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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UPDATE: This thread is closed – see the newest one “A matter of some Gravity” where the discussion continues.
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Robert Murphy says:
January 5, 2012 at 3:10 pm
That’s nuts. What do you think would happen to life on Earth as a result of this reduction by 53% of the Earth’s atmosphere? Did you think of that?
====================================
It evolved.
Joel Shore, January 5, 2012 at 3:07 pm :
So then, your multi-day tour de force has produced the following:
You started with: “This is all nonsense.”
And now you say: “OK, ¾ of it is obvious, but the other ¼ is still nonsense.”
Hmm…
/dr.bill
Joel Shore, January 5, 2012 at 3:07 pm :
So then, your multi-day tour de force has produced the following:
You started with: “This is all nonsense.”
And now you say: “OK, ¾ of it is obvious, but the other ¼ is still nonsense.”
Hmm…
/dr.bill
Joel Shore;
You have correctly concluded that averaging T^4 is better than averaging T and yet you are going with N&Z, who have defined the temperature by averaging T>>>
But they didn’t.
They averaged the fourth root of T which for the way they went about their calcs is the right way to do it. I used average of T^4 in my explanation, but averaging 4th root of T works just as well.
It is right there in their description just prior to equation 2, followed by equation 2 itself. You can tell Joel by that big box in the first line with the hook shape on the left hand side and the number FOUR written beside it. That would be high school math, would it not?
You’ve now managed to dispute their results by claiming they used a mathematical construxt which they most certainly did not.
I’m going to assume that it was a mistake on your part rather than a deliberate attempt at misdirection.
I know you’re probably speechless right now, having a PhD in physics and all and losing an argument to a dim wit computer salesman who learned calculus so long ago that slide rules were high tech, so let me help you out. I think the words you are looking for are:
Sorry. I was wrong.
OzWizard,
I apologize for not coming back to look at this thread for so many days. I wasn’t ignoring you anyway–the duel at 10 paces worried me, though!
The Venusian atmosphere is not structured cool at the surface and hot higher up. It is a gradual decrease from surface to about 60km above the surface. What I am saying is that on Venus the temperature of the atmosphere at 60km elevation is very high (where it is around 250-260K )compared to what it is on Earth at the tropopause (230K). Incoming irradiance is scattered and absorbed quite high in the atmosphere, not much reaches the surface. The atmosphere is not transparent to incoming irradiance, the atmosphere on Venus is like 90 times the mass of that on Earth, and even at 60km it is not especially “thin” (pressure is about 300mb at this height). But enough irradiance does reach the surface to drive convection. The adiabatic lapse rate resulting from this convection, projected from the temperature 60km above the surface (where the convection must end) leads to a very high surface temperature. Let me make my point in another way.
If, somehow, the Earth’s atmosphere were to absorb more radiation at 10km (top of troposphere) and reach a temperature that is, say 10K higher than at present, and the current lapse rate to be maintained (the result of a variety of processes including convection) then the surface would be 10K warmer also. This additional absorbed radiation could have come from LWIR welling up from ground surface (a greenhouse effect), or from Solar irradiance if there were gases that could absorb such.
Joel Shore would maintain that this is all “greenhouse effect” on Venus, that IR absorption by CO2 determines the high temperature at 60km height, but I am not so certain it is entirely. Venus has 90 times as much atmosphere, the atmosphere is not transparent to SW, and it is composed of not only CO2, but also sulfur compounds. I’m rambling a bit here, so I’ll stop, but I just wanted to make my point more clear.
Joel Shore;
Sorry…This is a little unclear. What I mean is that it is impossible for the Earth’s surface to be at a temperature of 288 K and for the Earth + atmosphere to be emitting only 240 W/m^2 as seen from space unless there are GHGs>>>
Wake up Joel. 288K is the average of T which you’ve already admitted is a math error. If there are no GHG’s the temperature of the earth is 255K plus the “ehancement” due to conduction/convection. If there are GHG’s, then the temperature of the earth surface is 255K plus the “enhancement” due to conduction/convection plus the enhancement due to GHG back radiation MINUS the reduction in conduction/convection due to REDUCED conduction/convection as a by-product of back radiation.
Catching on yet?
words…sorry….wrong….
davidmhoffer says:
It is hard to know how one can pack so many incorrect statements into two sentences. Let’s deconstruct this, shall we:
(1) It is not the 4th root of T; it is the fourth root of a something having the units power per unit area divided by the appropriate constants. Taking the fourth root gives you a temperature (since the power is proportional to T^4); that is what they averaged.
(2) Why would that work just as well as averaging something directly proportional to the power? You were complaining before that the should have been averaging the appropriate power of the temperature (T^4) so that they are averaging P instead of averaging the temperature. Now, all of a sudden, it simply doesn’t matter; apparently, averaging temperature to the power of pi would be fine and dandy if that is what they did. [In fact, it is interesting, because what you have claimed is that averaging T^(1/4) power is just as good as averaging T^4 power. Now that I have shown you that they are averaging T, and assuming you are willing to admit the obvious, I imagine it will turn out that averaging T “works just as well”.]
Let me explain to you what they did, since you seem to have no actual conception:
(a) They computed the local insolation at each point on the Earth. This is an incoming intensity in W/m^2.
(b) They then derived a temperature from this by dividing by epsilon*sigma and taking the 4th root. This means that they are simply assuming that the temperature at that point is determined by the local insolation at that particular point, at that particular time, i.e., that there is absolutely no storage or horizontal flow of energy.
(c) They averaged the resulting temperature distribution over the earth’s surface.
David, I am not losing this argument amongst anybody who actually has the ability to follow this….And, I think you know that.
davidmhoffer says:
What I and Willis have very patiently tried to explain to you is that for an Earth-like temperature distribution, the difference you would get for the temperature between averaging T and averaging T^4 and then taking the 4th root is very small. If you want to argue that we should really be saying 289 K or 287 K, I won’t dispute you.
There is no enhancement due to conduction / convection. 255 K is the absolute maximum average temperature that the Earth can have and be emitting 240 W/m^2. It can have considerably lower temperatures if the temperature distribution is quite uneven but it cannot have any higher temperatures.
“Joel Shore says:
January 5, 2012 at 10:37 am
The most important thing for anyone to understand about energy balance is that it is the top-of-the-atmosphere energy balance that is fundamentally the most important. It is much easier to figure out what happens with that and then work down to the surface than it is to figure out the surface on its own. This is because the surface energy balance is complicated, since it involves conduction and convection (including evaporation) as well as radiation. The top-of-the-atmosphere balance involves radiation only.”
A fundamental energy balance based on conservation of energy does not exist. Energy balances are the result of the Second Law not the First. The Earth could stop radiating and start accumulating energy until it gets as hot as the Sun, the energy will be conserved. There is no direction for an energy flux in a Universe without a Second Law.
There is no balance at TOA, but rather one throughout the system mostly developing near Earth surface. Radiation from the Sun enters and gets absorbed at the surface (or reflects). Emission will follow only because of the Second Law when energy can get dispersed (entropy), and this is a fast process.
But a large part of the energy dissipates (entropy); flows into the ocean, vaporizes water, heats the atmosphere – , is used in chemical processes/photosyn., doing work, maintains hydro-/carboncycle etc. often followed by other processes and interconnected. All these have various speeds (up to years, or hundreds in the ocean) and are governed or balanced by the Second Law.
So there is a multi-faceted time varying energy balance by Second Law at work, mainly from the ground up that eventually works it’s way up and leaves as downgraded radiation. So there is no surprise that over a certain time frame (but how long?) radiation in = radiation out, and real time differences tell you nothing about what’s all happening inside. You can’t derive temperatures from it, certainly not for the small mass of the atmosphere.
Earth system does not care about a radiative balance at TOA, all processes one by one including weather follow the path of dissipation of energy and have no knowledge of an outside TOA balance and do not respond to such a thing.
The energy fluxes respond to gradients of temperature, pressure and concentration. The Second Law tells which way to go but even then it is not clear at which speed the processes will take place. Nature has all these speed bumps otherwise all energy would dissipate in a jiffy. So we have activation energy for the chemical processes, and the speed of the atmospheric transport from equator to poles seems not to be simply correlated to dT or dP but happens under the Maximum Entropy Production Principle.
I thought I should lay out my idea for a maximum greenhouse effect (GHE) here on the UCT thread. My idea is simple. Rather than the findings of Nikolov and Jelbring being independent of the GHE they describe a method to discover the maximum possible GHE.
This way of thinking about the UCT eliminates the problems that would occur when one tries to discuss an atmosphere without GHGs. It also accepts that the work of climate scientists for many years is completely valid up to a point. Finally, it provides what many skeptics have seen in the data. Temperatures do not follow CO2 variations. The currently defined GHE just isn’t showing up in the data.
The idea is pretty simple. The GHE starts off strong when a few GHGs are added to an atmosphere. However, as the concentration grows the added effect becomes smaller and approaches the maximum GHE (maxGHE) asymptotically. Eventually, the gain becomes inconsequential.
It turns out the maxGHE is defined by the atmospheric mass and surface pressure for any given value of solar input. The reason the UCT initially thought the heating was independent of GHG concentration was due to the fact that different mixes of gases on different planets all led to the same predictable temperature profile. However, Willis supplied the thought process that demonstrated a planet surface could not warm without GHGs. Hence, there had to be some kind of relationship to GHGs. The concept of a maxGHE allows many different atmospheres to give the same temperature profile as long as they have sufficient GHGs to reach the maxGHE.
@Kevin Kilty (January 5, 2012 at 7:12 pm): I’ll address your question in two parts –
(1) Is the issue you talk about relevant to the current discussion?
The answer here is clearly NO. We have explained that the highest average temperature that you could possibly have for any distribution that radiates 240 W/m^2 is 255 K. We know that the average temperature of the Earth is somewhere around 288 K. Whether it is actually 287 or 289 K won’t make a difference.
(2) Is the issue that you talk about relevant to the issue of temperature trends under global warming?
Basically, the issue that you raise is closely related to one that was raised by Essex et al.: http://ruby.fgcu.edu/courses/twimberley/EnviroPhilo/Exist.pdf The only real substance of their paper applied to real world data was when they looked at temperature trends for 12 different stations and purported to show that different ways of averaging produced different trends. In order to demonstrate this, they averaged T^r where r is a positive or negative integer and then took the rth root. When they made r really large in magnitude (either positive or negative), they did find a substantially different trend, but by really big or really small, you have to understand that they used a range of r going from -125 to +125. If you look at their data and just compare r=1 and r=4 (which is what we are talking about here), the difference in the trend is not very large.
Furthermore, it is easy to diagnose why the trend did change when they made r really big in magnitude: When r was a large positive value, their average essentially just put all of the weight on the highest temperature data point for each month in their temperature series. When r was a large negative value, their average essentially just put all of the weight on the lowest temperature data point for each month. Clearly, this is not going to be a good average and when you have a relatively sparse set of 12 temperature records, this can produce a large effect…but when you have hundreds of temperature records it will be more difficult to weight just one temperature each month and there is very good reason to believe that the effect will be largely washed out. [And, at any rate, as I noted, even for 12 records, the effect was only very dramatic if you started choosing ridiculous values of r, not if you chose 4 instead of 1.]
And, it is not hard to understand why this is not going to make a large difference: Yes, you might be able to get a difference of a degree or two for an Earth-like temperature distribution depending on how you do the average. However, your temperature distribution is not going to radically change as the Earth warms…To the first approximation, the distribution will just shift to warmer temperatures while not changing shape. To a better approximation, there might be a small change in the shape of the distribution (e.g., because the arctic warms faster than the tropics) but this is change in shape is going to be very small (after all, we’re not expecting the arctic not to be cold and the tropics not to be hot).
A good analogy might be if I tried to use a yardstick that was off by 1 inch over its 36 inch length to measure how much a bar of length 30 inches expanded when it was heated. If the bar expanded by only, say, 1 inch, you might worry that this ruler was not up to the task since it is off by 1 inch! However, with a little thought, I think you can convince yourself that in fact this ruler will be able to correctly measure how much the bar expands to within less than 3%.
Ned Nikolov says:
January 5, 2012 at 2:09 pm
Reply to Robert Murphy (January 5, 2012 at 12:24 pm)
Robert,
I address the Mercury and Mars temperature issues in my official reply. But here is the situation in a nutshell. The Mercury temperature of 440K reported by NASA is an estimate using the S-B equation, and not based on actual observations. As such, it suffers from the same problem as the 250K estimate for the Moon temperature – an incorrect application of the S-B law! So we used our Eq. 2 to estimate Mercury’s termperature.
Which has a blatantly false model for the temperature distribution which leads to a large underestimation, a far larger error than the assumption of a uniform temperature. The assumption of a Lambertian profile for the sunlit hemisphere is a good one for an atmosphere-less planet as is demonstrated by the data from the Moon. Your assumption of the dark side being at absolute zero is a huge underestimate as is demonstrated by the data you quoted for the Moon (which would be a close candidate with its long night). It is this assumption which leads to an error of ~100K in your estimate for the Earth.
Phil. says:
Joel, the Lambertian profile is basically how you described it, a cos^0.25 profile, for the Moon it’s a good approximation and for a planet without an atmosphere it should be good. The real problem with N & Z is the assumption of absolute zero for the dark side which is absolutely terrible however!
Phil and Joel,
About the temperature of an airless planet:
Apparently you are confusing (unable to make distinction between) a temperature DISTRIBUTION over the surface of a body and the MEAN temperature of that body. The mean temperature depends on the shape of the celestial object (e.g. sphere vs. flat disk) and the distance of the object from the Sun. Those two factors along with the albedo are responsible for the amount of solar energy absorbed by the object. The DISTRIBUTION of the temperature across the surface, on the other hand, depends on thermal properties of the substrate of the object such as thermal capacity and thermal conductivity as well as on the speed of axial rotation (faster rotation will produce a more uniform temperature field, while a slow or absent rotation will result in a highly non-uniform ‘contrast’ temp environment).
Our gray-body model in Eq. 2 assumes a non-rotating planet that has reached an equilibrium with the incoming solar radiation. This assumption is ‘bad’ only if one is concerned with the surface temperature distribution, but has no consequence whatsoever if one is interested in the MEAN planetary temperature. Think about it …
Any real rotating planet with no atmosphere will have a temperature on the dark side greater than 0.0K. In fact, the lowest temperature in Deep Space is about 2.72K, and not zero. This is accounted in our model by the small constant added to So. If So = 0, Eq. 2 produces 2.725K.
After talking to Dr. Siegler yesterday (the person in charge of the Diviner lunar temperature data), he agreed that the mean diurnal temperature on the lunar equator is around 210K (in fact his own estimate was 206K), and that the mean diurnal temp. at the lunar poles is about 100K. So, the moon average diurnal temperatures span the range 206K – 100K, which gives a mean of (206 + 100)/2 = 153K. Our Eq. 2 produces 154K … In reality, the true MEAN temperature of the Moon may be shifted a bit towards the warmer side (206K) due to the spherical distribution of the temp. field, and it may deviate somewhat above the arithmetic mean of 153K, but it will still be MUCH closer to our theoretical estimate than to the 250K currently believed by climatologists … What’s amazing about the 250K is that this temperature as a diurnal mean does NOT occur ANYWHERE on the surface of the Moon!
So, please drop your arguments and embrace the reality.
Thank you!
Ned Nikolov says:
I have thought about it and it is a manifestly silly statement. In fact, there are plenty of different temperature distributions that result in the same power output from the surface (which is what is constrained by the solar input). In general, these will not have the same mean temperature. In fact, two that clearly do not are your distribution and a uniform temperature distribution (the former giving the mean temperature that you got and the latter giving the standardly-assumed blackbody temperature of the Earth of 255 K)…They differ by 100 K! [I am a little confused about what you used for the albedo and epsilon in your model…but this doesn’t really seem to matter since others who have used the conventional values of alpha = 0.3 and epsilon = 1 report about the same mean temperature as you.]
The reason this is so, of course, is because the 4th root of the average of T^4 is not the same as the average of T for any distribution T other than a uniform distribution.
Ned
You need to get a grip on reality yourself, a strange way to average for the surface of a sphere, what do you suppose the relative areas of the poles and the tropics are? Your idea that your model produces a true mean for a rotating planet is a fantasy as demonstrated by the Moon.
Ned: While you are stopping in here, would you mind telling me what values of alpha_gb and epsilon you used for the planets in order to calculate your T_gb? I find that I get pretty close to your T_gb if I choose and alpha_gb = 0.125 (which you mention in the context of earth) and epsilon = 0.949 for all of the celestial bodies. Is this what you used and where did the values for these two parameters come from?
Thanks,
Joel
…Never mind my last question…I see now where you say what epsilon and alpha_gb you chose.
Mr. Shore, the highest temperature one can have is not 255K on an earth without atmosphere, but depends on other factors. It could be well over 325K if the region most directly illuminated radiates away its absorbed energy. It is a maximum of 255K only if you demand that the earth radiate uniformly, yet transfer absorbed heat perfectly; but it does not, wouldn’t even if the rest of your assumptions held true. It radiates much more strongly beneath the sun, and much less so at night. The moon does so as well. I have attempted to show that there is a range of mean temperature that is compatible with equilibrium at any given irradiance/albedo/etc. If one drifts from one such configuration to another mean temperature will rise or fall–perhaps by enough to be significant in terms of our ongoing AGW debate.
I say the places that actually act as radiators, be they polar regions, deserts, equatorial ocean, or cloud tops, will affect the mean temperature even if driving does not change one iota. I say the actual distribution of temperature matters–you say it hardly does. We have reached the end of this discussion, I suppose.
Kevin Kilty says:
January 6, 2012 at 6:24 pm
Joel Shore says:
January 6, 2012 at 5:27 am
@Kevin Kilty (January 5, 2012 at 7:12 pm): I’ll address your question in two parts –
Mr. Shore, the highest temperature one can have is not 255K on an earth without atmosphere, but depends on other factors. It could be well over 325K if the region most directly illuminated radiates away its absorbed energy. It is a maximum of 255K only if you demand that the earth radiate uniformly, yet transfer absorbed heat perfectly; but it does not, wouldn’t even if the rest of your assumptions held true.
Joel is talking about the average temperature for which the maximum value corresponds to a uniform distribution because of the non-linearity of the response.
It radiates much more strongly beneath the sun, and much less so at night. The moon does so as well. I have attempted to show that there is a range of mean temperature that is compatible with equilibrium at any given irradiance/albedo/etc. If one drifts from one such configuration to another mean temperature will rise or fall–perhaps by enough to be significant in terms of our ongoing AGW debate.
I say the places that actually act as radiators, be they polar regions, deserts, equatorial ocean, or cloud tops, will affect the mean temperature even if driving does not change one iota. I say the actual distribution of temperature matters–you say it hardly does. We have reached the end of this discussion, I suppose.
Joel doesn’t say that the distribution doesn’t matter, on the contrary he says that it does, what he does say is that the distribution which gives the highest mean temperature is a uniform distribution.
Keven Kelty says:
For a surface emitting an average of 240 W/m^2, I am not saying the highest temperature that exists on the planet can’t exceed 255 K. Sure it can. I am saying the ****AVERAGE**** temperature can’t exceed 255 K. If the planet is at a uniform temperature, then that uniform temperature is 255 K; if the temperature is non-uniform then the average temperature will be less than 255 K. This is due to a rigorous mathematical theorem called Holder’s Inequality that, applied to this problem, tells us that the fourth root of the average of T^4 is always greater or equal to the average of T for any distribution T.
If you want to see how this works, try some simple distributions. For example, look at a planet where the dark half of it is at 0 K and figure out what the other half has to be if this other half is at uniform temperature in order to get an average emission of 240 W/m^2. What you will find is that it has to be at 303 K. This gives an average temperature of the planet of 152 K, which is much less than 255 K. This example also shows you why it works out this way: Because power emitted depends so strongly on temperature, the fact that you have to emit twice as much power (480 W/m^2) on the bright side of the planet in order to have the average over the planet work out to be 240 W/m^2 does not necessitate going to a temperature of twice 255 K…You only have to go up from 255 K by a factor of the fourth root of 2.
Yes…The distribution does indeed matter. A planet emitting 240 W/m^2 will only have an average temperature of 255 K if the distribution is uniform. If it is non-uniform, the average temperature will necessarily be LOWER.
Sorry, Kevin. I appeared to have banished “i”‘s from my keyboard when I tried to type your name.
Love it, “So, please drop your arguments and embrace the reality.”