Review and Summary of three Important Atmospheric Physics Papers

By Andy May


In 2014, Dr. Michael Connolly and Dr. Ronan Connolly posted three important, non-peer reviewed papers on atmospheric physics on their web site. These papers can be accessed online here. The papers are difficult to understand as they cover several fields of study and are very long. But, they present new data and a novel interpretation of energy flow in the atmosphere that should be seriously considered in the climate change debate.

By studying weather balloon data around the world Connolly and Connolly show that the temperature profile of the atmosphere to the stratosphere can be completely explained using the gas laws, humidity and phase changes. The atmospheric temperature profile does not appear to be influenced, to any measurable extent, by infrared active gases like carbon dioxide.

Figure 1, source Connolly and Connolly.

Figure 1 shows the “U.S. standard atmosphere.” The black curve is the standard atmospheric temperature as a function of altitude (Y axis). There are several key points that are important for this post. First, notice that the temperature decreases with altitude in the troposphere, then rises vertically in the tropopause, then it reverses course and increases in the stratosphere. Since we are discussing weather balloon data in this post, we are only concerned about the curve to about 35 kilometers. This region contains about 99% of the atmospheric mass. We will also be discussing the ozone layer, which is at the very top of our layer of investigation.

They evaluate available weather balloon data in terms of molar density and pressure. They find that, above the boundary layer (roughly the surface to 2 kilometers, the atmospheric layer that contains most of our weather), the trend of molar density and pressure is a line until the tropopause is reached. Above the tropopause it is also a line, but with a steeper slope, see figure 2. In figure 2, pressure increases to the right and altitude decreases to the right. Above the tropopause molar density decreases more rapidly with pressure, this suggests a change in the equation of state for the atmosphere above the tropopause. Region 3, the boundary layer, shows much more variability than the higher regions of the graph. This variability is due to changes in humidity and precipitation.


A change in the equation of state in the atmosphere means that it will respond to external forces (“forcings”) differently. For the atmosphere, the equation of state is the ideal gas law, modified to account for factors that affect real gases, but not ideal gases. These include varying specific heat capacity, Van der Waals forces and compressibility effects among others. While the molar density versus pressure plots, like figure 2, strongly suggest that the equation of state has changed above the tropopause it does not tell us exactly what happened. Connolly and Connolly think that oxygen and nitrogen multimers form in and above the tropopause (see figure 3). Multimers are called trimers if they contain three molecules and tetramers if they contain four.

Figure 2, after Connolly and Connolly (2014) paper 1.

Figure 3 (source Connolly and Connolly, 2013)

This suggests that the atmosphere above the tropopause has a lower molar density, at a given pressure, than the tropospheric trend would suggest. The atmospheric composition and humidity above and below the tropopause are nearly identical, so composition is not the cause of this change.

The formation of oxygen and nitrogen multimers is a state change that can be called a phase change. If multimers form in the tropopause, they release the energy of formation to the surroundings. This may increase the temperature of the surroundings. The larger multimers have more degrees of freedom than the diatomic monomers (for example O2) and every additional degree of freedom increases the internal energy of a mole of multimers by ½RT. R is the universal gas constant and T is temperature. This is described in more detail in Connolly and Connolly, paper 2, section 2.2. In their section 2.2, the heat of formation (or enthalpy of formation) of the multimer is designated as ΔH. The molar enthalpy (H) of a gas is defined as,

H = U + PV (1)

Where U is the internal energy of the gas, P is pressure and V is the volume.

U = ½αRT (2)

The internal energy of the gas is equal to ½ of the degrees of freedom (α) times the gas constant (8.3145) times temperature (T). Degrees of freedom of a gas are defined here as the number of independent ways a gas can have energy. This includes translation, rotation and vibration. Internal energy is the sum of the energy in all the degrees of freedom of the gas. If ΔH is set to zero for a diatomic monomer, it is 4RT with 34 degrees of freedom (α) for a tetramer, according to table 2 from Connolly and Connolly paper 2. So, the heat of formation of a multimer can be significant and will affect the temperature of the tropopause and stratosphere. The formation of oxygen multimers probably involves the emission of microwave radiation.

In the tropopause, the lapse rate is near zero, this means, according to Connolly and Connolly, that the increase in internal energy, due to multimer conversion, is balanced with the loss of thermal energy converted to potential energy, due to gravity, at this altitude. I realize that thermal energy can be defined in different ways, but here we define it as the internal energy of the gas due to its temperature. As altitude increases and we enter the stratosphere, either more multimers are formed or they get larger and internal energy increases more rapidly than thermal energy is converted into potential energy and the air temperature begins to increase. In the troposphere, there are no multimers and thermal energy is transformed into potential energy as the altitude increases and the air temperature steadily decreases (the “lapse rate”). This causes the slope change shown for region 1 (tropopause and stratosphere), seen in figure 2.


Ozone concentration starts to increase with altitude in the stratosphere as well. The classical explanation for the formation of ozone is called the Chapman mechanism and it is illustrated in figure 4. Chapman hypothesized that ultraviolet light (UV) striking oxygen molecules will split them into individual oxygen atoms. He then speculates, that some of these would combine with nearby oxygen molecules and form ozone.

Figure 4 (source Connolly and Connolly, 2013)

There are several problems with the Chapman mechanism. First, it requires a great deal of energy to break a diatomic oxygen molecule’s bonds. Further, if the Chapman mechanism were the only mechanism forming ozone, why would ozone concentrations, in the Northern Hemisphere, be the highest in the Arctic in the spring? The equator (the red line in figure 5) receives the most UV from the sun, yet the ozone concentration there is much less than in the Arctic, the dark blue line in figure 5. Further, one would think that the Arctic and Northern Hemisphere ozone concentration would peak in the summer, yet it peaks in the spring and falls in the summer, and begins to increase in the winter. The Chapman mechanism also has other flaws as documented here.

According to classical theory, the extra energy in the tropopause and stratosphere that reverses the negative lapse rate seen in the troposphere, comes from “ozone heating.” Ozone absorbs UV light from the sun and radiates heat which warms the tropopause and stratosphere. Yet, the tropopause stays in place during Arctic and Antarctic winters when there is no sunlight. Given these contradictions, Connolly and Connolly came up with an alternative mechanism.

Figure 5 (source Connolly and Connolly, 2014, paper 2)

Ozone formed directly from oxygen multimers also requires UV radiation, but it requires much less than is required in the Chapman process. Figure 6 shows the process described in Connolly and Connolly (2014). There a multimer of eight oxygen atoms and four oxygen molecules is transformed into two ozone molecules and one regular oxygen molecule. This process requires sunlight and abundant multimers to work, but less energy. Further, the formation of the multimers, themselves, can occur without sunlight and the formation process releases heat of formation, which helps form the tropopause and warms the stratosphere.

Figure 6 (source Connolly and Connolly, 2013)

Their idea allows ozone to form more easily and with less energy and it provides additional energy during the Arctic and Antarctic winters when there is no sunlight for months. The idea that multimers make ozone easier to form, is only one of the potential impacts of possible multimer formation in the tropopause and stratosphere. Multimer formation may also influence tropospheric weather as discussed in Connolly and Connolly paper 2.

The Weather balloon data

Weather balloons record temperature (T), pressure (P) or sometimes altitude (h), horizontal wind speed and direction, and relative humidity. Relative humidity is converted into absolute humidity using the temperature. There have been one to four launches a day from about 1,000 stations around the world – in some cases since the 1950s or earlier. That is about 13 million datasets containing data from the ground to the mid-stratosphere (~30-35km altitude). A weather balloon launch in Chile is shown in figure 7.

Figure 7 (Weather balloon launch in Chile, source: European Southern Observatory)

Nobody had analyzed the weather balloon data in terms of molar density before, but it is quite straightforward to do. Molar density, D = n/V = P/(RT) (where R=8.314, is the universal gas constant). So, all you need to do is divide the P (Pressure) values by the corresponding T values (multiplied by 8.314). The units of “D” are moles/m3.

From a climate perspective, it is better to view the molar density versus pressure plot in terms of temperature and height as in figure 8. To compute temperature, we first have to compute best fit lines to each region of figure 2 to obtain slopes and intercepts. Connolly and Connolly call the slopes “a” and the intercepts “c,” such that:

D = aP + c  (3)

Therefore, since D = P/(RT) and using the ideal gas law:


“R” is still the ideal gas constant equal to 8.3145 J/(mol.K). The coefficients, “a” and “c,” are not constants and vary from place to place. Typical a and c coefficients are shown in table 1. In figure 2, the “humid” phase in table 2 is region 3, the “light” phase is region 2 and the “heavy” phase is region 1 or the tropopause and stratosphere. A spreadsheet for computing temperature from the coefficients, using equation 4, is in the supplementary materials for Connolly and Connolly, paper 1. In table 1, there are two entries for the near Artic Norman Wells site. One is for the ground (g) and other is for the tropopause/stratosphere (u). Near the poles the heavy phase (multimer formation) can occur near the ground.

Table 1, from Connolly and Connolly, paper 1.

Using equation 4 and the coefficients of the best fit lines, like those in table 1, we can estimate temperature (T). This has been done in figure 8. Most of the balloon launch sites can be fit with two or three best fit lines. In figure 8, both are fit with three lines. Lake Charles, Louisiana is sub-tropical and the boundary layer requires a separate fit due to high humidity. Norman Wells, Northwest Territories, Canada requires three because the boundary layer, in winter time, can show a phase change very like the phase change observed in the tropopause. This might be due to the formation of multimers at the surface.

Figure 8, after Connolly and Connolly, paper 1

The boundary layer is defined, in the papers, as where the absolute humidity is greater than one gram of water per kg of air. This is roughly greater than 0.1%. As figure 2 shows, the slope is relatively more variable in this region (region 3). Changes in temperature, humidity and precipitation affect the slope in this region. The boundary layer may not exist in the Arctic and Antarctic in winter, where surface humidity can be very close to zero in cold weather. Yet, slope anomalies exist there as well, sometimes going the other way as seen in the Arctic (figure 8B). These Arctic and Antarctic winter anomalies look suspiciously like the tropopause anomalies.

Connolly and Connolly found that there is a change of state, that might be a phase change, at the top of the troposphere and a similar change occasionally at the surface, in the polar regions, in the winter. After accounting for this apparent phase change, they could describe the atmospheric temperature profiles of all ~13 million weather balloons entirely in terms of the thermodynamic properties of the bulk gases and humidity. For the Earth’s atmosphere, the bulk gases are N2, O2, argon and sometimes H2O. By “thermodynamic properties”, they mean the gas laws, the role of gravity, changes in state (i.e., phase changes), differing heat capacities, etc. Of the four bulk gases, only H2O is infrared-active and the influence H2O has on the atmospheric temperature profile has nothing to do with its infrared activity. Instead, it is related to its phase changes and the fact that it has a higher heat capacity than the other bulk gases.

The temperature fits did not require consideration of the CO2 concentration or any of the other infrared-active (“IR-active”) gases. If the effect of CO2 and other greenhouse gases were as strong as predicted by the climate models, one could reasonably expect that they would affect these temperature profiles.

Most versions of “the greenhouse effect” theory argue that the infrared activity of greenhouse gases (“GHG”) alters the atmospheric temperature profile. In particular, the models suggest that as carbon dioxide is added to the troposphere by man’s emissions, the troposphere should warm. This is supposed to be counteracted by increasing the speed of cooling. Thus, they predict that the troposphere warms and the stratosphere cools due to man’s carbon dioxide emissions changing the atmospheric temperature profile. Therefore, a debate exists over whether there is a “tropospheric hotspot” signature from GHG warming. Some also argue that there must be “stratospheric cooling.” But, the key to these theories is that the IR activity of the GHGs is supposed to in some way alter at least some part of the atmospheric temperature profile. This IR-based effect is the greenhouse effect. But, if the IR activity of the GHGs doesn’t influence atmospheric temperatures, as the Connolly’s found, then there isn’t a greenhouse gas greenhouse effect!

As mentioned above, their analysis of molar density versus pressure reveals a change in slope, probably due to a phase change, that occurs above the troposphere. This phase change can explain most, if not all, of the changes in temperature behavior associated with the tropopause and stratosphere. The tropopause and stratosphere are treated as distinct regions from the troposphere because they have different temperature behaviors than the troposphere. That is, the lapse rate approaches zero in the tropopause and becomes positive in the stratosphere. While this is true, the tropopause and stratosphere share the same molar density vs. pressure slope, intercept, and equation of state.

Multimers and the Ozone Layer

In Connolly and Connolly’s paper 2, they argue that the phase change identified in their paper 1 is due to the formation of oxygen (and possibly nitrogen) multimers, i.e., (O2)n, where n>1. The formation of multimers in the atmosphere is not a new idea and has been studied by Slanina, et al., 2001.

They also noted that if multimers are forming in the tropopause and the stratosphere, there is an alternative mechanism for the formation of ozone, which is much more rapid than the standard Chapman mechanism. That is, ozone (O3) could form directly from the photolysis of oxygen multimers, for example, a trimer (three linked O2 molecules) of oxygen could dissociate into two ozone molecules: (O2)3 + uv light → 2O3.

There is a remarkable correlation between the proposed phase change conditions and ozone concentrations, see figure 9. This is consistent with the Connolly’s mechanism for the formation of ozone, and suggests that the ozone is generated rapidly in situ. Table 2 lists the computed phase change conditions for 12 different regions, separated by latitude, around the world:

Table 2, Source: Connolly and Connolly paper 2

Figure 9, Source: Connolly and Connolly paper 2

Figure 9 shows the monthly variation of the optimal phase change pressure for several of the regions versus ozone formation (from NASA’s Total Ozone Mapping Spectrometer) for the same region. The correspondence between them is clear. It is interesting that the optimal pressure conditions for the phase change vary dramatically from month to month in each latitude band in figure 9 and that the level of ozone also varies dramatically from month to month. This suggests that ozone creation is very fast in the upper atmosphere, something that is consistent with the Connolly’s hypothesis, but not consistent with Chapman’s. It is also not consistent with the hypothesis that chlorofluorocarbons destroy the ozone layer, but that is another story.

Local Thermodynamic Equilibrium

Connolly and Connolly have shown, using the weather balloon data, that the atmosphere from the surface to the lower stratosphere, is in thermodynamic equilibrium. They detected no influence on the temperature profile from infrared active (IR-active) gases, including carbon dioxide. This is at odds with current climate models that assume that the atmosphere is only in local thermodynamic equilibrium as discussed by Pierrehumbert 2011 and others.

Climate models split the atmosphere vertically into many different layers, each a few kilometers thick, then the layers are broken up geographically into grid boxes. Each grid box is assumed to be in local thermodynamic equilibrium (LTE). These boxes are assumed to be thermodynamically isolated. However, within each grid box, the total energy content is assumed to be completely mixed. Because each box is isolated from the surrounding boxes, the rates of IR emission and absorption from the box are a function of:

  • The IR flux passing vertically through the box
  • The current average temperature of the box
  • The concentrations of each of the IR-active gases in the box

Since they are thermodynamically isolated from each other, if a grid box absorbs more (or less) IR radiation than it emits, this will alter the energy content and average temperature of the box. For this reason, a grid box can develop an energetic imbalance relative to the surrounding grid boxes through radiative processes. Therefore, in the models, the presence of “greenhouse gases” (e.g., CO2) alters the underlying atmospheric temperature profiles. But, is this LTE assumption valid? So far, it has simply been assumed to be the case.

What would happen if the grid boxes are not thermodynamically isolated? Well, if one grid box becomes “hotter” or “colder” due to radiative heating/cooling than the surrounding boxes, then energy would flow between the neighboring grid boxes until thermodynamic equilibrium was restored. If the rates of energy flow are fast enough to maintain thermodynamic equilibrium then the radiatively-induced imbalances from the IR-active gases would disappear. Instead, the atmospheric temperature profile would be determined by the thermodynamic properties of the bulk gases. This is what Connolly and Connolly found was happening.

With thermodynamic equilibrium, we would still expect to see, the often observed, up-welling and down-welling IR radiation. We would also still expect the total outgoing IR radiation to remain roughly in balance with absorbed incoming solar radiation, as we currently observe. And, we would expect the IR spectrum to show the peaks and troughs characteristic of the main IR-active gases, i.e., H2O, CO2 and O3. However, Connolly and Connolly found that the IR-activity of these gases does not alter the atmospheric temperature profile.


The standard mechanisms for energy transmission within the atmosphere usually considered are radiation, convection (of which there are three types: kinetic, thermal and latent) and conduction. Because air is a poor heat conductor, conduction’s role in atmospheric energy transmission is negligible. That initially would appear to leave just radiation and convection. Both radiation and convection move thermal energy slowly, too slowly to keep the atmosphere in thermodynamic equilibrium. However, we know from thermodynamics that thermal energy can be converted to work and transmitted and then turned back into thermal energy. Thermal energy transfer is not the only method of energy transfer at work in this equilibrium process.

Connolly and Connolly found that there is almost no experimental data on the rates of vertical convection outside of clouds and above the boundary layer. But, from the limited data they have, the rates of vertical convection appear to be too slow to maintain thermodynamic equilibrium from the surface to the stratosphere.

They found an additional energy transmission mechanism which seems to have been neglected, “through-mass” mechanical energy transmission. Unlike convection where the energy is only transported by a moving air mass, this mechanism allows mechanical energy to be transmitted through the air mass without the air itself having to move significantly. This is like conduction, except that conduction involves the transmission of thermal energy, while this mechanism involves the transmission of mechanical energy. To distinguish it from “convection” (which comes from the Latin for “carried with”), they use the term “pervection” (from the Latin for “carried through”). In this process, molecules collide transmitting mechanical energy to one another. An analogy would be a long tube filled with ping-pong balls and the tube is only wide enough for one ball. If a ping-pong ball is forced in one end of the tube, one will immediately be forced out the other end. None of the ping-pong balls move very far, but the energy is quickly transmitted, mechanically, a long distance.

In Connolly and Connolly paper 3, they designed a series of controlled experiments to try to quantify the relative rates of energy transmission of each of these mechanisms in air. Their experiments showed that, at ground level, energy transmission by pervection (aka “work”) is several orders of magnitude faster than conduction, convection or radiation! This then explains why the troposphere and stratosphere are not thermodynamically isolated, as the climate models assume.

Pervection is a mechanical energy transmission mechanism, not a thermal energy transmission mechanism, in common thermodynamic terms it can be considered “work.” Mechanical and thermal energy can be converted to one another as thermodynamics teaches us. So, either energy transmission mechanism can, and will, act to restore thermodynamic equilibrium. This also highlights why it is important to consider multiple types of energy and energy transmission mechanisms.


The three papers by Connolly and Connolly provide new data and analysis that show the IR-active trace gases in the atmosphere have an insignificant effect on the atmosphere’s vertical temperature profile. They show the atmosphere, at least to the lower stratosphere, is in thermodynamic equilibrium which invalidates the local thermodynamic equilibrium assumption used by the global climate models.

Unlike other critiques (Jelbring, 2003, Johnson 2010, O’Sullivan, et al. 2010, Hertzberg, et al. 2017, and Nikolov and Zeller, 2011) of the carbon dioxide climate control knob hypothesis (Lacis, et al., 2010), this analysis explains two lines of evidence often used to justify the carbon dioxide greenhouse effect:

  1. Why is the lapse rate positive (temperature increasing with height) in the stratosphere?
  2. Why do we observe both upward and downward traveling IR radiation in the atmosphere?

The lapse rate, which averages about -6.5°C per kilometer in the troposphere, goes vertical and eventually reverses sign in the tropopause and stratosphere due, at least in part, to the formation of multimers according to Connolly and Connolly. The formation of multimers releases energy, which can account for at least some, of the tropopause and stratospheric heating. IR-active atmospheric gases like water vapor and carbon dioxide do radiate IR in all directions and this can be detected, it is just that this radiation does not affect the atmospheric temperature profile significantly according to Connolly and Connolly’s work.

It takes less energy to form ozone directly from oxygen multimers than from splitting diatomic oxygen molecules, although both require UV light. Further, ozone formation does correlate well with the conditions required for multimer formation. Multimer formation does not require sunlight and can occur at night. Also, ozone concentrations in the ozone layer vary rapidly, suggesting ozone is created and destroyed monthly. This is inconsistent with the Chapman process.

The key problem with the conventional idea of IR-active gases, like carbon dioxide, influencing atmospheric temperatures is the concept that the atmosphere is only in local thermodynamic equilibrium. The weather balloon data strongly suggest that the atmosphere is in thermodynamic equilibrium, meaning IR-active gases have little to no influence on atmospheric temperatures. For this to be true a very fast energy transfer mechanism must be at work. Connolly and Connolly suggest that this transfer mechanism is mechanical in nature. Using thermodynamic terminology, the mechanism is “work.” They have proposed a name for the mechanism and call it “pervection.”

Currently, the multimer formation in the tropopause and stratosphere is speculative and requires experimental verification. Likewise, the details of forming ozone from oxygen multimers need to be worked out and documented. Pervection is a proposed name for a relatively obvious form of energy transfer that we observe all the time and has just been overlooked for some reason in climate science. Air is compressible, of course, but it does transmit mechanical energy. BB guns, air compressors and inflatable tires wouldn’t work without this energy transfer process.

So, clearly the Connolly and Connolly ideas need further work, but they have put together a very coherent and detailed hypothesis that deserves serious consideration. It is, at least, as well documented and supported as the conventional carbon dioxide greenhouse theory.

For those that want to read a more detailed summary of the Connolly’s work that includes a description of their laboratory work, I refer them to the Connolly’s summary here and to their three papers, linked at the top of this post.

Published by Andy May

Petrophysicist, details available here:

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