Kees Le Pair

Kees Le Pair

Guest contribution by Kees le Pair – Category: Atmosphere

The gap between measured temperatures and the radiation equilibrium is more than 33 ºC as assumed in present day greenhouse considerations. Either the atmospheric greenhouse is not understood well enough, or rather there may be other mechanisms that help to bridge part of or nearly all of a perhaps 60+ ºC gap. Some are listed.

Het verschil tussen de actueel gemeten gemiddelde temperatuur van de aarde en de gemiddelde temperatuur van een aarde zonder atmosfeer met broeikaseffecten is veel groter dan de veronderstelde 33 graden. Òf de werking van het broeikaseffect is onvoldoende begrepen òf kunnen er andere mechanismes werken om het werkelijke gat te overbruggen van misschien wel 60+ ºC. Een aantal kandidaten daarvoor worden hier kort beschreven.

Textbooks and other treatises often explain the earth’s climate with a sphere in space irradiated by the sun. It would have an average surface temperature of 255 K (-18 ºC) without an atmosphere. Thanks to multi atomic gases in the atmosphere such as CO2 and H2O, we live in a greenhouse, in which the average temperature according to measurements is ~ 288 K (+15 ºC). Which means: the greenhouse effect is 33° warming. And with more CO2 it would become warmer.

Public media speak of warming the Earth due to more CO2. This is inaccurate. The earth core has a temperature of around 5000 K(1), in the mantle and the crust all possible intermediate temperatures occur toward the surface. In the atmosphere a height of 12 km and the surface at the poles, the temperature is often lower than 223 K. The average result of the measurements, 288 K, only tells us something about a minimal part of ‘the earth’. Meteorologists indicate it as the temperature of the atmosphere at 2 m above the surface. Above the sea this is a sharp demarcation, but above land it is strange physics. Think of mountain ranges and high plains. What makes a useful concept for weather reports, means little about the condition of other parts of the earth. Although they do play a role in the climate. The mass of 13 meters of the ocean, which is certainly part of the formation of weather and ultimately, the climate, is just equal to that of all air up to 300 kilometers. And the heat content of that first 13 m is higher than that of the atmosphere.

If we try to recalculate how to reach a 255 K radiation balance temperature, it seems that it was assumed, that the earth would be a perfect conductor, distributing heat equally instantaneously everywhere, hence it always has the same temperature everywhere. With a homogeneous temperature, the earth at 255 K would send as much radiant energy into the universe as the sun delivers to the earth. Then there is equilibrium and the temperature is stable. However, the earth does not have the same temperature everywhere, the arithmetic is wrong. In the calculation of incoming and outgoing energy – the law of Stefan-Botzmann, I = εσT4 – we deal with temperature T in the fourth power. The average of T4 is not equal to the average of T to the fourth power (<T4> ≠ <T>4, ‘Hölder’s’ inequality).

The other extreme is a sphere in the solar radiation field, which as a perfect insolator does not transport heat at all. Its equilibrium is at equal irradiation and emission everywhere at all times. Such an instantaneous and local radiation balance would mean ~ 0 K(1) where the sun does not shine and elsewhere the Stefan-Boltzmann temperature at that location (geographical latitude) and that time of the day and the year. If we calculate the average temperature for such a sphere without heat transport, we find an average temperature of 145 K(3) for the same values ​​of ε and σ(2).Compare this to the moon at an average temperature of 213 K(2a).

Earth Rise. Photo NASA AS11-44-6550

Keep in mind that because of rotation the moon does distribute heat by retaining and loosing it at another place. The conclusion that the state of the Earth is somewhere between the two extremes is obvious. The radiation equilibrium temperature is thus significantly lower than 255 K. Which means that the so-called greenhouse effect should be much stronger than for bridging a gap of 33º, or there are other processes besides the atmospheric greenhouse that bring the surface to a livable temperature and to save the ocean from freezing.According to Nikolov and Zeller(4), the temperature gap to be covered is approximately 90°. They compare the outcome with the temperature of other planets. Which they say supports their claim.

Nikolov and Zeller cite 6 recent leading publications (Science, Springer NY, Academic Press Cal., Tellus & J. Geophysics Res) by well known climatologists assuming 33° warming caused by the atmospheric greenhouse effect. Hence 2 or 3 times too small to bridge the gap with the radiation equilibrium temperature. Obviously other processes are stronger than the much-discussed greenhouse, to bring our environment to a suitable temperature. Also the stability of those processes must be investigated.

We know of three such processes.

  • First, the temperature equalization on earth through the earth’s rotation, through ocean currents and wind.
  • Secondly, the influence on the radiation equilibrium temperature as a result of partial transparency of the components of the earth that contribute to the climate.
  • There could be a third process, signaled by Hughes(6), Rörsch(5) and others: the stabilizing effect of heat transport via latent heat.

The magnitude of the possible influence of the first process is indicated above. Between the best possible and the worst possible temperature equalization the resulting average temperatures differ 110°. How well would the earth actually do that? And couldn’t something be changing there over time? In a recent publication, Rörsch(5), calculated the influence of the rotation on the measured temperatures and compared it with site measurements. The retention of heat in soil and water and the displacement by rotation to a position with less or no radiation changes the temperature which would prevail there wihout.The rotation also means a huge heat transport that accounts for a large part of the temperature equalization.Ocean currents and winds also equalize the temperature. They are not constant and thus the equalization and thus the radiation equilibrium changes. But with the degree of equalization alone, the measured surface temperature can not be explained. That would lift it from 145 to 255 K at most. That is still 33º short.

The second process that has to do with the influence of turbid transparency receives little attention in climate science. In a turbid transparent body radiation is only absorbed progressively with depth of penetration. It has a different temperature pattern than an opaque body that heats up at the surface due to the radiation according to the law of Stefan-Boltzmann. The radiation that leaves the body at equilibrium does not only come from the surface, but also from the layers beneath it, so the surface temperature cannot be used for a Stefan-Boltzmann calculation. The atmosphere is such a turbid transparent medium as well as the oceans, which cover 70% of the earth’s surface. We measure our 288 K inside a complex of different transparent media. The temperature of the radiation equilibrium can be significantly higher here than that of Stefan-Boltzmann at the surface. I hope to address this here later(7). According to Hughes(6).

The third process, heat transport by latent heat, would reduce the effective emissivity of the oceans, which would then be compensated by a higher radiation equilibrium temperature. Rörsch(6)  follows directly the course of the temperature in his treatment of the diurnal cycle, which also results in a smaller influence of the atmospheric greenhouse effect.

Conclusion.The aforementioned complications of the heat exchange processes on Earth challenge the basic greenhouse effect. The gap between actual temperatures and hypothetical temperatures without an atmosphere is much larger (60+ ºC ) than the greenhouse effect is supposed to bridge (ca. 33 ºC) Either the atmospheric greenhouse effect is not understood, or there are other mechanisms at work here.


(1) The radiation temperature of the universe is about 3 K. But at that temperature the radiation is so small compared to that of the sun, that it may be neglected. The same applies to the heat that reaches the surface from the core and the shell of the earth.

(2) ε is a material constant, ε = 1 for an ideal black body. That is the maximum value. ε = 0 for the other extreme, a body that does not radiate at all (copper and aluminum foil get close to it). σ = 5,6703.10-8 Wm-2K-4, the Stefan-Boltzmann constant. It is a universal constant of nature.


(3) C. le Pair: Climate, radiation and temperature equalization-2 ( In Dutch.)

(4) N. Nikolov & K. Zeller: New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model; Environment Pollution and Climate Change (2017) 1: 2.

(5) A. Rörsch: In search of autonomous regulatory processes in the global atmosphere; Rethinking the model of the Earth’s greenhouse. , November 2018.

(6) G. Hughes: The watery planet effect;  .

(7) C. le Pair: Radiation balance and transparent media-3;


About: Kees le Pair

His lifelong question: which scientific research is worthwhile? After studying mathematics and physics in Leiden, he stayed at that university for several years, then the American university in Beirut and research agencies in the United States. He was director of the national institutes for physics and technical research, FOM and STW In the Netherlands; in addition, he was advisor to the government for energy, ICT, technology and defense research. He wrote several books and was an editor or co-author of other. He was also Middle East correspondent and columnist for NRC Handelsblad and various magazines. In the recently published novel ‘The Second Apocalypse’ he incorporated some of his newly acquired knowledge about climate and energy, about which he also published less romantic pieces. His hobby is sea sailing. Kees is Knight O.N.L., honorary doctor TU Delft, Ehre Mitglied Deutsche Wissenschafts Forscher and he received the distinction of merit for the science of the Royal Academy.