Guest essay by Roger A. Pielke Sr.
Main Points
1. The difference in ocean heat content at two different time periods provides the global average radiative imbalance over that time [within the uncertainty of the ocean heat measurements]
2. This global average radiative imbalance is equal to the sum of the global average radiative forcings and the global average radiative feedbacks.
3. The global average radiative forcing change since 1750 is presented in the 2013 IPCC WG1 Figure SPM.5 as 2.29 [1.13 -3.33] Watts per meter squared.
4. The global average radiative imbalance is given in the 2013 IPCC report as 0.59 Watts per meter squared for 1971-2010 while for 1993-2010 it is 0.71 Watts per meter squared.
5. Thus, assuming that a large fraction of the global average radiative forcing change since 1750 is still occurring, the global average radiative feedbacks are significantly less than the global average forcings; i.e. a negative feedback.
6. Such a negative feedback is expected (since the surface temperature, and thus the loss of long wave radiation to space would increase).
7. However, the water vapor and cloud radiative feedback must also be part of the feedback. This water vapor feedback is a key claim in terms of amplifying warming due to the addition of CO2 and other human inputs of greenhouse gases. The IPCC claims that the net cloud radiative feedback is also positive.
8. The IPCC failed to report on the global average radiative feedbacks of water vapor and clouds in terms in Watts per meter squared, and how they fit into the magnitude of the diagnosed global average radiative imbalance.
9. The reason is likely that they would to avoid discussing that in recent years; at least, there has been no significant addition of water vapor into the atmosphere. Indeed, this water vapor feedback, along with any other feedbacks must be ALL accommodated within the magnitude of the global average radiative imbalance that is diagnosed from the ocean heating data!
It certainly appears that, even using the 2013 IPCC WG1 assessment estimates, that the vapor amplification of global warming is not, as least yet, occurring.
I explain and elaborate on these issues below.
Introduction
As I wrote above, the 2013 WG1 IPCC assessment of the magnitude of the radiative forcings on the climate system persists in missing discussing a key fundamental issue, namely the estimated magnitudes of
· the global annual average radiative imbalance,
· the global annual average radiative forcing
· the global annual average radiative feedbacks
and how these quantities are related to each other.
Section 1 The Fundamental Budget Equation
The relationship between the annual global average radiative forcings, radiative feedbacks and radiative imbalance can be expressed by this budget equation
Radiative Imbalance = Radiative Forcing + Radiative Feedbacks
where the units are in Joules per time period [and can be expressed as Watts per area].
The fundamental difference with this approach and that presented in papers such as Stephens et al (2012) – see http://bobtisdale.files.wordpress.com/2013/10/05-figure-1-from-stephens-et-al-2013.png
is that instead of computing the radiative imbalance as a residual as a result of large positive and negative values in the radiative flux budget with its large uncertainty as shown by Stephens et al, this metric is a robust constraint on the analysis of the radiative fluxes.
As Bob Tisdale reports, the Stephens et al value of the global average radiative imbalance [which Stephens et al calls the “surface imbalance”] is 0.70 Watts per meter squared, but with the large uncertainty of 17 Watts per meter squared!
The Stephens et al paper is
Stephens et al, 2012: An update on Earth’s energy balance in light of the latest global observations. Nature Geoscience 5, 691–696 (2012) doi:10.1038/ngeo158 http://www.nature.com/ngeo/journal/v5/n10/abs/ngeo1580.html [as an aside, that paper, unfortunately, makes the typical IPCC type mistake in stating that the
“Climate change is governed by changes to the global energy balance.”
Changes in the climate system on any time scale is much more than just any changes in the global energy budget as we discuss, for example, in
Pielke Sr., R., K. Beven, G. Brasseur, J. Calvert, M. Chahine, R. Dickerson, D. Entekhabi, E. Foufoula-Georgiou, H. Gupta, V. Gupta, W. Krajewski, E. Philip Krider, W. K.M. Lau, J. McDonnell, W. Rossow, J. Schaake, J. Smith, S. Sorooshian, and E. Wood, 2009: Climate change: The need to consider human forcings besides greenhouse gases. Eos, Vol. 90, No. 45, 10 November 2009, 413. Copyright (2009) American Geophysical Union. http://pielkeclimatesci.files.wordpress.com/2009/12/r-354.pdf
Section 2 The Radiative Imbalance
With respect to the Radiative Imbalance, as I proposed in my paper
Pielke Sr., R.A., 2003: Heat storage within the Earth system. Bull. Amer. Meteor. Soc., 84, 331- 335.
http://pielkeclimatesci.files.wordpress.com/2009/10/r-247.pdf
the radiative imbalance can be estimated based on the changes in the ocean heat content. As written in
Levitus, S., et al. (2012), World ocean heat content and thermosteric sea level change (0-2000), 1955-2010, Geophys. Res. Lett.,doi:10.1029/2012GL051106
“The world ocean accounts for approximately 90% of the warming of the earth system that has occurred since 1955”
Jim Hansen had provided his value of the heating rate in a communication to me in 2005 http://pielkeclimatesci.files.wordpress.com/2009/09/1116592hansen.pdf]
as
The Willis et al. measured heat storage of 0.62 W/m2 refers to the decadal mean for the upper 750 m of the ocean. Our simulated 1993-2003 heat storage rate was 0.6 W/m2 in the upper 750 m of the ocean. The decadal mean planetary energy imbalance, 0.75 W/m2 , includes heat storage in the deeper ocean and energy used to melt ice and warm the air and land. 0.85 W/m2 is the imbalance at the end of the decade.”
More recent information, with respect to the Radiative Imbalance is reported in
Levitus, S., et al. (2012), World ocean heat content and thermosteric sea level change (0-2000), 1955-2010, Geophys. Res. Lett.,doi:10.1029/2012GL051106
“The heat content of the world ocean for the 0-2000 m layer increased by 24.0×1022 J corresponding to a rate of 0.39 Wm-2 (per unit area of the world ocean)…. This warming rate corresponds to a rate of 0.27 Wm-2 per unit area of earth’s surface.”
The IPCC WG1 Chapter 3 [http://www.climatechange2013.org/images/uploads/WGIAR5_WGI-12Doc2b_FinalDraft_Chapter03.pdf]
writes
“It is virtually certain that Earth has gained substantial energy from 1971–2010 — the estimated increase in energy inventory between 1971 and 2010 is 274 [196 to 351] ZJ (1 ZJ = 1021 J), with a rate of 213 TW from a linear fit to the annual values over that time period (Box 3.1, Figure 1). Ocean warming dominates the total energy change inventory, accounting for roughly 93% on average from 1971–2010. Melting ice (including Arctic sea ice, ice sheets, and glaciers) accounts for 3% of the total, and warming of the continents 3%. Warming of the atmosphere makes up the remaining 1%. The 1971–2010 estimated rate of oceanic energy gain is 199 TW from a linear fit to data over that time period, implying a mean heat flux of 0.55 W m–2 across the global ocean surface area. Earth’s net estimated energy increase from 1993–2010 is 163 [127 to 201] ZJ with a trend estimate of 275 TW. The ocean portion of the trend for 1993–2010 is 257 TW, equivalent to a mean heat flux into the ocean of 0.71 W m–2.”
Using the 93% dominance of the ocean in this heating, then from the 2013 IPCC report
· 1971-2010 the total earth surface heating rate is 0.59 Watts per meter squared
· 1993-2010 it is 0.71 Watts per meter squared.
Of course, there is the question as to whether the Levitus et al 2012 calculation below 700 meters before 2005 is even robust. The 2013 IPCC WG1 Chapter 3 report writes [highlight added] – http://www.climatechange2013.org/images/uploads/WGIAR5_WGI-12Doc2b_FinalDraft_Chapter03.pdf
“Below 700 m data coverage is too sparse to produce annual global ocean heat content estimates prior to about 2005, but from 2005–2010 and 0–1500 m the global ocean is warming (von Schuckmann and Le Traon, 2011). Five-year running mean estimates yield a 700–2000 m global ocean heat content trend from 1957 to 2009 (Figure 3.2b) that is about 30% of that for 0–2000 m over the length of the record (Levitus et al., 2012). Ocean heat uptake from 700–2000 m continues unabated since 2003 (Figure 3.2b); as a result, ocean heat content from 0–2000 m shows less slowing after 2003 than does 0–700 m heat content (Levitus et al., 2012). “
Remarkably, the IPCC report persists in making claims regarding deeper ocean heating before 2005. But that is a subject for another time.
Section 3 The Radiative Forcing
Using even the largest value [the 0.85 W/me value for the Radiative Imbalance from Jim Hansen], however, it is still significantly less than the total anthropogenic change in radiative forcing since 1750 reported by the IPCC.
In Figure SPM.5 in the 2013 IPCC WG, they report that the total anthropogenic change in radiative forcing since 1750 is
2.29 [1.13 -3.33] Watts per meter squared.
They write that
“The largest contribution to total radiative forcing is caused by the increase in the atmospheric concentration of CO2 since 1750.”
and
“The total anthropogenic RF for 2011 relative to 1750 is 2.29 [1.13 to 3.33] W m−2 (see Figure SPM.5), and it has increased more rapidly since 1970 than during prior decades.”
Unfortunately, the IPCC did not provide an estimate of the CURRENT “total anthropogenic RF”.
Some of this forcing would have been accommodated with warming of the climate system since 1750. When I served on the NRC (2005) assessment [http://www.nap.edu/openbook/0309095069/html/], one of my colleagues on the Committee (V. Ramanthan), when I asked him this question, he said that perhaps 20% of the CO2 radiative forcing was already equilibrated to. In any case, the CURRENT forcing must be somewhat less, but not probably by more than 20% or so.
Regardless, unless the IPCC estimates of the Radiative Forcing are too positive, this means that the
Radiative Imbalance < Radiative Forcing.
4. Radiative Feedbacks
However, while the warming of the climate system is a negative radiative feedback, and thus we should expect this part to be a negative feedback [since a surface temperature results in an increase of the outgoing long wave radiation to space], added water vapor, if it is there, would be a positive radiative feedback.
In my book
Cotton, W.R. and R.A. Pielke Sr., 2007: Human impacts on weather and climate, Cambridge University Press, 330 pp
in Section 8.2.8 we reported on an analysis of the water vapor feedback by Norm Woods using column assessments for three selected vertical soundings. Norm showed that the positive significant radiative forcing from even modest (e.g. 5% increase is atmospheric water vapor) is significant. [See also http://pielkeclimatesci.wordpress.com/2006/05/05/co2h2o/].
Norm Woods’s further analysis can be read on this posts
http://pielkeclimatesci.wordpress.com/2007/08/24/further-analysis-of-radiatve-forcing-by-norm-woods/
Among the conclusions for the representative soundings Norm used are
“with the tropical sounding ….adding 5% more water vapor, results in a 3.88 Watts per meter squared increase in the downwelling longwave flux. In contrast, due to the much lower atmospheric concentrations of water vapor in the subarctic winter sounding, the change from a zero concentration to its current value results in an increase of 116.46 Watts per meter squared, while adding 5% to the current value results in a 0.70 Watts per meter squared increase.”
and
“The effect of even small increases in water vapor content of the atmosphere in the tropics has a much larger effect on the downwelling fluxes, than does a significant increase of the CO2 concentrations.”
However, there appears to be no long trend in atmospheric water vapor! This can be seen in the latest analysis we have;
Vonder Haar, T. H., J. L. Bytheway, and J. M. Forsythe (2012), Weather and climate analyses using improved global water vapor observations, Geophys. Res. Lett., 39, L15802, doi:10.1029/2012GL052094. [http://onlinelibrary.wiley.com/doi/10.1029/2012GL052094/abstract]
Although they write in the paper
“at this time, we can neither prove nor disprove a robust trend in the global water vapor data.”
just the difficulty in showing a positive trend suggests a very muted water vapor feedback at most.
The figure from their paper with respect to this analysis is shown below
The 2013 IPCC WG1 SPM report states with respect to the radiative feedbacks that
“The net feedback from the combined effect of changes in water vapour, and differences between atmospheric and surface warming is extremely likely positive and therefore amplifies changes in climate. The net radiative feedback due to all cloud types combined is likely positive. Uncertainty in the sign and magnitude of the cloud feedback is due primarily to continuing uncertainty in the impact of warming on low clouds.” [http://www.climatechange2013.org/images/uploads/WGIAR5SPM_Approved27Sep2013.pdf]
They also write, in contrast to what is seen in the Vonderhaar et al 2012 paper,
“Anthropogenic influences have contributed to observed increases in atmospheric moisture content in the atmosphere (medium confidence)”
This report also write that
“The rate and magnitude of global climate change is determined by radiative forcing, climate feedbacks and the storage of energy by the climate system.”
Of course the report also fails to distinguish “global climate change” [which is much more than just the global average radiative forcings and feedbacks; a mistake also made in Stephens et al 2012].
The IPCC WG1 report discuss the reduced heating and Radiative Forcing in recent years as follows
“The observed reduction in surface warming trend over the period 1998–2012 as compared to the period 1951–2012, is due in roughly equal measure to a reduced trend in radiative forcing and a cooling contribution from internal variability, which includes a possible redistribution of heat within the ocean (medium confidence). The reduced trend in radiative forcing is primarily due to volcanic eruptions and the timing of the downward phase of the 11-year solar cycle. However, there is low confidence in quantifying the role of changes in radiative forcing in causing the reduced warming trend. There is medium confidence that internal decadal variability causes to a substantial degree the difference between observations and the simulations; the latter are not expected to reproduce the timing of internal variability. There may also be a contribution from forcing inadequacies and, in some models, an overestimate of the response to increasing greenhouse gas and other anthropogenic forcing (dominated by the effects of aerosols)…”
Nowhere in this discussion, except implicitly in the mention of internal variability, is the role of the radiative feedbacks including the role of water vapor and clouds presented.
5. The IPCC Failure
The IPCC report has failed to report on the implications of the real world radiative imbalance being significantly smaller than the radiative forcing. This means not only that the net radiative feedbacks must be negative, but they failed to document the magnitude in Watts per meter squared of the contributions to positive feedbacks from surface warming, and from atmospheric water vapor and clouds.
These must be smaller than what the IPCC models are producing.
One clear conclusion from their failure is that the climate system has larger variations in the Radiative Imbalance, Forcing and Feedbacks than is predicted by the model and accepted in the 2013 IPCC assessment report. Judy Curry David Douglass, Roy Spencer, Bob Tisdale, Anastasios Tsonis, Marcia Wyatt and others have been pioneers in advocating this perspective, and the failure in the SPM of the 2013 IPCC WG1 report to discuss this issue is a major failing of the assessment.
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Stephen Wilde says:
“GHG’s create the temperature gradient ”
The decline in density with height causes the gradient. GHGs can distort it but changes elsewhere negate the effect over the atmosphere as a whole.
————–
Density and height have nothing to do with temperature. You are obviously confusing the act of expanding a volume of gas which does lower the temperature with energy going into and out of the volume of gas.
Enjoy being wrong 🙂
Stephen Wilde says:
October 23, 2013 at 8:44 am
Enjoy being wrong 🙂
It’s you who is wrong about the gas laws and the use of the qualifier ‘specific’ in chemistry.
Compressibilty factor of air at 300K and 1 bar is 0.9999 and at 5bar is 0.9987. Water is the one component of air at atmospheric conditions that might depart from ideality but its contribution is negligible, based on the T-v diagram for water the error would be less than 1% for temperatures below ~80ºC and subatmospheric pressure.
Phil.
I pointed out to you that it is specific heat that matters.
It is clear that specific heat is also involved as well as mass:
“Another important relationship comes from thermodynamics. Mayer’s relation relates the specific gas constant to the specific heats for a calorically perfect gas and a thermally perfect gas.
Rspecific = cp – cv
where cp is the specific heat for a constant pressure and cv is the specific heat for a constant volume”
from here:
http://en.wikipedia.org/wiki/Gas_constant#Specific_gas_constant
and of course radiative and absorption capabilities would affect specific heat.
So it cannot be right that “the use of ‘specific’ is simply an alternative value expressed in terms of mass” since it clearly adjusts for characteristics other than mass, in particular, specific heat.
Stephen Wilde says:
October 23, 2013 at 1:27 pm
Phil.
I pointed out to you that it is specific heat that matters.
It is clear that specific heat is also involved as well as mass:
“Another important relationship comes from thermodynamics. Mayer’s relation relates the specific gas constant to the specific heats for a calorically perfect gas and a thermally perfect gas.
Rspecific = cp – cv
where cp is the specific heat for a constant pressure and cv is the specific heat for a constant volume”
from here:
http://en.wikipedia.org/wiki/Gas_constant#Specific_gas_constant
and of course radiative and absorption capabilities would affect specific heat.
No they don’t.
So it cannot be right that “the use of ‘specific’ is simply an alternative value expressed in terms of mass” since it clearly adjusts for characteristics other than mass, in particular, specific heat.
Stephen, you’re completely confused, that is exactly what ‘specific’ means.
Molar heat capacity for a gas can be evaluated in two ways:
at constant pressure, Cp
at constant volume, Cv
For a gas when evaluated at constant volume work is done to raise the pressure so Cv is not equal to Cp.
using the ideal gas law and the first law of thermodynamics leads to the relationship:
Cp=Cv +R
If the specific heats are used then the same equation results:
cp=cv+Rspec, where all the values are /kg.
Your initial statement that ‘Rspec’ relates to non-ideal gases is wrong.
Cp=M*cp, and Cv=M*cv, where M is the molar mass of the gas.
Phil.
I realise that you may be pointing me to a better understanding of the terms of expression but I feel that the main point is being missed.
How does one calculate the actual value of Rspecific for a given gas or mixture of gases when, say, the specific heat of that gas or mixture of gases can vary independently from the amount of mass involved ?
For example, C02 molecules have absorption and radiative characteristics very different from say Argon.
Other types of molecules vary in their chemical behaviour.
Therefore the values of Rspecific for CO2 and Argon would differ for the same amount of mass wouldn’t they ?
Are you saying that the specific heat, specific enthalpy et al are all rigidly tied to mass in exactly the same proportion for every type of molecule and that every type of molecule of a particular mass behaves identically to every other molecule within a gravitational field ?
If features other than mass affect the behaviour of a molecule within the gravitational field then the actual value of Rspecific must vary accordingly.
As soon as one varies the value of Rspecific for the same amount of mass then the atmospheric volume can change without changing T.
Stephen Wilde says:
October 23, 2013 at 2:53 pm
Phil.
I realise that you may be pointing me to a better understanding of the terms of expression but I feel that the main point is being missed.
How does one calculate the actual value of Rspecific for a given gas or mixture of gases when, say, the specific heat of that gas or mixture of gases can vary independently from the amount of mass involved ?
For example, C02 molecules have absorption and radiative characteristics very different from say Argon.
CO2 and Ar indeed have different heat capacities but it doesn’t depend on their absorptive or radiative characteristics. The heat capacity of a gas depends on the number of degrees of freedom the molecule has to store energy.
For a monatomic gas like Ar there are only three translational DoF, at constant volume each DoF can store a maximum of R/2 Joules so the heat capacity is 3R/2, for polyatomic gases like CO2 additional DoF corresponding to rotational and vibrational motions must be added (R/2 at a time).
So polyatomic gases will have higher heat capacities than Ar, in each case though Rspec will be equal to R/M. so for the same mass of gas you will have different Rspec but not different R. This is nothing to do with non-ideality.
For air at atmospheric conditions the ideal gas law applies almost perfectly as I showed above.
Other types of molecules vary in their chemical behaviour.
Therefore the values of Rspecific for CO2 and Argon would differ for the same amount of mass wouldn’t they ?
Yes by the ratios of their molar masses, nothing to do with specific heat.
Are you saying that the specific heat, specific enthalpy et al are all rigidly tied to mass in exactly the same proportion for every type of molecule and that every type of molecule of a particular mass behaves identically to every other molecule within a gravitational field ?
Specific heat, specific enthalpy etc. are all related to the relevant molar quantity by the molar mass of the molecule, nothing to do with ideality.
In the lower part of our atmosphere (the homosphere, up to 70km) all gases behave as a mixture of constant composition.
If features other than mass affect the behaviour of a molecule within the gravitational field then the actual value of Rspecific must vary accordingly.
As soon as one varies the value of Rspecific for the same amount of mass then the atmospheric volume can change without changing T.
Such a change would require a major change in composition far greater than we observe, say an increase of CO2 to 10% which would change Rspec by about 5% but since the Molar mass of the atmosphere would also have changed there would be no change in the Gas Law unless you also changed the number of moles in the atmosphere. A doubling of CO2 would have no observable effect on Rspec or Specific heat of the air.
The Rspec argument is a red herring.
I entered this comment at http://wottsupwiththatblog.wordpress.com/2013/10/23/watt-is-up-with-roger-pielke-sr/
where my post was erroneously reported.
“Radiative forcing is the change in the net, downward minus upward, irradiance
(expressed in W m–2) at the tropopause or top of atmosphere due to a change in an external driver of climate change, such as, for example, a change in the concentration of carbon dioxide or the output of the Sun.” http://www.climatechange2013.org/images/uploads/WGIAR5_WGI-12Doc2b_FinalDraft_AnnexIII.pdf
as you noted in your post. The IPCC further writes
“The traditional radiative forcing is computed with all tropospheric properties held fixed at their unperturbed values, and after allowing for stratospheric temperatures, if perturbed, to readjust to radiative-dynamical equilibrium. Radiative forcing is called instantaneous if no change in stratospheric temperature is accounted for. The radiative forcing once rapid adjustments are accounted for is termed the effective radiative forcing.”
Are you actually claiming that the radiative forcing is the same as the radiative imbalance? If so (and this is not my definition), than you still need to explain where the added water vapor and cloud positive radiative contributions fit into the observed changes in ocean heat content.
Now, why do not you start with the physics definition that I present in my post that
Radiative Imbalance = Radiative Forcing + Radiative Feedbacks
and present the magnitudes of each term on the right (since we have a good estimate of the imbalance from the ocean heat content changes.
Also, it would be courteous to identify yourself (or maybe you have, and I have not seen that).
Cordially
Roger A. Pielke Sr.
P.S. It would not let me post on their weblog. Very sad. However, it does tell you something about a weblog where the person does not give their name.
Just clarifying (to prevent a silent reader’s being misled) the following statement in B. W.’s well-reasoned and essentially accurate post (at 10:26am on Oct. 21):
(emphasis mine)
— Assuming that “those times scales” are > 1,000 years, bw was correct, but, to prevent misunderstanding, I note here that over shorter time scales, CO2 lags temperature.
In Dr. Murry Salby’s April 18, 2013 Hamburg, Germany lecture he explains this in terms a non-scientist can understand (You Tube video linked below):
from my Guide to Video:
[4:25] Proxy evidence of past atmospheric composition
– Ice cores (air bubbles in column sink under pressure of ice above them)
– Proxy temperature is inferred from isotopic oxygen
[6:47] CO2 and atmospheric temperature have strong coherence (.8) throughout the entire proxy record (when longer than 10,000 years); if one changes, so must the other
– At small (< 1,000 years) positive lag (of CO2 echoing temp.) is maximum coherence
– Phase of temperature and CO2 hovers near 0 (i.e., cohere nearly in-phase) [8:20]
[8:50] Observed Modern Changes
– 50 years of data
– Max correlation of .5 where CO2 lags temperature by 10 months
[9:06] (and CO2 lags temperature at significant correlation over wide range of time scales)
– CO2 is conserved in atmosphere, rate of change in CO2 level must EQUAL net emission from earth’s surface from all sources and sinks.
[9:45] (formula drCO2/dt = net emission CO2)
– [10:32] Native (natural) emission of CO2 depends strongly on temperature
– [10:58] Net CO2 emission has .63 correlation with temperature
– [11:35] CO2 evolves like the integral of temperature, i.e., it is proportional to the cumulative net emission of CO2 from all sources and sinks
– [13:52] Temp. and CO2 evolve coherently on all times scales longer than 2 years
– [14:03] CO2 lags temp. by a quarter cycle (i.e., in quadrature, using cosine and sine, lags by 90 degrees)
Source:
Phil.
I think I can see where we differ and how my terms of expression could be improved.
The issue should be a matter of distinguishing between the universal gas constant and the individual gas constant rather than using the terms Rspecific. and R.
See here:
http://www.engineeringtoolbox.com/individual-universal-gas-constant-d_588.html
Here are the values of R for the three gases mentioned in my article.
Nitrogen is 296.8
water vapour is 461.5
Carbon Dioxide is 188.9
It seems that the values of both R (and Rspecific) vary from gas to gas and for different mixtures of gases.
R is a universal constant only for an Ideal Gas.
The lower is the individual gas constant for a gas the less energy is needed to provide the Joules required to lift 1kg to a height where it cools by 1K
The less energy is needed the higher the gas will rise off the surface at a given temperature and the greater will be the volume of the atmosphere.
The more energy is needed the less high the gas will rise off the surface at a given temperature and the volume of the atmosphere will be less.
Nitrogen is relatively inert and comprising most of the atmosphere is close to that of air with Nitrogen at 296.8 and air at 286.9
Water vapour is light once formed but has required a lot of latent heat to form in the first place so the energy requirement to lift it from the surface is high even though it is a lighter gas. Thus 461.5
CO2 is heavier than air but acquires energy from absorption capability so the amount of energy required from the surface to lift it is less at 188.9
So it turns out that whether one refers to R, Rspecific or the individual gas constant the relevant number is indeed a variable and atmospheres of different compositions can have different volumes for the same mass and temperature.
R is only a constant for an Ideal Gas and in the real world there is no such thing.
Having established that that number is a variable within the Gas Laws the basic contention in my article is correct in that Volume will change with a change in the composition of the gas mixture without a corresponding change in T.
I need to revise my article to remove the red herring of Rspecific and make it clear that it is the individual gas constant that provides the system with the necessary flexibility.
I am grateful to Phil for focusing on the relevant issue so that I could refine the concept.
Very interesting!
Thanks Phil and Stephen.
Stephen Wilde says:
October 24, 2013 at 1:15 am
Phil.
I think I can see where we differ and how my terms of expression could be improved.
The issue should be a matter of distinguishing between the universal gas constant and the individual gas constant rather than using the terms Rspecific. and R.
Well the individual and specific gas constants are alternate terms for the same thing, but use whichever works for you.
See here:
http://www.engineeringtoolbox.com/individual-universal-gas-constant-d_588.html
Here are the values of R for the three gases mentioned in my article.
Nitrogen is 296.8
water vapour is 461.5
Carbon Dioxide is 188.9
All given by dividing the universal constant by the molar mass of the gas, multiply the values by the molar mass of each gas and you get 8.31J/K.mole, those are all expressed in J/K.gm.
This is what you must do if you wish to work in mass units as engineers usually do. Note that CO2 and propane which have the same molar masses have the same value (as do CO and N2).
It seems that the values of both R (and Rspecific) vary from gas to gas and for different mixtures of gases.
In mass units yes, but the universal gas constant does not change since it’s a molar unit.
R is a universal constant only for an Ideal Gas.
No it’s also true for Real gases. The simplest (and first) equation of state, van der Waals equation is given by:
RT= (P+a/V^2)(V-b)
where ‘a’ corrects for attraction between molecules and ‘b’ accounts for the volume of the molecules. R is the universal gas constant. There are other more complicated equations but they all use the same R (since at low pressures such as in our atmosphere they must describe an ideal gas). However as I pointed out above the Ideal gas law is all that is required in our atmosphere, not in Venus though where the lower atmosphere is super-critical!
The lower is the individual gas constant for a gas the less energy is needed to provide the Joules required to lift 1kg to a height where it cools by 1K
The less energy is needed the higher the gas will rise off the surface at a given temperature and the greater will be the volume of the atmosphere.
The more energy is needed the less high the gas will rise off the surface at a given temperature and the volume of the atmosphere will be less.
Here you go astray because to describe this process you must go to the first law of thermodynamics and adiabatic expansion because as the gas rises it expands and cools and in that case PV^k = constant where k=Cv/Cp which depends on the gas, 1.4 for diatomics like N2 and O2 and ~1.3 for CO2.
Nitrogen is relatively inert and comprising most of the atmosphere is close to that of air with Nitrogen at 296.8 and air at 286.9
Water vapour is light once formed but has required a lot of latent heat to form in the first place so the energy requirement to lift it from the surface is high even though it is a lighter gas. Thus 461.5
CO2 is heavier than air but acquires energy from absorption capability so the amount of energy required from the surface to lift it is less at 188.9
So it turns out that whether one refers to R, Rspecific or the individual gas constant the relevant number is indeed a variable and atmospheres of different compositions can have different volumes for the same mass and temperature.
If you work in mass units but not if you work in molar units.
R is only a constant for an Ideal Gas and in the real world there is no such thing.
Not true, R is constant for all gases, and our atmosphere in any case can be described as an ideal gas to at least 4 decimal places, i.e. compressibility factor at one bar is 0.9999!
Having established that that number is a variable within the Gas Laws the basic contention in my article is correct in that Volume will change with a change in the composition of the gas mixture without a corresponding change in T.
Only if there is a substantial change in the composition of our atmosphere such as the addition of huge quantities of CO2, e.g. raise it to 10% of the atmosphere! Adding a few hundred ppm won’t change anything.
PV=n*8.3145T and PV^1.4 works very well for the atmosphere in molar units.
PV=m*286.9T and PV^1.4 works very well for the atmosphere in mass units.
I need to revise my article to remove the red herring of Rspecific and make it clear that it is the individual gas constant that provides the system with the necessary flexibility.
I am grateful to Phil for focusing on the relevant issue so that I could refine the concept.
You need to do rather more than that as shown above.
Hi Phil.
Whilst I respect your superior technical expertise I think you have missed the point.
You will get no disagreement from me that for all practical purposes the Ideal Gas Law is good enough to work with.
Nor that atmospheric compressibility is small.
It is interesting that you now agree that the individual gas constant and Rspecific are interchangeable so I don’t need to change my article after all.
Let me try to put the point across another way.
To raise 1kg of CO2 from the surface to a height where it cools by 1K ‘costs’ 188.9 units of surface energy.
To raise 1KG of air from the surface to a height where it cools by 1K ‘costs’ 286.9 units of surface energy.
Air is a mixture of gases including CO2 and the atmosphere as a whole has a volume V determined by both surface temperature T and the energy cost of lifting the constituent molecules of the entire mixed atmosphere off the surface to the observed height.
If one then adds an additional CO2 molecule the energy cost of that molecule is less than the average for the atmosphere as a whole so it will rise to a higher level than the average height of all the other atmospheric molecules at a given temperature. At that higher level it will be at the same temperature as the other air molecules around it due to the lapse rate.
I seem to recall reading that at some specific height CO2 molecules outnumber H20 molecules so that would be evidence in support of the proposition that CO2 rises higher than average.
That higher level increases total atmospheric volume, infinitesimally as you say, but the higher than average height achievable by CO2 at a given temperature means that the extra CO2 molecule has more potential energy than average for the atmosphere as a whole.
That additional potential energy has then mopped up the kinetic energy difference between the surface energy cost of 188.9 units and the average energy cost for the atmospheric molecules as a whole which is 286.9 units.
Can you not see that ?
Logically, CO2 must rise to a height that converts any extra energy that it absorbs to potential energy rather than kinetic energy so it can only increase V and not T.
Phil, you have agreed that R. Rspecific or the individual gas constant does vary if one works with mass rather than moles.
If one can vary that term on one side of the equation then one can vary V on the other side without involving T.
That is sufficient to dispose of any addition to the mass and gravity induced greenhouse effect from CO2 molecules.
CO2 increases potential energy but not kinetic energy due to it requiring less Joules per kg per degree K than air to raise it above the surface at any given temperature.
It achieves that quite simply by rising higher than the average atmospheric molecule.
Stephen Wilde says:
October 24, 2013 at 11:00 am
Hi Phil.
Whilst I respect your superior technical expertise I think you have missed the point.
You will get no disagreement from me that for all practical purposes the Ideal Gas Law is good enough to work with.
Nor that atmospheric compressibility is small.
It is interesting that you now agree that the individual gas constant and Rspecific are interchangeable so I don’t need to change my article after all.
That was never a problem, it was identifying the Rspecific with non-ideality which was wrong.
Let me try to put the point across another way.
To raise 1kg of CO2 from the surface to a height where it cools by 1K ‘costs’ 188.9 units of surface energy.
To do this you need PV^k=constant for an idiabatic expansion not the gas law.
To raise 1KG of air from the surface to a height where it cools by 1K ‘costs’ 286.9 units of surface energy.
Air is a mixture of gases including CO2 and the atmosphere as a whole has a volume V determined by both surface temperature T and the energy cost of lifting the constituent molecules of the entire mixed atmosphere off the surface to the observed height.
OK
If one then adds an additional CO2 molecule the energy cost of that molecule is less than the average for the atmosphere as a whole so it will rise to a higher level than the average height of all the other atmospheric molecules at a given temperature. At that higher level it will be at the same temperature as the other air molecules around it due to the lapse rate.
No this is a fundamental mistake, the gases in air do not rise independently they rise together as a mixture, only once the homosphere has been left does composition depend on molecular mass (above 70km+).
I seem to recall reading that at some specific height CO2 molecules outnumber H20 molecules so that would be evidence in support of the proposition that CO2 rises higher than average.
That is because water vapor is not a permanent gas in the atmosphere so its concentration drops once it has reached the saturation altitude, the ratio of N2 to CO2 will remain the same up to about 100km.
That higher level increases total atmospheric volume, infinitesimally as you say, but the higher than average height achievable by CO2 at a given temperature means that the extra CO2 molecule has more potential energy than average for the atmosphere as a whole.
That additional potential energy has then mopped up the kinetic energy difference between the surface energy cost of 188.9 units and the average energy cost for the atmospheric molecules as a whole which is 286.9 units.
Doesn’t happen for the reason stated above.
Can you not see that ?
Logically, CO2 must rise to a height that converts any extra energy that it absorbs to potential energy rather than kinetic energy so it can only increase V and not T.
Phil, you have agreed that R. Rspecific or the individual gas constant does vary if one works with mass rather than moles.
If one can vary that term on one side of the equation then one can vary V on the other side without involving T.
That is sufficient to dispose of any addition to the mass and gravity induced greenhouse effect from CO2 molecules.
CO2 increases potential energy but not kinetic energy due to it requiring less Joules per kg per degree K than air to raise it above the surface at any given temperature.
It achieves that quite simply by rising higher than the average atmospheric molecule.
It does not do so it rises to the same height as the other molecules in its local parcel of gas. Look up mean free path, at atmospheric pressure it’s about 70 nm.
Thank you Phil. You are making me work and certain aspects are becoming clearer.
If you still have the patience let me try a slightly different tack.
I note that R is high for light gases such as Helium but low for heavier gases such as CO2.
The size of R is therefore proportionate to molecular weight as you pointed out which leaves no room for any influence on R from molecular characteristics other than mass.
I’ll pull my article pending further thought.
Furthermore, Joules are a measure of work done so the reason why R is higher for light gases than heavy gases would presumably be that for a light gas more work can be achieved for the same expenditure of surface energy.
That means that R is not primarily a measure of the energy cost of the work done (though it is that as well) but rather a measure of the work achievable from any given energy cost.
Is that a reasonable summary so far ?
Assuming it is then one needs another way of accounting for the extra conversion of kinetic energy to potential energy that would be needed to support any proposal that GHGs do not change surface temperature.
How about the proposition that radiative and absorption characteristics would allow GHGs to reach a higher temperature than that imparted to them by energy at the surface so that they would rise to a higher location than would be predicted from their weights and their value of R ?
I note that they do not rise independently because they would conduct some of their extra energy to surrounding non GHGs and the whole parcel would rise higher with kinetic energy being converted to potential energy to a greater extent than for a radiatively inert atmosphere.
Presumably total V would not be affected because any rising molecule would simply displace another molecule in an enhancement to the speed of the general circulation. So instead of a change in V we see a faster circulation.
That would be an acceptable alternative to a volume change for the purpose of neutralising an effect on surface T from GHGs.
Given that CO2 is heavier than air we would expect it to be mostly at the surface but in fact it is a ‘well mixed’ gas in terms of height and there is plenty high up in the atmosphere. Therefore one could suppose that their height and mixing ability is a result of radiative characteristics supplementing the energy they acquire from the surface.
Any enhancement of the general circulation would deliver energy back to the surface faster on the descent part of the adiabatic cycle and so would be returned to space sooner.
So, insofar as CO2 molecules acquire more than their fair share of kinetic energy that does not slow down the throughput of solar energy through the system since their rise speeds up the adiabatic cycle and that ‘excess’ energy gets expelled from the surface faster to compensate.
That would explain the absence of a tropospheric ‘hot spot’ since the energy that was supposed to accumulate higher up would simply have been dragged back to the surface faster in the accelerated descent of the adiabatic cycle for earlier radiation out from the surface.
In the process of all that, CO2 molecules are simply placed higher in the atmospheric column than can be explained just from their value of R.
Does that make sense to you ?
Stephen Wilde says:
October 24, 2013 at 8:51 pm
Thank you Phil. You are making me work and certain aspects are becoming clearer.
If you still have the patience let me try a slightly different tack.
I note that R is high for light gases such as Helium but low for heavier gases such as CO2.
The size of R is therefore proportionate to molecular weight as you pointed out which leaves no room for any influence on R from molecular characteristics other than mass.
I’ll pull my article pending further thought.
Furthermore, Joules are a measure of work done so the reason why R is higher for light gases than heavy gases would presumably be that for a light gas more work can be achieved for the same expenditure of surface energy.
That means that R is not primarily a measure of the energy cost of the work done (though it is that as well) but rather a measure of the work achievable from any given energy cost.
Is that a reasonable summary so far ?
Assuming it is then one needs another way of accounting for the extra conversion of kinetic energy to potential energy that would be needed to support any proposal that GHGs do not change surface temperature.
R is a constant for all molecules, it is related to Boltzmann’s constant, k, which relates energy at the molecular level with temperature, R is the product of k and Avagadro’s number. If you want to compare different numbers of molecules then you have to adjust for the differing number, this is what you are doing when you compare equal masses. If you want to get into energy costs of raising parcels of gases you should not be using PV=nRT anyway, as I’ve told you above.
How about the proposition that radiative and absorption characteristics would allow GHGs to reach a higher temperature than that imparted to them by energy at the surface so that they would rise to a higher location than would be predicted from their weights and their value of R ?
I note that they do not rise independently because they would conduct some of their extra energy to surrounding non GHGs and the whole parcel would rise higher with kinetic energy being converted to potential energy to a greater extent than for a radiatively inert atmosphere.
…………….
Does that make sense to you ?
No it does not, rather than answer each point I’ll attempt to cover it below.
Your whole premise seems to be based on the idea that gas molecules can behave differently in a mixture depending on their type, for example:
“Given that CO2 is heavier than air we would expect it to be mostly at the surface but in fact it is a ‘well mixed’ gas in terms of height and there is plenty high up in the atmosphere. Therefore one could suppose that their height and mixing ability is a result of radiative characteristics supplementing the energy they acquire from the surface.”
This is a complete misconception about how gases behave. If you have a chamber which is divided into two parts and on one side you have N2 at a pressure of one bar and on the other side CO2 at one bar, remove the separator and the two gases will mix by diffusion and will subsequently behave as a mixture. Even though one gas is 50% denser than the other they will not segregate under the influence of gravity. The reason is that the gas molecules are flying around at velocities of ~500m/s but at atmospheric pressure will travel about 70nm before they hit another molecule and change direction, these collisions occur about 10 time per nanosec.
Each gas molecule has three translational degrees of freedom which on average adds up to 3RT/2 J/mole. That’s all there is for a monatomic gas like Argon, polyatomic gases like N2, CO2, H2O have in addition internal modes due to rotation and vibration which add potential for additional factors of R/2 for each mode. When a CO2 molecule absorbs an IR photon it gains energy in the rot/vib modes, it has the option to emit that extra energy as light or to pass it on via collisions to other molecules (mostly N2 and CO2). At atmospheric pressure there are so many frequent collisions that most of the energy is shared with the neighboring molecules so the effect is to raise the temperature of the whole mixture. CO2 behaves as a component of the mixture, it does not reach higher altitudes than any other of the gases (at least up to 70km, above that altitude gases do segregate by mass because the collisions are so rare).
Hope that helps?
Would a pure CO2 atmosphere have a different volume to a pure Nitrogen atmosphere ?
Of the same mass and at the same temperature and pressure, that is.
Same mass yes, same # of moles no.
A pure CO2 atmosphere with the same pressure as ours would be crazy hot!
That’s what I thought.
The differences in molecular weight require different volumes for the same mass, temperature and pressure.
Hence the differing individual gas constants.
Thus we must look elsewhere for the thermal effects of other characteristics such as radiative absorption capability.
Additional energy absorption capability would affect volume and / or temperature so we need to examine the Gas Laws to see what they can tell us about overall atmospheric behaviour when something which is not a term of the Gas Law tries to force changes.
My conclusion is that the gas constant determines the atmospheric volume so as to balance surface temperature with the need to maintain energy balance at ToA and hold the atmosphere off the surface.
If anything else seeks to upset the atmospheric volume and surface temperature balance set by the gas constant then the system can only respond by changing the balance between kinetic and potential energy otherwise the surface would become too hot or too cold and the atmosphere would eventually be lost.
Too cold a surface would allow a permanent excess of energy in and too warm a surface would allow a permanent excess of energy out.
The Gas Law should be adapted thus:
PV = mRspecificE
Where E represents total system energy content and the value of Rspecific determines how much of E can be in kinetic form as heat and how much in potential form as height.
Stephen Wilde says:
October 27, 2013 at 4:58 am
The Gas Law should be adapted thus:
PV = mRspecificE
Where E represents total system energy content and the value of Rspecific determines how much of E can be in kinetic form as heat and how much in potential form as height.
Absolutely not, RT is kinetic energy, the units of your equation don’t balance!
PV is proportional to the average molecular kinetic energy of the gas (the translational modes not the internal modes)
Average KE of a molecule=3kbT/2, for a mole of the gas: KE=3RT/2
Hence PV=nRT
I know RT is kinetic energy and that is all the kinetic energy one can have if mass is the only determinant of how much energy a molecule can hold.
Why have you switched back to moles ?
Radiative theory says that GHG molecules have additional ability to absorb energy which is apparently not related to their mass.
Or do you dispute that ?
Any such additional energy acquired must place them and other molecules they collide with higher in the atmosphere for an increase in V and total energy (PE + KE).
How would you propose to deal with that ?
I suggest that ALL the energy in the atmosphere whether PE or KE determines PV but that the value of R sets the proportion of that energy that needs be in kinetic form to comply with PV = nRT.
The thing is that PV = nRT only works for a parcel of gas that expands within an atmosphere. Such expansion is equal both up and down so gravitational potential energy stays the same. Intermolecular forces are too small to consider.
For an atmosphere around a planet the rules have to change because PE is about 50% of the energy in the atmosphere but is not dealt with in the standard equation.
If molecules can absorb additional energy over and above that needed to support their mass then it all has to go to PE.
It is the shifting of that additional energy to PE that balances the equation when V increases more than one would expect from the mass alone.
There might be a better way to formulate a new equation though.
Slight clarification.
GHGs appear to be able to acquire more energy than is required to support their mass at a given level of irradiation from outside the atmosphere.
It is the level of irradiation from outside working on the available mass which produces
PV = nRT.
If some other factor than mass can alter T without more energy coming in from outside which is what radiative theory proposes then it is that which unbalances the equation.
If T gets altered by a factor other than mass then V must change to regain balance but one cannot raise T again or the equation remains unbalanced.
The only way one can regain balance is by shifting the excess energy to PE.