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.
davidmhoffer: Your latest comment is a hopeless confusion:
(1) We are not discussing the issue of feedbacks. In particular, we are discussing what is responsible for the OBSERVED surface temperature enhancment on various planetary bodies.
(2) Your claims that most of the empirical data supports your notion that the net effect of CO2 (once feedbacks are included) is small not correct, but this is not the appropriate thread to discuss them. Let’s stick to one topic at a time. Don’t try to bring other things into the discussion in a desperate attempt to derail the topic and save a doomed “theory”.
(3) Yes, the Laws of Thermodynamics are violated. Feedbacks are irrelevant: It is simply not possible to have the Earth emitting 390 W/m^2 from its surface when it is only absorbing 240 W/m^2 from the sun unless the atmosphere is absorbing the difference. [And, in fact, we know that the Earth as seen from space is not emitting 390 W/m^2 but only about 240 W/m^2, confirming the fact that the atmospheric absorption is what prevents a violation of conservation of energy…and the spectrum of that emission even agrees with what radiative transfer models predict it to look like.]
(4) A curve fitting exercise only shows predictive skill if it actually PREDICTS, i.e., if it actually can predict the value for the surface temperature of planetary bodies that were not used in deriving the empirical formula. (And, for the reasons I noted above, one would expect a generally positive correlation between pressure and surface temperature enhancement.)
David: I think you are intelligent enough not to be taken in by this nonsense. I would strongly suggest you think a little more before associating yourself in any way with this “theory”.
@Ned Nikolov
> 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!
Yes, higher pressures causes the apparent thickness of spectral lines to increase, and heat absorption increases too. But I believe that this ‘spectral broadening’ is just a macroscopic artifact induced by the increased Doppler shift spread across the distribution of velocities.
At the microscopic level, this is just equipartitioning or “thermalization” caused by increased collisions and more interactions between translational, vibrational and rotational degrees of freedom, ultimately a very non-linear process.
In other words, individual molecules don’t carry barometers in their shirt pockets, and thus have no concept of ‘pressure’. They merely transfer momentum and energy when bumped into by other molecules.
Your statement,“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[….],” is a false statement. The atmosphere most certainly does not “maintain a temperature profile which decreases with height.” A particular lapse rate is not applicable to the Earth’s atmosphere as a whole, so any effort to construct a model based upon such a false assumption can only produce an unreal model and and a false conclusion.
Joel Shore says:
January 2, 2012 at 8:13 pm
The glass shell will radiate 240 W/m^2 up and 240 W/m^2 down. The Earth’s surface will radiate 480 W/m^2 up and hence will be at an elevated temperature of 255K * (fourth root of 2) = 303 K. [Note that because of the lack of an atmosphere, there is no convection to worry about…It is purely a radiative problem.]
If the original energy source provides 240 W/m^2 then any energy level measured within your system will be 240 W/m^2 or less.
How you can imagine 480 W/m^2 appearing is a mystery to many.
Steve Richards says:
That statement is simply and demonstrably wrong. The equations of radiative transfer for this case are trivial to write down and solve (and they explicitly obey conservation of energy). If you are incapable of doing this, then you are incapable of making pronouncements about it. You are just speaking from ignorance.
If you want to understand via analogy why your claim is nonsense, see here: http://wattsupwiththat.com/2011/12/28/sense-and-sensitivity-2/#comment-848185
I am noting two very interesting and very different approaches to a very complex problem.
One approach (typical of Joel & me in these discussions) follows these lines:
The other approach is rather the opposite.
Both are useful approaches. Both provide insights. The challenge is to find a way to meet in the middle. Yes, GHGs and IR radiation affect the temperatures in a very basic and important way. Yes, GHG’s and IR radiation are only a part of the overall equations governing climate.
When people get caught-up focusing only at one end or the other, then understanding suffers.
Here’s a thought experiment for you all…
If you had a column of IR transparent gas (pick a mass if it floats your boat) over a completely dry surface with sunlight pouring in at the top (only) and you were able to isolate it from any horizontal energy influences, what would its temperature profile be? I’m assuming no evaporation and nothing to start convection. Leave it that way for 1000 years. It will obtain some steady state won’t it? What does it look like?
Wouldn’t one end be heated to some temperature by the constant temperature hot surface while the other was constant at 0K? And doesn’t there have to be a temperature lapse rate, else you’ve got to incur some discontinuous temperature change somewhere in the column? Nature hates discontinuities so molecular collisions alone would erode any discontinuity into a nice non-linear lapse rate (column is gaining volume per unit height as it goes up).
Wouldn’t this define the natural state that the atmosphere wants to be in? You still have (once the bottom reaches constant temp) shortwave watts in equal to longwave watts out but you have to have a temperature gradient. The longwave watts out would be a combination of surface radiation and radiation originating throughout the column.
D. Patterson:
For heaven’s sake, stop picking nits! As a general rule, the temperature in the troposphere is a decreasing function of height and an average lapse rate cited is 7.5 K per km. If you want to run a full-fledged climate model that computes the temperature at various points on the earth’s surface and heights in the atmosphere, then go ahead. It is intellectually immature and dishonest to play the sort of game you are playing…You are not making any sort of substantive argument; you are just coming up with reasons to believe what you want to believe.
Joel Shore:
In response to my explanation provided for your edification at January 3, 2012 at 5:41 am you have replied at January 3, 2012 at 6:16 am by saying to me:
“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 am truly astonished that you have the gall to write such twaddle.
I have NOT “forgotten about Holder’s Inequality”. IT IS NOT RELEVANT.
As I pointed out, the planet is heated on its day-side and not on its night-side.
Therefore, THE PLANET IS NEVER AT THE LIMIT set by Holder’s Inequality.
If that is the best excuse you can provide for your sticking to your error then it is certain that you know you are plain wrong.
Richard
Steve Richards says: January 3, 2012 at 11:38 am
If the original energy source provides 240 W/m^2 then any energy level measured within your system will be 240 W/m^2 or less.
How you can imagine 480 W/m^2 appearing is a mystery to many.
How you misunderstand this is a mystery to me.. First of all, these are RATES, not QUANTITIES, so there is no “energy appearing”. But the main point is that there is a balance in all the rates.
I find analogies with money (or water) to be rather effective here, so lets do a very simple analogy. Consider four people named Mr. Sun, Mr GHG, Mr Ground and Mr Space. Every second, Mr Sun pays $240 to Mister Ground (Mr Sun has infinite cash, so he will never run out). Every second, Mr GHG pays $240 to Mister Space and $240 to Mr Ground. Every second, Mister Ground pays Mr GHG $480.
It is very easy to work out that
* Mr Sun loses $240 every second
* Mr GHG holds even
* Mr Ground holds even
* Mr Space gains $240 every second.
There is no “mystery money” that is being created or destroyed. No CPA would have trouble balancing the books.
Of course, these are averages for a whole day.over the whole earth (with no convection and a complete blocking of IR by the GHGs, and a few other simplifying assumptions). A particular square meter of ground will absorb more than 240 W/m^2 during the day, sorting the extra energy in the form of elevated temperatures. At night, the extra energy gets siphoned away as the ground cools. Same thing for the atmosphere.
It is really no mystery at all.
The hot ball gedanken experiment.
Versus an ice ball theory.
Why start with a gedanken experiment of a solid planet with a very low surface temperature, warmed solely by radiation from a sun? How did a solid Si, Fe planet came into being in the very cold gaseous cosmos?
Why is the nucleus of the earth still very hot?
Some speculative early cosmology
Probably the earth originated from an other very hot body. Or from a single very large body (at a big bang) that split in a number of other ones, of which one large one became the gravitational centre of a system, (a ‘sun’) with smaller ones (the ‘planets’) rotating around the centre one. The bodies are hot, because they have a particular density in which nuclear fusion occurs, and heaver elements come in to being. The bodies will cool their surface by radiation to space. Whereas the warming from within continues by nuclear reactions. In a ‘sun’ the gaseous state continues to exist and warming from inside will match the radiative cooling. In a ‘planet’ we can assume that the inside nuclear power decreased so that at the surface a solid crust is formed. (Thanks to the radiative cooling to space).
This is of course speculative but let’s assume we have a the end of the early evolution process a solid ball with a surface temperature of a 1000 C, with gravity and consequently a gaseous atmosphere with a temperature lapse rate.. We have no idea where the water originated from, but it would have been at this temperature all in the vapour phase. But the system as a whole (solid planet + gaseous atmosphere) will continue to cool at its top (TOA) producing liquid water which, thanks to the gravity, will not escape to space but return to the surface. The solid planet becomes partly a water planet at its surface. Then continued evaporation at the surface will cool the surface further and enhance the transport of heat from surface to space, through the atmosphere. But it continues to keep the atmosphere warm, without violating laws of conservation of energy. The initial coming into being of a warm atmosphere, with a temperature lapse rate, is just due to the assumption that we start the gedanken experiment with an originally hot planet, instead of a solid ice ball, of which it is not easy to imagine how it could have come into being, consisting of many heavy elements like Fe and Si. in a cold and empty cosmos. It is obvious that if there was water vapour from the beginning, this must have been coming to help to reduce the initial temperature to a value which allows the water to exist at the surface as a liquid.
And apparently an equilibrium state was reached over billions of years, with temperatures between – 40 C and + 40 C, depending on latitude and local insolation..
Why is not the cooling continuing? Here may be brought in the radiative temperature effect (RTE) , causes by the vapour phase and the clouds. But it should be kept in mind that this is the secondary effect of the water cycle that came into being by an evolution process from an initially hot planet with an already warm atmosphere. Then we can see the RTE as a stabiliser for a particular surface temperature and atmospheric temperature lapse rate. The gravitational temperature effect (GTE) is still the cause.
Then two questions arises (1) what would become the equilibrium temperature state at the surface withhout an IR active gas in the troposphere? (2) And what would it be if there is an additional IR active molecule (CO2) present.?
Ad (1) NZ&J theories starts reasoning from the existence of a certain specific surface temperature and claim that it can be argued to arise from the GTE by applying physical laws such as PV=kRT . If so, I see a difficulty if there is no contribution from radiative processes in the troposphere. The surface is, in my opinion, at first sight, than expected, to continue radiation at its emission temperature and will continue to cool. We see it demonstrated strongly (over land) during the night. The surface temperature may fall 10 C, causing an inversion in the lapse rate. The cooling is, however intercepted by the rise of the sun. If the sun does not rise, e.g. during the polar night, the surface temperature falls to – 40 C. During the tropical night (12 h) the troposphere temperature at some altitude above 3 km, does, however not show much temperature change. Probably because the radiative capacity which leads to heat loss, of the gasses is much less than then of solid surface emitting at a broad spectrum. This looks like a support for the NZ&J theories: If the troposphere was holding some heat from the beginning, it will continue to keep the surface warm, despite a low contribution from continued insolation over the surface as a whole.
Or is there still a flaw if we consider the long run over centuries? Where is the radiation emission to space coming from in the system as a whole (surface + troposphere) if there are no IR active molecules in the air? There would not be an TOA with an emissive capacity at a particular emission temperature, different from the surface.. All radiation to space should originate from the surface, and it would continue to cool.
In all these considerations are neglected the processes above the tropopause, in the stratosphere, where the temperature rises again, even to above the surface temperature. We may have to pay more attention to the influences of the stratospheric processes on the troposphere below it, before we can come to a better understanding.
Ad (2) What is the expected effect of an additional active IR molecule like CO2? If we can agree that the surface temperature is mainly established by a combined RTE and GTE effect, cause by the water cycle, and by the important redistribution of heat entering the system through very uneven distribution of insolation, then we need to try to understand these processes on a global scale first, before we can come to an “unified theory of climate”. And come to on conclusion what CO2’s role is in it.
Lastly, I find it surprising how rapidly discussants on this blog are capable to respond to an
argument of somebody else. It takes me an hour to try to understand the way of reasoning of a particular person and then how to digest it in my own view.
Joel Shore says:
January 3, 2012 at 8:12 am
mkelly says:
A simple first law is Q=U+W. sign depends on work done by or work on the system
PV = W
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.]
Joel, I said simple on purpose as there are folks here that read the comments trying to learn. They have limited knowledge on some issues (as most of us do) but everyone can understand equality formula. So, please cut down on your little snipes.
You content that no work is done in the atmosphere by anything ie gravity , DWLWIR, convection?
Also if the atmosphere per you statement “transparent to the radiation emitted by its surface” where did the 390 W/m^2 come from?
Richard S. Courtney says:
Only the hoplelessly lost or naive will be fooled by what you are saying here. Whether or not the planet is at the limit set by Holder’s Inequality is not relevant. What is relevant is that if you have an INEQUALITY, hence my statement: “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.”
[By the way, in practice the Earth actually comes pretty close to the limit set by Holder’s Inequality, that is to say, the temperature variation on an absolute scale is such that the difference between averaging T^4 and taking the fourth root OR just averaging T is not that great, as Willis has pointed out by direct calculation using HadCRUT3 data: http://wattsupwiththat.com/2011/12/29/unified-climate-theory-may-confuse-cause-and-effect/#comment-850001 The day-side, night-side issue is a red herring for a planet for which there is enough thermal inertia and advection of heat that the temperature remains fairly uniform. But, again, this is not relevant because all we need from Holder’s Inequality is the inequality, not how close it is to the limit of that inequality.]
Joel Shore says:
January 3, 2012 at 9:55 am
(3) Yes, the Laws of Thermodynamics are violated. Feedbacks are irrelevant: It is simply not possible to have the Earth emitting 390 W/m^2 from its surface when it is only absorbing 240 W/m^2 from the sun unless the atmosphere is absorbing the difference. [And, in fact, we know that the Earth as seen from space is not emitting 390 W/m^2 but only about 240 W/m^2, confirming the fact that the atmospheric absorption is what prevents a violation of conservation of energy…and the spectrum of that emission even agrees with what radiative transfer models predict it to look like.]>>>>
Where did N&Z say that the atmosphere doesn’t absorb the difference? In fact, they said the opposite! and yes, as seen from space, in going and out going balance at 240 w/m2. What does the spectrum have to do with it? If the composition of the atmosphere was different, then the spectrum of emission would also be different. And in coming and out going would still equal each other. Don’t you get it? Composition influences the emission spectrum, but NOT the total amount emitted!
Joel Shore says:
January 3, 2012 at 9:55 am
(4) A curve fitting exercise only shows predictive skill if it actually PREDICTS, i.e., if it actually can predict the value for the surface temperature of planetary bodies that were not used in deriving the empirical formula. (And, for the reasons I noted above, one would expect a generally positive correlation between pressure and surface temperature enhancement.)>>>>
Exactly. They DID predict the value of other celestial bodies using only a single equation with two variables. That’s the whole point! As you agree that one would expect correlation between pressure and surface temperature, the fact that their two variable equation has predictive skill without considering composition ought to sound that giant gong inside your head that rings when you have an epiffany regarding the falsity of your world view.
Joel Shore says:
January 3, 2012 at 9:55 am
David: I think you are intelligent enough not to be taken in by this nonsense. I would strongly suggest you think a little more before associating yourself in any way with this “theory”.>>>>
I dumped all over this theory when I first read it. Then I realized that what I have been saying for some time now about calculating energy balance from averaged surface temps instead of averaged fourth root of surface temps applies 100% to what N&Z are saying about how to determine surface temps. I was dumping on them for using in their calculations exactly the same approach I was advocating for a related purpose. In other words, that giant gong in my head went off, I had an epiffany! I started by admitting that my first impression of what they were saying was wrong. Yes, I admitted I was wrong about something!
You could do well to admit the same.
mkelly says:
I don’t see where there were any snipes in my previous response to you. In fact, I thought it was remarkably restrained especially given that our previous interactions have hardly led me to believe that you are someone who can be convinced on even the most basic scientific issues…But perhaps you’ve turned over a new leaf for the New Year.
The things you mention do not do work on the Earth-atmosphere system as a whole. In order to explain where an additional source of energy is for the earth-atmosphere system, you have to identify an actual source of additional energy, not just energy being moved around. For example, a ball of gas undergoing gravitational collapse has a source of energy: Gravitational potential energy is being lost by getting converted to other forms of energy. However, the Earth and its atmosphere are not undergoing gravitational collapse.
Besides which, the emissions seen from the Earth by satellites confirm that the Earth + atmosphere as seen from space is not emitting more than ~240 W/m^2. And, its emissions, as one would expect, look like the blackbody emission of an object of ~288 K (that would emit ~390 W/m^2) but with “bites” taken out of the emission spectrum, just where they are expected to be based on our knowledge of the various absorption bands of the greenhouse elements in the atmosphere.
[Also, I am not sure what you mean by “DWLWIR” as my whole point is that one can’t satisfy conservation of energy without invoking the fact that the atmosphere is not transparent to radiation from the surface, but absorbs and emits, some.]
The 390 W/m^2 is the amount of radiation emitted by the surface of the Earth, which emits very nearly as a blackbody of temperature ~288 K.
Joel Shore says:
January 3, 2012 at 12:04 pm
Steve Richards says:
If the original energy source provides 240 W/m^2 then any energy level measured within your system will be 240 W/m^2 or less.
How you can imagine 480 W/m^2 appearing is a mystery to many.
That statement is simply and demonstrably wrong. The equations of radiative transfer for this case are trivial to write down and solve (and they explicitly obey conservation of energy). If you are incapable of doing this, then you are incapable of making pronouncements about it. You are just speaking from ignorance.
Indeed, the equation (2) in the OP is in fact derived from doing such an energy balance for a 4 layer model (that’s where the 2/5 comes from). For some reason N & Z fail to point that out.
“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.”
In your bad dream Joel.
davidmhoffer says:
Is that supposed to be some new exciting result? Of course the total amount emitted doesn’t change; it is determined by radiative balance. However, the temperature of the surface necessary to have this emission does change.
No…They used Equation (7) to fit to the data for the celestrial bodies. That equation contains 4 free parameters. Then going from N_TE to T_E seems to involve at least one more free parameter. That makes 5 free parameters fit to 8 pieces of data (and some of the data points, for the planets with very tenuous atmospheres are kind of boring). Hardly impressive that they get a good fit.
They didn’t do this correctly whatsoever. They made a huge conceptual error in assuming that the temperature is determined by the local insolation and then they made some calculational errors in implementing that. Our Earth is actually much closer to the limit of a uniform temperature distribution than the temperature distribution you obtain by considering the local insolation…Willis has showed you this using actual temperature data.
Your first impression was correct.
And, I plainly admit when I am wrong about something. For example, in this very thread, when cba claimed that Nikolov et al had made a calculational error in determining their T_sb, I said that he was wrong and that they had made only a poor assumption but had implemented their poor assumption for the surface temperature distribution correctly ( http://wattsupwiththat.com/2011/12/29/unified-theory-of-climate/#comment-849077 ). I believed this because Gerlich and Tscheuschner had gotten almost the same numerical answer making the same poor assumption. However, cba persisted that they had in fact made calculational errors and then, after looked more closely, I realized that he seemed to be correct…and I told him so: http://wattsupwiththat.com/2011/12/29/unified-theory-of-climate/#comment-849744
Ned Nikolov says:
January 3, 2012 at 8:18 am
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.
Not ‘any gas’ only those that have absorption lines in the frequency range of interest, N2, O2 and Ar do not have such lines in the emission range of the Earth’s surface so there’s nothing to broaden. CO2 does have many such lines which are substancially broadened, this is the reason why the Martian atmosphere doesn’t have much of a GH effect, since its absorption lines are very narrow due to the lack of broadening. Below is an illustration of the difference between Mars and Earth for a portion of the CO2 spectrum.
http://i302.photobucket.com/albums/nn107/Sprintstar400/Mars-Earth.gif
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.
No that’s why I use N2 gas as the diluent in my FTIR spectrometer, because it’s transparent in the IR!
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!
Only if it absorbs in the first place!
… 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.
The pressure is a secondary effect.
tallbloke says:
January 3, 2012 at 1:34 pm
“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.”
In your bad dream Joel.
No Joel’s right, it’s your bad dream.
I said to Ned Nikolov here( http://wattsupwiththat.com/2011/12/29/unified-theory-of-climate/#comment-851821 ):
Correction: I no longer believe that there are calculational errors in T_sb. It seems only to be a conceptual issue, what I would call a poor approximation, to assume that the local (in space and time) insolation alone determines the local temperature.
tallbloke says:
It would be helpful if you would actually explain WHY you believe this is wrong using correct physics that actually obeys laws like Conservation of Energy. So far, we haven’t seen that from you…The only semi-coherent statement we got from you was easily shown to be nonsense that didn’t address the point: http://wattsupwiththat.com/2011/12/29/unified-theory-of-climate/#comment-851644
Tim Folkerts says:
January 3, 2012 at 12:23 pm
I wonder if you would do me a favour by extending your analogy a little.
Add a 2nd Mr GHG to stand alongside the 1st Mr GHG
Start passing the money around.
@Phil.
> CO2 does have many such lines which are substancially broadened,
> this is the reason why the Martian atmosphere doesn’t have much
> of a GH effect, since its absorption lines are very narrow due to
> the lack of broadening.
You are implying that these broadened spectral lines somehow enhance the ability of CO2 molecules to capture more IR energy, as if the increased line width corresponded with some kind of “cross section” property, which is somehow a function of pressure.
But ‘pressure’ per se doesn’t exist at the microscopic molecular level. Pressure is a macroscopic property of an atmosphere, which appears to be a scalar field: a unique real-number value at each x,y,z location, with a Markovian flavor, such that nearby locations tend to have the same pressure.
But microscopically, such a scalar field doesn’t exist. You might say ‘speed corresponds to pressure’, but that’s not the same because at that level ‘speed’ is a distribution, not a scalar field. Some molecules move fast, some are slow. A collision can transfer all of the momentum from a fast molecule to a stationary molecule. So reversing their “pressures”?
Pressure corresponds to the average of these speeds at the macro level. Individual molecules know nothing about this ‘average speed’.
So, in reality, the line spreading is caused by a Doppler shift at the receiving instrument, due the molecules traveling to and from the instrument. This shift is not detectable by the molecules themselves, in the same sense that you can’t perceive the Doppler shift of a train whistle if you’re riding on the train.
Then why does Mars, which has 30 times more CO2 per unit of surface area than Earth, have a tiny GHE?
You are correct that it’s because of reduced pressure. But it has nothing to do with “line widths”. It’s because the reduced density (1% of Earth) reduces the opportunities for collisions with other molecules, thus preventing the vibrational energy from the absorbed IR photon diffusing as heat.
I think I’m reading here that the N&Z theory doesn’t account for this absorption, but I will wait for the expanded paper before making any further remarks about that.
Joel Shore;
Willis has showed you this using actual temperature data.>>>
No he did not.
He calculated P using T averaged and raised to the power of four and then compared to P calculated by T raised to power of 4 and then averaged.
As the two numbers were close to one another (they differed by about 6 w/m2 which is actually huge in the context of the climate debate, he concluded that the two methods were roughly comparable. In brief, he made less of a mistake, but he still made a mistake, as I pointed out to him in my reply.
In order to arrive at a number of any value, one must not only take the average of T raised to the power of 4, one must also do it over time. The data Willis used was (I believe, I have to admit I did not check for certain) annual.
Annual data is the average of monthly T. Monthly T is the average of daily T. Daily T is the average of hourly T. Given that T can vary by 20 degrees in a single day, and in the spring and fall months, daily average can swing by 30 or 40 degrees in temperate zones, taking the average of annual data raised to the power of 4 is nothing more than taking the proper mathematical approach to annual data which is already wrong in the first place!
Really Joel, you are fooling yourself to no end on this issue. There are legitimate criticisms to be made of N&Z, but I’m not going to shout about them until I see the full explanation in the follow on article they have promised. That said, if you truly think there are problems, you haven’t managed to put your finger on any of significance, and your rebuttal amounts to no more than criticizing them for things you claim they said which they did not.