Foreword – I’ve had this document since January 17th, and it has taken some time to get it properly reproduced here in full due to formatting issues. Some equations have to be converted to images, and I have to double check every superscript, subscript, and symbol for accuracy, then re-insert/re-format many manually since they often don’t reproduce properly in WordPress. WordPress doesn’t manage copy/paste of complex documents well. I hope that I have everything correctly reproduced, if not, please leave a note. A PDF of the original is here: UTC_Blog_Reply_Part1 This is a contentious issue, and while it would be a wonderful revelation if it were proven to be true, I personally cannot see any way it can surmount the law of conservation of energy. That view is shared by others, noted in the opening paragraph below. However, I’m providing this for the educational value it may bring to those who can take it all in and discuss it rationally, with a caution – because this issue is so contentious, I ask readers to self-moderate so that the WUWT moderation team does not have to be heavy handed. I invite you take it all in, and to come to your own conclusion. Thank you for your consideration. – Anthony
Part 1: Magnitude of the Natural ‘Greenhouse’ Effect
Ned Nikolov, Ph.D. and Karl Zeller, Ph.D.
- Introduction
Our recent paper “Unified Theory of Climate: Expanding the Concept of Atmospheric Greenhouse Effect Using Thermodynamic Principles. Implications for Predicting Future Climate Change” spurred intense discussions at WUWT and Tallbloke’s Talkshop websites. Many important questions were raised by bloggers and two online articles by Dr. Ira Glickstein (here) and Dr. Roy Spencer (here). After reading through most responses, it became clear to us that that an expanded explanation is needed. We present our reply in two separate articles that address blog debate foci as well as key aspects of the new paradigm.
Please, consider that understanding this new theory requires a shift in perception! As Albert Einstein once noted, a new paradigm cannot be grasped within the context of an existing mindset; hence, we are constrained by the episteme we are living in. In that light, our concept requires new definitions that may or may not have exact counterparts in the current Greenhouse theory. For example, it is crucial for us to introduce and use the term Atmospheric Thermal Effect (ATE) because: (a) The term Greenhouse Effect (GE) is inherently misleading due to the fact that the free atmosphere, imposing no restriction on convective cooling, does not really work as a closed greenhouse; (b) ATE accurately coveys the physical essence of the phenomenon, which is the temperature boost at the surface due to the presence of atmosphere; (c) Reasoning in terms of ATE vs. GE helps broaden the discussion beyond radiative transfer; and (d) Unlike GE, the term Atmospheric Thermal Effect implies no underlying physical mechanism(s).
We start with the undisputable fact that the atmosphere provides extra warmth to the surface of Earth compared to an airless environment such as on the Moon. This prompts two basic questions: (1) What is the magnitude of this extra warmth, i.e. the size of ATE ? and (2) How does the atmosphere produce it, i.e. what is the physical mechanism of ATE ? In this reply we address the first question, since it appears to be the crux of most people’s difficulty and needs a resolution before proceeding with the rest of the theory (see, for example, Lord Monckton’s WUWT post).
- Magnitude of Earth’s Atmospheric Thermal Effect
We maintain that in order to properly evaluate ATE one must compare Earth’s average near-surface temperature to the temperature of a spherical celestial body with no atmosphere at the same distance from the Sun. Note that, we are not presently concerned with the composition or infrared opacity of the atmosphere. Instead, we are simply trying to quantify the overall effect of our atmosphere on the surface thermal environment; hence the comparison with a similarly illuminated airless planet. We will hereafter refer to such planet as an equivalent Planetary Gray Body (PGB).
Since temperature is proportional (linearly related) to the internal kinetic energy of a system, it is theoretically perfectly justifiable to use meanglobal surface temperatures to quantify the ATE. There are two possible indices one could employ for this:
- The absolute difference between Earth’s mean temperature (Ts) and that of an equivalent PGB (Tgb), i.e. ATE = Ts – Tgb; or
- The ratio of Ts to Tgb. The latter index is particularly attractive, since it normalizes (standardizes) ATE with respect to the top-of-atmosphere (TOA) solar irradiance (So), thus enabling a comparison of ATEs among planets that orbit at various distances from the Sun and receive different amounts of solar radiation. We call this non-dimensional temperature ratio a Near-surface Thermal Enhancement (ATEn) and denote it by NTE = Ts / Tgb. In theory, therefore, NTE should be equal or greater than 1.0 (NTE ≥ 1.0). Please, note that ATEn is a measure of ATE.
It is important to point out that the current GE theory measures ATE not by temperature, but by the amount of absorbed infrared (IR) radiation. Although textbooks often mention that Earth’s surface is 18K-33K warmer than the Moon thanks to the ‘greenhouse effect’ of our atmosphere, in the scientific literature, the actual effect is measured via the amount of outgoing infrared radiation absorbed by the atmosphere (e.g. Stephens et al. 1993; Inamdar & Ramanathan 1997; Ramanathan & Inamdar 2006; Houghton 2009). It is usually calculated as a difference (occasionally a ratio) between the total average infrared flux emanating at the surface and that at the top of the atmosphere. Defined in this way, the average atmospheric GE, according to satellite observations, is between 157 and 161 W m-2 (Ramanathan & Inamdar 2006; Lin et al. 2008; Trenberth et al. 2009). In other words, the current theory uses radiative flux units instead of temperature units to quantify ATE. This approach is based on the preconceived notion that GE works by reducing the rate of surface infrared cooling to space. However, measuring a phenomenon with its presumed cause instead by its manifest effect can be a source of major confusion and error as demonstrated in our study. Hence, we claim that the proper assessment of ATE depends on an accurate estimate of the mean surface temperature of an equivalent PGB (Tgb).
- Estimating the Mean Temperature of an Equivalent Planetary Gray Body
There are two approaches to estimate Tgb – a theoretical one based on known physical relationships between temperature and radiation, and an empirical one relying on observations of the Moon as the closest natural gray body to Earth.
According to the Stefan-Boltzmann (SB) law, any physical object with a temperature (T, oK) above the absolute zero emits radiation with an intensity (I, W m-2) that is proportional to the 4th power of the object’s absolute temperature:
where ϵ is the object’s thermal emissivity/absorptivity (0 ≤ ϵ ≤ 1 ), and σ = 5.6704×10-8 W m-2 K-4 is the SB constant. A theoretical blackbody has ϵ = 1.0, while real solid objects such as rocks usually have ϵ ≈ 0.95. In principle, Eq. (1) allows for an accurate calculation of an object’s equilibrium temperature given the amount of absorbed radiation by the object, i.e.
The spatially averaged amount of solar radiation absorbed by the Earth-Atmosphere system (Sα ̅̅̅, W m-2) can be accurately computed from TOA solar irradiance (Sα ̅̅̅, W m-2) and planetary albedo (αp) as
where the TOA shortwave flux (W m-2) incident on a plane perpendicular to the solar rays. The factor ¼ serves to distribute the solar flux incident on a flat surface to a sphere. It arises from the fact that the surface area of a sphere (4πR2) is 4 times larger than the surface area of a disk (πR2) of the same radius (R). Hence, it appears logical that one could estimate Earth’s average temperature in the absence of ATE from using the SB law. i.e.
Here (TeK) is known as the effective emission temperature of Earth. Employing typical values for S0 =W m-2 and αp = 0.3 and assuming, ϵ = 1.0 Eq. (3) yields 254.6K. This is the basis for the widely quoted 255K (-18C) mean surface temperature of Earth in the absence of a ‘greenhouse effect’, i.e. if the atmosphere were missing or ‘completely transparent’ to IR radiation. This temperature is also used to define the so-called effective emission height in the troposphere (at about 5 km altitude), where the bulk of Earth’s outgoing long-wave radiation to space is assumed to emanate from. Since Earth’s mean surface temperature is 287.6K (+14.4C), the present theory estimates the size of ATE to be 287.6K – 254.6K = 33K. However, as pointed out by other studies, this approach suffers from a serious logical error. Removing the atmosphere (or even just the water vapor in it) would result in a much lower planetary albedo, since clouds are responsible for most of Earth’s shortwave reflectance. Hence, one must use a different albedo (αp) in Eq. (3) that only quantifies the actual surface reflectance. A recent analysis of Earth’s global energy budget by Trenberth et al. (2009) using satellite observations suggests αp≈ 0.12. Serendipitously, this value is quite similar to the Moon bond albedo of 0.11 (see Table 1 in our original paper), thus allowing evaluation of Earth’s ATE using our natural satellite as a suitable PGB proxy. Inserting= 0.12 in Eq. (3) produces Te = 269.6K, which translates into an ATE of only 18K (i.e. 287.6 – 269.6 = 18K).
In summary, the current GE theory employs a simple form of the SB law to estimate the magnitude of Earth’s ATE between 18K and 33K. The theory further asserts that the Moon average temperature is 250K to 255K despite the fact that using the correct lunar albedo (0.11) in Eq. (3) produces ≈270K, i.e. a15K to 20K higher temperature! Furthermore, the application of Eq. (3) to calculate the mean temperature of a sphere runs into a fundamental mathematical problem caused by Hölder’s inequality between non-linear integrals (e.g. Kuptsov 2001). What does this mean? Hölder’s inequality applies to certain non-linear functions and states that, in such functions, the use of an arithmetic average for the independent (input) variable will not produce a correct mean value of the dependent (output) variable. Hence, due to a non-linear relationship between temperature and radiative flux in the SB law (Eq. 3) and the variation of absorbed radiation with latitude on a spherical surface, one cannot correctly calculate the mean temperature of a unidirectionally illuminated planet from the amount of spatially averaged absorbed radiation defined by Eq. (2). According to Hölder’s inequality, the temperature calculated from Eq. (3) will always be significantly higher than the actual mean temperature of an airless planet. We can illustrate this effect with a simple example.
Let’s consider two points on the surface of a PGB, P1 and P2, located at the exact same latitude (say 45oN) but at opposite longitudes so that, when P1 is fully illuminated, P2 is completely shaded and vice versa (see Fig. 1). If the PGB is orbiting at the same distance from the Sun as Earth and solar rays were the only source of heat to it, then the equilibrium temperature at the illuminated point would be (assuming a solar zenith angle θ = 45o), while the temperature at the shaded point would be T2 = 0 (since it receives no radiation due to cosθ < 0). The mean temperature between the two points is then Tm = (T1 + T2)/2 = 174.8K. However, if we try using the average radiation absorbed by the two points W m-2 to calculate a mean temperature, we obtain = 234.2K. Clearly, Te is much greater than Tm (Te ≫ Tm), which is a result of Hölder’s inequality.
Figure 1. Illustration of the effect of Hölder’s inequality on calculating the mean surface temperature of an airless planet. See text for details.
The take-home lesson from the above example is that calculating the actual mean temperature of an airless planet requires explicit integration of the SB law over the planet surface. This implies first taking the 4th root of the absorbed radiative flux at each point on the surface and then averaging the resulting temperature field rather than trying to calculate a mean temperature from a spatially averaged flux as done in Eq. (3).
Thus, we need a new model that is capable of predicting Tgb more robustly than Eq. (3). To derive it, we adopt the following reasoning. The equilibrium temperature at any point on the surface of an airless planet is determined by the incident solar flux, and can be approximated (assuming uniform albedo and ignoring the small heat contributions from tidal forces and interior radioactive decay) as
where is the solar zenith angle (radian) at point , which is the angle between solar rays and the axis normal to the surface at that point (see Fig. 1). Upon substituting , the planet’s mean temperature () is thus given by the spherical integral of , i.e.
Comparing the final form of Eq. (5) with Eq. (3) shows that Tgb << Te in accordance with Hölder’s inequality. To make the above expression physically more realistic, we add a small constant Cs =0.0001325 W m-2 to So, so that when So = 0.0, Eq. (5) yields Tgb = 2.72K (the irreducible temperature of Deep Space), i.e:
In a recent analytical study, Smith (2008) argued that Eq. (5) only describes the mean temperature of a non-rotating planet and that, if axial rotation and thermal capacity of the surface are explicitly accounted for, the average temperature of an airless planet would approach the effective emission temperature. It is beyond the scope of the current article to mathematically prove the fallacy of this argument. However, we will point out that increasing the mean equilibrium temperature of a physical body always requires a net input of extra energy. Adding axial rotation to a stationary planet residing in a vacuum, where there is no friction with the external environment does not provide any additional heat energy to the planet surface. Faster rotation and/or higher thermal inertia of the ground would only facilitate a more efficient spatial distribution of the absorbed solar energy, thus increasing the uniformity of the resulting temperature field across the planet surface, but could not affect the average surface temperature. Hence, Eq. (6) correctly describe (within the assumption of albedo uniformity) the global mean temperature of any airless planet, be it rotating or non-rotating.
Inserting typical values for Earth and Moon into Eq. (6), i.e. So = 1,362 W m-2, αo = 0.11, and ϵ = 0.955, produces Tgb = 154.7K. This estimate is about 100K lower than the conventional black-body temperature derived from Eq. (3) implying that Earth’s ATE (i.e. the GE) is several times larger than currently believed! Such a result, although mathematically justified, requires independent empirical verification due to its profound implications for the current GE theory. As noted earlier, the Moon constitutes an ideal proxy PGB in terms of its location, albedo, and airless environment, against which the thermal effect of Earth’s atmosphere could be accurately assessed. Hence, we now turn our attention to the latest temperature observations of the Moon.
- NASA’s Diviner Lunar Radiometer Experiment
In June 2009, NASA launched its Lunar Reconnaissance Orbiter (LRO), which carries (among other instruments) a Radiometer called Diviner. The purpose of Diviner is to map the temperature of the Moon surface in unprecedented detail employing measurements in 7 IR channels that span wavelengths from 7.6 to 400 μm. Diviner is the first instrument designed to measure the full range of lunar surface temperatures, from the hottest to the coldest. It also includes two solar channels that measure the intensity of reflected solar radiation enabling a mapping of the lunar shortwave albedo as well (for details, see the Diviner Official Website at http://www.diviner.ucla.edu/).
Although the Diviner Experiment is still in progress, most thermal mapping of the Moon surface has been completed and data are available online. Due to time constraints of this article, we did not have a chance to analyze Diviner’s temperature data ourselves. Instead, we elected to rely on information reported by the Diviner Science Team in peer-reviewed publications and at the Diviner website.
Data obtained during the LRO commissioning phase reveal that the Moon has one of the most extreme thermal environments in the solar system. Surface temperatures at low latitudes soar to 390K (+117C) around noon while plummeting to 90-95K (-181C), i.e. almost to the boiling point of liquid oxygen, during the long lunar night (Fig. 2). Remotely sensed temperatures in the equatorial region agree very well with direct measurement conducted on the lunar surface at 26.1o N by the Apollo 15 mission in early 1970s (see Huang 2008). In the polar regions, within permanently shadowed areas of large impact craters, Diviner has measured some of the coldest temperatures ever observed on a celestial body, i.e. down to 25K-35K (-238C to -248C). It is important to note that planetary scientists have developed detailed process-based models of the surface temperatures of Moon and Mercury some 13 years ago (e.g. Vasavada et al. 1999). These models are now being successfully validated against Diviner measurements (Paige et al. 2010b; Dr. M. Siegler at UCLA, personal communication).
What is most interesting to our discussion, however, are the mean temperatures at various lunar latitudes, for these could be compared to temperatures in similar regions on Earth to evaluate the size of ATE and to verify our calculations. Figure 3 depicts typical diurnal courses of surface temperature on the Moon at four latitudes (adopted from Paige et. al 2010a).
Figure 2. Thermal maps of the Moon surface based on NASA’s Diviner infrared measurements showing daytime maximum and nighttime minimum temperature fields (Source: Diviner Web Site).
Figure 3. Typical diurnal variations of the Moon surface temperature at various latitudes. Local time is expressed in lunar hours which correspond to 1/24 of a lunar month. At 89◦ latitude, diurnal temperature variations are shown at summer and winter solstices (adopted from Paige et al. 2010a). Dashed lines indicate annual means at the lunar equator and at the poles.
Figure 4. Temperature maps of the South Pole of the Moon and Earth: (A) Daytime temperature field at peak illumination on the Moon; (B) Nighttime temperature field on the Moon; (C) Mean summer temperatures over Antarctica; (D) Mean winter temperatures over Antarctica. Numbers shown in bold on panels (C) and (D) are temperatures in oK. Panels (A) and (B) are produced by the Diviner Lunar Radiometer Experiment (Paige et al. 2010b). Antarctica maps are from Wikipedia (http://en.wikipedia.org/wiki/Antarctic_climate). Comparison of surface temperatures between Moon’s South Pole and Antarctica suggests a thermal enhancement by the Earth atmosphere (i.e. a ‘Greenhouse Effect’) of about 107K in the summer and 178K in the winter for this part of the Globe.
Figures 4A & 4B display temperature maps of the Moon South Pole during daytime peak illumination and at night (Paige et. al 2010b). Since the Moon has a small obliquity (axial tilt) of only 1.54o and a slow rotation, the average diurnal temperatures are similar to seasonal temperature means. These data along with information posted at the Diviner Science webpage indicate that mean temperature at the lunar-surface ranges from 98K (-175C) at the poles to 206K (-67C) at the equator. This encompasses pretty well our theoretical estimate of 154.7K for the Moon mean global temperature produced by Eq. (6). In the coming months, we will attempt to calculate more precisely Moon’s actual mean temperature from Diviner measurements. Meanwhile, data published by NASA planetary scientists clearly show that the value 250K-255K adopted by the current GE theory as Moon’s average global temperature is grossly exaggerated, since such high temperature means do not occur at any lunar latitude! Even the Moon equator is 44K – 49K cooler than that estimate. This value is inaccurate, because it is the result of an improper application of the SB law to a sphere while assuming the wrong albedo (see discussion in Section 2.1 above)!
Similarly, the mean global temperatures of Mercury (440K) and Mars (210K) reported on the NASA Planetary Fact Sheet are also incorrect, since they have been calculated from the same Eq. (3) used to produce the 255K temperature for the Moon. We urge the reader to verify this claim by applying Eq. (3) with data for solar irradiance (So) and bond albedo (αo) listed on the fact sheet of each planet while setting ϵ = 1. This is the reason that, in our original paper, we used 248.2K for Mercury, since that temperature was obtained from the theoretically correct Eq. (6). For Mars, we adopted means calculated from regional data of near-surface temperature and pressure retrieved by the Radio Science Team at Stanford University employing remote observations by the Mars Global Surveyor spacecraft. It is odd to say the least that the author of NASA’s Planetary Fact Sheets, Dr. David R. Williams, has chosen Eq. (3) to calculate Mars’ average surface temperature while ignoring the large body of high-quality direct measurements available for the Red Planet!?
So, what is the real magnitude of Earth’s Atmospheric Thermal Effect?
Table 1. Estimated Atmospheric Thermal Effect for equator and the poles based on observed surface temperatures on Earth and the Moon and using the lunar surface as a proxy for Earth’s theoretical gray body. Data obtained from Diviner’s Science webpage, Paige at al. (2010b), Figure 4, and Wikipedia:Oymyakon.
Figure 5. Earth’s mean annual near-surface temperature according to Wikipedia (Geographic Zones: http://en.wikipedia.org/wiki/Geographical_zone).
Table 1 shows observed mean and record-low surface temperatures at similar latitudes on Earth and on the Moon. The ATE is calculated as a difference between Earth and Moon temperatures assuming that the Moon represents a perfect PGB proxy for Earth. Figure 5 displays a global map of Earth’s mean annual surface temperatures to help the reader visually verify some of the values listed in Table 1. The results of the comparison can be summarized as follows:
The Atmospheric Thermal Effect, presently known as the natural Greenhouse Effect, varies from 93K at the equator to about 150K at the poles (the latter number represents an average between North- and South- Pole ATE mean values, i.e. (158+143)/2 =150.5. This range encompasses quite well our theoretical estimate of 133K for the Earth’s overall ATE derived from Eq. (6), i.e. 287.6K – 154.7K = 132.9K.
Of course, further analysis of the Diviner data is needed to derive a more precise estimate of Moon’s mean surface temperature and verify our model prediction. However, given the published Moon measurements, it is clear that the widely quoted value of 33K for Earth’s mean ATE (GE) is profoundly misleading and wrong!
- Conclusion
We have shown that the SB Law relating radiation intensity to temperature (Eq. 1 & 3) has been incorrectly applied in the past to predict mean surface temperatures of celestial bodies including Mars, Mercury, and the Moon. Due to Hölder’s inequality between non-linear integrals, the effective emission temperature computed from Eq. (3) is always significantly higher than the actual (arithmetic) mean temperature of an airless planet. This makes the planetary emission temperature Te produced by Eq. (3) physically incompatible with any real measured temperatures on Earth’s surface or in the atmosphere. By using a proper integration of the SB Law over a sphere, we derived a new formula (Eq. 6) for estimating the average temperature of a planetary gray body (subject to some assumptions). We then compared the Moon mean temperature predicted by this formula to recent thermal observations and detailed energy budget calculation of the lunar surface conducted by the NASA Diviner Radiometer Experiment. Results indicate that Moon’s average temperature is likely very close to the estimate produced by our Eq. (6). At the same time, Moon measurements also show that the current estimate of 255K for the lunar average surface temperature widely used in climate science is unrealistically high; hence, further demonstrating the inadequacy of Eq. (3). The main result from the Earth-Moon comparison (assuming the Moon is a perfect gray-body proxy of Earth) is that the Earth’s ATE, also known as natural Greenhouse Effect, is 3 to 7 times larger than currently assumed. In other words, the current GE theory underestimates the extra atmospheric warmth by about 100K! In terms of relative thermal enhancement, the ATE translates into NTE = 287.6/154.7 = 1.86.
This finding invites the question: How could such a huge (> 80%) thermal enhancement be the result of a handful of IR-absorbing gases that collectively amount to less than 0.5% of total atmospheric mass? We recall from our earlier discussion that, according to observations, the atmosphere only absorbs 157 – 161 W m-2 long-wave radiation from the surface. Can this small flux increase the temperature of the lower troposphere by more than 100K compared to an airless environment? The answer obviously is that the observed temperature boost near the surface cannot be possibly due to that atmospheric IR absorption! Hence, the evidence suggests that the lower troposphere contains much more kinetic energy than radiative transfer alone can account for! The thermodynamics of the atmosphere is governed by the Gas Law, which states that the internal kinetic energy and temperature of a gas mixture is also a function of pressure (among other things, of course). In the case of an isobaric process, where pressure is constant and independent of temperature such as the one operating at the Earth surface, it is the physical force of atmospheric pressure that can only fully explain the observed near-surface thermal enhancement (NTE). But that is the topic of our next paper… Stay tuned!
- References
Inamdar, A.K. and V. Ramanathan (1997) On monitoring the atmospheric greenhouse effect from space. Tellus 49B, 216-230.
Houghton, J.T. (2009). Global Warming: The Complete Briefing (4th Edition). Cambridge University Press, 456 pp.
Huang, S. (2008). Surface temperatures at the nearside of the Moon as a record of the radiation budget of Earth’s climate system. Advances in Space Research 41:1853–1860 (http://www.geo.lsa.umich.edu/~shaopeng/Huang07ASR.pdf)
Kuptsov, L. P. (2001) Hölder inequality. In: Encyclopedia of Mathematics, Hazewinkel and Michiel, Springer, ISBN 978-1556080104.
Lin, B., P. W. Stackhouse Jr., P. Minnis, B. A. Wielicki, Y. Hu, W. Sun, Tai-Fang Fan, and L. M. Hinkelman (2008). Assessment of global annual atmospheric energy balance from satellite observations. J. Geoph. Res. Vol. 113, p. D16114.
Paige, D.A., Foote, M.C., Greenhagen, B.T., Schofield, J.T., Calcutt, S., Vasavada, A.R., Preston, D.J., Taylor, F.W., Allen, C.C., Snook, K.J., Jakosky, B.M., Murray, B.C., Soderblom, L.A., Jau, B., Loring, S., Bulharowski J., Bowles, N.E., Thomas, I.R., Sullivan, M.T., Avis, C., De Jong, E.M., Hartford, W., McCleese, D.J. (2010a). The Lunar Reconnaissance Orbiter Diviner Lunar Radiometer Experiment. Space Science Reviews, Vol 150, Num 1-4, p125-16 (http://www.diviner.ucla.edu/docs/fulltext.pdf)
Paige, D.A., Siegler, M.A., Zhang, J.A., Hayne, P.O., Foote, E.J., Bennett, K.A., Vasavada, A.R., Greenhagen, B.T, Schofield, J.T., McCleese, D.J., Foote, M.C., De Jong, E.M., Bills, B.G., Hartford, W., Murray, B.C., Allen, C.C., Snook, K.J., Soderblom, L.A., Calcutt, S., Taylor, F.W., Bowles, N.E., Bandfield, J.L., Elphic, R.C., Ghent, R.R., Glotch, T.D., Wyatt, M.B., Lucey, P.G. (2010b). Diviner Lunar Radiometer Observations of Cold Traps in the Moon’s South Polar Region. Science, Vol 330, p479-482. (http://www.diviner.ucla.edu/docs/paige_2010.pdf)
Ramanathan, V. and A. Inamdar (2006). The Radiative Forcing due to Clouds and Water Vapor. In: Frontiers of Climate Modeling, J. T. Kiehl and V. Ramanthan, Editors, (Cambridge University Press 2006), pp. 119-151.
Smith, A. 2008. Proof of the atmospheric greenhouse effect. Atmos. Oceanic Phys. arXiv:0802.4324v1 [physics.ao-ph] (http://arxiv.org/PS_cache/arxiv/pdf/0802/0802.4324v1.pdf ).
Stephens, G.L., A. Slingo, and M. Webb (1993) On measuring the greenhouse effect of Earth. NATO ASI Series, Vol. 19, 395-417.
Trenberth, K.E., J.T. Fasullo, and J. Kiehl (2009). Earth’s global energy budget. BAMS, March:311-323
Vasavada, A. R., D. A. Paige and S. E. Wood (1999). Near-surface temperatures on Mercury and the Moon and the stability of polar ice deposits. Icarus 141:179–193 (http://www.gps.caltech.edu/classes/ge151/references/vasavada_et_al_1999.pdf)
Ned Nikolov says: January 24, 2012 at 9:24 am
“No one argues that the atmosphere emits a substantial flux of IR radiation towards the surface. The question is – does this flux on average cause any increase (warming) of the surface temperature? There answer is NO, because this flux gets neutralized (cancelled out) completely by the convective cooling at the surface. This can be easily proven using an energy balance model that couples convection and radiative transfer and solves simultaneously for both.”
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Care to explain this?
Why should convective cooling increase without the surface temperature increasing first?
Makes no sense to me!
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“Also, how do you explain this fact? Globally, the atmosphere emits on average 343 W m-2 of LW radiation towards the surface, while the total radiation absorbed from the Sun by the ENTIRE Earth-atmosphere system is only 238.3 W m-2, i.e. the atmosphere emits down 44% more radiation than the total amount provided by the Sun!! These are real measurements! Does this not tell us that there is MORE energy in the lower atmosphere that the Sun can account for? It does! And it raises the question where is that extra energy coming from? ”
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I quoted referen ces to real measurements. The downward LW IR is coming from somethin. The only thing radiating at these wavelengths at night is GHGs.
Note that the solar TSI is greater than these DLR levels (but in a different part of the spectrum. These geat the ground/water and then these radiate at a lower “temperature” some of which gets re-radiated back down (hence the difference between day and night.
So, sorry but your explanatuion seems totally wrong to me.
“”””” JJThoms says:
January 24, 2012 at 5:01 am
George E. Smith; says: January 23, 2012 at 10:18 pm
please look at my referenced documents about measuring LWE IR upwards.
In both documents the night time downward LW IR is about 75% of the daytime IR.
There is no sun at night! Where is this IR coming from? “””””
“”””” George E. Smith; says:
January 23, 2012 at 10:18 pm
“”””” Ralph says:
January 23, 2012 at 9:45 pm
<<>>>>
Nonsense.
A cloud layer can move in from a totally different weather system hundrds of miles away, and the effect will be the same. Whether the night air is still convective (rare), or whether the airmass is completely stable (more usual), a cloud layer will ALWAYS result in higher nighttime temperatures – because the cloud is ‘insulating’ the LW radiation from the surface.
And I have been watching the weather for 30 years. “””””
So I could have a cloudless day with surface Temperatures of say 40 deg F, and typical wintertinme low humidity, and after sundown a cloud layer at 20,000 feet comes in on some jet stream, and my surface Temperature will go up above 40 deg F ??
So the cloud might be -50 deg C, so just where does the energy come from to raise the surface Temperature; it’s after sundown, so it isn’t solar, and my cold air was going all the way up along with the lapse rate to where that 20,000 ft cloud came in, and my surface is getting even colder, as it radiates its 400 Watts per m^2 or more.
I will grant you that a massive storm of air might sweep in from some hot place with clouds, and simply replace all the cold air I had during the day, and presumably I will be warmer; but it wasn’t radiation trapping from my surface that warmed me up; and notwithstanding that storm cloud, it will still cool down as the night progresses; it won’t continue to get hotter, unless even hotter air contines to come in from somewhere else.
If you need to invoke a Santa Ana to make your case; then I submit, that you have no case; and i’ve been working at this for more than twice as long as you’ve been watching the weather. “””””
So II, I just reposted the entire post that I placed here on Jan 23 2012, at 10:18 pm
So please tell us the line numbers where you found this:
“”””” “”””” JJThoms says:
January 24, 2012 at 5:01 am
George E. Smith; says: January 23, 2012 at 10:18 pm
please look at my referenced documents about measuring LWE IR upwards.
In both documents the night time downward LW IR is about 75% of the daytime IR.
There is no sun at night! Where is this IR coming from? “””””
I submit that on Jan 23 2012, at 10:18 pm, I made no such statement.
Joel Shore @ur momisugly January 24, 2:03 pm
YAWN!
Very quickly, I will simply repeat what I wrote before but with bold emphasis added to some key words, (although it is tempting to put it all in bold), in the hope of you achieving English language comprehension:
BTW, my native tongue is SE England born, but corrupted by Oz lingo since 1969. During the 1980’s I worked in the USA maybe 30% of the time and additionally worked with Americans in Oz and Italy. Whilst I and colleagues were sometimes confused by Americano lingo, we usually managed to translate it OK. (probably). With that experience, and more, I doubt that my expose above has any ambiguity to you, if you try really hard to understand it. But then you have difficulty emerging from the covers of your apparently favorite book by Raymond Pierrehumbert, despite that he is by popular definition* not a gentleman.
* DEFINITION; Gentleman: A man who can play the accordion but doesn’t
“”””” Ralph says:
January 23, 2012 at 11:10 pm
>>>George Smith
>>>So I could have a cloudless day with surface Temperatures
>>>of say 40 deg F, and typical wintertinme low humidity, and after
>>>sundown a cloud layer at 20,000 feet comes in on some jet stream,
>>>and my surface Temperature will go up above 40 deg F ??
Who says the temperature goes up? You are distintly bad at reading, George, try again. I NEVER SAID THE TEMPERATURE GOES UP, is that clear enough for you??
Clouds reduce cooling, because of the Greenhouse Effect. Note the term here, George, REDUCE COOLING. This results in a warmer temperature than a night without clouds. Do you understand that this is not warming, George, it is reduced cooling. Warmer than without clouds, but still a net cooling effect (but slightly reduced).
Clear?? “””””
Yes Ralph it is perfectly clear; and you might want to critique your own reading prowess before criticising mine.
Yes I totally agree with you: THE TEMPERATURE DOES NOT GO UP AT NIGHT; EITHER WITH CLOUDS OR WITHOUT CLOUDS.
Ergo, and I do so hope we can agree on this; the previous day, THE TEMPERATURE MUST HAVE BEEN HIGHER, during the day THAN IT WAS THE FOLLOWING NIGHT.
And if on the cloudy night it was a higher Temperature, than on the cloudless night, THE DAY TIME TEMPERATURE BEFORE THE CLOUDY NIGHT WAS HIGHER THAN THE DAYTIME TEMPERATURE ON THE CLOUDLESS NIGHT.
Besides Ralph, what is in contention is the CLIMATE CONSEQUENCE of clouds; NOT last night’s weather.
So the question is quite simple.
If the long term average mean global cloud cover (whatever that means) is say 61%, as some NOAA/NASA source has been quoted as suggesting; and then that number increases to 62% for a period of time of relevence to climate; such as 30 years for example. Will the mean ghlobal Temperature rise as a result of the increased cloud cover or will it decrease, due to a net reduction of total solar energy that gets stored in the earth system; mostly the oceans.
I fully agree the clouds DO NOT make the night time Temperature go up. The higher DAYTIME temperature was the cause of the clouds (along with some moisture), not a consequence of the clouds, and the higher the daytime temperature is, the higher will be the altitude of the subsequent clouds, other conditions being equal.
The problem of a diffuse emitting surface irradiating a second distant receiving surface, is a very well researched problem in the electronics industry. We might call it the “Opto-coupler” problem.
Well some people will call it the “Opto-isolator” problem. It’s a very common signal transmission device for transmitting electronic signals over an electrically isolated path.
Typically,an LED emitting some red or near IR radiation, illuminates a silicon detecting chip, separated by some light conducting insulator that might be required to withstand 25,000 Volts electrical isolation; or a million for that matter. Modulating the current of the LED creates an anlog signal that is propagated over the isolated path. Modern ones actually transmit digital signals rather than analog, so that high signal fidelity can be achieved.
As early as 1960, Tektonix Inc built a complete Oscilloscope plug in vertical amplifier, that was isolated from ground for many kV, and the amplified signals were passed on to the mainframe via optocouplers.They even powered the isolated circuits using an ordinary incandescent lamp in the plug in, and solar cells on the isolated component.
For such products it was of course desirable to have the highest signal coupling efficiency commensurate with the required isolation Voltage capability. These devices were produced in the multimillions in the 1970s. Hewlett Packard was one manufacturer of a line of these products. As it happens, I worked for a competitive company making similar products. The various manufacturers collaborated on some industry standards for these products, so we did get together to discuss mutually interesting questions.
A very competent engineer at HP, and I set out to calculate the theoretical optical signal coupling for a general geometry for such devices. I won’t name him, because he is no longer with us, and we were good friends. The problem involves a quadruple integral over two areas, sending and receiving, and two solid angles. It so happens that I selected a poor choice of order to do the four integrals, and generated a real birdsnest of mathematics, that I never did solve. The HP chap, lucked out and made a better choice of order, and he succeeded in getting an accurate closed form solution for the signal coupling for a fairly generic system design.
He sent me the solution, and when I looked at it, I realized that the equation was not a good equation to use for calculation; especially in a computer program, because the equation contained a small difference of two large numbers, so large errors could arise, when part of a transparent design process, with nobody watching the details. I worked on it, and was able to transform the quation into an equivalent form which instead contained the sum of those two large numbers, instead of their difference, so it was computer tractable and would go haywire in some special case. So I sent him the transformed equation, which he ended up writing up in an HP application note. We celebrated later with lunch together.
His equation can be used to calculate the total energy coupling between two parallel coaxial areas at any distance apart, such as an earth surface area and some cloud area, and in the surface cloud case, the reverse transmission problem can also be solved, and then the two combined, for the round trip.
So there is no great mystery to calculating the return signal energy in the surface/cloud/surface round trip problem. Well you don’t have to do eight integrals since the same result works both ways, and since the solution already exists, you just need to use the formula. I’ll let all you hotshot math PhDs do the quadruple integral for yourselves.
Now there is one aspect of this problem that seems to have been overlooked somewhat.
Take away the clouds, and we already have a surface to atmosphere (GHG bearing) to surface round trip, that handles the specific GHG such as CO2 absorption band spectral energies.
The apparent consequence of this (I’ll take their word for it), is that not too much of the GHG band energy makes it up to where higher clouds might be; it’s largely been absorbed by GHGs lower down and returned.
So much of the cloud situation revolves around the rest of the surface thermal LWIR spectrum, that runs afoul of the very broad liquid water absorption in the 5-50 micron region. The interesting thing is that absent the clouds, and much water vapor, the CO2 round trip mechanism is fully operational; yet nobody seems to notice much effect from it. In the high dry deserts sans clouds and much water vapor; CO2 seems to be remarkably inefficient, in keeping the surface warm at night.
So much for the power of CO2.
By the way Ralph, My use of CAPS is not shouting; its one way of my indicating I want to emphasize something. Sometimes I might use (….) instead or “…….” but sometimes that is misconstrued as a quotation; I’ve tried ‘………..’ to demark something without it looking like a quote.
To be sure when I am quoting someone else, I like to use “””””…………””””” which is supposed to be five double (‘)s, but sometimes I over or undershoot. So when you see all those (“””””) you can be fairly sure I am cut and pasting what someone else said. Now I do often erase part of what someone said, that isn’t germane to the point I want to make and I try to always put in a ………. to indicate I slashed. I do try to not alterthe meaning of what someone posted, so if my deletions ever change someone’s intent, by all means call me on it, because that is NOT my intent.
And no, we don’t really need to shout here at WUWT.
George
George E Smith, some questions for you please. Joel Shore has ignored these questions.
Please consider the following assertions to also be questions.
A planet (earth, ocean atmosphere) can only cool by radiating to space.
Non GHG store conductive specific heat, but cannot radiate it to space. (Insulation)
They can however conduct specific heat to radiating GHGs.
Conducted specific heat from a non GHG molecue to another non GHG molecue stays within the atmosphere (increased residence time) longer then if the non GHG molecue conducts that heat to a GHG molecue, where that energy can radiate to space.
Adding more GHGs to an atmosphere accelerates the loss of conducted heat to space, while it slows the loss of radiated heat from the surface. (cooling and warming)
So GHG reduce the TSI reaching the surface, (cooling)
Intercept UWLWR from the surface and return a portion towards the surface, (warming)
Recieve conducted specific heat from non GHGs (which insulate conducted heat ) and allow some of this to zip to space, (cooling)
George could you outline some possible paths of a LWIR photon within the CO2 absorbtion band? How many times can that energy be redirected before leaving to space? How long does this take? Is the residence time of conducted energy in non GHGs far longer then it is with GHGs? How can adding more of the the only gases (GHGs) which can cool (radiate to space) warm the planet?
@Bob Fernley-Jones: Your reply doesn’t address anything I wrote in any way whatsoever. I’ll just assume that you implicitly concede that you are wrong but are too embarrassed to admit it.
Joel Shore,
I’ll just assume that you implicitly concede that you are wrong but are too embarrassed to admit it.
After all, that’s exactly what the planet is saying, too.☺
So here’s an experiment for all of you budding Meteorologist / Climatologist afficionados to perform; it’s very simple from the Meteorology 0.01 textbook.
I first studied this problem while I was raising a New Zealand white rabbit (NZWR) for a 4-H club project (to see if NZWR tastes “just like chicken”). I would probably have done it in 8th grade science; but then we didn’t have “grades” in NZ. I was killing time in between sorting NZWR pellets; separating a pile of pellets into two classes. Fresh virgin pellets, and pellets that had already been once through the rabbit, which don’t taste as good.
So we need to define some variables since the brain dead editor in this box is even less like an IBM 360 typewriter than Micro$oft WORD.
TNn is the Temperature at any time t at Night, where t = 0 represents the time at which the last vestige of the sun upper limb disappears on the horizon, with NO clouds present, at t = 0.
TNc is the night time Temperature at time t when clouds ARE present, at t = 0.
TDn is the daytime Temperature at some time, t = – epsilon, where epsilon can be any positive number, when no clouds are present at t = 0.
TDc is the daytime Temperature for t = – epsilon , when clouds are present at t = 0.
Mn is the gradient of the night time Temperature decay when no clouds are present at t = 0.
Mc is the gradient of the Temperature decay when clouds are present at t = 0.
Both Mn and Mc are positive , and constant for any particular night, since in climatology, trends are ALWAYS straight line, by definition.
The following axioms apply from the meteoroclimatology 0.01 text book.
Axiom # 1 TNc > TNn Cloudy nights are always warmer than cloudless nights.
Axiom #2 Mc 0
TNn = TDn – Mn.t
TNc = TDc – Mc.t
So we have from axiom #1, TDc – Mc.t > TDn – Mn.t
This “miracle” inequality is universally true for 0 <= t TDn Quite Easily Done !
It is ALWAYS warmer on a cloudy night,than on a cloudless night, because it was warmer during the previous day time, and those warmer conditions at night and the clouds themselves are the result of that simple fact; the clouds are NOT the cause of the warmer night, they are the consequence of the warmer day.
And yes as I recall NZWR does taste just like chicken.
This version is correct
“”””” David says:
January 25, 2012 at 1:52 am
George E Smith, some questions for you please. Joel Shore has ignored these questions.
Please consider the following assertions to also be questions. “””””
David, I am NOT a chemist, and my formal chemistry was limited to one Unit, Chem-1 at University, but following five years at high school. I went to a fabulous high school. I haven’t followed too closely your discussion with Joel, but I generally treat his postings quite seriously, and I have never doubted his sincerity.
As for my Physics, that stopped just short of getting heavily into Quantum Mechanics to where I could dash off solutions to Schroedinger’s equation for common problems; but I’ll take a whack at your questions.
First it does seem self evident that EM radiation is the only substantial process for losing energy from earth. What is less certain is where that energy originates (the long wave IR) I presume that it starts at either the solid or liquid surface, so it is somewhat black body like; but I choose to not accept that it is an emission at some uniform isothermal grey body at the 288 K putative global mean surface Temperature. OK that number may actually be the lower troposphere Temperature (izzat two metres above the ground, or over the top of the Weber grill as the case may be?)
Now on any ordinary midsummer northern day, the earth surface Temperature (simultaneously) can be as low as -90 deg C at places like Vostok Station, which will be in winter midnight, or it can be as high as +60 deg C in the tropical deserts. Due to an argument by Galileo, every single Temperature between those Temperature extremes, can be found somewhere on earth, in fact there is an infinite number of such places.
So it is absurd to talk of the earth as a black or even grey body radiator, but any small area can be close to grey; they all have different characteristic Temperatures.
Secondly, I am not a believer of the notion that ONLY GHGs radiate EM radiation. Every assemblage of molecules that can interract thermally with each other (collisions), and every such molecule, can be said to have a Temperature, and it can and will radiate and absorb EM radiation as a consequence of those collisions, which is what Temperature is all about.
Isolated molecules that are in free flight, and don’t collide don’t radiate “Thermal” radiation. Well they also don’t have a Temperature, sans collisions.
The “excited states” of say CO2 that result in the absorption or emission of the 15 micron band of spectral lines have lifetimes, that are generally much longer than the time between collisions at STP conditions, so a molecule that has captured such a photon, seldom gets a chance to spontaneously re-emit such a photon; collisions terminate the condition, which transfers that photon energy to the regular N2, O2, Ar molecules of the atmosphere, as thermal energy.
As Phil has pointed out on several equations, in the higher cooler lower density atmosphere, the longer mean time between collisions is long enough to allow spontaneous re-emission, so the upper atmosphere would then radiate the characteristic 15 micrton CO2 resonance lines. These wavelengths would not be first order Temperature dependent; they are not a consequence of Temperature.
Some people believe that the way a heated atmosphere loses energy by radiation, is for a typical molecule , N2, O2, Ar for example, to collide with say a CO2 molecule, with sufficient energy exchange to set the CO2 ringing (bending) at the 15 micron resonance frequency, and then that molecule subsequently radiates a 15 micron photon, so the only emission from the atmosphere would be that 15 micron radiation. Assuming of course for the moment that CO2 was the only GHG present. Now the CO2 could also emit a 4.0 micron photon, as a result of having its assymmetric stretch mode of oscillation excited by the collision; but that would take a collisions with about 4 times the energy required for a 15 micron event.
Problem with that thesis, is that we already decided that the mean time between collisions is much shorter than the CO2 excited state lifetime, so that spontaneous re-emission is highly unlikely. Now suddenly, it becomes the primary mechanism of atmospheric cooling.
So CO2 is an intelligent molecue;it is capable of distinguishing between a molecular collision, and a surface emitted LWIR 15 micron photon that set it ringing .A surface captured photon is quickly dumped, but energy received from a collision is automatically retained until spontaneous re-emission occurs !!
So try pulling my other leg.
In any case, once an excited CO2 molecule collides with another air molecule, and loses its enhanced energy, it is now reloaded to grab another 15 micron photon from the surface, and repeat the process. That is why the “CO2 is saturated” theory simply doesn’t hold H2O. Continuous cascades of absorption, thermalization, absorption occur, and more CO2 simply means a thinner air layer is needed to absorb a given amount of 15 micron radiation. It is quickly unloaded ready to do the same thing again, and the process repeats for a slightly thicker layer above that one, and so on.
I hope some of that is understandable; it is the wee hours, and I need some sleep.
BenAW says:
January 23, 2012 at 3:51 pm
Hi Lars, seems nobody wants to see this elephant, I called it a 600 pound gorilla on another blog.
Hi Ben. Yes you are right. So I will take the popcorn and watch. Maybe a little post now and then…. I ask myself how long will it take until the oceans will be properly addressed in the effort of defining Earth equilibrium temperature? What are your expectations, do you think a new theory based on the oceans will come before summer 2012, after it or “never” (not in the next 10 years or so). Have you seen anywhere in the web something that would explain sufficiently this part yet?
“””””Something went ape and this got all garbled; let’s try to fix it up.
************
Axiom # 1 TNc > TNn Cloudy nights are always warmer than cloudless nights.
Axiom #2 Mc TDn – Mn.t
This “miracle” inequality is universally true for 0 <= t TDn Quite Easily Done !(QED, not quantum electrodynamics)
The Temperatures never cross, if the cloudy night is warmer than the cloudless night, at all times during the night, then the previous daytime Temperture must have been higher too
It is warmer on a cloudy night,than on a cloudless night, because it was warmer during the previous day time, and those warmer conditions at night and the clouds themselves are the result of that simple fact; the clouds are NOT the cause of the warmer night, they are the consequence of the warmer day.
And yes as I recall NZWR does taste just like chicken.
This version is correct
Joel Shore @ur momisugly January 25, 3:59 am
Ah well, I guess us mere mortals should understand that certain academics sure do make a lot of assumptions
R. Gates says:
January 22, 2012 at 3:27 pm
Just to add to the notion that the Moon is a very poor gray-body body proxy for Earth– if you took away Earth’s atmosphere and ocean and measured the radiation curve of the Earth’s surface, it would look very different than the Moon’s. … so the two bodies would have very different radiation curves.
———————————–
Not so much on the surface. Earth has a substantial temperature gradient under the surface for four different reasons. However, all four combined are about 0.04% of solar insolation.
1. Radioactivity, leading to a high crustal temperature. Rocks are an effective insulator, so the rate of energy transfer to the surface is in the range of milliwats/m^2.
2. Tidal forces. Since Earth has a liquid surface and core, this leads to frictional forces that are probably many times that of radioactivity. Geologists would probably have a better idea of the magnitude of tidal forces.
2a. Luna also has tidal forces, which are larger than Earth’s since Earth exerts more force per volume on Luna than the reverse. However, much of Luna’s tidal forces are tied into its rotational wobble. Since Luna shows only one side to Earth (wobble makes that close to 60%) the location of the Earth-Luna tidal bulge moves less than 18 degrees off its center. This should cause some heating, but in the absence of other internal heating and a GHG atmosphere, not enough to make Luna significantly geologically active or warm at night.
3. Electromagnetic heating. Since the core and the surface rotate at slightly different rates, among other things, and both the core and surface have iron and nickel, some of the electromagnetic forces will be dissipated as heat.
4. Pressure gradient. This should have minimal current effects; the heat form planet creation has long since dissipated, and the annual increase in Earth’s mass is small compared to Earth’s total mass.
However, we now know that Luna gets *very* cold in places where the sun doesn’t shine. Antarctica has liquid water under the ice, obviously from internal heating. So the latitudinal profile of Earth vs. Luna is very different. Going from 4K to 150K, Earth’s internal heat is significant, less so from 150K to 288K.
If temperature is set by pressure and solar input then in the end the effects of other processes or events such as volcanoes and GHGs must be neutral unless they affect total atmospheric mass.
When either tries to alter the lapse rate set by pressure then the entire atmospheric circulation must adjust to neutralise the effects.
The lapse rate in any given atmosphere actually appears to be set by pressure alone such that the level of solar input is relevant only to atmospheric height.
No sun and the atmosphere would freeze on the surface and the atmospheric height would be zero. Add sunshine and the atmospheric height would increase commensurate with the level of solar input.
The lapse rate for a given planet would appear not to be any different at different levels of solar input.
We all know that severe volcanic outbreaks have an effect on atmospheric circulation don’t we?
Those changes in circulation constitute the inevitable negative system response to the volcanic event. In due course the system returns to the previous equilibrium.
The system responds similarly to rising or falling quantities of GHGs and to all other forcings such as variations in the rate of energy release from the oceans.
More total atmospheric mass or higher solar input are the only things that will raise the system equilibrium temperature but the lapse rate set by pressure must remain the same for any planet of a given mass.
Anything other than planetary mass that might seek to alter the basic lapse rate can only do so by altering the atmospheric height but what goes up must come down so for every location where the heights are pushed up by warmth rising from the surface there is another location where the heights are pushed down by cooled upper air descending to the surface for a zero net effect on heights globally.
The only exception would seem to be solar input which would raise absolute atmospheric height. Everything else seems only to affect relative atmospheric heights.
There would be a climate consequence though because a warmer world gives deeper surface low pressure cells and more intense surface high pressure cells.
However that climate effect from more GHGs would appear to be miniscule compared to similar such variability from sun and oceans interacting together in an ever changing dance.
To summarise:
i) The gravity field alone seems to determine the slope of the lapse rate on any given planet.
ii) Adding solar input appears to affect only the ABSOLUTE height of the atmosphere and NOT the slope of the lapse rate.
iiI) Anything other than solar input only affects the RELATIVE atmospheric heights.
iv) The consequence is that anything other than solar input will only affect the rate at which energy flows from surface to space and not the equilibrium temperature of the planet.
“I ask myself how long will it take until the oceans will be properly addressed in the effort of defining Earth equilibrium temperature?”
Well, since you asked:
http://climaterealists.com/attachments/ftp/TheSettingAndMaintainingOfEarth.pdf
“The Setting and Maintaining of Earth’s Equilibrium Temperature”
Basically atmospheric pressure sets and maintains ocean temperature by fixing the energy cost of evaporation and the oceans then control the air temperatures above.
Stephen Wilde says:
How many times do we have to explain this to you? The lapse rate alone does not determine the surface temperature. You also need to know the temperature at one height. The constraint from radiative balance of the Earth is that the effective radiating level has to be at an average temperature of 255 K. As the concentration of greenhouse gases increases, the effective radiating level rises and, hence, the surface temperature (determined by extrapolating from 255 K at the effective radiating level using the average lapse rate) rises.
Is real science so difficult to understand that you have to fall back on pseudoscience?
I wonder if Professor Robert G. Brown knows anything at all about computer science !
Well wait a minute, this thread is about Thermodynamics, not computer science.
Just for grins, google “rgb beowulf”. The hit count is way down because the old beowulf archives aren’t active much any more, but it is still pretty respectable.
The answer is “yes”. I teach computer science (usually in independent studies). I’m an ubercoder, defined to be somebody with over some absurdly large number (pick one) of lines or bytes of code they have written, lifetime. Not to brag or anything, but I’m better known for my work on beowulf style computing than I am for my papers in physics. But the bulk of my work in physics over the last 20 years was statistical thermal simulations in the context of magnetic critical phenomena.
None of which really matters in this argument. Anybody who thinks the second law of thermodynamics will be violated, in steady state, for a system as simple as this one is is simply wrong. No, it won’t. One doesn’t have to think twice about it. No, it won’t. Anybody who asserts otherwise simply hasn’t learned physics, at least not properly. They believe in magic, because a stable violation of the second law of thermodynamics in an otherwise ordinary gas in a gravitational field would be friggin’ magic.
rgb
What I think he should have based it on is a showing that a system exhibiting the specific lapse rate Jelbring argues for would not be in a maximum-entropy state.
Joe, I have such an algebraic demonstration and would (and may yet) post it, but it is a) boring. Of course isothermal is maximum entropy — otherwise you could violate the second law! b) how many people would understand it? I can’t even get them to understand the far simpler and entirely valid second law argument.
You cannot have a nonzero thermal lapse because if you did, and connected the two ends of the gas with a heat engine, it would turn all of the heat energy in the gas into work (dropping the temperature of the gas to zero) as Joules correctly stated.
That’s why you can’t. That is a direct violation of both Kelvin-Planck and Clausius statements of the second law. It would be friggin’ magic, the air in the column growing colder and colder not only without outside work, but turning all of that heat directly into work!
Now here’s a very, very simple “maximum entropy” exercise, one that anybody can do. We’re removing heat from the gas at nonzero temperatures, so its entropy is strictly decreasing. The heat is showing up in the Universe as nice, reversible, work, \Delta S = 0, quite independent of the temperature of the room outside.
What is the net entropy change of the Universe while all of this is going on?
Now that’s a maximum entropy computation, and I didn’t even use stat mech.
rgb
George E. Smith; says:
January 25, 2012 at 7:09 am
Close, but no cigar. The rate of emission is proportional to the number of molecules in the excited state only. The lifetime of an individual molecule before it is de-excited by collision makes no difference at all in the rate of emission. The proportionality constant is the Einstein A21 coefficient. That coefficient can be use to calculate a half life, t_12, for a free excited molecule, but an excited molecule can emit at any time. It just means that if you have, say a thousand excited molecules at t(0), the probability is that 500 of them will have emitted at t = t_1/2. But notice that they did emit at less than the half life time.
Kirchhoff’s Law that absorptivity equals emissivity only holds if Local Thermodynamic Equilibrium (LTE) exists. A requirement for LTE to exist is that the energy distribution of the molecules follows Maxwell-Boltzmann statistics. If collisional excitation/de-excitation is not the dominant form of energy exchange, MB statistics don’t exist, nor does LTE. MB statistics determine the fraction of the population that is excited. That fraction decreases with temperature. The effective height of emission at a given wavelength depends on the optical density which depends on the number density of molecules in a unit volume, i.e. the partial pressure, not the volumetric mixing ratio and the absorption coefficient. Emission to space peaks at an optical density of 1. For CO2, that happens quite high in the atmosphere where it’s much colder than the surface or the altitudes where water vapor optical density reaches 1. But at lower altitudes CO2 molecules still emit and absorb. However, the probability that any of those photons will escape to space becomes vanishingly small as the optical density (measured from infinity or wherever you pick as the top of the atmosphere) becomes much greater than 1.
Joel Shore @ur momisugly January 23, 6:13 am
You wrote in response to Konrad’s low budget experiments, which gave evidence that the basic premise of N&Z may be correct, my bold added:
Oh really? Were you there to observe the detail of the experiment? Given some resource restraints on Konrad, please do not abuse the use of a rubber hot water bottle as an air pressure bladder/regulator, and house-bricks atop a plywood pressure base as an invalid mass. To me as an engineer I think it is a highly valid and quite impressive low budget/capacity approach.
How about you elaborate as to why you assume it all to be wrong. Do you get what I say? Describe the errors that you elusively assert!
Oh, and you might like to read this here for additional context: http://tallbloke.wordpress.com/2012/01/17/nikolov-and-zeller-reply-to-comments-on-the-utc-part-1/#comment-15583
“”””” DeWitt Payne says:
January 26, 2012 at 5:05 pm
George E. Smith; says:
January 25, 2012 at 7:09 am
The “excited states” of say CO2 that result in the absorption or emission of the 15 micron band of spectral lines have lifetimes, that are generally much longer than the time between collisions at STP conditions, so a molecule that has captured such a photon, seldom gets a chance to spontaneously re-emit such a photon; collisions terminate the condition, which transfers that photon energy to the regular N2, O2, Ar molecules of the atmosphere, as thermal energy.
Close, but no cigar. The rate of emission is proportional to the number of molecules in the excited state only. The lifetime of an individual molecule before it is de-excited by collision makes no difference at all in the rate of emission. “””””
So Dewitt,
Could you extract or point to the specific words in the piece of my post that YOU
chose out of my longer post; which piece I have recopied above from your post, that you consider are contrary to either of the two statements that you then made; which I have also repeated above; to whit:-
“”””” The rate of emission is proportional to the number of molecules in the excited state only. “”””
“”””” The lifetime of an individual molecule before it is de-excited by collision makes no difference at all in the rate of emission. “””””
And I say TWO statements, because the two pieces, I have referenced immediately above are contradictory with each other.
You first state that the rate of emision (actually spontaneous emission) is proportional to the number of molecules in the excited state. I have no disagreement with that; nor does my post and particularly the piece you chose above refute that.
But then you claim that the lifetime of an individual molecule before it is de-excited by collision (which will remove it from the number of molecules that are in the excited state) makes no diference at all in the rate of emission.
Now you can’t have it both ways. Either removing a given molecule from the count of excited molecules reduces the rate of emission or it doesn’t.
The process of spontaneous emission from an excited molecule; let’s say CO2 (isolated from ANY OTHER MOLECULE) , is a property of that particular molecular species, and that excited state has some statistical “lifetime” , presumably calculable from quantum mechanics; somewhat akin to how radioactive decay has some statisticl “lifetime”, commonly expressed as a half life.
Moreover, the spontaneous emission lifetime of our excited molecule is absolutely Temperature independent; it HAS to be that way, because a molecule that is isolated from any other molecule clearly hasn’t undergone any collision with any such other molecule, and any such free flight molecule has NO Temperature anyway.
So the spontaneous radiative lifetime of some specific excited state of some GHG molecule is Temperature independent.
On the other hand, both the Temperature and pressure of the ambient atmosphere, in which our free flight GHG molecule exists effect the mean time between molecular collisions, according to the statistical mechanics of ordinary gases.
So we have on the one hand the possibility of a spontaneous emission of a GHG characteristic photon, at any time with the appropriate statistical probability for that species and excited state, and we also have the probability that the GHG molecule may undergo a collision with an ordinary gas molecule, which presumably will terminate the excited state, resulting in thermal redistribution of the energy, rather than a spontaneous emission event.
The collision induced de-excitation is dependent on the gas Temperature, the spontanous emission is not Temperature dependent; but depends on having molecues in the excited state.
Now ALL that I have said, was that Phil has pointed out that spontaneous emission may be common in the cold rarified stratospheric atmosphere BECAUSE of the much longer mean time between collisions but at the lower (2 metre) STP atmosphere conditions, the mean time between collisions is much shorter so that it is more likely that collisions will de-excite the GHG molecule, rather than spontaneous emissions, because collisions reduce the number of molecules in the excited state.
We are then asked to believe that since the thermal energy of the ordinary atmosphere gases can’t be radiated away by those ordinary gas molecules, it can ONLY be given up to a GHG molecule in a collision which presumably is sometimes able to excite one of the resonances of the GHG molecule; but that process is still dependent on the GHG molecule being abe to spontaneously decay, emitting it’s characteristic wavelength photon.
Now I agree that at higher Temperature and pressure, the number of collisions with enough energy transfer to excite the GHG molecule, will be higher, so there will be more molecules going to the excited state; and by inference, more of them in the excited state at any moment; so yes, the rate of spontanous emissions will increase with Temperature.
BUT the photon energies emitted will still be the Temperature independent spectral lines of the GHG molecule, not ones representative of the atmospheric Temperature.
So according to the prevailing belief that atmospheric gases do not radiate themal spectra, the radiant emission from the atmosphere, must consist ONLY of GHG characteristic lines and bands.
So any black body like radiation seen in the earth emission spectrum from space MUST have originated from the ground; not the atmosphere, and its specrum has to be characteristic of the surface Temperature; not some upper atmosphere Temperature.
By the way Dewitt,
I don’t smoke; so why not leave out the condescending “no cigar” bit.
Kirchoff’s law of equal spectral radiant emittance and spectral radiant absorptance requires thermal equilibrium, between the radiating/absorbing material and the EM radiation field.
George E. Smith; says:
January 27, 2012 at 1:56 pm
Sure I can. The reason is that for every molecule that is de-excited by collision, another is excited, keeping the total number constant. That’s required by MB statistics and LTE.
Correct. The radiative temperature and the kinetic energy temperature must be the same. That, however, can only happen if MB statistics apply to the kinetic energy distribution and the temperature calculated from determining the fraction of molecules in a particular excited state by measuring the radiant emission from that excited state matches the temperature determined by measuring the average kinetic energy of the gas molecules.
I used to do plasma emission spectrometry before I retired. In a plasma, there are lots of ways to measure the temperature besides the average kinetic energy.