The Earth’s Gravitational Field and Near Sea Level Atmospheric Temperatures – Slaying the Sky Dragon Excerpt
Written by Charles R. Anderson
The primary source of warmth for the Earth is radiant energy provided by our Sun. Just as the Sun radiates energy into space, the Earth, being warmer than space, also radiates energy out into space. Most of the energy it radiates into space is in the form of infra-red radiation, though light is a contributor as well. The Earth will radiate about the same amount of energy into space as it receives from the Sun on average. The Earth is often called a black body radiator, though this is not technically correct.
The energy equilibrium with the Sun ignores some heat from the Earth’s core, energy due to the Earth’s magnetic field interactions with the magnetic field of the Sun, gravitational tide effects due to the moon, or energy due to material from space entering our atmosphere at high speeds. It is commonly claimed by those who advocate catastrophic global warming due to man’s emissions of carbon dioxide that the total greenhouse gas effect is a warming of the Earth’s surface by about 33ºC.
They say this warming is caused by the infra-red (IR) radiation absorbing gases of water vapor, carbon dioxide, and methane in the atmosphere. These gases are said to cause the Earth to retain and even multiply the energy it receives from the Sun, so that the Earth’s surface is warmer than it would otherwise be. Of these gases, water vapor is much the most important, but carbon dioxide is said to have a large enough effect that man’s additions to the concentrations in the atmosphere will do serious harm to the Earth’s flora and fauna, as well as man himself.
That CO2 might have such a big effect is due to a gross exaggeration of the total effect of the atmosphere’s IRabsorbing gases. The exaggerated scale of the effect comes from the observation that the temperature of the Earth as seen from space is about 33ºC cooler than the average temperature of the Earth’s surface. That entire temperature difference is attributed by them to the greenhouse gas effect, or the effect of IR-absorbing gases. Exaggerating that effect allows them to exaggerate the effect of man’s emissions of carbon dioxide and methane. This chapter will discuss the real sources of the 33ºC difference between the average temperature of the Earth’s surface and its radiation temperature as seen from space, with primary focus on the contribution of the Earth’s gravitational field.
Back in 1976, before the politicization of the Catastrophic Greenhouse Gas Warming hypothesis, the National Oceanic and Atmospheric Administration, the National Aeronautics and Space Administration, and the United States Air Force collaborated on a project to calculate the properties for a U.S. Standard Atmosphere as a function of altitude. They calculated the temperature, pressure, density, and molecular speeds, among other parameters for an ideal gas in the Earth’s gravitational field as a function of altitude. “The equations used are those adopted 15 October 1976 by the United States Committee on Extension to the Standard Atmosphere (COESA), representing 29 U.S. scientific and engineering organizations. The values selected in 1976 are slight modifications of those adopted in 1962. The equations and parameters used are documented in a book entitled U.S. Standard Atmosphere, 1976 published by the U.S. Government Printing Office, Washington, D.C.”
The tables are based on rocket and satellite data and perfect gas theory to provide atmospheric densities and temperatures from -5,000 meters below sea level to 1000 kilometers altitude. Below 32 kilometers altitude, the U.S. Standard Atmosphere is identical with the Standard Atmosphere of the International Civil Aviation Organization.
My copy of these tables is in the 71st Edition of the Handbook of Chemistry and Physics for 1990 – 1991. The preface to the table says: “The U.S. Standard Atmosphere, 1976 is an idealized, steady-state representation of the earth’s atmosphere from the surface to 1000 km, as it is assumed to exist in a period of moderate solar activity. The air is assumed to be dry, and at heights sufficiently below 86 km, the atmosphere is assumed to be homogeneously mixed with a relative-volume composition leading to a mean molecular weight M. The molecular weights and assumed fractional-volume composition of sea-level dry air were” and a list of the gas molecules followed. I will leave out the molecular weights and just give the gas molecules, their fractional volumes, and the translation of the chemical symbol.
N2, 0.78084, nitrogen
O2, 0.209476, oxygen
Ar, 0.00934, argon
CO2, 0.000314, carbon dioxide [Note this is less than the usual fraction used now]
Ne, 0.00001818, neon
He, 0.00000524, helium
Kr, 0.00000114, krypton
Xe, 0.000000087, xenon
CH4, 0.000002, methane
H2, 0.00000005, hydrogen
For many purposes, the molecules of the atmosphere are well represented by an ideal gas model. Note again that the primary greenhouse gas is water vapor and it is left out entirely. Now let us list some values for the temperature, pressure, density, and speed of the average gas molecule of molecular weight M for various altitudes as calculated from the volume fractions in this U.S. Standard Atmosphere. They are given in the table below:
The temperature at sea level here is 288.15 Kelvin, which is 15.00ºC, and a change of 1K, equals a change of 1ºC. This temperature will vary with the time of year and the time of day. The change of temperature will then shift the values of this table as the sea level temperature changes from the near average value of 15ºC.
The main source of energy affecting this sea level temperature is solar radiation, which is affected by the time of day, the time of year, cloud cover, the humidity, volcanic ash and aerosols, and industrial and transportation aerosols. Energy also comes from the Earth’s hot interior, the interaction of the Earth’s magnetic field with the sun’s magnetic field, the solar wind, debris from space, the decay of radioactive elements, and the gravitational effects of the moon. These sources of energy can shift the sea level temperature relative to that given in this table, but then other values will shift with it. The very fluid atmosphere will seek out an equilibrium temperature distribution as a function of altitude for each such sea level temperature.
It will do this by means of gas molecule collisions, convection, radiation, and evaporation or sublimation of water. With a sea level temperature of 288.15K or 15ºC, this table gives the values of other parameters which represent the equilibrium condition.
Now let us note that the black body temperature of the Earth as seen from space is 255K. This is almost identical to the temperature of the Standard Atmosphere at an altitude of 5000 m. Thus, the effective altitude at which radiative cooling of the atmosphere takes place with respect to space is 5000 m. Above about 4000 m, radiative cooling becomes the dominant mechanism, so the effective altitude should be higher than that as this implies. Now, the Greenhouse Gas hypothesis claims that the reason the temperature at sea level is 288K, rather than 255K, is because greenhouse gases such as water vapor, CO2, and methane absorb the long wavelength IR radiation from the sunlight heated surface of the Earth and re-emit half of it back to the ground. That “extra” radiation heats the Earth’s surface to a temperature 33K higher than it would otherwise be.
Let us now take a look at the below sea level temperatures of this ideal gas with no water vapor. The lowest open area on the surface of the Earth’s land masses is the Dead Sea shore.
The altitude there is about -413 m, or 413 meters below sea level. At -500 m, the temperature would be 3.25K higher than at sea level according to this table. Interpolating from the table, the temperature at -413 m would be about 2.68 C or K warmer than it would be at sea level. Indeed, the Dead Sea area is very often warmer than the surrounding sea level areas. This tends to be true of other areas below sea level also. Yet, there is no reason to think that IR emissions from the surface and their capture by water vapor and CO2 should be very different, so this suggests that the mechanism of IR-absorbing gases is not the primary reason for any temperature difference between the Dead Sea and the surrounding sea level areas.
Why does the table give values down to -5000 m altitude? Because the table is of value to deep mine engineers who have to deal with air ventilation in deep mines. Deep mines become warm primarily because the surrounding rock becomes warm due to the Earth’s high core temperature, which also means that some of the energy at the Earth’s surface causing it to be warm is due to heat from the core. Deep mines also become warm due to the effect of gravity on air molecules! That effect is an important effect and has to be taken into account. Let us see how important the U.S. Standard Atmosphere tables imply it is. At -5000 m, the temperature of the standard atmosphere is given in the table as 320.676K, which is 32.526 K or C higher than the temperature at sea level and at atmospheric pressure. Now note that this is almost the same temperature increase that the surface of the Earth has relative to the altitude with the same temperature as its effective ‘black body’ radiation temperature, that is, 5000 m.
Now the bottom of a mine shaft 5000 m deep does not have any sunlight being absorbed and it is not emitting IR because sunlight has warmed it only to have much of that energy radiated as IR which is reflected back onto the bottom of the mine. No, the higher temperature of the atmosphere at the bottom of the mine shaft is due to the higher kinetic energy of gas molecules that comes from them having about as much less potential energy in the Earth’s gravitational field compared to sea level as those at sea level have compared to the potential energy at 5000 meters altitude. An ideal gas molecule at a lower altitude has as much more kinetic energy compared to a molecule at higher altitude as that higher altitude molecular has more potential energy.
Recalling high school physics, the total energy of a mass M in the Earth’s gravitational field near the surface is E = ½ Mv2 + Mgh, where g is 9.8 m/s2 and h is an altitude small compared to the radius of the Earth. This is an approximation of course. The U.S. Standard Atmosphere tables include the variation of g with altitude. At sea level it is 9.8066 m/s2, while at 5000 m altitude it is 9.7912 m/s2, for instance. This instance of conservation of energy is very important because the temperature of an ideal gas is proportional to the square of its particle velocity, which is proportional to its kinetic energy.
The ideal gas law is PV = nRT. P is the pressure, V is the volume, n is the number of moles of the gas in the volume, R is a constant, and T is the temperature in Kelvin. Let’s go down our mine shaft. Let’s say it is 5000 m deep and we will calculate the average T for each horizontal slab 1 meter tall as we go down the shaft. Assuming the air density is increasing as the pressure increases, we know that n is proportional to the air density and increasing. It is not constant as in your simple high school science class calculations. The tables show us that this is the case. Now if the pressure, P, were proportional to this density, then T would remain constant. It is not, however.
The pressure P is proportional to the product of the density and the kinetic energy of the molecule. This is why T for the ideal gas is proportional to the kinetic energy of the molecules.
So, the temperature change upon going 5000 m below sea level is about a 33K increase, while the temperature change on going from 5000 m altitude to sea level is about a 33K increase. Now if the temperature at sea level is due to greenhouse gas effects smuggled into the table by the use of some inputs from rocket and satellite data, then the temperature increase values in the table for below sea level should be nonsense.
Yet similar tables were generated in 1958, 1962, 1966, and 1976. This table is still widely used. Over those years, deep mine engineers would surely have had input to correct the values of temperature for the below sea level entries if they did not hold up in their calculations for mine heat management and temperature, pressure, and air density measurements. Or would they? We will discuss this more.
Let us illustrate this mining application problem. The Tau Tona gold mine in South Africa is 11,760 feet deep or 3,584.4 meters deep. The air in the mine reaches a temperature of 130 F. The gravitationally determined air temperature at that depth is 311.46K or 38.31ºC or 100.96ºF as interpolated from the full table of the U.S. Standard Atmosphere given in 500 meter altitude increments. Clearly the rock wall temperature is higher than the temperature of air in gravitational equilibrium in this deep mine. The air at sea level from the table is at 288.15K or 59ºF. The mine engineer would love to bring this air at 59ºF down to the bottom of the mine and be able to keep it at 59ºF as he does so. Air at 59ºF would be much more effective in cooling the bottom of the mine than is air at 101ºF.
But, even if the mine engineer flows this air down to the bottom of the mine in well-insulated pipes, it is still in the Earth’s gravitational field. So, he can keep it from being warmed much by the very warm rock walls of the mine, but he cannot keep it from rising to a temperature of 101ºF, according to the tables! When he calculates the necessary air flow to achieve a given cooler temperature in the bottom of the deep mine, he should be very aware of the temperature increase in the air due to bringing it down to that depth.
So, if the increased gas molecule kinetic energy in the atmosphere at -5000 m creates an increase in temperature of about 33º C, then the increased gas density and kinetic energy in the atmosphere at sea level compared to that at 5000 m, is also responsible for the 33ºC increase in temperature at the surface of the Earth compared to its black body radiation temperature of 255K and the temperature of air at 5000 meters altitude according to the logic of the tables.
That the temperature of a gas in a gravitational field increases as the strength of the field increases is further confirmed by the temperature and pressure relationships to altitude of the other planets with gaseous atmospheres or compositions. The actual gases vary widely as does the amount of radiation incident upon them from the sun. The reflectivities of those gases also differ greatly. Despite that, as the pressure increases as one moves deeper into the gas atmosphere of each planet, the temperature increases. When the gravitational field is extremely high, as in the case of Jupiter, the temperatures become extremely high in the interior. Yet, Jupiter receives a pitiful 50.5 watts/sq. m of solar radiation compared to the Earth’s incident solar radiation of 1368 W/sq. m.
The examples of the gaseous planets being heated by gravitational field effects have often been presented by critics of the greenhouse gas hypothesis with no effective reply. Somehow, the Earth is different. On the Earth, only manmade effects are claimed to be important.
Now we can bring this back closer to home again. The materials at the core of the Earth are extremely hot due to the very high pressures caused by the very high gravitational field strength there. The molten core liquids heat up due to high pressure, but the gases of the Earth’s atmosphere do not? We should be asking the Greenhouse Gas hypothesis advocates why liquids under pressure become very hot, but a gas under increased pressure in a gravitational field does not?
You may want to ask where the energy is coming from that is heating the gas deep in the mine shaft. The gas at the surface of the Earth has a potential energy due to gravity. The gas at the bottom of the mine shaft has a lower potential energy, with the difference in energy converted into a higher kinetic energy because energy is conserved. The gas molecules therefore have a higher mean velocity. The gas temperature is proportional to the kinetic energy of the gas molecules, so it also goes up. The effect on the pressure is that it goes up as the number density of the molecules goes up and it also goes up in proportion to the increase in kinetic energy.
The pressure is increasing faster than either n or T. In fact it is increasing as the product of these two increasing properties, as stated in the ideal gas law, PV = nRT. Note that the temperature does not depend on any flow of gases, according to the tables. It only depends upon the kinetic energy of the air molecules, which is a function of the strength of the Earth’s gravitational field at a given altitude.
The pressure has a more complex functionality, because it depends both on the strength of the gravitational field and the weight of the atmosphere above a given altitude.
It is gravity which accounts for the increased pressure and density of the atmosphere at the bottom of the mine shaft. This is also where most of the energy comes from to heat the Earth’s core or the atmosphere of Jupiter. But the pressure is proportional to the product of the density and the temperature and both are increasing, so the pressure is increasing faster than the density does.
Alternatively, the temperature is proportional to the pressure divided by the density. Since the pressure is increasing faster than the density is, the temperature goes up as we go down the mine shaft.
For the same reason, the temperature goes up as we go 5000 meters downward from the effective black body radiation altitude of about 5000 meters to the surface of the Earth. There is simply no need to posit a complex and unproven theory of greenhouse gas warming to explain why the surface of the Earth is 33ºC warmer than the black body temperature of the Earth as seen from space and as in equilibrium with the incident energy from the sun. The tables seem to imply the cause of this difference is the Earth’s gravitational field. However, despite the fact that one would think that the calculations of mine engineers would have confirmed or invalidated the table for below sea level air temperatures, we will find that the tables do imply a stronger gravitational field effect on the atmosphere than makes sense.
In my article called Do IR-Absorbing Gases Warm or Cool the Earth’s Surface?, I pointed out that:
“If we assume that the sphere [at an altitude of 5000m] with the temperature of 255K is in equilibrium with a slightly smaller black body sphere of the radius of the Earth at sea level, we can calculate the temperature of that surface given that it must radiate a power equal to the power of the surrounding sphere which is in equilibrium with space. The temperature will be higher, since the surface area of the sphere is smaller. In fact, the temperature of the Earth’s surface as a black body would be 255.100K or 0.1ºC warmer than the sphere at the altitude of 5000 meters above sea level which is in equilibrium with space. But the Earth’s surface is not really a black body, so the Stefan-Boltzmann equation has to have an emissivity factor multiplied times the temperature side of the equation. For the Earth’s surface this emissivity factor is about 0.7 on average. This causes the Earth’s surface to have to be at the more elevated temperature of 278.89K to be in equilibrium. This is only about 9K or 9ºC below its usual temperature of 288K. Anything otherwise violates the Law of Energy Conservation.”
So, the increased kinetic energy of air molecules at sea level when compared to that at the effective black body temperature of the Earth altitude of 5000m does not account for the 33K temperature difference despite the tables seeming implication. The effect is real, but its size must be exaggerated. Unless there are counteracting cooling effects, the gravitational temperature increase would be limited to about 9K when changing altitude from 5000m to sea level. There are countervailing cooling effects, so the gravitational effect may be larger than 9K, but it is unlikely to be as large as 33K.
Apparently, the tables did smuggle in effects due to other heating effects and then improperly projected those to the below sea level altitudes.
Yet, mine engineers do attest to such an effect, but they have not apparently been effective in getting the U. S. Standard Atmosphere tables adjusted to any good scientific measurements of the effect.
This is another of many examples of contributing warming effects which have not been properly taken into account by the climate models and which appears to have an inadequate basis in experimental measurements by physicists.
There are still other sources of warming that can claim to contribute to the 9K remaining temperature increase at sea level. As mentioned above, one is the conduction of heat from the Earth’s core. Another is the retention of heat by the oceans with their very high heat capacity. The land surface also retains heat and releases it slowly as the brightest part of the day passes and is replaced with night.
The atmosphere itself, especially when laden with water vapor, holds and retains considerable heat. These heat retention materials with significant heat capacities, even out the temperatures between day and night and when clouds momentarily block strong sunlight. In doing this, they raise the average temperature somewhat through the course of the day. At this time, the size of the average increased temperature contribution of each effect is not known, but they are each making a contribution.
The major difference between the sea level temperature and the effective altitude at which radiation into space balances the energy fluxes into and away from the Earth, a temperature difference of about 33ºC, is not properly attributed to greenhouse gases. These gases are gases that absorb IR radiation effectively. The main greenhouse gas is water and CO2 and methane gas are minor greenhouse gases. Those who promote the idea that man’s emissions of CO2 and methane are likely to cause catastrophic global warming, claim that these greenhouse gases are responsible for this substantial heating of the Earth’s surface by an additional 33ºC. As we have seen here, this is not so.
This argument does not mean that it is not possible for greenhouse gases to shift the sea level temperature a degree or two from the present average temperature or to influence the temperature through the course of a short time, such as between night and day. Whether there are such effects caused by IR-absorbing gases needs to be examined in other ways. What has been established here is other effects, including warming due to the Earth’s gravitational field on its atmosphere, make significant contributions to the warming usually attributed to greenhouse gas theory. Most of the warming is simply a radiative equilibrium having nothing to do with greenhouse gases. Some is due to gravitational effects on the gases of the atmosphere or on the Earth’s core. Some is due to heat retention by the materials near the Earth’s surface which have significant heat capacities.
As I discussed in Do IR-Absorbing Gases Warm or Cool the Earth’s Surface? the effect of carbon dioxide and methane is a net cooling effect, not a warming effect. Water has a much more complex role because it can retain absorbed heat in ways that CO2 and methane cannot.
It is the main greenhouse gas, but it has many properties and many roles not well-described by that name. In many of those roles, it also acts to cool the surface by evaporation and sublimation. In fact, its cooling power is probably presently underestimated in climate models. Water vapor as a cloud former is not yet well-understood, as the nucleation of clouds by cosmic rays makes clear. Water and the IR-absorbing gases keep the Earth’s surface from becoming much warmer during the day when there is direct sunlight. Their role at night in net heat retention is very complex and is not yet understood at all well.
Instead of creating evermore fanciful computer climate models, there are many real warming and cooling effects which will only be well-understood when good scientific measurements from well-designed experiments are performed.
After a huge expenditure of monies and effort on global climate models it is clear that the basic science needed as input into such models is sadly lacking. The effort has been badly misplaced.
Climate modeling without an adequate basis in the understanding of the physics of radiation and heat transfer and transport is pointless.
It is very telling when well-known climate modelers make fun of physicists, chemists, geologists and engineers who take a look at the very effects which are essential inputs to their climate models.