A riddle for climatologists

Fig 1. Earth's surface temperatures (W.J. Keller)(7)
1,1 ℃ increase in 140 year. (NASA-GISS & HadCRUT)

The Dutch version of this article
appeared on Climategate.


There is a fierce battle about CO2 from coal, oil and gas (of fossil origin), which we put into the air. We do this by burning those substances.
Part of the world's population wants to reduce the amount of CO2 in the air. They are afraid of "global warming". I call them AGW-ers for the sake of convenience.
Another - smaller - part does not want that. In their eyes, CO2 has little to do with global warming. On the other hand, they fear the social consequences of the CO2 reduction. (Less energy is less prosperity.) I call them skeptics.
Both groups are partly right and partly wrong, but both parties see only the other's wrong and not their right. That is why it is difficult to settle the dispute. In this article I try to explain that CO2 is a game changer; that is why.

1. Habitable shell

We do not inhabit the Earth, as we often proudly tell each other. We inhabit only a thin shell of the Earth. Say from a depth of 5 km below the surface, to about 50 km up in the air. What happens in it is of direct importance. It is also the play field of the weather.

The radius of the globe is 6300 km. And in the core the temperature is ~5000 ℃. The fact that we do not burn our feet is due to the well-insulating Earth's crust.
The really empty space of the universe, above the Top Of the Atmosphere (TOA), where satellites hardly experience any drag, starts about 200 km high.
In climatic considerations, the heat that penetrates from the Earth's core into the habitable shell is neglected. It is small compared to the energy that the Sun sends us.

Energy is constantly entering our habitable shell in the form of solar radiation. Part of this is reflected by clouds and the surface, and disappears into the universe. The rest is absorbed in the residential envelope and converted into other forms of energy, especially heat. Eventually we have to get rid of that energy, otherwise we would be boiling to death. This is only possible through radiation that passes through the TOA outwards.
What happens within the habitable shell affects us and our climate. If more energy comes in than goes out, we heat up and if more energy goes out than comes in, we cool down.
The sea and soil absorb most of the radiant energy that reaches us and convert it into heat energy. (Plants convert some into chemical energy.) In other words, the temperature would be rising. So we have to get rid of that heat energy.
It can't go down to that warm Earth core. That would have to be through heat conduction and heat only flows from hot to cold. So it has to go up. That should be possible. Because it is cold at the TOA. It borders the empty space of the universe, where it is 3 K (-270 ℃).
There are 5 processes that can send energy from the sea and land surface and the lower atmosphere to the TOA zone. They almost entirely take care of the outward transport. Being:

  1. Convection; that is hot air or water that rises and cold air and water that sinks.
  2. Convection of H2O-containing air, for which liquid water evaporates (= absorbs heat) and condenses higher up. So it releases heat in the TOA area.
  3. Expansion of ascending air and compression of descending air. (I won't elaborate on this. The process is pretty much cyclical with negligable nett result.)
  4. Conduction; that is heat conduction; energy transfer where hot and cold masses touch.
  5. Heat radiation; mainly infrared (IR). Matter warmer than 0 K (-273 ℃) radiates and thus loses energy, provided the environment is colder than the emitter.

Ultimately, the Earth loses the captured solar energy only through radiation to the universe from the TOA. Processes 1 to 4 no longer play a role there due to the thinner atmosphere. That does not apply to our habitable shell. In addition to IR-radiation, it has at least three other mechanisms to get rid of the received energy. So that we don't overcook.

2. Effect of CO2

There is a qualitative difference between the effect of low and high CO2. It is because of that qualitative difference that AGW-ers and skeptics quarrel. With little CO2, the AGW people are right. There, CO2 really does a lot about the temperature. With a lot of CO2, the skeptics are right. At least, if they say that a little more or less CO2 makes no difference to the temperature.

A CO2 molecule in the atmosphere has properties to absorb radiation. I.e. to store the energy. It then has to re-emit it, or pass it on as heat (more molecular motion) to surrounding air molecules. Close to the earth's surface the air pressure is ~1000 hPa (= 1 Bar, also called 1 atmosphere). There the density is great and heat transfer is much easier than re-radiation. High in the air, where the pressure is much lower, an excited molecule meets fewer air molecules to transfer the energy as heat. There the excited molecule has more time to transfer energy through radiation. The change from transfer via heat to transfer mainly via radiation takes place gradually. Mostly between 15 and 80 km altitude and pressures between 1.2 hPa and and 0.2 hPa.

The capture (storage) of radiant energy by a CO2 molecule is limited to radiation of certain frequencies. With a slightly different frequency, the catch decreases and there is less heat transfer and less radiation. More IR then passes through unhindered.

     2.1 Low CO2 (< 200 ppM)

An atmosphere without CO2 also absorbs part of the outward energy transport via IR radiation. And energy transport via radiation from the sea and land surface to the TOA is hindered. This is due to the water vapor in the atmosphere. The H2O molecule, like CO2, absorbs long wave/IR radiant energy. The frequencies at which it happens differ slightly, so that adding CO2 undeniably absorbs some extra. There is little human can do to add or take away from water vapour. It is a so-called condensable greenhouse gas, which means that humidity is strongly linked to temperature.
But we can add CO2.

Atmospheric CO2 thus still reduces some of the outward energy transport by IR. At a low concentration, the effect is directly proportional to the amount of CO2. At a concentration of ~200 ppM, the absorption of certain wavelengths is already complete. More CO2 increases the absorption slightly, because there is still absorption at slightly different wavelengths, but less. With more CO2 there is therefore still some extra absorption to be achieved. However, it quickly decreases at more deviating wavelengths. The effect is then no longer proportional to the concentration, but decreases 'logarithmically'(2).
We are therefore entering a zone where energy transport decreases less quickly with more CO2. More about that in the next paragraph. The AGW-ers are right, that CO2 has a major influence, is only correct for the situation with little CO2 ( < 200 ppM ). Where, by the way, plants only grow poorly. (Another 50 ppM less makes the Earth uninhabitable.)

The absorption by greenhouse gases does not mean that there is no further outward energy transport of that absorbed radiant energy. The greenhouse gas simply converts the absorbed energy into heat of the surrounding air. There the transport continues its way up through the four other transport mechanisms mentioned above. Only higher than 40-50 km the total outward transport by means of IR-ransport gradually takes over as only exporter .

For outward transport of heat energy, a temperature difference between high and low is required. The TOA radiation remains the same and the temperature practically as well. So the temperature of and near the surface of the sea and soil must be higher than without CO2. The AGW people are right there, because the effect of CO2 is not small. I estimate that at 200 ppM it makes about 5, maybe even 10 ℃ difference, with an atmosphere without CO2.
That is pretty much the difference between living in an ice age and our comfortable world today. So we should not only be happy with CO2 because plants live off it, but also because otherwise it would be too cold.
However, above 200 ppM, the effect of more CO2 decreases quickly, because the transport mechanism changes, see below, § 2.2. In the year 2023 the CO2 concentration is ~420 ppM, which will only add ~1 ℃ to the aforementioned contribution of approx. 5-10 degrees.

     2.2. A lot of CO2 (>200 pM)

At the current concentration, practically all the IR, which CO2 blocks, has been converted into heat after about 100 m. If we could double that concentration, it would already be the case after 50 m. I.e. everything it does is then not done in 100, but already in 50 m. The heighth, where extra heat energy is added to the air, is then reduced by 50 m.
It is physically inconceivable that an extension of the road to TOA regions, approx. 100 km higher, would give a measurable increase in the resistance to heat transport by extending the upward road by 50 m.
The convective properties of the air do not change either. i.e. no additional increase in the temperature difference between surface and TOA is necessary to keep the total outward energy transport constant.
That is why the skeptics are right in saying that more CO2 now has barely measurable influence on the temperature at the lower part of the Earth's habitat.

Above 200 ppM, additional CO2 only increases the frequency effect referred to in § 2.1. The collision cross-section (chance of absorption) decreases rapidly in case of deficient resonance. That soon goes faster than the chance of more absorptiongoes up with more molecules.

Two little bits that do one thing, also do little together. The effect of CO2 increase on the outgoing energy transport is therefore small, if the concentration is already higher than 200 pM. And the required temperature rise as well(3). A guess of ~1 ℃ when doubling, ~1 ℃/(2 x CO2), is probably still too high. Even 100 ppM less now would have no measurable effect on the temperature in the lower habitabel shell.

3. Discussion

An obvious objection is: the measured surface temperatures are increasing more. What causes that increase, if not CO2? We don't know the answer to that. The Earth's climates have always changed, with or without humans. The increase in temperature since 1880 is nothing special, as Fig.2 shows. We also have little or no knowledge of the causes of those earlier changes. Why should the Earth stop doing, what it always did? Countless processes control the complex climate system. That is therefore unpredictable(4).
Extrapolating system indicators is the only thing we can do meaningfully for now.

Figure 2

Fig.2 2500 yr. Eath's tempeatures [℉].

That is why I recommend taking measures for the next forty years based on extending Keller's temperatures in Figure 1. Research into individual factors such as CO2, sunspots, clouds, dust particles, sea level rise, etc. etc. can be scientifically interesting in itself, but not to predict the course of the climate. Adapting to the observations and quick response to alarming weather- and earthquake forecasts a few days ahead is the only sensible thing to do for a long time.

Statements about the development of the CO2- concentration can be made on the basis of system indicators. Assuming that the system, as it was in the period 1960-2020, has not changed drastically. You do need to know how much fossil CO2 we put into the atmosphere every year(5). This should not lead to temperature(6) or climate forecasts. We are only sufficiently certain of the CO2.

C. (Kees) le Pair,
Nieuwegein, 2023 06 15
Add Note 6, 2023 06 20.
Add Note 7, 2023 08 21.

References & additions

  1. A little CO2 changes the climate considerably. And above a reasonably known amount, more or less hardly anything changes. Neither towards a higher nor towards a lower temperature.
  2. By decreasing logarithmically we mean that with a factor of 10 increase in the extra amount of CO2 the extra effect is 1x, with a 100x greater increase the effect is 2x and with 1000x 3x.
  3. "Little, small & low" compared to the much larger temperature effect of more and less CO2 at low concentrations.
  5. C. le Pair & A. Huijser: HOW DOES OUR CO2 ESCAPE? In the period 1960-2020 we found an "equilibrium concentration" of 287 ppM. Calculating back to 1880, the equilibrium concentration was then 280 pM. Which surprisingly matches proxy values. We suspect that it will turn out to be 295 pppM from 2020 to 2080. The difference with the current (Mauna Loa) value is the "excess concentration" with which the annually disappearing CO2 is proportional. The half-life of excess settlement is 37 years. However, at current global CO2 emissions of 5 pM/year, based on that analysis, we will never reach that "notorious" 2x pre-industrial CO2-concentration, and with 555 pM we will even remain below it.
  6. NASA-GISS published an average absolute temperature over the year 2021 of 14.9 ℃; up 1.1 ℃ since 1880.
  7. I inserted the picture on top only to draw attention to the hoax of the climate emergence. It was meant to depict the futillity of the changes, the whole world talks about, by using 'instrumental language' everybody understands. The originator Dr. Keller meticulously noted that his five living room thermometers were indicating the thru averaged temperatures of the eras. It should show a temperature rise as in note (6). An artist's copy I used was less meticulously done.
    Anyway, the rise over 140 years is futil in view of the geological history of the Earth, when no humans spewed CO2.

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