Note: This was a poster, and adopted into a blog post by the author, Ned Nikolov, specifically for WUWT. My thanks to him for the extra effort in converting the poster to a more blog friendly format. – Anthony
Expanding the Concept of Atmospheric Greenhouse Effect Using Thermodynamic Principles: Implications for Predicting Future Climate Change
Ned Nikolov, Ph.D. & Karl Zeller, Ph.D.
USFS Rocky Mountain Research Station, Fort Collins CO, USA
Emails: ntconsulting@comcast.net kzeller@colostate.edu
Poster presented at the Open Science Conference of the World Climate Research Program,
24 October 2011, Denver CO, USA
http://www.wcrp-climate.org/conference2011/posters/C7/C7_Nikolov_M15A.pdf
Abstract
We present results from a new critical review of the atmospheric Greenhouse (GH) concept. Three main problems are identified with the current GH theory. It is demonstrated that thermodynamic principles based on the Gas Law need be invoked to fully explain the Natural Greenhouse Effect. We show via a novel analysis of planetary climates in the solar system that the physical nature of the so-called GH effect is a Pressure-induced Thermal Enhancement (PTE), which is independent of the atmospheric chemical composition. This finding leads to a new and very different paradigm of climate controls. Results from our research are combined with those from other studies to propose a new Unified Theory of Climate, which explains a number of phenomena that the current theory fails to explain. Implications of the new paradigm for predicting future climate trends are briefly discussed.
1. Introduction
Recent studies revealed that Global Climate Models (GCMs) have significantly overestimated the Planet’s warming since 1979 failing to predict the observed halt of global temperature rise over the past 13 years. (e.g. McKitrick et al. 2010). No consensus currently exists as to why the warming trend ceased in 1998 despite a continued increase in atmospheric CO2 concentration. Moreover, the CO2-temperature relationship shows large inconsistencies across time scales. In addition, GCM projections heavily depend on positive feedbacks, while satellite observations indicate that the climate system is likely governed by strong negative feedbacks (Lindzen & Choi 2009; Spencer & Braswell 2010). At the same time, there is a mounting political pressure for Cap-and-Trade legislation and a global carbon tax, while scientists and entrepreneurs propose geo-engineering solutions to cool the Planet that involve large-scale physical manipulation of the upper atmosphere. This unsettling situation calls for a thorough reexamination of the present climate-change paradigm; hence the reason for this study.
2. The Greenhouse Effect: Reexamining the Basics
Figure 1. The Atmospheric Greenhouse Effect as taught at universities around the World (diagram from the website of the Penn State University Department of Meteorology).
According to the current theory, the Greenhouse Effect (GHE) is a radiative phenomenon caused by heat-trapping gases in the atmosphere such as CO2 and water vapor that are assumed to reduce the rate of surface infrared cooling to Space by absorbing the outgoing long-wave (LW) emission and re-radiating part of it back, thus increasing the total energy flux toward the surface. This is thought to boost the Earth’s temperature by 18K – 33K compared to a gray body with no absorbent atmosphere such as the Moon; hence making our Planet habitable. Figure 1 illustrates this concept using a simple two-layer system known as the Idealized Greenhouse Model (IGM). In this popular example, S is the top-of-the atmosphere (TOA) solar irradiance (W m-2), A is the Earth shortwave albedo, Ts is the surface temperature (K), Te is the Earth’s effective emission temperature (K) often equated with the mean temperature of middle troposphere, ϵ is emissivity, and σ is the Stefan-Boltzmann (S-B) constant.
2.1. Main Issues with the Current GHE Concept:
A) Magnitude of the Natural Greenhouse Effect. GHE is often quantified as a difference between the actual mean global surface temperature (Ts = 287.6K) and the planet’s average gray-body (no-atmosphere) temperature (Tgb), i.e. GHE = Ts – Tgb. In the current theory, Tgb is equated with the effective emission temperature (Te) calculated straight from the S-B Law using Eq. (1):
where αp is the planetary albedo of Earth (≈0.3). However, this is conceptually incorrect! Due to Hölder’s inequality between non-linear integrals (Kuptsov 2001), Te is not physically compatible with a measurable true mean temperature of an airless planet. To be correct, Tgb must be computed via proper spherical integration of the planetary temperature field. This means calculating the temperature at every point on the Earth sphere first by taking the 4th root from the S-B relationship and then averaging the resulting temperature field across the planet surface, i.e.
where αgb is the Earth’s albedo without atmosphere (≈0.125), μ is the cosine of incident solar angle at any point, and cs= 13.25e-5 is a small constant ensuring that Tgb = 2.72K (the temperature of deep Space) when So = 0. Equation (2) assumes a spatially constant albedo (αgb), which is a reasonable approximation when trying to estimate an average planetary temperature.
Since in accordance with Hölder’s inequality Tgb ≪ Te (Tgb =154.3K ), GHE becomes much larger than presently estimated.
According to Eq. (2), our atmosphere boosts Earth’s surface temperature not by 18K—33K as currently assumed, but by 133K! This raises the question: Can a handful of trace gases which amount to less than 0.5% of atmospheric mass trap enough radiant heat to cause such a huge thermal enhancement at the surface? Thermodynamics tells us that this not possible.
B) Role of Convection. The conceptual model in Fig. 1 can be mathematically described by the following simultaneous Equations (3),
where νa is the atmospheric fraction of the total shortwave radiation absorption. Figure 2 depicts the solution to Eq. (3) for temperatures over a range of atmospheric emissivities (ϵ) assuming So = 1366 W m-2 and νa =0.326 (Trenberth et al. 2009). An increase in atmospheric emissivity does indeed cause a warming at the surface as stated by the current theory. However, Eq. (3) is physically incomplete, because it does not account for convection, which occurs simultaneously with radiative transfer. Adding a convective term to Eq. (3) (such as a sensible heat flux) yields the system:
where gbH is the aerodynamic conductance to turbulent heat exchange. Equation (4) dramatically alters the solution to Eq. (3) by collapsing the difference between Ts, Ta and Te and virtually erasing the GHE (Fig. 3). This is because convective cooling is many orders of magnitude more efficient that radiative cooling. These results do not change when using multi-layer models. In radiative transfer models, Ts increases with ϵ not as a result of heat trapping by greenhouse gases, but due to the lack of convective cooling, thus requiring a larger thermal gradient to export the necessary amount of heat. Modern GCMs do not solve simultaneously radiative transfer and convection. This decoupling of heat transports is the core reason for the projected surface warming by GCMs in response to rising atmospheric greenhouse-gas concentrations. Hence, the predicted CO2-driven global temperature change is a model artifact!
Figure 2. Solution to the two-layer model in Eq. (3) for Ts and Ta as a function of atmospheric emissivity assuming a non-convective atmosphere. Also shown is the predicted down-welling LW flux(Ld). Note that Ld ≤ 239 W m-2.
Figure 3. Solution to the two-layer model in Eq. (4) for Ts and Ta as a function of atmospheric emissivity assuming a convective atmosphere (gbH = 0.075 m/s). Also shown is the predicted down-welling LW flux (Ld). Note that Ld ≤ 239 W m-2.
Figure 4. According to observations, the Earth-Atmosphere System absorbs on average a net solar flux of 239 W m-2, while the lower troposphere alone emits 343 W m-2 thermal radiation toward the surface.
C) Extra Kinetic Energy in the Troposphere.
Observations show that the lower troposphere emits 44% more radiation toward the surface than the total solar flux absorbed by the entire Earth-Atmosphere System (Pavlakis et al. 2003) (Fig. 4). Radiative transfer alone cannot explain this effect (e.g. Figs. 2 & 3) given the negligible heat storage capacity of air, no matter how detailed the model is. Thus, empirical evidence indicates that the lower atmosphere contains more kinetic energy than provided by the Sun. Understanding the origin of this extra energy is a key to the GHE.
3. The Atmospheric Thermal Enhancement
Previous studies have noted that the term Greenhouse Effect is a misnomer when applied to the atmosphere, since real greenhouses retain heat through an entirely different mechanism compared to the free atmosphere, i.e. by physically trapping air mass and restricting convective heat exchange. Hence, we propose a new term instead, Near-surface Atmospheric Thermal Enhancement (ATE) defined as a non-dimensional ratio (NTE) of the planet actual mean surface air temperature (Ts, K) to the average temperature of a Standard Planetary Gray Body (SPGB) with no atmosphere (Tgb, K) receiving the same solar irradiance, i.e. NTE = Ts /Tgb. This new definition emphasizes the essence of GHE, which is the temperature boost at the surface due to the presence of an atmosphere. We employ Eq. (2) to estimate Tgb assuming an albedo αgb = 0.12 and a surface emissivity ϵ = 0.955 for the SPGB based on data for Moon, Mercury, and the Earth surface. Using So = 1362 W m-2 (Kopp & Lean 2011) in Eq. (2) yields Tgb = 154.3K and NTE = 287.6/154.3 = 1.863 for Earth. This prompts the question: What mechanism enables our atmosphere to boost the planet surface temperature some 86% above that of a SPGB? To answer it we turn on to the classical Thermodynamics.
3.1. Climate Implications of the Ideal Gas Law
The average thermodynamic state of a planet’s atmosphere can be accurately described by the Ideal Gas Law (IGL):
PV = nRT (5)
where P is pressure (Pa), V is the gas volume (m3), n is the gas amount (mole), R = 8.314 J K-1 mol-1is the universal gas constant, and T is the gas temperature (K). Equation (5) has three features that are chiefly important to our discussion: a) the product P×V defines the internal kinetic energy of a gas (measured in Jules) that produces its temperature; b) the linear relationship in Eq. (5) guarantees that a mean global temperature can be accurately estimated from planetary averages of surface pressure and air volume (or density). This is in stark contrast to the non-linear relationship between temperature and radiant fluxes (Eq. 1) governed by Hölder’s inequality of integrals; c) on a planetary scale, pressure in the lower troposphere is effectively independent of other variables in Eq. (5) and is only a function of gravity (g), total atmospheric mass (Mat), and the planet surface area (As), i.e. Ps = g Mat/As. Hence, the near-surface atmospheric dynamics can safely be assumed to be governed (over non-geological time scales) by nearly isobaric processes on average, i.e. operating under constant pressure. This isobaric nature of tropospheric thermodynamics implies that the average atmospheric volume varies in a fixed proportion to changes in the mean surface air temperature following the Charles/Gay-Lussac Law, i.e. Ts/V = const. This can be written in terms of the average air density ρ (kg m-3) as
ρTs = const. = Ps M / R (6)
where Ps is the mean surface air pressure (Pa) and M is the molecular mass of air (kg mol-1). Eq. (6) reveals an important characteristic of the average thermodynamic process at the surface, namely that a variation of global pressure due to either increase or decrease of total atmospheric mass will alter both temperature and atmospheric density. What is presently unknown is the differential effect of a global pressure change on each variable. We offer a solution to this in & 3.3. Equations (5) and (6) imply that pressure directly controls the kinetic energy and temperature of the atmosphere. Under equal solar insolation, a higher surface pressure (due to a larger atmospheric mass) would produce a warmer troposphere, while a lower pressure would result in a cooler troposphere. At the limit, a zero pressure (due to the complete absence of an atmosphere) would yield the planet’s gray-body temperature.
The thermal effect of pressure is vividly demonstrated on a cosmic scale by the process of star formation, where gravity-induced rise of gas pressure boosts the temperature of an interstellar cloud to the threshold of nuclear fusion. At a planetary level, the effect is manifest in Chinook winds, where adiabatically heated downslope airflow raises the local temperature by 20C-30C in a matter of hours. This leads to a logical question: Could air pressure be responsible for the observed thermal enhancement at the Earth surface presently known as a ‘Natural Greenhouse Effect’? To answer this we must analyze the relationship between NTEfactor and key atmospheric variables including pressure over a wide range of planetary climates. Fortunately, our solar system offers a suitable spectrum of celestial bodies for such analysis.
3.2. Interplanetary Data Set
We based our selection of celestial bodies for the ATE analysis on three criteria: 1) presence of a solid planetary surface with at least traces of atmosphere; 2) availability of reliable data on surface temperature, total pressure, atmospheric composition etc. preferably from direct measurements; and 3) representation of a wide range of atmospheric masses and compositions. This approach resulted in choosing of four planets – Mercury, Venus, Earth, and Mars, and four natural satellites – Moon of Earth, Europa of Jupiter, Titan of Saturn, and Triton of Neptune. Each celestial body was described by 14 parameters listed in Table 1.
For planets with tangible atmospheres, i.e. Venus, Earth and Mars, the temperatures calculated from IGL agreed rather well with observations. Note that, for extremely low pressures such as on Mercury and Moon, the Gas Law produces Ts ≈ 0.0. The SPGB temperatures for each celestial body were estimated from Eq. (2) using published data on solar irradiance and assuming αgb = 0.12 and ϵ = 0.955. For Mars, global means of surface temperature and air pressure were calculated from remote sensing data retrieved via the method of radio occultation by the Radio Science Team (RST) at Stanford University using observations by the Mars Global Surveyor (MGS) spacecraft from 1999 to 2005. Since the MGS RST analysis has a wide spatial coverage, the new means represent current average conditions on the Red Planet much more accurately than older data based on Viking’s spot observations from 1970s.
Table 1. Planetary data used to analyze the physical nature of the Atmospheric Near-Surface Thermal Enhancement (NTE). Information was gathered from multiple sources using cross-referencing. The bottom three rows of data were estimated in this study using equations discussed in the text.
3.3. Physical Nature of ATE / GHE
Our analysis of interplanetary data in Table 1 found no meaningful relationships between ATE (NTE) and variables such as total absorbed solar radiation by planets or the amount of greenhouse gases in their atmospheres. However, we discovered that NTE was strongly related to total surface pressure through a nearly perfect regression fit via the following nonlinear function:
where Ps is in Pa. Figure 5 displays Eq. (7) graphically. The tight relationship signals a causal effect of pressure on NTE, which is theoretically supported by the IGL (see & 3.1). Also, the Ps–NTE curve in Fig. 5 strikingly resembles the response of the temperature/potential temp. (T/θ) ratio to altitudinal changes of pressure described by the well-known Poisson formula derived from IGL (Fig. 6). Such a similarity in responses suggests that both NTE and θ embody the effect of pressure-controlled adiabatic heating on air, even though the two mechanisms are not identical. This leads to a fundamental conclusion that the ‘Natural Greenhouse Effect’ is in fact a Pressure-induced Thermal Enhancement (PTE) in nature.
NTE should not be confused with an actual energy, however, since it only defines the relative (fractional) increase of a planet’s surface temperature above that of a SPGB. Pressure by itself is not a source of energy! Instead, it enhances (amplifies) the energy supplied by an external source such as the Sun through density-dependent rates of molecular collision. This relative enhancement only manifests as an actual energy in the presence of external heating. Thus, Earth and Titan have similar NTE values, yet their absolute surface temperatures are very different due to vastly dissimilar solar insolation. While pressure (P) controls the magnitude of the enhancement factor, solar heating determines the average atmospheric volume (V), and the product P×V defines the total kinetic energy and temperature of the atmosphere. Therefore, for particular solar insolation, the NTE factor gives rise to extra kinetic energy in the lower atmosphere beyond the amount supplied by the Sun. This additional energy is responsible for keeping the Earth surface 133K warmer than it would be in the absence of atmosphere, and is the source for the observed 44% extra down-welling LW flux in the lower troposphere (see &2.1 C). Hence, the atmosphere does not act as a ‘blanket’ reducing the surface infrared cooling to space as maintained by the current GH theory, but is in and of itself a source of extra energy through pressure. This makes the GH effect a thermodynamic phenomenon, not a radiative one as presently assumed!
Equation (7) allows us to derive a simple yet robust formula for predicting a planet’s mean surface temperature as a function of only two variables – TOA solar irradiance and mean atmospheric surface pressure, i.e.
Figure 5. Atmospheric near-surface Thermal Enhancement (NTE) as a function of mean total surface pressure (Ps) for 8 celestial bodies listed in Table 1. See Eq. (7) for the exact mathematical formula.
Figure 6. Temperature/potential temperature ratio as a function of atmospheric pressure according to the Poisson formula based on the Gas Law (Po = 100 kPa.). Note the striking similarity in shape with the curve in Fig. 5.
where NTE(Ps) is defined by Eq. (7). Equation (8) almost completely explains the variation of Ts among analyzed celestial bodies, thus providing a needed function to parse the effect of a global pressure change on the dependent variables ρ and Tsin Eq. (6). Together Equations (6) and (8) imply that the chemical composition of an atmosphere affects average air density through the molecular mass of air, but has no impact on the mean surface temperature.
4. Implications of the new ATE Concept
The implications of the above findings are numerous and paradigm-altering. These are but a few examples:
Figure 7. Dynamics of global temperature and 12-month forward shifted cloud cover types from satellite observations. Cloud changes precede temperature variations by 6 to 24 months and appear to have been controlling the latter during the past 30 years (Nikolov & Zeller, manuscript).
A) Global surface temperature is independent of the down-welling LW flux known as greenhouse or back radiation, because both quantities derive from the same pool of atmospheric kinetic energy maintained by solar heating and air pressure. Variations in the downward LW flux (caused by an increase of tropospheric emissivity, for example) are completely counterbalanced (offset) by changes in the rate of surface convective cooling, for this is how the system conserves its internal energy.
B) Modifying chemical composition of the atmosphere cannot alter the system’s total kinetic energy, hence the size of ATE (GHE). This is supported by IGL and the fact that planets of vastly different atmospheric composition follow the same Ps–NTE relationship in Fig. 5. The lack of impact by the atmospheric composition on surface temperature is explained via the compensating effect of convective cooling on back-radiation discussed above.
C) Equation (8) suggests that the planet’s albedo is largely a product of climate rather than a driver of it. This is because the bulk of the albedo is a function of the kinetic energy supplied by the Sun and the atmospheric pressure. However, independent small changes in albedo are possible and do occur owning to 1%-3% secular variations in cloud cover, which are most likely driven by solar magnetic activity. These cloud-cover changes cause ±0.7C semi-periodic fluctuations in global temperature on a decadal to centennial time scale as indicated by recent satellite observations (see Fig. 7) and climate reconstructions for the past 10,000 years.
Figure 8. Dynamics of global surface temperature during the Cenozoic Era reconstructed from 18O proxies in marine sediments (Hansen et al. 2008).
Figure 9. Dynamics of mean surface atmospheric pressure during the Cenozoic Era reconstructed from the temperature record in Fig. 8 by inverting Eq. (8).
D) Large climatic shifts evident in the paleo-record such as the 16C directional cooling of the Globe during the past 51 million years (Fig. 8) can now be explained via changes in atmospheric mass and surface pressure caused by geologic variations in Earth’s tectonic activity. Thus, we hypothesize that the observed mega-cooling of Earth since the early Eocene was due to a 53% net loss of atmosphere to Space brought about by a reduction in mantle degasing as a result of a slowdown in continental drifts and ocean floor spreading. Figure 9 depicts reconstructed dynamics of the mean surface pressure for the past 65.5M years based on Eq. (8) and the temperature record in Fig. 8.
5. Unified Theory of Climate
The above findings can help rectify physical inconsistencies in the current GH concept and assist in the development of a Unified Theory of Climate (UTC) based on a deeper and more robust understanding of various climate forcings and the time scales of their operation. Figure 10 outlines a hierarchy of climate forcings as part of a proposed UTC that is consistent with results from our research as well as other studies published over the past 15 years. A proposed key new driver of climate is the variation of total atmospheric mass and surface pressure over geological time scales (i.e. tens of thousands to hundreds of millions of years). According to our new theory, the climate change over the past 100-300 years is due to variations of global cloud albedo that are not related to GHE/ATE. This is principally different from the present GH concept, which attempts to explain climate changes over a broad range of time scales (i.e. from decades to tens of millions of years) with the same forcing attributed to variations in atmospheric CO2 and other heat-absorbing trace gases (e.g. Lacis et al. 2010).
Earth’s climate is currently in one of the warmest periods of the Holocene (past 10K years). It is unlikely that the Planet will become any warmer over the next 100 years, because the cloud cover appears to have reached a minimum for the present levels of solar irradiance and atmospheric pressure, and the solar magnetic activity began declining, which may lead to more clouds and a higher planetary albedo. At this point, only a sizable increase of the total atmospheric mass can bring about a significant and sustained warming. However, human-induced gaseous emissions are extremely unlikely to produce such a mass increase.
Figure 10. Global climate forcings and their time scales of operation according to the hereto proposed Unified Theory of Climate (UTC). Arrows indicate process interactions.
6. References
Kopp, G. and J. L. Lean (2011). A new, lower value of total solar irradiance: Evidence and climate significance, Geophys. Res. Lett., 38, L01706, doi:10.1029/2010GL045777.
Kuptsov, L. P. (2001) Hölder inequality, in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1556080104.
Lacis, A. A., G. A. Schmidt, D. Rind, and R. A. Ruedy (2010). Atmospheric CO2: Principal control knob governing earth’s temperature. Science 330:356-359.
Lindzen, R. S. and Y.-S. Choi (2009). On the determination of climate feedbacks from ERBE data. Geophys. Res. Lett., 36, L16705, doi:10.1029/2009GL039628.
McKitrick, R. R. et al. (2010). Panel and Multivariate Methods for Tests of Trend Equivalence in Climate Data Series. Atmospheric Science Letters, Vol. 11, Issue 4, pages 270–277.
Nikolov, N and K. F. Zeller (manuscript). Observational evidence for the role of planetary cloud-cover dynamics as the dominant forcing of global temperature changes since 1982.
Pavlakis, K. G., D. Hatzidimitriou, C. Matsoukas, E. Drakakis, N. Hatzianastassiou, and I. Vardavas (2003). Ten-year global distribution of down-welling long-wave radiation. Atmos. Chem. Phys. Discuss., 3, 5099-5137.
Spencer, R. W. and W. D. Braswell (2010). On the diagnosis of radiative feedback in the presence of unknown radiative forcing, J. Geophys. Res., 115, D16109, doi:10.1029/2009JD013371
Trenberth, K.E., J.T. Fasullo, and J. Kiehl (2009). Earth’s global energy budget. BAMS, March:311-323
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This post is also available as a PDF document here:
Unified_Theory_Of_Climate_Poster_Nikolov_Zeller
UPDATE: This thread is closed – see the newest one “A matter of some Gravity” where the discussion continues.
hotrod (Larry L) and John Day:
Larry, at December 30, 2011 at 4:59 pm you say;
“Wow — the Jelbring hypthosis certainly does appear to be essentially the same work. The current Unified Climate Theory discussion being an elaboration to extend and independently validate the concept.”
Indeed, that is what I pointed out in my post at December 30, 2011 at 3:34 pm.
And I stand by my request to Anthony for an update at the top of this thread to state what you and I agree.
Also, you ask me;
“how did the original paper get ignored or pushed under the rug? It would be interesting to dig through the climate gate emails to see if any of them mention the Jelbring paper!”
The Team ignored it and, therefore, it is not mentioned in the Climategate emails.
John:
You say at December 30, 2011 at 5:06 pm
[snip]
“But I think the N&Z regression analysis of planetary surface temps (Eq 8 and Fig 5) still stands as ‘novel’.”
Perhaps, but Jelbring assessed his hypothesis by comparison to planetary temperatures. A novel way to do the same comparison is NOT “a novel analysis of planetary climates in the solar system”: it is merely a novel method to validate Jelbring’s work that Nikolov & Zeller fail to mention and/or reference.
Happy New Year
Richard
Hello Everyone
As an author of the paper discussed on this blog, I have been watching in amazement the diverse views and perspectives expressed over the past 2 days, some of them quite predictable while other totally ‘out of the blue’. Overall, I find this exchange quite useful for it helps us understand the type of challenges people face when presented with this new paradigm. Your comments gave me several ideas on how to better address and explain key aspects of our theory.
Instead of responding to individual comments, I thought it would be more beneficial for the whole group, if we (the authors) prepare a brief ‘reply’ article that clarifies the main issues/questions raised on this blog such as the magnitude of the GH effect, the meaning of the terms ‘extra energy’ and ‘pressure thermal effect’, the role of GH gases and their relationship to convection, the physical meaning of the ‘effective emission height’ in radiative transfer, and a few others.
We will try to post our reply/clarification by the end of next week (Jan 6). In the mean time, I urge everyone seriously interested in the subject to read our paper in full at least twice while taking time to contemplate on different aspects of it. We know from experience that digesting a new paradigm takes time since it requires a SHIFT in perception (hence, the term ‘new paradigm’!). The way to reach that mental shift is by trying to think about the issue (in this case the GH effect) from a different (new) vantage point … It took us close to 12 months to fully realize all implications of Equations 7 and 8 with their amazing accuracy in predicting the mean temperature of planets over such a broad range of conditions. We then spent another 8 months to figure out how this relationship fits in with the climate forcings proposed by other studies before we were able to craft Figure 10.
As far as we understand it now, all pieces of the new paradigm fit together very nicely, but this has to be conveyed to others in a way they can see it too. And that’s where our current challenge and commitment is … One should always remember, though, that this type of situation is not new to the history of science. Think about Copernicus and the 250 years it took for his idea of the Sun-centered solar system to become a mainstream science concept. The history repeats itself! We just hope that this time the paradigm shift will happen much quicker … -:)
Happy New Year!
Erinome:
Even by troll standards your post at December 30, 2011 at 5:33 pm is weak. The statement you dispute is correct.
The statement is;
“Recent studies revealed that Global Climate Models (GCMs) have significantly overestimated the Planet’s warming since 1979 failing to predict the observed halt of global temperature rise over the past 13 years.”
And you dispute it by saying;
“In fact, UAH lower temperatures have increased at a rate of 0.18 C/decade over the last 13 years (Jan-1999 to Oct-2011).”
But the IPCC AR4 said “committed warming” (i.e. warming certain to occur because it was already ‘in the pipeline’) would be 0.2 C per decade averaged over the first two decades of this century:
see http://www.ipcc.ch/publications_and_data/ar4/wg1/en/tssts-5-1.html
So, the warming you cite as having happened is less than a tenth of that which the IPCC said was certain to happen over that period (unless you think global temperature is going to jump 0.4 C now and stay that high for the next decade).
And nobody – not even a troll – is going to claim the 0.4 C jump is possible, so the GCMs cited by the IPCC “have significantly overestimated the Planet’s warming since 1979 failing to predict the observed halt of global temperature rise over the past 13 years”.
Richard
Ned Nikolov:
Thankyou for your post at December 30, 2011 at 6:10 pm. I especially thankyou for your promise to respond to comments.
I ask that your response acknowledges Jelbring’s prior work. I feel sure that you were not aware of it which is why you dfid not reference it. But I am cognisant with the objections to the Jelbring Hypothesis that arose in 2003/4 so I may be able to help address some points of dissent that you had not anticipated but which have already been discussed.
Please note that I do not know if the Jelbring Hypotghesis is right or wrong, but I have seen some very flawed objections to it.
Happy New Year
Richard
Ned Nikolov says:
Think about Copernicus and the 250 years it took for his idea of the Sun-centered solar system to become a mainstream science concept. The history repeats itself! We just hope that this time the paradigm shift will happen much quicker … -:)
Dr. Nikolov: Unfortunately, for every Copernicus, there are probably at least 1000 people who think they are Copernicus but are just plain wrong. This included many people such as yourself who are very intelligent and have strong scientific backgrounds.
The scientific community is not rejecting your notions because it involves a paradigm shift; it is rejecting them because upon perusal they are seen to be wrong (as I have discussed here: http://wattsupwiththat.com/2011/12/29/unified-theory-of-climate/#comment-846787 , here http://wattsupwiththat.com/2011/12/29/unified-theory-of-climate/#comment-846836 , and here http://wattsupwiththat.com/2011/12/29/unified-theory-of-climate/#comment-847131 )
Your work is flawed from the outset: It doesn’t even obey the First Law of Thermodynamics (i.e., energy conservation)! It ignores the fact that lapse rates below the adiabatic lapse rate are not unstable to convection when considering the effect of convection! And, it ignores the work of others who have considered the thermodynamics principles correctly. You are not the first people to realize that one can apply the ideal gas law to the atmosphere or that convection is important in doing quantitative calculations… In fact, I challenge you to find anybody in the field who believes otherwise. I would strongly suggest that you read a textbook on climate science, one particularly good one being Ray Pierrehumbert’s “Principles of Planetary Climate”. I think you will be surprised to see what is already considered and understood.
[Moderator’s Note: Joel, thankyou for your courtesy and understanding. Happy New Year to you. -REP]
Phil says that (many) Astro-Physicists see everything as a star, so their views on simple planetary climate issues, may not be believable.
Perhaps that is the problem that Dr Willie Wei Hock Soon, and Dr Sally Baliunas have with their associations with the Harvard Smithsonian Center for Astro-Physics. I must say, that I have found Dr Soon’s book on the Maunder Minimum, and the variable sun-earth connection to be quite illuminating and informative.
It turns out, that the Director of that institution; Professor Charles Alcock, is a graduate of the University of Auckland (BSc (hons)), and PhD Cal Tech.
Professor Alcock is the recipient of the 2012 UofA Distinguished Alumni Award in the Science and Engineering category; facetiously described as the University “knighthoods”, and thery are a big deal to the University, and its community. The annual dinner at which Professor Alcock will receive his award will be in March 2012.
I am planning to attend the dinner and award ceremony, since they invite me, and give me and a guest a free ticket every year (since 2000), so maybe I will get a chance to ask the good professor about his view of the shenanigans relating to the Baliunas/Soon Paper and donnybrook.
Dr Chris de Freitas is also on the staff at UofA, so I am hoping I can meet with him again at the same time, and find out what is happening there.
The UofA Society may award up to five of these awards in any year; but only one in Science and Engineering. It turns out that for 2012, one of the other recipients will be Dr Mark Sagar, who is some sort of engineering software guru. His PhD research at UofA lead to the systems for rendering anatomically correct simulations of parts of critters for use in digital movies. Moviegoers have and can see the results of his work in the movies King Kong, Spiderman 2, and that blue green propaganda film Avatar. I have no idea of his association with the politics of Avatar; but I guess his animations are pretty cool. I hav;t seen either of the other two movies.
So maybe I can get a word with him too. small world it is.
When radiation is absorbed by the molecules of a gas, the energy can go into one of four places:
(1) Translational Energy,
(2) Rotational Energy,
(3) Vibrational Energy,
(4) Electron Transitions.
Only (1) is involved in determining temperature.
While (2) and (3) can “suck up” energy, and thus contribute to the heat capacity of the gas, the energy absorbed in this way does not make the molecules move faster, it just makes them spin or vibrate to a greater extent, and thus does not raise their temperature, which (if I may repeat myself) only depends on their Translational Kinetic Energy. Case (4) will also generally not result in a permanent increase in the speed of the molecules, apart from a “jolt” on absorption and a “counter-jolt” upon emission of the radiation that is produced when the electrons drop back to their normal states.
To the extent that any of these routes depend on pressure and density, it is apparent that the amount of temperature change obtained for a given energy input will be a variable quantity. It may well be that the authors have identified the extent to which this is true, thus possibly explaining their “enhancement” effect, at least in phenomenological terms.
/dr.bill
dr.bill:
Thankyou for your helpful post at December 30, 2011 at 10:58 pm.
As an addition to that I copy here something I wrote on the other thread to avoid it being missed by those who only read this thread.
The Jelbring Hypothesis (now also presented by Nikolov & Zeller) amounts to the following.
‘All the radiative, convective and evaporative effects in a planet’s atmosphere adjust such that the atmosphere obtains a temperature lapse rate approximated by –g/cp, and this lapse rate defines the planet’s average surface temperature. The average surface temperature is observed to agree with the Jelbring Hypothesis on each planet with a substantial atmosphere that has a mass which varies little through the year.’
Clearly, some effects (e.g. convection) do adjust. At issue is whether the interaction of all the radiative, convective and evaporative effects provides the suggested adjustment.
Happy New Year
Richard
@ur momisugly dr. bill
> … radiation is absorbed by the molecules of a gas …
> (1) Translational Energy,
> (2) Rotational Energy,
> (3) Vibrational Energy,
> (4) Electron Transitions.
>
> Only (1) is involved in determining temperature.
That is incorrect. At the molecular all three degrees (translation, rotation and vibration) of kinetic freedom contribute to heating. Proof: microwave ovens exploit the vibrational degree of water dipoles to heat your food and beverages.
http://en.wikipedia.org/wiki/Heat_capacity#Degrees_of_freedom
So how is the kinetic energy distributed among these degrees of freedom? Good question. For starters read up on the Equipartition Theorem, which holds, up to quantum effects, for most substances:
http://en.wikipedia.org/wiki/Equipartition_theorem
😐
By the way, I have realized that Nikolov and Zeller’s calculation of the “natural greenhouse effect” (and, in particular, the temperature in the absence of a greenhouse effect) done here is basically the same as that performed by Gerlich and Tscheuschner in their paper and it is wrong for the same reason: It assumes no heat storage or transport, i.e., that the local temperature is determined purely by the local insolation. While an Earth without greenhouse gases might have a larger temperature range than the current Earth, it is hard to imagine it being particularly close to the assumption that is made. A better way to look at things is what actually is done by the climate science community: To calculate what the average temperature would have to be if the temperature were uniform across the Earth’s surface and then to note that to the extent that the temperature deviates significantly from this, Holder’s Inequality tells us that the average temperature would be lower than this value.
At some point someone seems to have decided that atmospheric composition involving radiative processes makes a significant difference to the temperature set by thermodynamic and gravitational influences.
I think one can deal with the resulting confusion by accepting BOTH scenarios but putting them in proper proportions.
As I see it the GHG aspect is in the air only and the gravitational pressure aspect is in air and ocean but mostly in ocean.
Gravity is blind to anything other than mass so the thermal characteristics of GHGs are an irrelevance to that portion of the story.
Since downwelling IR from GHGs cannot get into the oceans it is limited in its effects to the air but the oceans control air temperaure.
The only way the system could deal with the GHG portion of the effect is to alter the rate of energy flow from surface to space.
In other words the GHGs fractionally alter the balance between sea surface and surface air temperatures by increasing the energy content of the air (mostly in the form of latent heat) and reducing the energy content of the oceans by converting incoming solar energy to longwave before it can get into the oceans.
The system then has to correct that GHG induced imbalance between sea surface and surface air temperatures and must do so by shifting the surface air pressure distribution and the positions of the permanent climate zones.
I think that tops and tails it very effectively.
But the GHG effect remains miniscule compared to what sun and oceans achieve on multicentennial timescales.
Joel Shore:
At December 31, 2011 at 6:41 am you present a ‘straw man’ when you write:
“By the way, I have realized that Nikolov and Zeller’s calculation of the “natural greenhouse effect” (and, in particular, the temperature in the absence of a greenhouse effect) done here is basically the same as that performed by Gerlich and Tscheuschner in their paper and it is wrong for the same reason: It assumes no heat storage or transport”
NO!! It assumes no such thing. Have you never heard of convection?
There are some good arguments against the hypothesis. Please provide a good argument instead of imagining one that does not exist. In other words, please try to think before making a post.
Richard
The principal reason why “Venus managed to hold its thick atmosphere” is because of its lack of aerobic lifeforms which convert atmospheric carbon dioxide into biosphere mass and deposits of carbon compounds and oxygen compounds into the lithosphere and atmosphere, and oxygen into the atmosphere.
The Solar planets began with atmospheres dominated by the high proportion of Hydrogen and Helium and some other components such as methane present in the primordial Solar nebula from which they coalesced by gravitational accretion.. These first atmospheres underwent immediate change as the Solar wind of the awakening Sun stripped the inner planets of much of their lightest atmospheric gases, Hydrogen and Helium, creating the planets’ second atmospheres.
The Earth’s second atmosphere has been described as being about 100 times greater in mass than Earth’s present atmosphere, and it was composed of nearly all carbon dioxide. Nitrogen, Oxygen, and other gases were present in only trace amounts. Oxygen could not exist in the Earth’s second atmosphere in any but very minor trace amounts, because there was too much iron and other reactants present which combined with what little oxygen was released to produce iron oxide or rust and other compounds. When aerobic life consumed nearly all of the atmospheric carbon dioxide, the exhaled oxygen combined with the available iron in the lithosphere to create the great beds of iron oxide minerals mined for iron today, and Oxygen began to accumulate in the atmosphere in large percentages once the available reactants had been saturated with Oxygen.
Surface air pressures in the massive carbon dioxide dominated second atmosphere were staggeringly heavy, and the effects upon optics, geochemistry, geomorphology, weather, and hydrodynamics were somewhat alien to current understandings of the Earth’s current environment. Venus and Mars retained remnants of their massive carbon dioxide dominated second atmospheres because they didn’t have Earth’s kind of experience with aerobic lifeforms eating all but trace amounts of the carbon dioxide out of the atmosphere.
There are a number of fatal problems with this stuff. First off, they use a very simplistic model and then start to overcomplicate it and try to do a rather advanced analysis on it that appears to be unrelated to the foundational physics. They then come up with wild answers that should be a warning of fatal errors yet they make the claim that there is a problem with the conventional result, that of 133 C rise due to ghgs and the presence of the atmosphere.
It appears the problem concerning this 133 deg C value rather than the conventional 33 deg C occurs because of eqn 2. It would seem they are integrating over a sphere assuming a unit radius (or surface area) and only integrating over half the sphere. That is the integration range of 0 to 1 for du, a cosine function. That’s an integration of 0 to pi/2 (or 0 to 90 deg) which would be half the sphere. Double the value and one finds a result that is about 3 deg C higher than the 287 or 288 K.
Another obvious ‘problem’ is their inclusions of the background radiation of cs = 13.025×10^-5 and since that adds to the solar incoming power and referenced with the microwave background radiation caused by 2.72K temperature of space radiation, one can assume this number must be the incoming power due to that source. The give away is that the accuracy of the incoming solar is assumed only to 1 W/m^2 and the value they provide is 0.00013025 W/m^2. This is far too many significant figures tosssed in for an accuracy that can be no better than +/- 0.5 W/m^2 and quite frankly, that accuracy value is dreaming because we don’t know the average solar flux to that accuracy nor do we know the albedo to that level. This is a freshman physics class error. Also, if we try to use S-B to find the incoming power from the microwave background radiation of the universe, we have a number that comes out to be 0.3 x 10^-5 W/m^2 and that suggests that either the constant is improperly described or calculated incorrectly.
At present, I don’t see any reason to continue going through their presentation as it appears to be totally FUBAR.
John Day, December 31, 2011 at 6:28 am :
Gas molecules, John, gas molecules…
Liquids and solids have their own rules for degrees of freedom.
/dr.bill
REPLY
The Earth’s second atmosphere has been described as being about 100 times more massive than the present atmosphere, and it was composed of almost all carbon dioxide. Methane, nitrogen, and the other gases were trace amounts by percentage of the second atmosphere. This second atmosphere lasted a couple of billion years from not long after the Earth was formed to about 2.2 billion years ago. Aerobic lifeforms developed, and they ate the atmospheric carbon dioxide until its percentage remaining in the composition of the atmosphere was reduced to only trace amounts about 2.2 billion years ago. Where the atmospheric carbon dioxide concentration was once something like 966,000 parts per million in the second atmosphere 100 times more massive some 4 billions of years ago or less, it was reduced to the current 300-400 parts per million in the recent centuries. During the last 550 million years, the carbond dioxide concentrations have varied fro around 6,000 or 8,000 parts per million to less than 200 parts per million during the latest ice ages.
That’s simple. You change the atmospheric mass.
The Earth’s second atmosphere was something like 100 times more massive and composed of almost all carbon dioxide. Aerobic life ate the atmospheric carbon dioxide, removing its mass from the atmosphere.
On the temporal scale of the past century or centuries, atmospheric mass is constantly being added and subtracted by a number of natural events. One of the most important examples if the water cycle, which is constantly exchanging mass between the atmosphere, hydrosphere, cryosphere, lithosphere, and biosphere. These exchanges affect orbital mechanics by tidal influences on the hydrosphere and atmosphere, atmospheric pressure distributions by wind, oceanic thermal distribution by currents, and much much more.
No, the atmosphere was about 100 times more massive, and it was composed of almost all carbon dioxide. Aerobic life ate the carbon dioxide, removing it from the atmosphere. The one percent of the atmosphere remaining to day was enriched with oxygen from the biosphere converting the carbon dioxide and returning oxygen to the atmosphere. Oxygen could not persist in the second atmosphere, because the rocks and other minerals reactive to oxygen rusted or reacted to remove the oxygen as fast as it was released into the atmosphere. It wasn’t until the biosphere released enough oxygen into the atmosphere from the conversions of carbon dioxide to rust all of the iron into the geological iron band formatons that free oxygen was able to accumulate in the atmosphere. During the great extinctions, however, the biospheric production of oxygen was interrupted and oxygen concentrations fell to dangerously low levels. Likewise, the biosphere keeps consumes carbon dioxide until the trace amounts become too low to support the life forms dependent upon carbon dioxide.
Atmospheric pressure can never reach equilibrium so long as the Earth has an atmosphere. Equilibrium of the atmosphere requires a static atmosphere. The atmosphere can never become static due to orbital mechanics, Coriolis force, tidal forces, mass exchanges of water in and out of the atmosphere, biosphere variability, and more. The atmosphere will always seek equilibrium and never attain it.
A little historical note you have touched upon. In 1970-1972, a handful of us representing futurist groups lobbied Congress to get the appropriations to build the Space Shuttle Transport System. We made our case before the U.S. House of Representatives Space and Aeronautics Sub-Committee with publications and presentations. They were impressed enough to invite take us over to NASA and speak with Dr. Fletcher and onwards to dinner, (where a grilled cheese sandwich cost $30.00), for further discussion of the space program goals. Present at the dinner were Senators, Congressmen, a NASA Deputy Director, and President Nixon’s White House representatives. We were more than a little surprised by all of this attention, having expected to be gently patted on the head and then studiously ignored after the committee meeting. On the contrary, it was a very unexpected event.
The political background going before the Congressional subcommittee was very very discouraging. The Nixon Administration and the Republican Party were not really wanting to take on a major budgetary increase for a new NASA program, especially with the budgetary problems being faced at the time. They could see merit in the ideals, but the budget and political hurdles and obstructions the Democrats were threatening to employ diminished the Republican enthusiasm for what they saw as a non-essential program. The Democrats were generally opposed to using the budget to fund a NASA program giving a Republican Administration good public relations for years to come and reducing the funds available for the Democrat’s social welfare projects. So, we were warned the idea of continuing the space program, especially a manned spaceflight program, with major funding was an unwelcome idea with both of the major political powers.
At the dinner, however, we were met by leaders from both parties and houses in Congress, and they let us know they wanted to hear our ideas about the future of manned spaceflight and the role of one of the three proposed space shuttle designs. When my turn came to speak, I explained why it was vital for humanity to expeditiously develop a permanent presence and communities beyond the Earth before one of many catastrophes I named could destroy the current civilization and humanity’s opportunity to ever again develop the technological capacity to colonize new homes beyond the Earth and insure the survival of humans. It may please you to know that this argument was well received and enthusiastically agreed upon by many of the government leaders at that dinner. They shared your own sentiments.
While we were mildly disappointed by their subsequent choice of the lowest cost design proposal at the insistence of President Nixon, we were more than pleased to have contributed at least some small effort towards seeing to it that the two political parties did not kill manned spaceflight or at least some form of the space shuttle. After the 1971 cancellation of NASA’s manned spaceflight to Mars in 1987, the future of manned spaceflight was very much in debate and doubt at the time.
Regarding the moon, 255K:
http://www.asi.org/adb/02/05/01/surface-temperature.html
Otherwise, I think the water is key. We don’t have another example with water to compare to.
“”””” Bill Illis says:
December 29, 2011 at 2:51 pm
The back radiation measured at 2 metres height, originates millimetres to a few metres above the instrument.
The molecules at this level are colliding with each other 6.7 billion times per second, many times faster than the average relaxation/emission timeline for GHGs.
The backradiation is coming from all the gaseous molecules since the emission spectrum for backradiation is very close to a blackbody spectrum (at the temperature of the 2 metre air) – Not the signature of CO2 or H2O high up in the troposphere as so many people assume.
When it is not cloudy, (35% of the time), there is small loss in the atmospheric window region, but when clouds are present (65% of the time), it is a perfect blackbody spectrum. “””””
Bill,
I take it from your wording, that YOU have actually observed/measured the “back radiation” or “down radiation” from the atmosphere, and in your final sentence you say it is a “perfect blackbody spectrum”.
Can I assume that you mean by that, that the wavelength or frequency dependent spectrum of such observed back radiation actually matches the calculated Planckian spectrum corresponding as you say, to the Temperature of the atmosphere, in the immediate vicinity of the instrument ?? Of course, one would not expect the spectral radiant intensity or irradiance, to match that computed for a true black body at that Temperature; but the frequency spectrum should.
Now why is it, that YOU and I seem to be the only people around these parts, who seem to believe that the ordinary atmospheric gases, N2, O2, and Ar, DO in fact radiate a continuum thermal spectrum, that is characteristic of the Temperature of those molecules; as distinct from the resonance molecular spectra of the GHGs that have or can adopt a sizable non zero electric dipole moment. H2O of course has a permanent non zero moment, and CO2 which is symmetrical in the ground state, can easily adopt a non zero moment, by bending; as in the 15 micron band, or assymmetrically stretching, in the 4 micron band.
I have pointed out now several times here at WUWT, that the ordinary neutral gases, even Argon, that are charge symmetrical in the free flight state, become highly assymmetrical during collisions between molecules; which of course are the characteristic of TEMPERATURE, since the molecular nuclear mass is about 3675 times as massive as the electron cloud, so all the momentum is in the nuclei, not the electron cloud, so the nuclei simply continue on during a collision, while the electron clouds repel, and decelerate, and eventually reverse in a head on collision; so the colliding molecules develop a varying and decidedly non zero electric dipole moment during a collision, and that is all that is required to radiate EM waves according to Maxwell’s equations. What the particle physicist sees as an accelerated electric charge; which MUST radiate, the Radio-Physicist, sees as a time varying electric current flowing for a non zero distance, aka a radio antenna; which also must radiate.
The exact same mechanism, also allows those colliding molecules to absorb EM radiation, which also can have a frequency or wavelength continuum spectrum, as distinct from the molecular line spectra of polar molecules.
Can you describe the type of spectrometer equipment that is used to make such measurements as you apparently have observed. I’m almost ready to go and buy my own damn spectrometer, and go make the observations myself.
I’m encouraged to hear that you seem to have actually observed, what I have only theoretically presumed MUST happen.
One final point; you say when there is cloud cover, that the spectrum is true BB shape, but absent clouds, there is some line specral leakage. Does that mean that the clouds are not the source of the observed down radiation spectrum, but simply block the energy escape via absorption and then thermalize it to establish an atmospheric Temperature ?
I must say that this post of yours, is probably the most valuable single post of this whole double thread about this alleged “unified theory” of climate.
If you would care to comment off line about these observations, you have my permission to ask Anthony for my working e-mail, and I hereby give him permission to give you that.
Thanks
George
http://climate-change-theory.com says:
December 29, 2011 at 7:45 pm
Myrrh says “Wjat I would like to see … is the real basic properties and processes discussed in English”
Try my site: http://earth-climate.com and (seriously) I would appreciate feedback on anything you or others question, as this will become the basis of a planned small “simple English” book.
Thanks, I’ll take a closer look at it. But what concerns me is that the ‘basic physics’ as presented by the AGW crowd is being taken seriously by non AGW crowd and I think the discussion needs to go back to this in basic English… For example, as shown in this discussion, y’all (generic) seem to have bought into the nonsense that visible light heats land and oceans.., a physical impossibility in the real world, and the water cycle is missing completely which cools the Earth by 52°C, and this mythical background well mixed CO2 which magically defies gravity to accumulate for hundreds and thousands of years and never joins in the the cooling of of the Earth because it never joins the water cycle in evaporation and rain and fog and dew (all pure clean rainwater is carbonic acid) but again somehow magically gets taken into ‘carbon sinks’ in this static fanatasy world without convection, etc. etc.
The problem is not so much the maths, but maths which describes and has nuanced arguments about nonsense concepts, it’s the concepts that have to be cleared up first because unless it can be shown to make sense in common language the maths just makes it appear that something intelligent is being said when no such reality in place..
Lucy Skywalker had a project going to get a web site up with counter arguments, don’t know if that is still happening, but you could add your book’s info to it in some form perhaps.
.
Ok, at low density/temperature, molecular gases may behave like monatomic gases. But in general, in gases where the molecules collide, vibration and rotation also contribute to the internal energy of a gas, 1/2 kT per degree of freedom.
So I would still quibble with your assertion that ‘only translational energy is involved in determining temperature’. The gas molecular energy is transferred among the different degrees of free according the Equipartition Theorem, such that the energy is equally distributed. If I could somehow make the molecules vibrate faster, that raises the internal energy and is shared with the other degrees via collisions, and the temperature goes up accordingly.
I invite you to read Tom Vonk’s excellent post on LTE (local thermal equilibrium) for more info on this:
http://wattsupwiththat.com/2010/08/05/co2-heats-the-atmosphere-a-counter-view/
Vonk’s post should also be of interest to D. Patterson et al. because it shows how the atmosphere can be in equilibrium locally.
Richard S Courtney says:
Perhaps you misunderstood what I was talking about: I was talking specifically about their calculation of the average surface temperature in the absence of a greenhouse effect that they gave in the section entitled “Magnitude of the Natural Greenhouse Effect.”
But, since you asked the question seemingly about their larger hypothesis: Convection does not explain how the Earth and its atmosphere could be absorbing 240 W/m^2 but emitting 390 W/m^2, unless you are suggesting that convection transfers heat from the colder atmosphere to the warmer Earth surface, which would of course really violate the Second Law of Thermodynamics.
cba says:
I hate to be defending this silly paper…but they did not make the factor of two error that you seem to think they did. Their integration is correct for what they are trying to do, but what they are trying to do is silly: I.e., they are calculating what the average surface temperature of the Earth would have to be if radiative balance had to be satisfied locally, i.e., if the local temperature were determined by the local (and instantaneous) insolation. It is a pretty silly approximation but they have done the calculation correctly as near as I can tell and have obtained about the same answer that Gerlich and Tscheuschner obtained for the same calculation (except neglecting the 3 K background temperature). And, they have gotten an answer that obeys Holder’s Inequality, whereas your proposed result does not.
Their result is wrong because it is too naive conceptually, not because they made any calculation error.