Temperature Regulated Cooling Dominates Warming and Why the Earth Stopped Cooling At 15°C

Guest Post by Wim Röst

Abstract

It is said that the Earth’s surface temperature variations are controlled by [human-induced] greenhouse gases1. This is not the case. When cooling systems dominate, surface temperatures are set by the cooling system and not by the system that is warming the surface. On Earth the surface cooling system dominates; temperatures are set by the natural cooling system. The strength of natural surface cooling is set by temperature. Adding greenhouse gases to the atmosphere does not make any difference for surface temperatures. Their initial warming effect is neutralized by extra surface cooling and by a diminished uptake of solar energy. The cooling system dominates.

Introduction

The Earth was assembled from ‘space debris’ orbiting the Sun. Gravity made objects like ‘space rocks’ and ice comets coalesce. When accretion took place, gravity melted all assembled objects and a big ‘snooker ball’ of molten material was built. The proto-Earth was also warmed by the Sun, but eventually it cooled down until ‘energy in’ equaled ‘energy out.’ Currently, the surface of the Earth is at balance at around 15 degrees Celsius. A similar planet, with no oceans or atmosphere would have stopped cooling at around 5.3 degrees Celsius, if it reflected no sunlight. Why did the surface of the Earth stop cooling at 15 degrees? And why didn’t the Earth’s surface stop cooling at, for example, 50 degrees Celsius?

Answering those questions reveals that it is not greenhouse warming that sets the level of the Earth’s surface temperatures but the mechanisms cooling the surface. The Earth’s additional cooling systems determine surface temperatures: evaporation, convection, and cloud cooling. All are H2O related.

And the main reason the Earth stayed about ten degrees warmer than its 5.3°C ‘rock temperature? ‘ As will be argued, it is the existence of large oceans in combination with their self-produced water vapor greenhouse effect.

5.3°C

The temperature an Earth-like object in space would have if the planet did not have an atmosphere while receiving the same amount of solar radiation as the Earth is 5.3°C. Only radiation would warm and cool the object. This Stefan-Boltzmann calculator shows that such a planet would have a surface temperature of 5.3 degrees Celsius or 278.5K. But our Earth has a higher global surface temperature, 15 degrees Celsius. The atmospheric greenhouse effect partly accounts for this.

Greenhouse effects

On Earth greenhouse effects are huge, but that does not mean they are decisive in setting the final temperature of the surface of the Earth. There is not just one greenhouse effect, there are two, and each have their own surface warming effect. The first greenhouse effect is back radiation. After surface radiation is absorbed by greenhouse gases the atmosphere is warmed. A warmer atmosphere radiates more energy back to the surface: back radiation. Back radiation adds 333 W/m2 to the 161 W/m2 of surface absorbed solar energy. Back radiation is a strong surface warming force.

The second greenhouse effect warms Earth because of the diminished efficiency of radiative surface cooling. When effective cooling is diminished, more energy remains at/near the surface and both the surface and Earth warm. On Earth only about 40 W/m2 out of 396 W/m2 surface radiation directly reaches space: an efficiency of about 10% or a direct emissivity of only 0.1.

Both greenhouse effects each have their own surface warming effect. For each greenhouse effect its consequence for surface temperatures can be calculated. Separately and together the two greenhouse effects result in huge initial surface warming effects.

Without additional cooling: 270.1°C

Figure 1. Stefan-Boltzmann Calculator, source: here.

Figure 1 shows the surface temperature of an Earth-equivalent ‘rock planet’ with greenhouse effects added, but only warmed and cooled by radiation. Our real Earth has additional systems cooling the surface: cooling by evaporation, convection, and clouds. These additional surface cooling systems cool the surface much further than ‘by radiative cooling only.’ From the initial greenhouse temperature of 270.1°C to the actual surface temperature of 15°C. The additional cooling sets the final surface temperatures. Of decisive importance: the strength of Earth’s additional cooling depends upon water and temperature.

Temperature dependency of additional cooling

The Earth’s additional cooling is predominantly H2O related. Surface temperatures determine the quantity of water vapor in the air. And the quantity of atmospheric water vapor determines the total cooling effect. In this way, surface temperatures determine the strength and the dynamics of H2O related cooling.

Figure 2. Equilibrium vapor pressure and temperature. After: here.

Figure 2 shows the equilibrium vapor pressure and temperature according to the Clausius-Clapeyron relation. As shown in the graphic a rise in temperature from zero to 30 degrees Celsius multiplies the equilibrium vapor pressure of water vapor by six times.

When surface temperatures go down by one degree Celsius/K, the quantity of water vapor goes down by about 7% and by consequence all water vapor related cooling processes diminish in strength. At a certain temperature level, ‘energy in’ will equal ‘energy out’. When surface temperatures don’t change, H2O related surface cooling will remain constant. But the small rise in temperature by only one degree Celsius (or one K, a 0.3% rise in temperature) will result in about 7% more water vapor. That huge rise in water vapor content empowers all H2O related cooling processes, often with a more than a proportional cooling result (tropical convection, tropical clouds). As shown by figure 2, H2O related cooling is very dynamic, especially in the higher temperature range. Dynamic additional cooling even limits the temperature of open oceans.

Limitation

Open tropical oceans have a maximum average yearly temperature of 30°C to 32°C. Richard Willoughby reports that less than one percent of the ocean surface exceeds 32 °C for more than a few days at a time. Additional cooling factors limit ocean temperatures to this temperature level. Oceans comprise 71% of the Earth’s surface.

Redistribution of tropical energy

Tropical oceans distribute warm water to the poles in quantities varying over time. The higher the inflow of warm tropical water at higher latitudes, the higher the local quantity of atmospheric water vapor, the main greenhouse gas. Rising water vapor over high latitudes results in a diminished efficiency of local surface radiation in reaching space. Less radiative cooling means that these high latitudes will warm and also that the Earth as a whole will warm. Over time, countervailing processes at the surface (adapting oceans and weather systems) will restore the previous equilibrium temperature (if all other things, like the Milankovitch orbital parameters remain the same). The time frame involved is decades and/or centuries.

Why not 50°C?

Why didn’t the surface of the Earth stop cooling at a temperature level of 50°C? At a surface temperature of 50°C, upward convection of surface energy is huge. High convection will be present over large surface areas. At 50 degrees Celsius oceans will actively be cooled day and night and during the day clouds will reflect most of incident sunlight back to space before it can warm the oceans. Under these circumstances, oceans cool quickly. At the current global temperature of 15°C cooling by evaporation and associated cooling processes diminish enough to balance ‘surface energy in’ and ‘surface energy out’.

Why 15°C?

Why are oceans at a global temperature of 15°C evaporating exactly the quantity of water vapor needed to equal ‘surface energy in’ and ‘surface energy out’? This temperature level is determined by the intrinsic properties of the H2O molecule. The H2O molecule is very hygroscopic; there is a strong bond between molecules, and it is not easy for an individual molecule to escape from the water surface to the atmosphere. To escape a molecule needs to have a very high kinetic energy. To have enough energy, the surface temperatures has to be high enough and at a global average surface temperature of 15°C enough water vapor molecules can escape to achieve thermal equilibrium.

Intrinsic properties of the H2O molecule set the general global level for surface temperatures. Is there still some role left for greenhouse gases? Well, there is.

Oceans create their own greenhouse

Water vapor is the main greenhouse gas, responsible for about half of the greenhouse effect while clouds (also H2O) count for another 25%. Are oceans able to create a greenhouse effect strong enough to raise their own temperatures? Sure, they are.

At the equator insolation is intense and no ice is possible over the oceans: solar uptake of energy is large and when oceans are still at low temperatures, effective radiative and evaporative surface heat loss is low. Therefore, tropical oceans have to heat up. The small quantity of water vapor released at temperatures just above zero Celsius is high enough to get a strong greenhouse warming effect: the first water vapor molecules are most effective in absorbing spaceward surface radiation. When oceans cannot lose 100% of the solar energy absorbed, they will warm. By the evaporation of water vapor, oceans create their own greenhouse effect: not all surface radiated energy disappears to space and oceans need an additional way to lose their accumulated solar energy. Oceans must warm to the point that rising evaporation and enhanced tropical clouds fully compensate for the strongly diminished efficiency of ocean surface emission. If started at low temperatures, oceans will warm till the Earth has an average surface temperature (for present orbital and continental configuration) of 15 degrees Celsius and ‘energy in’ equals ‘energy out’.

Why surface temperatures are not sensitive to greenhouse gases, except for water vapor

Adding an extra 3.7 W/m2 (for a doubling of CO2) to the calculator only increases the initial surface temperature one degree Celsius/K, from 270.1°C to 271.1°C. Additional cooling then must rise by 1/270.1 or 0.37% to compensate for the extra warming force. What would happen with surface cooling when surface temperatures rise by that one degree Celsius?

  1. Evaporative cooling (responsible for 78 W/m2 of surface cooling) would speed up by some 7% (Clausius-Clapeyron)
  2. Convection would speed up to a large degree because of both the higher surface temperature and the higher content of water vapor (+7%) in the warmest and most humid air columns
  3. As result of higher convection, more tropical clouds will form over larger surface areas and earlier in the day and more sunlight will be reflected to space before it can reach and warm the surface, thus solar absorption diminishes.

Because all surface cooling occurs in concert, the slight 0.37% initial warming following CO2 doubling is potentially more than compensated by the huge cooling resulting from the H2O-related processes. Additional surface cooling easily compensates for any greenhouse warming caused by ‘CO2 doubling’. Whatever the level of greenhouse warming, additional cooling dominates surface temperatures and surface temperatures regulate additional H2O based surface cooling in order to have surface temperatures remaining at the level prescribed by the intrinsic properties of the H2O molecule.

Only a change in orbital and/or continental configuration will change the general temperature level upward or downward. Under unchanged circumstances surface temperatures have a very strong tendency to remain at the same general level because of ‘built-in’ physical properties of H2O molecules involved in additional cooling.

Reserve capacity

At current temperatures, Earth’s H2O related cooling processes operate at a low level. Strong convective updraft of surface energy is visible above 25°C. Thus, at the surface of the Earth a large capacity to cool is currently dormant. A slight rise in temperature is sufficient to activate multiple powerful cooling systems in a very dynamic way. Most of the time (nights, mornings) and over most locations (all locations below 25°C) H2O related surface cooling is dormant but easy to activate. Any rise in temperatures activates many forms of surface cooling, while at diminishing temperatures H2O surface cooling activities diminish accordingly. The system seems to be made to keep surface temperatures at about the same level.

How to understand present warming?

A change in the distribution of tropical ocean absorbed energy to the North Pacific (El Niño effect) and/or to the Arctic (by warm subsurface inflows into the Arctic Ocean that cause ice melt) enhances atmospheric water vapor over large surface areas at higher latitudes. As argued before, a warming of higher latitudes results in a diminished radiative cooling of the Earth and so in warming. But, on the Earth’s time scale those (and other) changes are only temporary: they can last decades, a century or a bit more. Although not always easy to recognize, warming and cooling periods alternate in cyclic patterns. Those cyclic patterns are irregular by the ever-changing chaotic interactions of the many components of the ocean/atmosphere temperature system. Cooling always follows warming, like the night always follows the day. Sometimes we need more patience to discover how nature regulates and stabilizes surface temperatures – as it has always done.

Conclusions

The Earth cooled from a hot molten mass just after its formation to the present Earth with its solid crust and its lower surface temperatures. Two greenhouse effects (back radiation and blocking surface radiation) were not able to maintain the surface temperature at 270 degrees Celsius. This is the temperature Earth would have if it were only cooled by surface-emitted radiation. Earth’s additional surface cooling systems, all dominated by the various phases of water, kicked in to cool the surface to its average 15 degrees Celsius.

The additional surface cooling systems of the Earth depend on the H2O molecule. H2O related cooling processes are progressively temperature dependent: the warmer the surface, the stronger the cooling. Temperature itself regulates and limits surface temperatures. For a given configuration the level of surface temperatures is set by the intrinsic properties of the H2O molecule and not by the strength of greenhouse warming; additional H2O based surface cooling compensates for any radiative warming. Cooling is dominant. The immediately available H2O related surface cooling is huge, and its reserve capacity is as endless as the oceans.

Decadal and centennial temperature variations around the current global average of 15°C result from a changed distribution of tropical ocean absorbed energy over the latitudes. Natural warming events are temporary, because over time enhanced surface cooling cancels extra surface warming. Cooling always follows warming, but cooling the Earth takes time, often more time than warming. We need to think in timescales of the Earth to see the changes in surface temperatures in the right way. Earth’s warming and cooling periods happen over decades, centuries and sometimes over millennia.

With regards to commenting, please adhere to the rules known for this site: quote and react, not personal. And when commenting, please don’t use abbreviations but words.

About the author: Wim Röst studied human geography in Utrecht, the Netherlands. The above is his personal view. He is not connected to firms or NGOs or funded by government(s).

Andy May was so kind to correct and improve the English text where necessary or helpful. Thanks!

Footnote

1Lacis, A., Schmidt, G., Rind, D., & Ruedy, R. (2010, October 15). Atmospheric CO2: Principal Control Knob Governing Earth’s Temperature. Science, 356-359. Retrieved from https://science.sciencemag.org/content/330/6002/356.abstract

Published by Andy May

Petrophysicist, details available on linkedin.com https://www.linkedin.com/in/andymaythewoodlands

34 thoughts on “Temperature Regulated Cooling Dominates Warming and Why the Earth Stopped Cooling At 15°C

  1. 1) Nobody claims that the earth’s surface temperature is “controled” by human CO₂ emissions. It is “influenced” by these. That is why the problem is called climate CHANGE. Anthropogenic emissions influence the climate, they are not controlling it. And these emissions have changed (increased) considerably over the last 150 years.
    2) Water vapour is indeed an important contributor to infrared absorption in the atmosphere.
    However, since water vapour is under the conditions in the atmosphere a condensing gas. This prevents significant changes in averaged concentrations.
    CO₂ is not a condensing gas. Therefore additional (anthropogenic) emissions lead to a significant increase of CO₂ in the atmosphere (from around 275 in 1850 to 415 ppm now).
    Climate CHANGE is a problem of CHANGING the composition of the atmosphere. That is why H₂O is not important as a main driver of the observed warming.
    On the other hand the atmosphere can contain about 7% more H₂O for each °C warming. So water vapour concentrations may increase as a consequence of warming. It is not the cause.
    So this post tells a story that is completely missing the point. It is wrong!

    1. Tinus,
      1. The Lacis, et al. article referenced in the post (see the footnote) claims that Earth’s surface temperature is controlled by the CO2 concentration and this paper is cited in all the IPCC reports.
      2. How water vapor changes as surface temperature and CO2 changes is still unknown, observations go both ways. The Clausius-Clapeyron model says it should go up with temperature, but there are no observations to prove that. How clouds change with surface temperature and changes in water vapor is also unknown. Water vapor is a condensing gas, this makes its distribution uneven relative to CO2, we do not know if significant changes in it are precluded, I doubt they are.
      3. Water vapor, water, ice, and clouds are the biggest influence on climate and climate change and also the biggest unknowns, see attached graphic from AR6.
      AR6_assessment of climate feedbacks Fig 7.10

    2. So water vapour concentrations may increase as a consequence of warming. It is not the cause.
      So this post tells a story that is completely missing the point. It is wrong!

      I think you miss Wim’s point. He is saying that water and water vapor cool the planet, they do not warm it. Humans are adding CO2 to the atmosphere and this has a minor direct warming effect of about one degree per doubling of CO2, everyone acknowledges this. It could only be dangerous if the net feedbacks to this warming were positive and somehow increased the direct CO2 warming. Wim’s point is that water acts as a cooling agent, not a warming agent. I think he is correct. He also points out that it has excess capacity.

      The graphic in my last comment shows the net cloud effect to be positive, but acknowledges it might be negative (Wim’s view). Overall, satellite data shows clouds (for example) are negative, -18 to -19 W/m2. Why are they currently negative, yet a positive feedback, makes no sense.

      1. He is saying that water and water vapor cool the planet, they do not warm it.

        He is wrong, Where is this energy associated with a lower temperature going? His statement is against the law of conservation of energy.
        Let us not m ake this a game of words. You are native English speaker. I am not.
        CO2 concentrations are not the only variable “controling” the temperature. It influences the radiation blance of the earth system. Antropogenic emissions change the CO2 concentration and with that change the climate.
        As to the relation between CO2 and average temperature on earth, see the nice animation by Rohde (https://twitter.com/RARohde/status/1094656134835781633?s=20). Measurements show that temperature is about 2.3 ‘C higher when CO2 concentrations double. No theory, just measured facts!

        1. With all due respect to Dr. Rohde, there are no measurements of the warming effect of CO2 on Earth’s surface. What measurements we do have, tell us the direct effect of CO2 is about one degree, and these measurements are done in a laboratory under controlled conditions. Rohde got to 2.3 by assuming that the net water vapor and cloud feedback would be positive and about 1.3, no other feedbacks are significant. But, measurements, with the CERES satellite shows that the net cloud feedback is currently negative, about -18 to -19. See Figure 4 here:
          https://andymaypetrophysicist.com/2021/04/28/clouds-and-global-warming/

          This does not mean that as surface temperatures go up, cloud feedback has to be negative or more negative, but it suggests clouds are a net negative feedback to surface warming. Clouds are a huge unknown in all respects. My work suggests Rohde is incorrect.

          1. You are wrong!

            1) warming since 1850 is well documented and based on several sets of independent measurements.
            2) CO₂ since 1850 increased from 275 in 1850 to 415 ppm now, as established in various independent studies and measurements.
            If you claim this is incorrect you must show why and where temperature measurements and/or CO₂ measurements would be wrong.

            These measurements are simply plotted against each other in the animation from Rohde. No tricks, no theories, simply plotting both measured variables against each other.

            If you want to insist that the correlation between the two is 1 °C for doubling CO₂ concentration, you must come up with your explanation for the additional 1.3 °C as compared to Rohde’s graphic.
            You probably cannot and will not provide a physical correct explanation for the observed 2.3 °C..

            The clouds are mainly of interest for the distribution of changes in the climate over the full globe and on shorter time scales, not for the long term (≃ 30 years) global averages. You should make a clear distinction between short term effects (cloud formation etc), representing the wheather and long term averages as determined climate.

          2. Furthermore: I’d like to see your comment on my statement that water “cools” the surface and atmosphere is in conflict with the law of conservation of energy. Your complexification (I like this word!) by bringing clouds in the discussions does not solve that.

        2. Furthermore: I’d like to see your comment on my statement that water “cools” the surface and atmosphere is in conflict with the law of conservation of energy.

          Tinus, Where did you get your education in physics! Water cools the surface through evaporation (carrying away latent heat) and by forming clouds that reflect incoming radiation from the Sun. The other way it helps is from its enormous heat capacity, the oceans store a lot of absorbed thermal energy that otherwise would warm the atmosphere. 99.9% of the thermal energy in the atmosphere and oceans is stored in the oceans. The oceans store four times the thermal energy in the atmosphere of Venus, but the oceans have an average temperature of 8.5 deg. C and the surface temperature on Venus is 464 deg C. Venus has no water, its main problem. The difference is heat capacity, Earth’s is huge and Venus’s is very small.

          You will have to explain how this violates the law of conservation of energy. I’m very well educated in physics and I do not see any connection.

          Water works, overall to cool Earth. More details here:
          https://andymaypetrophysicist.com/2016/09/03/earth-and-venus/

        3. The clouds are mainly of interest for the distribution of changes in the climate over the full globe and on shorter time scales, not for the long term (≃ 30 years) global averages.

          On what basis do you make this claim? There is nothing in the Earth’s climate system that prevents cloudiness changing on a long-term basis, perhaps in association with other elements of the Hydrosphere such as ocean currents. Processes like these could play out over centuries or millenia.

          It is very likely the case that the Arctic amplification that has occurred in recent decades of warming is caused in part due to interaction between open oceans and clouds.

    3. Tinus,
      One more point:
      Planck feedback means the higher the temperature of a radiating body, the more energy it radiates. This is a negative feedback, and it is very strong, so the total feedback is negative for our Earth. In climate science, the Planck feedback is often not mentioned and explained explicitly. Water vapor feedback is the second largest feedback.

        1. Sorry, Planck feedback is always negative, it has to be negative. It simply says warmer objects emit more radiation.
          “Every climate model has a Planck feedback. The Planck feedback is the most basic and universal climate feedback, and is present in every climate model. It is simply an expression of the fact that a warm planet radiates more to space than a cold planet.

          As we will see, our estimate of λ0=−3.3 W m−2 K−1 is essentially the same as the Planck feedback diagnosed from complex GCMs. Unlike our simple zero-dimensional model, however, most other climate models (and the real climate system) have other radiative processes, such that λ≠λ0 .”
          More here:
          http://www.atmos.albany.edu/facstaff/brose/classes/ATM623_Spring2015/Notes/Lectures/Lecture03%20–%20Climate%20sensitivity%20and%20feedback.html

          1. Sorry, Planck feedback is always negative, it has to be negative. It simply says warmer objects emit more radiation.

            True, but this “more radiation” must be less than the additional radiation that warmed the surface itself, since a warmer surface “holds” more energy than the colder surface before. Hence, the surface will always be warmer when more radiation is absorbed.

        2. Tinus, You are confused about what a feedback is. Doubling CO2 has the potential to increase surface temperature one degree. That warming can cause a feedback. Positive means more warming, negative means less, even cooling. Planck is a negative feedback, a strong one. If warming increases the total water vapor in the atmosphere, that might be a positive feedback, a warming feedback. Clouds probably are a negative feedback to warming, but no one knows for sure, it can’t be measured. The sum of all feedbacks is unknown, that also has never been measured, but there have been some estimates. Some say the total is negative (Lindzen and colleagues, several papers). Some say positive, but no one really knows.

          Read up on the subject.

          1. You are wrong. Measurements and detailed models from physics show around 2.3 °C increase for doubling CO₂. You have only one set of laboratory measurements underpinning your claim of 1 °C and no explanation for the additional 1.3 °C as measured in real life.
            At the same time you do not answer my point on the first law of thermodynamics: conservation of energy.

            I understand that you are not accepting these real life measurements since they contradict you erroneous ideas.

            I’ve made my points quite clear.
            Enjoy!

        3. The only way for the earth’s surface to deal with the higher temperature, indeed is to increase radiation intensity.

          Err, no. The Earth’s surface can and does lose heat in multiple ways, not only via radiation. Evaporation and convection are significant processes and most certainly react to higher temperatures at the surface.

          Measurements and detailed models from physics show around 2.3 °C increase for doubling CO₂.

          The detailed models, such as described in Wijngaarden and Happer’s 2020 paper, apply to clear sky conditions only and give a climate sensitivity for CO2 of 1.4C on its own, rising to 2.3C only if H20 behaves so as to maintain fixed relative humidity. Measurements of humidity in the atmosphere are difficult, but there are indications that fixed relative humidity does not apply, at least over the topics. The detailed models don’t tackle the 2/3rds of the Earth’s surface that is cloudy – it’s too complex.

          1. Mike, Good comment. I might add that conduction and sensible heat transfer, enhanced by wind, is also a significant way the surface loses thermal energy to the atmosphere.

          2. Again, Andy: you and Mike are talking on issues of where exactly the energy is going, once in the system.
            The issue is not the imbalence within the system or at the surface, but the imbalance between the earth system as a whole and space.

            The only interaction between the earth system and empty space is through radiation.

            So if at the boundary between the earth system and space (often referred to as “top of the atmosphere”) there is an imbalance between incoming and outgoing radiation, the earth system will warm if there is more incoming than outgoing, or cool if there is more outgoing than incoming radiation.
            Since climate is defined at longer time scales (30 years or so) you also need to look at the imbalance between incoming and poutgoing radiation over a similar period.

      1. You are wrong. Measurements and detailed models from physics show around 2.3 °C increase for doubling CO₂. You have only one set of laboratory measurements underpinning your claim of 1 °C and no explanation for the additional 1.3 °C as measured in real life.
        At the same time you do not answer my point on the first law of thermodynamics: conservation of energy.

        The 2.3 deg of warming, which is composed of one degree of CO2-caused warming and 1.3 deg of net feedback from the sources in my first comment is from models, only the one degree has been measured, the feedbacks, except for Planck, have never been measured in nature, only estimated.

        I do not see how the “first law of thermodynamics: conservation of energy” applies here and you have not explained it. No energy is lost, water just supplies a very efficient additional means of heat transfer, as latent heat. It also supplies a large heat capacity in the oceans. This is why there is more surface heat (actually thermal energy) on Earth, but the temperature is hundreds of degrees less than on Venus. Venus has no water. Water takes thermal energy from the surface, as water vapor, makes clouds to reflect solar energy, transports it to higher latitudes and altitudes where it can be radiated to space. Water makes Earth’s cooling system more efficient and faster.

    4. The 2.3 °C in Rohde’s animation is measurements only. No models involved apart from the exponential curve fit on the measured data.

      Now I see the confusion! You consider a curve fit to observations a measurement. Sorry, correlation is not causation, and the quality of the fit is terrible! Remember, a least squares fit assumes zero error on the X axis and it assumes no other factors are at work. Neither assumption is valid.

  2. Tinus, I’m well qualified in statistics, thank you. R^2 is a measure of linearity only, or in this case the a linear fit to the logarithm of CO2. It says nothing about the validity of the underlying assumptions – basically that y is a function of x and nothing else. The plot provides no proof of anything, all kinds of things correlate:
    https://www.statology.org/correlation-does-not-imply-causation-examples/

    This is a high school error in logic that is beneath both Robert Rohde and you.

  3. The atmosphere is divided into two parts: Into troposphere (convection determines the temperature gradient) and stratosphere (radiative transfer determines the temperature gradient). The height of the tropopause follows from the Schwarzschild criterion. Water vapor is largely only in the troposphere and because of convection is no water vapor effect.

    Because of the increased CO2 concentration, the tropopause height increases and from this follows the temperature increase of the earth’s surface.

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