Infrared Radiation and Planetary Temperature

by Raymond T. Pierrehumbert, Physics Today

Infrared radiative transfer theory, one of the most productive physical theories of the past century, has unlocked myriad secrets of the universe including that of planetary temperature and the connection between global warming and greenhouse gases.

In a single second, Earth absorbs 1.22 × 1017 joules of energy from the Sun. Distributed uniformly over the mass of the planet, the absorbed energy would raise Earth’s temperature to nearly 800 000 K after a billion years, if Earth had no way of getting rid of it. For a planet sitting in the near-vacuum of outer space, the only way to lose energy at a significant rate is through emission of electromagnetic radiation, which occurs primarily in the subrange of the IR spectrum with wavelengths of 5–50 µm for planets with temperatures between about 50 K and 1000 K. For purposes of this article, that subrange is called the thermal IR. The key role of the energy balance between short-wave solar absorption and long-wave IR emission was first recognized in 1827 by Joseph Fourier, 1,2 about a quarter century after IR radiation was discovered by William Herschel. As Fourier also recognized, the rate at which electromagnetic radiation escapes to space is strongly affected by the intervening atmosphere. With those insights, Fourier set in motion a program in planetary climate that would take more than a century to bring to fruition.

Radiative transfer is the theory that enables the above to be made precise. It is a remarkably productive theory that builds on two centuries of work by many of the leading lights of physics. Apart from its role in the energy balance of planets and stars, it lies at the heart of all forms of remote sensing and astronomy used to observe planets, stars, and the universe as a whole. It is woven through a vast range of devices that are part of modern life, from microwave ovens to heat-seeking missiles. This article focuses on thermal IR radiative transfer in planetary atmospheres and its consequences for planetary temperature. Those aspects of the theory are of particular current interest, because they are central to the calculations predicting that global climate disruption arises from anthropogenic emission of carbon dioxide and other radiatively active gases.

An atmosphere is a mixed gas of matter and photons. Radiative transfer deals with the nonequilibrium thermodynamics of a radiation field interacting with matter and the transport of energy by the photon component of the atmosphere. Except in the tenuous outer reaches of atmospheres, the matter can generally be divided into parcels containing enough molecules for thermodynamics to apply but small enough to be regarded as isothermal and hence in local thermodynamic equilibrium (LTE).

The local radiation field need not be in thermodynamic equilibrium with matter at the local temperature. Nonetheless, the equations predict that the radiation field comes into thermodynamic equilibrium in the limiting case in which it interacts very strongly with the matter. For such blackbody radiation, the distribution of energy flux over frequency is given by a universal expression known as the Planck function B(ν,T), where ν is the frequency and T is the temperature.

Integrating the Planck function over all directions and frequencies yields the Stefan–Boltzmann law for the flux F exiting from the surface of a blackbody, F = σT4, where σ = 2π5kB4/(15c2h3) ≈ 5.67 × 10−8 W m−2 K−4. Here, kB is the Boltzmann thermodynamic constant, c is the speed of light, and h is Planck’s constant. The fourth-power increase of flux with temperature is the main feedback allowing planets or stars to come into equilibrium with their energy source. Since such bodies are not actually isothermal, there is a question as to which T to use in computing the flux escaping to space. Radiative transfer is the tool that provides the answer.

The appearance of h and c in the Stefan–Boltzmann constant means that relativity and quantization—the two nonclassical aspects of the universe—are manifest macroscopically in things as basic as the temperatures of planets and stars. It is intriguing to note that one can construct a universe that is classical with regard to quantization but nonetheless is well behaved with regard to the thermodynamics of radiation only if one also makes the universe classical with regard to relativity. That is, σ remains fixed if we let h → 0 but also let c tend to infinity as h−3/2.

A few fundamentals

At planetary energy densities, photons do not significantly interact with each other; their distribution evolves only through interaction with matter. The momentum of atmospheric photons is too small to allow any significant portion of their energy to go directly into translational kinetic energy of the molecules that absorb them. Instead, it goes into changing the internal quantum states of the molecules. A photon with frequency ν has energy , so for a photon to be absorbed or emitted, the molecule involved must have transition between energy levels differing by that amount.

Figure 1. Three isothermal layers model the atmosphere in this illustration of upward-moving electromagnetic radiation with frequency ν. The radiation, assumed not to scatter, propagates at an angle θ with respect to the vertical and emerges from layer 3, the topmost atmospheric slice. The ground below the atmosphere emits as an ideal blackbody, characterized by the Planck function B. Each layer, at its own temperature T, emits with its own emissivity eν and, by Kirchhoff’s law, absorbs a proportion aν = eν of the incident radiation. The radiation flux distribution incident on layer 3 is Iν. It is the sum of the thermal emission from the ground, layer 1, and layer 2, attenuated by absorption in the intervening layers 1 and 2. Squiggly arrows indicate thermal emission; straight arrows indicate transmitted radiation.

Coupled vibrational and rotational states are the key players in IR absorption. An IR photon absorbed by a molecule knocks the molecule into a higher-energy quantum state. Those states have very long lifetimes, characterized by the spectroscopically measurable Einstein A coefficient. For example, for the CO2 transitions that are most significant in the thermal IR, the lifetimes tend to range from a few milliseconds to a few tenths of a second. In contrast, the typical time between collisions for, say, a nitrogen-dominated atmosphere at a pressure of 104 Pa and temperature of 250 K is well under 10−7 s. Therefore, the energy of the photon will almost always be assimilated by collisions into the general energy pool of the matter and establish a new Maxwell–Boltzmann distribution at a slightly higher temperature. That is how radiation heats matter in the LTE limit.

According to the equipartition principle, molecular collisions maintain an equilibrium distribution of molecules in higher vibrational and rotational states. Many molecules occupy those higher-energy states, so even though the lifetime of the excited states is long, over a moderately small stretch of time a large number of molecules will decay by emitting photons. If that radiation escapes without being reabsorbed, the higher-energy states are depopulated and the system is thrown out of thermodynamic equilibrium. Molecular collisions repopulate the states and establish a new thermodynamic equilibrium at a slightly cooler temperature. That is how thermal emission of radiation cools matter in the LTE limit.

Now consider a column of atmosphere sliced into thin horizontal slabs, each of which has matter in LTE. Thermal IR does not significantly scatter off atmospheric molecules or the strongly absorbing materials such as those that make up Earth’s water and ice clouds. In the absence of scattering, each direction is decoupled from the others, and the linearity of the electromagnetic interactions means that each frequency can also be considered in isolation. If a radiation flux distribution Iν in a given propagation direction θ impinges on a slab from below, a fraction aν will be absorbed, with aν ≪ 1 by assumption. The slab may be too thin to emit like a blackbody. Without loss of generality, though, one can write the emission in the form eνB(ν,T); here eν ≪ 1 is the emissivity of the slab (see figure 1). Both aν and eν are proportional to the number of absorber–emitter molecules in the slab.

The most fundamental relation underpinning radiative transfer in the LTE limit is Kirchhoff’s law, which states that aν = eν. Gustav Kirchhoff first formulated the law as an empirical description of his pioneering experiments on the interaction of radiation with matter, which led directly to the concept of blackbody radiation. It can be derived as a consequence of the second law of thermodynamics by requiring, as Kirchhoff did, that radiative transfer act to relax matter in a closed system toward an isothermal state. If Kirchhoff’s law were violated, isolated isothermal matter could spontaneously generate temperature inhomogeneities through interaction with the internal radiation field.

Given Kirchhoff’s law, the change in the flux distribution across a slab is ΔIν = eν[−Iν + B(ν,T)], assuming eν;> ≪ 1. The radiation decays exponentially with rate eν, but it is resupplied by a source eνB. The stable equilibrium solution to the flux-change iteration is Iν = B(ν,T), which implies that within a sufficiently extensive isothermal region the solution is the Planck function appropriate to a blackbody. The recovery of blackbody radiation in that limit is one of the chief implications of Kirchhoff’s law, and it applies separately for each frequency.

In the limit of infinitesimal slabs, the iteration reduces to a linear first-order ordinary differential equation for Iν. Or, as illustrated in figure 1, one can sum the contributions from each layer, suitably attenuated by absorption in the intervening layers. The resulting radiative transfer equations entered 20th-century science through the work of Karl Schwarzschild (of black hole fame) and Edward Milne, who were interested in astrophysical applications; Siméon Poisson published a nearly identical formulation of radiative transfer 3 in 1835, but his equations languished for nearly 100 years without application.

Spectroscopy of greenhouse gases

Because of its numerous uses throughout science and technology, gaseous spectroscopy is a highly developed subject. The application of gaseous spectroscopy to atmospheric constituents began with John Tyndall, who discovered in 1863 that most of the IR opacity of Earth’s atmosphere was attributable to two minor constituents—CO2 and water vapor. All spectral absorption lines acquire a finite width by virtue of a number of processes that allow a molecule to absorb a photon even if the energy is slightly detuned from that of an exact transition. For reasonably dense atmospheres, the most important of those processes is collisional broadening, which borrows some kinetic energy from recent collisions to make up the difference between the absorbed photon’s energy and a transition.

Figure 2. Absorption coefficients for water vapor and carbon dioxide as a function of wavenumber are synthesized here from spectral line data in the HITRAN database. The upper panel gives the Planck function B(ν,T) for a 260-K surface, which indicates the spectral regions that are important for planetary energy balance. The wavenumber, defined as the reciprocal of the wavelength, is proportional to frequency. If a layer of atmosphere contains M kilograms of absorber for each square meter at the base of the layer, then light is attenuated by a factor exp(−κM) when crossing the layer, where κ is the absorption coefficient. The horizontal dashed lines on the CO2 plot give the value of absorption coefficient above which the atmosphere becomes very strongly absorbing for CO2 concentrations of 300 ppm and 1200 ppm; the green rectangle shows the portion of the spectrum in which the atmosphere is optically thick for the lower concentration, and the orange rectangle indicates how the optically thick region expands as the concentration increases. The inset shows fine structure due to rotational levels.

Databases of spectral-line properties lie at the foundations of all calculations of IR radiative transfer in gases. The HITRAN database, 4 culled from thousands of meticulously cross-validated, published spectroscopic studies, provides line properties for 39 molecules; it has been extensively used for applications across engineering and atmospheric sciences. The database is freely available at http://www.cfa.harvard.edu/hitran/.

Measurements of absorption cross sections allow one to relate the absorption–emission properties of a layer of atmosphere to its composition. Figure 2, for example, shows absorption cross sections for CO2 and water vapor as a function of wavenumber, which is proportional to frequency; the thermal IR ranges from 200 cm−1 to 2000 cm−1. The spectra there are computed from the HITRAN database with lines broadened by collision with air at a pressure of 5 × 104 Pa, which corresponds to about the middle of Earth’s atmosphere by mass. The CO2 molecule has four main groups of absorption features in the thermal IR, of which the most important for Earthlike conditions is the one with the wavenumber near 667 cm−1. (The corresponding wavelength is 15 µm.) The feature arises from vibrational bending modes of the linear triatomic molecule, which are given a fine structure by mixing with rotational transitions; the inset to figure 2 shows the corresponding lines. Water vapor is a polar molecule, and its richer set of vibrational and rotational modes allows it to absorb effectively over a much broader range of frequencies than CO2.

Gases exhibit continuum absorption, as does the condensed matter making up clouds of all kinds. In some cases continua result from the overlap of nearby lines, but in other cases continua appear where no lines are in the vicinity. Loosely speaking, those continua arise because, over the finite duration of a collision, a pair of colliding molecules acts somewhat like a single, more complex molecule with transitions of its own. Equivalently, they result from the overlap of the tails of remote collisionally broadened lines. The statistical mechanics governing the far regions of long line tails is not at all well understood; 6 nonetheless, the continua have been quite well characterized, at least for those cases relevant to radiative transfer in Earth’s atmosphere. For present-day Earth, the only important continuum is the water vapor continuum in the window around 1000 cm−1. Carbon dioxide continua are unimportant for conditions that have prevailed on Earth during the past several billion years, but they are important for plugging the gaps in the line spectra for the dense CO2 atmospheres of Venus and early Mars. Diatomic homoatomic molecules like N2, which are transparent to IR in Earthlike conditions, have collisional continua that become important in cold, dense atmospheres. For example, the continuum makes N2 one of the most important greenhouse gases on Saturn’s largest moon, Titan.

The intricate variation of absorption with frequency makes it difficult to efficiently solve the radiative transfer equations. In line-by-line models, the equations are solved separately on a grid of millions of frequencies and the results are summed to obtain net fluxes. Climate models, however, require greater computational efficiency; one needs to compute the frequency-averaged radiation flux at each of several thousand model time steps for each of several thousand grid boxes covering a planet’s atmosphere. Modelers use various approximations to represent the aggregate effects of spectral lines averaged over bands about 50 cm−1 wide. Such approximations are validated against line-by-line codes that have, in turn, been validated against laboratory and atmospheric observations. When averaged over a broad band, radiative flux decays algebraically rather than exponentially with distance traversed, because the progressive depletion of flux at strongly absorbed frequencies leaves behind flux at frequencies that are more weakly absorbed.5

Confirmation by observed spectra

The Sun radiates approximately like a blackbody having a temperature of 6000 K, even though the temperature of the solar interior is many millions of degrees. That’s because the visible-wavelength and IR photons that predominate in solar radiation can escape from only the cooler outer layers of the Sun. Similarly, the 2.7-K cosmic microwave background radiation gives the temperature of the radiating layer of the very early universe, redshifted down from its original, much higher temperature.

Figure 3. Satellite measurements of emission spectra are not limited to Earth. (a) The left panel compares a computed global-mean, annual-mean emission spectrum for Earth (blue) with observations from the satellite-borne AIRS instrument (red); both are superimposed over a series of Planck distributions. Two arrows point to absorption spikes discussed in the text. The temperature profile to the right, also an annual and global average, is based on in situ measurements. (b) The panel to the left shows a summer-afternoon emission spectrum for Mars observed by the TES instrument on the Mars Global Surveyor. Its accompanying temperature profile was obtained from radio-occultation measurements corresponding to similar conditions. (c) The panels here show a Venusian equatorial night thermal spectrum as measured by the Venera 15 orbiter 14 together with a typical temperature profile for the planet. The upper portion (dashed curve) of the temperature sounding is based on radio-occultation observations from the Magellan mission; the lower portion (solid curve) was observed by a Pioneer Venus descender probe. For all three planets, squiggly arrows on the temperature profiles indicate the range of altitudes from which IR escapes to space.

The radiating layer of a planet is the IR equivalent of the Sun’s photosphere. When a planet is viewed from above, the emission seen at a given frequency originates in the deepest layer that is optically thin enough for significant numbers of photons to escape. The effective emission temperature for that frequency is a suitably weighted average temperature of that layer. If the atmospheric temperature varies with height, variations of the absorption coefficients of atmospheric constituents with frequency show up in planetary emission spectra as variations of emission temperature; the more transparent the atmosphere is, the deeper one can probe.

For atmospheres heated partly from below—either as a consequence of solar absorption at the ground as in the case of Earth, Mars, and Venus, or due to internal absorption and escaping interior heat as with Jupiter and Saturn—the lower layers of the atmosphere are stirred by convection and other fluid motions, and the constant lifting and adiabatic cooling establish a region whose temperature decline with height approximates that of an adiabat. That region is the troposphere. At higher altitudes, heat transfer is dominated by radiative transfer instead of fluid motions; the corresponding region is the stratosphere. Stratospheric temperature is constant or gently decaying with height for pure IR radiative equilibrium, but in situ absorption of solar radiation can make the stratospheric temperature increase with height. Ozone facilitates such absorption on Earth, and organic hazes have a similar effect on Titan. Typical temperature profiles for Earth, daytime Mars, and Venus are shown in the right-hand column of figure 3.

The top panel of figure 3 compares global-mean, annual-mean, clear-sky spectra of Earth observed by the Atmospheric Infrared Sounder (AIRS) satellite instrument with spectra calculated after the radiative transfer equations were applied to output of a climate model driven by observed surface temperatures.7 The agreement between the two is nearly perfect, which confirms the validity of the radiative transfer theory, the spectroscopy used to implement it, and the physics of the climate model. The AIRS instrument covers only wavenumbers above 650 cm−1, but the theory and spectroscopic data sources used for radiative transfer at lower wavenumbers do not differ in any significant way from those used in the wavenumber range probed by AIRS. Numerous observations—notably, downward-looking radiation measurements from high-altitude aircraft—have confirmed the validity of radiative transfer models in the low-wavenumber water-vapor region.8

In the window region from roughly 800 to 1300 cm−1, Earth radiates to space at very nearly the mean temperature of the ground, except for a dip due to ozone near 1050 cm−1. At higher wavenumbers, one can see the reduction of radiating temperature due to water-vapor opacity. The main CO2 absorption group leads to a pronounced reduction of radiating temperature in a broad region centered on 667 cm−1. The emission spike at the center of the feature arises because CO2 absorbs so strongly that the radiating level is in the upper stratosphere, which is considerably warmer than the tropopause; the ozone feature exhibits a similar spike. The spectrum thus reveals the presence of CO2, water vapor, ozone, and other gases not discussed here. We can infer that the planet has a stratosphere in which temperature increases with height, indicating the presence of an upper-level solar absorber. We can determine that temperatures of the atmosphere and ground range at least from 220 K to 285 K. But absent additional information, we cannot tell that the high end of that range actually comes from the ground.

Climate scientists routinely use spectral inferences such as those discussed above to monitor the state of Earth’s atmosphere from space. Every time you see an IR weather satellite image, you are seeing radiative transfer in action. Earth’s liquid or frozen water clouds act essentially as blackbodies. They emit at the cloud-top temperature, which is cold if the clouds are deep. On an IR satellite image, clouds appear as regions of weak emission, though by convention IR weather satellite images are usually presented with an inverted gray scale that makes clouds look white, as one expects from everyday experience. Weather forecasting centers worldwide use such images many times every day, as they show cloud patterns even on Earth’s night side and, unlike visible-light images, allow forecasters to determine the height of cloud tops. Observations in selected IR and microwave bands are routinely used to retrieve temperature profiles and patterns of atmospheric constituents such as water vapor and CO2.

Figure 3 also shows emission spectra for Mars and Venus. The Martian spectrum, obtained on a summer afternoon, mainly takes the form of blackbody emission from a 260-K surface, but as with Earth’s spectrum, it has a region centered on the main CO2 absorption band where the radiating temperature is much colder. As far as one can tell from its IR spectra, nighttime Venus looks about as cold as daytime Mars. However, based on microwave emissions (to which the atmosphere is largely transparent), Venera landers, and Pioneer descenders, we now know that Venus has an extremely hot surface, a nearly pure CO2 atmosphere, and a surface pressure of nearly 100 Earth atmospheres. Because of the thick atmosphere, essentially all the IR escaping from Venus originates in the top region of the atmosphere, where the pressure is less than 2.5 × 104 Pa. The highest-temperature radiating surface in that layer is primarily attributable to CO2 continuum absorption, which fills in the transparent regions of the line spectrum shown in figure 2. Sulfuric-acid clouds and trace amounts of water vapor also contribute to plugging the gaps.

Energy balance and surface temperature

The same considerations used in the interpretation of spectra also determine the IR cooling rate of a planet and hence its surface temperature. An atmospheric greenhouse gas enables a planet to radiate at a temperature lower than the ground’s, if there is cold air aloft. It therefore causes the surface temperature in balance with a given amount of absorbed solar radiation to be higher than would be the case if the atmosphere were transparent to IR. Adding more greenhouse gas to the atmosphere makes higher, more tenuous, formerly transparent portions of the atmosphere opaque to IR and thus increases the difference between the ground temperature and the radiating temperature. The result, once the system comes into equilibrium, is surface warming. The effect is particularly spectacular for Venus, whose ground temperature is 730 K. If the planet were a blackbody in equilibrium with the solar radiation received by the planet, the ground temperature would be a mere 231 K.

The greenhouse effect of CO2 on Earth and Mars is visually manifest as the ditch carved out of the Planck spectrum near 667 cm−1. That dip represents energy that would have escaped to space were it not for the opacity of CO2. On Venus, the CO2 greenhouse effect extends well beyond the ditch, owing to the opacity of the continuum associated with so much CO2. In the Earth spectrum, one can also see a broad region in which water vapor has reduced the radiating temperature to a value well below the surface temperature.

For Earth and Mars, the width of the CO2 ditch corresponds approximately to the width of the spectral region over which the atmosphere is nearly opaque to IR. Increasing atmospheric CO2 increases the width of the ditch and hence increases the CO2 greenhouse effect. But the increase occurs in the wings of the absorption feature rather than at the center (see figure 2). That limitation is the origin of the logarithmic relation between CO2 concentration and the resulting perturbation in Earth’s energy budget. It has been a feature of every climate model since that of Svante Arrhenius in 1896. Per square meter of surface, Mars has nearly 70 times as much CO2 in its atmosphere as Earth, but the low Martian atmospheric pressure results in narrower spectral lines. That weakens absorption so much that the Martian CO2 ditch has a width somewhat less than Earth’s.

The planetary warming resulting from the greenhouse effect is consistent with the second law of thermodynamics because a planet is not a closed system. It exchanges heat with a high-temperature bath by absorbing radiation from the photosphere of its star and with a cold bath by emitting IR into the essentially zero-temperature reservoir of space. It therefore reaches equilibrium at a temperature intermediate between the two. The greenhouse effect shifts the planet’s surface temperature toward the photospheric temperature by reducing the rate at which the planet loses energy at a given surface temperature. The way that works is really no different from the way adding fiberglass insulation or low-emissivity windows to your home increases its temperature without requiring more energy input from the furnace. The temperature of your house is intermediate between the temperature of the flame in your furnace and the temperature of the outdoors, and adding insulation shifts it toward the former by reducing the rate at which the house loses energy to the outdoors. As Fourier already understood, when it comes to relating temperature to the principles of energy balance, it matters little whether the heat-loss mechanism is purely radiative, as in the case of a planet, or a mix of radiation and turbulent convection, as in the case of a house—or a greenhouse. Carbon dioxide is just planetary insulation.

For present Earth conditions, CO2 accounts for about a third of the clear-sky greenhouse effect in the tropics and for a somewhat greater portion in the drier, colder extratropics (see Reference 9, figure 12.1); the remainder is mostly due to water vapor. The contribution of CO2 to the greenhouse effect, considerable though it is, understates the central role of the gas as a controller of climate. The atmosphere, if CO2 were removed from it, would cool enough that much of the water vapor would rain out. That precipitation, in turn, would cause further cooling and ultimately spiral Earth into a globally glaciated snowball state.10 It is only the presence of CO2 that keeps Earth’s atmosphere warm enough to contain much water vapor. Conversely, increasing CO2 would warm the atmosphere and ultimately result in greater water-vapor content—a now well-understood situation known as water-vapor feedback.9,11

Though the first calculation of the warming of Earth due to CO2 increase was carried out by Arrhenius in 1896, accurate CO2 and water-vapor spectroscopy and a fully correct formulation of planetary energy balance did not come together until the work of Syukuro Manabe and Richard Wetherald in 1967.2,12 With that development, the theory was brought to its modern state of understanding. It has withstood all subsequent challenges and without question represents one of the great triumphs of 20th-century physics.

Planets far and near

The foundations of radiative transfer were laid by some of the greatest physicists of the 19th and 20th centuries—Fourier, Tyndall, Arrhenius, Kirchhoff, Ludwig Boltzmann, Max Planck, Albert Einstein, Schwarzschild, Arthur Eddington, Milne, and Subrahmanyan Chandrasekhar—plus many more whose names are not well known, even among physicists, but probably deserve to be. The subject has had a century of triumphs (and, as Saturation Fallacies, below, describes, some wrong turns) 13 and is about to go into high gear because of the dawning era of extrasolar planet discovery. What kind of atmospheres would render a planet in the potentially habitable zone of its star actually habitable,13 and how would astronomers detect it? If they see a high-albedo object with CO2 in its atmosphere, how will they determine if it is a snowball or a large Venus-like rocky planet?

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Saturation Fallacies: The path to the present understanding of the effect of carbon dioxide on climate was not without its missteps. Notably, in 1900 Knut Ångström (son of Anders Ångström, whose name graces a unit of length widely used among spectroscopists) argued in opposition to his fellow Swedish scientist Svante Arrhenius that increasing CO2 could not affect Earth’s climate. Ångström claimed that IR absorption by CO2 was saturated in the sense that, for those wavelengths CO2 could absorb at all, the CO2 already present in Earth’s atmosphere was absorbing essentially all of the IR. With regard to Earthlike atmospheres, Ångström was doubly wrong. First, modern spectroscopy shows that CO2 is nowhere near being saturated. Ångström’s laboratory experiments were simply too inaccurate to show the additional absorption in the wings of the 667-cm−1 CO2 feature that follows upon increasing CO2. But even if CO2 were saturated in Ångström’s sense—as indeed it is on Venus—his argument would nonetheless be fallacious. The Venusian atmosphere as a whole may be saturated with regard to IR absorption, but the radiation only escapes from the thin upper portions of the atmosphere that are not saturated. Hot as Venus is, it would become still hotter if one added CO2 to its atmosphere.

A related saturation fallacy, also popularized by Ångström, is that CO2 could have no influence on radiation balance because water vapor already absorbs all the IR that CO2 would absorb. Earth’s very moist, near-surface tropical atmosphere is nearly saturated in that sense, but the flaw in Ångström’s argument is that radiation in the portion of the spectrum affected by CO2 escapes to space from the cold, dry upper portions of the atmosphere, not from the warm, moist lower portions. Also, as displayed in the inset to figure 2, the individual water-vapor and CO2 spectral lines interleave but do not totally overlap. That structure limits the competition between CO2 and water vapor.

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Whatever the future holds for newly discovered planets, interest remains intense in maintaining the habitability of the planet likely to be our only home for some time to come. The contributions of fundamental physics to achieving that aim are clear. The CO2 greenhouse effect is directly visible in satellite observations of the bite taken out of the IR spectrum near 667 cm−1, a feature whose details agree precisely with results of calculations based on first-principles radiative transfer calculations. Laboratory spectroscopy demonstrates that the width of the bite will increase as CO2 increases, and warming inevitably follows as a consequence of well-established energy-balance principles. The precise magnitude of the resulting warming depends on the fairly well-known amount of amplification by water-vapor feedbacks and on the less-known amount of cloud feedback. There are indeed uncertainties in the magnitude and impact of anthropogenic global warming, but the basic radiative physics of the anthropogenic greenhouse effect is unassailable.

I am grateful to Yi Huang for providing me with AIRS spectra, to David Crisp for providing Venera digital data and for many illuminating discussions on the subject of radiative transfer over the years, and to Joachim Pelkowski for pointing out Poisson’s work on radiative transfer.

Raymond T. Pierrehumbert is the Louis Block Professor in Geophysical Sciences at the University of Chicago.

References

  1. R. T. Pierrehumbert, Nature 432, 677 (2004) [MEDLINE].
  2. D. A. Archer, R. T. Pierrehumbert, eds., The Warming Papers: The Scientific Foundation for the Climate Change Forecast, Wiley-Blackwell, Hoboken, NJ (in press).
  3. S. D. Poisson, Théorie mathématique de la chaleur, Bachelier, Paris (1835).
  4. L. S. Rothman et al., J. Quant. Spectrosc. Radiat. Transfer 110, 533 (2009) .
  5. R. T. Pierrehumbert, Principles of Planetary Climate, Cambridge U. Press, New York (2010).
  6. I. Halevy, R. T. Pierrehumbert, D. P. Schrag, J. Geophys. Res. 114, D18112 (2009) [SPIN], doi:10.1029/2009JD011915.
  7. Y. Huang et al., Geophys. Res. Lett. 34, L24707 (2007) [SPIN], doi:10.1029/2007GL031409.
  8. See, for example, D. Marsden, F. P. J. Valero, J. Atmos. Sci. 61, 745 (2004) [INSPEC].
  9. R. T. Pierrehumbert, H. Brogniez, R. Roca, in The Global Circulation of the Atmosphere, T. Schneider, A. Sobel, eds., Princeton U. Press, Princeton, NJ (2007), p. 143.
  10. A. Voigt, J. Marotzke, Clim. Dyn. 35, 887 (2010) .
  11. A. E. Dessler, S. C. Sherwood, Science 323, 1020 (2009) [MEDLINE].
  12. S. Weart, The Discovery of Global Warming, Harvard U. Press, Cambridge, MA (2008), and online material.
  13. R. T. Pierrehumbert, Ap. J. Lett. (in press).
  14. V. I. Moroz et al., Appl. Opt. 25, 1710 (1986) [INSPEC].

41 thoughts on “Infrared Radiation and Planetary Temperature”

  1. Leonard Weinstein

    The first part of this is excellent. In fact, he says the right thing about how the absorbing gas causes the heating of the ground (lapse rate plus raised atmosphere). Unfortunately, he blows it later. Both my writeup (G1), and Al’s (G2) clearly describe the net average effect. However, Raymond T. Pierrehumbert goes on to use the description as an insulation effect. He does not even mention that then the energy is transported by evaporation of water and free convection, and that clouds are a negative feedback. He also completely misses the fact that water vapor increases in the lower troposphere are not important, only the upper region, where the radiation to space occurs. His emphasis also misses the fact that most of the CO2 effect occurs at a relatively low concentration, and thus it would take huge increases to slightly increase temperature directly. He is hand waving in the later part of the writeup, with much of the detail assumed, and not supported (unknown aerosol effects, cloud feedback, sea current lag).

  2. @1 Leonard,

    This article by Pierrehumbert represents the Gospel of the American Physical Society. When a lead article in the APS Physics Today gets the calculation of the GHG effect wrong, it demonstrates the complexity of the problem. I notice he uses wave number which is misleading, when he should be using wavelength for a proper energy presentation.

    The APS printing does not allow criticism or comments. I will be interested to see how many comments we get on this article. What do you think of his Saturation Fallacies?

  3. Leonard Weinstein

    The statement: “Hot as Venus is, it would become still hotter if one added CO2 to its atmosphere.” is curious. Venus is over 96% CO2, with 240,000 times as much as Earth. If the CO2 fraction increased to 99%, it likely would be slightly cooler, since it would be replacing water vapor and other gases that fill in some of the spectral holes. The only way increasing CO2 would make Venus hotter, is to increase the total gas quantity in the atmosphere, and adding any gas to increase the total gas quantity would do that (by raising the level of outgoing radiation).

    The point about CO2 saturation not occurring is partially valid. There is edge broadening that allows more bulk absorption effect with increase, and the radiation is from the upper atmosphere. However, the change in water vapor pressure in the upper atmosphere has not acted as he indicates. The absolute water vapor not only did not increase with temperature, it slightly decreased at some altitudes. This counters that claim of positive feedback. I do expect the increased CO2 to BY ITSELF tend to increase temperature slightly, but with no positive feedback. However if clouds increase (as seems to be the case), for there in fact to be negative feedback.

  4. My take on the Physics Today article by R.T. Pierrehumbert about
    infrared affects on planet temperature, AKA Global Warming (GW) is that his exposition ends is a “He said, She said” qualitative argument that proves nothing while carefully avoiding criticism of academic politically correct support of the GW hypothesis. I think that
    this strategy is a ploy, likely aimed at protecting the reputation of the
    academic scientific community and the continuity of their Federal grants. My
    position is that in this time of economic crisis, it’s no time to spend
    another dime on this highly speculative field. That includes Climate Change,
    Cap and Tax and the foolish charade of Carbon Sequestration. The same goes
    for environmental “protection” as well. Throwing them out will be handy to
    balance the federal budget. EXTREME! you say. How much better off will be the USA economy if we do this? How much worse off if we don’t? I’m getting the same feeling of our federal (childish) behavior on GW as I get when an insurance salesman tries to sell me life insurance. I can;t wait until he leaves the room because his propositions are so ridiculous. My children are long out of the nest, etc. So selling GW involves just another barrage of salesman “what-ifs?”.

    Even for the simplistic problem of predicting the rise of Earth average
    temperature due to heat release due to fuel combustion as compared to solar
    influx, Pierrehumbert provides NO calculated solution. He throws around a few physical constants, then shuffles away from the issue. I HAVE made the calculation, and
    my results indicate about a +0.2 C temperature rise; stop that combustion and
    that +0.2C goes away. Others are invited to make the same calculation),

    My take on GW is, and has been for some years, that all significant CO2
    action takes place in the upper atmosphere – above any clouds. the degree of
    such CO2 affect is trivial and would if anything only cause slightly colder
    winters and slightly warmer summers. The extent of this effect is very small
    compared to the variation of surface temperature on any given day due to the
    common chaos of global atmospheric mixing effects. I’m now 81 years old, and
    I can safely say that the weather today is quite familiar to me; that there
    have been no surprises since the Ohio Blizzard of 1978.

    What I dearly want to see now is for someone to quantify the
    Pierrehumbert innuendos into real temperature increments vs global
    atmospheric CO2 concentration. Keep in mind that the only relevant affect
    lies in the intensification of CO2 infrared radiation absorption lines.
    Between those absorption lines, the atmosphere is transparent to visible and
    IR energy transmission. That is, adding more CO2 gas into the atmosphere
    only very, very slightly broadens the bandwidth of each absorption line, or
    in another aspect, raises the altitude where heat is retained. I have seen NO
    quantification by anyone of this aspect of this phenomenon.

    I “view” the effect of CO2 on the externally visible atmosphere as being similar to our spectroscopic view of sunlight. We all have seen pictures of the emission spectrum of sunlight which comprises a bright continuum but with narrow dark absorption lines due to gaseous iron and other elements clearly posited. No one will deny that the energy intercepted by these gaseos atoms remains in the solar corona remote from Old sol. To be sure, this at the same time results in a certain diminishing of the sunlight energy that arrives to our orbit.

    Consider then the infrared emission spectrum issuing from the dark side (night) of Earth. Again, we would see a bright continuum interspersed by dark lines of CO2. The same diminishing of escaped CO2 line IR radiation occurs, but the energy so “retained” remains in the upper atmosphere. Note that Pierrehumbert refers to the apparent fact that the upper atmosphere is warm… warmer than the stratoshphere. It will do well to revisit the hard data that has been used to advance the (warm upper atmophere) fact. What is the temperature distribution vs altitude day and night?

    With so much grant money flying around, and so many competent (or so they say) “scientists” assigned to the task of GW analysis, I find the paucity of such first principle calculations to be highly disturbing and somewhat suspicious. Is it because the quantitative results show surprisingly little CO2 affect on earth temperature? I suspect THIS to be the case.

    Angelo Campanella

  5. Leonard Weinstein

    @ 10 Dr Eric,
    I am having a hard time believing you are misunderstanding what I stated as much as you seem to be. First I examined two modes of increasing CO2. The first was to take part of the 4% of other gases and replace it with an equal amount of CO2, so as to maintain the same total mass (this is one possible definition of increase in the amount of CO2, so is included for completeness). The 4 % contained mostly N2, but also contained SO2, H2O and other gases in small but significant quantities. These other gases are important to fill in some of the absorption lines missed by CO2. The result was that there would be a slight cooling. I then made the other example of adding new mass to the atmosphere rather than replacing some. This has two parts: 1) add CO2, 2) add another gas (such as N2). Both cases would result in an increase in ground temperature, due to raising the altitude of the out going radiation. The added CO2 would raise it a bit more for the same added mass, but both would raise it.

    What part of this do you not now understand?

  6. @14 Eric,

    The last thing I want to get involved in would be to determine where everyone makes comments. The gray areas are too large. I can encourage subject areas by establishing separate posts but that is as far as I wish to go.

    I am sure Angelo @12 is aware of our PCA and decided to put his comment here. We must allow him to make his own decision.

  7. Continuing from @12:

    Noting that this is the place to ask Eric questions, I pose:

    Have you considered the distribution of temperature at high altitudes?

    A useful depiction of such is found at

    http://www.windows2universe.org/earth/Atmosphere/layers_activity_print.html

    Note that the temperature remains at freezing and colder from 10km to 100 km (30,000′ to 300,000′) in the Stratosphere and the Mesosphere. . Note also that the temperature increases rapidly above 300,000′.

    In reality there has to be a diurnal and a seasonal variation in this temperature profile. It can’t be just the one line depicted. Have you found any real world data of those periodic variations in temperature?

    Assume for the moment that the above figure is accurate enough to make some useful conclusions. The question arises; “What is it about the Stratosphere and Mesosphere that keeps them cold and symmetrically, what is there about the Thermosphere that keeps it hot?” what’s the source of the A/C in the Stratosphere and Mesosphere?

    The former distinguish themselves as being more dense and interfaced to earth surface constituents, the major of which are CO2 and H2O. H20 is lesser because it’s vapor pressure diminishes greatly around freezing. CO2 on the other hand has a higher vapor pressure and will mix upwards.

    The Thermosphere may be distinguished for one by its first in line to attenuate ultraviolet energy, a broadband phenomenon, so we can say that the UV is absorbed (an atomic phenomenon, not a polar phenomenon) there regardless of any CO2 and H2O presence. The result is the creation of Ozone (O3) which is indeed a polar molecule capable of infrared energy back to outer space. (Hence my expectation that the Thermosphere temperature has a diurnal variation.)

    The Mesosphere and Stratosphere have greater density and hence a greater heat capacity, so their effect on earth surface temperature might be significant.

    The presence of CO2 primarily should have a direct effect on Strato-Meso temperatures.

    Where are the experimental studies and the resulting data that detail these effects?

  8. @11 Angelo,

    Your are entitled to your own gut level opinions, of course. If there is any specific question of a scientific nature that I could attempt to answer, please let me know.

  9. Leonard Weinstein

    @ 13 Dr Eric.
    I now understand that you do not understand how the atmospheric greenhouse gas effect works. The cause of the high temperature on Venus requires two features. There has to be enough absorbing gas to move the effective altitude of outgoing radiation (outgoing to space), and there has to be an adiabatic lapse rate due to sufficient convection. Increasing the amount of any gas significantly moves the location of outgoing radiation to higher altitude, which due to the lapse rate , increases the surface temperature. Assume we add enough gas to increase the atmospheric thickness by 10%. The present location of outgoing radiation is about 50 km (remember we are talking about Venus here). With average lapse rate of 8 C/km, this added 400 C to the temperature of the atmosphere at 50 km (which only depended on absorbed solar radiation). Thickening the atmosphere by 10% with pure CO2 would raise the location of outgoing radiation by about 5 km, and thus add about 40 C. Thickening the atmosphere by 10% with N2 would not quite raise the location of outgoing radiation as much due to the location of partial greenhouse gas pressure being the critical factor, not the location of total pressure. However, the dilution would only change the location of partial pressure of CO2 by about 10% of the 5 km, and thus raise the temperature only 36 C. Thus the added N2 is NEARLY AS LARGE AN EFFECT (36/40=0.9)! If the added gas were a dense non-greenhouse gas such as Argon, the temperature increase would be LARGER than for CO2, due to the smaller Cp (and lapse rate is -g/Cp). The preceeding assumed no change in albedo, and is approximate but basically valid.

  10. @17 Leonard,

    While I will readily admit that I need to learn more about how the GHE works, I’m afraid your discourse on the subject in G1 is not where I will improve my knowledge.

    Concerning you discourse in G1:

    1. Have you understood yet why the decreased pH of the oceans is not evidence that the ocean is absorbing more CO2 as you suggests. You have that part backwards – a decreased pH means that the oceans will absorb a smaller fraction of the total CO2 in the future.

    2. Have you learned yet that the residence time of the EXTRA CO2 in the atmosphere is one the order of centuries or more, and not decades.

    3. Have you not yet recognized that increase water vapor in the lower atmosphere will increase the lapse rate throughout those altitudes so that the temperature at ground level will be thereby increased due to the effect of water vapor on the lapse rate effect in addition to the GHE?

    4. Have you learned yet that increased clouds, due to increased water vapor will not necessarily cause a net cooling due to an increased albedo but might be either a wash or even a net warming effect due to the fact that clouds absorb IR?

    After I have gained some addition insight on this subject from better sources, I will get back to you concerning your comments in @17 – in which you claimed that the addition of CO2, rather than N2, to a planet’s atmosphere would have essentially the same effects on temperature.

  11. Leonard Weinstein

    @ 18, Dr Eric,
    1. The absorption coefficient of sea water decreases with increasing temperature, but the quantity able to be absorbed increases with increased partial pressure of CO2 (in the atmosphere). The partial pressure increase effect is much larger than the temperature increase effect. In addition, the surface layer is being diluted over a large volume by mixing, and it is also removed by the currents North then then dives deep (thermohaline current) with a time constant of only about a century, so fresh unsaturated water upwells to absorb more CO2 at the higher partial pressure. While I think the net result is what I claim, I don’t think all factors are well enough known to be certain of the net effect over long times (mainly because we don’t know what CO2 levels will be released in the future), but your positive statement is also not supported.
    2. The residence time of the upper 75% to 80% of the excess is only the order of 50 years. A progressively smaller amount lasts longer. However it is the larger amount that matters if there is a large AGW effect, and I don’t even think the AGW effect is large. All asymptotic process persist many time constants, but this effect becomes unimportant in just one or at most two time constants.
    3. The water vapor amount is small compared to the total atmosphere mass, but all effects of water vapor result in a DECREASE in lapse rate. In the vapor state, the higher Cp lowers the lapse rate a small amount. As the vapor condenses, the phase change decreases the lapse rate (note the dry lapse rate is about -9 C/km, and wet lapse rate is about -6 C/km). You are reversed.
    4. This is not a fully resolved issue, but seems to favor a negative feedback.

  12. Where is the experimental data that shows that CO2 causes any change in temperature? No one has shown with creditable experimental data that can correlate a given concentration of any IRag-CO2 or CH4 etc with a given temperature rise.
    With out experimental data the “ghg effect” is a hypotheses and no more.
    A question I am looking into is “What is the thermocondutivity of CO2?” So far what I’ve found indicates that CO2 has a slightly higher thermocondutivity than air thus adding CO2 will cause a higher rate of heat loss and cool the atmosphere not heat it. I believe this is the point Dr. Leonard has made several times. This should be able to be demonstrated in a lab experiment as the procedure to determine “thermocondutivity ” is well documented .
    If CO2 is this great “insulator” it should have a measurable difference in thermocondutivity- lower that AIR.

  13. Leonard Weinstein

    @ 23, Dr Eric,
    How much does the temperature change for DOUBLING the CO2 concentration on Earth. I say less than 1.2 C, CAGW scientists say probably 3 C. Let us use the larger value here. Note: this is for doubling. If that relationship held, and all else was the same, 98% CO2 would only be 3 C warmer than 49% CO2. However, adding both CO2 or N2 in large quantities would THICKEN the atmosphere. This is a different effect than relative composition, and doubling the thickness in both cases would effectively double the total previous effect (due to the lapse rate time change in altitude), however much it is. For Venus, the thickness increase effect would dominate the small change due to relative composition. I used an example of a 10% thickness increase. You use a doubling. The thickness change is so strong an effect, that your case is even a smaller fractional difference than my case.

  14. Leonard Weinstein

    @ 24 Berthold,
    The thermal capacity or thermal conductivity of the air or CO2 do not matter (except for their small effect on the average value of Cp as it affects the lapse rate, which is =-g/Cp), as the absorbing gas effect is radiation insulation, but free convection, not thermal conduction carry most of the energy from the ground to the upper atmosphere. The radiation insulation effect only is important in that the location of radiation to space is raised from the ground to a location (on average) in the mid troposphere.

  15. There are some clumsy , misleading and partly wrong statements in the following :

    Coupled vibrational and rotational states are the key players in IR absorption. An IR photon absorbed by a molecule knocks the molecule into a higher-energy quantum state. Those states have very long lifetimes, characterized by the spectroscopically measurable Einstein A coefficient. For example, for the CO2 transitions that are most significant in the thermal IR, the lifetimes tend to range from a few milliseconds to a few tenths of a second. In contrast, the typical time between collisions for, say, a nitrogen-dominated atmosphere at a pressure of 104 Pa and temperature of 250 K is well under 10−7 s. Therefore, the energy of the photon will almost always be assimilated by collisions into the general energy pool of the matter and establish a new Maxwell–Boltzmann distribution at a slightly higher temperature. That is how radiation heats matter in the LTE limit.

    and then

    According to the equipartition principle, molecular collisions maintain an equilibrium distribution of molecules in higher vibrational and rotational states. Many molecules occupy those higher-energy states, so even though the lifetime of the excited states is long, over a moderately small stretch of time a large number of molecules will decay by emitting photons. If that radiation escapes without being reabsorbed, the higher-energy states are depopulated and the system is thrown out of thermodynamic equilibrium. Molecular collisions repopulate the states and establish a new thermodynamic equilibrium at a slightly cooler temperature. That is how thermal emission of radiation cools matter in the LTE limit.

    Actually what he doesn’t say clearly is that the rate of the first process (collisional decay) is EQUAL to the rate of the second process (collisional excitation) in LTE .
    Statements like Therefore, the energy of the photon will almost always be assimilated by collisions into the general energy pool of the matter and establish a new Maxwell–Boltzmann distribution at a slightly higher temperature. That is how radiation heats matter in the LTE limit
    and
    Molecular collisions repopulate the states and establish a new thermodynamic equilibrium at a slightly cooler temperature. That is how thermal emission of radiation cools matter in the LTE limit

    are misleading and lead many people to misunderstand the basics of LTE by focusing only on the former statement and completely zapping the latter .
    From there come many uninformed statements on the Net like “infrared radiation heats the atmosphere” which is how people interpret the first statement of Pierrehumbert .

    Of course the statements I quoted above are only valid when the system is NOT in LTE !
    If you mix hot N2 with cold CO2 (what happens in a CO2 laser f.ex) , you are out of equilibrium and the N2 will cool down by entering in collisions with the CO2 molecules and exciting their vibrational states . The collisionaly excited CO2 molecules will emit and this is how the mixture will cool down and achieve equilibrium .

    However when we consider the atmosphere , there is no such process because the atmosphere already IS in LTE below some 70 km .
    That’s why in the real atmosphere there is neither “heating” nor “cooling” by IR interacting with GHG because the rates of both are equal in LTE .

    The word always in : Therefore, the energy of the photon will almost always be assimilated by collisions into the general energy pool of the matter and establish a new Maxwell–Boltzmann distribution at a slightly higher temperature.
    is wrong because the above decription is only relevant for a mixture out of LTE .

    One can also notice that this statement taken alone contradicts the Kirchoff’s law because it implies that there is no emission of IR radiation by GHG . In other terms the absorptivity would be non zero (the GHG absorbs the photon) but the emissivity would be zero (the GHG decays by collision before having the time to emit “almost always”) .

  16. Eric

    There must be a misunderstanding .
    My domain of expertise is quantum mechanics and be sure that I don’t need any “help” in these matters .
    I merely wanted to tell to interested readers who are not as familiar with QM as I am that what Pierrehumbert writes is misleading and partly wrong .
    The standard stuff (well it is not “standard” for everybody) is telling that a gas in LTE is neither “heated” nor “cooled” by IR .
    This presentation which you basically repeat is indeed clumsy and misleading .

    The non clumsy and non misleading presentation consists to say that the distribution of the quantum states in LTE is given by the Maxwell-Boltzmann distribution .
    As this distribution depends only on temperature and the temperature is constant in the neighbourhood of the considered point (this is the very definition of LTE) , then for every single Q1->Q2 transition there is necessarily a Q2->Q1 transition .
    If there were not , the gas would not be , again per definition , in LTE .
    This is standard stuff .

    And I repeat that this Pierrehumbert presentation very obviously violates the Kirchhoff”s law what is enough to say that it is clumsy and misleading .
    Indeed if one says that Therefore, the energy of the photon will almost always be assimilated by collisions into the general energy pool of the matter and establish a new Maxwell–Boltzmann distribution at a slightly higher temperature. then this violates the Kirchhoff’s law unless one adds : Therefore any ground state will almost always be excited by collisions from the general energy pool of the matter and this process makes sure that the temperature doesn’t vary in LTE.

    If only the former process took place , one would obtain an absurd unphysical situation in which a mixture of CO2 and N2 initially at the same temperature and submitted to IR would spontaneously separate in hotter and hotter N2 and colder CO2.

    At room temperature and atmospheric pressure, the air is in LTE and about 5% of the V2 quantum states of the CO2 molecules are in the first quantum level . 95% are in the ground state .
    This is independent of any IR . CO2 is of course absorbing the resonant photons but there is no “heating” by collisions because the number of CO2 molecules stays at 5% forever as long as we have LTE .
    The rates of the processes of collisonal decay and collisional excitation are simply equal what is another non clumsy way to say that the gas neither “heats” nor “cools” by radiative processes in LTE .

    Btw I am not saying that Pierrehumbert doesn’t understand the “standard” stuff even if most people involved in climate science that I met REALLY believe that IR radiation “heats” a gas by collisions and generally have no clue about what LTE means .
    I am saying that he is a bad writer and expressed the processes in a very clumsy way which is bound to mislead many of those who are not experts in QM .

  17. Pierrehumbert’s article includes the following false claim:
    ” The same considerations used in the interpretation of spectra also determine the IR cooling rate of a planet and hence its surface temperature. ”
    The title of his piece is also misleading, suggesting that temperature is determined by radiation.
    You cannot determine the surface temperature unless you can quantify the heat flux from all sources, including convection and evaporation.
    Leonard made this simple point in comment #1.
    See also the following thread G7 on climate science’s blind spot.

  18. Pingback: Comment On Raymond T. Pierrehumbert’s Article In Physics Today Titled “Infrared Radiation And Planetary Temperature” | Climate Science: Roger Pielke Sr.

  19. Eric

    You wrote

    “The standard stuff is telling that a gas in LTE is neither “heated” nor “cooled” by IR”

    Makes no sense whatsoever to me.

    I will then try to show how it makes very much sense .
    Let’s consider again the following Pierrehumbert statement :

    Therefore, the energy of the photon will almost always be assimilated by collisions into the general energy pool of the matter and establish a new Maxwell–Boltzmann distribution at a slightly higher temperature .

    This statement unmistakenly says that IR “heats” the atmosphere via absorption by CO2 and you apparently agree .
    So we’ll just think 5 minutes and follow the movie .
    You will surely agree that the process doesn’t stop there because after this first photon considered by Pierrehumbert , a second will come .
    The statement then reads :
    Therefore, the energy of the SECOND photon will also be assimilated by collisions into the general energy pool of the matter and establish a new Maxwell–Boltzmann distribution at a still slightly higher temperature .

    If you are consistent and if you agree with the first statement , you will also agree with the second one , right ?
    But can you see now where all this is heading ?
    There are billions of billions of these photons every second !
    And as each one brings the system to a slightly higher temperature what do you think happens to a series S = Sum over i of (Delta T)i when i goes to infinity ?
    Right , within a short time the atmosphere is so hot that it ionizes .

    You will also surely agree that we do not observe in the Earth’s troposphere ionized atmosphere at thousands K .
    So as we don’t observe that , then obviously this statement is wrong .
    I have already explained why it was wrong but will try to repeat it more in detail .

    Because it is true that most of the excited vibrational CO2 states will decay by collisions and that this would indeed lead to an unbouded heating of the gas , it is necessary that there be another mechanism that works exactly in the opposite direction .
    It is not necessary to look far for it – this mechanism is simply the emission of the IR photon which leaves the gas .

    So it is obvious that for every photon absorbed somewhere , there must be a photon emitted somewhere else .
    As long as it is not the case , the gas either heats or cools . But as its temperature is varying , it is by definition not in LTE .
    Eventually a temperature is achieved in which for a given gas volume the absorbed IR is exactly equal to the emitted IR .
    At this temperature the gas is in LTE and the IR radiation neither “heats” nor “cools” it .
    Observation shows us that all of the atmosphere is in LTE .

    From there follows trivially that :
    “The standard stuff is telling that a gas in LTE is neither “heated” nor “cooled” by IR”

    Does it make full sense to you now ?

  20. @34 For more information on this subject, I recommend reading the comments on Judith Curry’s blog:

    http://judithcurry.com/2011/01/19/pierrehumbert-on-infrared-radiation-and-planetary-temperatures

    Your summaries of the many comments are welcome here.

    Roger Pielke wrote on his blog:

    http://pielkeclimatesci.wordpress.com/2011/01/21/comment-on-raymond-t-pierrehumberts-article-in-physics-today-titled-infrared-radiation-and-planetary-temperature

    However, there is one major error in my view in the article.
    Pierrehumbert concludes:

    “… increasing CO2 would warm the atmosphere and ultimately result in greater water-vapor content—a now well-understood situation known as water-vapor feedback.”

    This significantly overstates our understanding of the water vapor feedback on Earth since phase changes of water are intimately involved. In a world without these feedbacks, but in which evaporation from the surface increases if surface temperature increases from the added CO2, his conclusion would be correct.

    Graeme Stephens wrote on Roger Peilke’s post:

    “Models contain grave biases in low cloud radiative properties that bring into question the fidelity of feedbacks in models”

    “The presence of drizzle in low clouds is ubiquitous and significant enough to influence the radiative properties of these clouds and must play some role in any feedbacks”

    ”….our models have little or no ability to make credible projections about the changing character of rain…”

    To which Pielke commented:

    The water vapor feedback in the real climate system remains incompletely understood.

    Referring to Graeme Stephens’ slide presentation, Peilke wrote:

    This presentation by Graeme Stephens highlights the inability of the IPCC models to make skillful predictions of climate decades into the future on the global scale, much less regional spatial scales.

    Regional assessments based on the IPCC model results in such reports as the CCSP series (as well as the set of talks moderated by Tom Karl, Director of the National Climate Data Center and current President of the American Meteorological Society (e.g. see) are flawed, scientifically unsupported reports and are misleading policymakers.

  21. Eric

    Now you completely lost me .

    You wrote in the last post transmitted by Ed I think we have the same view of this and our difference lies in our view of the dynamics involved and our perceived importance of a near Boltzmann versus a perfect Boltzmann distribution.

    How is this consistent with “The standard stuff is telling that a gas in LTE is neither “heated” nor “cooled” by IR”

    Makes no sense whatsoever to me. that you wrote in the post just above ?

    Yet my post which made no sense whatsoever to you said EXACTLY the same thing as the post that ellicited the comment I think we have the same view of this

    Namely that : The standard stuff is telling that a gas in LTE is neither “heated” nor “cooled” by IR”

    It’s a rather easily understandable statement that allows a clear yes or no answer .
    If I am not mistaken, you agree with this statement now what would be a good thing because it puts at rest this nonsense that one reads much too often on the Net namely that the IR DOES heat the atmosphere – you surely agree that this would mean that the function T(t) is monotonously increasing.

    I do not think that there may be 2 different points of view on the “dynamics” involved.
    The “dynamics” is very easy and consists only of 2 processes that I will write below :
    1) radiative process
    photon + M [-] M* where
    M is a molecule with an electric dipole and M* is the same molecule in a vibrationaly excited state
    the symbol [-] means that the process happens in both directions
    2) collision process
    M* + N [-] M + N* where
    M* is a molecule in a high energy state (which may be vibrational , rotational or translational or a combination of all)
    N is another molecule in a low energy state
    the symbol [-] means that the process happens in both directions

    There is no room to have different views on these processes.

    I also don’t see what you mean with our perceived importance of a near Boltzmann versus a perfect Boltzmann distribution
    A “perfect” Boltzmann distribution, like any statistical distribution is only valid in the infinte limit.
    As we deal with finite systems, they are obviously not infinite even if they are extremely large.
    So it is a somewhat trivial remark to say that the real life distributions are never “perfectly” Boltzmanian but they converge to Boltzmanian when their size increases .
    This has nothing to do with the discussion which as I remind boiled down to the statement that The standard stuff is telling that a gas in LTE is neither “heated” nor “cooled” by IR

  22. Addendum to the above

    Eric you wrote :
    The other is the absorption and emission of IR radiation transferring energy into and out of the body of gas under consideration. The latter process it constantly trying to disruption the Boltzmann distribution

    Allow me to correct this statement which is incorrect because you are probably not very familiar with QM .
    The distribution of the quantum states is given by the Maxwell Boltzmann distribution.
    As this distribution depends only on temperature, in LTE it must be kept constant.
    Therefore what does disrupt this distribution is precisely the IR absorption and collisional excitation because it increases the number of high energy states what would be inconsistent with the M-B distribution.
    Therefore the emission is a necessary correcting mechanism which in addition to collisional decay , to the contrary of what you wrote , doesn’t disrupt anything but decreases the number of high energy states thus bringing the distribution of the quantum states back to the M-B distribution.

    This is btw the deep Qmechanical explanation of why the Kirchhoff’s law holds .

  23. @39 by Dr. Eric
    (NOTE: Ed is posting this comment for Dr. Eric, at his request, because we are having a problem getting Eric logged in.)

    Tom,

    Maybe this will help you see my point. Consider a clear solution containing various dissolved substances sitting in an IR transparent container (such as a salt box) at in a larger box held at room temperature.

    The IR active molecules in that solution will be absorbing and emitting IR radiation continuously. Do you think that a Boltzmann distribution will exist within the various vibrational and rotational states of the molecules at all times in this system at rest ?

    Now increase the temperature of the wall so the external box wall by one degree C. As the solution then warms up eventually by 1 degree, due you think the distribution of molecules in those same states will continuously readjust as the T increases so that a near perfect Boltzmann distribution is maintained at all times even during the T change as well as before and after? Note that the collisional quenching of existed states in the condensed liquid phase typically occur on times scales of about 10< -12> seconds (picoseconds).

    Perhaps your response to this question will help me understand where our differences lie.

    So please try to humor me in this exercise, just for the moment, rather than reflexive attack.

    Eric

  24. Eric

    Do you think that a Boltzmann distribution will exist within the various vibrational and rotational states of the molecules at all times in this system at rest ?

    Yes of course . Your box is in LTE and the quantum states are necessarily M-B distributed .

    Now increase the temperature of the wall so the external box wall by one degree C. As the solution then warms up eventually by 1 degree, due you think the distribution of molecules in those same states will continuously readjust as the T increases so that a near perfect Boltzmann distribution is maintained at all times even during the T change as well as before and after?

    Yes of course . I have already written somewhere (but not in this post) that convection and conduction can be neglected when collision/radiative processes are considered because the latter happen on time scales 6 ordres of magnitude smaller than the former .
    So the solution will need some seconds or more (depending on this and that) to heat up by 1 °C .
    During this time billions of collisons , absorptions and emissions will take place .
    From the point of view of the molecules , the external warming coming from the walls is infinitely slow . So the only thing that matters for them is LTE or not LTE .

    But there will be an extremely small increase of the number of excited states (proportional to exp(-h.µ/kDT)) so that the M-B distribution after some seconds will be very slightly different from the initial one . But it will be an almost perfect M-B during the whole process because the molecules adjust their quantum states to such slow processes quasi instantaneously . The change is so small in this example that one would hardly see the difference but there would be one as long as LTE holds .

    Btw why would you think that I might “reflexively attack” ? “Attack” what anyway ?
    I still don’t see where could be different points of view/interpretations on what I wrote in the post 38 , especially the second part .
    Neither did you state something since your “doesn’t make any sense for me” what would show some difference to what I say .

  25. Leonard Weinstein

    Tom and Dr. Eric,
    LTE is a continuum approximation. Also classical thermodynamics and fluid mechanics uses continuum approximations. If you are going to talk about temperature, you need to use continuum approximations. Tom is correct based on that approximation. If you now go to kinetic theory and look at individual molecules and small groups of molecules, Dr. Eric’s arguments make some sense, but then the whole concepts of thermodynamics is thrown out, and you must use statistics to examine what is occurring. Dr. Eric, you are making an issue on the difference between the two approaches. LTE’s last letter stands for EQUILIBRIUM, but within the continuum approximation, it is exactly valid.

  26. Leonard

    I would prefer to say that LTE is an approximation in the infinite limit instead of “continuum” (the number of molecules is always discrete as well as the distribution of the quantum states) .
    It is then tautological to say that one considers only very large ensembles when one uses the LTE concept .
    That excludes by definition small ensembles or even worse – single molecules .
    Clearly as soon as I use the word “temperature” (as f.ex in the M-B distribution) , the least I need is that a temperature exists .
    A single molecules has no “temperature” in any usual thermodynamical sense what has for consequence that its quantum states are whatever they are .
    If you want to know what a single molecule or a small number of molecules really do , there is only ONE way – you must solve the Schrodinger equation for the system and then find the correct probability distributions of all dynamical variables (energies , momenta etc) from the wave function .
    There are no classical statistics (mean , standard deviation etc) that could help in any way .

    All these macroscopical concepts simply need that all the microscopical degrees of freedom interact often and strongly . It is from these conditions that emerges energy equipartition , energy and quantum states distributions , temperature and all those statistical beings .

    I still don’t see with what Eric disagrees .
    Actually I am even less and less sure that he disagrees with anything .

    In the several posts I wrote , the only part that is important is the second part of the post 38 .
    I would greet with enthousiasm to read clearly stated what part of the post 38 is being contested/misunderstood/disagreed by Eric .
    Everything else I wrote are just variations on the same theme .

  27. Leonard Weinstein

    Tom,
    Use of the word “continuum” implies the number of molecules considered in a sample is very large and is considered effectively as giving the value for the number at the infinite limit. We are saying the same thing. This is just terminology.

  28. G6 – Perrehumbert article. Yep. Prof. Pierrehumbert does not seem to be overly concerned with stretching scientific truth, coherently.

    To begin, all the mumbling about centuries of research is a masquerade, a good sales pitch. All this gobbledegook about “speed of light” and “Planck constant” is used to create an impression that fundamental science of relativity and quantum physics is behind climatology. This is not true. While half of the factors are indeed based on good resolved physics, the other part of the overall “equations” — temperature distributions and fluid dynamics — are still unsolved problems of physics and mechanics.

    Now I want to comment on few spots of the article.

    RP: “Gases exhibit continuum absorption”

    AT response: yes, everything is theoretically continuum, but this kind of statement hides the fact that gaseous absorption spectrum is highly “uneven”, which creates some specifics when irradiance calculations have to be done along complex vertical profile of temperature.

    RP: “… gaseous spectroscopy is a highly developed subject”

    AT response: yes, but the application of spectroscopy to an atmosphere with sign-changing temperature gradient is not.

    RP: “Stratospheric temperature is constant or gently decaying with height for pure IR radiative equilibrium, but in situ absorption of solar radiation can make the stratospheric temperature increase with height.”
    AT response: RP mentions this fact, but later completely ignores it when dealing with “radiative imbalance”.

    Figure 3 – as usual. Prof. Pierrehumbert stretches a bit the definition of tropopause. It is known from indirect estimations that globally-averaged emission layer is at about 6km, while globally-averaged tropopause is at 12km.

    RP: “The agreement between the two is nearly perfect, which confirms the validity of the radiative transfer theory, the spectroscopy used to implement it, and the physics of the climate model.”
    AT response: Not really if you look into details. The comparison between observed and calculated spectra have a good agreement where the absorption is strong, or where it is negligibly weak (what a surprise). However, in every transitional area (wings of fine spectral peaks) there is a substantial deviation, about 3%. Unfortunately, this is precisely the area that contributes to changes in irradiance from changes in CO2.

    Also, panel (a) is more likely a “clear-sky” spectrum [need to check].

    Again, space instruments have limited spectral resolution and produce smoothened spectra. There is no doubt that smoothened spectra “match” spectra calculated from HITRAN database, because the lines are calibrated from the data. However, as it is well known, the real apbsorption-emission spectrum has high peaks and deep valleys between, so integration of total flux changes cannot be correct when spectrum is averaged first. So the agreement between band-averaged spectra does not really mean anything.

    RP: “Adding more greenhouse gas to the atmosphere makes higher, more tenuous, formerly transparent portions of the atmosphere opaque to IR and thus increases the difference between the ground temperature and the radiating temperature. The result, once the system comes into equilibrium, is surface warming.”

    AT response: As it is known, the effect of adding (doubling) CO2 is limited to 0.1um-0.2um spectral area. Increase of emission height in 14-16um area however results in HIGHER radiating temperature relative to ground, which must result in opposite effect. This is well-admitted effect of “stratospheric cooling”. AGW climatology uses a special trick and declares this area as “fast-equilibrating”, and excludes its influence on overall temperature profile.

    RP: “radiative transfer equations were applied to output of a climate model driven by observed surface temperatures”
    AT response: As one can see from physics of GH effect (as described in G2), atmospheric dynamics and how it approaches its stationary (on average) state is not driven by surface temperatures. Instead, surface temperatures are results of indirect atmosphere self-adjustments to radiative balance at the TOA. Given that no model calculates vertical structure of atmospheric dynamics as “prognostic variable”, starting from “observed surface temperatures” means sophisticated curve fitting, no more.

    General remark: in partitioning the atmosphere into layers, the layer can have physical meaning only if they are big enough for a particular wavelength to be in LTE. Since the absorption coefficients drop rapidly outside main absorption band (and between strong lines), this LTE condition should be violated at some points of spectrum for any given layering scheme. Therefore, partition of atmosphere into fixed layers must violate the LTE condition for about half of wavelengths, so the entire atmospheric model seems to be a big unphysical kludge.

    RP: “The recovery of blackbody radiation in that limit is one of the chief implications of Kirchhoff’s law, and it applies separately for each frequency.”
    AT response: this sounds like nonsense.

    RP: “For present Earth conditions, CO2 accounts for about a third of the clear-sky greenhouse effect”
    AT response: good plug, please note the “clear-sky” standard excuse of climatology.

    RP: “radiation in the portion of the spectrum affected by CO2 escapes to space from the cold, dry upper portions of the atmosphere, not from the warm, moist lower portions. Also, as displayed in the inset to figure 2, the individual water-vapor and CO2 spectral lines interleave but do not totally overlap. That structure limits the competition between CO2 and water vapor.”

    AT response: good professor forgets here that the clouds are made of liquid water and absorb-emit with continuous spectrum. So they do compete with CO2 wings, and overwhelmingly. More, radiation in “CO2-affected” regions does escape from dry cold areas, but 95% of this region emits from really-really “upper portion”, which is stratosphere, where higher==warmer, so the effect of CO2 increase is opposite to “global warming”.

    In conclusion, the entire article is a good sales pitch to unsuspecting climatartds.

  29. @ 24 Berthold Klein, I don’t know who has done which experiments, but, if you have a better theory about our climate, you should present it. What sure proof evidence do we have that gravity exists? Are you denying gravity exists? Gravity is part of a model that fits simply into the whole. Along with other theories, it seems to be consistent with observed results tried under a wide array of scenarios. The more we test something and the theories appear to hold, the more likely they are good useful theories (eg, able to make useful predictions). Climate models appear to use tried and true understanding of various models of our world. The climate models may be incomplete or have various problems, but if you don’t have a better alternative or can find evidence to argue strongly that the models are broken, then it would probably be a good idea to give their predictions some respect.

  30. @ 25 Leonard Weinstein >> If that relationship held, and all else was the same, 98% CO2 would only be 3 C warmer than 49% CO2.

    I am not sure what the 2CO2 assumptions are, but I will assume that this means we double the amount of CO2 period.

    Now, when we are dealing with small fractions of the whole (ie, if the CO2 is a small percentage of the atmosphere), say x, then adding another x roughly leads to twice the percentage.

    Eg, for 1%, we add another 1% to get (1+1)/(100+1) = 2/101 which is 1.98% or approximately 2%.

    However, if the percentage is not a small fraction of the whole, adding that same quantity again does not result in twice the percentage of the new whole.

    Eg, for 49%, we add another 49% to get (49+49)/(100+49) = 98/149 which is 65.8% which is rather far from 98%.

    If your question is, what percentage of CO2 would exist so that doubling it would give 98%, then we can compute (98-49)/(100-49) = 49/51 = 96.1%. Note that half of 98 is 49, so 49 is how much CO2 we subtract from the final CO2 (98) and the final total gases (100).

    To verify this in the other direction, let’s double the CO2 when we start off at 96.1%: (96.1+96.1)/(100+96.1) = 192.2/196.1 = 98.0%

    >> However, adding both CO2 or N2 in large quantities would THICKEN the atmosphere. This is a different effect than relative composition

    Dr. Eric has been using the doubling/thickening approach. Also, I believe the double CO2 3 degrees calculation, as just mentioned, likely refers to thickening and not relative composition as you appear to suggest it does.

    Eg, Dr. Eric said: “Venus1: Let’s double the amount of CO2 in the atmosphere of Venus. The molar fraction of CO2 will thereby be increased from 96% to about 98%.”

    If you go back and reread Dr. Eric’s comments, they might make a little more sense.

  31. @TomVonk
    >> If you mix hot N2 with cold CO2 (what happens in a CO2 laser f.ex) ….

    I looked up http://en.wikipedia.org/wiki/Carbon_dioxide_laser and the impression I get is that the laser and the atmosphere are not the same. The higher percentage of high energy states in the laser (population inversion) means that you get emission much more frequently than in the atmosphere.. relative to collisions.

    The explanation Dr. Eric seems right to me although an important point is not clear perhaps.

    You caught that point, but appear to be denying the effect he describes.

    I have taken some physics (and not much thermo at all) and don’t work in the field; however, this is the impression I am getting:

    1: A photon comes and is absorbed. This happens “slowly” as Dr. Eric mentioned. Then, on a much shorter time scale, we have LTE (local “thermodynamic” equilibrium.. which is an approx) so that surrounding molecules capture some of this energy through collisions (not emissions). The temperature goes up.

    2: There is an opposite effect for cooling down.

    First, the LTE I think refers to thermodynamic collision effects and the averaging at near instant time. I don’t think it refers to identically matching emissions with absorptions, as you mentioned. There is no requirement that absorbed photon immediately and always results in emission.

    Second,

    (a) when the intensity of photons is growing (eg, sunrise after the night time, as the temperature is rising), we get that (1) occurs a little more frequently than (2). This would mean that the average time to the next emission is longer than the time to the next absorption. Over time more photons are absorbed than released leading to a net increase in temperature as the “deltas” accumulate. Note, that we aren’t considering LTE or collisions here; that has already taken place at the shorter time range. With this increased temperature, the rate of emission now rises a little but can still lag the still increasing rate of absorption.
    (b) At constant temperature, we have (1) and (2) occuring roughly matched.
    (c) At decreasing temperature (ie, as sunlight goes down), we have (1) happening less frequently than (2). This time the rate of emission is slowing down but it also lags the faster decreasing rate of photon absorption.

    BTW, a more accepted model of “collision” might involve emission and absorption of various subatomic particles. I haven’t studied that, and it is not part of standard QM. I think you also created a distinction between collisions and radiation, so I didn’t worry about also using those two distinct models.

    FWIW (and for others reading), I believe the radiation (emissions) is simply “blackbody” (or graybody) radiation.

    >> I have already written somewhere (but not in this post) that convection and conduction can be neglected when collision/radiative processes are considered because the latter happen on time scales 6 ordres of magnitude smaller than the former .

    I think the “collision” terminology is closely associated with “conduction” rather than with “radiation”.

    >> There are some clumsy , misleading and partly wrong statements

    As to the quality of Pierrehumbert’s presentation, I haven’t read it all yet so won’t judge now.

  32. josex,
    We are talking about % doubling, not amounts added. If the amount of CO2 doubled so that the % went from 96% to 98%, the atmosphere would be much thicker (nearly twice surface pressure and much higher altitude for given pressures). The lapse rate would not significantly change, so the surface temperature would be several HUNDRED degrees C higher (added temperature would be approximately lapse rate times added altitude to average new location of outgoing radiation to space). I hope this is not what Dr. Eric meant, or he is even more off reality than I stated. The new effective altitude would not be double the previous (but would be a large number), and depending on cloud adjustments, the exact details would be more complex, but clearly the 3 C increase is not near valid.

  33. >> If the amount of CO2 doubled so that the % went from 96% to 98%, the atmosphere would be much thicker (nearly twice surface pressure and much higher altitude for given pressures).

    Just a quick review.

    You drew attention to this quote:

    “Hot as Venus is, it would become still hotter if one added CO2 to its atmosphere.”

    You added:

    “If the CO2 fraction increased to 99%, it likely would be slightly cooler, since it would be replacing water vapor and other gases”

    You did recognize:

    “The only way increasing CO2 would make Venus hotter, is to increase the total gas quantity in the atmosphere”

    Dr. Eric replied:

    “why would you suggest that the amount of water vapor would have to be diminished by the same amount – as if the total atmospheric pressure of Venus must somehow remain constant?”

    I think the original comment in the article (quote at top) makes sense and you appear to agree with it, but perhaps you misunderstood it the first time and thought it was a statement about %.

    >> so the surface temperature would be several HUNDRED degrees C higher

    Since I am somewhat new to this, I haven’t thought about what would be the increase, but, whatever it is, we, on Earth, are very far from having CO2 be at 98%. That figure might make sense for Venus, but I don’t think anyone claimed it would be that hot here.

    >> We are talking about % doubling, not amounts added.

    I think you would agree if you read it again that the original article quote (which started this comment discussion) makes sense and was referring to amounts doubling.

    For CO2 present levels on Earth, as I already mentioned, doubling the amount is about the same as doubling the percentage. You would be referring to either when you say “doubling”. This works for small percentages but not for large ones (relative to 100%).

    I now think (contrary to what I guessed before) that the 2xCO2 climate sensitivity reference used by the IPCC refers to % technically speaking, but it’s probably used because at our current CO2 levels talking about amounts or % of CO2 is almost identical.

    In any case, I really don’t think that 3 degrees C is something you should at all utilize if you wanted to talk about doubling CO2 percentage from 49% to 98%. That 3 value would be way out of context and is not supported by calculation. It’s likely nowhere in the ballpark (in fact, you spoke of 100s deg increase simply by going from 96% to 98% by adding more CO2, never mind from 49% to 98% by adding more CO2).

  34. josex,
    You appear to not have read the write-ups on adiabatic lapse rate and atmospheric thickness effects. Just increasing the % of Earth’s atmosphere that is CO2 from 390 ppm to 98% by replacing the nitrogen and oxygen with CO2, so that the total mass stayed the same, would result in a large DECREASE in surface temperature (assuming the same albedo). This is due to two causes of decrease and one of increase. The causes of decrease are: 1) The Cp of CO2 is much larger than for air, and 2) the thickness of the atmosphere would actually decrease. The bigger effect is due to the higher Cp, since lapse rate is -g/Cp. The cause of increase is similar to present causes: The average altitude of outgoing radiation is raised to a lower total pressure level compared to less CO2.

    Continually increasing CO2 while retaining N2 and most of the O2 (making CO2 uses up O2 from the atmosphere) and water vapor would cause an increase for a while, but eventually level off and eventually a drop as average Cp increased. Cloud effects and details make this a complex issue, but CO2 effects are limited due to lapse rate and effective thickness (Venus has an atmosphere nearly 100 times as massive as Earth, and many times as thick, so more than compensates for the lower CP compared to air, so it is a different case).

  35. I have ask the following question many times and to date no one has answered it: Where is the “credible experiment and data that proves the greenhouse gas effect”? Everything else is circumstantial evidence.

    As I have submitted my experiment at G-3 section 10 The demonstration that I believe provides the proof that the Greenhouse gas effect does not exist. NO one seems to bother to even read it let alone try to duplicate the experiment. Shortly I will be providing my Hypotheses of why Venus is so hot and it has nothing to do with the “greenhouse gas effect” ,which NASA proved 40 years ago did not exist.

    The work of Dr. Roy Spencer providing data that the amount of heat lost to space from IR radiation shows that the “Science is not settled”. Many other factors need to be studied but we must start with “Where is the “creditable experiment that proves that the “greenhouse gas effect “exists.

    One major factor that seem to have been forgotten is the work of Robert W. Wood,1909, Dr. Niels Bohr and his Nobel Prize 1922 and the confirmation of R.W. Wood by Dr. N. Nahle July , 2011. Any “greenhouse gas effect” work on IR absorption done before 1922 is probable wrong. So Svante Arrhenius is wrong and Anders Ångström is more correct.

    Any discussion about “absorption of radiation” that ignores the Bohr model is missing the facts.

  36. @51, lweinstein, I can’t tell if you are disagreeing with something I said or not. Can you quote me if in fact you are disagreeing?

  37. @52 Berthold Klein, I am interested in reading G3, but the webpage I get doesn’t have a place to submit a comment.

    I started reading and noticed this:

    As the atmosphere is receiving constantly changing amounts of energy from the sun in the form of UV, visible light IR, gamma, electromagnetic radiation, there is no such thing as LTE.
    Assumed definition of LTE = light transmission equilibrium

    I get the feeling that you are interpreting LTE wrongly.

    Local Thermodynamic Equilibrium appears to be the common definition and is how it was defined in this article.

    I’ll read that page if I can comment over there.

  38. @54 Josex, Thanks for pointing out the missing comment area in G3. It was a webmaster error and it is now fixed. – Ed

  39. Josex : Thank you for the correction on what LTE stands for. My point with various input energy from the Sun is still valid. This variation has far more to do with weather conditions on earth and every other planets in the solar system thus I would question any statement implying that there is” Local Thermodynamic Equilibrium ” Ask anyone about the weather where they are, the usual answer is “What 10 minutes and it will change” There many be a few exceptions like the middle of Death Valley or the heart of the Amazon but generally weather/ thermodynamic conditions are changing .
    Shortly I’ll be ready to post my Hypotheses of why Venus is so hot. AS most AGW use Hot Venus as an example of the “Greenhouse gas effect” we need to shed some real light (based on physics) on the subject.

  40. @lweinstein

    >> You appear to not have read the write-ups on adiabatic lapse rate

    Can you provide a link to what you mean specifically?

    >> The causes of decrease are: 1) The Cp of CO2 is much larger than for air, and 2) the thickness of the atmosphere would actually decrease.

    First, the Cp of CO2 (using wikipedia) appears to be comparable to that of air (they aren’t even a factor of 2 different, much less 1 or more orders of magnitude).

    Second, the lapse rate is not a measure of temperature but of temperature decrease. If you start from a higher (perhaps much higher) temperature, it would be reasonable that you would decrease faster, but decreasing a little faster from say 1000 “degrees” than from 100 “degrees” doesn’t imply 100 is higher than 1000. I don’t see how you addressed the actual temperature to be expected by appealing to lapse rate.

    Third, what do you mean by “thickness” and what does that have to do with temperature and absorption of photons?

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