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.
Tim,
I’ll also go on to say what I think happens in 4). In this case, radiation alone will be trying to create a temperature gradient larger than the adiabatic lapse rate…This will actually spark convection which will bring the temperature difference down to the adiabatic lapse rate. The final temperatures will then be obtained from the following three equations for the surface temperature T_s, glass shell temperature T_a, and convective intensity C:
Energy balance at the surface: 240 W/m^2 + sigma*(T_a)^4 = sigma*(T_s)^4 + C
Energy balance at the shell: sigma*(T_s)^4 + C = 2*sigma*(T_a)^4
Enforcement of lapse rate condition: T_a – T_s = 10 K.
The solution to these three equations is: T_a = 255 K, T_s = 265 K, and C = 200 W/m^2. (We could have guessed T_a had to be 255 K because that’s obviously the only way we have radiative balance for the whole system.)
I would note that 4B) no longer is very interesting…You just get somewhat different numerical values than 4A). However, if we raised the shell to, say, 10 km, then we would get the same temperatures that we got in 3) because the lapse rate of ~4.8 K per km would be less than the adiabatic lapse rate and hence would be stable to convection. (Some heat transfer would occur due to conduction through the N_2 but it would be negligible.)
Tim: Just to note something that is implicit in my discussion above, but is worth stating explicitly: There is no GTE that tries to keep the lapse rate at the adiabatic lapse rate (as should be clear from the parts of the atmosphere that are nowhere near the adiabatic lapse rate, such as the stratosphere). Rather, the adiabatic lapse rate represents a stability boundary for the actual lapse rate. That is to say, the atmosphere is perfectly happy with a lapse rate less than the adiabatic lapse rate. However, if the lapse rate exceeds the adiabatic lapse rate, the atmosphere becomes unstable to convection, which transfers heat up through the atmosphere until the lapse rate is lowered back down to the adiabatic lapse rate.
Dang, you are right Joel. And I had seen that argument before (even made it myself) but seem to have had a mental lapse.
That then begs the question what happens with an atmosphere. The shell by itself wants to be ~ 255 K. The surface wants to be ~ 60 K warmer. The lapse rate still wants to be ~ 10 K/km for the pure N2 atmosphere. So if the shell is at an altitude of 6 km, everything is fine — the ground is ~ 305 K radiating 480 W/m^2 and the shell is ~ 255 K radiating 240 W/m^2 both up and down, and energy is balanced and the lapse rate is where is wants to be.
If the shell is LOWER, then there will be a large temperature gradient, and strong convection set up. If the convection is carrying 100 W/m^2 from the surface to the TOA, then the surface only needs to radiate 480-100 = 380 W/m^2 for an effective surface temperature of 286 K.
If the shell is HIGHER, then there will be a small temperature gradient. The air will be stable and not convect. Conduction will carry a very small amount of energy downward. This would warm the surface a very small amount compared to the shell at the optimal altitude.
If the shell is back at 6 km, but a second shell is added at 12 km, then top shell radiates 240 up and 240 down. The lower shell radiates 240 * 2 = 480 up and 480 down. The ground radiates 240 * 3 = 720 up. This should balance with no serious convection, and a temperature of ~ 336 K at the surface.
OK — now it gets to the point where you need to calculate the IR absorption at each location (altitude, latitude, longitude) along with the convection at each location, which depend in complicated ways on pressure, temperature, chemical composition, humidity, ….
In other words, either you live with overly simple models that gives the gist, or you go for intense computer models. You can’t hope to get a “good” answer with a “simple” model.
My revised conclusions are:
*RTE is real and very important. The “number of layers” is of primary importance, and adding more GHGs will raise the temperature even if the absorption is already “saturated”.
*GTE is real, but a much smaller effect (and fundamentally different that the GTE that many people are discussing), primarily important when the true lapse rate exceeds the adiabatic lapse rate.
By the way: There is one thing that is puzzling me that I will throw out to Tim and others for their thoughts. I found above that the surface temperature in the case of “no atmosphere” and the surface temperature in the case of an N_2 atmosphere are different (at least if the glass shell is close enough to the surface that convection occurs). A natural question that arises is this: How do things transition between these two cases, i.e., what happens if we have a really tenuous (low density) N_2 atmosphere?
My guess is that one of the two following things must be true:
(1) There is some limit on the rate of heat transfer due to convection, and this limit is lower as one makes the atmosphere more tenuous. This seems reasonable intuitively, but I’d be curious to know what the limit is.
(2) The adiabatic assumption breaks down, i.e., it becomes impossible to satisfy the adiabatic condition if the atmosphere becomes tenuous enough; hence the adiabatic lapse rate is no longer the appropriate stability limit on the lapse rate. This seems like a less likely explanation to me, but I can’t rule it out.
Joel,
It looks like you discussed many of the same points while I was composing my post.
Let me just address two quick points:
“There is no GTE that tries to keep the lapse rate at the adiabatic lapse rate ” (ALR)
I would now say that the “non-RTE” tries to keep the lapse rate near the adiabatic lapse rate. If observed lapse rate is larger than the ARL, then convection will carry energy upward. If the observed lapse rate is smaller than the ALR, then there will be conduction carrying energy downward. (But since the thermal conductivity of the air is so small, this will almost certainly be insignificant (as I now see you discussed — you beat me to it again!) and we can pretty accurately conclude that “the GTE tries to keep the lapse rate from going above the ALR”. )
“However, if the lapse rate exceeds the adiabatic lapse rate, the atmosphere becomes unstable to convection, which transfers heat up through the atmosphere until the lapse rate is lowered back down to the adiabatic lapse rate.”
I would say it is lowered back CLOSE to the ALR. In a steady state situation that would lead to a steep observed lapse rate, if convection could get you back to the lapse rate by cooling the surface sufficiently, then the air would again start to heat near the surface and convection would resume. The stable solution would be a combination of convection and a slightly larger lapse rate than the ALR.
But these are both minor points.
Joel Shore (Jan. 2. 2012 at 3:03 pm):
It seems to me that I refuted your contention that there is necessarily a violation of energy conservation in my post of Jan. 1, 2012 at 1:30 p). In particular and in reference to the estimated energy budget of Trenberth et al (2008), energy is conserved by the various upward and downward energy fluxes that are described by Trenberth and his colleagues. That in this budget there is, at the top of the atmosphere, an upward facing heat flux vector of 239 W/m^2 and that at the bottom of the atmosphere there is a radiative energy flux vector with an intensity of 390 W/m^2 is irrelevant to the issue of the conservation of energy or lack of same..
Joel Shore says:
January 2, 2012 at 6:14 pm
Stephen: This makes no sense. How is gravity supplying 150 W/m^2 of power? Gravity cannot supply energy unless the gravitational potential energy of the Earth and its atmosphere is decreasing.
Stephen, allow me to try again.
Joel,
Keep re-reading this until you grasp it:
“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 [expected] amount supplied by the Sun. This additional energy is responsible for keeping the Earth surface 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”
[My italics and I’ve taken out the given quantity so we can concentrate on the concept without getting sidetracked]
Pressure does not have to supply energy ex nihilo to make this work: it is merely responsible for the way it is distributed. Perhaps you’d find it easier to understand if the Authors had used the word ‘more’ instead of ‘extra’, and added the redundant (but in your case seemingly necessary) statement: and less than expected in the upper atmosphere.
Energy is conserved, as it must be. The authors are not stupid people, much as you would like to paint them to be so.
Please treat people with respect.
Tim Folkerts said:
“My revised conclusions are:
*RTE is real and very important. The “number of layers” is of primary importance, and adding more GHGs will raise the temperature even if the absorption is already “saturated”.
*GTE is real, but a much smaller effect (and fundamentally different that the GTE that many people are discussing), primarily important when the true lapse rate exceeds the adiabatic lapse rate.”
Here we come to the nub of the issue namely the relative significance of the radiative and gravitational thermal effects.Joel currently denies ANY gravitational contribution even though he previously accepted the contribution of gravity to creating the adiabatic lapse rate. That is an inconsistency on its own but doesn’t matter for this post.
I agree that atmospheric layering is very important and also the GHG contributions to the thermal behaviour of each layer.
We can see that in the effects of changes in ozone amounts in the stratosphere and mesosphere as a result of variations in the mix of particles and wavelengths from the sun wnen the level of solar activity changes.
Apparently the sign of the atmospheric ozone response is the opposite between stratosphere and mesosphere when the level of solar activity changes.
That has an effect on the entire vertical temperature profile of the atmosphere thereby altering ALL the heights and in particulat the height of the tropopause.
I aver that the top down solar effect has a far, far greater effect on the global energy budget than changes in man made GHGs.We can see that in the changes between MWP and LIA and LIA to date.
Likewise there are cyclical variations in the rate of energy release from the oceans which again alter atmospheric heights between surface and tropopause from the bottom up. Again, a far far greater effect than can be aschieved by human GHGs as we can see from the rapid effects of SST changes on troposheric temperatures.
So let us then consider what happens at the surface when the heights change for whatever reason.
Change the height of the tropopause or the gradient in the height of the tropopause between equator and pole and you then change the entire tropospheric pressure distribution and the relative sizes, intensities and positions of ALL the permanent climate zones.
THAT is what adjusts the system back to or nearly back to the lapse rate set by gravitational pressure.It precisely controls the rate of energy flow through the system from surface to space.
The same response occurs WHATEVER the forcing process that tries to push the lapse rate away from the gravitationally induced temperature gradient.
The ENTIRE troposphere simply slides poleward or equatorward in each hemisphere below the tropopause in order to maintain the gravitationally set lapse rate WHATEVER the forces trying to disturb it.
And as I have pointed out the effect of human emissions is unmeasurable compared to the effect of natural variability from sun and oceans.
Climate change on the surface is nothing more and nothing less than the process in action as the system response seeks always to move bacxk towards the gravitationally induced lapse rate.
In that light the significance of the N & Z equations is that they show the system to be highly effective. They show that whatever effect GHGs have is negated by the system response.Indeed the effects of sun and oceans are also negated by the system response but they produce much larger climate zone shifts.
I have been saying that for 4 years now and N & Z provide the quantitative underpinning for my qualitative climate description.
Joel Shore:
At January 2, 2012 at 5:55 pm you say to me:
“As I have explained to you again and again, an earth with a hypothetical IR-transparent atmosphere would be emitting back out into space more radiation than it absorbs. You cannot remedy this by transferring additional energy away from the Earth. It only makes the “deficit” worse.”
THE EARTH DOES NOT HAVE “AN IR TRANSPARENT ATMOSPHERE”!
Nobody is claiming it does (except, perhaps, you?)
And
WE ARE DISCUSSING THE REAL EARTH THAT HAS A PARTIALLY IR-OPAQUE ATMOSPHERE.
Please read the post by Terry Oldberg at January 2, 2012 at 11:01 pm. It provides a complete explanation of your gross misunderrstanding.
When you grasp your misunderstanding then you will be able to recognise why you are very, very wrong to repeatedly assert the falsehood that the Nikolov and Jelbring hypotheses contradicts conservation of energy.
Please try to learn.
It is obvious to almost everybody that you have great difficulty learning anything so you search for security by clinging to your prejudices. But, in this case, you really do need to try to learn.
Richard
Joel Shore:
I have been trying to think of ways to explain your error to you in another way in hope that I can help you to see your error. I think this may do it.
At January 2, 2012 at 5:55 pm you say to me:
“As I have explained to you again and again, an earth with a hypothetical IR-transparent atmosphere would be emitting back out into space more radiation than it absorbs. You cannot remedy this by transferring additional energy away from the Earth. It only makes the “deficit” worse.”
OK. So, for the sake of argument, I will consider your “earth with a hypothetical IR-transparent atmosphere”.
In this hypothetical case the atmosphere would not absorb any IR and it would not emit any IR.
Therefore, the only heating of the atmosphere would be by conduction from the planet’s surface so the atmosphere and surface would obtain a thermal equilibrium with no net energy flow between them.
Importantly, radiative absorbtion and emission would be to and from the planet’s surface alone.
The absorbtion and emission would be equal because there could not be any radiative heating of the surface from the atmosphere which does not absorb or emit IR.
This is somewhat simplistic because IR is not the only radiation, but for this explanation only IR needs to be considered because the same argument applies to all other electromagnetic wavelengths.
THERE IS NO “DEFICIT”.
Richard
Joel Shore:
This is a second part to my attempt to help you understand your error. I did not include it in my first part because this is a clarifying addendum which may have introduced confusion if not kept separate from the basic explanation.
IR is emitted as an energy flux proportional to the fourth power of the temperature of the emitting surface (i.e. the flux is proportional to T^4). And a planet has a wide range of surface temperatures.
A small change to hot planetary surface (e.g. in a tropical region) provides a large change to emitted IR (because the flux is proportional to T^4). But a large change to cold planetary surface (e.g. in a polar region) provides a small change to emitted IR (because the flux is proportional to T^4).
Atmospheric convection transfers heat from the tropics and day-time surfaces to the polar and night-time surfaces.
An average surface temperature of a planet can be obtained by an infinite number of temperature distributions over the surface. Therefore, the average surface temperature can change while the emitted flux of IR energy remains constant (and vice versa). And, thus, the equilibrium average surface temperature of a planet with an IR-transparent atmosphere is governed by atmospheric convection.
Richard
Tim Folkerts says:
Yeah…I think you are right. And, this would provide a nice resolution of the issue that is puzzling me ( http://wattsupwiththat.com/2011/12/29/unified-theory-of-climate/#comment-851299 ) because I imagine that the rate of convection would be proportional to the amount by which the lapse rate is exceeded but the proportionality constant would also involve the density of the atmosphere in some way, so as you made the atmosphere more tenuous, the deviation from the ALR would become larger and larger.
Terry Oldberg says:
Terry: Yes, the budget balances in Trenberth et al.’s case but that is only because we have an atmosphere that absorbs some of the 390 W/m^2 emitted by the Earth’s surface. If we still had 390 W/m^2 being emitted from the surface and no absorption by the atmosphere, it would be impossible for it to balance. If you think it is possible, then show me.
tallbloke says:
Sorry, this doesn’t work. The problem is not an issue of energy distribution in the atmosphere. The problem is that a certain surface temperature necessarily leads to a certain amount of radiative emission and, if there is nothing to prevent that radiative emission from escaping to space, then there is no way to prevent the Earth-atmosphere system from emitting energy at a rate higher than it is receiving energy from the sun.
There are many lapse rates in the atmosphere, temperature being the ‘default’ one when the term is commonly used. But, there’s a density lapse rate. There’s a pressure lapse rate. And, I would submit there is an energy lapse rate, a portion of which is derivative of the pressure lapse rate.
It baffles me why anyone would think that the paper is advocating the creation of energy from pressure. To me the energy lapse rate creates the temperature lapse rate since temperature is nothing more than a proxy for energy content. No magic has to be invoked to see this.
Each meter in a column of air contains less and less energy as you move away from the surface. If we were talking about a column of steel heated at one end and cooled at the other no one would question a temperature gradient along its length.
Wouldn’t it be true that the pressure gradient sets up an ‘idealized’ energy storage profile and EVERYTHING else that is going on in the real world simply serves as perturbation to this ideal? In fact it could even be that the paper is simply saying that all the various feedbacks combine to seek this ideal.
You can’t invoke the static logic for a can of air on my column of air because it always has an energy differential across its height. You can’t claim an IR transparent atmosphere would equilibrate to no temp lapse rate because it will not ever equilibrate with the warm earth on one end and outer space on the other.
Stephen Wilde says:
Actually, it is not an inconsistency at all and your statement above has been helpful to me in realizing exactly what it is that I am saying. It is this — The adiabatic lapse rate matters but rather in sort of the opposite way as people are contending: The radiative effects are what provide the greenhouse effect and the adiabatic lapse rate is what limits the extent to which the radiative greenhouse effect can be offset by convection. So, in other words, if the adiabatic lapse rate were zero, i.e., any temperature decrease with height spurred convection, then the greenhouse effect would basically be canceled out by convection. However, the fact that the adiabatic lapse rate is non-zero is what allows the atmosphere to maintain a temperature profile which decreases with height and hence insures that the radiative greenhouse effect is not canceled out by convective effects (although its magnitude is reduced somewhat).
This also explains where Nikolov has screwed up in Section 2.1B) where he discusses convection: His Equation (4) has put in convection in such a way that it tries to equalize the temperatures T_a and T_s even if they are such that the lapse rate is less than the adiabatic lapse rate. This is WRONG, WRONG, WRONG.
Richard S Courtney says:
You have just proven my point: In a planet without an IR-absorbing atmosphere, you would not get the temperature enhancement at the surface that we call the greenhouse effect. Ergo, this effect is due to the IR-absorbing properties of the atmosphere, not to any “pressure effect”
But, you have forgotten about Holder’s Inequality, which even Gerlich and Tscheuschner know about. You are correct that the average temperature is not uniquely determined by the amount of power emitted. However, there is a bound on the average temperature…and that bound is that the highest average temperature that leads to the emission of a certain amount of radiative power is that which occurs when the temperature distribution is uniform. From this, it follows that the highest average temperature for a planet with an IR-transparent atmosphere that absorbs 240 W/m^2 (and is essentially a blackbody emitter over the wavelengths of its emission) is 255 K. Any non-uniform temperature distribution emitting this amount of power will have a lower average temperature.
I said:
By the way, since the dry adiabatic lapse rate is proportional to the gravitational acceleration g, this means that people who want to believe that gravity is somehow responsible for the surface being warmer, while wrong, do have a small germ of truth in their idea. The actual fact is that it is the radiative greenhouse effect that is responsible for the surface being warmer; however, gravity (and, in particular, the nonzero adiabatic lapse rate in a gravitational field) is what prevents convection from canceling out the greenhouse effect.
Richard S Courtney says:
January 3, 2012 at 2:20 am
To: Joel Shore:
When you grasp your misunderstanding then you will be able to recognise why you are very, very wrong to repeatedly assert the falsehood that the Nikolov and Jelbring hypotheses contradicts conservation of energy.
A simple first law is Q=U+W. sign depends on work done by or work on the system
PV = W
So Joel where is the violation you speak of?
You are repeating the same fallacy I referred to before. You are using the unreal conditions of a conjectural model and erroneously attempting to say they represent the real world conditions. There is a real difference between taking the lapse rate of a particular air mass whose temperature decreases with height within an atmosphere versus making the unreal assumption that the temperature profile of a column of air through the Earth’s atmosphere always “decreases with height,” which of course it most certainly does not.
mkelly says:
Actually, that should be Delta_U (i.e., change in internal energy), not U. The point is that if you consider the Earth-atmosphere system as a whole and you assume that the Earth has an atmosphere that is transparent to the radiation emitted by its surface, then Q /A*(delta_t) = 240 W/m^2 – 390 W/m^2 = -150 W/m^2, delta_U has to be at least approximately zero on any reasonable timescale…and W is zero. Hence, Q = U + (Delta_U) is not satisfied. [Here, delta_t is the time over which you consider the energy accumulation and A is the surface area of the Earth.]
D. Patterson: I’ve read your comment over 3 times now and I haven’t a clue what you are trying to say.
Fellows,
The whole concept of a ‘greenhouse gas’ is somewhat distorted in the mind of the average person and even the average scientist. Most people (including Roy Spencer) seem to think that what makes a GH gas is the molecular structure of the gas. This is only partially true! The other big component is pressure. There is a phenomenon in gas spectroscopy called ‘pressure broadening of absorption lines’. Higher pressure makes any gas absorb more IR due to broadening of its absorption spectrum by reducing the gaps between absorption lines. So, any gas can become a significant GH gas under high enough pressure! This physical fact is not widely known, and rarely emphasized in undergraduate school, which is why most people have this ‘black & white’ image in their minds about what constitutes a GH gas … 🙂
The reality is that N2 and O2 (the major gases in our atmosphere) are not at all 100% transparent to IR radiation. From what I know, the IR opacity of an atmosphere is closely related to (correlated with) total surface pressure (and the vertical pressure gradient), so that there is no such thing as a 100% IR-transparent atmosphere. The IR opacity grows in parallel with pressure, meaning that anytime you have a gas in a gravitational field (i.e. under some pressure), its IR emissivity/absorptivity will always be greater than ZERO! … For example, Mars’ atmosphere is 95% CO2, yet radiative physicists tell us that it’s very ‘leaky’ with respect to IR radiation with a rather weak ‘Greenhouse effect’ due to low overall pressure. In other words, the IR radiative transfer within an atmosphere is regulated by the vertical pressure gradient as much as (or even more than) by composition. Since atmos. pressure is independent of the energy balance (or radiative transfer), it must be considered as a controlling factor of the latter.
“Wouldn’t it be true that the pressure gradient sets up an ‘idealized’ energy storage profile and EVERYTHING else that is going on in the real world simply serves as perturbation to this ideal? In fact it could even be that the paper is simply saying that all the various feedbacks combine to seek this ideal.”
Nicely put.
And the N & Z equations (together with real world observations) confirm that negative feedbacks are extremely effective at attaining that ideal.
Hence the constant latitudinal shifting of the global climate zones to continually adjust the lapse rate between surface and tropopause.
Joel Shore;
You’re losing it bud!
Please allow me to summarize this dogs breakfast of a discussion at the big picture level.
The theory of AGW is founded upon the notion that absorption and re-radiation of earth radiance by CO2 and other GHG’s increases the temperature of the earth. The theory further rests upon the notion that the effect of the GHG’s has an additional “positive feedback” that increases temperatures further by some amount. The debate has condensed into two seminal issues:
1. What is the magnitude of the direct effect of CO2 (and other GHG’s)?
2. What is the magnitude) and sign (+/-) of the feedback effects of CO2?
What we know from direct observation:
1. The combined direct and feedback effects of CO2 have been substantively less than expected which further implies that;
2. The feedbacks are not only less positive than expected, they may actually be negative.
What, at day’s end, are N&Z saying? They are saying that:
1. The combined direct and feedback effects of CO2 are insignificant.
2. The feedback effects are most likely negative, cancelling or nearly cancelling the direct effects of CO2.
3. Given that the net direct and feedback effects of CO2 appear to approach zero, the governing factors remaining in regard to temperature of earth surface are mean insolation at TOA and mean surface pressure.
They have developed forumulas dependant upon mean insolation at TOA and mean surface pressure in order to predict surface temperatures, and appear to have done so accurately. The fact that they can do so suggests that the GHG effects of CO2 etc are in fact negated nearly 100% by feedbacks, and real world observations strongly suggest that this is the case as well.
There is nothing in what they have presented that violates the laws of thermodynamics ad you have claimed. Your refutation of their position by focusing on what happens from the perspective of radiative physics is immaterial unless you can present with certainty what the combined direct and feedbadck effects of GHG’s are and that they are a) significant and b) don’t cancel each other out. You can spout theory all you want, but real world data compared to theory suggests that the net including feedbacks is, in fact, insignificant. Your accusation that they are curve fitting is equally spurious. Yes, in fact, they ARE curve fitting! How else does one derive constants? If you have a problem with this, then might I suggest you review the work of Stefan and Boltzmann in arriving at SB Law.
Curve fitting that shows predictive skill is, in fact, science. Curve fitting that shows no predictive skill but is nonetheless presented as being accurate requires “faith” to merit any consideration and as such lies outside the field of science. You’ve accused others of drifting into the realm of faith based acceptance of facts, but at days end the truth is:
1. The data shows that feedbacks are most likely negative, making the combined direct and feedback effects of GHG’s such as CO2 negtligible and;
2. The formulas arrived at by N&Z to quantify surface temperature show predictive skill.
@Ned Nikolov:
In your latest comment ( http://wattsupwiththat.com/2011/12/29/unified-theory-of-climate/#comment-851749 ), you have introduced two new issues:
(1) Pressure-broadening of the absorption lines of greenhouse gases.
(2) The idea that all gases, even those like N_2 and O_2 whose molecules cannot absorb radiation are in fact able to absorb at higher pressures due to collisional effects.
You are correct about (1): The total atmospheric pressure is relevant for the width of the absorption lines of the greenhouse gases in the atmosphere.
You are technically correct about (2), although the amount of absorption present at Earth pressures makes it basically irrelevant.
So, yes, there are reasons to believe that there ought to be some positive correlation between pressure and “surface temperature enhancement” due to the greenhouse effect. (The third, and probably most important, reason for a correlation to exist is that planets with low atmospheric pressure don’t have much atmosphere at all and hence necessarily don’t have much greenhouse gases. And, planets with high surface pressures have a considerable atmosphere and, unless it is made up exclusively…or nearly exclusively…of non-greenhouse gases, they will have enough greenhouse gases to have a considerable greenhouse effect.)
However, none of this says that the pressure alone quantitatively determines the enhancement. And, in particular, none of it demonstrates that the greenhouse effect is not responsible for the enhancement. In fact, it clearly is, as the effect is necessary to have conservation of energy, and abundant empirical evidence in the case of the Earth (e.g., the emission spectrum observed from space) show that it is indeed the greenhouse effect that is responsible for the temperature enhancement.
In addition, we have pointed out fatal errors in your calculations: (1) Your estimate of the surface temperature in the absence of the enhancement suffers from a number of calculational and conceptual errors. (2) Your calculation that convection cancels out most of the greenhouse effect is wrong because you have put convection into the equation in such a way that it drives the system toward an isothermal profile with height, whereas we know that in reality convection drives the system toward having the profile given by the appropriate (dry or saturated) adiabatic lapse rate. The cancellation of most of the greenhouse effect in your Equation (4) is due to this error.