Buy

Books
Click images for more details

Support

 

Twitter
Recent comments
Recent posts
Currently discussing
Links

A few sites I've stumbled across recently....

Powered by Squarespace
« On geography | Main | Post-truth media »
Monday
Aug122013

A new look at the carbon dioxide budget - Part 4

In this final part of his paper on carbon dioxide control mechanisms, David Coe draws together all the different strands of the paper.

 

Carbon budget Part 4

PrintView Printer Friendly Version

Reader Comments (60)

I hope that in the not too distant future this paper can be revised and published. I cannot pretend to understand it all and I look forward to reading informed comments. If I read it right it reinforces much of what Murry Salby put forward in his talk.

Aug 12, 2013 at 11:16 AM | Unregistered CommenterRoss Lea

Many thanks.
Unfortunately he seems to have missed a few salient facts. The claim that we are the biggest CO2 atmospheric contributor is wrong. Our proportion of the annual CO2 budget is 3-4%. Nature contributes 97% mostly volcanic from deep ocean vents on the ridges. Ants produce more CO2 than we do.

Claims that pre-industrial levels of CO2 were 280ppmv +/- 10ppmv are in error. This proxy figure is based on old ice core data which has been shown to be in error. The true figure could have been far higher and dependent on temperatures 800 years previously. It has been shown that atmospheric CO2 levels in the 19th century were much higher, one measurement was 490ppmv. I say measurement because these were done by chemical methods still in use not by proxy.

The claim about the CO2/O2 exchanges assumes that forests contribute more O2 rather than the true picture that it is the oceans that do most of this vital conversion of CO2 to O2.

Good paper shame about some of the content.

Aug 12, 2013 at 11:17 AM | Unregistered CommenterJohn Marshall

John Marshall

I make no claims about historical CO2 levels. The figures in this paper are those of the IPCC assessment reports.

I similarly make no claims about the various sources of CO2 and their relative magnitude. I simply dispute in the strongest terms that the biosphere is in equilibrium with a zero net biome production and have used the undoubted relationship between anthropogenic emissions and increases in atmospheric CO2 levels to "calibrate the equations". The rest spills straight from those same equations.

You need to be very wary of historical CO2 measurements. Depending upon location current CO2 levels are known to vary by over 100ppm from the established global average figures.

Aug 12, 2013 at 11:51 AM | Unregistered CommenterDavid Coe

Ross Lea

Unfortunately, much as I would like to be in the same camp as Murry Salby, his views and mine are substantially different. Murry believes that current CO2 trends can be sourced back to natural variation. The fact that there is a linear relationship between observed CO2 increases and the actual rates of emission of anthropogenic CO2, in my opinion, cannot be attributed to fluke and cannot be ignored. I have tried to produce a concept that gives a rational and consistent explanation for the varied atmospheric observations. Whether I have succeeded in that task remains to be seen.

Aug 12, 2013 at 12:00 PM | Unregistered CommenterDavid Coe

Good luck with this project David. I have struggled with some of the maths (Lit graduate) but I think I have grasped the overall concept. It will be good to see further discussion, evaluation and (reasoned) criticism.

Aug 12, 2013 at 12:22 PM | Unregistered CommenterGixxerboy

Here is what I consider to be the most important statement from the analysis. It is on page 6 of part 4-

"Atmospheric CO2 levels are directly proportional to the rate of CO2 emissions."

Aug 12, 2013 at 1:48 PM | Unregistered Commenterchris y

David,

Yesterday I have reacted on part 3, but still need to read part 1 and 2. Now on part 4:

The Revelle factor is a matter of chemistry: seawater can hold a lot more CO2 than fresh water, thanks to its buffer capacity. The Revelle factor shows how much more. Thus instead of a restriction on CO2 uptake, it shows the increase of uptake. The chemistry is explained here:
http://www.eng.warwick.ac.uk/staff/gpk/Teaching-undergrad/es427/Exam%200405%20Revision/Ocean-chemistry.pdf
Thus while the exchanges between the atmosphere and the ocean surfaces is fast (1-3 years), the uptake or release of the ocean surfaces is restricted to 10% of what happens in the atmosphere (or reverse), mainly in mid-latitude oceans.
That is so for every amount of CO2, natural or man-made, no matter the isotopic balance. The pre-industrial equilibrium was maintained between all processes as what did go into the oceans near the poles did return near the equator (with a lot of delay), which gives a continuous flow of CO2 from the tropics, mainly from the upwelling near Chili to the main sink place at the NE Atlantic. Temperature was the main driver for global changes at about 8 ppmv/K over the past 800 kyr.

That the Revelle factor is real can be seen in a few longer term series that measured DIC in the oceans: BATS (Bermuda) and ALOHA (Hawaii, what did you expect...):
See halfway http://www.seafriends.org.nz/issues/global/acid2.htm for the graph of BATS: an increase of 50mmol/kg (1.4%) in DIC over 20 years.
In the same period CO2 levels in the atmosphere increased some 9% or a factor 7.5. Not the 10 times, but far from 1:1...

The Revelle factor is of less importance at the source/sink places, as at the sink places the temperature is so low that the pCO2 difference is high and still the waters are not saturated when they sink into the deep. Thus there still is plenty of room for absorption before the Revelle factor comes in.
BTW, the Thermohaline Circulation largely bypasses the surface layer at the sink and source places and can be used as different exchanges than the exchange with the surface layer. The more that the exchange rate is much slower than with the surface, as the fate of the 13C/12C ratio shows:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_zero.jpg

The decay rate for deep ocean exchanges and more permanent storage in vegetation (soils, roots,...) is about 53 years, the decay rate for 13C (and 14C) is ~3 times faster, because what returns from the deep oceans is old 13C enriched (and 14C poor) CO2...

Aug 12, 2013 at 2:08 PM | Unregistered CommenterFerdinand Engelbeen

John Marshall: It has been shown that atmospheric CO2 levels in the 19th century were much higher, one measurement was 490ppmv.

Thank you for the details John, can you tell me where you found this fact please, or indeed any research into C02 prior to 1860?

It appears that every 'known' fact put forward by the warmists can be challenged.

Aug 12, 2013 at 2:12 PM | Registered Commenterscribblingscribe

John Marshall,

Many historical CO2 measurements were unreliable, not because the method itself (although...) but because of the "CO2 heat island" effect: CO2 levels between 200 and 650 ppmv within hours at the same place somewhere near vegetation in a semi-rural surrounding. Others were taken in the middle of towns (Paris...). Even without or less cars at that time, more CO2 thanks to heating and cooking...
See the difference between the raw data (including all local outliers) from Giessen (Germany), semi-rural, on a few summer days and the data from Mauna Loa, Barrow and the South Pole on the same days:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/giessen_background.jpg
The historical data at Giessen (one of the longest continuous series) were taken 3 times a day, of which 2 were at the flanks of the highest variation in CO2 level... The stdv of the historical Giessen data was 132 ppmv (1 sigma!) with a range of 200-650 ppmv.

The historical measurements taken during seacruises and coastal with wind from the sea all are around the ice core values of the same age, taken decennia later.

Aug 12, 2013 at 2:40 PM | Unregistered CommenterFerdinand Engelbeen

Ferdinand Engelbeen

Thank you for your comments on Parts 3 and 4 of this paper. I have put this paper up for challenge and that is precisely what you are doing. It is a challenge that I must rise to.

My issue with the Revelle factor is that I believe it to be a prime example of circuitous logic. An awkward problem, that of lack of uptake of anthropogenic CO2 by the oceans was resolved by the introduction of an arbitrary artifact, the Revelle factor, which has no grounding in science (or more specifically chemistry). That artifact is subsequently used to justify the same apparent anomalous relationship between ocean and atmosphere. The only reason to modify Henry's law in the way required by the Revelle factor is to explain the narrative behind the concept of climate change. This factor does not appear in any other discipline of science.

Please read parts 1 and 2 of this paper. They explain in detail my objections to the science promoted by working group 1 of the IPCC assessment reports with an alternative explanation based upon the simple reasoning that equilibrium is achieved by a balancing of CO2 fluxes and that any inbalance will result in a partial pressure differential between ocean and atmosphere thus creating a balancing flux to or from the ocean, in other words, negative feedback control.

Aug 12, 2013 at 3:02 PM | Unregistered CommenterDavid Coe

http://en.wikipedia.org/wiki/Revelle_factor

The information on the Revell factor on Wikipedia is simply amazing - it is a masterpeice on non-statement of anything, totally devoid of any science references, and even by Wiki standards is shite.

Hence, in modern day oceans, it is possible to see the concentrations of anthropogenic CO2 by measuring the Revelle factor; the lower the Revelle factor, the greater the amount of anthropogenic CO2.

As David has said, you can't get much more circular than this ;)

Aug 12, 2013 at 3:08 PM | Registered Commentersteve ta

David,

The history of the Revelle factor is in fact the opposite of what you think: Revelle and Suess did introduce the last paragraph without taking the consequences into account (although they had them calculated from the chemical equilibria), because they feared that the "consensus" of that time would not accept it, as most scientists were sure that all human CO2 would be absorbed by the oceans, thus nothing to worry.

The Revelle factor doesn't alter Henry's Law in any way. Henry's Law only says that the ratio of CO2 levels in atmosphere in equilibrium with CO2 in (sea)water are always the same for the same temperature. That is obeyed for all levels of CO2 in water and air. The problem is that Henry's Law only is applicable for free CO2 in water, not for bicarbonate and carbonate ions. In the case of fresh water at saturation, near 99% of DIC is free CO2. In the case of seawater less than 1% of DIC is free CO2. Thus seawater may contain 100 times more CO2 in different forms than fresh water for the same CO2 pressure in the atmosphere, while the concentration of free CO2 in both cases is exactly the same. Thus the Revelle factor for seawater is 100, compared to fresh water.

For seawater already saturated with CO2 of a certain pressure, the Revelle factor is less for changes in the atmosphere. That is a matter of how far the buffer capacity of seawater is already saturated.
Anyway, the Revelle factor stands on firm (chemical equilibrium) grounds...

Aug 12, 2013 at 3:34 PM | Unregistered CommenterFerdinand Engelbeen

I like very much your series and investigation into this weak area of climate science. I am still digesting the concepts and maths.

A comment on presention in part 4. After conditioning the readers in several graphs that Series 2 red=IPCC and Series 1 blue=Ocean Control theory, we come to figures 4.6 and 4.7, where these associations don't hold. Why not refer there to series 1.a and 1.b using light and dark blue, and series 2.a and 2.b with light and dark red?

Aug 12, 2013 at 4:05 PM | Unregistered CommenterRon C.

David,

A very minor suggestion before I forget it.

When presenting graphs, it's a good principle to design them so that they remain intelligible even when printed (or photocopied) in monochrome. Having printed parts of your paper on a B/W laser printer, I have to go back to look at the screen to figure out which curve is which.

I'm not colour blind but I know that people with degrees of colour blindness often have difficulty with graphs that use two colours to distinguish between two curves.

Aug 12, 2013 at 4:08 PM | Registered CommenterMartin A

"...You need to be very wary of historical CO2 measurements. Depending upon location current CO2 levels are known to vary by over 100ppm from the established global average figures."

Aug 12, 2013 at 11:51 AM | David Coe
/////////////////////////////////////////

Sir,

And CO2 is claimed to be a well mixed gas!

Is there a correspondingly higher amount of back radiation (DWLWIR) over these areas?

Can we measure the temperature effect of this 100ppm differences, if not why not?

Aug 12, 2013 at 5:02 PM | Unregistered Commenterrichard verney

Richard, CO2 is quite good mixed in 95% of the atmosphere. The only exception is over the first few hundred meters over land. That is because over land there are lots of fast sinks and sources and wind speed / turbulence in general is not fast enough to mix the changes into the rest of the atmosphere.

Even if the first 1000 meter was at 1000 ppmv, the radiative effect would give less than 0.1 K extra warming. Thus the few hundred ppmv more or less over the lower few hundred meters over land are negligible in the radiation budget.

Aug 12, 2013 at 6:47 PM | Unregistered CommenterFerdinand Engelbeen

Many congratulations on completing this outstanding work. It must have taken a considerable time and effort to cover all this.The paper needs to be properly peer-reviewed. I suspect very few readers here would be qualified to do this. Is this the next stage for you, David?

Aug 12, 2013 at 7:34 PM | Unregistered CommenterDerek

Ferdinand Engelbeen

"For seawater already saturated with CO2 of a certain pressure, the Revelle factor is less for changes in the atmosphere. That is a matter of how far the buffer capacity of seawater is already saturated."

The problem here Ferdinand, is that sea water is not saturated with CO2, far from it. The concept of the Revelle factor is thus inappropriate. Henry's law is known to hold for pressures up to 1000atmos.

Aug 13, 2013 at 3:38 AM | Unregistered CommenterDavid Coe

Ron C and Martin A

Your comments on the graphs are appreciated. I will try to do better

Aug 13, 2013 at 3:46 AM | Unregistered CommenterDavid Coe

David,

You need to make a distiction between ocean surface waters and deep ocean waters. The ocean surface waters are quite readily mixed with the atmosphere, that is the "mixed layer" which is fast equilibrating with the atmosphere (half life ~1 year). As the C content of the mixed layer is ~1000 GtC and the increase in the atmosphere ~30%, taking into account the Revelle factor, the whole uptake of the mixed layer in the past 160 years is ~30 GtC, hardly a change. That is what is measured as DIC increase over time at Bermuda and Hawaii (and other places, including regular ships cruises).

The deep oceans are far from saturated, but the exchanges between deep oceans and atmosphe are limited, thus that needs far more time to equilibrate (~40 years half life time).

Aug 13, 2013 at 10:25 AM | Unregistered CommenterFerdinand Engelbeen

(deleted by MA)

Aug 13, 2013 at 11:15 AM | Registered CommenterMartin A

Many congratulations on completing this outstanding work. It must have taken a considerable time and effort to cover all this.The paper needs to be properly peer-reviewed. I suspect very few readers here would be qualified to do this. Is this the next stage for you, David?
Aug 12, 2013 at 7:34 PM Derek

Jeremy Harvey (professor of chemistry at Bristol University) used to comment on BH from time to time. If he were interested in looking at David's paper, he'd give authoritative comments on the equilibrium chemistry aspects.

Aug 13, 2013 at 12:05 PM | Registered CommenterMartin A

chris y


Here is what I consider to be the most important statement from the analysis. It is on page 6 of part 4-

"Atmospheric CO2 levels are directly proportional to the rate of CO2 emissions."


As you say this is the crucial point. The linear relationship between atmospheric CO2 levels and rate of anthropogenic emissions has somehow been missed by climate science. I have simply proposed a simple mechanism to explain this relationship. The consequence of this is that atmospheric CO2 levels will not increase inexorably while CO2 emissions continue. The atmosphere will stablise at a predictable CO2 level once emissions have been stabilised. This pretty much eliminates the need to actually reduce CO2 levels, and certainly to act immediately without delay. All we need to do is stabilise that rate of emission.

The rest, by comparison is fluff, although the resulting rational explanation of all the other atmospheric observations is not unwelcome.

Aug 13, 2013 at 3:10 PM | Unregistered CommenterDavid Coe

David -

If you are reading a map, it is easier to find your way if you already know the destination. Perhaps you could help me...

A year or two back I tried to make sense of the Revelle factor, which was clearly the jewel in the crown of explaining why emitted CO2 was not going to be absorbed by the sea.

I struggled, doing my best to make sense of what I found, trying to remember equilibrium chemistry from A-level. I noticed that only climate science discussions mentioned it and I never managed to find an explanation starting from first principles. I did notice that non climate science explanations of air-water equilbria did not mention it, which seemed to indicated something or other, although I was not sure what. In the end, I abandoned the effort and got on with other things, so I never made sense of what it was all about.

Please tell me frankly whether the Revelle factor is....

1. Total bollocks
2. Argued from physical principles but not yet validated by physical measurements
3. A well-established physical effect but of negligible consequence in reality
4. A well-established physical effect that has been precisely quantified and has very significant effect on how CO2 is exchanged between atmosphere and ocean
5. A well-established physical effect that has been mis-applied to reach spurious conclusions
6. None of the above. It is _ _ _ _ _ _ _ _ _ _ _ _ _

tia for pointing me in the right direction.

Aug 13, 2013 at 8:02 PM | Registered CommenterMartin A

Martin A

I have similarly struggled. My conclusion would have to be along the lines of your item 1. i.e. total bollocks.

My contention is that Henry's law applies. The partial pressure exerted by the solvated CO2 is proportional to the concentration of that CO2. It doesn't matter what confusions you throw into the argument by the equilibrium conditions of carbonate chemistry, Henry's law applies. Because of its widespread use in the food and drink industry the dissolution properties of CO2 are probably the most widely studied of all gases. The paper by Carrol and Mather summarised the results of dozens of researchers and concluded that it applies with only slight modification up to pressures of a 1000atmos, and not a single mention of a Revelle factor.

I am afraid that I support the view that it is simply an artifact, wrapped up in mumbo jumbo, to explain something that was not understood 60 years ago. Nobody has since thought to question it or perhaps, more significantly, wanted to question it. It is outside the mainstream arguments of climate science. That it forms part of the syllabus of university oceanography courses is nothing short of a disgrace. A generation of so called scientists have been conned. As you say it would be interesting to hear what a real chemist might have to say.

My intention in persuading Andrew to post this paper was to hopefully draw out some expert comment. If I am also preaching bollocks the sooner I know about it and stop, the better. You may have gathered that I am not impressed by the incestuous peer review process, thus it is difficult to know how to acquire really expert review on a topic like this which covers so many different strands of science. And the maths doesn't help. While the solution of second order differential equations is no great deal for most mathematicians and physicists it is something of a turn off for most others. It is however fundamental to the case. Climate science is a science bereft of maths. Nature is too complicated I always hear. Rubbish! Science, like knitting, is only complicated when you don't understand it. The "complications" of climate science simply provide a smoke screen for wacky science.

Aug 13, 2013 at 11:51 PM | Unregistered CommenterDavid Coe

Aug 13, 2013 at 3:10 PM | David Coe

"The linear relationship between atmospheric CO2 levels and rate of anthropogenic emissions has somehow been missed by climate science."

But, it really isn't. They just happen, here in the early portion of the new century, to both be increasing approximately with linear trends. How hard is it to find an affine transformation between two series which are 1st order dependent in time? Trivially so. It is tautological - the transformation between two such series is affine.

No, the striking relationship is between temperature and the rate of change of atmospheric CO2. This matches more than just a linear trend. Every bump and wiggle matches.

The notion that human inputs just must be having some significant effect is not a scientific statement. It is akin to the Ptolemists insisting that the Sun just must go around the Earth. It is an expression of personal bias.

In fact, the idea is really quite ordinary. Feedback control systems are employed widely for the very reason that they attenuate disturbances. The planet has its own CO2 regulatory system, and it will resist perturbations. To significantly influence such a system, you must change its fundamental equilibrium level. That is something only nature itself has the power to do.

I apologize that I have not read your papers yet, David. I just do not have a lot of time for such matters at present, but will get to it as soon as I can. So, I am at a disadvantage in that I cannot critique specific points of your work. But, I feel a need to point out to you that, from my viewpoint, you are asserting things as being remarkable which, in reality, are not very.

Aug 14, 2013 at 2:52 AM | Unregistered CommenterBart

Bart

There is no known physical mechanism to explain a 40% increase in atmospheric CO2 levels by means of a 0.8 degC increase in temperature over the same period. There is indeed, however, a temperature dependancy of CO2 by temperature. As shown in part 3 the interannual variation in CO2 is explained precisely by the known variation in Henry constant due to temperature. There are no mysterious cyclic effects required to explain observations. A 0.8 degC change in sea surface temperature has produced an increase in atmospheric CO2 of only 9 ppm. On this issue Murry Salby has got it totally wrong.

I agree that there has to be a control mechanism for CO2. Just the simple postulate that a partial pressure differential between ocean and atmosphere results in a balancing CO2 flux and leads inevitably to such a feedback control. Not only that, but that mechanism also provides an explanation for every other atmospheric and sea surface observation, including seasonal variation of both CO2 and O2, interannual variations of CO2, carbon isotope variations in both sea surface and atmosphere, including a reason for the differential between the isotope ratios of sea surface and atmosphere.

The relationship between CO2 and rate of anthropogenic emissions is no accident. We are influencing the CO2 levels of both the sea surface and atmosphere. The key point is that that influence will not result in a continuous, never ending, increase in CO2 as averred by the IPCC but only a limited increase the magnitude of which is completely predictable and CONTROLLABLE.

Aug 14, 2013 at 7:27 AM | Unregistered CommenterDavid Coe

"Many congratulations on completing this outstanding work. It must have taken a considerable time and effort to cover all this. The paper needs to be properly peer-reviewed. I suspect very few readers here would be qualified to do this. Is this the next stage for you, David?"

Derek

"David Coe is a regular reader at BH. He is simply sick of reading the tripe published about global warming and has decided to ask some simple questions and search for some simple answers. Whether the answers I suggest are correct or not, will be determined by hopefully by a broad church of "expert" opinion rather than the corrupt peer review process. If I am ultimately proved wrong then I and hopefully others will have learned something. My only desire is for scientific truth."

David Coe

Aug 14, 2013 at 3:22 PM | Unregistered CommenterRichard

Aug 14, 2013 at 7:27 AM | David Coe

I really will have to read your exegesis in detail to understand where you are coming from, but I disagree with this:

"There is no known physical mechanism to explain a 40% increase in atmospheric CO2 levels by means of a 0.8 degC increase in temperature over the same period."

Just because something is unknown does not mean it can be wholly discounted. There is a lot which quite apparently is not known about this system. Your own mechanism is new. My own candidate is as follows.

There is no reason to expect CO2 distribution within the THC pipeline to be homogeneous. If a quantity, a bubble if you will, of upwelling waters turned out to have a richer CO2 concentration than the surface waters, then as that bubble surfaced over a number of decades, all things being equal, it would start to enrich the CO2 content of the surface waters in general. All things are not equal, however, and those enriched waters would start to outgas to the atmosphere.

This would constitute a pumping action into the atmosphere which would integrate over time. Because the rate at which CO2 outgases, and the waters are then carried back down, is temperature dependent, we end up with a temperature dependent pumping action whose dynamics could be described to first order as

dCO2/dt = k*(T - Teq)

CO2 = atmospheric concentration
k = sensitivity factor (which could vary slowly over time, or perhaps effectively in steps, with the concentration of upwelling waters)
T = a global temperature metric (best fits appear to be either with SH temperatures or satellite temperatures)
Teq = an equilibrium point for T, which also might vary over time

As shown in the plots, the relationship has been remarkably stable with constant parameters since at least 1958 when good measurements of CO2 began to be made.

A more complete toy system which mimics the full system would be

dCO2/dt = (CO2eq - CO2)/tau + H
dCO2eq/dt = k*(T - Teq)

where tau is a time constant, and H is the rate of human inputs. In this system, sinks are represented by the time constant tau. If tau is "short", then H will be severely attenuated, not effectively integrated, and CO2 will track CO2eq. This is a fairly ordinary and common-type control action.

It is worth noting that, with tau "short", the effect of H is approximately CO2_due_to_H = H*tau, so there would be a relationship such as you suggest. However, because tau would be short, it would never amount to the magnitude of observations. When I get a chance to look into your equations, I want to see if there is some modification possible indicated by your analysis which would amplify this relationship. However, at this time, I see such a nearly perfect match between the temperature related part and the actual measurements that I do not see the possibility of significant influence of H.

Aug 14, 2013 at 5:58 PM | Unregistered CommenterBart

Bart

I know its a chore but please try to read part 2 of my paper. Hopefully you will find that it presents an entirely logical explanation for both atmospheric and sea surface CO2 variations, based upon very simple principles of physics.

Aug 14, 2013 at 11:31 PM | Unregistered CommenterDavid Coe

Bart

An additional thought. You must also explain reducing O2 levels and increasing isotopic carbon ratios. These I suspect cannot be explained by temperature effects. You cannot simply focus on CO2.

Aug 15, 2013 at 1:46 AM | Unregistered CommenterDavid Coe

David Coe
I hope this thread is still active, as I needed time to digest your presentation.

As I understand you -
1. The IPCC asserts that there is exactly zero global Net Primary Production, which you deny.
2. Minor relaxation of that equilibrium allows you to use a simple linear approximation, so diffusion coefficients etc have meaning (this is implied in your equations).
3. You distinguish terrestrial biomes + humans (which happens to be a net source of CO2) from the marine biome, which must be a sink.
4. The linear model directly requires that air CO2 concentration be proportional to rate of addition. Your plot is (I think) a correlation of time series, which is known to be the trickiest sort. If so, that plot's linearity is a necessary condition only. However, credible alternative explanations of it have to be similarly simple and direct.
5. Your model assumes removal of NPP carbon from the system.
6. To work, your model requires a persistent CO2 source below the thermocline (essentially, a constant partial-pressure of CO2).
For the last, you offer an unfamiliar mechanism, which I think unnecessarily weakens your case.

There are several plausible subsurface "CO2" sources, and they aren't all mutually exclusive.
The obvious one is dissolution of CO2 in polar water, with transport everywhere below the thermocline.
Elsewhere, DocMartyn has suggested DOC sedimentation/oxidation to provide a CO2-rich zone below the themocline.
I offer a similar one following.
Some of those studying the geological carbon cycle refer to it as the *biogeochemical carbon cycle*, as they infer a significant biological influence over geological time. A necessary biological component in your model thus isn't surprising.

Several issues could "slay your beautiful hypothesis":
> If the uncertainty in global NPP estimates is much less than your required imbalance (I guess not);
> If the diffusion coefficients implied by your model are unrealistically high;
> If one of your required vertical concentration gradients doesn't exist.

You (I think) explain the "winter" increase in CO2 to equilibration with the mixed layer, so mediated by a time-constant (your 3 yrs?). If so, the high-latitude seasonal record should approximate an exponential decay of that order; this would be useful corroboration.

Aug 16, 2013 at 1:02 PM | Unregistered CommenterPeter Shaw

A possible upward CO2 transport scheme for discussion -

CO2 exists in seawater essentially as calcium bicarbonate (commonplace temporary hardness).
Organisms above the thermocline build shells/skeleta of CaCO3; this removes half the CO2, leaving the rest as dissolved gas.
Solid CaCO3 gravitates until it dissolves at depth under pressure, reforming calcium bicarbonate using ambient CO2.
The resulting concentration gradient should drive upward diffusion (of bicarbonate, not dissolved CO2) across the thermocline.
To persist, this mechanism requires a continual but uncritical source of CO2 from deeper water.

This scheme would maintain a substantial upper zone exactly saturated with CaCO3, as needed for many marine lifeforms.

Aug 16, 2013 at 1:05 PM | Unregistered CommenterPeter Shaw

David - I was thinking of posting the URL's to the four BH postings giving the four parts of your paper on Discussion - so that they will remain more easily accessible.

Do you think this is a good idea?

Aug 16, 2013 at 9:41 PM | Unregistered CommenterMartin A

"The consequence of this is that atmospheric CO2 levels will not increase inexorably while CO2 emissions continue. The atmosphere will stablise at a predictable CO2 level once emissions have been stabilised. This pretty much eliminates the need to actually reduce CO2 levels, and certainly to act immediately without delay. All we need to do is stabilise that rate of emission."

We radical denalists say, "So what?" The higher the CO2 levels in the atmosphere, the better. The little remaining hypothetical warming the declining log curve has left to offer can only be beneficial, as in all previous warm periods (which we would be lucky to match). CO2 greening of the planet is already happening apace, and is also beneficial.

So stabilising CO2 levels and emissions is neither desirable nor possible (given the survival drive of the developing nations).

Aug 17, 2013 at 4:28 PM | Unregistered CommenterBrian H

Martin A

"David - I was thinking of posting the URL's to the four BH postings giving the four parts of your paper on Discussion - so that they will remain more easily accessible.

Do you think this is a good idea?"


Yes that would be a good idea in my opinion.

Aug 17, 2013 at 9:49 PM | Unregistered CommenterDavid Coe

Martin A,

Sorry for the delay in reaction, there was an interesting discussion at WUWT at the defence of Murry Salby, where Bart's reasoning was critisized...

About the Revelle factor, your point 4 is the right one, with one word replaced:

4. A well-established chemical effect that has been precisely quantified and has very significant effect on how CO2 is exchanged between atmosphere and ocean.

As I said before, seawater can hold much more CO2 in different forms than fresh water. That is mainly a matter of pH. The lower the pH, the less CO2. Simply add some acid to a saturated (or not) bicarbonate (baking soda) or carbonate (soda) solution and watch what happens: a lot of CO2 escapes to the atmosphere. In both cases Henry's law is at work: when you add an acid to the strong alkaline solution of soda or the less strong alkaline baking soda solution, the chemical equilibrium is driven from carbonate to bicarbonate to free CO2. The latter then is in excess to what Henry's Law approves for the 400 ppmv in the atmosphere and escapes from the solution.

Thus again: Henry's law is fully aplicable for all solutions of CO2 in water and seawater, but only applies to free CO2, not to bicarbonate or carbonate ions. The amount of free CO2 depends of the equilibrium reactions in the solution and are mainly pH dependent.

With an increase of CO2 in the atmosphere more CO2 is pushed into seawater as free CO2. More free CO2 pushes the whole chain of equilibria towards more carbonate and more H+ ions. The latter pushes the equilibria back towards more free CO2.
The net result is that a new equilibrium is reached where Henry's law is obeyed: a 100% increase of CO2 in the atmosphere gives a 100% increase of free CO2 in solution, but only a 10% increase of total carbon, as the bicarbonate and carbonate amounts don't follow the free CO2 increase, because of the reduction in pH.
As free CO2 in seawater is less than 1% of all carbon, its doubling has little effect on the total mass of carbon in seawater.

All what the Revelle factor tells is how much more CO2 can be dissolved in seawater than in fresh water at the same atmospheric CO2 pressure for both...

See further my previous message for the references.

Aug 17, 2013 at 9:52 PM | Unregistered CommenterFerdinand Engelbeen

Peter Shaw

My paper is based on the premise that the flow of CO2 across the thermocline and sea surface/atmosphere interface is proportional to the partial pressure differential across them. I have made one critical assumption that the deep ocean can be considered as a stable and infinite source of CO2. Setting up the CO2 transfer equations for the sea surface (mixed layer) and atmosphere results in a second order differential equation, the solution to which is the exponential response equation relating both sea surface and atmospheric CO2 levels to the net CO2 fluxes. These equations predict precisely the observed linear relationship between the rate anthropogenic CO2 emissions and atmospheric CO2 levels.

The most important "unknowns" in these equations are the response times governing the flow of CO2 across the thermocline and sea surface/atmosphere interface. I have selected a figure of 3 years for the sea surface response on the basis of the many estimates of atmospheric CO2 residence times. I have then simply used the known data for rates of human CO2 emissions and CO2 levels from CDIAC to effectively calibrate the equations and determine a value for the thermocline response (70 years). These simple equations provide a rational explanation for every atmospheric CO2, O2 and isotope ratio variation.

The one assumption that the deep ocean is a constant and infinite source of CO2 is open to debate. Over the very short period of the industrial age this seams to hold. For longer periods I have absolutely no idea.I have offered a contentious possible explanation for deep ocean CO2 generation which has caused some debate. I am totally receptive to new thoughts on this issue.

Aug 18, 2013 at 5:46 AM | Unregistered CommenterDavid Coe

David, I have some comments on part 1...

Here is the problem. Where does the CO2 come from, to restore the atmospheric levels during the winter months?

Indeed, as the IPCC wrote, that comes from vegetation decay in winter. It seems that not only a (large) part is returned when leaves are falling in fall, but that soil bacteria go on with breaking down a lot of cellulose and other stuff under a snow deck, enough to compensate for (near) the whole summer gain, here from near the treeline in Alaska:
Results showed that greater wintertime C loss from forests could offset greater summertime C gain.
Further, there is a lot of fall shutdown and falling leaves of trees in other (NH) latitudes where there are few or no frost days, so that helps to spread the response over time...

That the response of decay is near the same as the NPP is a matter of availability of fast decaying material. Part of the decay is from sugars and proteins, which is fast, part is from cellulose and lignin, which is much slower and may need several years and part remains in the soils and compacts into peat or browncoal or ultimately coal.
The IPCC doesn't say that there is an exact balance between NPP and decay: until 1990 there was slightly more decay than NPP (about 0.5 GtC/yr), since then there is a growing ~1 GtC/year more NPP than decay. See:
http://www.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf

The CO2 emissions between latitudes 30° and 40° N are equivalent to around 14 ppm CO2, assuming that they remain stratified during the year, in the same way that seasonal photosynthetic variations are stratified.

Two comments on this: the human emissions maybe good for 14 ppmv/year in that latitude band (globally 4.5 ppmv), but as the emissions are spread over a year and atmospheric mixing between latitudes and altitudes is a matter of months, that is measurable at Barrow, Mauna Loa and other stations as a lag with altitude and a lag between the NH and the SH as the exchange of air between the NH and SH is limited to about 10% per year:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_trends_1995_2004.jpg
The CO2 changes in the biosphere are globally 90 GtC or 45 ppmv in and out, largely within 3-4 months in each direction, and mainly in the NH. That is about ten times larger over a much shorter time and largely cyclic compared to the rather flat increasing human emissions...

More coming later...

Ferdinand

Aug 18, 2013 at 7:02 PM | Unregistered CommenterFerdinand Engelbeen

More on part 1:

By the year 2000, atmospheric CO2 levels were rising at a rate of around 1.4ppm/yr or expressed as a percentage of atmospheric CO2 at 0.35%/yr. Assuming this CO2 resulted from the emissions due to the burning of fossil fuels it would be depleted in δ13C by −21.6‰.

You don't take into account the dilution of the human "fingerprint" by the exchanges with other reservoirs. Some 20% of all CO2 in the atmosphere is exchanged each year with the oceans and vegetation. That means that also some 20% of the "human" (low 13C) CO2 is exchanged with (13C richer) CO2 from other reservoirs. For the ocean surface and vegetation, much of the captured CO2 comes back the next season/year(s), but not so for the deep ocean exchanges. Anyway, the 13CO2 deficiency in the atmosphere is diluted over more reservoirs (vegetation and ocean surface) ànd is diluted with deep ocean waters from 1000 years ago... This allows us to calculate the deep ocean exchanges:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_zero.jpg

Nowhere within the climate science literature has anyone attempted an explanation for these measurements. There is not even a single reference to this uncomfortable anomaly in any IPCC Assessment Report to date.

Sorry, but that is basic knowledge for anybody involved in isotope exchanges over gas-liquid borders and back. It is explicitely mentioned in the work of Battle e.a. (your reference [5]). Here are the calculations:
http://dge.stanford.edu/SCOPE/SCOPE_16/SCOPE_16_1.5.05_Siegenthaler_249-257.pdf

in order to absorb a fixed percentage (25%) of the CO2 emitted. An even stranger concept is that the 50% of the CO2 that is retained in the atmosphere induces no further photosynthesis but simply resides there, inert for centuries, neither partaking in photosynthesis nor ocean dissolution.

As far as I know, the IPCC doesn't say that or imply what you say here. That seems to be your own interpretation of what the IPCC says...
- the biosphere doesn't absorb a fixed percentage of the human emissions. Battle and others showed that the whole biosphere was a net, small source of CO2 until 1990 and an increasing sink thereafter. Bender e.a. extended that to 2002, including years that vegetation was suddenly a source (the 1998 El Niño) within years of increasing sink capacity.
The remaining CO2 is taken away by the deep oceans (besides 10% in the ocean surface, that is a fixed percentage of the increase in the atmosphere). That is a differential pressure dependent process, hardly influenced by temperature but influenced by the total increase in the atmosphere, not by the yearly emissions. That the sum of these processes gives a remarkable constant ratio with the emissions is pure coincidence, partly because the emissions increased somewhat quadratic over time...

Further, your story about the reason that the oceans can't be cooled by the poles doesn't look very scientific to me. The cold sinking waters have little to do with the volume of ice at the poles but by radiative cooling of the surface waters and the increasing salt content when water freezes out the seasalts. Both increase the density of the remaining waters, which sink at a temperature of less than 0°C. Cold enough to maintain the low temperature of the deep oceans with that little heat coming from the mantle...

But I need to read further part 2 to see what your solution to that "problem" is...

Aug 18, 2013 at 8:17 PM | Unregistered CommenterFerdinand Engelbeen

Ferdinand

The IPCC line, I must say, describes quite clearly the consensus opinion voiced in almost every paper that I have read. It is however entirely inconsistent and irrational. Carbon isotope variations are only 1/6 of that which would be expected from human emissions. How do you explain the serious difference in isotope ratios between the mixed layer and atmosphere? As you rightly point out a significant % of CO2 is transferred between the two by natural diffusion. In such a scenario would you not expect those ratios to be similar. If as you say the biosphere is balanced with a zero net biome production, how can it be that some 25% of CO2 emissions are taken up by the biosphere. This implies that anthropogenic emissions are somehow promoting immediate and additional biospheric activity causing the biosphere to be no longer in equilibrium.

How is it possible to argue that at every point on the globe seasonal photosynthetic absorption is EXACTLY balanced by decomposition so that every year the cycle remains without bias. Photosynthesis and decomposition are entirely different biological mechanisms. There is absolutely no reason to believe that they have the same net magnitude over a year, not only one year but hundreds and thousands of years. What is the winter restoring CO2 source in the arctic circle at Alert and Barrow. It needs to be some 60ppm/yr, by far the highest flux in the globe at a time when everything is frozen solid. The existence of fossil fuel deposits and the more recent peat bogs are examples of a non zero net biome production. Why should we believe that it should be zero now when past evidence points to non zero?

I am sorry Ferdinand but the IPCC line stretches credibility just too far. A more consistent and rational approach is called for.

Aug 18, 2013 at 9:01 PM | Unregistered CommenterDavid Coe

David,

I haven't read paper 2 yet, but I want to react on what you wrote in a comment here:

My paper is based on the premise that the flow of CO2 across the thermocline and sea surface/atmosphere interface is proportional to the partial pressure differential across them. I have made one critical assumption that the deep ocean can be considered as a stable and infinite source of CO2.

Forget diffusion between the deep ocean and the ocean surface. The diffusion of CO2 within seawater is extremely slow. The only way to get it in or out the ocean surface out or in the atmosphere is with thorough mixing. That means that the ocean-air and reverse fluxes not only are dependent of the pCO2 difference but also of wind speed. No wind is equivalent to no exchange, even with pCO2 differences of 350 microatm.

That implies that there is no practical exchange of CO2 (and other stuff like nutritients) between the deep oceans and the surface layer besides downwelling and upwelling of ocean currents and the dropout of organic and inorganic rests of biolife from the surface layer into the deep oceans...

Aug 18, 2013 at 9:05 PM | Unregistered CommenterFerdinand Engelbeen

David,

Carbon isotope variations are only 1/6 of that which would be expected from human emissions. How do you explain the serious difference in isotope ratios between the mixed layer and atmosphere?

The isotopic difference between mixed layer and atmosphere existed already from long before human emissions. See the difference in d13C for CO2 in atmosphere - firn - ice core bubbles and what coralline sponges show over the past 600 years:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.gif
Corraline sponges build their skeleton from CO2 in seawater without altering the isotopic composition.

The change in composition is a matter of differences in diffusion/evaporation speed between heavier and lighter isotopes. That is so for carbon isotopes, for oxygen isotopes or any other isotopes. The O2 isotope ratio changes in water molecules can be used to calculate the temperature of the ocean waters where the vapour originated that formed the snow/ice of the Antarctic (and Greenland) ice caps.

Thus there is nothing special in the difference in 13C/12C ratio of the ocean surface layer and the atmosphere. Emissions from the ocean surface will give a drop of ~10 per mil in d13C in the atmosphere, the reverse will give a drop of ~2 per mil in the oceans. The average (if both fluxes are balanced) gives a drop of ~8 per mil between ocean surface and atmosphere.

Thus the ocean surface at ~ +1.5 per mil and the atmosphere at ~ -6.4 per mil were about in equilibrium in pre-industrial times.

The decrease in 13C from human emissions is partly dilluted by the redistribution of low 13CO2 over the other reservoirs but mostly by the deep oceans: what goes into the deep is today's isotopic composition. What comes out is the composition of ~1000 years ago, long before the current human emissions...

Aug 18, 2013 at 9:38 PM | Unregistered CommenterFerdinand Engelbeen

David -
One invaluable outcome of your presentation is your drawing of attention to the relationship between CO2 emission rate and air concentration. The former (IEA data) is less uniform than the latter (ex NOAA Mauna Loa, seasonally corrected) - as your plot indicates.
If the IPCC description of CO2 emissions is adequate, the year-on-year fluctuations in emission rate should produce lagged and smoothed changes in concentration. These are not observable in the Mauna Loa record, either in annual (adjusted) or seasonal maxima & minima (I checked).
Assuming the IEA data is consistent (I've no reason to think otherwise) -
**year-on-year fluctuations in emission rate don't propagate to Mauna Loa, whereas shorter seasonal natural variation from comparable latitudes does**.

I'm at a loss to explain this (as also, I guess, the IPCC). Bright ideas, anyone?

Aug 18, 2013 at 10:10 PM | Unregistered CommenterPeter Shaw

If the IPCC description of CO2 emissions is adequate, the year-on-year fluctuations in emission rate should produce lagged and smoothed changes in concentration. These are not observable in the Mauna Loa record, either in annual (adjusted) or seasonal maxima & minima (I checked).
Assuming the IEA data is consistent (I've no reason to think otherwise) -
**year-on-year fluctuations in emission rate don't propagate to Mauna Loa, whereas shorter seasonal natural variation from comparable latitudes does**.

I'm at a loss to explain this (as also, I guess, the IPCC). Bright ideas, anyone?
Aug 18, 2013 at 10:10 PM |Peter Shaw

Man's emissions have no impact on the atmosphere? Salby is right? http://www.youtube.com/watch?v=YrI03ts--9I

Aug 19, 2013 at 7:52 AM | Unregistered CommenterBrian H

Peter Shaw:

the year-on-year fluctuations in emission rate should produce lagged and smoothed changes in concentration.

The year-on-year fluctuations in emission rate are so small that they can't be detected within the accuracy of the Mauna Loa rate of change, but the total accumulated emissions are followed by the increase in CO2 levels at an incredible constant rate:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2.jpg
The wobbles in the year-on-year increase rate are mainly caused by temperature variability, which influences the sink rate of CO2 in different sinks (mainly vegetation):
http://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_em2.jpg
The largest changes were with the 1992 Pinatubo eruption (more uptake) and the 1998 El Niño (less uptake).

Aug 19, 2013 at 8:53 AM | Unregistered CommenterFerdinand Engelbeen

Peter Shaw

"**year-on-year fluctuations in emission rate don't propagate to Mauna Loa, whereas shorter seasonal natural variation from comparable latitudes does**.

I'm at a loss to explain this (as also, I guess, the IPCC). Bright ideas, anyone?"


The IPCC cannot explain this simply because their model does not reflect reality. The beauty of the ocean control theory is that it is based upon the very simple premise that CO2 transfer is governed solely by partial pressure differentials. This leads to a set of simple equations demonstrating a damped control system. The test for its success is that the equations can be used to calculate very single observation set with extremely good agreement with observation, including the example you have quoted above. The IPCC don't do equations, they prefer qualitative hand waving.

Aug 19, 2013 at 9:06 AM | Unregistered CommenterDavid Coe

Ferdinand

I have attempted to devise a set of equations which describe in some detail the mechanism for CO2 exchange between deep ocean, sea surface mixed layer and atmosphere. Those equations predict with some accuracy the observed effects of seasonal variation of CO2 and O2 in both northern and southern hemispheres, interannual variations of CO2, noted originally by Roy Spencer and more recently by Murry Salby, reducing atmospheric O2 levels, reducing isotope ratios within both the mixed layer and atmosphere in addition to predicting the stark difference in levels between those two.

In short I have shown you my equations, now please show me yours. I am a physicist of the old school. If I cannot describe the system mathematically I do not understand it. I suggest that climate science would do well to follow that example.

Aug 19, 2013 at 2:45 PM | Unregistered CommenterDavid Coe

David, before going into equations, one need to agree on some basic principles. If your or my interpretation of what happens in nature is different, one can "prove" anything that seems to fit reality...

At this moment, I am looking at paper 2. Here already a few remarks:

The IPCC claim very specifically that 50% of anthropogenic CO2 emissions are simply accumulating in the atmosphere.

You are misinterpretating what the IPCC says: currently indeed about halve the human emissions (as mass, not the original man-made emissions) remain in the atmosphere. That is a matter of total accumulated pressure difference with the oceans (and plant alveoles), not from the emissions over one or another year. That fits the increase in the atmosphere far more perfectly than the emissions over one year:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_1960_cur.jpg
That is for two stations: Mauna Loa and the South Pole. Notice the difference in accumulation between these two, which shows that the source of the increase is in the NH.

The usual definition of Henry’s law states that the partial pressure of a gas in solution is proportional to its dissolved concentration and the proportionality constant is Henry’s constant.

That is right, but be careful: Henry's law is about a gas in solution, that is free CO2. Not about bicarbonate or carbonate ions, which represent the bulk of all carbon in the oceans. The 50 times more carbon in the oceans than in the atmosphere in fact is only halve the CO2 of the atmosphere, as free CO2 (gas) is less than 1% of all carbon in the oceans... Thus it may be a constant source of CO2 or not, depending of the pCO2 differences with the atmosphere.

It is often argued that the complex chemistry involved in the dissolution of CO2 in water invalidates the application of Henry’s Law.

Nobody disputes Henry's law, but you use that law for all carbon forms present in water. That is not what Henry's law says. Bicarbonate and carbonate ions are not CO2 and have nothing to do with Henry's law for CO2 as gas in solution.

Then your model:

In the absence of any external CO2 fluxes the partial pressure of CO2 in both the atmosphere and sea surface would be the same as that of the deep ocean, and because of the much higher concentration of CO2 in the deep ocean we would witness significantly higher atmospheric and sea surface CO2 concentrations..

In pre-industrial times, the different fluxes and levels were more or less in (dynamic) equilibrium. Despite that, the CO2 levels in ocean surface (not so much) and in the atmosphere were (much) lower than today...

What your model implies is that there is a continuous stream of CO2 from the (deep) oceans via the ocean surface and further via the atmosphere into vegetation where it is more or less permanently stored. But there is a small problem: the current uptake by the biosphere is ~1 GtC/year. Human emissions are ~9 GtC/year. Thus the current biosphere is only a small sink for CO2. Does that mean that the pre-industrial releases from the (deep) oceans were (far) less than 1 GtC/yr? The extra uptake by vegetation is a direct result of the extra pCO2 in the atmosphere, no matter its origin...

There is simply no question of anthropogenic CO2 emissions being partitioned between the oceans, biosphere and atmosphere.

Again the same problem: if the biosphere is only a sink for 1 GtC/yr and the atmosphere increases with 4 GtC/yr, where does the remaining 4 GtC/yr from the emissions go?

As a rough first estimate let us assume that net biospheric CO2 absorptive fluxes are
equivalent to a reduction in atmospheric CO2 levels of 20ppm/yr (20μatmos/yr).

Sorry, but this is way out of reality. Here you are mixing the observed seasonal back and forth fluxes with the NET removal of CO2 by the biosphere. These have nothing to do with each other. The net removal of CO2 is the difference between influx and outflux. For the whole biosphere (landplants + seaplants + microbes + insects + animals) that is a net removal of ~1 GtC/yr (0.5 ppmv/yr). Not 20 GtC/yr (20 land + 20 sea microatm/yr):
http://www.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf

A value for τ1 of 93 years is necessary to produce the agreement with observation as shown
in Figure 2.4.

Sorry again, but this is curve fitting, not based on any known or unknown diffusion transfer rate between the deep oceans and the mixed layer. As said before, diffusion of CO2 in water is extremely slow. The only real, measurable transfers (via tracers like CFC's, the 14CO2 bomb spike, etc.) are from deep ocean - surface currents.

Enough for today. It seems to me that many of the assumptions you have made for your model are not based on reality...

Aug 19, 2013 at 8:24 PM | Unregistered CommenterFerdinand Engelbeen

Ferdinand

I repeat. Show me your equations instead of waffle wrapped up in complexity in such a way that no-one can either deny or substantiate your claims. Nature obeys the laws of physics which in all disciplines of science other than climate science are represented mathematically. If you cannot represent your arguments quantitatively and hence mathematically then you do not understand your subject.

The crux of the issue is that atmospheric CO2 levels are increasing linearly with the rate of emission of CO2. It can't be so difficult to explain that in a simple and consistent manner. Can it?

Aug 19, 2013 at 9:48 PM | Unregistered CommenterDavid Coe

PostPost a New Comment

Enter your information below to add a new comment.

My response is on my own website »
Author Email (optional):
Author URL (optional):
Post:
 
Some HTML allowed: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <code> <em> <i> <strike> <strong>