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KRONOS Vol V, No. 1 HEAT TRANSFER MODELS, HOTHOUSE CALCULATIONS, AND THE TEMPERATURE OF VENUSGEORGE ROBERT TALBOTTIt is universally accepted that heat energy in substantial quantity is present at the surface of Venus. Equally acceptable is the thesis that some of the Sun's energy is absorbed by Venus' thick cloud layer, while the majority incident at the cloud surface is reflected away The controversy is concerned with whether or not absorbed sunlight can account for a surface temperature of 750 Kelvin. Thus the following questions may be posed: How much sunlight is reaching the surface through the clouds? What is the load in watts per square centimeter of surface, given the amount absorbed by each layer of the atmosphere? Take the usual case in which the source of radiation is characterized by a Planckian distribution. The Sun is itself such a source, with a distribution temperature of about 59006000 Kelvin. This means that the total energy from the source cannot be characterized by a single frequency or "color", but must be packaged into a set of energy bundles, each characterized by a narrow band of wavelengths. For example, between 1.35 and 1.45 microns, 11.95% of the Sun's energy at the Venus cloudtops is present; between 1.5 and 2.0 microns, 6.09%, and so forth. It is merely an exercise for undergraduate physics students to produce – for any given radiation temperature – the Planckian distribution and a table of percentages of the total energy between pairs of wavelengths across the spectrum. The hard part is to determine, for a total energy load incident on some surface, how much of the energy is present as the radiant photons are "transported" through the material. The absorption coefficients for the material are not only material dependent, that is, different for each distinct atomic or molecular structure, but also these coefficients are dependent upon the wavelengths of the acting radiation. To really find out how much of the Sun's energy is passing through the atmosphere of Venus, we need a twodimensional array of absorption coefficients, each horizontal row of that array containing the coefficients for the various atmospheric components at only one frequency. Each column of the array is for one material, showing the variation of its absorption coefficient with frequency of the acting source. This computation, using such an array, has not been done for Venus, for the simple reason that we do not know the absorption coefficients for the atmosphere with any practical accuracy. Playing games with transport phenomena and scatter equations does not yield any dependable result, only approximations for argument without surcease. We have noted that sunlight at the Venus cloud surface is in the form of a Planckian distribution. The known incident energy per unit time and per unit area is 0.27 watts per square centimeter of atmospheric surface. The "albedo", or ratio of radiation energy reflected to that incident, is also frequency dependent, but is by custom given as a sort of average figure. Albedo is a direct function of atmospheric thickness, amounting to about 7% for the Moon, 35% for the Earth, and about 80% for Venus. (Some sources cite slightly lower figures for the average Venusian albedo.) For the Earth's upper atmosphere, the solar load is 0.14 watts per square centimeter of atmospheric surface. What is the relation between energy to be absorbed for Venus versus that for Earth? For Venus, we take 0.27 – (0.8 x 0.27) = 0.054 watts per square centimeter. For Earth, we take 0.14 – (0.35 x 0.14) = 0.091 watts per square centimeter. Therefore, even though the incident load on Venus is about 1.93 times that of Earth the actual energy available for absorption into the atmospheric layers is only about 59% of the energy available for the Earth's atmosphere. Besides, Venusian clouds are incomparably more difficult to penetrate than the gaseous envelope surrounding Earth. It is quite true that even a tiny thermal flux over a very long time can raise the temperature of a body to an indefinitely high level, provided that there is no escape for the incoming flux. The socalled "greenhouse effect" hangs its astronomical hat on the hope that incoming radiation from the Sun can enter the thick cloud bank of Venus, change its wavelength in the course of penetration, and be trapped at the surface by virtue of the opacity of the atmosphere to the new wavelength characterizing the energy. In view of the complexity of calculations governing interactions between radiation and matter, it is quite clear that various "models" can be invented virtually ad infinitum and, with a "proper" choice of constants, almost anything can be "shown". On the other hand, if it can be demonstrated in an experimentally verifiable manner that the absorption characteristics of Venus' atmosphere are such that there is not enough solar energy in the first place to do the "greenhouse job", then the matter, at least for rational people, is settled. For some valid discussions of the "greenhouse effect" in relation to the terrestrial environment, the reader should consult the following current and enlightening book, Carbon Dioxide, Climate and Society, edited by Jill Williams (Pergamon Press, 1978). Many important messages come through if one studies that volume. First, the temperature shifts under discussion amount to a few degrees Centigrade – dramatic in consequences for earthly weather patterns, but decidedly in a world apart from generating a 750 Kelvin surface temperature after radiant passage through a Venusian cloud filter. Secondly, upward shifts in temperature as a function of carbon dioxide concentration are not linear with concentration, but diminish rapidly so that, for a fixed cloudtop temperature scale, an increase from 400 ppm to 800 ppm produces a 4°C rise, while an increase from 800 ppm to 3200 ppm produces only an additional 8°C rise. The curve becomes flatter with still higher concentrations of CO_{2} until there is insignificant temperature rise with massive increases in concentration. Most significant of all is the repeated insistence by virtually all of the authorities represented in this work that even the best models involve extremely serious problems and are not known to be accurate, much less proven beyond dispute. One must contrast this with the selfassured and groundless insistence that a determination of some miniscule quantity of water vapor in the Venusian atmosphere "proves" that the Icarus articles by Sagan and Pollack(14) are precise predictions of a "verified" greenhouse effect on Venus.(5) Anyone who actually wishes to read the Icarus articles should procure the work edited by Jill Williams, and also keep by his side a copy of the Handbook of Geophysics and Space Environments, edited by Shea L. Valley (Air Force Cambridge Research Laboratories, McGrawHill). Some perspective will then be maintained. The problem we have with Venus is not strictly mathematical. One could easily "assume" a collection of radiation absorption coefficients, interspersed with sophisticated remarks about "generous assumptions", and by choosing the coefficients to suit the desired answer, "prove" that no radiant energy arrives at Venus' surface from the Sun. The computational methods will work accurately only if the absorption characteristics of Venus' atmosphere, as they really are, are included as program inputs. When they are so included, sunlight should be a minor energy source relative to the "Hothouse" effect.(6)[*] But most important, the recently gathered Pioneer data should be scrutinized to determine the following: (1) Are there active volcanoes in substantial quantity on Venus? (2) Is Venus in "an early stage of cooldown"? (3) Is the sulfurous atmosphere a volcanic effect, a mammoth extension of the fumes around Earth's Halemaumau? (4) If a long probe is inserted into Venus' soil, and in enough places to yield a fair sample, does the temperature increase or decrease with depth? Scattered reports keep coming to us of volcanoes, giant electrical storms, and chemical fires, among other things  all of which is suggestive of phenomena at contradiction with science's earlier concepts of planet formation in general and Venus in particular. . . . to be continued. REFERENCES
1. C. Sagan and J. Pollack, "On the Structure of the Venus Atmosphere," lcarus 10 (1969), pp.
274289. 

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