Tuesday
Apr142015
by 
Bishop Hill
Bishop Hill The Salby lecture
Apr 14, 2015 Climate: Sceptics Climate: carbon budget Murry Salby's recent lecture in London can now be seen on YouTube.
Apr 14, 2015 Climate: Sceptics Climate: carbon budget
Reader Comments (179)
Apr 20, 2015 at 5:51 PM | kim
"...isn't there a way for nature to be a net sink and for the warming to be a cause of the rise?"
Yes. Let me give an analogy. Suppose you have one of those lavatory sinks with separate hot and cold faucets. You partially obstruct the drain and turn the cold water on to a high rate of inflow, until you establish an equilibrium level of water in the sink.
Now, you turn on the hot water faucet at a trickle. Ten minutes later, you observe the water level has risen 2 cm, and you note that the sum total of the trickle of hot water would have been enough that, had it been completely retained, would have raised the level 4 cm. Do you thereby conclude that the trickle of hot water was what produced the increase in the level?
Hardly. I have not given you enough information. For one thing, I have not specified whether the cold water faucet has also been turned higher, and I have not stipulated that the drain was not further blocked. We have a torrent of cold water coming in. Even a slight drain blockage will cause the water level to rise.
One can write the equation describing the level as
dL/dt = -L/tau + H + C
L = level of the water
H = hot water trickle rate (known and constant after turning on)
C = cold water inflow
The -L/tau term describes the outflow from the drain, which is proportional to the level of the water in the column above it. The time constant "tau" quantifies the degree of drain blockage.
Before the hot water is turned on, the equilibrium level reached will be
L = tau1*C1
where C1 is the amount flowing in before, and tau1 quantifies its rate of removal.
After it is turned on, we will reach an equilibrium of
L = tau2*(H + C2)
We only have one observational equation, which is
tau2*H + (tau2*C2 - tau1*C1) = 0.5*H*t
where t is the time since hot water turn-on, but several unknowns. How can we tell if H is responsible for the rise if we do not know tau2? In particular, if tau2 is less than 0.5*t, then H cannot be completely responsible for the observed rise.
Indeed, as tau2 becomes small (drain opened wide), then (tau2*C2 - tau1*C1), whatever it may be, must become responsible for essentially the entire observed rise. The fact that H*t is greater than 0.5*H*t is a trivial fact. It does not, in any way, determine attribution for the observed rise in the water level.
That, in analogy, is the "mass balance" argument: H*t is greater than 0.5*H*t. It is trivial. It is not enough to make a conclusion. It is a very poorly reasoned argument.
Please note that the sink rate, L/tau = H + C2, is always greater than the natural input rate C2. That is because the sink rate is influenced by the input H. So, again, the argument that nature is a net sink is trivial, and has no bearing on the question of attribution.
Thanks, Bart. It's funny, peculiar, that I can intuit it better than I can follow the math. It's all very perplexing. Do you think, as is suggested at Watts Up, that the new satellite may help settle this in just a few short years?
=============
Settle it? Only if the data cannot be tortured in some way to allow the establishment to maintain in some fashion that they were right all along, and I think the chance of that is slim. I anticipate a theory so convoluted and ridiculous that it defies refutation, because peoples' eyes will simply glaze over at the prospect of untangling it all.
Bart,
Let us begin with the first blunders (the rest is for tomorrow, it is getting late here...):
It is higher in the Southern Hemisphere than the Northern.
Which shows a picture of six weeks of satellite data in late late fall when NH CO2 levels are minimal.
Years of data show that the SH lags the NH CO2 data with 1-2 years:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_trends_1995_2004.jpg
There is more CO2 in the Northern Hemisphere summer than in the winter.
Seems rather reverse to me:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/seasonal_CO2_d13C_MLO_BRW.jpg
The differences in the SH are much smaller, but still less CO2 in SH summer than in SH winter.
If the oceans were the source, the differences in the SH would be largest and the δ13C changes would parallel the CO2 changes: both would increase over time.
What is observed is that the CO2 increase is first in the NH and that the seasonal changes are dominated by vegetation, as δ13C and CO2 changes are opposite to each other. But vegetation is not the cause of the increase, it is a net, increasing sink for CO2, as can be deduced from the oxygen balance. The earth is greening.
The δ13C level reduces over time as result of fossil fuel burning, again in the NH first:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/d13c_trends.jpg
Vegetation is not the cause of the increase, it is a proven sink
Oceans are not the cause of the increase, as most oceans are in the SH, but the cause is in the NH and the higher δ13C level excludes the oceans as main source.
Human emissions fit all observations...
"Years of data show that the SH lags the NH CO2 data with 1-2 years:"
All this shows is slightly different levels at a few different spots on the globe measured independently. There is nothing to indicate whether there is a transmission lag, because there is barely any deviation from a straight line, and no reason that the levels should necessarily be equal.
"Seems rather reverse to me:"
The plot shows peaking at mid-year. That is Northern Hemisphere summer. Frankly, I don't know why Eli cares about the annual variation, and what the point is with regard to long term CO2 evolution, but the fact remains that what he claimed was untrue.
"If the oceans were the source, the differences in the SH would be largest and the δ13C changes would parallel the CO2 changes: both would increase over time."
You think so, but that does not mean that they necessarily would. This is one of those things you keep presenting as evidence which is, in fact, merely an interpretation. It has not been verified. It has not been proven. It is merely what you think should happen.
Many things are like this in science. It seems that the speed of light one measures should depend on the velocity of the source, but it doesn't. Prior to the discovery of nuclear fusion, it seemed that the Sun should burn up its fuel within a few thousand years, but it won't. It seems that the shape and size of a person's head should correlate to intelligence, but it doesn't. Google "theories that were wrong", and you will find many examples of things that seemed reasonable to people at the time which turned out to be completely wrong.
You can't just toss off something that you think should be the way something works, and proclaim it proof. That is not how the scientific method works.
"Human emissions fit all observations..."
It doesn't fit this.
Bart:
there is no significant reduction within the timeframe of observation
Come on Bart, that is elementary process dynamics: as long as the total increase is above the equilibrium, nature is a net sink for CO2, whatever the cause of the increase. With or without human emissions.
You can't have it both ways: either human emissions are the cause of the increase and nature still is a net sink long after human emissions stopped, or nature is the cause of the increase and still must be a much larger net sink as the increase is less than the human emissions alone. In the latter case it takes some strange reasoning to hide the human emissions somewhere, somehow...
You call that stupid, but I want to see where the human emissions go if they are not the cause of the increase in the atmosphere and how that can be measured in any observation. Until now, your theory violates all observations...
It isn't static. Every second of every day, new CO2 is coming in from the depths. A like amount has to be channeled back into the depths, or it will accumulate in the surface system.
Doesn't matter at all: equilibrium pCO2 of seawater is measured by constantly spraying seawater in a container where a small stream of air passes and CO2 is measured in the outgoing air flux. That is "dynamic" with a decay rate of CO2 levels towards the equilibrium in a matter of seconds.
The deep oceans do the same at a much slower rate. If the temperature increases with 1°C at the upwelling side, the local pCO2 increases with 8 μatm at both source and sink areas. That makes that the influx increases with less than 3% and the outflux decreases with less than 3% (both are in direct ratio with the pressure difference between ocean and atmosphere). That makes that the CO2 levels in the atmosphere increase, reducing the influx and increasing the outflux until 8 ppmv (=~μatm) extra in the atmosphere is reached. At that moment the original CO2 pressure difference and thus original in and out fluxes are restored at exactly the same 8 ppmv increase as for a static equilibrium...
That will take a few years, but the time needed doesn't change the equilibrium between atmosphere and oceans.
About the Sky Dragons: some projection of your own behavior on others? You haven't accepted one single observation of the many which refute your own theory...
Bart,
You claimed that the increase is from the SH oceans, where most of the deep oceans is reaching the warm surface. Your answer is just avoiding what is observed. The measured increase per year is ~2 ppmv. The lag is 1-2 years. Even if the absolute difference is small, that is significant.
All stations (over 70 today) that measure CO2 levels in the atmosphere show that the SH lags the NH increase with 1-2 years. Thus the source of the extra CO2 is in the NH, not in the SH, opposite to your theory.
The seasonal CO2 levels at MLO peaks in May, as far as I know still in spring, and MLO at 3400 meter lags sealevel CO2 changes with ~1 month. New growth of leaves does override the decay of old organic debris in April until late fall. Vegetation changes in the NH are dominant for the seasonal variation.
But agreed, that isn't important for the long term trend.
Neither is the 1-3 years variation, as that also is caused by the influence of temperature variations on (tropical) vegetation, opposite to seasonal changes: higher temperatures give more temporarily increase in the atmosphere
The long term trend is NOT caused by vegetation, as vegetation is a net, growing sink for CO2...
You think so, but that does not mean that they necessarily would. This is one of those things you keep presenting as evidence which is, in fact, merely an interpretation.
Bart, your theory of temperature as driver for the increase is surely only interpretation, as there is no connection at all between the cause of the variability (which is temperature variability) and the cause of the overall increase in the atmosphere.
All kinds of observations may be a matter of interpretation, but if your theory violates every single current observation then I think it is time to revise your theory...
Bart,
About your sink rate example, a few remarks:
Your example doesn't completely fit with what happens with CO2 in the atmosphere. Here the differences:
tau1 depends of temperature: short term (1-3 years): 4-5 ppmv/°C very long term (multi decades to multi millennia): ~8 ppmv/°C. Thus tau1 is a few years for short living (vegetation) processes to many hundreds of years for long term (ocean) processes.
tau2 depends of the pressure difference between what is in the atmosphere and the equilibrium as dictated by temperature: currently 110 ppmv / 2.15 ppmv/year = 51.3 years.
Thus tau1 and tau2 are known for CO2 over all times in the past 800,000 years...
Further your term 0.5*H*t in the formula tau2*H + (tau2*C2 - tau1*C1) = 0.5*H*t is just coincidence. There is no reason that the factor must be 0.5. It is 0.1 in one year and 0.9 in the next year, due to the natural variability in sink rate. That is the year by year variability in C1 (and thus also of C2). Thus even if the net result is 0.1*H*t, then the term (tau2*C2 - tau1*C1) still is negative and smaller than tau2*H and H still is fully responsible for the increase, while all variability is caused by (the temperature influence on) C1.
"The lag is 1-2 years."
Show meaningful evidence to back this up. You have offered none.
"Thus the source of the extra CO2 is in the NH, not in the SH, opposite to your theory."
Even if it were true, that is just how the mixing dynamics work out. It is a slow leaching of CO2 into the atmosphere, which is rapidly mixed in the atmosphere.
"...your theory of temperature as driver for the increase is surely only interpretation..."
No, it is unique. For there to be a separated response such as you claim, there would have to be a phase distortion. There isn't any observable phase distortion.
"...as there is no connection at all between the cause of the variability (which is temperature variability) and the cause of the overall increase in the atmosphere."
That is how you want it to be, but the lack of phase distortion says you are wrong.
"tau1 depends of..."
No, in my example, tau1 simply quantifies the drainage in the first part, and tau2 in the second.
The point of the analogy is that the sink rate being greater than the cold water input rate is entirely dependent on how open the drain is. The fact that the sink activity is greater than the input is a trivial tautology - as long as any hot water is being input, the inequality will hold. It does not determine attribution.
The example is not 1-to-1 with the CO2 dynamics of the Earth. It's purpose is merely to show the general failure of this pseudo-mass balance argument you keep harping on to have any applicability to the attribution problem.
It all depends on the power of the sinks, Ferdinand. Active sinks can take out essentially everything we put in, leaving up to zero residual. Beyond a particular level of sink activity, it becomes impossible for the human input to be the driving force, even as your pitiful mass balance argument keeps claiming otherwise.
It is a very stupid and naive argument, which is why you only see it being made by the SkS kids, and not any serious scientist (and, if you find a "scientist" claiming it, then you have unmasked him as not serious, because it is not even a close call).
"Thus even if the net result is 0.1*H*t, then the term (tau2*C2 - tau1*C1) still is negative and smaller than tau2*H and H still is fully responsible for the increase, while all variability is caused by (the temperature influence on) C1."
Not if tau2 is less than 0.1*t. Whatever you choose the fraction to be, 0.1 or 0.5 or anything less than unity, the fact that it is less than unity has no bearing on the attribution question. There is always a tau2 which would make it impossible for the rise to be significantly due to H, and the slack has to be taken up by the cold water input.
Ferdinand, it has become apparent by now that you just don't have the maths, and you really should not be weighing in on the topic at all. You are spreading disinformation based on your own limitations. I am sorry to say it, because I do believe you are a genuinely nice guy, even as you probably suspect I am a nasty one. But, I have to call things as I see them. Your arguments are unsophisticated, and lacking in rigor.
It all depends on the power of the sinks. And, the temperature relationship tells us the Earth's CO2 sinks are powerful enough that human inputs are not making a significant impact.
And, that is going to be my last word for now. I have other things to do, and continuing to argue the same elementary points over and over again is very taxing on my emotional state.
I feel a little like Josh's image of a roof solar panel fire; too much direct high voltage upstairs. Well, tally ho ho ho, OCO2, oh.
====================
Bart,
You are a smart guy and your math is far superior than mine. But you have somewhere a blind spot, which I have encountered with many brilliant persons: once they have made up their mind/theory, everything that refutes that theory is rejected. Like this one:
Show meaningful evidence to back this up. You have offered none.
I did give the evidence that CO2 measurements in the SH lag the NH with 1-2 years, but you just don't accept it and don't give any counterargument.
I did prove that the variability of the CO2 rate of change and the trend in rate of change are from different processes, but you just don't accept it and don't give any counterargument.
I did show (and Paul_K proved it mathematically) that any sinusoid of any frequency can be combined with a straight increase without phase distortion, if the overall decay rate is slow enough, but you just don't accept it and don't give any counterargument.
I did prove that the only way that human emissions can be suppressed by the natural cycle is if the natural cycle increased a fourfold in the past 55 years - for which is no sign - as human emissions, the increase rate in the atmosphere and the net sink rate did, but you just don't accept it and did give a calculation that violates the equality of CO2 whatever its origin.
Last but not least, as is said by much smarter people: one observation can destroy the nicest theory. In this case, your theory violates all known observations, but you don't accept any observation that refutes your theory...
Thus I think that we will meet again next time...
One addition:
It all depends on the power of the sinks. And, the temperature relationship tells us the Earth's CO2 sinks are powerful enough that human inputs are not making a significant impact.
The "power" of temperature on CO2 levels on short term (seasonal, 2-3 years, vegetation dominant) is 4-5 ppmv/°C for (very) long changes it is ~8 ppmv/°C (oceans dominant).
Meet the "powerful" impact of temperature on the increase of CO2 in the atmosphere at WfT...
"...once they have made up their mind/theory, everything that refutes that theory is rejected..."
Pot, meet kettle.
"I did give the evidence that CO2 measurements in the SH lag the NH with 1-2 years..."
No you didn't. You just showed some straight lines with different offsets taken in different parts of the world with different methods, personnel, and equipment.
"I did show (and Paul_K proved it mathematically) that any sinusoid of any frequency can be combined with a straight increase without phase distortion..."
He didn't, and I'm quite sure he would not appreciate your twisting of his words to suit your agenda.
But, aside from that, no, you still do not get the problem.
Temperature is composed of a trend plus variation.
dCO2/dt reacts directly to that temperature series.
The variation is passed through directly through to the dCO2/dt.
It is your contention that the trend is not.
In order for the trend NOT to go through, it must be filtered out by some natural process.
That filtering process would lead to readily observable phase distortion in the dCO2/dt record relative to the temperature record.
There is no observable phase distortion.
Therefore, the trend in temperatures is causing the trend in dCO2/dt.
There is no way around it.
"In this case, your theory violates all known observations, but you don't accept any observation that refutes your theory..."
There is no violation of any observation. There is only a disagreement with your interpretation of the observations.
On the other side, your hypothesis violates the fact that the trend in temperature is causing the trend in dCO2/dt. That destroys your hypothesis.
"One addition:"
It is an integral relationship, not direct proportionality.
Bart,
You have not given a shred of evidence that the trend must be caused by temperature or the variability would show a phase distortion. I have added a sinusoid series of three different frequencies to a straight increase and through an integrating function: no phase distortion at all, only a 90 deg. shift:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/matlab_sin_t_co2_slope.jpg
Only - as expected - a decrease in amplitude for the higher frequencies.
Paul_K wrote literally:
I have used two sine cycles of different amplitude and frequency superimposed on a straight line. You can see the temperature input on the graph.
http://img837.imageshack.us/img837/8824/a7uw.jpg
(ignore any safety warning)
Further:
Note the near perfect match between dCO2/dt and Temperature.
and
The output response is phase-shifted relative to any sinusoidal temperature input; as response times get larger, the phase shift asymptotes to a shift of exactly pi/2. Hence, putting any realistic (i.e. long) transient response in place brings temperature exactly into phase with dCO2/dt. All that is required is that ocean equilibration for a change in temperature is a longer term process than the longest periodicity of the temperature cycles we are considering here. This seems to me to be a very safe assumption.
My interpretation of what Paul_K says is that there is no phase distortion if the response time is slow enough.
That is the case: all variability of dCO2/dt levels off in 2-3 years, while the shift in temperature caused equilibrium between ocean surface and atmosphere has a half life of 1-3 years, thus for a five times decay is 5-15 years and the equilibrium with the deep oceans needs decades.
Your interpretation may be different, as you assume that the response time is very fast, thus there must be phase distortion if temperature is not responsible for the trend.
As it is proven that the variability is caused by the rapid response of vegetation to temperature variations, but the trend is not from vegetation changes, there is no reason at all to assume that the response time of the trend is by a rapid process.
In addition:
T is directly related to the CO2 variability and increase, with a 90° lag of CO2 changes, but that is not more than 4-5 ppmv/°C short term to 8 ppmv/°C long term. Thus the whole trend of T in the past 55 years is good for 5 ppmv increase in the atmosphere. That is all.
T is not responsible for the variability and trend in the derivative, but dT/dt is: again with a 90° lag for dCO2/dt and zero slope and a very small offset of 0.01°C/year, corresponding to a very small CO2 rate of change of 0.08 ppmv/year.
Bart,
As an illustration of your behavior:
Your assumption of the natural increase is that the ocean upwelling (mainly in the equatorial SH) is the cause of the increase. That would be easy to prove by providing a few CO2 stations which show that the SH is leading in CO2 increase. None is provided, only theory, not a shred of evidence.
When I provide the evidence that the NH is leading by looking at a few stations, you just discard the evidence, because that are only a few stations and some fuss about people and measurements.
If you had looked longer than a few seconds at the way CO2 is distributed and measured over the globe, you should have known that:
- There are some 70 stations distributed over the oceans and coastal places (where there is least local contamination).
- Local CO2 levels can be measured with an accuracy better than 0.2 ppmv.
- CO2 levels worldwide (except within a few hundred meters height over land) don't differ more than 2% full scale between stations at any moment for uncontaminated data. CO2 is well mixed (as 20% of all CO2 is going in and out over the seasons, a 2% change is small).
- Most variability is seasonal in the NH.
- The difference between stations for yearly averages all over the globe is less than 5 ppmv.
- The increase is first in the NH for all stations and the SH follows with a lag. The reason is that the ITCZ near the equator hinders the exchange of air masses between NH and SH (including CO2) with only some 10% of total air exchanged (thus also 10% of the CO2 difference).
The balance is that with high confidence, the increase of CO2 starts in the NH, whatever the source, not in the SH oceans.
"I have added a sinusoid series of three different frequencies to a straight increase and through an integrating function: no phase distortion at all, only a 90 deg. shift:"
That is NOT AT ALL what is happening, Ferdinand. You've got to create a model which is an actual model of the actual system under study.
Take a sinusoid and a trend. Input this signal into a high pass filter with corner frequency near that of the sinusoid. The trend will be removed, but you will see phase distortion of the sinusoid.
That is the system description here. Temperature is composed of a broad spectrum of variational terms, and a trend. It is driving dCO2/dt. In order for the trend in temperature NOT to produce a trend in dCO2/dt, it must be filtered out. That filtering will produce phase distortion.
"My interpretation of what Paul_K says is that there is no phase distortion if the response time is slow enough."
And, the ultimate slow response time is a direct integration. Paul_K was basically saying that he could get rid of the trend by imposing a high pass filter with a very low frequency cutoff. But, this has no bearing on the question. Yes, you could do that, if the frequency content were limited so that no variation occurred near or below the high pass cutoff frequency, and the cutoff were placed in that range. But,
A) The signal is very broadband, and there is no low frequency limit to the variational spectrum within the observation window.
B) The high pass cutoff would,at the very least, have to be much lower than the frequency associated with the ~60 year periodicity in the temperature data, or that component, at the very least, would have its phase distorted. So, we're talking a cutoff at a frequency associated with a perhaps 600 year periodicity. Such a cutoff would have no observable effect on the data set we have. That data set is well modeled by
dCO2/dt = k*(T - T0)
and the trend in temperature, within the observation window, is causing the trend in dCO2/dt.
"As it is proven that the variability is caused by the..."
It is by no means proven at all. The lack of phase distortion contradicts it.
"T is directly related to the CO2 variability and increase, with a 90° lag of CO2 changes, but that is not more than 4-5 ppmv/°C short term to 8 ppmv/°C long term."
If the lag is 90°, then the model is an integrator, and the sensitivity is in ppmv/°C/unit-of-time. As it accumulates over time, its impact is large.
"That would be easy to prove by providing a few CO2 stations which show that the SH is leading in CO2 increase. None is provided, only theory, not a shred of evidence."
But, it is not disproved by a putative lack of that.
"When I provide the evidence that the NH is leading by looking at a few stations, you just discard the evidence, because that are only a few stations and some fuss about people and measurements."
Yes, I demand a proper scientific experiment which produces conclusive results. Guess I'm just funny that way.
Diffusion process are very complicated, and not at all amenable to intuitive speculation on how they might or might unfold. What you think ought to happen is not at all guaranteed to be that which does.
But, we do not need to know at this point of the game. There is no doubt that the trend in temperatures causes the trend in dCO2/dt. There is also a trend in emissions, but little to no room for it. Therefore, human emissions are not the most significant driver of atmospheric CO2.
Take it as established that human emissions are not the driving force, then start speculating on how it evolves in the system. You will be able to find explanations for all your objections. You've gone the other way, and assumed it is not. Then, finding specific results which agree with your intuition, you have pronounced the problem resolved. But, this is confirmation bias on your part. Complex systems are <complex. They can evolve in surprising ways. If you start with the wrong premise, it is easy to lead yourself astray.
Allow the Bunny to go a bit further, by tracing CO2 packets at individual stations, it is possible to follow the bouncing packet and trace where the CO2 is emitted and where it is deposited. This has been done. The oceans are sinks for CO2 from fossil fuel burning. If course, Bart will now go Lalalalala
Best
Eli
If it had been done, Eli, then why did they launch OCO2? What would be the point, if you already know the answer?
In fact, it hasn't been done. It has only been inferred by first assuming that the rise is of human origin, and then working out tidy little sums based on that assumption. It is a circular exercise, which unsurprisingly leads one right back to where one started.
"The first principle is that you must not fool yourself and you are the easiest person to fool." - Richard P. Feynman
Bart,
Your essential error is here:
Temperature is composed of a broad spectrum of variational terms, and a trend. It is driving dCO2/dt.
Temperature is NOT driving dCO2/dt, it is driving CO2 with 4-5 ppmv/K for the short term variability and 8 ppmv/K for (very) long term changes. The integration of T to CO2 is towards a new equilibrium, thus going to zero over time. It doesn't matter if the time constant is seconds (by spraying seawater into a small air flow) or hundreds of years as is the case for the deep oceans - atmosphere equilibrium over the ice ages.
dT/dt is driving dCO2/dt, it has similar variability, only shifted pi/2 back in time for all frequencies. It has zero trend, thus no measurable influence on the trend of dCO2/dt and a small offset of 0.01°C which gives a small offset of 0.08 ppmv in dCO2/dt. That is all:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_co2_der.png
But, it is not disproved by a putative lack of that.
Bart if ALL available data of CO2 measurements at some 70 stations for every year since they were established show that the CO2 in the NH is increasing faster than in the SH, how many more series do you need to convince you that the source of the extra CO2 is in the NH?
Take it as established that human emissions are not the driving force, then start speculating on how it evolves in the system. You will be able to find explanations for all your objections.
In my working life as process engineer, I was extremely good in detecting the source of problems by starting at the other side: not looking at the possibilities, but by eliminating the impossibilities, which was often a much faster way to isolate the remaining cause...
If some natural source would be the cause of the CO2 increase, it has to fulfill all observations.
- An extra source out of vegetation violates the oxygen balance: the whole biosphere is a net sink for CO2.
- An extra source from the oceans violates the δ13C balance: that would increase the δ13C level in the atmosphere while we see a firm decline in ratio with human emissions.
Thus neither vegetation, nor the oceans are the cause of the increase in the atmosphere.
As all other possible sources are either too small or too slow and also would violate the δ13C balance, there is only one important source left...
Bart,
Let us expand your lavatory source/sink example further with what is known in the real world.
Between [ ] is the real life equivalent for CO2 in the atmosphere.
- We start with a cold water equilibrium at ~750 cm3 (0.75 liter) of water in the lavatory (for a cubic lavatory, that equals height/pressure changes).
- We add warm water and measure a small increase in the lavatory.
Without further information it is impossible to attribute the increase to the warm water input, as the cold water input may have increased at the same time.
But there is a lot of extra information available:
- The input of hot water is measured and starts at 0.1 liter/minute and is gradually increased to 0.4 liter/minute.
- The resulting volume in the lavatory at equilibrium was 760 cm3 and 790 cm3.
That gives that only if the cold water also increased a 4-fold the cause of the increase is not distinguishable, in all other cases, the increase is from the warm water influx only.
Thus still a (small) possibility that the cold water inlet is the main cause of the increase.
But there is even more information:
- There are several estimates of the residence time, based on different observations. These show a residence time of about 5 minutes for all water in the lavatory [for CO2 in the atmosphere: http://www.co2web.info/ESEF3VO2.htm].
That makes that a rough estimate for the cold water input alone is 750 cm3 / 5 min = 150 cm3/min
- Moreover, the residence time estimates after opening the warm water faucet did lengthen somewhat, which indicates little change in the cold water flow in an increasing volume.
- There is a thermometer [δ13C levels] in the lavatory which indicates that the temperature increase exactly follows the warm water input. If the cold water inlet also increased, there would be less or no increase in temperature, or even cooling.
Taking all information together, the whole increase in volume (and temperature) is caused by the additional warm water inlet...
Well, they could've had a whole year of OCO2 data well before the Paris talks. Will they?
===================
Since I believe the rise in CO2 is a good thing with its great greening and gentle warming, and further believe it will be so recognized someday, I'd like for man to be able to take the credit for it. We'll know in a few years if this is just another anthropocentric conceit.
=======================
Better resolution both in time and position, real time measurements of CO2 emissions and column depth coordinated with measurements of other climate parameters as part of the A Train, and more.
C'mon, you need a reboot.
"Temperature is NOT driving dCO2/dt, it is driving CO2 with 4-5 ppmv/K for the short term variability and 8 ppmv/K for (very) long term changes."
This is getting ridiculous. That's just delusional, Ferdinand. The relationship is right here.
"That gives that only if the cold water also increased a 4-fold the cause of the increase is not distinguishable, in all other cases, the increase is from the warm water influx only."
This, too. Ridiculous. You're still claiming you can uniquely solve for two variables with only one equation. No, Ferdinand, you cannot. Not in this universe.
"There are several estimates of the residence time, based on different observations. These show a residence time..."
Estimates aren't just sent from heaven, Ferdinand. They have to be mathematically calculated, too, from the same available information. Using an estimate based on an assumption to prove the assumption is circular logic.
"Moreover, the residence time estimates after..."
More rationalization of a mathematical impossibility.
"There is a thermometer [δ13C levels] in the lavatory which indicates that the temperature increase exactly follows the warm water input..."
I never specified that the sink was not heated or cooled, or the sink material's thermal capacity. You don't know where the heat might be coming from, or how it might be dissipating.
You are talking in circles, claiming you can do the mathematically impossible, and rationalizing a guess.
"dT/dt is driving dCO2/dt, it has similar variability, only shifted pi/2 back in time for all frequencies. "
Only shifted back in time. In other words, wrong.
It is a unique relationship. If it is lagging 90 degrees, then there is an integral relationship, and if there is an integral relationship, then there is a 90 degree phase lag.
It is if and only if. No possibility of anything else. None.
Bart:
You're still claiming you can uniquely solve for two variables with only one equation. No, Ferdinand, you cannot. Not in this universe.
With the fact that there is a fourfold increase in two known variables (hot water input, height increase) there is an extra equation which can be used to solve the unknown variable:
First, in in all cases tau is the same for any combination of inflows, as the outflow is directly proportional to the height in the lavatory, thus a doubling of the sum of inflows will equilibrate at the double height.
L1 = tau*C1
L2 = tau*(H + C2)
L3 = tau*(4*H + C3)
where L3 - L1 = 4*(L2 - L1)
thus
tau*4*H + tau*C3 - tau*C1 = tau*4*H + tau*4*C2 - tau*4*C1
which gives:
C3 - C1 = 4*(C2 - C1)
which has two solutions and only two:
- The increase in cold water inflow was exactly the same fourfold as for the warm inflow.
- There was no increase in cold water inflow at all, thus C1 = C2 = C3.
The fourfold increase in CO2 emissions and increase in the atmosphere is what is observed. Thus either the natural cycle did increase a fourfold (for which is no indication) or the natural cycle remained the same...
Estimates aren't just sent from heaven, Ferdinand. They have to be mathematically calculated, too, from the same available information.
The "estimates" are calculated from different observations, like the 14C bomb spike decay, but still with quite large margins of error. But even so, most are around 5 years or a in/out flux of ~150 GtC/year. And none, based on the same indicator, show a fourfold decrease in residence time over the past 55 years, as is necessary to overwhelm the human cause of the increase.
I never specified that the sink was not heated or cooled
Of course you didn't but the δ13C rate in the atmosphere is measured and it shows the ratio between natural and human fluxes, as the other possible source of low-δ13C, vegetation, is a net sink (thus an extra cold water inflow).
In your example, equivalent to a thermometer in the lavatory which shows the ratio between cold and warm water flow, where both have constant temperatures and the lavatory has no heat loss.
Bart,
It is a unique relationship. If it is lagging 90 degrees, then there is an integral relationship, and if there is an integral relationship, then there is a 90 degree phase lag.
It is if and only if. No possibility of anything else. None.
Totally agreed, but then please apply that to your own math.
Have a good look at the lags in the data:
T changes cause CO2 changes with a pi/2 lag, that is thus an integral relationship, where the integral is towards an equilibrium and approaching zero change over time.
Taking the derivatives shifts both derivatives pi/2 back in time, thus still with a pi/2 lag, thus dT/dt integrates into dCO2/dt.
Taking temperature and the derivative of CO2 synchronizes without a lag, thus there is no integral relationship between T and dCO2/dt.
The last one is where your (and Salby's) theory is based on...
"Apr 23, 2015 at 10:15 PM Ferdinand Engelbeen "
"First, in in all cases tau is the same for any combination of inflows, as the outflow is directly proportional to the height in the lavatory"
As I pointed out in the original problem setup, I have not stipulated that the drain was not further blocked. Just so, in the Earth's CO2 regulatory, there is no assurance that the "drain" is constant. In fact, we know it varies with temperature.
But, even if that were not the case, we still have only one observational equation
tau*H + tau*(C2 - C1) = 0.5*H*t
If tau is less than 0.5*t, then H cannot be completely responsible for the rise. If tau is, in fact, quite small, then it cannot be responsible for much of the rise at all.
You cannot solve for two variables with one equation, Ferdinand. Drill that into your head, and have it inscribed above your doorway. You are chasing a dead end.
"Taking the derivatives shifts both derivatives pi/2 back in time, thus still with a pi/2 lag, thus dT/dt integrates into dCO2/dt."
I don't know what you're drinking, but it must be good stuff. dT/dt integrates into d^2CO2/dt^2, the second derivative
dCO2/dt = k*(T - T0)
Take the derivative of both sides, and
d^2CO2/dt^2 = k*dT/dt
You've got to keep the one derivative offset to get the 90 deg phase lag, Ferdinand. None of this silly wordplay changes the mathematics.
Bart,
You simply ignore everything that may be remotely proof that your theory is wrong...
As the increase rate in the atmosphere increased a fourfold in 55 years (whatever the cause) and the net sink rate increased a fourfold in the same period, then the whole CO2 cycle reacts as a simple first order process on disturbances. That is what the data say.
Which makes that we have more equations which may solve the remaining variables, be it in this case with two and only two possible solutions.
Which makes that the fourfold increase of human emissions is the cause of the increase except if the natural cycle also increased a fourfold, for which is no shred of evidence and a lot of counter-evidence.
I don't know what you're drinking, but it must be good stuff. dT/dt integrates into d^2CO2/dt^2, the second derivative
Bart, now you are talking nonsense: a change in T does integrate CO2 in the atmosphere towards a new equilibrium at ~8 ppmv/°C, no matter if that is static or dynamic.
The integration is between T and CO2 with a pi/2 lag for CO2, as can be seen for the period 1990-2001, which includes the large temperature excursions from the 1991 Pinatubo and the 1998 super El Niño.
The integration is between dT/dt and dCO2/dt, as taking the derivatives retains the pi/2 lag.
The integration is not between T and dCO2/dt. There is no lag between T variability and dCO2/dt variability, thus in your own words there is no integration, or do you just change the definition if that is inconvenient for your theory?
dCO2/dt = k*(T - T0) is just your own theory, which violates about all observations, including Henry's law for the solubility of CO2 in seawater and completely ignores the feedback from the increasing CO2 pressure in the atmosphere on the CO2 rate of change, whatever the temperature influence.
The real stuff, per Henry's law is:
ΔCO2 = k*(T - T0)
No matter if that is static or dynamic and no matter if that is reached in seconds or in millennia.
"You simply ignore everything that may be remotely proof that your theory is wrong..."
No, Ferdinand, I ignore bad reasoning and mathematical arguments which, frankly, should be embarrassing to you.
"dCO2/dt = k*(T - T0) is just your own theory"
No, Ferdinand. It is right there in front of you. The picture is a statement of the fact that dCO2/dt = k*(T - T0).
I am saying, "Look, the sky is blue", and you are responding, "That's just your theory", while obstinately staring at the ground, and insisting through tortured logic that it is necessarily red, that all the evidence says it is red, and that I am ignoring that evidence.
The sky is, indeed, blue, Ferdinand, and dCO2/dt = k*(T - T0) in the modern era. It is not open to negotiation. It is empirical fact.
Bart,
You may believe that your theory is the one and only because you can match two straight lines with an arbitrary factor and offset, but I think that the laws of nature are a little more solid...
ΔCO2 = k*(T - T0) is the one and only theoretical and empirical formula, proven already in 1803 by William Henry:
At a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid
Since then Henry's law was confirmed by lots of laboratory tests and millions of direct measurements in the oceans.
If you change the temperature, you change the pCO2 of the oceans, which reaches a new equilibrium with the atmosphere at the moment that the increase in the atmosphere is the same as in the oceans. No matter if that is reached more static (from the ocean surface) or dynamic (from deep ocean exchanges).
Anyway, there is no constant CO2 inflow from the deep oceans for a fixed temperature step, as the increase in the atmosphere reduces the pCO2 difference and thus the inflow of CO2 (and increases the outflow) until inflow and outflow are equal again. See:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/upwelling_temp.jpg
As said to you many times before: nobody disputes that the CO2 variability is caused by temperature variability, but as variability and trend are proven not caused by the same process, there is no reason to assume that the trend is caused by temperature.
1) Henry's law is not directly applicable in a non-equilibrium situation
2) ΔCO2 = k*(T - T0) for this system is directly contradicted by the data
3) If continuous inflow of CO2 from the deep oceans could not budge atmospheric CO2, then neither could human inputs
Your hypothesis is just a mass of contradictions, Ferdinand. Filled with arbitrary assumptions, and denying direct measurements. I'm sorry to be harsh, but your math is just atrocious.
Bart,
Henry's law is directly applicable to any situation: it shows what the equilibrium pCO2 is for any temperature of seawater. The exchanges with the atmosphere are directly proportional to the difference between pCO2 in the atmosphere and the equilibrium pCO2 of the oceans per Henry's law.
ΔCO2 = k*(T - T0) in no way is contradicted by the data. Not for the current situation where the short term variability is 4-5 ppmv/K, not for the long term changes where the change is 8 ppmv/K. Only if you wrongly attribute the slope in dCO2/dt to temperature instead of human emissions, then you create a discrepancy which doesn't exist in reality.
If continuous inflow of CO2 from the deep oceans could not budge atmospheric CO2, then neither could human inputs
The continuous inflow of CO2 from the deep oceans near the equator is more than compensated by the continuous sink of CO2 into the deep oceans near the poles: the oceans too (besides ~1 GtC into vegetation) are more sink than source: about 0.5 GtC/year in the ocean surface (measured as pCO2 and DIC increase) and about 3 GtC/year in the polar sinks measured as area weighted fluxes between pCO2 oceans and pCO2 atmosphere:
http://www.pmel.noaa.gov/pubs/outstand/feel2331/maps.shtm
Human emissions currently are around 9 GtC/year, thus near fully responsible for the increase in the atmosphere.
Ferdinand, I'm surprised to see you write that. The partial pressure of CO2 in the aqueous phase is also dependent on the coupled chemical equilibrium with bicarbonate. Henry's Law does apply to equilibrium situations as Bart points out. The rate of this chemical reaction is also quite a slow one about 6 orders of magnitude slower than a diffusion-limited reaction rate. Which is why all of biology uses carbonic anhydrase to speed up the reaction. I still haven't found any evidence that this is even considered in carbon cycle models.
Further, the net (thermal) sources and sinks for CO2 may be separated by thousands of miles. It seems highly unlikely that they are in equilibrium.
"ΔCO2 = k*(T - T0) in no way is contradicted by the data. "
It is contradicted by the plot that shows
dCO2/dt = k*(T - T0)
"Only if you wrongly attribute the slope in dCO2/dt to temperature instead of human emissions, then you create a discrepancy which doesn't exist in reality."
There is no doubt at all that the trend in temperature is causing the trend in dCO2/dt.
Apr 25, 2015 at 9:47 PM | michael hart
Thank you, Michael. One would think this would be self-evident.
I must leave, so this will be the end of the discussion on my part for now.
Michael,
The In/out fluxes from/to the oceans are directly proportional to the pCO2 difference between oceans and atmosphere.
I know that the pCO2(oceans) is dependent of a host of reactions between free CO2, bicarbonate and carbonates (and physically by salt content), which all are influenced by pH, evaporation and bio-life... But it is Henry's law for free CO2 and only free CO2 which says what the momentary equilibrium should be. Ultimately it will be the Revelle/buffer factor which will give how much CO2 is absorbed in or released from the ocean surface layer: about 10% of the change in the atmosphere...
But it is already difficult enough to understand for most audience here, so that I didn't mention all the underlying reactions...
I have no knowledge of equilibrium reactions which limit the exchange speed, but that will only influence the time needed to reach a new equilibrium, but that doesn't change the equilibrium itself... But it can influence the net result of dynamic processes over shorter periods.
The ocean's pCO2 differences makes that there is a continuous influx of some 40 GtC/year extra CO2 at the upwelling zones near the equator, because the pCO2 there is ~750 μatm in the oceans and only 400 μatm (~ppmv) in the atmosphere. Near the poles there is the reverse situation: 400 μatm in the atmosphere, 150 μatm in the oceans, which gives a continuous outflux of ~43 GtC/year or an overall net sink rate of ~3 GtC/year into the deep oceans.
The overall, area weighted pressure difference between atmosphere and ocean surface is ~7 μatm higher in the atmosphere than in the oceans. See Feely e.a.:
http://www.pmel.noaa.gov/pubs/outstand/feel2331/exchange.shtml and following pages.
Thus indeed it is a highly dynamic process, where a lot of CO2 is continuously circulating through the atmosphere from equator to poles, but still obeying Henry's law for the direction and magnitude of the fluxes and the net result, which is the difference between influx and outflux, which depends of the pressure difference between oceans and atmosphere. The first is influenced by up/down welling and the surface temperature changes and the pressure difference depends of the CO2 pressure in the atmosphere.
The latter is where Bart's formula goes wrong: he didn't include any feedback from the increased CO2 pressure in the atmosphere as caused by the increase of the net influx from increasing temperatures...
Thus all together, the current situation is a near continuous stream of CO2 of ~40 GtC/year circulating over deep oceans and atmosphere and a net sink of ~3 GtC/year caused by a continuous increase in pCO2 in the atmosphere, of which ~6 ppmv is caused by warming oceans and ~105 ppmv by the ~200 ppmv human emissions...
Michael, Ferdinand,
There is a delightful app for that @ colorado state which incorporates the various steps of the equilibrium. You can find any number of explanations of the equilibria on the web.
If you run the app at fixed alkalinity and dissolved inorganic carbon the fit of pCO2 to T is slightly second order aT^2+bT+C, which of course, means that d[pCO2]/dT = 2aT where a is small. Of course, the temperature you should use is the sea surface temperature, not the temperature a few km up in the atmosphere, and since the response is second order, you should not use a global average, but you should use the local temperature and sum over the ocean area.
Glad to be of service.
Eli
Bart,
Your formula has an essential error: CO2 is not the integral of k*(T – T0), it is the integral towards the new equilibrium, thus of the difference between current level and new level which has a finite endpoint.
That difference evolves towards zero over time:
dCO2/dt = k2*[k*(T – To) – ΔpCO2(atm)]
Where k = ~8 ppmv/K and ΔpCO2(atm) the difference between current CO2 level in the atmosphere and the CO2 level at the old equilibrium.
The moment that k*(T – T0) and ΔpCO2(atm) are equal, dCO2/dt is zero:
ΔpCO2(atm) = k*(T – T0)
which is what Henry’s law says…
There is no continuous increase in the atmosphere from a sustained small change in temperature without feedback from the increased pressure in the atmosphere...
“dCO2/dt = k2*[k*(T – To) – ΔpCO2(atm)]”
Wrong. There is no such dynamic observable in the modern era. Any such extra terms would therefore necessarily have k2 tiny and k2*k the only significant scaling factor.
That means that dCO2/dt = k*(T – T0) is the only equation we need concern ourselves with to diagnose attribution, and the clear implication is that human inputs do not significantly influence atmospheric CO2 levels.
You should fit your theory to the data, rather than futilely trying to fit the data to your theory.
Incidentally,
dCO2/dt = k*(T - T0)
has a transfer function
H(s) = k/s
from re-baselined temperature anomaly T - T0, i.e., it is an integration. On the other hand,
dCO2/dt = k2*[k*(T – To) – ΔpCO2(atm)]
has a transfer function
H(s) = k2*k/(s + k2)
which can be written
H(s) = (k2*s/(s+k2)) * (k/s)
The transfer function k2*s/(s+k2) is a high pass filter. It has a phase response which is +90 degrees at low frequency, and 0 degrees at high frequency.
As I have been telling you forever, such a high pass filtering operation would produce a phase distortion, because of that phase response.
There is no phase distortion evident in the record, down to the lowest observable frequency.
It additionally has a high pass magnitude response, which is to say, gain at low frequency is zero, increasing to k2 at high frequency. Higher frequency content would be amplified at the expense of lower frequencies. Again, there is no such distortion of the magnitude response observable in the record.
As a result, we can say that k2 is very small, to the point that it is unobservable in the past 57 years. And, that means that for all practical purposes, we can neglect its influence. The only equation we need concern ourselves with to analyze what has been happening for the past 57 years is the first one
dCO2/dt = k*(T - T0)
The point of all this is that, when I tell you there is no phase distortion observable, I mean that there is no observable action of a k2 factor. And, that is why it is necessary that the trend in T produces the trend in dCO2/dt.
If any are interested, this conversation has been going on in parallel at WUWT.
Bart,
H(s) = k2*k/(s + k2)
How did you transfer – ΔpCO2(atm) into + k2?
ΔpCO2(atm) itself is the integrating function of dCO2/dt up to time t. Thus the transfer function anyway is not time invariant.
OK, my knowledge of transfer functions is near zero, but I don't see any problem with a filtering function if the low to higher frequency process integrates: that is opposite to your:
"gain at low frequency is zero, increasing to k2 at high frequency"
If you integrate a sinusoid with different frequencies, the amplitude at higher frequencies gets smaller, not larger.
And there is no filtering at all for the slope part if the slope is mostly caused by a process which is independent of temperature and has hardly any variability:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/matlab_sin_t_co2_slope.jpg
I am still learning Matlab - again - used it last time some 35 years ago, but the above gives already a nice impression of the integration of a sinusoid cycle with an independent slope as input to a container...
Still here, still perplexed. As mentioned earlier, I can intuit a way in which nature is a net sink and the CO2 rise is from temperature. I can't yet know if that is right, but don't yet know that that is wrong. Obviously, something interesting and unknown is going on with the sinks.
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Kim,
I know, not easy stuff...
In this case the clash between theoretical knowledge and practical knowledge...
In short: nature can't be the cause of the increase in the atmosphere, as long as the net increase in the atmosphere is smaller than human emissions. That means that natural sinks are larger than natural sources, which is the case for every year of the past 55 years, no matter the small temperature increase (which gives maximum 5 ppmv extra).
There is one exception and only one: if the natural carbon cycle increased a fourfold, in lockstep with human emissions and the sinks react extremely fast on any disturbance in the atmosphere. For both is not the slightest evidence in any observation. To the contrary: all evidence is that humans are the cause of the increase...
My following blog-post explaining why the CO2 increase is probably natural because of Henry's law is in agreement with Salby if anyone is interested in checking it out and explains why the Revelle Factor (as Ferdinand cites above) is nonsense: http://chipstero7.blogspot.co.uk/2013/11/why-increase-in-co2-is-probably-natural.html
Who is observing what the oceanic biome is sequestering?
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