This month’s open thread.
Seed topics: The genealogy of climate models, how to compare different greenhouse gases, whether a 2 deg C temperature target makes sense (Stoat has already weighed in), or reflections on the Nenana Ice classic (which has just concluded for this year). But you decide.
300 Ed said “CA has none.”
Huh?
Diabolo Canyon nuclear reactor in CA
http://www.energy.ca.gov/nuclear/images/diablocanyon.gif
http://www.energy.ca.gov/nuclear/california.html
Edward Greisch wrote: “Illinois has the most nuclear power plants. CA has none.”
What in the world are you talking about? California has operating nuclear power plants at Diablo Canyon and San Onofre:
http://www.nrc.gov/info-finder/region-state/california.html
Edward Greisch wrote: “California is being ‘decorated’ with renewable sources. We have some of those decorations here in Illinois as well.”
With all due respect, that’s just plain silly.
As I wrote above, 35 percent of all new electric generating capacity brought online in the USA since 2007 is wind power. At the end of 2010, the USA had over 40,000 megawatts of wind power capacity, with another 5,600 MW under construction. Fourteen US states have over 1,000 MW of operating wind power capacity and 38 states have utility-scale wind power. The top states are Texas (over 10,000 MW) and Iowa (over 3,600 MW providing 14 percent of the state’s electricity); California is third.
The DOE’s National Renewable Energy Laboratory reports that the contiguous USA has over 10,000 Gigawatts of onshore wind power potential and over 4,000 Gigawatts of offshore wind power potential — enough to generate 9 times the USA’s total electricity demand.
What does it mean to call this “decoration”? Nothing. It’s just nonsense.
Meanwhile, there is a nuclear power station that is “decorating” a chunk of Japan with radioactivity.
Edward Greisch wrote: “I do not now and never have received any money or anything else of value from the nuclear power industry”
I believe you. I would think that if the nuclear power industry was paying someone to promote nuclear power on blogs, they would want someone who knows some basic facts — such as whether or not there are nuclear power plants in California.
I can’t recall if/when this has been covered – but why is there no peer reviewed paper (is there?) addressing attribution/apportionment of last 50yrs’ warming to human vs natural causes, as has been done (e.g. Annan & Hargreaves) with climate sensitivity?
It seems that given the import of attribution of GMST warming (to human vs natural), and given the IPCC’s addressing it, and given Gavin’s “80-120%” estimate, etc, there should already be a paper or papers directly addressing this.
One of my community’s doubters has thrown this up as a challenge.
(I know about Lacis et al’s Oct 2010 “Atmospheric CO2: Principal Control Knob Governing Earth’s Temperature”, but that’s over geologic timescales, right?)
(and caveat, it’s quite possible that mention of such a paper has flown in one eye and out the other; but if you could refresh my memory…?)
re my #304
s/as has been done/along the lines of what has been done/
Re 297 Rod B – sounds okay to me. (Although the actuality of vibration and rotation modes gets a bit complicated – I think they aren’t independent but I’m not sure.)
– a single interaction in a large population won’t cause significant deviation from LTE – with a sufficiently small sample you would actually expect to see things that *appear* to break the second law of thermodynamics (two molecules in a box may occasionally be found in the same half of the box, etc.) anyway. It’s only an accumulation of one type of interaction without some other interactions that results in significant deviation from LTE (this may be obvious but perhaps worth stating).
– fraction of molecules exceeding some energy – I’ve seen that, I think it also approximately applies to the fraction of available states occupied by electrons/holes in a conduction/valence band if one is sufficiently far from the fermi level (closer to the fermi level a more exact expression is necessary).
– And of course emission/absorption =not emissivity/absorptivity.
– If your reference to reduced collision rates allowing significant perturbation from LTE via absorption and emission of photons is in the context of the effective altitude of emission to space…
(which can be thought of, roughly, as the centroid of the emission weighting function(s), though different shapes in the temperature profile and Planck function’s nonlinearity makes this inexact)
…, the vast majority of optical thickness for at least most LW wavelengths is below the level where collisions are too infrequent to hold the air near enough to LTE. Consider that LW photons have energies on the order 0.1 eV (though some are less than 0.01 eV); near the center of the CO2 band it would be ~ 0.08 eV (see below).
I’m (partially) just going by memory here, so things could be a bit off but I don’t think too much for a rough sense of things: something like 30 % of the radiant flux emitted by a blackbody at Earthly-atmospheric temperatures is in the signiicant portion of the CO2 band; and a representative flux would be 240 W/m2, so 72 W/m2 could be absorbed by atmospheric CO2 – neglecting the partial transparency in the wings. For ~ 10,000 kg/m2 of air / roughly 30 g/mol average = roughly 333 kmol/m2 air or roughly 1.3 E26 molecules, and rounding up from a preindustrial value to 300 ppmv CO2, we get 3.9 E22 molecules CO2 /m2.
http://en.wikipedia.org/wiki/Electronvolt
1.602 E-19 J = 1eV
photon energy 1.24 eV at 1 um,
so 0.08267 eV at 15 um
72 W/m2 / 1.602E-19 J/eV ~= 4.494 E20 eV/(m2*s); at 0.08 eV/photon, 72 W/m2 ~= 5.62 E21 photons/(m2*s)
First, if the optical thickness of the atmospheric CO2 were ~ 1 (setting aside optical thicknesses at angles from vertical will be larger – but smaller numbers of photons travel nearly horizontally, so as far as order of magnitude goes this is okay):
5.62 E21 photons/s absorbed by roughly 3.9 E22 molecules ~= 0.14 photons absorbed per molecule per second (and a similar number of emissions)
In the wings of the band, a flux originating from the surface would be absorbed nearly as much or more by water vapor, but that doesn’t affect absorption per CO2 molecule so much at higher altitudes (setting aside variations in the flux itself, which drops less rapidly with height due to emissions from the air, clouds, etc.). Clouds will also intercept some photons. Near the center of the band, though, optical thickness may be great enough that most emissions and absorptions are by CO2 (even within clouds? not sure offhand). Of course, few clouds are above the troposphere.
From a spectrum in my notes (which may or may not be smoothed to some extent), optical thickness of CO2 is near or above 1 from somewhere near 13 microns to somewhere near 17 microns – I am very quickly graphically estimating this and there will be some larger errors because the graph is linear in wavenumber, not wavelength. For something over a 1 micron interval the optical thickness is over 100, approaching 1000 for somewhere under under a 1 micron interval; it peaks just above 10,000 for a range that is less than 1/20 of a micron.
I think (from memory) that 72 W/m2 (out of 240 W/m2) would be (very roughly) for a 6-micron interval, so taking a sum of terms of optical thickness * fraction of a 6 micron band and multiplying it by previous results:
(10,000 * 1/20 + 1000 * 1 + 100 * 1 + 10 * 1 + 1 * 1)/6 ~= 1611. Absorption and emission in the wings would add relatively very little.
1.611 E3 * 0.14 ~= 2.255 E2, and doubling to get emissions+absorptions: about 450 photon interactions per molecule per second
… and the altitude where collisional frequency approaches that is …(to be cont.)
(PS spectral texture and overall optical thickness per unit of material changes with height)
301 John E. Pearson: Thanks for correcting me on nuclear power in CA. Now I know. What is California’s policy on nuclear? I heard California doesn’t like nuclear power.
302 SecularAnimist: I see you didn’t comment on the price of electricity in California. I used the word “decoration” because all that renewable capacity isn’t doing you a lot of good if it results in doubling the price of your electricity. California’s goal was 30% renewable electricity by when? And what % is renewable now? How much will Californians be paying for electricity when 30% renewable is reached?
Price matters to most people.
I do not really get this:
http://arxiv.org/abs/1105.0968
Does this count as a publication? If not what is Hansen up to?
Anna #304,
Have a look at this, and references therein (Stott 2006, etc.), for starters:
http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch9s9-4-1-4.html
The actual scientists here may be able to guide you to the newer work. I’ll just list a few attribution-related references I have at hand that may or may not pertain directly to your question.
Schmidt, Gavin A., Reto A. Ruedy, Ron L. Miller, and Andy A. Lacis. “Attribution of the present-day total greenhouse effect.” Journal of Geophysical Research 115, no. 20 (October 2010). http://pubs.giss.nasa.gov/cgi-bin/abstract.cgi?id=sc05400j.
Stone, Dáithí A., Myles R. Allen, Peter A. Stott, Pardeep Pall, Seung-Ki Min, Toru Nozawa, and Seiji Yukimoto. “The Detection and Attribution of Human Influence on Climate.” Annual Review of Environment and Resources 34, no. 1 (November 2009): 1-16.
Stott, Peter A., Nathan P. Gillett, Gabriele C. Hegerl, David J. Karoly, Dáithí A. Stone, Xuebin Zhang, and Francis Zwiers. “Detection and attribution of climate change: a regional perspective.” Wiley Interdisciplinary Reviews: Climate Change (March 5, 2010).
Hope this helps.
#307 Ed. Yes, price matters. That is why new nuclear power plants are poor investments in the USA.
BTW, electricity rates are FAR lower in North Dakota than in Illinois. ND has no nuclear power.
And yes, we know that you “have heard” many things. We know that you just make things up, too. We also know that haven’t done any research or learned any facts.
[Meant to write this here:
The recent tornado and high moisture events get the usual media treatment.
As often explained, its a cold dry overlaying upper atmosphere capping a hot moist one which creates these rainy and violent conditions. So I read along with everyone else, obvious half explanations. All a while no one really bothers to explain why
the upper atmosphere is particularly colder this season, and why the lower atmosphere is significantly more moist. Is like sleep walking through events, or inspired as one documentary producer told me long ago “speak to an 11 year old audience” otherwise they’ll flip to another channel. I deal with the why’s its so cold, because I live where its from. I got insight into this matter, and I can tell to most of you out there, cold isn’t cornered by media weather presenters. Its shown
as some sort of “thing from Canada” , that is the only way they describe it. All the while the formation and in particular variation on how cold it gets up in the higher atmosphere is seriously dealt with by science papers, these get the scant attention they don’t deserve, a brief 300 word explanation next to to car ad. Thank goodness for RC, may this site prosper further.
Meanwhile, as we continue to argue about how clean and safe nuclear is things aren’t looking too good in Japan.
http://www.washingtonpost.com/blogs/blogpost/post/tepco-surprises-us-with-meltdown-of-two-more-reactors-at-fukushima-plant/2011/05/24/AFtEfTAH_blog.html
http://www.greenpeace.org/international/en/news/Blogs/nuclear-reaction/marine-life-soaking-up-radiation-along-fukush/blog/34979
http://www.nytimes.com/2011/05/26/world/asia/26japan.html?_r=2&pagewanted=all
I had posted a comment/question yesterday and had trouble with CAPTHCA. 3 times it told me I had entered the wrong word. After switching to the audio version it then notified me I had double posted. Twice.
After all that my post never saw the light of day. So either it was a posting malfunction or the subject of La Nina and increased mid-latitude shear is too controversial for this site.
The former is annoying. The latter would be troubling.
Comment by Wayne Davidson — 26 May 2011 @ 9:55 AM
Brilliant…simply brilliant.
Always a good chuckle available here.
Chairman US House Foreign Affairs committee: “old trees cause global warming; let’s subsidize clearing rainforests”: http://politi.co/TreeGW
Climate modeling has to be redone since we in the USA now have repealed the Second Law of Thermodynamics. I am not sure if it has been made official in the UK, but Dr. David MacKay is trying to get this in place.
Look at the fueleconomy.gov site and go to the electric
vehicle tab. You will eventually discover that a gallon of gasoline represents 33.7 kWhr of electric energy.
A gallon of gasoline has never produced more than about 11
kWhr of electric energy.
The only equivalence is the amount of heat that can be produced
by these two forms of energy.
MPGe as thus defined by our EPA is an outrageous lie. And it
will trick people into buying electric vehicles that have no special merit in limiting CO2. The trick will be ok as long as coal remains cheap and we think it is a good thing to shift from oil to coal.
The implications for climate modeling are more complex, but the same processes of conversion of heat to other forms of energy are fundamental to atmospheric dynamics.
There’s a former meteorologist called Brian Sussman sitting in for Mark Levine tonight. He begged for anyone to call in and claim a connection between this years severe weather and Global Warming. Or anything about AGW. No matter how many PhD’s they had. He’s apparently written a AGW denier book.
I’d love to hear someone from here take him on. He’s on until 9 PM EDT. I have no PhD’s in my title.
Jim. I think that is a misrepresentation of the argument. The question relates to how much renewable energy do you need to power a nations car fleet. If you did the calculation on basis that cars use x gallons of fuel, and 1 gallon = x J of energy then you would get the wrong answer, because an electric car goes further on say 1kWh then you would get by 1kWh of petrol by that naive calculation. MacKay does indeed take 2nd law into account though in a round about way.
Re 316 Jim Bullis – they don’t make that kind of mistake in climate modelling. (except maybe G&T and that one other person, etc.)
Use of language:
Patrick 027, I’m with you more or less on your #306 with possibly one exception. You said, “…. ~= 0.14 photons absorbed per molecule per second (and a similar number of emissions).” That little parenthetical phrase is opposite from what we have been discussing. However, if you are assuming no collisional transfer of energy, then you are correct — but this changes the crux of the discourse up to now.
Re 318 Phil Scadden – the concern is that it takes x J of fuel (or nuclear heat) to produce 1 J of electricity (1 Je) (although efficiencies vary, they tend to cluster in the U.S.), so when electricity is being produced by fuel, the fuel efficiency of an electric car that gets z mpJe is not z mpJ(fuel) but rather z*x mpJ(fuel).
On the other hand, things like wind, solar, and hydroelectric produce greater amounts of fuel-equivalent energy than the energy they actually produce, for a standard x.
But if non-fuel energy resources come to dominate to a point where there is significant value in using electricity to produce fuel, the fuel-equivalent of 1 Je would tend to be less than 1, not greater than 1. Yet due to fluctuations/cycles in supplies and demands and regional variations, one could concieve some conversion in both directions occuring.
Of course, if a plug-in EV car doesn’t actually get better fuel economy than a HEV or regular ICE car (presumably a good choice in either EV or HEV could do better than a regular ICE car because of idling and breaking losses, and also transmission, depending on car design), it could still be a good choice overall if the additional cost of the EV is more than offset by energy and maintenance cost reductions – except for the externalities such as climate change. But as the cost of oil goes up, it would be easier (depending on other costs) to add the additional necessary electricity production using clean energy such as solar power, perhaps with savings left over to help replace coal with yet more solar, etc (Of course, depending on prices, this may still require some government policies (some of which should be in place regardless of how transportation technology evolves), but those policies would then be less costly in the short term). Note that there is a benifit even if the solar power is not actually available when the batteries are charging (although wind power can certainly be available at night, and people with cars parked at work (or who work at home) may charge cars up during the day; there’s also the idea of having ‘gas stations’ that swap discharged batteries for recharged batteries, thus allowing greater charging time flexibility. And eventually some storage facilities may come online to help bring renewable energy from time of supply to time of use – but of course other things can help there (adjusting hydroelectric output, transmission on the scale of weather variations) – of course adding nuclear energy would also help charge cars cleanly if the nuclear is relatively clean, which I won’t go into).
correction: z/x mpJ(fuel), not z*x mpJ(fuel).
And of course x can be reduced with different power plants, and effectively reduced if the power plant’s heat output is utilized (cogeneration). PS wouldn’t it be cool if residential/commercial furnaces could be made with TPV cells, so that winter heating and electrical needs could be met by burning fuel (TPV output could go into the same inverter that rooftop solar cells use – and solar roofs can be hybrid with waste heat from PV cells going to (pre)heat water). Alternatively or additionally, fuel (of the right type) could run through fuel cells with waste heat being used. Of course, it can be more efficient to burn fuel at a power plant (or oxidize in a fuel cell) and use the electricity to run a heat pump to provide low-temperature heat, provided the COP of the heat pump is greater than the fuel-to-electricity ratio of the power plant – or even if not, if the power plant’s heat is also used.
Anyone care to comment (or perhaps make up a poem) about ‘Glaciers: art and history, science and uncertainty’? Somewhat of a stretch I fear…
Re 321 Rod B Patrick 027, I’m with you more or less on your #306 with possibly one exception. You said, “…. ~= 0.14 photons absorbed per molecule per second (and a similar number of emissions).” That little parenthetical phrase is opposite from what we have been discussing.
Temperature does vary with height of course, but by less than an order of magnitude (until the thermosphere). Of course, blackbody radiation corresponding to those temperatures will vary more – with the fourth power for the whole band, and approximately that near the peak wavelength (less at longer wavelengths, more at shorter wavelengths). On the other hand, the intensity where the optical thickness is small will not match the local Planck function (ie for the local temperature) – hence the radiation is not isotropic, with net fluxes in some directions, and also, the downward and upward fluxes each will vary more slowly with height; relatively warmer layers will tend to emit more than they absorb and relatively cool layers will tend to do the opposite. While at larger optical thicknesses, more of the photons will be emitted or absorbed from relatively nearby, thus emitted generally at more similar temperatures to where they are absorbed.
I was using a crude first-approximation that absorption and emission were similar, because as you can see, I wasn’t going for great precision (it was a rush job, but one could repeat the method more accurately).
But interestingly, with the central part of the CO2 band being saturated or nearly so for tropopause-level radiative forcing, and radiative forcing in general except getting near TOA (relative to optical thickness), net fluxes except near TOA approach zero because of the large optical thicknesses over distances short enough to be nearly isothermal (fluxes in opposite directions converge to the same value). Also interestingly, while it is generally away from the center that the greatest radiative forcing changes occur, much or most of the total photons emitted and absorbed are closer to the center.
Thus the 450 photon interactions per molecule per second derived from using the spectrum of optical thickness could have similar contributions from absorption and emission – significant (for weather and climate) net radiant cooling or heating would come from the differences which seem small in proportion to the total.
PS clarification/correction for earlier reference to water vapor overlap: While overlaps reduce the radiative forcing for a given change, they would only affect the rate of absorption per molecule by their effect on the incident fluxes, and in that they could tend to make the rate of absorption and emission more similar by increasing the optical thickness.
Of course, the 450 photon absorptions+emissions per molecule per second figure was for a representative temperature (near Te for the Earth). Also, there are variations in line strength with height. Line broadenning also changes – however, my understanding is that the spectrum-integrated optical thickness attributed to each line is unaffected by line broadenning, and that broadenning occurs on sufficiently small wavelength scales that the Planck function could be approximated as constant over the range of relevant wavelengths with significant optical thickness for an individual line; thus, this should have little effect on the rate of absorption and emission, except perhaps by openning up more partially-transparent gaps so that absorption depends more on non-local temperatures (But I haven’t actually don the math on that).
And of course, with all the rough approximations, especially in the spectrum of optical thickness, I wouldn’t be surprised if the 450 value is off by an order of magnitude. I might go through that again later.
Anyway, (***quickly and roughly estimated*** from a graph (CRC Handbook of Chemistry and Physics) with low resolution – collision frequency in logarithmic scale and height in 100s of km)
altitudes where collision frequency is equal to
450 per s: ~> 100 km
1000 per s: ~ 100 km
10^4 per s: ~ 80 or 90 km
10^5 per s: ~ 70 or 80 km
10^6 per s: ~ 60 km
10^7 per s: ~ 40 km
10^8 per s: ~ 20 – 30 km
~ 3E9 per s: ~ surface
the 450 photon interactions per molecule per second is at least broadly consistent with this as I have read that LTE is approximately maintained at least through the top of the stratosphere (which is at or around ~ 50 km).
I should note that the CO2 band has the greatest optical thickness in the LW portion of the spectrum going up through the stratosphere; stratospheric water vapor provides some significant optical thickness but is generally partially transparent even at the peaks – which doesn’t itself pertain to whether water vapor’s optical properties would leave it at LTE, but water vapor is a very small fraction of the atmosphere up there; the vast majority of collisions involving CO2 would be with N2 and O2 (even more so than lower in the atmosphere), so perhaps CO2 itself might still be in LTE even if/where H2O is not (?)(or vice versa?)(and as for ozone, …).
Patrick 027, I conceptually agree with your #325 but it is in a different context than what we have been discussing ala Sphaerica (Bob)’s question — whatever it was! However I’m very hesitant to explain my point here as it has created a tempest before and very few (none?) are interested in my resurrecting it. But, having no fear (or maybe smarts??) — for the record:
Greenhouse gas radiation transfer at the molecular level is NOT a Planck function. The Planck function and other related formulations have been found, as a construct, to match fairly close to observed physics, at least on a macro system level, if the proper assumptions and constraints are chosen. Since the physics and mathematics of Planck et al, as complex and difficult as they are, are majorly easier and better known than the physics and mathematics at the molecular level, they are what is used for the most part But they are not sufficient nor accurate at the molecular level. One example: when CO2 relaxes its vibration energy by emitting a photon, that photon radiates about 1.325×10^-20 joules at near 14.8 microns wavelength; this does not vary one iota if the gas amb_ient temperature (the sole independent factor in Stefan’s law) varies from 100K to 1000K, or any other temp one chooses.
The basic greenhouse warming is analyzed using Planck radiation functions and other physics working successively through slabs of atmospheric layers. It comes out quite well. But the majority of actual GHG emission and absorption follows a different physics. [It is partially dependent on temperature as the degree of absorption depends on the intensity of the radiation field which depends on temp — but the temp of the earth surface, not the absorbing gas; the degree of emission is indirectly dependent on the temperature of the gas per the Boltzmann factor mentioned earlier.] In fact there is an adamant difference of opinion among scientists whether any gas can emit or absorb ala Planck at all — (mentioned only as an aside — no way will I open two worm cans in the same post!) Even though, to repeat the point, if one assumes it does for analysis purposes it can come out pretty good.
RE this discussion: If one uses Planck function for analysis then emission and absorption will be together in the same ballpark as you say. But if one looks at it at the molecular level, at, say, very low altitudes, CO2 absorption will be magnitudes greater than emission.
Re Rod B. – before getting to that latest comment, first, corrections/clarifications for my 306, 325:
First, there are generally upward and downward fluxes, so I should have doubled the photon interactions per molecule per second (PIPMPS)(using the end result, 450, this gives 900). This is exactly true for emission (isotropic optical properties of randomly-oriented gas molecules); for absorption it will not be true and getting sufficiently near TOA, the downward flux approaches 0 (for the extreme wings of the band, absent other sources of opacity like clouds or water vapor, the surface would be sufficiently close to TOA in this context; for the center of the band, and especially for the centers of the lines near the center of the band, with sufficient CO2 (such as the Earth has had over geologic history), one must get to a higher altitude before the upward and downward fluxes are even much different. Thus, PIPMPS may go from ~ 900 down to ~ 680 (rounded from 1.5 * 450 – and I am of course treating the part from absorption approximately as it can and generally does depend on non-local temperature) going toward TOA.
Then, there is the factor, mentioned earlier but set aside, that photons are not all travelling vertically; generally they are travelling in all directions (a sphere of solid angle, 4*pi steradians) or at least half that (the upward flux at TOA). Intensity is the flux per unit solid angle in a particular direction. Integrating an isotropic (constant over direction) intensity over a hemisphere gives 2*pi steradians * intensity, but the flux per unit area is half that, because 2*pi steradians * intensity is a sum over directions of the fluxes per unit areas in those directions, but for the flux per unit area facing some direction, the projection of that area varies with angle over a hemisphere (it is proportional to the cosine of the angle from vertical for a horizontal area).
But for an isotropic optical properties, a unit 1 optical thickness (a photon’s mean free path) spans less vertical distance for directions closer to horizontal, which means a greater number of emissions and absorptions will occur spanning the same vertical distance. I did an integration to find, for isotropic radiation, the average vertical distance, for all the photons in an upward or downward flux (but not both together – that average would be zero) that a photon travels as a fraction of what it would travel going vertically – I think the answer was 2/3 but I’ll have to check to be sure. But that isn’t the needed value here – we’d need the average of the inverse of the vertical distance. Fortunately, there is a more direct way to find the answer: the optical thickness per unit distance is proportional to the density of molecules times each molecule’s cross-section in that direction. A molecule, on average, acts like a blackbody (at a given frequency, etc.) with that area facing that direction. For isotropic optical properties, the molecule has that same effective area facing all directions, and thus acts like a spherical blackbody with a surface area four times the cross section; Thus the flux emitted from a sphere is 4*pi times the intensity in any direction, which is twice the value of the upward and downward fluxes per unit area through a flat horizontal surface for an isotropic intensity. Thus multiply 900 to 680 by 2 to get 1800 to 1360 PIPMPS. Notice this also means that the fraction of isotropic radiation transmitted through a very thin horizontal layer with isotropic optical properties initially drops twice as fast from 1 as does the fraction of vertical intensity, as the layer is thickenned from initially zero.
Unless too close to TOA, provided the amount of CO2 is sufficient (as it has been on Earth) we can approximate the radiation as isotropic for determining PIPMPS from absorption because so many of the photons are near the center of the band and will be travelling over nearly isothermal distances. Even farther out from the center of the band, the anisotropy of the upward and downward hemispheres may sometimes partially cancel each other in total effect. So the local temperature might be used to get a better, perhaps good measure of PIPMPS, rather than using some representative flux per unit area as I did above.
On that note, CORRECTION: at the peak intensity per-unit-wavelength, the Planck function is proportional to the 5th power of temperature, not the fourth. It is proportional to T^3 at the peak per uni frequency or energy, and T^4 at the peak per unit logarithm of either.
As far as I know, there are no significant number of “sea level rise migrants” anywhere in the world. Am I correct in thinking this?
Re 327 Rod B
Greenhouse gas radiation transfer at the molecular level is NOT a Planck function. The Planck function and other related formulations have been found, as a construct, to match fairly close to observed physics, at least on a macro system level, if the proper assumptions and constraints are chosen.
My understanding is that the physical concept that originally allowed Planck to solve the ultraviolet catastrophe was itself flawed in some way but still led to the right equation – anyway quantum mechanics did eventually succeed.
Since the physics and mathematics of Planck et al, as complex and difficult as they are, are majorly easier and better known than the physics and mathematics at the molecular level, they are what is used for the most part But they are not sufficient nor accurate at the molecular level. … Even though, to repeat the point, if one assumes it does for analysis purposes it can come out pretty good.
I think that may be similar to pointing out that the physics of heat transfer through a slab on the molecular/crystal lattice/electronic level is not the same as flux per unit area = thermal conductivity * temperature gradient. In bulk it still adds up to the same effect; the thermal conductivity is determined by the microphysics and may itself be dependent on temperature and on the quantum scale you can have other complexities, but it’s a generally useful formula.
Or that scattering by cloud droplets requires Mie theory, spherical harmonics etc, but you can still assign a scattering cross section and a distribution of scattered rays as a function of variables, which might then be calculated so that another person doesn’t need to go through Mie theory.
One example: when CO2 relaxes its vibration energy by emitting a photon, that photon radiates about 1.325×10^-20 joules at near 14.8 microns wavelength; this does not vary one iota if the gas amb_ient temperature (the sole independent factor in Stefan’s law) varies from 100K to 1000K, or any other temp one chooses.
There are actually many lines clustered around 15 microns, the physics giving rise to that is not something I’m as familiar with but I’d guess it’s the effect of combined rotation-vibration changes.
Temperature-dependent doppler broadenning of the lines changes the energy of photons in a stationary (relative to bulk gas) reference frame via red-shift or blue-shift due to motions of molecules. Pressure broadenning – I’ll have to go look that up to see how that works; I’d guess distortion of molecules or their electromagnetic fields by other molecules changes the available energy transitions a little(?).
The basic greenhouse warming is analyzed using Planck radiation functions and other physics working successively through slabs of atmospheric layers. It comes out quite well. But the majority of actual GHG emission and absorption follows a different physics. [It is partially dependent on temperature as the degree of absorption depends on the intensity of the radiation field which depends on temp — but the temp of the earth surface, not the absorbing gas; the degree of emission is indirectly dependent on the temperature of the gas per the Boltzmann factor mentioned earlier.]
See above – macroscopic physics somehow arises from microscopic physics. Sometimes complexity arises from simplicity and sometimes the opposite happens. In order for the second law of thermodynamics to hold, if a material is at LTE than emissivity must equal absorptivity. Of course they can be temperature dependent themselves, but they must be equal (in the simplified case of a single available transition, based on a naive approach, absorptivity should be proportional to the fraction of the population in the ground state and emissivity should be proportional to the fraction of the population in the excited state. Something else in the physics must then compensate such an effect to hold them equal – and I don’t know what that is (I’m betting someone out there does); I infer it is there because nobody has yet succeeded in destroying entropy and building a perpetual motion machine). If emmissivity were not equal to absorptivity for a Planck function that applies to all materials, then the radiation that would be in equilibrium with one material would not be in equilibrium with another at the same temperature, and radiant heat would spontaneously flow to higher temperatures for some material combinations.
RE this discussion: If one uses Planck function for analysis then emission and absorption will be together in the same ballpark as you say.
Just to be clear, in general: only because I was using a very large ballpark and/or for sufficient amounts of CO2 not too close to TOA, a large share of the photons emitted and absorbed per molecule are at the more opaque wavelengths where temperature variations on the larger scale would have little effect.
But if one looks at it at the molecular level, at, say, very low altitudes, CO2 absorption will be magnitudes greater than emission.
No, that shouldn’t be the case. Consider that the upward flux only changes gradually up from the surface, and the downward flux also varies gradually from TOA to the surface – except where optical thickness is very large, in which case it should still be gradual relative to optical thickness (the temperature difference between the surface and the air would only lead to a relatively sharp change in the upward and downward fluxes when opacity is high enough that the surface temperature’s effect on the flux a short distance above the surface is small, and in this case, the change would be gradual relative to optical thickness.
Because pure radiative equilibrium would (in the global annual average) have a superadiabatic lapse rate from the surface up to some height, convection tends to cool the surface and heat the troposphere; this means the surface experiences net radiant heating and the troposphere experiences net radiant cooling. With some shortwave (solar) heating, the net LW cooling will be greater – both the surface and troposphere tend to experince net LW cooling, as does in particular the upper stratosphere. Attribution of that LW cooling to different gases and clouds requires farther discussion…
Furthermore, net cooling or heating can be from a difference in emission and absorption rates per molecule that are small relative to the totals, especially at optically thick parts of the spectrum (where, except near TOA, net LW radiant fluxes and net LW radiant heating and cooling get small).
fourth-to-last paragraph should have been italicized:
But if one looks at it at the molecular level, at, say, very low altitudes, CO2 absorption will be magnitudes greater than emission.
319 Patrick 027
I did not think for a minute that serious climate modelers would have made that mistake.
I was just trying to get their attention.
322 and 323 Patrick027
You explain correctly why the EPA rule for MPGE is simply wrong.
You strive to find reasons why an EV could still make sense, but the rule is still wrong.
The EPA simply legislates by administrative law that your x equals one. Dr. David MacKay asserts this also, though he also gives a curious discussion that says that he knows it is wrong to do so. (See page 17 of ‘Renewable Energy – without hot air’.
Both cases lead to misguided encouragement of the EV as a climate solution. This is a serious mistake.
Attorney General Cuccinelli’s father gave a speech in 2010 called “Using Social Media to Improve Sales & Customer Satisfaction.”
The elder Cuccinelli works for Quest Fore.
This speech before a conference organized by the American Public Gas Association is some evidence that his current company is an advocate for gas interests.
http://www.apga.org/i4a/headlines/headlinedetails.cfm?id=405&archive=1
Here is what it says about the elder Ken Cuccinelli on the Quest Fore site:
When he joined Quest Fore in 1999 as chairman, Ken brought with him a wealth of strategic marketing experience. A former head of marketing for a Fortune 500 company (CNG Pittsburgh), Ken was named 1994 Gas Marketing Executive of the Year and also served as chief operating officer of CNG Energy prior to joining Quest Fore. In addition to his chairman duties, he also serves as president of International Business Ventures LLC, a worldwide consulting and prospect development company that is active in Europe and Latin America. In 2005, Ken earned his ABC (Business Communications Accreditation) from the International Association of Business Communicators.
http://www.questfore.com/our-people
322 Patrick027
I notice though that you did not adequately convey the implication of ‘x’.
The fact is that for the USA, x = 3 for most situations, given that coal is the basis of marginal response for the new loads that would be the result of EVs. This is the overpowering reason why the EV fails in comparison with good hybrids.
Everything comes up wrong if the pretense continues that one Joule of heat can produce one Joule of electricity. This seems to be policy in both USA and UK.
Patrick 027, I can’t find anything to disagree with your #328 (though I have to dig deeper ;-) ), including the molecule’s emitting kind of like a blackbody (albeit arbitrarily constrained with specific assumed parameters) — part of the rational why Planck function etc. works closely in the analysis of what is not technically blackbody radiation.
It still avoids the factor of collisional transfer which accounts for low altitude absorption greatly exceeding emission. Maybe we’re past that point…
318 Phil Scadden,
When it comes to renewable energy the MPGE rating has no meaning at all. Nobody has any idea what an equivalent to a gallon is for Mother Nature’s heat engine.
Of course, when renewable energy exists in adequate amounts that there is a reserve capacity to respond to new loads, the problem is only to stay within that reserve capacity.
ps turns out there is more I have to get to……..
322 Patrick027
And the reason the x = 3 is important is that including it correctly changes the MPGE rating for the Nissan Leaf from 99 MPGE to 33 MPGE. That is a profound implication on our CO2 situation.
Re my:
1. photons are ‘attracted’ to higher n (real component of index of refraction) by bending toward n, with intensity, absent other effects, being proportional to n^2; in keeping with second law of thermodynamics while allowing this and the related total internal refraction, the Planck function is actually proportional to n^2. n presumably would change as air or any gas is made more dense. Thus rates of emission per molecule would be affected by density. Perhaps viewing this on the time scale of the emission and absorption process would help. Often people think of quantum energy transitions as being instantaneous, but they are not – the Schrodinger equation can be solved in a time-independent way to yield the energy levels/states that can be occupied indefinitely, but a time-dependent Schrodinger equation can describe the process of transition, where the system can be between such states so long as it is changing (at the necessary rate, I presume).
So (speculation on my part) when a molecule (or electron) starts to change states, it perhaps starts to emit or absorb a photon; the electromagnetic field generated by the change might then interact with the prexisting photon (for absorption) or with the bit of field that is generated by the next part of the change – ie interactions may be two-way between the photon and electron/molecule, so that perhaps when a photon is absorbed, a photon 180 degrees out of phase is emitted that cancels out the original photon, which might be how the photon is ‘ended’ – or maybe an emitted photon starts to stimulate its own emission – or alternatively, the emitted photon might start to be absorbed or the absorbed photon might start to be emitted, canceling the interaction. (?) And while the photon which may or may not go on to exist as a photon is present it would interact with other molecules on the wavelength scale … (?) thus allowing something like the index of refraction to affect the process (?)
2. emissivity shouldn’t necessarily be proportional to the population in the excited state – emission itself could be expected to be proportional to the population in the excited state.
More generally:
A. case of systems which can be excited or not independent of each other:
(note emissivity and absorptivity are proportional to cross sections)
emission/unit material = Planck function * emission cross section/unit material = ge * fraction of population in excited state
absorption cross section/unit material = ga * fraction of population in ground state
where ge and ga, expected to be functions of at least temperature and the energy difference between states, allow the cross sections to be equal.
B:
In the case where the same set of available states are shared (like for electrons in a solid or atom):
emission/unit material = Planck function * emission cross section/unit material = ge * fraction of excited states that are occupied (have electrons) * fraction of ground states that are not filled (have holes)
absorption cross section/unit material = ga * fraction of excited states that are not filled (have holes) * fraction of ground states that are occupied (have electrons).
The APGA says that it improves the regulatory environment for public gas companies.
According to the APGA:
“[The American Public Gas Association (APGA)] is the only nonprofit trade organization representing America’s publicly owned natural gas local distribution companies (LDCs). APGA represents the interests of public gas before Congress, federal agencies and other energy-related stakeholders by developing regulatory and legislative policies that further the goals of our members. In addition, APGA organizes meetings, seminars, and workshops with a specific goal to improve the reliability, operational efficiency, and regulatory environment in which public gas systems operate.
Through APGA, public gas systems work together to stay reliably informed about new developments in safety, public policy, operations, technology, and the marketplace that could affect the communities and consumers they serve.”
http://www.apga.org/i4a/pages/index.cfm?pageid=3277
The elder Cuccinelli seems very close to the APGA. He is described as their “partner” in some projects.
The document below discusses proposed legislation for a cap on greenhouse gasses and “issue mangagement.”
The APGA noted:
http://www.apga.org/files/public/weekly%20updates/Weekly%20Update%20-%20May%2028%202009.pdf
With Market Metrics, APGA and Quest Fore can help you research topics such as issue
management; market needs research, competitive analysis, product awareness and
general issue identification. To survey your current and potential customers with the most efficient and cost effective surveying technology available, get in touch with Quest Fore CEO Ken Cuccinelli at 412‐697‐4780 or kcuccinelli@questfore.com.
This APGA report says that “a federal scientist” believes that the Bering Sea has huge methane hydrates and that there should be a Manhattan Project to develop methane hydrates.
There is a map that shows where the hydrates are.
http://www.ilpea.org/InformationalPresentations/EvolvingLandscape_Kalisch.pdf
It’s a long document–search “methane.”
They are also very concerned about the topic of climate change.
Re 336 Rod B It still avoids the factor of collisional transfer which accounts for low altitude absorption greatly exceeding emission. Maybe we’re past that point…
No, there’s no particular reason why low altitude absorption should generally greatly exceed low altitude emission, and I’ve never heard that it does, and what I know suggests it does not in general. CO2 generally has net LW cooling except maybe near the tropopause where it may have some small net LW warming (notes, and p. 71 of Hartmann, “Global Physical Climatology”)
… also http://www.atmosphere.mpg.de/enid/20c.html (net LW cooling)
Patrick 027, re your # 330: The difference from Planck radiation is not from the minute physical differences like in your lattice example. Planck radiation stems directly and solely from temperature of the radiator; CO2 emission does not.
Your example of varying emission wavelengths or multiple emission lines (vibration and rotation) is accurate but orthogonal to the point. Substitute any CO2 emission line(s) you wish into my statement and my assertion still holds. It’s true that Doppler shift depends on temperature but nowhere near the factor in Planck. Doppler shift doesn’t amount to a hill of beans; on a good day Doppler will shift a 15 micron signal by less than 0.00008 microns.
The LTE is accurately stated but much care has to be taken when analyzing with the idealistic construct of LTE. For instance the system we are talking about is not strictly in LTE: the temperature of the earth’s surface which is providing the radiation is not the same as that of the atmosphere. Even within the gas there is a theoretical anomaly. A mole of atmosphere at 250K will contain billions of molecules, assuming it could be measured, which it can’t, at different temperatures.
Ignoring collisions, absorption will equal emission over a time period, though they are not driven by the same forces. Emission depends somewhat on am_bient temp and not at all on the radiation field; absorption depends mostly on the intensity of the radiation field and very little on temp. Again, with collisions absorption can greatly exceed emissions but there is no violation of the 2nd Law. However, I might be misleading. “Can” is the key word: depending on the circumstances and environment, including the collision factor absorption can also exceed emission by a little, be about equal, or even be less. This is more in agreement I think with your detailed analysis (which I appreciate).
310 JiminMpls: “BTW, electricity rates are FAR lower in North Dakota than in Illinois. ND has no nuclear power.”
http://www.eia.doe.gov/cneaf/electricity/epm/table5_6_a.html
North Dakota 6.92
THAT is FAR lower than 7.5 which I am paying?
As long as the Planck function came up I figured it might be nice to post something that I had worked on awhile ago – for future reference (a lot of this isn’t news to anyone but I put in some nice info about graphically manipulating the Planck function):
FUN WITH THE PLANCK FUNCTION PART I
For real component of index of refraction n = 1 (and including photons of all polarizations):
Where the blackbody flux per unit area, integrated over the whole spectrum
= π * Bint(T) = σ * T^4
where
Bint(T) is the blackbody intensity integrated over the whole spectrum
σ = 2 * π^5 * kB^4 /(15 * c^2 * h^3)
and
Where c, h, and kB, and σ are:
(Where there are two values, the second value is from a physics textbook (or calculated from physics textbook values), and the first value is from Wikipedia ( http://en.wikipedia.org/wiki/Boltzmann's_constant , http://en.wikipedia.org/wiki/Avogadro_constant , http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_constant ):
c = 2.99792458 E+8 m/s
h = 6.62606896 E-34 J*s
h = 6.626075 E-34 J*s
kB = 1.3806504 E-23 J/K
kB = 1.380658 E-23 J/K
σ = 5.670400 E-8 W/(m2 K4)
σ = 5.670511 E-8 W/(m2 K4)
—————————
Spectral blackbody intensity (at n = 1) is the absolute value of the derivative of Bint(T, ν or λ) over the spectrum if Bint(T, ν or λ) is a running total (the integration over the spectrum up to or down to a frequency or wavelength from either zero or infinity):
ν = frequency
λ = wavelength (in this context it is the wavelength in a vacuum)
Spectral blackbody intensity = Planck function B:
in terms of per unit interval of frequency: Bν(T,ν)
in terms of per unit interval of wavelength: Bλ(T,λ)
Bλ(T,λ) = |d[Bint(T,λ)]/dλ|
= ( 2*h*c^2 / λ^5 ) / ( exp[h*c/(λ*kB*T)] – 1 )
Bν(T,ν) = |d[Bint(T,ν)]/dν|
= ( 2*h*ν^3 / c^2 ) / ( exp[h*ν/(kB*T)] – 1 )
A necessary relationship between the two values:
If |dν| and |dλ| are the same portion of the spectrum, then
Bλ(T,λ) * |dλ| = Bν(T,ν) * |dν|
The relationship between |dν| and |dλ| can be found by finding |dν/dλ|:
c = λ * ν
ν = c/λ
|dν|
= c / λ^2 * |dλ|
= ν/λ * |dλ|
= ν^2 / c * |dλ|
Thus:
Bλ(T,λ) * |dλ| = Bν(T,ν) * c / λ^2 * |dλ|
dividing by |dλ| :
Bλ(T,λ) = Bν(T,ν) * c / λ^2 = Bν(T,ν) * ν^2 / c
—————
The λ of maximum Bλ(T,λ) is equal to
(2897 microns/K )/ T
(Wien’s displacement law, from class notes but can be found elsewhere.)
The λ of maximum Bλ(T,λ) is 10 microns at T = 289.7 K.
______________________________________
EXAMINING THE SHAPE OF THE PLANCK FUNCTION (AND HOW TO GRAPHICALLY MANIPULATE IT IN RESPONSE TO CHANGES IN T):
Look at B again:
Bλ(T,λ) = |d[Bint(T,λ)]/dλ|
= ( 2*h*c^2 / λ^5 ) / ( exp[h*c/(λ*kB*T)] – 1 )
Bν(T,ν) = |d[Bint(T,ν)]/dν|
= ( 2*h*ν^3 / c^2 ) / ( exp[h*ν/(kB*T)] – 1 )
Note that the denominators in both are equal, because ν = c/λ:
exp[h*c/(λ*kB*T)] – 1 = exp[h*ν/(kB*T)] – 1
These expressions stay constant as T is varied from T0 if λ and ν vary from λ0 and ν0 such that:
λ*T = λ0*T0
ν/T = ν0/T0
Letting ν/T = c/(λ*T) = V#,
Bλ(T,λ)
= ( 2*h*c^2 / λ^5 ) / ( exp[V#*h/kB] – 1 )
= ( 2*h*c^2*(c^3/c^3) / λ^5 ) / ( exp[V#*h/kB] – 1 )
=
T^5 * V#^5 * ( 2*h / c^3 ) / ( exp[V#*h/kB] – 1 )
Bν(T,ν)
= ( 2*h*ν^3 / c^2 ) / ( exp[V#*h/kB] – 1 )
=
T^3 * V#^3 * ( 2*h / c^2 ) / ( exp[V#*h/kB] – 1 )
For both Bλ(T,λ) and Bν(T,ν), the value at any V# is only proportional to a power (3 and 5, respectively) of T, and the shape of the function of V# divided by that power of T produces a temperature independent shape; thus, for any two V# values, the value of the function (Bλ or Bν) at one V# is always the same fraction of the value at the other V#.
Note that
ν = T*V#
λ = c/(T*V#)
and
|dν/dV#| = T
|dλ/dV#| = c/T * 1/V#^2
So as T changes, Bν and Bλ at constant V# stay proportional to T^3 and T^5, respectively, while otherwise not ‘shifting or changing width’ over V#, but with V# and |dV#| shifting relative to ν and λ, and |dν| and |dλ|.
Thus, as T changes (from T0 to T1), the functions Bν graphed over ν and Bλ graphed over λ can be mapped from what they are at one T to what they are at another T by:
Stretching the graph of Bν or Bλ, over ν or λ, in proportion to T^3 or T^5, respectively,
For Bλ, compress the width over λ so that the width is inversely proportional to T; Don’t shift the λ=0 position, so that at each V# value, the λ value of the point on the graph shrinks by the same factor as T1/T0 (or enlarges by the recip-rocal of that ratio).
For Bν, widen the graph over ν so that the width is proportional to T; Don’t shift the ν=0 position, so that at each V# value, the ν value of a point on the graph grows by the same factor as T1/T0 (or shrinks by the recip-rocal of that ratio).
Notice that the area under the graph, integrated over the whole spectrum, is proportional to:
height * width
=
T^5 * 1/T = T^4 for Bλ
T^3 * T = T^4 for Bν
Thus it can be shown without actually integrating the functions that Bint(T) is proportional to T^4.
Interestingly, since (for constant T), the change in Bν or Bλ over ν or λ is zero at the peak ν or peak λ (where Bν or Bλ is maximum), for infinitesimal changes in T, the change in Bν or Bλ at the peak ν or peak λ is proportional to the change in T^3 or T^5 whether following the peak as it shifts or staying at the same ν or λ, respectively. Thus a 1 % increase in T results in approximately 3 % and 5 % increases in Bν and Bλ at peak ν and peak λ, respectively.
The peak ν is proportional to T and the peak λ is inversely proportional to T.
Patrick 027, I don’t think I liked the cross section factor in your #340. Molecular cross section has very little effect on spontaneous emission, though some effect on absorption. But I had a difficult time following this post and might be misinterpreting what you said.
re #343: If the LW emission equals absorption in CO2 you would not have any atmospheric heating and have only surface warming by only that portion of the downward directed emission (nominally half of total emission) that makes it back to the surface. (Though I admit to not having gone through multiple mirror effect of the up/down emission now joined with up/down absorption.)
342 Snapple: How do you develop methane hydrates without triggering a huge “methane gun”? They are apparently going to drill through the hydrate [quasi] stability zone to the free gas zone. Would that lower the pressure so that quasi-stable hydrate would evaporate from the bottom due to geothermal heat?
I would like to read RC’s take on that one. I remember somebody saying that getting heat out of Yellowstone would destabilize the volcano. I don’t remember the reference. Neither permafrost nor “stable” hydrate is solid impermeable rock. Both are easily meltable. Count me out as labor on that one.
Are there any “sea level rise migrants” anywhere in the world today?