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.
Phil. says:
January 4, 2012 at 4:53 pm
Afraid not Joel, a hemisphere is from 0-180º.
>>>
ROTFLMAO!
Sorry, I thought both of you had at least Calculus for Dummies. If you did then I thought you two knew in science how to consider all possible paths. (and that at last explains the deficiencies we all have seen!)
OK guys, try considering the integral 0 to 1 is from the center of the hemisphere to the edge, OK?
Now do either of you know how far it is around the circumference or should I explain that too?
Reply to davidmhoffer (January 4, 2012 at 3:08 pm)
David,
At first glance, your thought experiment appears to provide a good insight about how a redistribution of energy by an atmosphere from the equator to the poles might increase the average global temperature and thus explain the thermal enhancement of the atmosphere. However, you have made one critical conceptual : Basically, your calculations show this effect due to the fact that radiation intensity changes very fast with temperature at low temperature values versus high temperatures. In other words, the partial derivative of P with respect to T is much larger at low temperatures compared to high temperatures. This is due to the 4th power of T. However, the problem is that the real atmosphere does NOT transport (redistribute) radiative fluxes but air masses of certain temperatures. In a sense, you can say that the atmosphere transports ‘temperatures’. This means that high temperatures must first be created in the tropics and then transported poleward, where they radiate and conduct/convect heat to air masses and land surfaces at high latitudes. This essentially nullifies the radiative effect you are talking about …
One cannot escape the physical fact that pressure enhances the energy content of a system compared to zero-pressure conditions thanks to increased rates of molecular collision, and this premise comes straight from the Gas Law! This fact was widely known and undisputed 30-40 years ago, but thanks to our modern ‘radiatively skewed’ physical education, it has been totally downplayed to the point that PhD scientists now believe that pressure brings NOTHING to a thermodynamic system…. I mean, it’s really embarrassing! This used to be a high-school level knowledge, at least during my high-school days in Europe anyway … 🙂
kzeller, January 4, 2012 at 2:55 pm :
That analogy (a good one, in my opinion) was made by davidmhoffer.
/dr.bill
davidmhoffer says:
January 4, 2012 at 7:41 pm
Tim Folkerts;
Agreed!
I used an extreme example to illustrate the issue, and I made a couple of mistakes along the way. Better would have been (using round numbers here just to simplify things) if I’d supposed insolation to be 1000 w/m2 after albedo, the scenario would look more like this:
“Average” insolation = 250 w/m2
“Average” insolation at tropics = 500 w/m2
“Peak” insolation at tropics = 1,000 w/m2
“Average” insolation at poles = 0
(because my pretend rock has no inclination to the orbital plain. Since it is MY make believe rock I can give it any inclination I want 😉 )
“Peak” insolation at poles = 0
This would provide for a power curve of “average” insolation of 250 w/m2 at the tropics that declines with altitude until you get to the poles where it is zero. It wouldn’t be a linear decline since my rock has a curved surface, but the exact power curve isn’t important in terms of understanding the concept.
However, “peak” insolation would be 1,000 w/m2 at the tropics, and decline to zero at the poles. This brings up a series of concepts. While the poles would obviously trend toward an equilibrium temperature of zero, calculating the equilibrium temperature of the tropics is not so straight forward. At night, insolation is zero, and so the tropics would cool toward zero at night. Assuming a 24 hour day, they’d never get anywhere near zero of course, the sun would rise long before that could happen. So what equilbrium temperature do the tropics tend toward in the day?
If we assume that P starts at zero, peaks at 1000 at noon, and then falls back to zero in evening, we could justify a rough estimate of 500 w/m2 average which would yield via SB Law an “average” temperature of 33.4 C. But for over half the daylight hours, insolation would actually be more than that. Briefly at noon, insolation would be at 1,000 w/m2 which would translate to 91.4 C. Of course it would never get to 91.4 C anymore than it would get to zero at night. The point being that the 250 w/m2 = -15.3 C is no more accurate than 500/33.4C or 1000/91.4 C. You’d have to integrate across the daylight curve to arrive at the equilibrium temperature for the tropics, and it would NOT be the same as what one would get by simply calculating from the “average” insolation.
With that in mind, let’s throw in an non absorbing non emitting atmosphere. What happens?
In my illustrative comment above, I invented some equilibrium temperatures at poles and tropics and tried to show what would happen if the processes of conduction and convection moved 50 w/m2 away from the tropics and to the poles. That’s not realistic of course. A better model would be that considerably more than 50 w/m2 would be removed from the tropics.
Again, just to illustrate the concept, I’m picking numbers here. Since the temperate zones and arctic zones are far cooler than the tropics simply due to angle of inclination to the sun, the atmosphere has little choice but to warm by conduction and convect. The warm air must rise, pulling cold air beneath it from the poles. The hot air rises to some height, then spill toward the poles.
Now we have a whole bunch of things happening at the same time. For starters, we can now suggest that the “average” temperature of the tropics themselves would be higher than without an atmosphere, and that not one single extra watt is required to accomplish that.
Since the atmosphere is warmed by conduction during the day, at night, it must give back by conduction. But because P varies with T^4, the number of degrees that the atmosphere “gives back” is greater than what what it took in the first place. The tropics have no choice but to warm the atmosphere, which then redistributes the energy absorbed in two ways. One is via convection which drives energy toward the poles, and the other is conduction BACK to the tropics as soon as night time temperatures fall below the temperature of the atmosphere.
So again, I’m making up rough numbers to illustrate the point that there is in fact a mechanism for a non absorbing, non emitting atmosphere to raise surface temps without violating the laws of thermodynamics.
Suppose for argument’s sake that the atmosphere removes an average of 100 w/m2 from the tropics during the day. It must distribute that energy absorbed in two ways. Convection forces some energy to be distributed toward the poles, and the night/day cycle means that some gets sent back to the surface at night time. For illustrative purposes, let’s suppose that 25 w/m2 of the 100 w/m2 get redistributed via conduction back to the tropics when they cool off at night.
So… the target equilibrium P during the day for the tropics with no atmosphere might have been 500 w/mw, but with an atmosphere it is only 400 w/mw. From SB Law:
500 w/m2 = 33.4 C
400 w/m2 = 16.8 C
The atmosphere reduces the “target” equilibrium temperature by 16.6 degrees. But what happens at night when the atmosphere “gives back” via conduction, 25 w/m2?
0 w/m2 = -273 C
25 w/m2 = -128.1 C
See what happened? Moving 100 w/m2 away from the tropics during the day reduces the equilibrium target temperature by 16.6 degrees, but taking just 25% of those watts/m2 back at night increases the night time equilibrium temperature by a whopping 144.9 degrees! All we need do is average the tropics night time and day time equilibrium temperatures to see that a miniscule 25 watts moved by conduction via the atmosphere to the night time results in a massive temperature increase without any change in the energy balance at all. But I said the atmosphere would in this example move 100 w/m2 away from the tropics in day time, and I only sent 25 w/m2 to the night time, let’s figure in them other 75 watts.
Convection ensures that warm air moves toward the poles, heating the earth below via conductance. The night time “temperature boost” applies across all latitudes. The day time temperature boost is lowest in the south temperate zones, higher in the north temperate zones and highest (on a degrees per watt/m2 basis at least) in the arctic zones. Surface areas being different, angle of incidence varying, and so on, we can actually say that our remaining watts/m2 are going to be distributed in a fashion that adds up to 75w/m2. Unless of course my invented rock has surface area irregularities that result in this being the case. Since it is my rock that I invented, and I’m way too lazy to do the math properly, I’m going to go with that.
Suppose that our south temperate, north temperate, and arctic zones each get a 25 w/m2 boost from conduction from the atmosphere, and that the areas equal out such that the square meters match that of the tropics (I know, rather addly shaped rock, but just ignore that and stick with the arithmetic).
The night time temperature boost of all three zones (the target equilibrium temperature they would now tend toward, though they would be unlikely to actually get there before sunrise) would be plus 144.9 degrees. The 100 watts/m2 we liberated via conduction from the tropics in the first place only dropped the temperature of the tropics by 16.6 degrees!
The day time equilibrium temperature of the arctic (previously with zero insolation) would now also be higher by 144.9 degrees. The temperature boost in the temperate zones would depend on what their “average” temperature without an atmosphere would be. Let’s guestimate that the “average” P of the south temperate zones was 300 w/m2 and the north temperate zone 200 watts/m2, and that each get a boost of 25 w/m2 from conduction from the atmosphere.
300 w/m2 = -3.3 C
325 w/m2 = 2.2 C
“warming” = 5.5 degrees
200 w/m2 = -29.3 C
225 w/m2 = -22.0 C
“warming” = 7.3 degrees
So we now have a planet that fluctuates between day time warming and night time cooling. Each day the warming tends toward the equilibrium high, but never makes it before cooling sets in. Each night, the cooling tends toward the equilibrium low, but never makes it before sunrise and warming starts again. In return for reducing the day time equilibrium high of the tropics by just a few degrees, the night time low equilibrium point of the entire planet increases by over 100 degrees. The equilibrium day time highs of the south temperate, north temperate and arctic zones also increase, collectively “on average” more than what the tropics lost, even though the tropics lost 4 times as much in watts/m2 as the other zones gained.
I’m getting bleary eyed and I’m pretty certain I’ve got some messed up math in there on all sorts of issues, but I think by now the mechanism that everyone is screaming cannot exist without breaking the laws of thermodynamics, does in fact exist, and need not add or substract a single joule of energy from the system to still arrive at higher surface temperatures, and without emitting or absorbing a single photon.
Which has what to do with surface pressure? Glad someone asked. I’ve made up the numbers to illustrate how surface temperatures can be increased without adding or subtracting energy from the system. But how much conductance actually occurs for any given atmosphere.
Well, that’s dependant upon one thing. The density of the gas. Which is dependant upon…
mean surface pressure. Exactly how N&Z have said it.
Ned Nikolov says:
Yes, to PRESSURIZE a system, you have to perform work, i.e., you have to input energy, and as a result the pressurized system has higher energy. However, the atmosphere of the Earth isn’t being pressurized. Yes, there is air that is descending and that air is being pressurized and gaining internal energy. However, there is also air that is ascending and that air is expanding and decreasing its internal energy (i.e., it is doing work on the rest of the atmosphere when it expands).
But…this doesn’t solve our energy balance problem: To explain how the temperature of the surface can be such that it emits 390 W/m^2 whereas the entire Earth-atmosphere system is absorbing only 240 W/m^2, you have to explain what SOURCE OF ENERGY is supplying the additional 150 W/m^2 to the earth-atmosphere system. In other words, you have to identify an external source (like the sun) or an internal source (like heat from the core of the Earth, with the ultimate source of that being radioactive decay, as I recall).
You won’t be able to do that, of course, because we in fact know that the Earth is NOT emitting 390 W/m^2 as seen from space; it is only emitting 240 W/m^2…And, the reason is that is that the atmosphere is absorbing some of the emission from the surface. This is what is called “the greenhouse effect” and it is the only thing that allows for the possibility that the surface can be at a temperature where it emits 390 W/m^2.
Ned Nikolov;
However, the problem is that the real atmosphere does NOT transport (redistribute) radiative fluxes but air masses of certain temperatures. >>>
My point was that the air mass, via simply conduction and convection, can redistribute energy. One doesn’t need radiative processes for that to happen. Willis Eschenbach and others were asking the question as to how temperature could be increased without violating the laws of thermodynamics. What I was trying to illustrate is that any redistribution of energy, including conductance and convection, must increase average T without increasing average P. In fact, it matters not what the mechanism is, as long as their is a mechanism. In this case, Willis had asked how surface temps could increase if there were no radiative processes at play, and I was attempting to answer that question.
Whoops, sorry about that davidmhoffer & thank you for the analogy & thank you dr.bill for the correcting the credit. Both of you are excused from having to do the experiment in any case! 🙂
Ned: The reason why radiation is considered is because that is the only way that the Earth+atmosphere can communicate energy (in any significant way) with the rest of the Universe. And, what is getting you (and a lot of others) hung up is that you are thinking about lots of things that move energy around in our atmosphere, which climate scientists know about and include in their models…But it doesn’t help you deal with the fundamental issue here, which is the “top of the atmosphere” energy budget.
Just stepping back for a second, what is it that makes you think that you are that much smarter than the entire climate science community? Can you even entertain the notion that the reason why you are getting a different answer than them is because of some boneheaded mistakes on your part? Is it within your abilities of self-awareness to understand this possibility?
On that we can definitely agree; we just disagree on what “it” is.
davidmhoffer says:
You have created a complete strawman. WIllis did not ask that. Willis asked how the Earth could be emitting about 390 W/m^2 when the Earth and atmosphere are only absorbing about 240 W/m^2 from the sun. For everybody but you, the fact that one can redistribute energy and get a different average temperature is not a brilliant new observation. We’ve known it for a long time.
Joel Shore says:
January 4, 2012 at 4:23 pm
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>>>
I find it unfortunate that you feel compelled to dispute me to your own detriment in two threads rather than one.
Joel Shore (Jan. 4, 2012 at 6:26 am):
Toward the end of progress in our scientific understanding of Earth’s climate, I request your stipulation to the proposition that if and when the previously described lapse rate control mechanism is operative and the intensity of the back radiation at Earth’s surface increases by Delta F, the intensity of the convective heat transfer at Earth’s surface increases by Delta F. It follows from energy conservation that the increase in the intensity of the electromagnetic radiation that is absorbed at Earth’s surface is nil.
Look Ned, if you really think that you, a forest ecologist, are going to come up with a better number for the Moon’s average surface temperature, a figure that has been well known for quite a while; that you, a forest ecologist, are going to overthrow all of atmospheric physics with an online manifesto; that you, a forest ecologist, are the next Copernicus about to usher in a new scientific revolution, you really need help. I hope you seek it, especially after nobody takes your claims seriously and the world of science passes you and your failed hypothesis by. That kind of rejection and failure can lead to all kinds of resentment and conspiracy theorizing about scientific censorship and intolerance. You already have enough issues (Dunning-Kruger Effect for one).
As is commonly done in figgering black-body transactions, put a continuous shell around the planet at the highest altitude that “receives” the 240 W/m^2. It is not possible, no matter the ingenuity of the vector bookkeeping, to have 390 W/m^2 outbound from that same altitude. Not for long, anyway.
Brian H (Jan. 5 at 1:54 am):
As the vector with intensity of 390 W/m^2 lies at the bottom of the atmosphere while the vector with intensity of 240 W/m^2 lies at the top of the atmosphere, the rules of vector addition do not apply to the situation you describe. At the bottom of the atmosphere, the heat flux is the vector sum of the upward pointing vector of intensity 390 W/m^2 and a downward pointing vector. If the latter vector is of intensity 390 W/m^2 then the intensity of the heat flux is nil. Similarly, at the top of the atmosphere, the heat flux is the vector sum of the downward pointing vector of intensity 240 W/m^2 and an upward pointing vector. If the intensity of the latter vector is 240 W/m^2 then the intensity of the heat flux is nil. In my example, the heat fluxes at both boundaries of the atmosphere are nil with the consequence that the atmosphere is not heating. Neither is the Earth heating. Heating is not happening despite the disparity in the intensities of the two vectors that you reference.
Wayne:
Please have patience with us lesser lights who still have difficulty with Ned’s Equation 2 (although you may remember that I verified that it comes out with essentially the right answer if you ignore its imposing anisotropy on background radiation).
Here’s why I think many of us have difficulty. Thinking of the earth, we tend naturally to integrate with respect to latitude and longitude. Testimony to that is that you and I both used that approach in computing Equation 2 numerically. But Ned didn’t, so he lost me right off.
What he did if I understand it is move the sun to Polaris’s position so that it shines directly on the North Pole. Then he translated the measure of latitude so that the North Pole’s latitude is zero and the South Pole’s is 180, and mu is the cosine of the resultant latitude. Another way of looking at it is that, for a point on the surface of a unity-radius sphere, mu is the distance along the axis in the direction of the sun from the sphere’s center to the plane perpendicular thereto that contains that point. Theta is longitude, or angular position around the circle in which the plane intersects the sphere. So Ned integrates along the axis and around the circle of intersection. mu < 0 implies nighttime, so integration limits for mu can be 0 and 1 if we want to ignore (de minimis) night-time background radiation. Fair enough, although it took me awhile to recognize what his coordinate system was.
But my problem with Equation 2 did not end there. Equation 2's radical is the expression for radiation power density at (mu, theta), so what's left in the integral, i.e., d mu d theta, should be differential area. But I don't see how d mu d theta is differential area.Yes, I recognize that simply integrating d mu d theta with his limits does indeed yield 2 pi, as it should. But that looks to me as though it's computing the area of a cylinder, not a sphere. I would have thought a sphere's differential area would be (again, for unity radius) cos(phi) d phi d theta, where phi is (Nikolov-translated) latitude. Since d phi = -d mu//sqrt(1 – mu^2), I would have expected to see -mu d mu d theta/sqrt(1 – mu^2) as the differential area. But I don't. Yet I've I verified Ned's numerical result, so he somehow got it right, whereas I would have expected too high a value: I've no doubt done the trig or calculus wrong.
Since you've had no trouble with that equation, might I impose upon you to help with my math?
davidmhoffer says:
The reason I am doing that is because you felt that your result that you can have the same emission with two different temperature distributions having two different average temperatures (something nearly everyone but you knew already) was so important that it warranted copying your post explaining this to both threads. I have continued the discussion in the other thread.
Wayne:
Actually, I guess I didn’t verify the equation; I just verified the result Ned reported he got when he applied it. Like you, I actually used a different equation, as any lurker can see from my (erroneously commented) R code in the Feedback about Feedbacks thread.
Terry Oldberg says:
Frankly, this is gobbly-gook. The point is that the Earth is emitting a flux of radiative energy that is 390 W/m^2 at the surface of the Earth. If none of that radiation is absorbed by the atmosphere, then the flux of radiation that escapes to space is 390 W/m^2. It is irrelevant what the net heat flow is.
No…That is not correct. It is correct if the increase in radiative transfer from the atmosphere to the Earth occurs without a reduction in the intensity of radiation emitted to space. However, in the case of adding greenhouse gases, where the amount of radiation emitted to space is reduced, this compensation does not occur.
The reason that the maintenance of the lapse rate does not imply that the convective heat transfer balances things is found from going through the argument about what happens: When you add more greenhouse gases, the Earth system is now emitting less energy to space then it receives from the sun because the emission is occurring from higher levels in the troposphere where it is colder. In other words, the “effective radiating level” was at 255 K but it has now moved up in the atmosphere and is at a colder temperature.
As a result, energy accumulates and the Earth system warms. Once the system has warmed and radiative balance is again restored, this new effective radiating level will have warmed to 255 K…And so, given the same lapse rate, you will now have a higher surface temperature (because the surface temperature is determined by taking the altitude at which the temperature is 255 K and using the lapse rate to extrapolate down to the surface and that altitude is now higher).
Robert Murphy says:
January 5, 2012 at 1:30 am
“Look Ned, if you really think that you, a forest ecologist….”
Aha, ad hominem attacks. The first sign that someone wants to discuss who’s authority is correct, instead of discussing the science.
Reply to Robert Murphy (January 5, 2012 at 1:30 am):
Robert to your comment above:
Look Ned, if you really think that you, a forest ecologist, are going to come up with a better number for the Moon’s average surface temperature, a figure that has been well known for quite a while; that you, a forest ecologist, are going to overthrow all of atmospheric physics with an online manifesto; that you, a forest ecologist, are the next Copernicus about to usher in a new scientific revolution, you really need help. I hope you seek it, …
First of all, thank you for your honesty! I would like to respond by pointing out two facts: 1) The number for the average Moon temperature I presented to you is not mine invention, but a product of NASA’s own research as documented in the peer-reviewed publications I referred you to; 2) I suppose you also have a problem with the Theory of Relativity, since it was proposed by a low-level clerk working for a Swiss Patent Office … 🙂
“The number for the average Moon temperature I presented to you is not mine invention…”
Sure it is Ned. That’s why the number NASA (and everybody else) gives is nowhere near the number you invented.
“I suppose you also have a problem with the Theory of Relativity, since it was proposed by a low-level clerk working for a Swiss Patent Office…”
So now you’re Einstein too? Copernicus no longer good enough for you?. Are you aware he was a doctoral student in physics working on his thesis while he was working at the patent office? Apparently your knowledge of science history is as bad as your knowledge of atmospheric physics. Look up the Dunning–Kruger effect and take an honest look in the mirror.
Hey Ned,
we had an agreement! You only got to be Copernicus because I got to be Einstein! You can’t be both it’s not fair. I’m going to tell my Mommy!
Robert, to your comment:
“So now you’re Einstein too? Copernicus no longer good enough for you?. Are you aware he was a doctoral student in physics working on his thesis while he was working at the patent office?”
Yes, I’m aware that Einstein was a doctoral student at that time … And I already got my PhD in biophysics 15 years ago! How about you? What kind of advanced degree do you have?
Again, read the papers I sent you earlier, and use you brain to figure out the Moon’s temperature from the official peer-reviewed research. And, please, stop ridiculing yourself with personal remarks .. Thank you!
We are not talking about heat flux. We are talking about radiative energy. If you want you could count photons and add up their energies. Can’t you guys have some self-awareness about when you are flailing around horribly in order to believe what you want to believe. This debate is not about science…It is about people desperate to believe what their ideology dictates they have to believe to be true.
Joel Shore (Jan. 5, 2012 at 10:47 am):
Your response evades the issue of the energy conservation.
By the way, I posted something in the other thread that I am re-posting here, because it is very important. There is a very important factor that I was leaving out that explains the strong positive correlation between surface pressure and “surface temperature enhancement” in the way that Nikolov has defined it:
They [Nikolov’s fit to the celestial data] are a 5-parameter fit and there is good reason to believe that in general the surface pressure enhancement will be positively correlated with surface pressure for the following three reasons:
(1) Pressure causes a broadening of the absorption lines of the greenhouse gases, increasing the greenhouse effect.
(2) Atmospheres with higher surface pressure have more of all substances that they consist of…and hence will tend to have a larger amount of greenhouse gases if any significant proportion of the atmospheric constituents are greenhouse gases.
(3) Since Nikolov has chosen to measure surface temperature enhancement by considering T_sb to be determined by the approximation that the local insolation determines the local temperature (no heat flow or storage), most of the “surface temperature enhancement” will occur due to the fact that larger atmospheric pressures means that the atmosphere will have more heat flow and heat storage in it. For example, Nikolov says the Earth’s temperature is enhanced by 133 K but we in fact know that the greenhouse effect only is responsible for 33 K. The other 100 K comes from the more uniform temperature distribution that results when one has a significant atmosphere and is most certainly correlated with pressure. In fact, of the 8 bodies considered, I think that the “surface temperature enhancement” only has any significant component due to the greenhouse effect in 3 of them (Earth, Triton, and Venus) and probably only in Venus is it the dominant component of the so-called “surface temperature enhancement”.
I hadn’t mentioned (3) before but in fact it is probably the most important reason why there is a strong correlation between surface pressure and “surface temperature enhancement” defined as Nikolov has defined it.
Joel Shore (Jan. 5, 2012 at 6:11 am):
I get frustrated when you refuse to stipulate to facts, change the topic when you’re about to be pinned down or evade the issue by issuing an insulting ad hominem argument. I suggest to you that Richard Courtney and I have pinned you down on a fact but you lack the decency to stipulate to this fact so we can move the conversation along. The fact to which you refuse to stipulate is that the feedback control mechanism which pins the lapse rate to the adiabatic lapse rate does not violate energy conservation.