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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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.
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Ned Nikolov says:
January 3, 2012 at 10:35 pm
Bill,
I think I can explain why the rush may be to discredit our work:
No-one’s trying to discredit your work just pointing out your mistakes, better to get them sorted out now than by the reviewer if you submit a paper.
2) We now have an alternative theory of the GH effect based on an irrefutable 160-year old Gas Law. This new theory has quite powerful predictive skills, so much so that it can accurately estimate the average temperature on hard-surfaced planets throughout the entire solar system, something that even 3D climate models have a challenge with. AND it does it by using only two parameters – TOA solar irradiance and mean surface pressure! …
You have done no such thing, you’ve fitted an equation with multiple constants and showed that you can recover the numbers you started with, you’ve demonstrated no predictive ability at all.
While you’re here perhaps you’ll address a few points:
Your equation 2 shows the limits of 0 to 1 for the integration wrt μ, it should obviously be from -1 to 1 which by symmetry is double the value of the integral you show. Perhaps you could explain where this factor of 2 has gone in your derivation (this point has been raised by others here but you haven’t addressed it).
Mysteriously you claim a perfect fit to the observed surface temperature of the Moon at 153K, which is far from the observed value, indeed it’s fairly close to the minimum temperature reached on the night side! Where did you get that value? The fact that it is exactly the same as the value obtained from your calculation is surprising!
The claimed similarity between Figs 5 and 6, is only striking if you ignore the axes! Especially since the exponent in the Poisson relationship is only appropriate for atmospheres which are composed of air, those which consist of mainly CO2 will have quite different exponents.
“Hölder’s inequality Tgb ≪ Te” This should be ‘less than or equal to’.
There are other problems which have been brought up by others but some answers to these questions would be appreciated.
Joel Shore:
I take extreme umbrage at your statement at January 4, 2012 at 9:11 am which says of me:
“Of course, Richard wants you to read only his sophistry”
I have posted nio “sophistry” and your only reason for suggesting I have is that I showed you were plain wrong and that you contradicted yourself.
Apologise then go away.
Richard
Joel,
You are experiencing the cognitive “blocking effect” of a wrong mental paradigm. You need to take off your ‘radiative transfer’-coated glasses and look at the GH phenomenon from an entirely different perspective. In my reply (currently in progress), I try to ‘force’ the reader to do just that. Without a shift in perception, one could never understand our new theory …
For starters, consider the possibility that the 390 W m-2 emitted by the surface is THE RESULT of a higher surface temperature (compared to that of an airless gray body) caused by solar heating and air pressure. In other words, what’s the chance that near-surface IR exchange is caused by the temperature rather than causing the temperature?
I am not sure why, but this debate reminds me of the early arguments on electrical flow. Of course, as humans, we get everything ass backwards, at first. We just are not very good at assigning + or – to our narrow calculations. Check any battery markings for verification. GK
Phil,
It’s not the perfect fit of a curve to some points in itself, which is significant, but the IMPLICATIONS that this fit carries, and that requires a change of glasses as I explained in my reply to Joel above …
To your question – I’m addressing the issue about Moon’s true temperature at length in my official reply. I will only say here that the IR temperature mapping of the Moon surface conducted by NASA’s Lunar Reconnaissance Orbiter Diviner from 2009 to 2011 show that the Moon is MUCH colder than 255K on overage, and the mean diurnal temperature of the surface is very close to our theoretical estimate of 154K! … What’s even more amazing is that NASA’s astrophysicists had already a model predicting accurately Moon’s temperature back in 1999! This model has now been verified by Diviner’s IR measurements… This raises the question, where have the climate scientists been for the past 12 years not realizing that our moon is much much colder that their simple (and mathematically incorrect) application of the S-B equation suggests? … In fact, the Diviner data show that there is NO latitude on the Moon surface, where the average diurnal temperature is even close to 255K. Even on the lunar equator, the mean temperature does not exceed 210K and it drops to about about 95K at the poles … You do the math!
Phil. says:
That particular issue is not a problem. See my post here, and Arthur’s nice paper in particular, for details: http://wattsupwiththat.com/2011/12/29/unified-climate-theory-may-confuse-cause-and-effect/#comment-852111
There is an issue, however, with defining an average surface temperature T_sb by assuming a temperature distribution to be given by requiring local energy balance at each point in space and time (i.e., ignoring heat storage or heat flow). It creates an artificially large “surface enhancement” to be explained, most of which can be explained away by having a uniform temperature distribution. That is why the scientific community attributes a rise of the surface temperature 33 K to the natural greenhouse effect on earth, not 133 K. The other 100 K can be obtained by making the surface temperature uniform in such a way that the outgoing radiation from the surface is still 240 W/m^2.
Phil,
One more comment regarding the integral of our Eq. 2 – Have you considered the fact that μ is the cosine of the solar zenith angle, and that a negative cosine implies that there is NO radiation reaching the surface (which is on the shaded part of the hemisphere), thus making the temperature ZERO in those areas and eliminating the need for an explicit integration? What Eq. 2 does is integrating the non-zero temperatures over the sunlit part ONLY and then dividing that number by the TOTAL surface area of the sphere to get the true average temperature … Do you understand it now?
Ned Nikolov says:
Ned,
Anything is possible if we don’t have to satisfy energy conservation! The hard part is explaining how pressure can cause a rise in surface temperature in a way that satisfies energy conservation.
And, sorry, but pressure can’t directly affect “near-surface IR exchange” unless there are elements in the atmosphere that absorb IR radiation, i.e., there is a greenhouse effect. Pressure can modulate the greenhouse effect in certain ways (e.g., by pressure-broadening of the absorption lines), but it can’t create something from nothing.
Ned Nikolov says:
Read this: http://arxiv.org/abs/0802.4324 And, note that Arthur is not claiming to have discovered any new physics. He is just explaining what is already known in light of Gerlich & Tscheuschner’s paper obfuscating the issue.
In other words, it is well-known that the convention calculation using the S-B Equation sets a maximum value on the average temperature that occurs in the absence of a greenhouse effect. That maximum is realized for a planet with a uniform (***in space and time***) surface temperature. For a planet with little or no atmosphere (and no liquid water), the temperature can be very non-uniform and the resulting average temperature considerably lower.
G. Karst says:
Perhaps because you are not qualified to judge the scientific merits of the arguments? Otherwise, it would remind you more of various screwball hypotheses by people who think they’re the next Galileo and ain’t.
http://wattsupwiththat.com/2011/12/29/unified-theory-of-climate/#comment-853213
“In fact, the Diviner data show that there is NO latitude on the Moon surface, where the average diurnal temperature is even close to 255K.”
That’s funny, the Diviner website says the following:
“Mean Surface Temperatures: Day: 380K; Night: 120K”
http://diviner.ucla.edu/science.shtml
Want to try again? It’s not like we haven’t had people on the surface of the Moon; it’s temperature isn’t a big secret.
Something to do while waiting for Friday’s further enlightenment (? a second coming?).
I really liked Dr. Bill’s analogy (somewhere above) of weighing the whole gravel bucket rather than propose weights of individual pieces. A better analogy since Dr. Nikolov & I typically deal with separating trees from the forest and haven’t figured out how to weight the forest.
Taking Dr. Bill’s suggestion, I would offer a simple grammar school (ok maybe high school) experiment for you folks who love science but are having problems (wasting time?) dealing with the pebbles. Here it is:
Given that: Nikolov & Zeller are obviously from outer space hence couldn’t have a clue about our planet’s surface temperature let alone GHG physics.
Hypothesis: The Nikolov/Zeller outer-space Equation 8 that they propose will predict the average surface temperature on any planet or moon in the entire universe with an atmosphere (including Earth!) is a joke and as such will not work. Furthermore clearly it won’t work because radiative transfer and greenhouse gases are not addressed in their equation.
Materials: Nikolov-Zeller Equations 2 & 7 (used in Eq. 8, above this blog), and measured data from either Nikolov-Zeller Table 1 (above this blog) or better obtain the same values as needed from Wikipedia and other sources.
Procedure: 1. Remove all thoughts and beliefs of GHG theories, etc. from your mind (may require serious religious council). 2. Use Equation 2 to calculate the grey-body temperature(s) for each planet or moon to be tested. 3. Use Equation 7 to calculate surface temperatures as a function of surface pressure and grey-body temperature calculated from Eq. 2. (clue: first using algebra, you will have to solve Eq. 7 for the surface temperature by multiplying both sides by the grey-body temperature)
Results: Compare the calculated average surface temperatures with independent temperatures that have been measured as available in the literature remembering that it is the global average(s) over time that is/are being addressed.
Discussion: talk about your findings and speculate what they mean. How does radiative transfer affect the results? How do the chemical constituents of the various atmosphere(s) impact the surface temperature calculations? Bonus: Given that Venus’s atmosphere is mostly CO2 and an obvious runaway greenhouse gas example, does the Nikolov-Zeller approach to calculate Venus’s surface temperature using Venus pressure & Venus grey-body temperature differ at all from the approach used to make the same calculation on Earth?
Conclusion(s): Draw conclusion(s) and then report to WUWT so that once and for all the truth about these 2 outer-space alien-cadets can be known.
Robert,
I saw that very statement on their website, but after reading some of the papers on the same website discussing data and models (look at the the publications section http://www.diviner.ucla.edu/publications.shtml ), it became clear to me that the 380K ‘mean daily’ temperature quoted on that page actually refers to the mean daily MAXIMUM temperature, NOT the temperature averaged over the light portion of a lunar day. The 380K temperature is only reached for couple hours in the middle of the lunar day and only at latitudes below 60 degree …The same goes for the reported 120K at night. This is the mean MAXIMUM nighttime temperature! Temperatures during a lunar night drop to about 80K at lower altitudes and to 40-50K at the poles! This is published in NASA’s research papers! … Please investigate further.
Also, direct temperature measurements taken at the Apollo 15 landing site (26 deg N) over a period of about 5 years in the 1970s, suggest as well that the 380K is the MAXIMUM daily temperature, see this peer-reviewed paper by Huang (2008):
http://www.geo.lsa.umich.edu/~shaopeng/Huang07ASR.pdf
One must always look beyond the first set of evidence to find the truth! That is what we have been doing over the past 2 years while working on our theory …
reposted from the Cause and Affect thread by Ira Glickstein>>>>
The more I watch this debate the more blindingly obvious it becomes that N&Z are right.
Willis et al, you’ve asked for a physical mechanism and Richard S Courtney gave it to you. If I may, here is his explanation in slightly different terms.
Assumptions
Rocky planet.
atmosphere that neither absorbs nor emitts
average insolation of 240 w/m2
Goal
Mechanism by which the presence of the atmopshere raises average T without raising average P.
Explanation
By SB Law, we expect an average T of -17.9 C
However, we CANNOT calculate average of T for a given average P since P doesn’t vary with T but with T^4!
FURTHER, the atmosphere, while it cannot absorb or emitt, must still participate in energy transfer via conductance and convection. This has no possible result but to remove energy from the “tropics” (which receive higher than average insolation and are at a higher than average T) to the “arctic zones” (which receive lower than average insolation and so are at a lower than average T)
Example calculation
Assumptions
Without presence of atmosphere:
Tropics are subject to an average P of 2 x 240 = 480.
Vis SB Law, T = 30 C
Arctic Zones are subject to an average P of 0
Via SB Law, T = -273 C
Assumptions
WITH presence of atmosphere
Some portion of P at the tropics is transferred to the atmosphere via conduction. This in turn causes convection. The convection in turn moves warm air from the tropics to the arctic zones, and cool air the other way. This cools the tropics and warms the arctic. For the purposes of simplicity, let us assume equal areas between the tropics and the arctics. Let us further assume that the net effect is to cool the tropics by 50 w/m2 and warm an equal area of the arctics by 50 w/m2. Let us apply SB LAw to see affect on temperatures.
Tropics = 480 – 50 = 430
Via SB Law, T = 22 C
Change = -8 degrees.
Arctics = 0 + 50 = 50
Via SB Law, T = -100 C
Change = + 173 degrees
And there you have your mechanism. By removing 50 w/m2 from the tropics, that area sees a reduction in temperature of 8 degrees. The 50 w/m2 added to an equal area in the artic sees an increase in temperature of 173 degrees. Since the areas are equal in size, and one decreased in P by the same amount as the other increased in P, the laws of thermodynamics are intact.
…continued, snipped off the bottom part by accident
Average T however is higher. MUCH higher.
Average T^4 HAS NOT CHANGED!
Average P HAS NOT CHANGED!
Of course you’d never actually get 0 degrees K at the poles even in a planet with no atmosphere because the planet ITSELF will conduct heat from the tropics to the poles to some extent. There are other minutia I can think of that would throw the numbers off, but this should serve to illustrate a mechanism by which the presence of an atmosphere increases average T simply by redistributing energy from the “hot” zones to the “cold” zones via conduction and convection.
And that is why relying on the average of T instead of the average of T^4 has bolloxed up this entire conversation for the last several decades. average of T means diddly squat. average of T^4 is the ONLY way to determine if the planet is in an energy imbalance and by how much.
Reply to Robert Murphy (January 4, 2012 at 1:43 pm):
Robert,
One additional comment regarding the ‘mean temperatures’ listed on the Diviner’s webpage.
http://www.diviner.ucla.edu/science.shtml
Note that they compare Moon’s ‘Mean Daily Temperature’ of 380K with Earth’s ‘Mean Daily Temperature’ of 295K … What’s the Earth actual average surface temperature? 287.6K! Where do we have 295K average temperature on Earth? On the equator! … This gives one also a clue how accurate the listed mean temperatures on that page really are. Apparently someone at NASA was not paying attention, when populating that page with content … 🙂
Ned Nikolov says:
January 4, 2012 at 1:22 pm
Phil,
One more comment regarding the integral of our Eq. 2 – Have you considered the fact that μ is the cosine of the solar zenith angle, and that a negative cosine implies that there is NO radiation reaching the surface (which is on the shaded part of the hemisphere), thus making the temperature ZERO in those areas and eliminating the need for an explicit integration? What Eq. 2 does is integrating the non-zero temperatures over the sunlit part ONLY and then dividing that number by the TOTAL surface area of the sphere to get the true average temperature … Do you understand it now?
Yes I always did, it appears that you do not. In order to integrate cosine over a hemisphere you would normally integrate from define the angle relative to the zenith and integrate from cos(-pi) to cos(pi) or (more easily) integrate from 0 to 1 and multiply by 2, integrating only from 0 to 1 only integrates over quarter of the sphere not a hemisphere hence the need for the x2. You appear to be unaware of this judging by your answer, so you are only integrating over half the sunlit part.
Do you understand the point now?
Joel Shore says:
January 4, 2012 at 1:20 pm
Phil. says:
“While you’re here perhaps you’ll address a few points:
Your equation 2 shows the limits of 0 to 1 for the integration wrt μ, it should obviously be from -1 to 1 which by symmetry is double the value of the integral you show. Perhaps you could explain where this factor of 2 has gone in your derivation (this point has been raised by others here but you haven’t addressed it).”
That particular issue is not a problem. See my post here, and Arthur’s nice paper in particular, for details:
Reproduced here:
Joel Shore says:
January 3, 2012 at 2:16 pm
However, the integral is more easily carried out if you make theta = 0 correspond to the point on the earth where the sun is directly overhead because you have symmetry about such an axis. And, in fact, the integral is then what Nikolov et al have written down.
Exactly my point, but if you do that the integral is twice what Nikolov has used!
“it became clear to me that the 380K ‘mean daily’ temperature quoted on that page actually refers to the mean daily MAXIMUM temperature, NOT the temperature averaged over the light portion of a lunar day.”
It’s still nowhere near 154K.
“Note that they compare Moon’s ‘Mean Daily Temperature’ of 380K with Earth’s ‘Mean Daily Temperature’ of 295K … What’s the Earth actual average surface temperature? 287.6K!”
It’s a helluva lot closer than your imaginary number for the Moon, 154K. It’s astounding how some people think they can invent numbers for well known values and revolutionize fields they have no training in. You can’t even *conceive* of the possibility that you might be wrong and all those PhD atmospheric scientists might have a better grasp of the subject than you. You’re too busy comparing yourself to Copernicus.
davidm hoffer: Since you apparently believe your post is so important that you need to repeat it here, I will just repeat the answer I gave over in the other thread:
davidmhoffer says:
Read this: http://wattsupwiththat.com/2011/12/29/unified-climate-theory-may-confuse-cause-and-effect/#comment-853148 , many times if you have to.
What you have just shown is why the vast majority of climate scientists talk about the “surface temperature enhancement” being 33 K and not 133 K (as Nikolov et al say it is): Those scientists understand that you can get different values by having a different temperature distribution. Hence, if you have a surface emitting 240 W/m^2 and having the distribution that Nikolov et al. talk about, the temperature will be ~155 K. If you move the heat around, you can indeed raise the average temperature up further. In fact, you can get it up to 255 K by having a perfectly uniform temperature distribtuion. But, no matter how hard you try, you are not going to get a surface emitting 240 W/m^2 to have a higher average temperature than that (for a surface with emissivity approximately equal to 1).
I think you are learning the hard way that climate scientists are a little smarter than you think and you and Nikolov might be just a little bit less smart than you think.
Phil. says:
No…Phi. 0 to 90 deg encompasses the entire sunlit hemisphere for that geometry.
Joel Shore says:
January 4, 2012 at 4:24 pm
Phil. says:
Exactly my point, but if you do that the integral is twice what Nikolov has used!
No…Phi. 0 to 90 deg encompasses the entire sunlit hemisphere for that geometry.
Afraid not Joel, a hemisphere is from 0-180º.
Phil. says:
The Northern hemisphere goes from 0 to 90 deg north latitude and zero to 360 degrees longitude. He is integrating over the “Northern hemisphere” except that the sphere is tipped by 90 deg so it is facing toward the sun. He needs to integrate from 0 to 360 deg in longitude and 0 to 90 deg in latitude on such a sphere. (Latitude is the polar angle. longitude is the azimuthal angle.)
Reply to Robert Murphy (January 4, 2012 at 4:03 pm)
Robert,
I did not expect that I have to spell out everything for you. Apparently, you do not know what a diurnally average temperature is, nor do you understand the meaning of a MAXIMUM mean temperature. So, let me try to clarify this for you one more time:
1) A diurnal mean temperature is an AVERAGE between the daytime mean temperature and the nighttime mean temperatures. The 380K quoted on the Diviner webpage is VERY close to the ABSOLUTE MAXIMUM temperatures measured on the moon, see these papers
http://diviner.ucla.edu/docs/fulltext.pdf
http://www.geo.lsa.umich.edu/~shaopeng/Huang07ASR.pdf
and
http://diviner.ucla.edu/docs/paige_2010.pdf
The diurnal temperature amplitude (i.e. the difference between daily max and daily min temp) on the Moon is VERY large. On the lunar equator, this amplitude is about 290K and declines to about 70-80K at the poles. Also, the daily max temperature on the Moon is only maintained (lasts) over a short period of the lunar day (which, by the way, equals 27.3 Earth days). At any given location on the Moon, the temperature drops quickly as one moves away from the a noon point. By sunset, the temperature is already around 120K for most latitudes (outside the polar regions), and continues to drop during the lunar night reaching about 75-80K just before sunrise. In addition, the polar regions have temperature about 150K during daytime and 40-50K during nighttime. Taking into account this pattern of temperature change and considering the fact that a lunar night nearly equals in length a lunar day, one can calculate the AVERAGE DIURNAL temperature at the lunar equator and at the poles using the information presented in the above papers. The result is about 210K mean diurnal temperature at the lunar equator, and 90-100K mean diurnal temperature at the poles. The actual mean temperature for the entire Moon surface falls between those two limits (210K and 95K), and given the purely radiative nature of the heating on the Moon, the final mean is very likely close to the average of the arithmetic extremes, i.e. (210 + 95)/2 = 152.2. So, there you have it! … I encourage you to study carefully the above references.
Phil,
What kind of a science background do you have? Apparently your calculus skills can use some improvement.
The cos(theta) gets integrated between 0 and 1, because on the sunlit hemisphere, the solar ZENITH angle (theta) varies from 0 to 90 deg. What’s a solar zenith angle? It’s the angle between the solar beam and the axis perpendicular to the surface. So, theta varies between 0 deg at the equator and 90 deg at the poles. Since we have 2 poles (2 quarter spheres), we use a second integral from 0 to 2*pi, which essentially doubles the estimate obtained from the first integration of cos(theta). Note that 2*pi is used to account for the surface of a hemisphere. This completes the integration of the temperature field over the SUNLIT hemisphere. Since the temperature of the shaded hemisphere is 0, to estimate the overall mean temperature for the entire sphere, we now have to divide the above integral by 4*pi … and voila! Do you get it now? …