 75 m depth estimated from the buoy temperatures in Figure 8.6b is shown in Figure 8.6c. During this 6 month interval, the average CO₂ concentration increased by approximately 1.2 ppm and the related downward LWIR flux increased by 0.017 W m^-2. The change in heat content for a 2.5 °C change temperature in a 1 x 1 x 75 m column of water is near 800 MJ m^-2. The cumulative increase in downward LWIR flux from CO₂ over 6 months was 0.26 MJ m^-2. This is approximately 3000 times less than the change in heat content to 75 m depth produced by the ENSO peak.

Not only is the magnitude of the increase in LWIR flux from CO₂ too small to produce a measurable change in ocean surface temperature, the LWIR flux is coupled to the wind driven evaporation or latent heat flux and any sensible heat flux at the surface and cannot accumulate in the bulk ocean below. The energy transfer processes are illustrated schematically in Figure 8.7. The latent heat flux is produced by the removal of water molecules from the water surface. The sensible heat flux is produced by the transfer of thermal energy including both kinetic energy and internal molecular energy (rotation and vibration) from the water molecules at the ocean surface to the air molecules above. The LWIR flux is absorbed and emitted within the first 100 micron layer at the surface. This is shown in more detail in Figure 8.8. The 50% and 90% penetration depths in micron for the absorption of LWIR radiation into the ocean surface vs. wavenumber are shown from 200 to 1500 cm^-1 (right hand scale) using data from Hale and Querry.^[27] The 300 K surface emission and downward atmospheric flux are also shown, W m^-2/cm^-1 (left hand scale). These are the results from a MODTRAN calculation, 200 to 1500 cm^-1, 2 cm^-1 resolution, 80% RH, 400 ppm CO₂.^[28] The approximate locations of the P and R branch and overtone absorption bands of CO₂ are also indicated. Approximately 90% of the LWIR flux from the P and R branches of the main CO₂ band is absorbed within the first 10 micron layer at the surface. In addition, approximately 5% of the solar flux is absorbed within the first millimeter layer of the ocean surface. The detailed description of the surface energy transfer is complex and requires consideration of the statistical mechanics of the molecular motion.

At higher latitudes, outside of the ocean equatorial gyre circulation, absorbed solar heat is stored below the surface during the summer and released during the winter as the rates of ocean heating and cooling change with the seasons. There is no requirement for an exact annual flux balance. Figure 8.9 shows the cumulative monthly changes in heat content for the upper 3 m reservoir at 60°, 50°, 40° and 30° N for the temperatures shown in the 20° W transect from Figure 6.1 above. Figure 8.10 shows the corresponding changes in cumulative heat content for the lower 122 m reservoir. Figure 8.11 shows the total annual change in heat content at each latitude. In this example, 1320 to 1420 MJ m^-2 of heat is stored and released each year. From one year to the next, the change in total annual stored heat content may easily reach 100 MJ m^-2 or more. For reference, the annual cumulative increase in LWIR flux from the 0.034 W m^-2 increase in downward LWIR flux from a 2.4 ppm increase in atmospheric CO₂ concentration is near 1.1 MJ m^-2.

Figure 8.12 shows the long term zonal average sensitivity of the latent heat flux to the wind speed. This is calculated from the long term zonal average ocean latent heat flux and wind speed data shown above in Figures 6.3c and 6.3d. Over the ±30° latitude bands, the sensitivity is at least 15 W m^-2/m s^-1. As shown above in Figure 2.20, the increase in downward LWIR flux to the surface produced by the observed 140 ppm increase in atmospheric CO2 concentration is approximately 2 W m^-2. Within the ±30° latitude bands, this is dissipated by an increase in wind speed near 13 cm s^-1. The average increase in CO₂ concentration at present is near 2.4 ppm. This corresponds to an annual increase of 0.034 W m^-2 in the downward LWIR flux to the surface which is dissipated by an increase in wind speed near 2 millimeters per second. As shown above in Figure 6.18h, the 1σ standard deviation in the long term average wind speed for the TRITON buoys along the equator is near 2 m s^-1. Any change in ocean temperature produced by the current annual increase in the atmospheric CO₂ concentration is too small to measure.

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[27] Hale, G. M. and M. R. Querry (1973), “Optical constants of water in the 200 nm to 200 µm wavelength region” Applied Optics 12(3) pp. 555-563. [https://doi.org/10.1364/AO.12.000555]

[28] MODTRAN (2021), [http://forecast.uchicago.edu/Projects/modtran.orig.html]

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