About Intensity of Terrestrial Radiation
Aleksandr Zhitomirskiy
June 17, 2025
The sharp decrease in the intensity of terrestrial radiation with distance from the surface, according to the inverse square law, is considered as an argument against the greenhouse effect theory.
The essence of the greenhouse effect, according to prevailing ideas, lies in the retention of heat emanating from the Earth. This retention is attributed to the absorption of terrestrial radiation by socalled greenhouse gases, which are opaque to infrared radiation within specific wavelength regions. Terrestrial radiation results from the Earth's absorption of a portion of incident solar radiation and (likely to a small extent) its internal heat. To characterize this radiation's role in atmospheric heat absorption, both its spectral composition and intensity are crucial. I was unable to find a detailed account of the latter factor in the literature.
First, it is necessary to clarify what is generally known about the absorption of heat by air during the passage of radiation. The NOAA website provides an example: “If you have stood in front of a fireplace or near a campfire, you have felt the heat transfer known as radiation. The side of your body nearest the fire warms while your other side remains unaffected by the heat. Although you are surrounded by air, the air has nothing to do with this transfer of heat” [1]. In principle, this explanation is not entirely correct: some amount of heat can be transferred from the source to the observer due to the thermal conductivity of the air (low), and in open areas, the upward convection flow can shift towards the observer due to gusts of wind. However, there are no facts that allow us to dispute the assertion that air is not associated with the transfer of heat by radiation. The question of how this is consistent with the basic idea of the greenhouse effect theory can be left to the supporters of this theory.
If we ignore the above statement and continue to assume that the energy of terrestrial radiation in the atmosphere is retained by greenhouse gases, then it makes sense to ask how exactly this energy reaches the gases. And first of all, we are talking about how this energy is distributed as it rises from the earth's surface, in other words, about the change in intensity with height.
Let's start, as in the previous description, with an example. You are standing on a sandy beach on a hot day. The sand has heated up to such an extent that it burns your feet (let's say its temperature is 50 °C). Your face feels warm, but the temperature is acceptable, no more than 30 °C. This difference in temperature can be interpreted taking into account the low thermal conductivity and density of air. But since radiative heat transfer cannot be ruled out, this example shows a decrease in the intensity of thermal radiation as you move away from the source of thermal radiation - the surface of the sand. Naturally, this also applies to the previous example, where the sources of radiation are a fireplace and a campfire.
These examples show a decrease in radiation intensity (I) with increasing distance (d) from the emitting object, which is known to be described by the inverse square law: I1 / I2 = d2 2 / d1 2 . For practical use of this equation it is necessary to know the value of radiation intensity at least at one specific distance. For example, if the solar constant for Venus is known as 2771 W/ m2 and the distance from Venus to the Sun is 1.08*1011 m, then the calculated value for the Earth at a distance from the Sun of 1.50*1011 m
will be 1441 W/ m2. Taking into account the inaccuracy of determining the average distance of the planets from the Sun, the coincidence of this value with the accepted value of 1361 can be considered quite satisfactory.
However, in the case of terrestrial radiation, it is unclear how to reliably determine the initial intensity value itself, not to mention its values at different distances from the surface. Obviously, this value is different in different places and at different times. The value of 390 W/m2 adopted in the energy balance of the Earth [2] is the result of calculating the energy using the Stefan-Boltzmann equation based on the arithmetic mean (?!) temperature value of 288 K. It is unclear how to explain the fact that this value exceeds not only the amount of energy absorbed by the surface (168 W/m2), but also the total amount of incoming solar energy (342 W/m2). In this regard, instead of discussing global values, it makes sense to estimate the radiation intensity based on measurements for specific cases.
Direct measurements of the change in infrared radiation intensity as a function of distance have not been found in the literature. However, such measurements have been made for high-energy X-ray radiation [3] and gamma radiation [4]. For X-ray radiation, the intensity attenuation was recorded in the range of distances from the source from 25 to 150 cm, and it was practically the same in the chamber with air and the vacuum chamber [3]. When measuring the gamma radiation of the isotope K-40 (radiation energy 1.36 MeV), a decrease in intensity of 7% was established at a distance of 10 m from the source [4].
Considering that the attenuation of intensity with distance should be greater for radiation with lower energy, it can be assumed that for infrared radiation such attenuation will be much greater than 7% at 10 m, although even in this case at a distance of 100 m the intensity would be 0.93/100, i.e. less than 1% of the original value.
It is also possible to roughly estimate the decrease in the intensity of terrestrial radiation using the above mentioned specific example. Let us assume that the surface temperature is 50 °C, and at the level of a person's mouth (1.5 m from the surface) 30 °C. The greenhouse effect theory takes into account only the radiative transfer of heat, and the emitted energy is related to the temperature by the Stefan-Boltzmann equation E = σ T4 , so E2 /E1 = (T2 /T1)4 = (303/323)4 = 0.774. In this case, the radiation already at a height of 1.5 m loses 23% of its initial intensity, and, consequently, at a height of 15 m it will be only 0.01 of this value. On a cold day, when the ground is covered with snow and the air temperature is around 0 °C, it is impossible to determine the change in radiation intensity by comparing the surface and air temperatures at different altitudes.
It follows that the intensity of terrestrial radiation drops so sharply with altitude that the radiation energy practically does not reach the main amount of atmospheric gases. This means that the main role in heating the atmosphere with heat from the surface is played by convection and thermal conductivity, but not radiation.
The question naturally arises as to where the radiation energy goes. The answer to this question, apparently, should be sought in Max Planck's statements on the nature of thermal radiation [5]. In making a theoretical derivation of the Stefan-Boltzmann (SB) equation, Planck considers the radiation of an ideal black body into a vacuum (p. 67). Since the temperature of the atmosphere is significantly higher than absolute zero, the flow of thermal energy from the surface to the atmosphere is, firstly, much less than that into a vacuum, and, secondly, is significantly different in different places and at
different times. In addition, Planck notes that the atmosphere partly absorbs incident solar radiation which changes into heat of the air while other part “changes into diffuse skylight” (p.10).
Since the absorption bands of greenhouse gases are mainly located in the spectral region of terrestrial radiation, a sharp decrease in radiation intensity with increasing distance from the surface is a significant argument against the greenhouse effect theory.
References
1. National Oceanic and Atmospheric Administration. Transfer of Heat Energy. Jan. 2, 2024. https://www.noaa.gov/jetstream/atmosphere/transfer-of-heat-energy
2. The Earth-Atmosphere Energy Balance -NOAA June 6, 2023. https://www.noaa.gov/jetstream/atmosphere/energy
3. F.H. Day, L.S. Taylor. Absorption of X-Rays in Air. US National Bureau of Standards. Research Paper RP1883, Volume 40, pp. 393-399, May 1948. https://nvlpubs.nist.gov/nistpubs/jres/40/jresv40n5p393_A1b.pdf
4. A .Mishra, R. Khana. Scattering of gamma radiation by air in the ambient environment using gamma ray spectrometry.- Kuwait J. Sci., Febr. 2022. https://www.researchgate.net/publication/359138527_Scattering_of_gamma_radiation_by_air_in_the_a mbient_environment_using_gamma_ray_spectrometry
5. Max Planck. The theory of heat radiation. Translated by M.Masius. Copyright, 1914, by P. Blakiston’s Son & Co. https://www.gutenberg.org/files/40030/40030-pdf.pdf