'Just-in-Case': How to Think About Uncertainty and Global Warming

TCS Daily ^ | 14 Feb 2007 | Arnold Kling

[edsheppa]

I'm not sure you understand how this works.

I'll be glad to address your other point but let's get something straight first. I *do* understand how it works. Please answer this question. If you have a well mixed gas containing A and B and if you add energy to A by some means like say shining a light on the mixture that A absorbs and B does not, do you think some of the heat added to A will be communicated to B or will the A molecules retain all the heat?

[spunkets]

I said it did.

[edsheppa]

Well, you did and you didn't IMO, but bear with me for just a little longer.

Let's say the fraction of A and B in the mixture is FA and FB resp. and that the heat capacities are CA and CB resp. And let's say the temperature of the mixture rises because heat has been added to A which passes some along to B so they're both at the same temperature. Don't you agree that the extra heat will be distributed between B an A in the ratio (FB*CB)/(FA*CA)?

I think you will. O2 and N2 together comprise 99% of the atmosphere and CO2 is 0.0383%. The heat capacity (at 25°C) of O2 and N2 are about 29 J/mol-K and CO2 is about 38 J/mol-K. Consequently the ratio of the heat taken up by the N2+O2 to the CO2 is about (99*29)/(0.0383*38) which is ~1973.

So now, when I said

the N2 and O2 in the atmosphere will take up about 2000 times the amount of heat as the CO2

(and I don't see the practical difference between 1973 and 2000), why did you say I don't understand how this works?

[jwalsh07]

The bottom line is actually not very much, as the direct radiative effect on surface temperature of doubling CO2 concentration in the atmosphere is only about 0.2oC.

Can you expond a bit on this geezer?

[spunkets]

What you said is alright. My point was and still is that the critical absorber is the polar molecules, CO₂ in this case. That is the gas responsible for the heat retention. The other gases are just responsible for taking up the ~6.5W/M² that the CO₂ absorbs at ~330ppmv.

[jwalsh07]

u

[spunkets]

" Actually doubling the concentration increments absorption of CO2 by a fixed increment due to the fact that CO2 spectal lines are saturated (i.e. not enough IR at the right wavelengths to go around for the density of CO2 molecules in the atmosphere). The only additional absorption that can occur by increasing CO2 concentration is in those areas of the spectrum at the tails of strong line responses and in the weak spectral lines of CO2 thus the absorption of IR is logarithmic as opposed to linear increasing at something less than 5.35*ln(C/Co) w/m2, how much less depending on amount of water vapor in the atmosphere overlapping CO2 spectral lines reducing the amount of IR available to CO2."

The CO₂ is contained in a bulk of other gasses. It transfers kinetic energy to those other gases, so that equation doesn't apply. The equation you posted is a version of Beer's law. That equation only applies if there is no other interactions. In this case there is. So, CO₂ is not near saturation and has considerable absorbing power. It absorbs about 6.5 W/M² and doubling the concentration, ~doubles the energy absorbed, because it transfers the energy to the atmosphere. edsheppa wrote out the idea in #103. The transfer is probably not complete though, because there's an equilibrium established here. The effective "C_o and the "5.xx", change with C, so it's pointless to use Beer's law. Here's a plot that shows the Earth's black body profile from space, showing the CO₂ is still strongly absobing.

[spunkets]

" I don't see the practical difference between 1973 and 2000"

Not sure what you mean here, but there is none. I don't see any significant diff between 1700 and 2060 either.

[ancient_geezer]

The bottom line is actually not very much, as the direct radiative effect on surface temperature of doubling CO2 concentration in the atmosphere is only about 0.2oC.

The temperature change due to direct radiation effects of CO2 by itself is at maximum only around 0.2^oC due to the fact that water vapor absorption of IR overlaps that of CO2 with more than 10 times the concentration of molecules to intercept thermal IR. The net effect on CO2 radiative effect is to reduce it to one third of what CO2 would otherwise be capable of in the absence of water vapor.

http://www.eia.doe.gov/cneaf/alternate/page/environment/appd_d.html

"Carbon dioxide adds 12 percent to radiation trapping, which is less than the contribution from either water vapor or clouds. By itself, however, carbon dioxide is capable of trapping three times as much radiation as it actually does in the Earth's atmosphere. Freidenreich and colleagues[106] have reported the overlap of carbon dioxide and water absorption bands in the infrared region. Given the present composition of the atmosphere, the contribution to the total heating rate in the troposphere is around 5 percent from carbon dioxide and around 95 percent from water vapor."

The direct radiative effect of CO2 without water vapor to get in the way is 5.35*ln(C/C_o), and approximately 1/3 that in the presence of water vapor at average atmospheric concentration of H2Oof about ~3600 ppmv for the whole atmosphere from surface to top of troposphere, against 380ppmv of current CO2 concentrations.

Thus a doubling of CO2 would yield 5.35*ln(2) = 3.71 w/m² Forcing without water vapor and about ~1.2 w/m² Forcing at the surface from re-emitted downwelling radiation of CO2 decreased by the presence of current average water vapor concentrations.

Some, pre-global warming hype, studies actually indicate downwelling IR due to a CO2 doubling might actually be below 0.55 w/m² as measured at the surface.

 

Kiehl, J. T. and V. Ramanathan, 1982: Radiative Heating Due to Increased CO2: The Role of H2O Continuum Absorption in the 12-18 mm Region . J. Atmos. Sci., 39: 2923-2926.

Introduction:

Within the 12-18mm region, both H2O and CO2 absorb and emit radiation giving rise to the so-called "overlap." This study examines the role of this H2O-CO2 overlap in the CO2-climate proble. The H2O absorpotion, within the 12-18mm region, that has been traditionally included in climate models (Manabe and Wetherald, 1980; Ramanathan, 1981) is the line absorption due to the pure rotational band of H2O. In addition to the pure rotaional band, there is very strong "continuum" absorption by H2O in the 12-18 um region (Roberts et al., 1976). The few climate model studies which include the effect of this continuum (e.g., Wang et al., 1976) have not examined its rl in the increased CO2 radiative effects. In order to isolate the overlap effects of various H2O radiation processes in the 12-18mm region, we comput the radiative heating of the surface/troposphere system due to double CO2 with and without the H2O overlap effects.

*** SNIP ***

[p. 3] We consider three cases in which CO2 is doubled and the changes in longwave fluxes are computed for no overlap between water vapor and CO2. This is achieved by setting the transmissivity of H2O in the 12-18mm region to be equal to 1. In the second case, the H2O overlap due to the rotaional band is included. Finally we include the H2O continuum and calculate the flux changes using both continuum and line transmissivity (for the pure rotation band) described in the previous section. These cases illustrate the most important aspects of the water vapor overlap.

*** SNIP ***

 

Table 1. The effect of CO2 increase on the hemispherically
averaged net radiative heating (wm^-2). DF_T^N is the change
in the net outgoing longwave flux (at the tropopause) due to
doubling of CO2; negative values of this quantity denote
heating of the joint surface/troposphere system. DF¯_s is the
is the change in the downward longwave flux at the surface.

Case	Comments	-DFTN	DF¯s
1	Without H2O absorption in 12-18 mm region	4.69	3.65
2	H2O line absorption	4.18	1.56
3	Line plus continuum absorption	3.99	0.55

 

But I'm content to just use a number that is in an acceptable range recongnizable by most researchers so will content myself with the ~1.2 w/m² estimate derived from the NOAA equation taken from, Myhre et al. 1998.

 

To determine the effects on temperature measurement at the surface from the downwelling back radiation of 2xCO₂ (1.2w/m²), the calculation proceeds as follows:

Starting with 288K initial surface temperature @ current atmospheric conditions.

One applies the Stefan-Boltzman relation:

F=sT⁴

where:

F = total amount of radiation emitted by an object per square meter (Watts m^-2)
s is a constant called the Stefan-Boltzman constant = 5.67 x 10^-8 Watts m^-2 K^-4
T is the temperature of the object in K

to determine the total radiative forcing necessary to maintain the atmosphere/surface greenhouse temperature at the current 288^oK surface temperature of the earth.

Flux (F₂₈₈) at the Earth's surface with atmosphere               = 5.67*10^-8(288^oK)⁴ = 390.08 w/m²

To which we add the increment of 2xCO2 direct radiative forcing at the surface DF = 1.2w/m² (i.e at the surface where we poor peons live as opposed at tropopause at the top of the atmosphere where their nobody to complain about the -56.5^oC deepfreeze.)

F = 390.08 + 1.2 = 391.28 w/m²

And solve for the resultant equilibrium blackbody temperature at the surface for the doubling of CO2 concentration in the atmosphere.

T = (E/s)^0.25 = (391.28/5.67*10^-8)^0.25 = 288.22K

Final step we determine our result in terms of change in temperature (DT) by subtracting our initial state temperature 288K for the resulting increment of temperature do (2 CO²) direct radiative forcing alone enhancing surface temperature.

DT = 288.22-288 = 0.22K

[ancient_geezer]

So, CO₂ is not near saturation and has considerable absorbing power.

Actually CO2 is near total saturation, that is why it's response it logarithmic.

The graphic you are displaying shows outgoing surface emissions (outer envelope), probably mid-latitude mediterranean or thereabouts, limited on the low side by blackbody emissions from tropopause at 217K (i.e. -56^oC), The spectrum include water vapor, and all other ghg emissions as well, that is why it is so ragged.

The actual strong band response of CO2 around wavenumber 666 is very saturated, and is why the absorption by CO2 is so wide in the graph. If it weren't saturated it would be a vary narrow dip in the graphic not showing skirt response.

The primary absorption spectrum of CO2 at current concentrations compared with H20 response looks like this:

 

http://earthobservatory.nasa.gov/Study/Iris/Images/greenhouse_gas_absorb_rt.gif

 

Note: Water vapor bounds the CO2 strong absorption line on either side as well as overlapping a dominant portion of CO2 response. The red jagged absorption lines between 5 & 10mm are the weak line responses of CO2 which are not saturated but are overwhelmed by H2O absorption.

The flat at the top is 100% absorption. When concentration is increased, all that happens is the skirts of the strong lines are raised alittle broadening the line, that is a logarithmic response, not linear. This is true of all strong line responses including water vapor.

Doubling CO2 only provides an additional 3.71 absorption of IR from the atmosphere, downwelling radiation from atmospheric CO2 heating the surface is actually limited by water vapor absorption to something less than 1.2w/m² heating reaching the surface due to CO2.

See my response to jwalsh07 in comment #109 above for more detail on that subject;

I highly recommend that you read Jack Barret's paper on the subject of CO2 absorption in the atmosphere.

PDF-> Greenhouse molecules, their spectra and function in the atmosphere

He has a very good explanation of how IR absorption works as well as a range of graphics demonstrating the effects on IR emissions from the equator through the polar regions.

[Jet Jaguar]

One more for you.

[M. Dodge Thomas]

At the moment, this sort of stuff is amusing to most conservatives - it's a hang over from the days when it was to our economic advantage to ignore the externatilities of a thoughtlessly carbon based economy because we were it's leading beneficiaries.

But a decade from now most of the same posters here - yourself included, likely - will be screaming bloody murder about that the fact that emerging industrial economies attempting to be equally thoughtless about such matters are starting to seriously screw up the world for the rest of us.

But...whatever,

Knock yourself out.

20 or 30 years from now I'll be dead.

And posters such as yourself - and your children - will be paying the substantially inflated bill for having delayed taking such matters seriously.

[Tarpon]

How about the terrorist deniers, do they count? Peloser is top of that list.

If man caused global warming, then obviously man can fix it.

Where is the proof that CO2 can cause the Earth to warm and is not just a signal of natural warming. There is little doubt the Earth is warming, been doing that since the end of the last ice age 15,000 years ago -- So what caused the last ice age to end?

[Jet Jaguar]

Are you seriously thinking that me and my car and the rest of us humans are wrecking the atmosphere?

If so, how, can it be corrected?

Can we drop the global temperature?

[arthurus]

The author still implicitly accepts that all the global warming that may be occurring is man-made and therefore addressable by shutting down civilization if it is serious. He is skeptical of rates not substance. The Sun's increased activity and evidence that the other planets are affected also doesn't figure.

[jwalsh07]

Thanks, I got it now. I was missing the IR crossover.

[ancient_geezer]

I've been doing some spreadsheet work as an extension of the measures done by Jack Barrett in his paper on greenhouse molecules:

PDF-> Greenhouse molecules, their spectra and function in the atmosphere

using the HITRAN calculator and other tools over on the GATS websites: http://www.gats-inc.com/spectral_browser/spectral_browser.php

I've been collecting integrations for CO2 & H20 concentrations ranging from 10->10,000ppmv for various standardized scenarios in order to test the log relationship of forcing as well as Barrett's results and extend on them somewhat as inspiration grabs me building the spreadsheet and implementing the numerical analysis involved.

It's getting to be a rather fascinating investigation, to say the least.

[edsheppa]

That is the gas responsible for the heat retention.

You mean heat capture, right? Retention is what is kept and the CO2 will keep it.

Virtually all (99.95%) the extra heat that is captured by the extra CO2 flows to the dominant gasses. Some of that captured heat will be eventually radiated into space or flows into the ground or oceans. The rest that stays in the atmosphere, the retained heat, goes to raising the temperature of the atmosphere.

If this has all been a terminological misunderstanding about what retention means, well then that's too bad.

Not sure what you mean here, but there is none. I don't see any significant diff between 1700 and 2060 either.

The differences between 2000 and 1973 is ~1% and between 1700 and 2060 is ~21%. If I'd been off by 21% in my estimate of the ratio of retained heats, well, that might be significant depending on the application.

The Oceans are essentially saturated.

That guy was saying that the saturation level is temperature dependent. If the Earth warms, the oceans will be oversaturated and give up CO2 to the atmosphere increasing its concentration. Conversely, if the Earth cools, the oceans can take up more CO2 and the atmospheric CO2 concentration will decrease.

He is proposing this mechanism as accounting for past observed correlations between global temperature and atmospheric CO2. AGW types have latched onto this to support their theory. He is trying to debunk that argument.

[spunkets]

"The graphic you are displaying shows outgoing surface emissions (outer envelope), probably mid-latitude mediterranean or thereabouts..."

The Plot is tropical, so it's ~equitorial. The dips are due to absorption.

The spectrum given in your post is unlabeled. Where did it come from? It means nothing to me w/o conditions.

"If it weren't saturated it would be a vary narrow dip in the graphic not showing skirt response."

The p, r and q branches are obscured.

It looks like the 5.xxln(C/C,sub>o) is a fitted eq. above a baseline of 278ppmv in 1750. I'll have to look into that.

[spunkets]

"The differences between 2000 and 1973 is ~1% and between 1700 and 2060 is ~21%. If I'd been off by 21% in my estimate of the ratio of retained heats, well, that might be significant depending on the application."

Not sure I understand. I don't see a big temp diff. Maybe 2^o, and probably half that. 2^o is only a 0.67% change in energy content.

"AGW types"

?

" He is proposing this mechanism as accounting for past observed correlations between global temperature and atmospheric CO2.

Those changes had to be driven by the Sun's output. The temp change is way too big. The temp probably drove the CO₂ out of the water, but that's ~saturated at each temp. So I don't see the Oceans as a sink, except for their Ca, Mg, and Cl^- content.