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.
G Castanza – the volume is not constant in your example.
I wouldn’t assume cloud variation is due to GCRs. Some proportion (and perhaps a large proportion) is due to variations in anthropogenic and natural aerosols (which seed clouds).
This affect will be exaggerated by surface temperatures being predominantly measured around urban areas where the anthropogenic aerosol effect is largest.
A study measuring cloud changes over urban areas versus non-urban areas would be interesting.
Basically that is what I am saying. The predominant effect on pressure is gravity. If you measure the actual air pressure up here in Wyoming it is 200mb lower than sea level on average simply because of “hydrostatic” equilibrium. There are small departures from this equilibrium pressure, and this leads to wind of course, but these are small departures. A few mb of difference results in the winds of a mid-latitude cyclone but a few mb is also the difference you experience going up in elevation by a few tens of meters.
At any rate, saying that atmospheric pressure determines temperature is wrong, just as saying that temperature declines with elevation because of pressure drop is wrong. Temperature declines with elevation because of a change in energy balance, and this balance also includes the mechanical work done when air is raised or lowered in elevation. The ideal gas law applies to all of this only indirectly.
Did I clarify my thinking?
Ugh. From wiki and “Mercury Fact Sheet”. NASA Goddard Space Flight Center. November 30, 2007. Retrieved 2008-05-28.
In Table 1 it says that the “observed” mean temperature is 248.2 K. I could not find why the authors are using 248.2 instead of 442.5 K as NASA Goddard Space Flight Center suggests. http://nssdc.gsfc.nasa.gov/planetary/factsheet/mercuryfact.html
Kevin Kilty says:
December 29, 2011 at 10:32 am
mkelly says:
December 29, 2011 at 9:21 am
Kevin Kilty says:
December 29, 2011 at 8:37 am
KKilty says: “…, that temperature is not determined by pressure, ….”
Thus temperature has no bearing on pressure in the case of a star or on a planetary atmosphere–gravity is the principal agent. The temperature rise is from gravitational work.
Sir, you change the discussion from pressure/temperature to work. In a star the gravitional force increases the pressure while the volume is shrinking thus T must rise. In regard PV =nRT if P is increased and V held steady then T must rise. If you ascribe the rise in P to work done by gravity I agree. Also with the diesel work. But we were just talking about the gas law and not about work.
Many commenters here are already getting pressure and density miss applied within their words resulting in non-science dribble. Don’t give the local agw zombies a hammer. Once more time…. pressure has only to do with mass (the mass of the atmosphere), acceleration (gravitational acceleration), and area (the area of Earth’s surface). That’s all. Look at the units:
Density: mass/volume = kg/m3
Pressure: Pa = force/area = N/m2 = kg (m/s2) / m2 = (finally, true but no meaning) kg/m/s2.
kg = mass of atmosphere
m/s2 = gravitational acceleration
m2 = area of Earth’s surface
In a mostly stable gravitationally held atmosphere:
Changes in pressure (the cause) reflects in changes in temperature (the effect), constant volume but an atmosphere is not constant volume.
Changes in temperature (the cause) reflects in changes in density (the effect), constant pressure, an atmosphere has a constant mean pressure.
Temperature cannot cause first order changes in pressure in atmospheres but it does change density.
Density cannot cause first order changes in either temperature or pressure, it is an end effect. But density does affect radiation passing through that mass.
Everyone seems to have P•V=n•R•T burned in their mind but in relation to a gravitation held atmospheres these equivalents are much more relevant and helpful:
P•V•M = m•R•T and
P•M = ρ•R•T or P/ ρ = T•R/M
M being molar mass, m being mass, ρ being density
Rearrange as needed.
Seemed to be needed here. Hope that might help some here and hopfully no mistakes.
Kevin Kilty says:
December 29, 2011 at 10:58 am
you’re not going to be able to get around, PV = nRT. ………. goobers.
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No one is trying to refute the ideal gas law, but its application here is a mess. Pressure does not determine temperature in this instance. Gravity in effect determines pressure, energy balance determines temperature, then once those two variables are set all that the ideal gas law can possibly do is determine density.
……….. Gravity has no impact at all on pressure in compressors or diesel engines–it has everything to do with pressure and lapse rate in atmospheres.
Folks, I love the ideal gas law as much as the next person, but you cannot misapply it. Period.
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And, yet, PV still equals nRT . So, instead of focusing on the pressure part of the equation, I’d look elsewhere. Of course, we should also note, our pressure isn’t constant, and the delta in temps that we’re talking about is about 0.5 Kelvin. (55° to 56° for instance)
I think what most people are getting hung up on is scale and sensitivity. Everyone likes to think our temp change has been dramatic. It hasn’t been. Everyone is used to seeing the temp graphs with the accelerating increase. But, if one scales it properly and puts it on a Kelvin scale…. it wouldn’t even be a noticeable bump on the line.
@ur momisugly GeologyJim says “Question: How has Venus managed to hold its thick atmosphere against the solar-wind flux? Is it just the greater molecular weight of CO2 compared to N2, O2, and such?”
Perhaps it hasn’t and it was once even greater than it is now. Or / and as Venus is that much nearer the sun it’s innards must be subject to far greater tidal churn and so is or has been much more volcanically active than earth.
Dale Huffman should be feeling happy that this paper vindicates him;
http://theendofthemystery.blogspot.com/2010/11/venus-no-greenhouse-effect.html
@ur momisugly Stephen Wilde, you said “It fits nicely with the description that I published back in May 2008”
you also said “My work then goes on to link all that to solar activity from above and oceanic variability from below for a more complete Unified Theory than that presented here (IMHO).”
Please post a link for this or better still ask Anthony to put it on WUWT as an article / paper, it sounds more than interesting enough and I like the idea of extending it to solar and sst.
So I guess the CO2 molecules are to blame for about 0.0392% of that “unprecedented” “catastrophic” warming we are suffering under now?
Here is my complaint. My engineering students constantly misapply the ideal gas law by confusing the relationship it suggests among P, V, n, and T with causation. P, V, and n do not cause temperature, and that is what the authors either do maintain or are implying here. Temperature in the long run is always the result of energy balance. So, I have no problem with N&Z saying that irrandiance at TOA is an important factor–it is. Period. However, to the extent that pressure has anything to do with this, it is just acting as a proxy for the true important factors. On earth you could think of pressure as a proxy for optical depth which is important; but it is only a proxy.
Let’s take Venus as an example. We know the surface temperature is very high. We also know the surface pressure is very high. But the surface pressure does not cause the high temperature. The surface temperature results from 1) irradiance that is absorbed predominantly high in the atmosphere leading to a high temperature there, and 2) then a lot of work input by gravity as convection takes parcels from up high to the surface. There is also a little irradiance absorbed at the surface which is what drives the convection. The high surface temperature results from the lapse rate, and we know the lapse rate depends on specific heat at constant pressure and the gravitational constant–pressure does not enter the problem explicitly.
Now you could object by saying, well the atmosphere absorbs irradiance so high because there is so much mass in Venus’ atmosphere and pressure is related to the mass in the atmosphere, and you could also say that the work involved in taking parcels of atmosphere to the surface is just pressure-volume work, and so involves pressure. But really irradiance and gravity are the factors, and pressure is but a proxy for the latter. Think of a planet like Venus, but with an argon atmosphere, that is far more transparent (less optical depth), yet has the same surface pressure. The difference in transparency would lead to a very different surface temperature, yet irradiance TOA and surface pressure would be the same.
I hope I am making myself clear.
Urederra
Yes, but Wikipedia says that the range is 90 – 700 K. It takes a bit of math to estimate the equivalent blackbody temperature from that.
Some explanation should be nice.
I get the colder planet equation. It makes sense and allows a global temperature comparison with a global temperature mechanism with and without an atmosphere. Otherwise u are only measuring a point on the Earth against a global average. This poster looks at the gray body as a sphere on an axis and explains the temp of the gray body at all points, those facing the sun and its angles, as well as those points facing away from the Sun. The authors then went looking for a mechanism with enough energy to get us to room temperature so to speak.
So, if the first equation holds true, greenhouse effects cannot alone explain why we are as warm as we are. So warmists, what are your thoughts on the temperature equation without an atmosphere?
Kevin, are you saying that high altitude areas are colder than low altitude areas because of differences in radiative balance, not the difference in pressure?
@ur momisugly Mr Kilty
I am not sure that you are arguing the same case. As far as I can tell what the authors are saying is that for a given gravity and a given energy balance if you increase the total amount of gas present the pressure at the surface will increase. Given (as stated) the unchanged energy balance, the surface temperature will increase. How is this a miss-application of the law?
Oops, I missed the fact that Dale Huffman had commented above on this paper. Having scanned through Dale’s comment, I remain of the view that the two papers are in fundamental agreement.
@Gengt
It is not only wikipedia, but also the NASA Goddard Space Flight Center that says that the average temperature on Mercury is 440 K
http://nssdc.gsfc.nasa.gov/planetary/factsheet/mercuryfact.html
Mkelly, I’m going to try to explain this better. The original temperature rise that got the star going in the first place was from gravitational work. Once that work is done, however, the star temperature results from energy balance, not from pressure. Oh, you do have to maintain a pretty high temperature and pressure to keep the nuclear reactions going, but pressure does not cause temperature.
I am not changing the topic from one thing to another. They are interrelated.
The ideal gas law is just an equation of state that relates one state variable (T say) to others (P,V, and n). Thermodynamics is the application of energy concepts to the system these state variables describe. I bring work into all of this because work+heat is the essence of energy balance. You cannot explain what goes on in an atmosphere or a diesel engine without considering heat+work. I am not changing the topic, I’m simply adding what has to be added to make sense.
“Life as we know it, perhaps, but there are plenty of extremophiles that will live on.”
For a while, but then even those will die. The point being that the planet Earth will be uninhabitable for human beings long before the Sun gets too hot because our atmosphere will blow away in the solar wind and volcanism will drop below the level required to sustain it.
Kevin, when Carl Sagan first estimated the surface temperature of Venus, he based it on radar depth to the surface, the known cloud top altitude and temperature, and two guesses at the atmosphereic composition, one entirely nitrogen and one CO2. His estimate for a nitrogen atmosphere was hotter than for a CO2 atmophere, purely due to the different lapse rates between N2 and CO2.
I think what the authors are arguing (or should be) is that the lapse rate determines the delta T’s, and then some aspect of the atmosphere system or planet will set the radiative equilibrium with the external environment, putting absolute temperatures to all the points in the system. The radiative equilibrium could be set at the surface (if the atmosphere was completely transparent to radiation), in which case the surface temperature would the same as with no atmosphere at all (and the atmosphere itself would of course get colder and colder than that temperature as you go up). Or the radiative equilibrium could be set much higher up, such as the cloud tops of Venus, in which case the atmosphere at deeper levels will remain much hotter than the cloud tops.
Let me try an analogy somewhat better than a diesel engine and switch us to a Brayton Cycle, using a multi-stage axial flow compressor followed by an expansion turbine. As air moves vertically through an atmosphere, the pressure changes result in temperature changes, just as the air gets hotter through each compressor stage and cooler through each expansion turbine stage. As long as the engine runs (and gravity runs forever), the high pressure air will be hotter than the low pressure air. If we connect the high pressure air to a heatsink at room temperature, it will equilibrate to room temperature and the low pressure air will be very cold. If we hook the low pressure air to our heatsink then the high pressure air will stay very hot. So the planetary question is what level of the atmosphere is locked in thermal equilibrium with the external environment.
Partially, let me elaborate a bit. High altitude areas are colder because the energy balance is different, and radiation is only a part of the energy balance. Work is a big factor. As air moves upward to higher elevation, either because of convection or general flow of the air, it has to do work against gravity and this leads to a cooling of about 6F per thousand feet or almost 10C per kilometer. That is a lot of cooling to be made up with only radiation. Also, while the surface heats well at high elevation from solar irradiance, the atmosphere is much more transparent to IR radiation loss back to space. So the result is that a difference in energy balance leads to lower air temperature at high elevation. Pressure is not the cause.
Uerderra
I agree that average temp is stated as 440 K.
My point is that arithmetic mean (T1 + T2)/2 may give a wrong answer to the question of the equivalent black (grey ?) body which depend on T^4.
J Martin says:
December 29, 2011 at 12:19 pm
“Please post a link for this or better still ask Anthony to put it on WUWT as an article / paper, it sounds more than interesting enough and I like the idea of extending it to solar and sst.”
I’ve posted it several times before but no real takers. However the Nikolov findings add relevance so here goes again:
For the top down solar influence see here:
http://climaterealists.com/attachments/ftp/How%20The%20Sun%20Could%20Control%20Earths%20Temperature.pdf
For the bottom up oceanic effect see here:
http://climaterealists.com/attachments/ftp/TheSettingAndMaintainingOfEarth.pdf
And the Unifying system response see here:
http://climaterealists.com/attachments/ftp/TheUnifyingTheoryofEarthsClimate.pdf
As far as I can see at present all is consistent with the Nikolov paper and with observations but inconsistent with established climate theory.
I see Nikolov as adding quantitative science to my qualitative description.
crosspatch said “…because our atmosphere will blow away in the solar wind and volcanism will drop below the level required to sustain it.”
If mankind faces extinction, then I imagine that future generations will not go down without a fight. Including trying to open up or create volcanos. Or import atmosphere from other planets. Use fusion somehow, pity there’s no nitrogen in H2o, but maybe we can liberate nitrogen from somewhere.
A fight for survival we thankfully won’t have to face.
@ur momisugly Will (says: December 29, 2011 at 12:19 pm )
This is one of those cases where you must take more than a single factor into account. You are right that if we had no atmosphere (and thus no water cycle) the temperature would be similar to that of the Moon. However, in order to isolate the atmospheric effect on temperature on an Earth which has both atmosphere and a water cycle, you must also eliminate the water cycle as a factor – which is currently keeping us cooler than we would otherwise be. (There will be other factors too). Factoring in the knowns, the figure of 133K is entirely reasonable and need not detract from the rest of the paper.
richard verney says:
December 29, 2011 at 5:58 am
I remember as a young boy back in the 60s/70s when there was great interest in space that my Dad told me that the reason why Venus was hot was due to the pressure of its atmosphere and he iullustrated it with a bicycle pump. I guess that different science was being taught back in that day and age.
——-
Nup. Same science then as now.
The whole idea is a common misconception. It results from confusing the process of compressing the gas with the state of being compressed.
The heating of the gas in the bicycle pump arises because the pressure is being CHANGED.
The heating does not arise because the gas is at a higher pressure.
A simple counter-example to your idea is a cylinder of compressed gas. That gas might be at 2000bar pressure. But you won’t burn your hand if you touch it. It will be at room temperature.
The atmospheric pressure on Venus is not changing so there is no pressure heating. Instead it’s temperature is maintained by solar heating.