A couple of months ago, we discussed a short paper by Matthews and Weaver on the ‘climate change commitment’ – how much change are we going to see purely because of previous emissions. In my write up, I contrasted the results in M&W (assuming zero CO2 emissions from now on) with a constant concentration scenario (roughly equivalent to an immediate cut of 70% in CO2 emissions), however, as a few people pointed out in the comments, this exclusive focus on CO2 is a little artificial.
I have elsewhere been a big advocate of paying attention to the multi-faceted nature of the anthropogenic emissions (including aerosols and radiatively and chemically active short-lived species), both because that gives a more useful assessment of what it is that we are doing that drives climate change, and also because it is vital information for judging the effectiveness of any proposed policy for a suite of public issues (climate, air pollution, public health etc.). Thus, I shouldn’t have neglected to include these other factors in discussions of the climate change commitment.
Luckily, some estimates do exist in the literature of what happens if we ceased all human emissions of climatically important factors. One such estimate is from Hare and Meinshausen (2006), whose results are illustrated here:
The curve (1) is the result for zero emissions of all of the anthropogenic inputs (in this case, CO2, CH4, N2O, CFCs, SO2, CO, VOCs and NOx). The conclusion is that, in the absence of any human emissions, the expectation would be for quite a sharp warming with elevated temperatures lasting almost until 2050. The reason is that the reflective aerosols (sulphates) decrease in abundance very quickly and so their cooling effect is removed faster than the warming impact of the well-mixed GHGs disappears.
This calculation is done with a somewhat simplified model, and so it might be a little different with a more state-of-the-art ESM (for instance, including more aerosol species like black carbon and a more complete interaction between the chemistry and aerosol species), but the basic result is likely to be robust.
Obviously, this is not a realistic scenario for anything that could really happen, but it does illustrate a couple of points that are relevant for policy. Firstly, the full emissions profile of any particular activity or sector needs to be considered – exclusively focusing on CO2 might give a misleading picture of the climate impact. Secondly, timescales are important. The shorter the time horizon, the larger the impact of short-lived species (aerosols, ozone, etc.). However, the short-lived species provide both warming and cooling effects and the balance between them will vary depending on the activity. Good initial targets for policy measures to reduce emissions might therefore be those where both the short and long-lived components increase warming.
“How about this:
Insulate.
Then the heat from outside takes a day to get in, where you can merely run a fan to exchange the colder air outside for the too warm one inside.
Best of all, it works even better in winter!
Use less.
It costs less in all measures of cost.”
When it’s 95 degrees with 85% humidity outdoors, do you really want to pump that into your house in order to make it cooler?
Silliness.
Rod B says #571
“Norman, It’s secondary to your main question, but I was curious about one piece from your link in #551. The LW downwelling seems to vary significantly over seasons (p5?). It’s not obvious why this would be (as opposed to SW/solar insolation). Can you explain this? (Or am I reading it”
My understanding is that with less solar energy hitting the ground (in winter), the ground is not warmed as much and will emit less radiation. Less Longwave radiation going up, less coming back down from the greenhouse effect. That is why I think the variation is seasonal. I could certainly be wrong.
“The other problem — and this is a fun one — is that running appliances indoors produces heat. Oh, and people make a LOT of heat and give off a lot of moisture.”
– advantage to winter efficiency, just when solar power would be at it’s minimum!
“My patents pending require NO WIDE AREA SMART GRID!”
Oh dear.
Everything’s become terribly clear to me.
PS The energy system we have needs a smart grid. We don’t have one, so we have engineers watching the system and bringing sources on and off line to manage loads.
I don’t think your system is going to manage either.
“Because I live in Texas where there is a very distinct possibility that there is no source of “colder air outside”.”
Yah, night time, remember?
“The other problem — and this is a fun one — is that running appliances indoors produces heat”
Here’s a tip: so does running AC.
A lot more than running a fan.
“Rod, when you place a population in inversion, you not only change the temperature, you make it negative!”
That was one of the most interesting things I learned in thermodynamics.
How to create negative temperatures:
1) Put a magnetic material in a magnetic field
2) Cool it
3) Swap the field around
4) Negative temperatures
5) (Bonus Step!) THIS IS HOTTER THAN INFINITE TEMPERATURE!!!
Heh.
Makes you realise that temperature really is a weird thing.
“589
Rod B says:
14 June 2010 at 4:19 PM
Ray (580),
How do you explain varying specific heat for a gas?”
By using all the physics of temperature. Not just selected elements of it.
“When it’s 95 degrees with 85% humidity outdoors, do you really want to pump that into your house in order to make it cooler?”
So in these places with 95 degrees and 85% humidity, what is the temperature in a cave?
Oh, aye, cooler.
How can that be?
Thermal inertia.
What is that?
It’s insulation.
What did I say to do?
Insulate.
What will this do?
It will mean that by the time your home has heated up from daytime maxima, it’s well past daytime maxima and the outdoors is now cooler.
Gavin, Norman 588, 600, 602 (Also Patrick 027 590, 591, 592, 593; Giles 594; Ray 596)
Gavin’s ($9.00) reference to Gunnar Mehr(1998)seems to me to be a very succinct (and I assume current) evaluation of LBL, NBM, and BBM model estimates for radiative forcing. At first I couldn’t find much physics back-referencing another $9.00, but then up popped a free PDF – Ramanathan (1976) “Radiative Transfer Within Earth’s Troposphere and Stratosphere:A Simplified Radiative-Convective Model” http://journals.ametsoc.org/doi/abs/10.1175/1520-0469(1976)033%3C1330:RTWTET%3E2.0.CO;2
which did seem (to me) to contain the physical reasoning for the radiative transfer calculations – at least for H2O, CO2 and O3. Also not only does Gunnar Mehre reference it but also 90+ others so maybe many of the radiative forcing calclations today employ Ram’s physics (Wouldn’t be the first time)
I am quite interested in radiative transfer and GH effect (why else spend $18.00?), but trying to learn from a thread with soooo much discussion makes my eyes glaze over. Not meant to be a criticism of this thread, just a descript5ion of the reactions in my tiny brain.
This post is meant as a public service to anyone interested in some good physics including approximations for radiative transfer calculations.
Well, I live in the Atlanta metro area, and I don’t use my AC. Actually, it doesn’t work anymore; I’ll probably be forced to replace it in order to sell someday, but it’s not too bad and in the meantime we have other priorities for our money.
We in fact do exactly what’s been discussed upthread: from about 8 PM to about AM, we run the attic fan, drawing cooler outside air into the house. At 8 AM we shut that down, as the outside air is warming up, and rely on ceiling fans in the room(s) where we actually are.
This works as well as it does because we have a house which–fortuitously, I’m pretty sure–is physically configured to warm slowly during the day: major axis NW to SE, large unheated garage on the SE as a buffer, and most importantly it is very well tree-shaded.
556: Patrick 027 wrote: an excellent post.
Patrick 027, it seems to me that if the polyatomic molecules have higher specific heats because some of the energy is added to (unfrozen) rotation and vibration, that added energy that goes into rotation and vibration does not raise the temperature.
Actually we’ve been down this road before and it won’t be reconciled. It’s my opinion that Ray et al and I et al have a difference in semantics or convention rather than physics. But, thanks.
FurryCatHerder, there is in the neighborhood of $12 billion ($4B by the feds) over a few years being spent to architect, make standards, develop and build prototypes for a national smart grid. What is this all about?
Norman (602), I don’t know if the numbers would match up, but the logic makes sense. Thanks.
“it seems to me that if the polyatomic molecules have higher specific heats because some of the energy is added to (unfrozen) rotation and vibration, that added energy that goes into rotation and vibration does not raise the temperature.”
It seems to me you’ve forgotten that that energy can be imparted to another molecule that isn’t excited rotationally, which can express it kinetically in movement. Which is temperature.
Rod@611
You are thinking of an equilibrium situation–and when you are adding energy, you are not at equilibrium. That is why the energy tends to flow into the kinetic degrees of freedom, so that the system can equilibrate.
CFU @ 604:
Actually, we don’t have a “smart grid”. We have a very dumb grid that’s based on scheduling large blocks of power, then having load-following generators balance the difference. Human beings do make some decisions, often times badly, and others are handled by computers. By and large, the system works by computing the existing frequency, and raising or lowering the output of a small number of generators in order to bring the frequency back to nominal and the time error back to zero. Historical data is used to calculate the rough amount of power that’s needed in the day ahead period, and weather forecasts are then applied to tweak things. From there, contingencies are planned for and managed, some by computers, some by humans.
And that’s about it.
I obviously can’t explain what I’ve done because I’m under a non-disclosure agreement until the PTO publishes the applications. But “there is no wide area smart grid” is an accurate statement. Indeed, during the several years I worked with other engineers (see, I’m an “engineer”), getting rid of the “wide area smart grid” was a key component in our work. How we did that is a secret :)
Rod B @ 612:
Mostly it’s about the way that technology works. Go with what looks like a good idea until it’s obvious that it’s a bad idea.
I don’t remember the order in which all the applications were filed, so I don’t know which ones will come out next (the first has published, but it’s a minor enabling invention). They should all be out by next summer, by which time I’ll be able to be a lot less vague.
CFU @ 607:
Caves are cooler because the surrounding earth is a heat sink. The warmth of the air inside the cave (assuming the air is warmer …) is transferred to the earth, which happily takes it.
A perfectly insulated home cannot transfer any of the heat from the interior to the non-existent exterior heat sink that is the outside air. For one thing, insulation prevents heat flow in both directions.
You could get around this by pumping cooler outside air in, but we often don’t have enough of a temperature difference for that to work — I need 72F air to bring the temperature down to where I set the A/C (78F), and I need that for =hours=. Which we don’t get this time of year.
“Caves are cooler because the surrounding earth is a heat sink.”
Yes, otherwise known as “insulation”.
“A perfectly insulated home cannot transfer any of the heat from the interior to the non-existent exterior heat sink that is the outside air.”
No, but it can stop the heat getting in.
And we have these things called “windows” and “fans” and so on for moving air between inside and outside.
So we open the windows or turn on the fans and swap the warmer air inside for the colder air outside at night.
Then we stop the fans and close the windows for the daytime.
The heat outside doesn’t get in very fast and so the cold night air inside stays cooler than the daytime air outside.
Then, when night falls again and the heat inside is higher than outside, open the windows and turn the fans on again.
Simples.
Speaking of commitments or lack thereof, news from Bonn:
Climate negotiators meeting over the past two weeks in Bonn, Germany, enjoyed a new spirit of bonhomie as they worked to heal the rifts created by the failure of UN talks in Copenhagen, Denmark, last December. At the close of talks on 11 June, they believed they were back on track to deliver a new climate agreement by the end of 2011.
But diplomatic harmony has come at a price: sacrificing a cool future for planet Earth.
Until Copenhagen, the aim was to set targets for major emitters of greenhouse gases that would limit warming to 2 °C. That required, as a first step, that by 2020 industrialised countries cut emissions by 25 to 40 per cent compared with 1990 levels.
While that target remains an option in draft deals, most negotiators say they will have to accept whatever pledges industrialised countries are prepared to make. Right now those pledges add up to cuts of between 12 and 19 per cent, according to the UN climate secretariat. And there are loopholes that could mean even these pledges amount to virtually nothing.
“As things stand now, we will not be able to halt the increase in global greenhouse gas emissions in the next 10 years,” UN chief negotiator Yvo de Boer said in Bonn. “The 2-degree world is in danger. The door to a 1.5-degree world is rapidly closing.”
http://www.newscientist.com/article/mg20627650.401-is-it-time-to-say-goodbye-cool-world.html
Words fail to describe how irritating it is watching us be humans.
CFU, I was talking only of the energy that went into rotation or vibration, not what if you then moved that energy somewhere else.
Ray (615), that sounds correct (if I’m reading you correctly). Like my response to CFU, I am talking only about the singular action of adding energy into rotation or vibration. Whether a microsecond or less later it equalizes into translation kinetic energy is highly probable but not part of my assertion.
FurryCatHerder, but if you got something that could affect the mad rush at the National Institute of Standards to write the standards (1/3 already done) by this year, some way ought to be found…
Wow, CFU, you actually know that my house is uninsulated, and that is why pumping hot, humid air inside is a great idea.
Or, possibly you are completely clueless as to how well my house is actually insulated and are just making stuff up.
We actually found the key is controlling the humidity – 80 degrees (where we set our AC) is actually rather comfortable if one brings the humdity down to fifty (45 is better) percent.
So a high efficiency de-humidifier is the better choice than popping open a window or cranking up the AC.
“Although some may disagree with me, setting up a lab test to get as close as possible to an atmosphere (like individual sealed containers at various pressures that create a large column to beam the same IR spectrum the Earth gives off…can be varied to match different parts of the Earth at different seasons) is not the same as a computer simulation.” Norman — 14 June 2010 @ 10:49 PM
I agree; a realizable physical model can’t be as good as a computer simulation.
Consider building an analog of the troposphere – 10 km thick, give or take a few km, depending on atmospheric pressure and surface temperature; for convenience, our initial design will be 100 meters long, 1 meter in diameter, and divided into 20 cells, with a linear pressure gradient (stepwise) from 1000 to 250 mbar. To get the equivalent absorption, we’ll just increase the CO2 concentration by 100 fold; this will increase the probability that an excited CO2 will transfer its energy to another CO2 instead of (N2,O2, H2O), but we can model that and apply a correction.
We can’t increase the H2O above 100% – it just condenses out on the temperature controlled walls; we’ll just have to measure at a few intervals from 0 to 100% RH, and model and extrapolate to what the results would be if we could increase the H2O by 100 fold. Or we can crank the temperature up to raise the amount of water vapor, but that will increase the pressure broadening of CO2 and H2O absorption lines, and the amount of thermal radiation. Plus, we have to correct for the fact that pressure broadening is dependent on the particular species – an increase in CO2 pressure causes 1.3 times as much broadening of the CO2 lines at the same increase of N2 pressure. Either way, modeling is required.
The real radiation in the atmosphere doesn’t just go straight up, but is emitted isotropically; the effective path length is root 2 time longer at 45 degrees, and so on. This means that there is a wavelength dependent anisotropy in the angular distribution of radiative transfer from parcels of air at various altitudes. We will gold plate the walls of our 100X1 meter cuvette to maximize the IR reflectivity – shouldn’t cost too much – so the parcels of air “see” reflected images of other parcels that look somewhat like the real atmosphere; we’ll measure the wavelength and angular dependence of the IR reflectivity of the gold plating, model how that differs from reality, and apply a correction to our measurements.
The optically transparent, low thermal conductivity, multilayer dielectric broadband antireflective coated unobtanium windows between cells aren’t perfect, so we will measure the wavelength/angular/thermal dependent properties and model how this effects our system, so we can correct these effects too.
So, even a giant, complicated (temperature, pressure, gas mixture controlled, multicell) gold plated experimental system can’t provide results without many mathematical corrections, and as soon as you start interpolating your corrections you are assuming some underlying physical process that can be described by a mathematical function (linear, logarithmic, exponential, polynomial, whatever), e.g., modeling.
And we haven’t even considered clouds and wall effects.
An enormous number of lab measurements on CO2 and H20 have been made since Tyndall first published his measurements in 1859, at a multitude of different pressures and temperatures, spanning beyond the limits in earth’s atmosphere. More importantly, these measurements have allowed scientists to elucidate the mathematical functions that describe its behavior, and the underlying physical processes that govern it. Because of this work, it is possible to calculate the IR spectrum of CO2 given only the masses of the atoms and the strength of the chemical bonds. Once you get the math, or even an approximation of the math that is accurate enough and computationally faster, there’s little reason to do more experiments; every time we build a AMSU satellite detector and it works, it provides another confirmation that the theory is correct and the math is accurate enough.
CFU —
IT IS NOT COOL ENOUGH OVERNIGHT, OR OF LOW ENOUGH RELATIVE HUMIDITY, FOR THAT TO WORK EVERYWHERE.
Equilibrium at my house, which is profoundly energy efficient, this time of year is well above where I set the thermostat. It’s just freakin’ hot here, sometimes of Biblical proportions hot. If I were to let all that (not very) cool outdoor air in, I’d have horrible problems with mold and mildew due to the humidity.
And no, a heat SINK is not called “Insulation”. Insulation is resistance to the flow of heat. A heat SINK absorbs heat. Insulation does not. This is why heat sinks work best when they conduct heat. Insulation works poorly when it conducts heat.
#614 the comment is correct throughout, but the phrasing could be misunderstood:
which can express it kinetically in movement. Which is temperature.
Your point is that movement is not the same as temperature although it can be an example of it. You just gave a good counter-example in #605. No translational movement but both positive and negative absolute temperatures can occur.
Just in case anyone might get the wrong idea from that example, scientists,unlike some deniers, are not saying that warming produces cooling. The negative absolute temperatures are actually physically hotter than the positive ones. The trouble is caused by the mathematical representation i.e. the scale.
Most of that particular weirdness would disappear if we used a more physical temperature scale of coldness i.e. 1/T where T is the usual absolute temperature.
Anyway this is unecessary for climate
because negative absolute temperatures require a finite upper bound to the available energy levels. The climate has nothing in it like spins in a magnet.
Furry 569: this isn’t a SciFi novel where you get to claim some magical solution…
BPL: Okay, that’s about the third or fourth time you’ve mentioned my profession disparagingly, and I’m tired of it. You’re on filter, Furry. I’ve never done that to someone on RC before; you’re the first. Congratulations, and have a nice day.
Norman 600: How much more actual energy does a double of atmospheric CO2 send in downwelling IR.
BPL: 3.7 watts per square meter.
Rod B @ 623:
There’s nothing I can do. I’m bound by a non-disclosure agreement that I’m not going to break. I’m trying to build my own IP portfolio and I’m not going to give IBM any excuses for whacking me upside the head.
The work that’s going on isn’t completely and totally pointless. Remember that there is a difference between measuring, monitoring and controlling. The problems with a “Wide Area Smart Grid” are — in my professional opinion — all in the “controlling” domain.
There is still a need for measuring and real time monitoring, if only because statistical data is very handy. Right now there is no way to do that monitoring with any significant granularity and that part of the “Wide Area Smart Grid” work =will= be useful when it’s completed. But actually controlling the grid? Yipes!
Rod, my point is that temperature is a rather dodgy concept in a system far from equilibrium–like an optically excited molecule.
Re C.F.U,F.C.H,Frank Giger, others – A large thermal mass can be helpful to ‘insulate’ the temperature from higher-frequency heating cycles, but only via conduction and convection with that thermal mass, which itself is not insulation (perhaps this is what you (CFU) meant, but it wasn’t clear). The underground material is insulated (by thermal mass and by actual insulation – the finite thermal conductivity of the material) from the daily and seasonal cycles but one has to break that insulation to get to it (send a fluid through it). Obviously one can still insulate the interface between a building and outdoor air and yet bring heat in or out to selected thermal masses. Maybe such ambi-ent or other artifically-maintained thermal masses (thermal masses alternately exposed/absorbing and then insulated/reflective to the conditions/radiation at different times/wavelengths to maintain a temperature different than the annual or diurnal average) are not at the desired temperature; they could still be used to preheat or precool various fluids. Water intake is often quite cold because of the temperature of the underground rock/soil; this is a resource in summer. Air and water outflows can be a thermal resource all year; the moisture and heat from bathrooms, kitchens, and laundry can sometimes be a burden (dealt with by having air leave the building from those rooms) and sometimes be helpful if managed. In dry climates, cooling can be achieved by evaporation (perhaps using seawater, thus producing salt, which can then be used as a dessicant in humid climates? – maybe not the most practical trade, but just thought I’d mention it). It may be easier to have good energy efficiency in winter if insulation is sufficient; this can complement the availability of solar energy. Not all solutions work everywhere at all times; this doesn’t mean they don’t make sense in many places at many times.
Re Rod B – Yes, I think I understood what you meant, and as heat capacity is the amount of heat per unit temperature change, and temperature is related to translational kinetic energy, the smaller that is as a fraction of internal energy, the larger the heat capacity per unit material.
Re Rod B. – with respect to Ray Ladbury’s comments – I am refering to the relationship between heat and temperature for a sufficiently large population of molecules/atoms/etc. which are maintaining (quasi)LTE as heat is added or removed.
629 (Barton Paul Levenson),
Your answer to Norman that a doubling of CO2 sends an extra 3.7 W/m2 extra in downwelling IR is not necessarily correct. This is the reduction in the OLR, not the increase in downwelling IR to the surface, which responds more to (sigmaT^4) as the atmosphere warms than the direct CO2 increase.
#625–“The optically transparent, low thermal conductivity, multilayer dielectric broadband antireflective coated unobtanium windows between cells aren’t perfect. . .”
Maybe not, but the independent clause quoted comes pretty damn close!
What I reduced was =waste=. But making much of what I use means I get to increase productive consumption, and I may even increase it beyond what I used previously.
Jevon’s Paradox. One reason technology is certainly not *the* answer. Another reason has to do with fixing complexity with complexity; doesn’t work too well.
Furry, you do know what Ol’ Al Bartlett has to say about yeast, right? Also, please extrapolate all scenarios planet-wide to equate your comments with reality.
Barton Paul Levenson #629,
I was reading through the link you sent me to your paper “The Irrevelance of Saturation: Why Carbon Dioxide Matters”.
Brian Dodge prefers the computer model to the empirical, but your paper demonstrates why models can be flawed. It has to do with the intitial assumptions. With an empirical test, initial assumptions do not matter. Example: I make an initial assumption that CO2 is a very good IR asorber. I then run an empirical test (run the entire spectrum of IR into a CO2 sample and measure the energy on the other side). With an empirical test it does not matter what the initial assumption might be. The assumption will not alter the reality. In a model the assumption is crucial to the reality derived.
Point: Barton Paul Levenson “The value of a for the ground and layer 1 is 1.0; they have been assumed all along to be perfect absorbers/ emitters.”
Where does this assumption come from? The empirical tested reality does not support this assumption at all.
IR atmpospheric absorption, not even close to a 1, lots of windows.
Or this one: Barton Paul Levenson “Let’s assume layer 2’s absorptivity is 0.5 — it absorbs half the radiation from Layer 1; the rest goes through it and out to space.”
Why would this assumption be made? The second layer is composed mostly of CO2. CO2 only absorbs about 8% of the total IR spectrum. You should use 0.08 for this layer and that is if it is entirely CO2. 92% will go on through since CO2 does not have the right resonant frequency in its bond-stretching to absorb it. In layer 2 if it was all CO2 it would abosorb about 8% of the IR coming up from layer 1.
The site I posted earlier shows how much of a contribution CO2 has for downwelling longwave radiation. It is less than 10%.
Anyway, Brian, that is what is also wrong with computer models. An assumption will not alter the results of an empirical test.
http://www.daviddarling.info/encyclopedia/A/atmospheric_window.html
Or
http://en.wikipedia.org/wiki/File:Atmospheric_electromagnetic_opacity.svg
One question I hope you can answer for me Barton Paul Levenson,
I am doing my best to research AGW hypothesis. The band saturation question still causes me some confusion. I look up various IR spectrometer graphs of CO2 absorption. They show the absorption go to 100% at certain frequencies (or wavelengths) or no transmission of energy.
Wouldn’t the layer theory show up in IR runs? Why wouldn’t the CO2 in the sample cell that is absorbing the incoming IR radiation, heat up and emit radiation in all directions and then reach the detector? How can a detector ever read 100% absorption of CO2? It seems if I am to buy the theory of perpetual emission, wouldn’t the best absorption be 50%? 50% would make it to the detector (regardless of concentration) and 50% would be reflected back to the IR source.
Re 610 John E. Pearson “556: Patrick 027 wrote: an excellent post.”
Thank You!
But I must correct an error. I wrote that the effective width of the band increases by 2*B or B1+B2, but it’s 2/B or 1/B1 + 1/B2:
Where: …log(OptCO2) ~= peak value – B*abs(frequency-peak frequency). this means that a 10-fold increase in CO2 will result in CO2 absorbtion exceeding any set threshold over an additional 2/B frequency interval, provided that the peak has already exceeded that threshold. Now, maybe B is different on one side of the band verses the other, so it would be 1/B1+1/B2 instead of 2/B … it’s an approximation, anyway…
Re 629 Barton Paul Levenson “3.7 watts per square meter.”
Yes, the forcing at tropopause level with equilibrated stratosphere. I actually attempted to estimate this graphically using the spectrum of OLR from K&T, knowing about the spectra of the gases, I drew a line across the CO2 valley/hill (valley in OLR, hill in ‘effective emitting altitude’) to estimate what it would be in the complete absence of CO2, no temperature change or other feedbacks – same clouds and water vapor, etc. (let’s call that the ‘potential forcing’ for CO2 – I think it’s a useful concept). Noting the maximum effect of adding CO2 would be at wavelengths where optical thickness from CO2 would have some intermediate value, estimated the slopes B of log(optical thickness) over wavelength, take 1/B1 and 1/B2, each multiplied by the potential forcing at the wavelengths where the band expands by 1/B1 and 1/B2, respectively, and take the sum. That’s the change in OLR for a 10-fold increase – multiply by log(2) to get the amount per doubling. Note, graphically, this is the decrease in area under the OLR curve – the exact shape of the curve depends on the way temperature varies with height, but knowing that the same set of optical properties are just translated by some wavelength interval outward from the center of the band, the shape of the curve from where CO2 starts to make a significant difference to where OLR becomes saturated stays the same. Thus, the change in area is equal to the height (the potential forcing per wavelength interval) times the wavelength shift – this is done for both sides of the CO2 band. NOTE, this is an approximation – because potential forcing is not actually constant over wavelength (the approximate works if it doens’t vary much over a wavelength interval the size of the shift), and also, because the log(optical thickness from CO2) = peak value – B*abs(wavelength-peak wavelength) (where B may be a different value, B1 or B2, on either side of the peak) is an approximation that glosses over some bumps and finer-scale texture (though if the finer scale texture is sufficiently self-similar over short wavelength intervals, then it won’t necessarily cause much of an error (unless the finer details correlate with finer details in other absorption spectra that shape the potential forcing) – the interval exceeding any threshold of optical thickness has fuzzy edges but the fuzz shifts outward in the same way).
Anyway, I don’t remember exactly offhand what numbers I got but I was able** to get something not far off from a 2.7 W/m2 reduction in OLR. But I did the same for tropopause level forcing – I didn’t have a graph of upward and downward LW fluxes to work with there, but the slope of the log(optical thickness) over the spectrum for CO2 would be the same for any layer of air for the same frequency – it’s just the total amount that changes (which means that there will be a shift in the frequency where the change in CO2 has greatest effect; the interval that is saturated will also be different (but with the same center), but I used an approximation of constant B1 and B2 over the relevant wavelengths). I know that at saturation within the atmosphere, the downward LW flux = the upward LW flux (because the photons are originating from such close locations that the intensities have the same brightness temperature as the temperature at that location for which the intensities and fluxes are calculated or measured). I also know that absent CO2, the stratosphere is essentially transparent at the relevant wavelengths. Thus the potential forcing is the difference between OLR without CO2 and zero. Using that, multiplied by the band-widenning, I was able to get something not too far from 4.7 W/m2.
The difference between top-of-atmosphere (TOA) forcing and tropopause level forcing is the forcing on the layer in between. It is negative, indicating cooling. Allowing a temperature change to occur to balance that, the combination of decrease in OLR at TOA and decrease in downward LW flux at the tropopause must sum to the original (instantaneous) stratospheric forcing. Much of the radiation from the stratosphere is emitted from water vapor, which adds significant but not large optical thickness at the wavelengths where it is significant. At wavelengths where the stratosphere is optically very thick, the changes in OLR and downward LW flux at the tropopause could be quite different, even possibly of opposite sign. But I don’t think this dominates the effect for Earthly conditions, so to a first approximation, one could assume that the changes in TOA OLR and downward LW flux at the tropopause are the same. This would transfer half of the stratospheric forcing to the tropopause level forcing, thus bringing that value down to near 4.7 + (2.7-4.7)/2 = 3.7 W/m2. Actually, in my calculation, I assumed 5/11 of the stratospheric forcing got transfered to the tropopause level, because that is the fraction of LW flux leaving the stratosphere that is downward through the tropopause (Hartmann, “Global Physical Climatology”) – though the change in LW fluxes isn’t necessarily apportioned the same way.
**I actually tried a few estimates of B1 and B2 and so got a range of values, but they were in the ballpark and some were not far off. It’s tricky because of the bumpiness of the CO2 spectrum. Well, this was just an approximation, after all. The actual scientific work has been done with more detailed information and calculation (and not just for global average/representative conditions – as I understand it, GCMs calculate radiative fluxes for different locations and times).
(Also, I completely skipped over the effect of the increase in OLR at the center of the CO2 band and the expansion and heightenning(?) of that with increasing CO2.)
The calculation of forcing at a particular wavelength depends on additional information. The shape of the CO2 spectrum (approximated as described above), when the central portion of the absorption band is saturated, happens to lend itself to such a straightforward approximation (but it IS an approximation, the way I did it).
Presumably something similar could be done for backradiation at the surface, but I think the ‘potential forcing’ would be (in global average effect) signficantly smaller. There is generally a concentration of water vapor near the surface (at wavelengths where it would affect the potential forcing of CO2, having greater effect on backradiation than OLR or tropopause-level fluxes).
Re 637 Norman – from the language you describe (let’s assume layer 2 has…), I assume BPL was trying to illustrate principles rather than calculate a particular real value. However, the surface emissivity truly is close to 1 over the LW part of the spectrum. Not exactly 1, but close. (That’s not refering to atmospheric absorption at all wavelengths)
These optical properties have been measured. Here is where more empirical work is not so necessary – if you know that the optical thickness of a 1 m distance through air with some composition and pressure and temperature is Opt, then you know that 10 m over the same conditions has 10 times that optical thickness. You can calculate the effects; you don’t need to redo all the measurements for 1 km. It’s a bit like knowing that 1 rock weighs 10 pounds, another weighs 5, and knowing that you have 100 rocks just like the first and 40 more just like the second. You don’t need to put them altogether and weigh them to know how much they will weigh.
But if you want confirmation, you can look at actual measurements of radiative spectra, from the Earth as seen from space, and looking up from the ground, etc.
Norman, the point is not just how many W/m2 is due to directly to CO2, but also the amount is feedback W/m2 as result of increase in CO2. (Ie the water vapour especially). You cant vary water vapour independently of temperature so have to worry about the forcings instead (GHG, solar, albedo, aerosol).
“621
Rod B says:
15 June 2010 at 2:23 PM
CFU, I was talking only of the energy that went into rotation or vibration,”
So there are never any collisions in your gas, then, Rod?
How strange.
How do you manage to get the ideal gas laws from a gas that doesn’t collide?
“The warmth of the air inside the cave (assuming the air is warmer …) is transferred to the earth, which happily takes it.”
http://en.wikipedia.org/wiki/Heat_conduction
http://en.wikipedia.org/wiki/Conduction_%28heat%29
http://en.wikipedia.org/wiki/Thermal_contact_conductance
I think you need to get into some actual science, FCH. You’re ignoring REALLY basic stuff.
The thermal heat loss is reduced by
a) increased resistance to thermal conduction
b) increased thickness
BOTH of which are involved equally.
Even your best insulator happily accepts heat from a warmer source.
Even your best conductor happily produces a heat gradient from inside to outside (therefore resists heat transfer).
“That is why the energy tends to flow into the kinetic degrees of freedom, so that the system can equilibrate.”
Or, for the scientists (Rod, are you a scientist?)
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/eqpar.html
Chris 634 — oops! You’re right. I got the radiative forcing confused with the sea-level downward flux.
Norman 637,
You are mistaking illustrative examples for an actual model of the climate system. To get the correct numbers you need to put together, at the very least, a radiative-convective model of the atmospheric column. Please rest assured that I have done that as well and that the standard theory holds up very nicely.
The point of the essay was that even if the lowest layer absorbs ALL the infrared from the ground, adding more greenhouse gases can still warm the ground.
Norman,
The main problem I see with your saturation argument is that satellites measure a nonzero radiation flux at the wavelengths in question. Thus, at some altitude, the atmosphere is no longer opaque. Adding CO2 pushes that level higher (and colder). It also broadens the absorption spectrum.
Second, when you say “AGW hypothesis” it seems that you do not fully understand the way the science has played out. Warming due to anthropogenic CO2 is a prediction of the consensus model of Earth’s climate. Under this model, such warming is inevitable. There are uncertainties to the exact amount, but the observation of a sustained period of warming is evidence (a confirmed prediction) of the consensus model.
AGW hypothesis implies that warming was observed, and anthropogenic causation was advanced to explain it. Not true.
Norman #637 said:
> An assumption will not alter the results of an empirical test.
Wrong assumptions can lead to a wrong experimental setup, to looking for the wrong results, or to the wrong interpretation of those results.
Assumption: The Moon is made of green cheese.
Hypothesis: Man has landed on the Moon.
Empirical test: Oh yeah? Show me the cheese!
Results (unaltered by assumption): Rocks. Dust. No cheese.
Conclusion: NASA faked the moon landing.