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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Note that T is surface temperature for a planet and not the Temperature of the gases. You seem to be conflating the two.
Stephen Wilde says:
October 28, 2013 at 7:54 am
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 ?
Because it’s the rational way to do it, using mass doesn’t help.
Radiative theory says that GHG molecules have additional ability to absorb energy which is apparently not related to their mass.
It’s related to the number of internal modes and their nature (rotational and vibrational), nothing to do with 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).
No, only if the energy is transferred to the translational modes, having more kinetic energy increases the temperature.
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.
It doesn’t work like that!
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.
No, the equation of state works for any parcel of gas that meets the ideal gas conditions
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.
Then you should use the hydrostatic 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 goes to both kinetic and potential energy of the rotational and vibrational modes, through collisions it can be converted to translational kinetic energy and hence T and V.
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.
No, see above and a good text on the Kinetic Theory of gases.
1) “No, the equation of state works for any parcel of gas that meets the ideal gas conditions”
It doesn’t work for an entire atmosphere because it isn’t a parcel and doesn’t meet the ideal gas conditions.
2) “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).
No, only if the energy is transferred to the translational modes, having more kinetic energy increases the temperature.”
Well it can’t affect kinetic energy otherwise the surface temperature becomes permanently too high for ToA radiative balance and the atmosphere will be lost. So it has to go to translational modes.
3) “Radiative theory says that GHG molecules have additional ability to absorb energy which is apparently not related to their mass.
t’s related to the number of internal modes and their nature (rotational and vibrational), nothing to do with mass.”
If it isn’t related to mass then the equation of state doesn’t work which is the problem that you seem not to appreciate. The equation of state deals with gravity working on mass and nothing else.
4) “Why have you switched back to moles ?
Because it’s the rational way to do it, using mass doesn’t help.”
You have to use mass because gravity does work on mass.
5) Earlier we had this exchange:
“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.”
That being the case we must work in mass units.
In summary, I don’t think you are seeing the problem that needs to be addressed.
The fact is that the equation of state deals ONLY with the interaction between gravity and mass. It fails to deal with anything that affects T or V other than mass.
Furthermore, anything other than mass that affects T upsets the equation of state resulting in a permanent ToA energy imbalance.
The only way top avoid that imbalance is to change V alone which involves more PE at the expense of KE.
If I follow your logic it seems that the answer is that radiative absorption affects translational modes only and that can result in more V without higher T at the surface.
I think I’ve misread one of your points.
The translational mode is kinetic energy so my comment at 12.23 is wrong.
That being the case your contention is that inevitably any extra radiative energy absorbed must go to translational mode / kinetic energy which must then affect both T and V.
Which again leaves us with a value of T at the surface which produces a permanent energy imbalance at ToA.
How would you address that problem ?
Phil.
The problem here is that we have been conflating the thermal behaviour of a discrete parcel of gas suspended above a surface (the Gas Laws apply) with the thermal behaviour of a surface overlain by a volume of gas (The Laws of Thermodynamics apply).
You have pointed me to the issue of thermodynamics a couple of times so perhaps it is my fault.
It has always been my contention that the surface temperature stays the same when the gas above it acquires more energy from anywhere other than the surface and that any such additional energy acquired by the gas from elsewhere simply results in more uplift and an increase in PE which mops up what would otherwise have been more KE. That results in a new compromise between the height of the atmosphere and the slope of the lapse rate.
Surface temperature is determined by insolation plus the weight of the atmosphere (m) resting on the surface (P) and so the surface temperature is ‘locked’ because volume (V) is irrelevant to it.
The temperature of the gases at any given height above the surface is then determined by the lapse rate which itself is derived from the decline in density with height which in turn is related to the pressure gradient. That involves the Gas Laws.
If a parcel of gas acquires more energy than is possible just from energy conducting or being lifted by convection up from the surface then it becomes too warm for its position in the atmospheric column and it will rise until it is at the right temperature.
In the process ALL such additional energy goes to PE.
So, for a free floating parcel of gas V is indeed tied to T as per the Gas Laws but if extra energy is added then atmospheric thermodynamics changes its position in the vertical column in accordance with Rspecific so that Rspecific does indeed determine the relative proportions of KE and PE.
Rspecific determines how much KE is needed to lift the parcel’s weight off the surface to the height set by incoming insolation at the surface and any excess energy then acquired goes to PE instead.
Not because of the Gas Laws (as you pointed out) but by virtue of thermodynamics.
Meanwhile, thermodynamics also requires that the entire energy content of an atmosphere (both PE and KE) determines the volume of the entire atmosphere (but not surface temperature) because ALL that energy content determines the height to which the atmosphere can rise off the surface.
The Gas Laws need to be applied differently for a free floating parcel of gas and for an atmosphere around a planet.
For the latter, one needs to combine the effects of the Gas Laws with basic thermodynamics.
Is that any form of progress ?
stephen-
energy delivered to the ocean surface causes water to evaporate.
change of phase from liquid to gas does not change temperature.
water gas is the lightest gas (of any significance whatsoever) in our atmosphere.
gnomish.
Not sure what your point is since I accept those facts.
There is no doubt that those features of water help to maintain stability but that is incorporated into what I said.
Stephen Wilde says:
October 29, 2013 at 12:17 am
1) “No, the equation of state works for any parcel of gas that meets the ideal gas conditions”
It doesn’t work for an entire atmosphere because it isn’t a parcel and doesn’t meet the ideal gas conditions.
The equation of state applies to any parcel of gas within the atmosphere, our atmosphere if accurately described as an Ideal gas, you need to get that particular ‘bee out of your bonnet’.
2) “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).
No, only if the energy is transferred to the translational modes, having more kinetic energy increases the temperature.”
Well it can’t affect kinetic energy otherwise the surface temperature becomes permanently too high for ToA radiative balance and the atmosphere will be lost. So it has to go to translational modes.
3) “Radiative theory says that GHG molecules have additional ability to absorb energy which is apparently not related to their mass.
t’s related to the number of internal modes and their nature (rotational and vibrational), nothing to do with mass.”
If it isn’t related to mass then the equation of state doesn’t work which is the problem that you seem not to appreciate. The equation of state deals with gravity working on mass and nothing else.
You are still confused, the equation of state is a formula describing the interconnection between various macroscopically measurable properties of a system.
For physical states of matter, this equation usually relates the thermodynamic variables of pressure, temperature, volume and number of molecules to one another.
The equation you need is the hydrostatic equation:
P = −g ∫ ρ dh
where g is gravity and ρ is the density of air.
Since density varies with height we need to use the Equation of State:
ρ=MP/(RT)
4) “Why have you switched back to moles ?
Because it’s the rational way to do it, using mass doesn’t help.”
You have to use mass because gravity does work on mass.
See above.
5) Earlier we had this exchange:
“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.”
That being the case we must work in mass units.
In summary, I don’t think you are seeing the problem that needs to be addressed.
The fact is that the equation of state deals ONLY with the interaction between gravity and mass. It fails to deal with anything that affects T or V other than mass.
No, the equation of state is as I’ve described it you need the hydrostatic equation which I’ve described above.
Furthermore, anything other than mass that affects T upsets the equation of state resulting in a permanent ToA energy imbalance.
The only way top avoid that imbalance is to change V alone which involves more PE at the expense of KE.
This makes no sense at all.
“The equation you need is the hydrostatic equation:
P = −g ∫ ρ dh
where g is gravity and ρ is the density of air.
Since density varies with height we need to use the Equation of State:
ρ=MP/(RT)”
Noted, thank you.
I was wondering how to get density into the mix of relevant factors.
Does my post at 3.03 make sense in light of the hydrostatic equation ?
Stephen Wilde says:
October 29, 2013 at 3:03 am
Phil.
The problem here is that we have been conflating the thermal behaviour of a discrete parcel of gas suspended above a surface (the Gas Laws apply) with the thermal behaviour of a surface overlain by a volume of gas (The Laws of Thermodynamics apply).
You have pointed me to the issue of thermodynamics a couple of times so perhaps it is my fault.
The Laws of Thermodynamics are applied, you’re trying to misapply them, see the post above concerning the hydrostatic equation.
It has always been my contention that the surface temperature stays the same when the gas above it acquires more energy from anywhere other than the surface and that any such additional energy acquired by the gas from elsewhere simply results in more uplift and an increase in PE which mops up what would otherwise have been more KE. That results in a new compromise between the height of the atmosphere and the slope of the lapse rate.
Now you bring in the lapse rate which is given by:
Lapse rate= g/Cp
Surface temperature is determined by insolation plus the weight of the atmosphere (m) resting on the surface (P) and so the surface temperature is ‘locked’ because volume (V) is irrelevant to it.
The temperature of the gases at any given height above the surface is then determined by the lapse rate which itself is derived from the decline in density with height which in turn is related to the pressure gradient. That involves the Gas Laws.
Surface temperature is determined by the balance between insolation and the heat loss into space. The lapse rate does not involve the Gas Laws!
Rspecific determines how much KE is needed to lift the parcel’s weight off the surface to the height set by incoming insolation at the surface and any excess energy then acquired goes to PE instead.
No it does not! For this you would refer to the equation for adiabatic expansion:
PV^k=constant
The Gas Laws need to be applied differently for a free floating parcel of gas and for an atmosphere around a planet.
For the latter, one needs to combine the effects of the Gas Laws with basic thermodynamics.
Is that any form of progress ?
That’s what I’ve been trying to tell you but apparently you don’t know the relevant thermodynamics.
Summary:
P = −g ∫ ρ dh
where g is gravity and ρ is the density of air.
Since density varies with height we need to use the Equation of State:
ρ=MP/(RT) where both P and T are functions of h.
Lapse rate= g/Cp
For a rising/falling parcel of air, PV^k is constant.
Any energy transferred by absorption to a GHG will first raise the energy of the internal modes (rotation/vibration) which either be converted to translation by collisions (and hence temperature) or will be emitted as radiation. The former is more likely near the surface and the latter near the tropopause.
stephen,
I have been following yours and Phil.’s conversation and I so much would like you to get this all sorted out. But I am going to stay on the sideline except this comment for Phil.’s feeding you exactly the same thing I was giving to you a ways back, it’s proper information he is giving you and clearer than I can do such. The only reason I jumped in is to say try picking up a calculator. It’s simple to see the relations if you see it in actual numbers in action, for instance:
ρ=MP/(RT)
Density at the surface is:
ρ = 0.02896 kg/mole * 101325 Pa / (8.314 J/K/mole * 288 K) = 1.225 kg/m³
You know, that is correct, 1.225 kg/m³ as given by the 1976 US Standard Atmosphere and you just calculated it from two variables, the pressure and the temperature.
Write down those that do not change (constants) and don’t lose them:
8.314 J/K/mole is the universal gas constant, it NEVER changes, even on Venus or Jupiter.
0.028964 kg/mole is air’s molecular mass, on Earth with constant composition it never changes.
So, that equation with those two constants and the pressure and temperature of any level will give you back the density there.
Now, watch carefully what Rspecific is, I am going to derive it and rewrite the equation above:
Rspecific of air = 8.314 J/K/mole / 0.028964 kg/mole = 287.05 J/K/kg instead of J/K/mole.
See, all that happened is kg took the place of moles and moles disappeared.
So also you can now say that
ρ=MP/(RT)
becomes
ρ=P/(Rspecific · T)
Notice no M in the numerator anymore, it merged with R, the universal form or R to be the specific form of R for Earth’s air.
So:
ρ = 101325 Pa / (287.05 J/K/kg * 288 K) = 1.225 kg/m³, correct.
So also write down this constant for Earth’s air:
287.05 J/K/kg is the specific gas constant for air, and DOES change for Venus and Jupiter for their atmospheric gases are of a different composition. Even better call it Rair instead of Rspecific.
Try to work through each of the equations until you know each by heart, frontwards and backwards. I did that same in the last few years, I didn’t have them memorized then either, but all I just wrote came not by Googling but out of my head. I bet when you get to that point you should know how all of these confusing variables all effect each of the others. It is not trivial.
I’ll step back in the background. 😉
Ok chaps.
I’ll pull back too and apply thought for a while.
Thank you for giving me your time.
“Any energy transferred by absorption to a GHG will first raise the energy of the internal modes (rotation/vibration) which either be converted to translation by collisions (and hence temperature) or will be emitted as radiation. The former is more likely near the surface and the latter near the tropopause.
If it rises higher it gains more PE and cools whilst at the same time radiating more effectively to space.
On that basis would it really lead to a warmer surface ?
Translational energy is independent from the internal modes, if the rot-vib energy is converted to translational energy it can no longer be emitted.
But then, in so far as radiative emission to space is insufficient, it would rise converting KE to PE for a cooling effect.
A molecule too low in the atmospheric column for its energy content radiates too much to the surface.
A molecule too high in the atmospheric column for its energy content radiates too much to space.
A molecule at exactly the correct height for its energy content does neither for a zero net effect.
I admit to not being a scientist which is why I value and accept the opinion of my betters in that discipline.
Against that, I have a lifetime of experience albeit as an amateur in climate and weather. In that arena I think I have a broader knowledge than most scientists.
What we have here is a conundrum whereby energy out must equal energy in for the atmosphere as a whole over millions of years but radiative theory simply cannot work because it relies on a permanent imbalance between energy in and energy out.
Observations show that the real world is not doing what the radiative theory requires.
The answer must lie in the interaction between the gas laws and thermodynamics.
I judge that any molecule acquiring additional energy from radiative absorption (whether directly or indirectly through collisions) must rise higher than it otherwise would have done and in the process settles at a height where it becomes cool enough for radiation to space to exactly match radiation back to the ground for a zero net effect on the top of atmosphere radiative balance.
Instead of an increase in surface temperature the rise in height leads to an increase in radiation out.
The atmosphere is full of molecules 50% rising and 50% falling so that overall on average the circulation ensures that top of atmosphere energy balance is maintained by having all molecules whether radiative or not at the correct heights for system stability.
I accept that I do not have the mathematical experience, or the opportunity to acquire it, to provide a formal proof.
I said “the rise in height leads to an increase in radiation out.”
That appears to be inconsistent with your comment that if rot-vib energy is converted to translational energy it is no longer capable of being emitted so the higher a molecule goes as a result of translational energy the less it will emit.
But you previously said that the higher the molecule the more likely it is that radiative emission would occur in preference to collisions increasing temperature.
I think the answer is that it is a matter of balance.
Taking the atmosphere as a whole the circulation will respond to the introduction of GHGs so as to ensure that the combined effect of rising as a result of increased translational energy and emission as a result of rot-vib will net out so as to affect neither surface temperature nor ToA radiative balance.
Stephen, you keep speaking of KE and PE and I have a question. Are the two effects you keep referencing located on opposite sides of the Earth? One on the day side rising due to additional solar energy, let’s say 50-100 meters, and the other side falling back during the twelve hours of nighttime? That is the only way I seem to see what you are saying as being a net effect and this is due to the conservation of local mass. This is a big globe and such effects can and do occur but they cannot be of very close proximity to each other, like a cloud and the air around the cloud. I get confused as to what is your references of locations, scales and times.
I remember us speaking of that months ago so maybe that is still you are speaking of.
wayne
At any given moment half the molecules in the atmosphere are rising and half falling relative to the surface.
That incorporates all times and all locations.
Even a horizontal air flow moves up and down relative to the ground.
All movements upward convert KE to PE for a cooling effect. All movements downward convert PE to KE for a warming effect.
Left to themselves all molecules with more KE rise whilst all molecules with less KE fall. In practice the presence of a global circulation makes it more complex.
If a GHG acquires additional energy over and above that expected from its mass then it will rise higher than it otherwise would have done, more KE than otherwise would go to PE for a cooling effect and the greater height would allow it to radiate more effectively to space.
Note that it only requires a specific amount of kinetic energy at the surface to raise the weight of each molecule in the atmosphere to a given height at a given level of external irradiation. If GHGs acquire more energy than that basic amount then they rise higher than non GHGs.
Quite simply, the GHG molecule would rise to a cooler height where radiation to space would match radiation back to the ground for a net zero effect on surface temperature and ToA radiative balance.
Increased DWIR from increased GHGs becomes a myth.
It is true that the GHG would involve other molecules in the process via collisional activity but that simply makes it easier for the atmosphere as a whole to rise higher and convert more KE to PE.
Stephen Wilde says:
October 29, 2013 at 3:06 pm
But then, in so far as radiative emission to space is insufficient, it would rise converting KE to PE for a cooling effect.
A molecule too low in the atmospheric column for its energy content radiates too much to the surface.
A molecule too high in the atmospheric column for its energy content radiates too much to space.
A molecule at exactly the correct height for its energy content does neither for a zero net effect.
I admit to not being a scientist which is why I value and accept the opinion of my betters in that discipline.
You still don’t get it. A molecule near the surface travels about 70nm before it collides with another molecule, your concept of a molecule travelling up in the atmosphere until it reaches the level appropriate to its KE just doesn’t happen. KE is rapidly exchanged with the neighboring molecules, probably all distributed in a mm.
What we have here is a conundrum whereby energy out must equal energy in for the atmosphere as a whole over millions of years but radiative theory simply cannot work because it relies on a permanent imbalance between energy in and energy out.
Where do you get this from? There is no such requirement, quite the contrary.
The answer must lie in the interaction between the gas laws and thermodynamics.
As stated earlier it’s all thermo.
I judge that any molecule acquiring additional energy from radiative absorption (whether directly or indirectly through collisions) must rise higher than it otherwise would have done and in the process settles at a height where it becomes cool enough for radiation to space to exactly match radiation back to the ground for a zero net effect on the top of atmosphere radiative balance.
No, see above.
Instead of an increase in surface temperature the rise in height leads to an increase in radiation out.
“You still don’t get it. A molecule near the surface travels about 70nm before it collides with another molecule, your concept of a molecule travelling up in the atmosphere until it reaches the level appropriate to its KE just doesn’t happen. KE is rapidly exchanged with the neighboring molecules, probably all distributed in a mm.”
It is obvious that bulk activity goes on just as you say but the net outcome of all that bulk activity is to lift the weight of an atmosphere away from the irradiated surface to a height determined by the power of that irradiation.
KE at a surface lifts an atmosphere off the surface. The more KE at the surface the higher it gets.
In the process of rising, KE converts to PE and the higher molecules are colder.
Radiative theory sets out a scenario where a surface can be warmer than the S-B equation predicts simply because of the absorption capabilities of GHGs. That involves less energy going out than coming in on a permanent basis. Not possible, because a surface warmer than S-B predicts must actually radiate more out than is coming in.
The Gas Laws show that only mass can cause a surface to be sustainably warmer than S-B predicts because the KE at the surface has to hold the weight of the atmosphere off the surface whilst at the same time matching energy in with energy out.
Once the energy exchange between atmospheric mass and the surface is deducted then the surface is at the temperature predicted by S-B.
In the case of Earth the difference is 33K.
If one then proposes additional DWIR from the atmosphere warming the surface further or preventing it from cooling as fast then that is the true breach of the S-B constant.
AGW radiative theory is illogical.
I’ve spent a couple of days on reflection.
When I suggested that for an atmosphere around a planet the formulation:
PV = mRspecificE should apply instead of the normal formulation PV = m RspecificT which applies for a parcel of gas within an atmosphere
Phil’s response was basically that it doesn’t work like that and in support of that assertion he said:
“A molecule near the surface travels about 70nm before it collides with another molecule, your concept of a molecule travelling up in the atmosphere until it reaches the level appropriate to its KE just doesn’t happen. KE is rapidly exchanged with the neighbouring molecules, probably all distributed in a mm”
In other words he does not accept that the introduction of GHGs causes atmospheric expansion.
I replied:
“Bulk activity goes on just as you say but the net outcome of all that bulk activity is to lift the weight of an atmosphere away from the irradiated surface to a height determined by the power of that irradiation.
KE at a surface lifts an atmosphere off the surface. The more KE at the surface the higher it gets.
In the process of rising, KE converts to PE and the higher molecules are colder.”
In other words I say that the introduction of GHGs does cause atmospheric expansion, a lifting higher away from the surface than justified by mass alone and creation of more PE at the expense of any excess KE.
Wayne’s interjection did not address that issue.
If GHGs cause atmospheric expansion then I am right. If they do not then Phil is right.
For the moment we must agree to disagree and readers must make up their own minds.
Phil. says:
October 30, 2013 at 6:16 am
You still don’t get it. A molecule near the surface travels about 70nm before it collides with another molecule, your concept of a molecule travelling up in the atmosphere until it reaches the level appropriate to its KE just doesn’t happen. KE is rapidly exchanged with the neighboring molecules, probably all distributed in a mm.
—
At some point you have to begin to doubt Phil’s sincerity in this conversation.
Thanks Eric.
I didn’t feel it appropriate for me to say that but if another says it I am gratified.
Eric Barnes says:
October 31, 2013 at 6:20 pm
Phil. says:
October 30, 2013 at 6:16 am
You still don’t get it. A molecule near the surface travels about 70nm before it collides with another molecule, your concept of a molecule travelling up in the atmosphere until it reaches the level appropriate to its KE just doesn’t happen. KE is rapidly exchanged with the neighboring molecules, probably all distributed in a mm.
–
At some point you have to begin to doubt Phil’s sincerity in this conversation.
Really, why is that? I’ve spent a lot of time in this thread trying to straighten out Stephen’s misguided physics. Everything I’ve posted here can be verified in texts, countered by a completely content-free post by Eric! Whoop-de-doo!