The Heating and Cooling of the Atmosphere of the Earth
Written by Karl L. Erdman Ph.D. Professor Emeritus UBC
The unrealistic picture of the regulation of the temperature of the earth that has led to the theory of Anthropogenic Global Warming has arisen because of a misunderstanding of how the energy arriving from the sun heats the earth. It was postulated that radiation arrives at the surface, heats it, and then the atmosphere is heated from the warmed surface by direct transfer of some of the energy by means of conduction, convection, and evaporation. The majority of the energy was thought to be transferred by radiation which was trapped by the “greenhouse gases” in the atmosphere in a layer at some distance from the surface. It was then thought to be re-radiated from this layer and equal amounts were radiated outward into space and back to the surface. The surface was postulated to be heated additionally by “backradiation” from this “blanket”. According to the progenitors of the theory of anthropogenic global warming (AGW) the surface is heated above the temperature calculated from the simplistic model used to define the black body temperature of the surface. In this note is a short description of what constitutes a black body and explains why the earth is not one and why the presence of the so-called greenhouse gases in the atmosphere leads to a drop in the temperature at the surface rather than a rise.
The detailed description outlines how the energy from the surface is transported to the level at which the radiation temperature measured from space corresponds to the physical temperature measured by the use of radiosondes and how this altitude if determined by energy arriving from the sun. It explains how the fraction of the energy arriving at the surface that is transformed into heat, and does not enter the atmosphere by physical means but leaves the surface by infrared radiation, is converted near to the surface into heat by means of the principal greenhouse gases, water vapor and carbon dioxide (CO2). The measured results of the variation of the surface temperature with the increased concentration of the “greenhouse gases,” of which water vapor contributes 95% to the so-called greenhouse effect and carbon dioxide only 4%, show that the temperature is lowered with an increase in their concentration rather than raised, and so if we wish to regard it as a blanket, it is an unusual one since it cools rather than heats. The idea that increasing the concentration of CO2 will warm the surface is not only wrong but has been experimentally determined to be a bit of malicious nonsense.
Although it is not discussed in this note, there is little difficulty in explaining how ice ages could occur with 4000ppm of CO2 in the atmosphere. There is an inverse correlation between high levels of it in the atmosphere and the surface temperature.
The Important Physical Concepts
The energy to heat the atmosphere arrives principally from the Sun, and the energy removed from it when it cools, is radiated into the cosmos. The average temperature of the surface is determined by a number of physical processes involving the transformation of the energy into various different forms and its storage at various stages of its passage between where it was created in the center of the sun by thermonuclear fusion and its dissipation into the universe after it leaves the surface of the earth. Its passage through the atmosphere is facilitated by radiation, conduction, and convection and temporary storage by the excitation of atoms and molecules into states of higher energy, and /or motion, and the energy stored and released during the changes in the state of the solids, liquids and gases that constitute the outer surface layer of the earth.
The initial difficulty we have in the description of the process is due to the changes in scale during the description, as we trace the path of the energy flow. As an illustration, if we think of the earth as a solid ball that is about 20 cm in diameter the atmosphere in which everything that we will be considering in this description takes place, from the bottoms of the oceans to the top of the atmosphere, is only a 1/2mm thick layer on the surface of the ball, about the thickness of a coat of paint. Even a big weather event such as a hurricane would only be a spot on this surface layer perhaps 4 mm in diameter. The “rivers” in this surface layer which distribute a lot of energy, such as the jet streams in the atmosphere, or the Gulf Stream in the Atlantic Ocean are like thin strings of woolen yarn embedded in the layer.
The mechanisms for the various methods of energy transfer are seemingly un-related. The way that energy is transferred by radiation requires an understanding of the quantum mechanical description of nature as the energy is transmitted in bundles called photons whose motion is described using formulae governing the passage of electromagnetic waves. Most of the energy that arrives at the earth from the sun is carried by photons and the amount of the energy in an individual photon depends on the frequency of the electromagnetic wave used in the description of its motion. Ultra violet radiation is described by high frequency photons and infra red radiation is described by low frequency photons. The old scientific idea that heat (and cold) was transferred by an invisible fluid called caloric refuses to go away and many of the mistakes made in the description of energy transfer by radiation is the persistence of this description in our thinking, in spite of the fact that it leads us to the wrong conclusions.
When the theory of atomic structure of the elements was developed, which is now the basis of all chemistry and solid state physics, it completely changed the way that we think about the ways that energy is stored in those bodies in specific discrete amounts. The picture of the energy stored as heat in a gas is due to the kinetic energy of the molecules and so it can change in a more continuous fashion. It has altered the picture of how energy is absorbed and emitted.
As an example, visible light can pass right trough glass as there are no energy levels in the atoms and molecules in the glass that can accept the specific energy carried by the photons in the visible spectrum. On the other hand carbon in its normal state has all sorts of energy levels that cover the band of energy carried by the visible light and so all photons of varying energy can be absorbed and carbon appears black. We call it a black body. The surface of the earth is not a true black body as 30% of the energy that falls on it is not absorbed but is reflected but many of the physical descriptions of energy transfer can be done using the formulae and ideas developed for black body radiation using the appropriate approximations.
If we heat up the carbon, we are putting energy into it in the form of heat which is how we describe it as the energy in the motion of the molecules. Atoms and molecules, and indeed the lattice of a crystal, can store energy by being raised into higher states of excitation. The carbon can radiate energy as atoms change from states of higher energy to states of lower energy by emitting photons whose energy is specific to the energy difference between those two states. We detect these photons as electromagnetic radiation and the amount of energy carried by each photon is described by what we call the color of the light. Photons carrying a lot of energy are at the violet end of the spectrum and photons carrying a lot less energy are at the red end of the spectrum.
If the way the way the carbon atoms are linked together as a solid body is changed those energy levels disappear and then photons can pass through the piece of solid material made of that same element without absorption. We then have a transparent lump of solid carbon which we call a diamond and it is no longer a black body like a lump of coal. In other arrangements when the photon is travelling through a medium it encounters a region where instead of being transmitted without absorption it is reflected or scattered like electromagnetic radiation, also without absorption.
The Application of the Concepts to Energy Transfer
The first idea that is an important addition to the above picture is that the surface of the earth is not a black body and the atmosphere surrounding the earth certainly is not as there is no physical association between the molecules and atoms. The emitted radiation comes from various locations that are all at different temperatures, as is also true of the radiation emitted from the sun. All parts of a “truly” black body are all at the same temperature and the spectrum of energies that are emitted has a characteristic shape that is only a function of the temperature at which the energy levels in the body are populated. By looking at the shape of the spectrum we describe its temperature in terms of the equations that are used to define black body radiation and so we say that the body has a certain black body temperature which is measured from absolute zero using the Kelvin temperature scale where the object whose temperature is being measured has no energy whatsoever. Such a region does not exist in our universe except perhaps in black holes which we do not yet completely understand.
The length of time that the quantized energy is stored in the higher energy levels in the atoms and molecules is very short. The de-excitation time is determined statistically as in all such decay processes described by quantum mechanics. There is a half life associated with the event. The half life is the time for ½ of all of the excited states to decay to lower energy so when an atom or molecule is raised to a state of higher energy by the absorption of a photon it can emit a photon, with the same energy as it absorbed, in a period of time after its absorption determined by the half life of that excited state. For the infra red photons absorbed by the so-called greenhouse gases that time is quite short, the order of a millisecond which is 1 thousandth of a second. The time that the energy can be stored is thus very short, and the idea that “greenhouse gases” store heat as radiation is rubbish.
But the energy in an excited state can also be lost by heating up another atom or molecule by a collision between the excited atom and one of the other atoms around it, which are a hundred times more numerous. Energy can be transferred from the excited state into kinetic energy of the other atom or molecule in the collision. The transfer can go in either direction but the change in the kinetic energy of the gas molecule has to be exactly right for transferring the energy to the excitation or it won’t take place, just like it was for the photons passing through the materials.
We can now estimate the length of time required for a collisional de-excitation of an energy level by looking at the collision rate between the molecules. First the speed of molecules in a gas is determined by the temperature and at our normal room temperature is about 400 meters per second. We can also get a rough idea of the average distance between the molecules or atoms since we know that a molar volume contains 6 x 1023 molecules. The distance between two molecules is thus about 0.3 x 10-8 meters and so the time between collisions is about 1 millionth of the length of time it takes for the emission of the radiation from the excited state.
As a result very little of the infrared radiation that is emitted from the surface of the earth that is absorbed by the “greenhouse gases” is re-radiated. Since these gases have their highest density near the surface of the earth, and 95% of them are molecules of water and only 4% of carbon dioxide, adding a little carbon dioxide will not change the rate very much. Almost all of the energy lost from the surface by radiation is transformed into heat in the oxygen and nitrogen that constitutes 99% of the atmosphere and whose density decreases exponentially with the altitude, as also does the temperature.
At the surface of the earth, where the collision rate is high, the excited “greenhouse gases” don’t have time to radiate the energy before it is transferred to the oxygen and nitrogen, which cannot radiate it because it is all in the form of heat (the kinetic energy of the atoms and molecules). The hot gases then carry the stored energy upwards where the collision rate progressively decreases and more and more energy can escape into space by radiation by the “greenhouse gases” at the rate controlled by the energy transfers that can occur at that temperature and pressure. When the rising gases reach 10 km in height, about half of the energy is being lost by radiation to space. The fractional rate of conversion of the heat to excitation increases as the pressure continues to drop (at 20 km altitude the pressure is 1/20 of its value at the surface) and the temperature is 70° colder.
The calculated black body temperature of the earth as measured from space is made up of the sum of the spectra emitted at various intensities from various altitudes at which the heat in the gas is transferred to the excitation of the atoms and molecules that do the radiating. There is no real radiating surface and only a small fraction (about 6%) of the infra red radiation leaving the atmosphere comes from a region near the surface where the rate of capture of the higher energy infrared radiation by the “greenhouse gases” is low.
In his paper entitled Climate Thermodynamics, Claes Johnson outlines how the heat energy captured by the oxygen and nitrogen is distributed throughout the atmosphere. It is here that the third effect that influences the temperature happens. The fractional concentration of all of the gases except water is relatively constant from the surface to a height of 100 km. The molar concentration ratio of water to carbon dioxide decreases from 50:1 to nearer 1:1. The thermodynamic lapse rate of the temperature in the atmosphere is determined by the concentration of water vapor which changes from a value of 5.5°C per kilometer where the humidity is high to 10°C per km at about 10 km in altitude, where it is almost the same as for a dry atmosphere.
At this altitude called the tropopause another mechanism begins to become important. The energy from the sun carried by the ultra violet end of its pseudo black body spectrum (high energy photons) is augmented by the presence of high energy ions. The energy of the ultra violet photons is sufficiently high that they no longer require vacant energy states in atoms to be captured by the atoms and molecules in the gases as they can ionize atoms. Along with the flux of incoming high energy ions they can be absorbed in the atmosphere at that altitude by producing chemical reactions such as converting oxygen to ozone and producing a large variety of other compounds that aid in the formation of clouds, among other effects. The table shows how the ozone concentration suddenly increases at this altitude.
The next graph is a collection of all of the parameters describing the properties of the atmosphere from the ground to a height of 100 km at which the atmosphere is considered to have ended. An inspection of this picture shows that the lapse rate that was defined by the thermodynamics of the atmosphere ends at the level called the tropopause. The temperature of the atmosphere no longer is decreasing with the altitude but is steady and even beginning to rise. The altitude at which this happens is determined by the energy that is being deposited by the absorption of the high energy ultra violet photons and the ions being emitted by the sun. We can even see this visually when the surface of the sun is highly active and an unusually large cloud of ions impacts the atmosphere. The radiation emitted by the excited atoms appears in the Technicolor display we call the Aurora Borealis or Aurora Austrialis (or Northern Lights). The green color in the display is due to the radiation from an excited state in Oxygen.
By looking at this graph we can also see that using the temperature at the tropopause as our reference, the temperature at the surface depends on the lapse rate (the line representing the temperature that begins at the tropopause and ends at the surface). For a low lapse rate the temperature at the surface is lower and for a high lapse rate the temperature of the surface is higher.
The next two graphs of measured lapse rates show how changes in the lapse rates change the temperature at the surface. The altitude at which this happens can be seen on the graphs of the temperature of the atmosphere as a function of altitude measured by radiosondes in different parts of the world, during existing local atmospheric conditions. The first measurements were taken at a location in Australia and shows what happens if there are more “greenhouse gases” near the surface, there is more water vapor in the air on the wet day and the temperature at the ground is lower. In the theory of AGW a small increase in the concentration of CO2 is amplified by an increase of water vapor, and the temperature is supposed to increase. Instead in the measured data the temperature falls when the concentration is increased and the theory of AGW is hopefully dead at last.
The measurements displayed of two temperature vs altitude sets of data taken in two different locations in the United States at the same latitudes at the same time is even more illuminating. They show how the surface temperatures are different although they begin at the same temperature at the same high altitude and how this high altitude is the same as it was in Australia. The temperature was lower in Little Rock because the air had a higher humidity than in the desert at Las Vegas. It is easy to understand why jungles are cooler than the deserts just next door particularly if the horizontal and vertical scales in our climate graphs are kept in mind.
The last and even more interesting correlation is that of the changes in the average temperature of the climate and the sunspot numbers which is now easy to understand. In the next two graphs we can see the correlation between the changes in the temperature of the earth and the sun spot cycles strength over a 130 year period.
There is an obvious correlation between the drop in the average temperature of the earth and the low point in the sun spot numbers and the increase in temperature during the high numbers. Historically the last two major cold periods in the climate (the Maunder minimum and the little ice age) were accompanied by a major decrease in the number of sun spots. The sun spot number in this last cycle (not displayed in this graph) is lower then it has been in 100 years and the winter temperatures in Europe have dropped.
As was discussed above, the height of the tropopause, which determines the altitude at which the lapse rate in the atmosphere begins, and consequently determines the temperature at the surface, is the height from which the average temperature of the earth is defined. Radiosonde measurements show that the height of the tropopause varies as a function of latitude but also is determined by the activity of the sun. This varies from high activity when the sunspot number is high to low activity when the sunspot numbers are low. Not only is the magnitude of the magnetic field of the sun connected to the number of sun spots, which affects the number ions from the sun that can reach the earth, but also the ultra violet flux from the sun is strongly influenced by the sunspot number. The change in level of the atmosphere at which energy from the sun is deposited was discussed above and the evidence for the definition of this altitude is displayed by the measurements of the ozone levels.
A Quick Review
The objection to the theory of anthropogenic global warming (AGW), which depends on the transmission of energy by radiation in the atmosphere, has caused much controversy concerning the behavior of the so-called greenhouse gases. It has led to the implementation of draconian policies to attempt to control the concentration of CO2 in the atmosphere. This article describes the physical processes involved in the manner that the energy produced in the sun warms the earth. The supposed trapping of the energy arriving on the earth by “greenhouse gases” is shown only not to lead to incorrect results but to be deficient in accounting for the lack of correlation between the theory and measured temperature variations on the surface of the earth. The theory is clearly wrong as the mechanisms postulated for the transmission and transformation of the energy in the atmosphere contravene the basic laws of both thermodynamics and how energy is transmitted by electromagnet radiation, which are explained in this note.
The energy flux arriving from the sun is converted into heat in the atmosphere by several different physical processes. It is then distributed throughout the atmosphere according to the laws of thermodynamics used to describe the behavior of the atmospheric gases, which also determine the lapse rate. The relatively small concentration of CO2 has a minor influence in the transformation of the surface radiation into heat in the atmosphere. The lapse rate determines how much the temperature of the atmosphere increases toward the surface from the altitude at which the tropopause begins. The height of the tropopause is determined mainly by the flux of ions and ultraviolet radiation arriving from the sun and their ability to ionize the gases in the atmosphere. The tropopause is the beginning of the altitude in the atmosphere at which the ozone in the atmosphere is created. The height of the tropopause and the lapse rate determine the temperature at the surface.
The “greenhouse gases” convert the energy carried by the infrared radiation emitted from the surface into heat in the oxygen and nitrogen in the atmosphere. The greenhouse gas (water vapor) that produces 95% of the “greenhouse effect” near the surface is also the component in the atmosphere that sets the lapse rate. The supposed amplification of AGW by the increase in the concentration of water vapor by an increase in the concentration of CO2 is contradicted by the measurements taken by radiosondes of temperature changes in the atmosphere, which clearly show that an increase in the concentration of water vapor causes the temperature of the surface to fall rather than rise.
The hot blanket of the friends of AGW has been discovered to be a cold blanket by those who took the trouble to go outdoors and take a few measurements. The theory of AGW is dead at last. The science fiction that led to its creation is being exposed. There will be no celebration at the burial. The damage it has done is measured in the hundred of billions of dollars wasted in a futile attempt at correcting a problem that does not exist by raising irrational fears about the use of coal and oil and gas and instituting crash programs for the creation of alternative sources of energy. It has been done by promulgating scenarios of death and destruction by a non existent physical phenomenon and attempting to reduce the concentration of CO2 in the atmosphere, which is a necessary gas for plant growth, and helps in the cooling of the atmosphere rather than warming it. How stupid can we be!