Guest Post by Steven Goddard


We have all seen lots of pictures of the Eyjafjallajokull eruption now, with steam and ash billowing up in the air. The eruption started one month ago, and as the Guardian reports, The eruption of the Eyjafjallajokull volcano is unlikely to have any significant impact on climate but has caused a small fall in carbon emissions, experts say.
The Guardian editors seem to have forgotten that the volcano itself is spewing massive amounts of CO2 in the atmosphere. Perhaps their kinship with Plane Stupid is having an impact? Plane Stupid’s goal is to stop plane traffic in the UK, and they must be thrilled by the flight ban and the damage to the economy.
Added:
Volcano CO2 budget (CO2 is emitted independent of ash) ~200,000 tons per day X 30 days of eruption = 6,000,000 tons of CO2.
Plane CO2 Budget – assumes half of EU planes haven’t flown for the past six days 340,000 EU tons per day X 0.5 EU shutdown X 6 days = ~1,000,000 tons of savings.
People using alternative transportation (as Anthony and the BBC pointed out) as a replacement for aircraft – cars, trains, battleships , etc. ~1,000,000 tons of extra CO2 Is a battleship more “green” than a jumbo jet?
The total gain is 6,000,000 – 1,000,000 + 1,000,000 = 6,000,000 tons of excess CO2 from the volcano. The temporary aircraft shutdown has little or no net impact on CO2 emissions, but the volcano has a large impact.
Video and reader poll follow.
Below is a video chronology of the glacier and volcano, giving a feel of the events of the past month. First video shows what the glacier looked like prior to the eruption.
The next video shows the first night of the eruption – March 21. Note the similarity to Hawaiian volcanoes – lava fountains and little steam or ash.
By March 24, some steam and ash is starting to appear as glacial meltwater begins to mix with the magma.
By April 14, flash flooding from glacial melt began to pour down the side of the glacier.
The flooding was widespread and devastating downstream.
By April 17, the eruption was primarily steam, CO2 and ash.
Should climate modelers start differentiating between man made CO2 and “organic” natural CO2?
Reader Poll :
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
Ferdinand Engelbeen (11:27:06) :
“…Plant photosynthetic biochemistry is remarkably specific preferring to fix 12C over 13C by a large margin. Thus during photosynthesis d13C rises due to the preferential abstraction of 12C…. Note also that Respiration is Temperature dependent roughly doubling with a ten degree increase in temperature whereas photosynthesis is by and large not temperature dependent.
The figure you quote for respiration is species dependent and varies by an order of magnitude. It also is observed only for the last few degrees of a particular species growing range. For example, respiration in a C-3 agronomic crop (soybean is my specialty) varies only marginally between ~50 F and ~89 F, but increases greatly from ~89 F to ~92F, where essentially the stomates close and the chloroplasts shut down, resulting in no flux.
Thus, thanks to the oxygen balance it is quite easy to calculate how much CO2 is absorbed by the oceans and how much by biolife (the “partitioning”). See:
http://www.sciencemag.org/cgi/content/abstract/287/5462/2467
and
http://www.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
I’ve never agreed with these papers. Those papers woefully neglect to incorporate ocean biomas in calculations. That would be expected from the educational expertise of the authors.
1 Department of Geoscience, Guyot Hall, Princeton University, Princeton, NJ 08544 USA.
2 National Oceanic and Atmospheric Administration/Climate Monitoring and Diagnostics Laboratory, R/E/CG1, 325 Broadway, Boulder, CO 80303 USA.
3 Institute for Arctic and Alpine Research, and Department of Geological Sciences, University of Colorado, Boulder, CO 80309, USA.
4 Graduate School of Oceanography, University of Rhode Island, South Ferry Road, Narragansett, RI 02882, USA.
5 Division of Atmospheric Research, Commonwealth Scientific and Industrial Research Organization, Mordialloc, Victoria 3195, Australia.
* Present address: Department of Physics and Astronomy, Bowdoin College, 8800 College Station, Brunswick, ME 04011, USA.
Even they admit that!
Calculations of interannual variability in land and ocean uptake are probably confounded by non-zero annual air sea fluxes of O2. The origin of these fluxes is not yet understood.
“”” Sjoerd Schreuder (11:48:23) :
“George E. Smith (10:05:46) :
Just one small nit to pick Steve:-
O=C-O , not O=C=O “””
So Sjoerd, you can join the party above too. Yes I know they are double bonds and the molecule is straight, and they look like my drawing in 3-D, since the four bonds are Tetrahedrally disposed.
Steve, glad someone is bringing some sense to the utterly inane coverage of this in the MSM.
“The eruption of the Eyjafjallajokull volcano is unlikely to have any significant impact on climate but has caused a small fall in carbon emissions, experts say.”
That should read self anointed experts. Prof Alastair Dawson has a somewhat different take in his book “So Foul and Fair a Day”.
http://europe.theoildrum.com/node/6387
“”” stevengoddard (11:40:03) :
George E. Smith (10:29:47) :
Here is an interesting article describing the spectral differences of various CO2 isotopic configurations. I do know that climate models do not differentiate between CO2 isotopes in their radiation budgets.
http://pubs.acs.org/doi/abs/10.1021/ac00284a060 “””
I’m sure you are right on that Steve; if the climate is sensitive to isotopic differences, then we are all in trouble. I certainly never would imply, that the isotopic differences are enough to flip us over some tipping point; just that the various nuclides are certainly distinguishable from spectral differences.
“Ferdinand Engelbeen (11:41:52) :
The reason is that in biological reactions, form and size matters. The chain of reactions which start to catch a molecule of CO2 and transfer that into hydrocarbons is done by large folded molecules (enzymes if you want) where CO2 (in form and electrical load) fits like a key in a lock. 13CO2 is fractionally larger, thus doesn’t fit that nice in the lock, still occasionally is used, but less frequently (at a slower rate? Don’t know exactly) than 12CO2.”
Are you sure that 13CO2 is larger? It goes a bit against my common sense: the size of molecules is determined by their electron cloud, and not by the protons and neutrons directly (indirectly they do as a aresult of the electrical force they apply on the electrons – but there is no difference between 13C and 12C there).
However, 13CO2 certainly is heavier and thus slower to engage and/or react. As there are a lot of steps before CO2 is captured as some hydrocarbon, a small difference in reaction speed in each step might add up to something measurable.
So I don’t doubt your conclusion, I’m just a bit surprised by the reasoning.
Scott (11:33:24) :
You’re discussing atomic spectroscopy here (you even use that term). I think everyone else is discussing IR spectroscopy (requires a change in dipole moment from the stretching/bending of a covalent bond). Thus, the effect of isotopic change is much less (though not zero, as it changes the reduced mass).
The difference in IR lines is even used to determine the 13C/12C ratio:
http://cio.eldoc.ub.rug.nl/root/2005/ApplPhysBCastrillo/
and several others…
Ferdinand Engelbeen (11:41:52)
How much larger is C13O2 than C12O2? I would guess it’s not larger AT ALL. Sizes of atoms/ions/molecules are governed by the electron cloud. The electron cloud is affected by protons in the nucleus, but not neutrons. Thus, size should not be changed at all.
Actually, thinking about it a bit more, I wouldn’t be surprised if C13O2 is SMALLER (at room temp) than C12O2, if only by a miniscule amount. That would be because the heavier C13 increases the reduced mass of a C=O bond (by ~4.3%), thus causing that bond(s) to stretch less. The change would be miniscule though, and certainly not enough to affect typical biochemical reactions.
Any hardcore Physical Chemists want to weigh in? I’d be curious if there is any finite size difference and in which direction that difference is.
My guess is the reaction difference is kinetic: via the kinetic isotope effect.
-Scott
Regarding
George E. Smith (11:51:08) :
The bonds are NOT tetrahedral, CO2 is definitely a linear molecule. See:
http://en.wikipedia.org/wiki/Molecular_geometry
This is well-known, and as mentioned in Sjoerd Schreuder (11:48:23) , this is predicted by VSEPR theory (though it wasn’t called that in the post). Note that, in CO2, carbon is in sp hybridization, not sp3 as in a diamond. This is standard general chemistry level stuff.
Additionally, even if CO2 were tetrahedral, the bond angles would be ~109 degrees, not 90 degrees. Remember, as you said, this is 3-dimensional. Octahedral structures have 90 degree bonds.
-Scott
And this is just one volcano.
“”” Scott (11:33:24) :
George E. Smith (11:03:53) :
You’re discussing atomic spectroscopy here (you even use that term). I think everyone else is discussing IR spectroscopy (requires a change in dipole moment from the stretching/bending of a covalent bond). Thus, the effect of isotopic change is much less (though not zero, as it changes the reduced mass).
-Scott “””
Well if you recall this: “”” Steve in SC (07:56:49) :
Isotopic composition doesn’t affect chemical behaviour or spectral absorption in any significant way.
Those properties are controlled by the electron shells, not the number of neutrons in the nucleus. “””
Steve in SC implies that the Nuclear size and mass doesn’t affect the spectra; yet they clearly DO affect the Atomic Spectra; which implies that the energy levels are affected by the nuclear composition.
And yes I know that the CO2 important absorptions are molecular spectra in the LWIR. The carbon bond lengths, and strengths must be different between 12C and 13C for the same reason the atomic spectra of Carbon are different; and that must make the bending moment of inertia of the CO2 molecule different between those two isotopes. In the end, it is all somewhat academic, since Doppler and Collision (pressure) broadening change all the frequencies anyway.
And no I don’t think that there are any climate effects from isotopic differences in any constituent of the atmosphere.
I don’t use Wiki as a reference for anything but Wiki’s opinion on whatever.
So maybe the Chemists are all mortified that I should draw a double carbon bond edgeways on the show the tetrahedral arrangement; but since I was not contesting the chemistry of CO2; but the Physical prestidigitations of the atoms in the IR molecular vibrations; I don’t particularly care if the Chemists are offended.
My Fly fishing buddies; would be astonished at the grab success of some of my new molecular “fly” patterns.
George
Anu (10:22:30) :
“Peter Hearnden (08:00:35) :
How much CO2 is the volcano spewing out? You seem to imply you know how much?
…..If the volcano is actually emitting 150,000 tons/day, then humans are emitting 530.66 times more, every day.”
SO that is just ONE volcano active at this time. As usual the first rule in science is to formulate the correct question. And you did answer the original question. However there is more than one active volcano.
“Ongoing Activity: | Arenal, Costa Rica | Batu Tara, Komba Island (Indonesia) | Dukono, Halmahera | Karymsky, Eastern Kamchatka (Russia) | Kilauea, Hawaii (USA) | Kliuchevskoi, Central Kamchatka (Russia) | Popocatépetl, México | Rabaul, New Britain | Sakura-jima, Kyushu | Shiveluch, Central Kamchatka (Russia) | Soufrière Hills, Montserrat
New Activity/Unrest: | Egon, Flores Island (Indonesia) | Etna, Sicily (Italy) | Eyjafjallajökull, Southern Iceland | Gaua, Banks Islands (SW Pacific) | Miyake-jima, Izu Islands (Japan) | Redoubt, Southwestern Alaska | Reventador, Ecuador “ http://www.volcano.si.edu/reports/usgs/
And then there are the undersea volcanoes: “…The team estimates that in total there could be about 3 million submarine volcanoes, 39,000 of which rise more than 1000 metres over the sea bed….” http://www.newscientist.com/article/dn12218
“….Currently there are over five thousand active volcanoes underwater varying from ones larger than any on the surface to cones no larger than an automobile….” http://www.crystalinks.com/volcanoesunderwater.html
So volcanic activity can be a major contributor to the CO2 level depending on the number and size of the active volcanoes.
Hockey Schtick (11:54:35) :
Why is it not equally plausible that CO2 has been rising since the last ice age primarily due to decreasing solubility with rising temperature?
http://hockeyschtick.blogspot.com/2010/01/co2-levels-in-atmosphere-are-damped-by.html
The long term temperature-CO2 ratio (where CO2 lags temperature) is more or less fixed (and surprisingly linear): about 8 ppmv/K:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/Vostok_trends.gif
The cooling from the MWP to the LIA also did give some 8 ppmv/K drop in CO2 levels.
Thus even if we assume 1 K warming since the LIA, that wouldn’t give more than 8 ppmv increase in CO2, while we see a 100+ ppmv increase.
The late Endersbee was completely wrong with his graph: first, what he did was a serious sin in statistics: never compare trends with such a large smoothing (21 years) with another variable (CO2) with far less smoothing (12 months). Second, he compared the last 20 years (with a 21 years smoothed variable!), where both temperature and CO2 go up, while if one extents the graph to 104 years, the correlation is quite different (even negative) in other periods. See:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_emiss_increase.jpg
As you can see there is a near perfect correlation between accumulated CO2 emissions and CO2 increase in the atmosphere, while the correlation between temperature and CO2 is rather variable. That is also visible in the 1:1 trends:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_1900_2004.jpg
and
http://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_co2_1900_2004.jpg
where big jumps in temperature have little effect on CO2 levels (about 4 ppmv/K around the trend).
After having been enlightened by a certain congressman from Atlanta I have become worried that this volcano could upset the delicate balance of Iceland thus causing the island to tip over and capsize.
Ferdinand Engelbeen (11:27:06) :
Furthermore, additional assumptions:
[9] As noted above, we can use atmospheric O2/N2 data
to partition anthropogenic CO2 sequestration between the
land biosphere and the ocean. In its simplest form, this
calculation assumes that the annually averaged oceanic O2
inventory is constant. However, this inventory is likely to be
changing, for two reasons. First, the ocean is warming
[Levitus et al., 2000], reducing gas solubility and driving
O2 from ocean to atmosphere [Keeling and Garcia, 2002].
Second, changes in oceanic stratification may be altering the
oceanic carbon cycle. These carbon cycle changes would
likely be accompanied by the transfer of O2 between ocean
and atmosphere.
[10] We calculate anthropogenic CO2 sequestration rates
by the ocean and the land biosphere assuming a constant
oceanic O2 inventory. We then summarize estimates of the
rate at which the oceanic O2 inventory is changing, and
associated changes in calculated anthropogenic CO2 sequestration
rates. Finally, we examine interannual variability in
land and ocean CO2 sequestration.
Also, the randomization of the locations of the sampling sites are obviously a little suspect:
Station Abbreviation, Station Name ,Latitude, Longitude ,Altitude above sea level, m
BRW Point Barrow, Alaska, United States 71.32 156.60, 11
SMO Tutuila, American Samoa 14.24 170.57, 42
AMS Amsterdam Island, France 37.95 77.53, 150
CGO Cape Grim, Tasmania, Australia 40.68 144.68, 94
MAC Macquarie Island, Australia 54.50 158.95, 12
SYO Syowa Station, Antarctica, Japan 69.00 39.58, 14
Tim Clark (11:56:04) :
The first remarks weren’t mine, but:
“I’ve never agreed with these papers. Those papers woefully neglect to incorporate ocean biomas in calculations. That would be expected from the educational expertise of the authors.”
The oxygen balance is not a simple one, as the year by year noise is quite high, and oxygen level differences are at the edge of analytical possibilities. But in the oxygen and CO2 balance, ocean biomass is included (and is relatively small compared to land biota, if the inventories are accurate). The main problem is the amount of oxygen released/absorbed from simple solubility in seawater (temperature…), which varies from year to year.
Well, first was E.M. Smith’s great article on why detecting an anthropogenic CO2 signature based on atmospheric C12/C13 ratios is bunk.
Now I have found Dr. Roy Spencer’s article right here on WUWT that lays out about the same.
So I am now up to two trusted sources which tell me that anyone telling me they can find a definite man-made CO2 signature and exact atmospheric amounts based on C12/C13 ratios, is not speaking out of the normal orifice used for transmitting verbal information.
“”” Like in the other arrangements, electrons must be spaced as far as possible. “””
That is a direct quote from the Wiki molecular shape citation Scott gave above.
And that is the very reason why the four bonds of the carbon atom are arranged tetrahedrally; because that is the ONLY geometrical configuration that pushes the four electrons as far apart from each other as possible.
And a Tetrahedron has its four vertices in two pairs which are exactly at right angles to each other. When an Oxygen atom latches on to any pair of those four bonds, we have the two nuclei and the shared electrons in a common plane.
When a second Oxygen atom latches on to the other pair of bonds; the nucleus of that third atom lies in exactly the same plane at the saem distance forming the linear molecule. BUT the shared electrons for the second oxygen atom ARE NOT in that plane with everything else; but are in a different plane at right angles to the first plane.
The molecule is still LINEAR as everybody claims (including me) but it is NOT PLANAR
A Planar Linear CO2 O=C=O looks like this O-C-O, when looked at IN the plane of everything; whereas O=C=O is looking at it PERPENDICULAR to the plane.
If all four bonds lie in a common plane, then the spacing between the electrons is not maximum; it is maximum when the four bonds are tetrahedrally disposed as they are in Carbon, Silicon, and Germanium; and also alpha Tin I believe. And I suspect their dioxides are all linear but non planar molecules.
Ferdinand Engelbeen (11:27:06) :
Gail Combs (10:20:59) :
However plants throw a monkey wrench into the whole “man’s signature CO2″
“…Plant photosynthetic biochemistry is remarkably specific preferring to fix 12C over 13C by a large margin….”
Part of the monkey wrench is plants emit CO2 at night AND as E.M. Smith and others noted different plants have an affinity for C12 or C13 and the ratio of those different plant types have changed over time….. I call that a monkey wrench.
Regarding
George E. Smith (12:22:52) :
Well clearly “Steve in SC” either wasn’t thinking about atomic spectroscopy or isn’t familiar with it, because of course it’s affected by the nucleus – it’s called atomic spectroscopy. As you’d expect, nuclear magnetic spectroscopy is also affected by the nucleus of an atom.
However, I contest the idea that the bond lengths/strengths are different for CO2 containing C12 vs C13. The reason their spectra are different is because they have different masses (thus, different reduced mass). Bond length/strength is the “spring” connecting the two masses. In this case, the “spring” is the same, but the masses on the end are different, thus the different spectra. And, yes, it is academic because of the collisional broadening. That was related to why I questioned it in the first place.
I agree with you about Wikipedia–it’s a piss poor reference (I particularly like to point out Wiki-gate, but you definitely know about that b/c you’ve been on this site for some time). So instead would you prefer me to reference books though? This is general chemistry, so I could reference the book I used for that class or any common OChem/PChem book for that matter. I used Solomon’s “Organic Chemistry” book and Atkins “Physical Chemistry” book, but I don’t remember my Gen Chem book.
And the chemists are not mortified about rotating molecules, the mortification comes from claiming that CO2 is tetrahedral when it’s linear.
—
In the end, none of the above is that important in this thread. However, where it does become important is in the impression left by some skeptics. If I was a newbie to this site and saw you claiming CO2 was tetrahedral, I would be prone to just ignore everything I saw you post in the future, regardless of its merit (or worse, just abandon this site assuming all the people here don’t know what they’re talking about). My expertise is chemistry, so that’s the lens I see things through.
In reality, I’ve seen a variety of quality posts/thoughts coming from you, so I realize that this is an aberration. However, I’d prefer to see the error corrected so that newbies (or even frequenters) to this site aren’t prone to think we’re full of crap.
As an example (and Steve Goddard can attest to this), I live in a town with quite a few environmental crazies who have an effect on the general population. Just walking through the CSU campus during a school day gets you attacked by multiple Greenpeace reps. Because of this, people look down on skeptics and if I pointed someone to this site and they saw CO2 being called tetrahedral (and knew better of it), they’d never come back, even if all your other information/comments were 100% valid.
I’m not trying to pick a fight, just trying to improve the quality of the science discussed here,
-Scott
Scott (12:04:47) :
The change would be miniscule though, and certainly not enough to affect typical biochemical reactions.
Any hardcore Physical Chemists want to weigh in? I’d be curious if there is any finite size difference and in which direction that difference is.
I don’t think you meant biochemical and then inferred a physical chemist would know. You should ask someone who has had Enzymology; and actually it makes 2.03% difference from corn chloroplasts in one of the most quoted pioneering work (peer reviewed ;~P) :
Fractionation of Stable Carbon Isotopes by Phosphoenolpyruvate
Carboxylase from C4 Plants1
Received for publication September 8, 1976 and in revised form November 22, 1976
PAUL H. REIBACH AND C. RoY BENEDICT
Department of Plant Sciences, Texas A&M University, College Station, Texas 77843
ABSTRACT
The active species of “CO2” and the amount of fractionation of stable
carbon isotopes have been determined for a partielly purified preparation
of phosphoenolpyruvate (PEP) carboxylase (EC 4.1.1.31) from
corn (Zea mays) leaves. The rates of the enzyme reactions, using
substrte amounts of HCO3-, CO2 or CO2 plus carbonic anhydrse,
show that HCO3- is the active species of “CO2” utilized by PEP carboxylase.
The K,. values for CO2 and HCO3- are 1.25 mM and 0.11 mM,
respectively, which further suggest the preferential utilization of HCO3-
by PEP carboxylase. The amount of fractionation of stable carbon
isotopes by PEP carboxylase from an infnite pool of H12C03- and
H13C03- was -2.03 %o. This enzyme fractionation (A), together with the
fractionation associated with absorption of CO2 into plant cells and the
equilibrium fractionation associated with atmospheric CO2 and dissolved
HCO3- are discussed in relation to the fractionation of stable carbon
isotopes of atmospheric CO2 during photosynthesis in C4 plants.
nah, you didn’t get it, you see, there is basically 3 types of CO2 molecules:
– good CO2, the natural one, the one that Gaia send to her plant-children, the volcano one
– the not so bad CO2, bad, but redempted because it is emmitted for a rightfull cause. The one emitted by Gore jetskis, or Grenpeace boats, or Nicolas Hulot planes. Also the one emitted by any poor (or not too rich) that is on the right frame of mind, i.e. not wanting a better standard of living but wanting to help the children (and make a lot of new ones), or traditional way of living (using fire wood is good, coal or petrol is bad). Basically any emission from non occidental, chinese, japanese or petromonarchy source is ok unless proved otherwise.
-the really really bad CO2: everything that is emitted by non-green megacorps (green megacorps are ok), by anything related to internal combustion engine or powered individual transportation (except for electric – but this is only temporary), or worse, motorsport, or to individual tourism without the eco or humanitarian excuse. In fact, if your co2 molecule is coming from human activity without the proper contrition, but to improve your material well being, it is really really bad, it makes mother gaia cry….
Sjoerd Schreuder (12:02:42) and
Scott (12:04:47)
I stand corrected. I was guessing larger, but in fact it should be somewhat smaller, and kinetics are probably more important in this case than size or form.
http://www.chem.ucsb.edu/coursepages/05spring/1C-Perona/hybridization.pdf
So their drawing is a bit more complicated than mine, so they show the structure as a sigma bond, and a pi bond for each oxygen; with the pi bond electron paires at right angles, in a still linear molecule.
It’s the pi bonds that have to deflect in two modes at right angles in the 15 micron bending mode of CO2.
Ferdinand Engelbeen (09:13:20) :”About 6% of the current atmosphere is from the use of fossil fuels, deduced from the 13C/12C ratio”
Are you suggesting that our atmosphere is now made up of 78% N2, 21% O2 and 6% man made CO2?
Perhaps you meant to say “6% of the CO2 in the atmosphere is from use of fossil fuels”. Since CO2 makes up approx .038 % of our atmosphere, and CO2 from fossil fuel use is 6% of that, the real number would be in the neighborhood of ….. a really, really tiny amount.
George E. Smith (12:50:11) :
Please go somewhere and read about molecular orbital hybridization. I don’t care if it is Wikipedia, a book, a lecture, or whatever. The bonding around the carbon in CO2 is sp hybridized, and is therefore NOT tetrahedral (which would be sp3 hybridization.
And don’t quote mine the Wikipedia link I gave. First, WIki is crap, as you yourself say. Second, the quote you gave is for BENT molecules, and CO2 is NOT BENT. Here’s what you should have quoted:
Just so you know, bent molecules have lone electron pairs on the central atom. Drawing a correct Lewis structure of CO2 shows that it clearly does not have lone pairs.
And no one ever said that all the electrons were exactly centered between the C and O atoms. Basic general chemistry tells us this! Linear/tetrahedral/octahedral/bent/etc are given by the arrangement of atoms in the system, not the electrons (though the electrons can in fact determine where the atoms go). Saying that you’ve rotated the rod of CO2 to hide some of the electrons doesn’t really work…at the very least the lines in O–C–O should have been bolded in your method (I don’t agree with that, but at least it’s representative of what you’re claiming).
-Scott