Murry Salby, who studies the carbon dioxide budget from his base in Australia, is visiting the UK at the start of November and will give a number of talks - two in London and one in Cambridgeshire.
Sorry, no, you are wrong. You have eliminated the data which shows how bad the fit is.
"As said many times before..."
And, you were wrong many times before. It works the same as with human emissions. There is CO2 coming in from the outside, pushing its way in. If human emissions can do it, so can this. If an arbitrarily large influx of CO2 from the oceans cannot change atmospheric CO2, then nothing else can, either. Since this is obviously not the case, the proposition is false, QED.
"...but that is hardly influenced by a temperature increase..."
The rate of outward flux is modulated by the temperature.
This has all been argued before, and we are going in circles. Time will tell...
Sorry, no, you are wrong. You have eliminated the data which shows how bad the fit is.
All what I have done is plotting the same data as you have done, but using the same units for both variables, which gives a clear view of the ratio between the slopes of dCO2(emissions) and dCO2(observed). Your plot gives a completely wrong impression, because both variables are plotted in different units...
And, you were wrong many times before. It works the same as with human emissions. There is CO2 coming in from the outside, pushing its way in.
I never said that there can't be an increase in CO2 from the (deep) ocean upwelling. Theoretically it may happen. But such an upwelling must increase the total circulation through the atmosphere in the same ratio as the human emissions (a threefold since 1960) in exactly the same time frame to dwarf the human emissions and to give the same effect in the atmosphere. It is that which violates all known observations. Thus in reality, there is no increase in deep ocean circulation (or whatever other natural cause) as the more recent estimates of the residence time of CO2 show a lengthening, which is what can be expected from a rather constant throughput in an increased atmospheric content. Neither is such an increase visible in the d13C ratio, etc...
The rate of outward flux is modulated by the temperature.
Hardly, according to Henry's law for 1 K temperature maximum 16 ppmv extra increase towards an equilibrium above the increase caused by the extra CO2 from the increased upwelling.
"But such an upwelling must increase the total circulation through the atmosphere in the same ratio as the human emissions (a threefold since 1960) in exactly the same time frame to dwarf the human emissions and to give the same effect in the atmosphere."
This is a very usual and unremarkable type of behavior for a feedback system. It is much more ordinary than CO2 tottering on the edge of a knife for centuries with no countervailing feedbacks maintaining stability.
"Thus in reality, there is no increase in deep ocean circulation..."
More meaningless narrative drivel.
"Hardly, according to Henry's law..."
Asserting this once again with no theoretical backing gets you nowhere. I have shown mathematically how it comes about. My math beats your assertion.
Bart, I don’t think you got the gist of what I was saying w.r.t. the time-derivative of CO2, but I’m not surprised - it wasn’t exactly spelled out. I took a couple of hours out late yesterday evening to build the model I briefly discussed in my previous post, and have tested it on synthetic data. One of its key features is that the match between temperature (as input) and the scaled time derivative of CO2 is perfect. In other words, it can match the key observations which are leading you to your conclusions, and yet this model requires no heroic assumptions at all. In fact all it requires is recognition of the fact that equilibration between ocean and atmosphere is not instantaneous. Rather than suggesting that we should be surprised to see a close relationship between the scaled time-derivative of CO2 and temperature, this model suggests that we should actually expect such a relationship, and yet it leads to a bounded solution for CO2 concentration.
For the transient behaviour, I am just using a simple response function of the form:-
τ * dCO2/dt = ΔT - f(T)* ΔCO2 where ΔT and ΔCO2 are measured from an arbitrary initial equilibrium condition. This equation is based on the assumption that the process of release of solute with temperature change starts off quickly and slows down as the concentrations adjust – a commonly observed phenomenon for the transient behavior of chemical equilibration processes. For a fixed step change in temperature its solution yields an exponential response function of ΔCO2 in time. The temperature function, f(T), is analytically derived so that the CO2 response function at large values of t for a fixed temperature step asymptotes to the equilibrium concentration predicted from Henry's Law - based on the accepted equation for how the Henry coefficient changes with temperature. The time it takes to get to equilibrium is controlled by the parameter τ ("tau"), but is also a weak function of T via the function f(T). Note that this model is completely compatible with Henry’s Law – including the fact that for a fixed temperature change, the model does, if left alone, equilibrate at a new constant concentration value of CO2. The model does not consider the effect of changing partial pressure. It assumes that over short timeframes, the change in atmospheric partial pressure of CO2 is sufficiently long wavelength that it has little impact on the phasing of dCO2/dt. In other words, the time derivative in the short term is dominated by the effect of temperature fluctuations.
The above equation is readily solved using a Runge-Kutta (RK4) routine. Having confirmed the numerical accuracy of the solution routine on simple step and analytic functions, I then checked out the model's behaviour on various temperature inputs involving combinations of sinusoidal cycles of differing frequencies and amplitudes and with different assumptions about the time taken to reach equilibrium.
Here is an example where, as the temperature input, 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
Note the near perfect match between dCO2/dt and Temperature.
You should mark well that it is very easy to bring the time-derivative of CO2 into exact phase with temperature inputs in all of the examples I tested, and this is the point I was trying to make in my earlier post. This is not just a “co-incidence of lag-time” as some have suggested, nor a simple integrative effect. For an assumption of instantaneous equilibration, which was what my previous post was expressly referring to, the time-derivative of CO2 should exactly lead temperature by pi/2 and be in phase with dT/dt. (This comes straight from a partial differential of the Henry coefficient w.r.t. T multiplied by dT/dt). 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.
The coincidence of amplitude variation stems from the same source. For a fixed step change in temperature, the response function (CO2 vs time) is very close to linear for durations which are short relative to the total response time of the system, and moreover the initial gradient is a function of the magnitude of the step temperature change. Hence there is an apparent simple linear relationship between dCO2/dt and deltaT if we are looking at cycles of short duration. The larger the response time of the system, relative to the periodicity of the cycles of interest, the closer this relationship appears to be.
The main message is that the observation of an approximate scale relationship between temperature and the time derivative of CO2 does not allow us to conclude that there is a simple underlying relationship of the form dCO2/dt = k(T-Te) . You cannot rule out the possibility that the actual functional relationship between CO2 and T (for an assumed invariant or long wavelength change in partial pressure) is of the form of the response equation above or something similar. In fact, it seems a lot more likely since it better fits other known science, including Henry’s Law, as well as observations.
This is a very usual and unremarkable type of behavior for a feedback system. It is much more ordinary than CO2 tottering on the edge of a knife for centuries with no countervailing feedbacks maintaining stability.
Bart, the observations show an increase of CO2 in lockstep with human emissions. That may be the result of a response time of the sink capacity of CO2 which is slower than needed to remove all human emissions in short time (which fits all observations, including ice ages for response times of ~50 years) or it may be the result of a huge increase in natural circulation with a response time which is short enough to remove most of the human emissions, but not fast enough to remove all of the extra natural circulation (which doesn't fit any observation). In the latter case, the natural circulation must mimic the human emissions in increase ratio over the time frame 1960-current, or the increase rate in the atmosphere wouldn't mimic the exact ratio shown by human emissions.
This is not just a “co-incidence of lag-time” as some have suggested, nor a simple integrative effect.
Paul_K, I was not sure about this, as I lack the theoretical background, but was suspecting it as the coincidence between T and dCO2 was too nice. Thanks for your input, the discussion gets more interesting now...
I was not sure about this, as I lack the theoretical background...
Understanding the proof in principle only requires the equivalent of A-level maths. See if this helps.
The only complicating factor in my response equation is introduced by the f(T) term to account for the non-linearity in temperature dependence in Henry’s Law. In practice, for the small temperature changes we are considering here, the relationship between equilibrium concentration and temperature can be linearised with only small error (about 2% for a 1 degree change in temperature), so strictly speaking this feature is gilding the lily. Another way of saying this is that the f(T) term can be replaced by a constant in the response equation to a very good approximation. Let’s call this constant β. The response equation above can then be written in a much simpler form as: τ*dCO2/dt = ΔT – β *ΔCO2 Now let’s set the (input) temperature signal equal to a sine function, ΔT = sin(ωt). The new simplified equation can be solved analytically and yields the following solution (for boundary conditions ΔCO2 = 0 at time t = 0).
ΔCO2 = Asin(ωt) – Aωτcos(ωt) + Aωτexp(-t/τ) Where A = 1/[β*(1+(ωτ)^2)] = a constant for fixed value of τ. . You can confirm for yourself that this is indeed a valid solution.
The third term is a short-term transient which disappears as time goes on, and so the system rapidly "stabilises" into an oscillatory function which is the weighted sum of the first sine term and the second cosine term. The first term is exactly in phase with T. The second term is exactly in phase with dT/dt but is exactly pi/2 out of phase with T.
If we assume a small value of τ, equivalent to a near instantaneous response, the first sine term has all the weighting and so the solution for CO2 is in phase with temperature. On the other hand, with a high assumed value of τ, the second term has all the weighting and so the solution for CO2 shifts pi/2 out of phase with temperature; this brings the time derivative of CO2 exactly in phase with temperature, and that is exactly what we see in the model solution of the synthetic data as well as in the observational data from Bart's plots. This phase shift cannot be greater than pi/2 - that's mathematically impossible. Hence, any large value of tau will deliver the observation that dCO2/dt is in phase with temperature. No extraordinary coincidence is required – just a “slow” ocean response time. Since estimates of theoretical equilibration times for ocean diffusive processes include some estimates between six hundred and three thousand years, I don’t think it is too much of a stretch to assume that the theoretical equilibration time for CO2 solute in response to temperature change is going to be a lot larger than a few decades.
thank you for this very clear exposition. You've elegantly put into maths the thought experiment I was trying to describe the other day. We know the response time of the ocean is slow and it is not surprising given this that dCO2/dt should be a function of Delta T.
There is a whole bunch of observational data that bart dismissed ad "narrative" that are wholly inconsistent with his model. Not least of these is the fact that the PCO2 of the atmosphere is greater than that of the surface ocean thus the dominant CO2 flux is from atmosphere to ocean despite the small temperature rise that has occurred.
Ferdinand, I managed to screw up the constants in the previous post. It should have read as follows:
τ*dCO2/dt = ΔT – β *ΔCO2 Now let’s set the (input) temperature signal equal to a sine function, ΔT = sin(ωt). The new simplified equation can be solved analytically and yields the following solution (for boundary conditions ΔCO2 = 0 at time t = 0).
Define a new parameter τ' = τ/β The solution is then ΔCO2 = Asin(ωt) – Aωτcos(ωt) + Aωτexp(-t/τ') Where A = 1/[β*(1+(ωτ')^2)] = a constant for fixed value of τ'. . You can confirm for yourself that this is indeed a valid solution.
Further references to τ should then equally be adjusted to be references to τ'.
Thanks a lot for the clear explanation! Even I could follow it with my 50 years ago (and hardly used) math...
Thus the take away message is that no matter the frequencies of the fast variations in T, with a response of the oceans (a lot) slower than the fast variations, one will always have that T is in phase with dCO2.
One remark: some of the ocean (and other natural) responses are fast, some slower and some are extremely slow: The ocean surface responds very fast (1-3 years) to changes in the atmosphere, but that is only for 10% of the change, because of the Revelle (buffer) factor. That is the part that also is responsible for the fast reactions on temperature. Vegetation currently is a net sink for ~15% of human emissions and the deep oceans for ~25%. The total sink rate is about ~4 GtC (2 ppmv) for ~210 GtC (100 ppmv) or slightly over 50 years for all sinks together.
As the main variability in dCO2 is much shorter (1-3 years), the 50 years is slow enough to allow for the observed phase lock between T and dCO2. And more than fast enough to allow for the thight response seen over ice ages, but where also other, slower responses (land ice / vegetation area, deep ocean currents,...) are at work...
"The main message is that the observation of an approximate scale relationship between temperature and the time derivative of CO2 does not allow us to conclude that there is a simple underlying relationship of the form dCO2/dt = k(T-Te) ."
Paul - That's fine. There are always multiple models which can mimic similar behavior over a finite interval of time. I have given you my hypothesis for how a particular model could come about. You are suggesting another one.
Either way, the important part is that they mimic similar behavior over the finite interval of time. If you match dCO2/dt as a function of temperature and integrate it, you will get the current CO2 concentration, without using any human inputs at all.
That is the important point. You cannot get a 90 deg phase shift at all observable frequencies without having an effectively integral action over the frequencies of observation. It is a necessity flowing from the Bode phase-gain requirement that the slope of the gain response function is proportional to the phase. A -90 deg phase lag always produces a -20 dB/decade gain slope, i.e., the gain response of an integrator, at least over the frequencies of observation.
And, when you integrate the temperature relationship, you will have accounted for the observed rise in CO2.
All roads lead to Rome. Humans are not responsible for the rise in CO2.
In case that is not clear enough, let me try to put it another way.
dCO2/dt integrates into CO2. This is a unique relationship, modulo an arbitrary constant offset. If you match dCO2/dt with any function and integrate it, you will get a match to the change in CO2 over that interval.
You cannot match a -90 deg phase shift without getting an effective integration. And, when you do that, the slope in the temperature record is going to integrate, too. It will account for all, or at least most, of the curvature in the accumulated CO2 plot.
The rate of human emissions also has a slope. If you try to add that into the integration, you will get too much curvature.
That is why human emissions cannot be responsible for the rise in CO2 - there is little to no additional room for them to integrate into the result.
T is coincident with dCO2/dt. What Ferdinand bascially wants to do is set
dCO2/dt = L*E + H*T
E = human emissions L = low pass filter operator H = high pass filter operator
The high pass filter operation is necessary in Ferdinand's paradigm because, otherwise, the scale factor which matches the variations in T already matches the slope in T to the slope in dCO2/dt.
Ferdinand considers this a fluke, and wants to eliminate the ramp in T and replace it with the scaled ramp in E. Ferdinand thinks you can do this by making H a least squares fit and subtracting the trend. But, of course, Nature has no way of doing this, as it amounts to an anti-causal filter.
In fact, in Nature, H is severely constrained. It can be no more than first or, at a stretch, second order. And, its cut-on frequency must be fairly high in order to take out the ramp in T within the given interval.
Here's the problem: any natural filtering function H satisfying these requirements is going to have serious phase distortion within plus or minus a decade of the cut-on frequency. That is going to ruin the widely observed -90 deg phase shift, and cause a lot of very observable phase distortion. Such phase distortion is not observed.
Ferdinand's paradigm is unphysical. It only exists in his mind.
T is coincident with dCO2/dt. What Ferdinand bascially wants to do is set
dCO2/dt = L*E + H*T
As Paul_K showed, the phase lock of T and dCO2/dt is pure a result of the fast response of a few processes on T changes and a slow(er) response of the oceans on any variability, whatever the source. Thus (at least) two different processes are at work with different response times. While T is the main driver for the fast responses, it may or may not be the driver for the slope of dCO2. In my opinion, based on Henry's law and the response of CO2 on (very) long time periods (50 years to multi-millennia), T has a limited influence on CO2 levels: from 4-5 ppmv/K short term to 8 ppmv/K long term. That is all. Thus T is not responsible for the bulk (70 ppmv since 1960) of CO2, neither for the slope of dCO2.
What I wanted to show is that:
dCO2/dt = m*dCO2(emissions)/dt + n*dT/dt minus the sink rate of CO2 for the current pCO2 difference with the equilibrium CO2 pressure.
Which can be seen in Wood for trees But because WFT doesn't have the emissions in its database, here a plot of emissions and increase in the atmosphere where m in the above equation is 0.53 over the past 111 years (since 1900): http://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2.jpg and the slope of dCO2(emissions)/dt is about twice the slope of dCO2/dt: http://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_em3.jpg
As the slope of T is near-linear, the slope of dT/dt is near zero, thus dT/dt is not responsible for the slope of dCO2/dt and only responsible for the (lagged) variability of dCO2, and both dCO2(emissions)/dt and dT/dt are simply additive without any filtering, as good as the influence of CO2(emissions) and T is additive in the atmosphere.
After I had gone through the above model-building process, I was seriously thinking about writing it up a little more seriously, including a full match to modern data, and bringing it to the direct attention of Professor Salby. However, I thought I should first listen to his latest thoughts on the subject.
The last time I heard him speak on his subject was over a year ago, and his position has clearly evolved. In the lecture I previously heard, he spoke about the relationship between dCO2 and T in the modern record, but did not underpin it with a complete mathematical model. Last night I watched the recent video of his Hamburg lecture – referenced by Ferdinand in a previous post. It is found here. http://www.youtube.com/watch?feature=player_embedded&v=2ROw_cDKwc0#t=0
I would particularly draw your attention to his presentation between 16 and 23 minutes, where he describes in some detail exactly the same mathematical model which I have been describing above. I don’t think I can teach him anything!
Incidentally, the entire lecture is brilliant and his arguments are very coherent with one exception in my mind – well worth watching. Even though I remain ultimately unconvinced by his dismissal of the human addition to CO2, wherein I believe he sets up a logical paradox, he left me convinced that we have underestimated the strength of the temperature control knob on atmospheric CO2. See also my response to Bart below.
Thanks for your responses. You, Murray Salby and I all share a common view that the modern observational data displays an approximate relationship of the form dCO2/dt = gamma* (T-Te) This is the only way that the modern observational data can be explained in terms of phasing, so you don’t need to pursue that argument further for me at least. However, your position appears to be much more radical than Salby’s. His full model for atmospheric concentration (using his choice of constants) includes a dissipative term while yours does not:- dCO2/dt = gamma*T – alpha*CO2
(Taken from his April lecture in Hamburg.) This is identical mathematically to the system I was solving above! The response time for this system varies inversely with alpha. With a small value of alpha, (long system response time), then short term behaviour is dominated by the first term - which is what we see in the observational data.
The difference between your position (if I understand it correctly) and Professor Salby’s is extremely important. His model recognises that the CO2 response to a temperature change is bounded – it just takes a long time. Your model recognises no bounding solution. Hence you conclude that CO2 cannot have a warming effect because it would have led to a runaway feedback situation. My previous posts were trying to highlight that this is a very unsafe conclusion, which relies on the use of a short-term approximation as a full model. Professor Salby stops a long way short of drawing this conclusion, although, from his lecture, he clearly thinks that the effects of CO2 have been overestimated (as do I).
Despite my admiration for the quality of the work Salby has done, I still cannot accept his inference that most of the change in atmospheric CO2 arises from a simple temperature dependency. In my view he sets up his own unnecessary paradox to reach this conclusion. It is this. In order to explain why dCO2/dt comes into phase with temperature, he needs to postulate or demonstrate that counteracting or dissipative forces are slow (small value of alpha in his model). This takes him towards a conservative model in short timeframes, in his own jargon. However, the atmosphere doesn’t know where a molecule of CO2 comes from. They are not labelled blue and red. If there is very slow dissipation of molecules put there by temperature effect, then there has to be equally slow dissipation of molecules put there by mankind. You cannot postulate separate dissipation rates for the blue and red molecules. Hence the more reasonable explanation has to be that the CO2 profile in time is controlled by both elements.
Another point where Salby goes wrong is his theoretical calculation of the migration of CO2 in ice cores. He calculated such a migration to fit his theory:
After 30 minutes in his lecture, he looks at the suppressing of high frequency variations in the ice core. While that is true, that highly depends of the resolution of the ice core in combination with the frequency of the variations, but his interpretation of a 10 fold suppression on time scales of 10 kyrs is completely out of reality for the higher resolution ice cores like Taylor Dome (resolution of ~40 years over 70 kyears).
That all is based on some calculated estimate of a huge CO2 migration in the ice (shown after 32 minutes) which is not seen in any ice core. If that would be the case, the ice core CO2 record in the far past would get flatter and flatter for every interglacial back in time, which is not measured at all: the CO2/temperature ratio remains the same for all glaciations/deglaciations over 800 kyears at around 8 ppmv/K, showing no measurable CO2 migration in the coldest (-40°C) ice cores like Vostok (420 kyears of data) and Dome C (800 kyears of data).
If there was a real 10-fold suppression of peaks over 10 kyrs, then the measured peak at 100 kyr of 300 ppmv would have been 3000(0) ppmv (on another time in his speach he says a 10-fold suppression over 100 kyr), but while ice cores filter out the high frequency data over the resolution period, that doesn't change the average over that period, which implies that the CO2 levels during the (90% of the time) cold periods would be negative...
BTW, any chance that you can be in London at Salby's speach on November 6th?
Doesn't work. dT/dt is out of phase with dCO2/dt. There is no way around this. It is in phase with T. It follows that CO2 itself must be essentially proportional to the integrated temperature anomaly with respect to a particular baseline, at least over the timeline of interest.
Oct 27, 2013 at 9:13 AM | Paul_K
"However, your position appears to be much more radical than Salby’s. His full model for atmospheric concentration (using his choice of constants) includes a dissipative term while yours does not:- dCO2/dt = gamma*T – alpha*CO2."
Not so much. I am simply more interested in the short term behavior. As I said above, over a finite interval of time, many models can produce virtually indistinguishable results. What I am most interested in is establishing that human inputs are NOT the driver. And, that fact is established by the fact that a temperature dependent model can explain virtually the entire behavior of CO2 since 1958, the year in which precise measurements of CO2 in the atmosphere began. That model does not allow human inputs to be a significant player, because it produces a slope in dCO2/dt which matches essentially perfectly, and there is little room for the slope in human rate of emissions to have additional impact.
"Hence you conclude that CO2 cannot have a warming effect because it would have led to a runaway feedback situation."
It doesn't matter so much. Your "alpha" above is small (long time constant), and hence cannot stabilize the system unless the sensitivity of temperature to CO2 is very weak, if not precisely zero.
"...I still cannot accept his inference that most of the change in atmospheric CO2 arises from a simple temperature dependency."
The process is quite apparently temperature dependent. That does not mean, however, that temperature is the only player. Going back to what we will now, in deference to your concerns, dub the "short term model",
dCO2/dt = k*(T - Teq)
Let's suppose that Teq is more or less equal to the global temperature anomaly in say 1945, and it had been at that level for some time, so that atmospheric CO2 more or less stayed in the neighborhood of a constant level. Then, at roughly that time, there is an abrupt shift in the CO2 content of upwelling ocean waters which knocks Teq down a few notches. This establishes an increasing trend in CO2. Over the next 53 years to about 1998, temperatures rise, and the atmospheric rate of change accelerates. Then, temperatures settle out at a plateau, and the rise in atmospheric CO2 decelerates in lockstep, with the rate of rise becoming nominally constant.
That is a pretty accurate description of what we observe in the modern temperature and CO2 records. If temperatures decline, as they appear poised to do for the next 20 or so years, we should see additional deceleration in the accumulation of CO2. This is my prediction of what is in store for us. Watch, and we will see what happens.
It is important to point out that the terms k and Teq are not necessarily constant. They just appear to have been fairly constant over at least the past 68 years. But, gradual evolution, or even sudden shifts, are not precluded.
Oct 27, 2013 at 11:52 AM | Ferdinand Engelbeen
"If that would be the case, the ice core CO2 record in the far past would get flatter and flatter for every interglacial back in time, which is not measured at all: "
It does not follow. A low pass filter filters out frequency components until they reach the corner frequency, and then does not filter out anything else.
Doesn't work. dT/dt is out of phase with dCO2/dt. There is no way around this. It is in phase with T. It follows that CO2 itself must be essentially proportional to the integrated temperature anomaly with respect to a particular baseline, at least over the timeline of interest.
Yes, dCO2/dt lags dT/dt, as good as CO2 lags T on all time frames. And as Paul_K showed, there is always a pi/2 shift between short term T variability and CO2 variability, which makes that T variability and dCO2 variability always align as result of the lag between CO2 variability and short term T variability. How does that prove that dT/dt is not the cause of the lagged variability of dCO2/dt?
Further the fact that the trend of dT/dt is essentially flat shows that there is not the slightest influence of dT/dt on the slope of dCO2/dt. That means that the influence of T on some CO2 producing process must be extremely non-linear to increase the total CO2 circulation through the atmosphere a threefold in the period 1960-current. Or a sevenfold if the deep ocean upwelling were the only cause and that all as result of an only 0.5 K temperature increase... Such a process, if it exists at all, would violate all known observations...
It does not follow. A low pass filter filters out frequency components until they reach the corner frequency, and then does not filter out anything else.
Filtering of the high frequency atmospheric CO2 changes in ice cores only happens during the open pore times between surface snow layers and fully closure of the air bubbles in the compacted ice. The filtering time and thus the resolution of the ice core depends of the yearly snow accumulation and average temperature and varies between less than a decade (Law Dome) and 600 years (Vostok). Migration in the ice itself (as Salby alludes) only ends (in dynamic equilibrium) when there are no CO2 level differences anymore...
Bart, what I got from what Paul_K did is that the short term variability in CO2 and CO2 rate of change is from the short variability of temperature and that you can only get the variability of T and dCO2 in phase if the removal of CO2 out of the atmosphere is slower than the slowest of the fast variability (which is not more than 2-3 years). That is completely contrary to what you expect: a very fast response of the sinks so that only temperature is responsible for all variations, short term and long term together. But the slower response of the sinks excludes temperature as the main cause of the longer term response, as we have human inputs which are more than sufficient to explain the whole trend.
If the variability and the trend of CO2 was caused by one and only one process, then you are right, but as Paul_K effectively decoupled the variability and the trend (as good as dT/dt and dCO2/dt show), there is no reason to expect that both are caused by temperature alone...
No, Ferdinand, that is not what he was saying. He was not disagreeing with me on the substance, he was simply suggesting that it cannot be (he believes) an open ended integration, and must have some sort of limiting feedback.
And, as I stated, he may well be right, but the question is moot as far as attribution is concerned. Over the timeline of interest, the open-ended integral model is just fine. Significant human culpability for measured atmospheric CO2 is still not in the cards.
Bart - You assert that your climate system is "unstable", using the equations:
dCO2/dt = a*T dT/dt = b*CO2 - c*T^4
Given these equations, of course it is. Your first equation says that CO2 levels will always increase with a>0, because T must be greater than 0 (3rd law and all that).
How would you propose that CO2 levels decrease in falling temperatures (like going into glacial periods) in your model?
OK Bart, let us repeat the attribution with a simple model I did make some time ago, where 95% of the increase in the atmosphere is caused by "human" input (slightly quadratic) and 5% by a linear temperature increase + a higher frequency sinusoid, no sinks involved:
There is a perfect match in timing of the short term variability between T anomaly and dCO2/dt and a pi/2 lag between dT/dt and dCO2/dt, just like Paul_K proved. And there is a (near) perfect match between the slopes of T and dCO2/dt, but also a perfect match between dCO2(emissions)/dt and dCO2/dt
According to your thesis, the perfect match in timing of the variability and similar slope between T anomaly and dCO2/dt proves that T is the only cause of the variability and slope of dCO2/dt and thus of the increase of CO2 in the atmosphere.
But there is a problem: we know that the model used 95% human and 5% temperature induced CO2 in the atmosphere. Which proves that the perfect match of the variability and slope between T and dCO2/dt doesn't say anything about the attribution of the origin of the increase in the atmosphere, but only proves that T is the origin of the short term variability.
I apologize that I muddied the waters here trying to get across a simple concept, but it was intended that this be a perturbation model, and a vastly simplified one at that. We can take it up one level of simplification by simply adding the equilibrium temperature and input Sun source as
dCO2/dt = a*(T - Teq) dT/dt = b*CO2 - c*T^4 + Sun
This, again, is unstable for a and b both greater than zero. Assuming it is stable, If Sun dips down, such that the temperature decreases below Teq, then CO2 levels start to trend downward.
Oct 28, 2013 at 8:51 PM | Ferdinand Engelbeen
"There is a perfect match in timing of the short term variability between T anomaly and dCO2/dt and a pi/2 lag between dT/dt and dCO2/dt, just like Paul_K proved."
That is what happens with the open integral in my model, too. Paul's model changes nothing, because it is the same as my model if you take the time constant approaching infinity. Over a short time period of observation, the models are indistinguishable. His model is still going to produce a significant slope, which is going to integrate into the curvature of the total CO2 plot. His model does not filter out that low frequency signal. It cannot, because it is a low pass filter model - it passes low frequencies. It will pass the ramp up in temperature, which is a low frequency phenomenon.
For your model to work, you need a high pass filter mechanism acting on the temperature signal. There is no physical basis for such a high pass natural response, and it could not preserve the phase characteristics which are clearly preserved if there were such a mechanism.
Paul had a very narrow objection, and you interpreted it to mean what you wanted it to mean. But, you have misapprehended it.
What you have done here and here is bizarre. You seem to be saying that, if you can match the temperature to the CO2, then take the derivative of the temperature and scale it so the amplitude of its cycles matches the amplitude of the cycles in actual temperature, then integrate it, you get something insignificant, and this somehow proves that the slope in temperature does not integrate into the observed CO2. Mathematically, that makes no sense at all.
Just integrate the temperature signal, scaled for the variations, and it accounts for everything, no human inputs required.
You must integrate the variable which matches dCO2/dt, and no other. The integral is a unique relationship, modulo only an initial offset constant, between the derivative of CO2 and its integral. If you integrate something other than that which matches the derivative of CO2, then of course you will not get anything resembling CO2 as output.
T matches the derivative of CO2, therefore you must integrate T, appropriately scaled and baselined, to match the CO2. There is a slope in T. That gets integrated, too. That slope accounts for the curvature in the CO2 plot. You cannot add in additional human forcing to any level of significance because that will increase the curvature beyond that observed.
It is really very simple. Stop resisting the obvious. It is only going to be that much more painful for you when you have to face reality.
Because of the unique relationship between the derivative and the integral, you do not have to even look at the integrated signal. All the information needed is in the dCO2/dt plot.
You have to match what is in that plot. You cannot do it with dT/dt - it is 90 degrees out of phase with the variations in dCO2/dt. You must use T. T has a slope, which matches the slope in dCO2/dt when it is scaled to match the variations, and those variations are perfectly in phase (or at least, as perfectly as you can expect with stochastic data).
Adding in human inputs also produces a slope, but now the slope is too high. The conclusion is necessarily that, human inputs cannot be significantly affecting things.
Bart, you still are convinced that one and only one (temperature controlled) process is controlling the increase of CO2 in the atmosphere. That is where it goes wrong: there are a multitude of processes at work, some mostly temperature controlled, some pressure (difference) controlled and some human controlled.
You have to match what is in that plot. You cannot do it with dT/dt - it is 90 degrees out of phase with the variations in dCO2/dt. You must use T.
As the short term variations of CO2 lag the variations of T, the short term variations of dCO2/dt lag the short term variations of dT/dt. The variations of CO2 are caused by variations of T with a lag, which gives that the variations of dCO2/dt are caused by variations of dT/dt with a lag, not by variations of T, even if these exactly matches dCO2/dt in timing because of the differentiation.
And as there is no trend in dT/dt, only a small offset, the integral of dT/dt gives a small increase of CO2 in the atmosphere for a small increase in temperature, as can be seen over many millennia. As the effect of the variability of dT/dt on dCO2/dt is shifted pi/2, the integral of the variability is shifted pi/2 too.
The slope of dCO2/dt is entirely the result of the slope in dCO2(emissions)/dt, which gives integrated the slightlly quadratic increase in the atmosphere.
The real increase in the atmosphere is thus the sum of the integral of the slope of dCO2/dt + the lagged integral of dT/dt and has nothing to do with any scale and offset of T.
The conclusion is necessarily that, human inputs cannot be significantly affecting things.
Have you already found the source of the 3-fold increase in natural circulation that doesn't violate all known observations?
"The variations of CO2 are caused by variations of T with a lag, which gives that the variations of dCO2/dt are caused by variations of dT/dt with a lag, not by variations of T, even if these exactly matches dCO2/dt in timing because of the differentiation."
"Lag" is not some arbitrary quantity which you can simply dismiss at leisure, to be filled in by some climatological God of the Gaps. The phase lag is an intrinsic quality of a unique process. That process has a 90 deg phase lag and, consequently, a -20 dB/decade gain slope. There is one, and only one, process which possesses those qualities, and that is an integration.
It does not matter if, as Paul suggested, it is not a pure integration over all time. Any feedback which would tend to produce deviation from a pure integral at very low frequencies is negligible over the bandwidth of observation.
"As the effect of the variability of dT/dt on dCO2/dt is shifted pi/2, the integral of the variability is shifted pi/2 too."
And that, of mathematical necessity, means that it is the integral of dT/dt, i.e., T, which is affecting dCO2/dt.
"The slope of dCO2/dt is entirely the result of the slope in dCO2(emissions)/dt, which gives integrated the slightlly quadratic increase in the atmosphere. "
Mere assertion on your part. It is not physically possible. You are just arranging things as you would like them to be. But, there is no physical or mathematical basis for it.
"The real increase in the atmosphere is thus the sum of the integral of the slope of dCO2/dt + the lagged integral of dT/dt and has nothing to do with any scale and offset of T."
Mere assertion on your part. It is not physically possible. You are just arranging things as you would like them to be. But, there is no physical or mathematical basis for it.
"Have you already found the source of the 3-fold increase in natural circulation that doesn't violate all known observations?"
Nothing I have stated violates any observations. Your narratives are not observations. They tell a story based on the observations, but they are not the only explanations.
In years gone past, the leaders of The Church of Rome told Galileo that the Sun went around the Earth. That was a narrative, which was consistent with all observations to date. But, it was not, itself, an observation. Your measurements of CO2 isotopes and such are observations. Your claim for how they arise is a narrative. It is not proof of anything.
And that, of mathematical necessity, means that it is the integral of dT/dt, i.e., T, which is affecting dCO2/dt.
And that is where you go wrong:
- As Paul_K showed, as the increase/decrease of CO2 with T is a linear process for small changes of T, CO2 variability follows high frequency T variability with a pi/2 lag. - The derivative of T and CO2 shifts the high frequency changes back with pi/2, still with a difference of pi/2 between dCO2/dt and dT/dt. - That gives that T and dCO2/dt now are synchronized as can be seen in Wood for Trees - The transformation of T into CO2 gives a lag of pi/2. The transformation of dT/dt into dCO2/dt also gives a lag of pi/2.
So far so good.
- Integrating dT/dt shifts T forward pi/2. Adding the transformation shift from T to CO2 (or equally from dT/dt to dCO2/dt before integration) shifts the result for CO2 forward pi/2 again, which was the original shift. - Integrating T as surrogate for dCO2/dt shifts the variability forward with pi/2, synchronizing the integral of T with CO2. Adding the transformation shift from integrated T to CO2 adds another pi/2 shift, thus a shift of in total 180 deg.
integrating T for dCO2/dt leads to a 90 deg. shift of the calculated CO2 variability with the real CO2 variability
Thus your calculated CO2 variability based on T is 90 deg. out of phase with reality...
Moreover, have a view of what happens if you have a simple linear temperature increase with a high frequency sinusoid around it, without any other influence:
The reaction of CO2 is supposed to be linear, as well as for the high frequencies as for the very low frequencies, as can be seen over 800 kyr in ice cores.
For the derivative, we have a problem: http://www.ferdinand-engelbeen.be/klimaat/klim_img/sim_dco2_dT_Tanom_00.jpg
As both the slopes of dT/dt and dCO2/dt are zero, one need to use a factor of 0 to align the slope of T and dCO2, but that makes that the amplitude of the calculated CO2 variability based on T variability also is zero.
The only escape is that the reaction of CO2 on temperature is highly non-linear, which isn't seen in any time frame.
Your measurements of CO2 isotopes and such are observations. Your claim for how they arise is a narrative. It is not proof of anything.
Bart, you are a genius in math, but you have little knowledge of the behavior of isotopes in nature. The observations of the 13C/12C ratio (expressed in per mil δ13C) in all oceans (deep and surface) indicates that any substantial increase of CO2 coming from the oceans, including the isotopic changes at the sea-air border, would increase the current δ13C level of CO2 in the atmosphere.
For your theory to work, you need an increase in deep ocean - atmosphere circulation from ~40 GtC in 1960 to ~290 GtC in 2010. That would give an increase in δ13C, not the firm decrease we see over the same period: http://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_increase_290.jpg
It seems that you are at the side of the Church of Rome instead of Galileo in this case...
This is absurd. I'm not going to dignify this nonsense with any further response. You have no idea of what you are talking about, and there is no point. You will see...
Bart, I have not the slightest problem with admitting that I am wrong if you have good arguments which show where I am wrong. Al what I have done is showing where the problems with your theory are, while I don't see any problem with the simple theory that temperature is responsible for the bulk of the variability around the trend, while human emissions are responsible for the bulk of the trend itself. That fits the observed increase of CO2 in all aspects.
That there is a shift between the integrated variability of T and CO2 is the result of the physical reaction of CO2 on temperature changes which causes a time delay and must be taken into account when integrating. Thus there is not the slightest problem with the timing of the integral of dT/dt and CO2.
The problem is with your timing of the integral of T (as far as that has a physical meaning), which doesn't take into account the delay of changes of CO2 after changes in T.
That all besides the troubles you have to get the slope and the amplitude of T variability equal to the slope and amplitude of the variability of dCO2/dt.
You are not even remotely in the ballpark, Ferdinand. The way you are trying to incorporate the temperature into the CO2 has no mathematical basis whatsoever.
You have to match the dCO2/dt. Once you have done that, you cannot do anything else to manipulate the integration which results in CO2. CO2 and dCO2/dt are not free to be specified separately. The change in CO2 from the beginning of the integration interval to the end is uniquely determined by dCO2/dt.
When dCO2/dt is in phase with T, then CO2 will not also be in phase with T, but with the integral of T. The games you are playing, trying to specify these two functions independently, are wrong on the most elementary level of calculus one could imagine. Your recipe is a Tower of Babble. It is not even math. It is magic. It is an incoherent ramble of the first order. It is not even possible to be more wrong. There is not even a glimmer of fact to it.
I suggest you recheck your work. You most likely have a sign error, and have gotten either the a or b feedback negative. At the unique equilibrium point, the characteristic equation is
s^2 + (4*c*Teq^3)*s - a*b = 0
One of the roots of this equation is always positive if a and b are positive. Hence, the equilibrium is unstable, and there is no other.
Bart, as my math indeed is too long (mostly some 50 years) ago, but I remember some of the basics, here a few questions where I like to have a clear answer from you:
- does a sinusoidal change in temperature without any increase over time give a sinusoidal change in CO2 with a 90 deg lag? - does the derivative of a sinusoidal variation as above lead to a 90 deg lead of both T and CO2 in the derivative, compared to the original values? - does that still show a 90 deg lag between dCO2/dt and dT/dt? - does the shift between the derivative and the original values make that T and dCO2/dt synchronize?
- does the integration of dT/dt shift the sinusoid again forward with 90 deg? - does one need to add another 90 deg lag to reflect the influence of the integrated dT/dt variation on the CO2 variation of the original values?
and finally: - can you match the slope and amplitude of T variability with the slope and amplitude of dCO2/dt variability in this case?
"- does the integration of dT/dt shift the sinusoid again forward with 90 deg?"
Integration always induces a 90 deg phase lag from the quantity being integrated.
"- does one need to add another 90 deg lag to reflect the influence of the integrated dT/dt variation on the CO2 variation of the original values?"
Let me restate that for you:
"- does one need to integrate once again to reflect the influence of the integrated dT/dt variation on the CO2 variation of the original values?"
The statements are equivalent. If you add a 90 degree phase lag, you are integrating. There is no other way to add precisely 90 deg of phase lag in a natural, minimum phase system. You cannot just add and subtract arbitrary phase variables as you please without changing other properties of the time series.
The answer is "yes". And, when you integrate again, you are doubly integrating dT/dt, which is thus the integral of T. And, that integral will have the curvature which results from integrating the slope in T. And, that curvature accounts for all of the curvature in CO2. As adding in human inputs would again increase that curvature, there is no room for them.
"- can you match the slope and amplitude of T variability with the slope and amplitude of dCO2/dt variability in this case?"
Perhaps with better data. When your data are uncertain, however, it is a fool's game to try to match everything perfectly.
Even then, these data are bulk quantities, and the true relationship is only broadly represented by them. To get variables with a precise relationship, we would need to know precisely the global distribution of temperatures, and of CO2 upwelling and downwelling, and the full solution of a set of coupled partial differential equations to weight accordingly. And, even then, there are other external forcings which can cause deviations between the variables, notwithstanding their underlying relationship.
This is a complex problem, and our data limited. But, that is how science works. None of the equations of our great theories hold perfectly. Even F = m*a fails in microscopic systems and in large, rapidly evolving ones. But, we can still manage a level of skill with them which allows us to determine, at least to some level of approximation, how particular systems will evolve.
I mean, the various temperature sets themselves do not agree with one another to the level you are demanding. Which one would I even choose? What if none of them are exactly right?
"- does that still show a 90 deg lag between dCO2/dt and dT/dt? - does the shift between the derivative and the original values make that T and dCO2/dt synchronize?"
I may have missed the meaning here, and answered hastily, so let me lay it out carefully.
dCO2/dt lags dT/dt by 90 degrees. If you integrate dT/dt to get T, then you are lagging dT/dt by 90 degrees, so now T and dCO2/dt will be synchronized in phase.
What I have been reading from you is that you want to have
CO2 = a*HA + b*T
for HA being the accumulated human inputs, T being the temperature, and a and b being constants.
But, in that case,
dCO2/dt = a*dHA/dt + b*dT/dt
dT/dt is not in phase with dCO2/dt, so this model fails. To get it into phase, you would need to lag dT/dt by 90 deg, which is equivalent to saying you would need to integrate it. The model is then
dCO2/dt = a*H + b*T
where H = dHA/dt. Then
CO2 = CO2(0) + a*HA + b*integral(T)
where CO2(0) is the initial value of CO2 and HA(0) = 0 and the integral of T starts at 0.
with Teq being nominally constant. This is OK because A) T being temperature anomaly has an arbitrary baseline to begin with B) H is not even approximately a constant, so it is not just substituting an arbitrary extraneous variable to take the place of H.
The conclusion that human inputs have little effect is not dependent on that offset, either. It follows from the fact that, to fit both the trend and the variability of dCO2/dt, b has to be such that a is necessarily insignificant.
The statements are equivalent. If you add a 90 degree phase lag, you are integrating. There is no other way to add precisely 90 deg of phase lag in a natural, minimum phase system. You cannot just add and subtract arbitrary phase variables as you please without changing other properties of the time series.
As Paul_K showed (Oct 26, 2013 at 8:19 AM and Oct 26, 2013 at 2:34 PM), the exact 90 deg shift of CO2 after T is the result of a (near linear) response function of CO2 to changes in T. But that is a response function that with a finite temperature increase will give a finite increase of CO2 in the atmosphere (according to Henry's law), not a continuous, indefinite increase.
This response function is seen on all time scales from decades to multi-millennia and is quite fixed around 8 ppmv/K.
Thus calculating the integral of dT/dt and adding a 90 deg shift * 8 ppmv/K for the response of CO2 on temperature changes is as valid as using the integral of T anomaly with an offset and a factor which fits the trend and amplitude of dCO2/dt.
The difference is that in the former case there is plenty of room for human emissions to cause the trend in CO2, while in the latter case there is no room for human emissions. Which is the right one? All observations show that it is the former...
Again, you misapprehend what Paul_K was saying. Please see his note to me at Oct 27, 2013 at 9:13 AM:
You, Murray Salby and I all share a common view that the modern observational data displays an approximate relationship of the form dCO2/dt = gamma* (T-Te) This is the only way that the modern observational data can be explained in terms of phasing, so you don’t need to pursue that argument further for me at least.
Over a very long period of time, constant values for gamma and Te in Paul_K's nomenclature, k and Teq in mine, may be inappropriate. We could always adjust these values over time to match current conditions. Or, perhaps a global model such as Paul_K suggested at 8:19 would require less maintenance in the long term, producing a more continuous fit and allowing greater insight with additional conclusions to be reached.
But, it is a moot question as far as our discussion here is concerned. For the timeline of interest reaching back to at least 1958, either model will produce essentially indistinguishable results. And, the ineluctable conclusion from those results is that there is very little room for significant influence of human inputs to atmospheric CO2.
One last thing, Ferdinand... We do not disagree that temperature alone cannot explain the rise in CO2. However, if there is a continuous influx of CO2 from a temperature dependent source, such as outgassing from the oceans of upwelling CO2 rich waters, then there will be a temperature modulated, continuous accumulation of atmospheric CO2. That is the type of behavior which is, in fact, observed.
Ferdinand, My apologies for the delay in response. I have been off the air for a while. In answer to your question, I cannot attend the Salby lecture unfortunately. I don't live in the UK and can't make the time for the trip.
I would urge you in light of some of your comments to watch Salby's Hamburg lecture a couple of times. Although I still do not agree with his final conclusions, his points are not trivial. In particular, you should try to follow his reasoning closely regarding (a) the source of the changing (atmospheric) carbon isotope ratio and (b) why he believes that the temperature sensitivity has been underestimated from ice-core data. His arguments in both cases are coherent and not to be lightly dismissed. W.r.t. (a) this doesn't prove his theory as such, but it removes one possible objection to it. W.r.t. (b) you need to note that he talks about two different phenomena which affect the measurements of CO2 in ice cores - one of which (diffusion) affects predominantly the high frequency changes and the second of which (attenuation from variation in depth of burial) affects the long period changes. This leaves maximum coherence in the mid-period changes, where the degree of underestimation of actual atmospheric CO2 levels is minimised. I have no expertise in this area, but these parts of Salby's story make sense to me, and would seem to merit a considered response.
Oct 31, 2013 at 4:35 PM | Unregistered CommenterBart
Bart, I think we are generally speaking the same language. However, I have yet to convince myself that the observations cannot be explained - as Ferdinand has suggested - by the high frequency variation (and derivative) being temperature dominated and the longer period change being dominated by anthropogenic addition.
Or, perhaps a global model such as Paul_K suggested at 8:19 would require less maintenance in the long term, producing a more continuous fit and allowing greater insight with additional conclusions to be reached.
I understood exactly what you meant by the above in context, but just to be pedantic, I consider this model to be at best a partial model to explain (only) the temperature contribution while holding partial pressure constant. I am still trying to figure out what a more general model needs to look like.
It simply is impossible that the oceans are a net source of CO2. They are a net sink. You can't have a continuous increase of CO2 in the atmosphere from the oceans and at the same time no influence on any observation, while all observations show the human influence.
Thus what is wrong?
It is certain that the short time variability is caused by temperature changes and it is pretty sure that the increase of 70 ppmv over the past 50 years is not caused by temperature changes.
While looking at possible problems, I encountered one which I didn't expect: if the CO2 increase lags T, it lags more if it is on a slope than without a slope for T, while T on the slope is synchronized with T without slope:
That gives a similar change in lag in the derivative: http://www.ferdinand-engelbeen.be/klimaat/klim_img/sim_dsin_dslope.jpg while the two temperatures are fully synchronized...
I suppose that the steeper the slope, the larger the extra lag will be. But I suppose that you can solve that with the right math...
Anyway, that gives doubts over the necessary integral to synchronize dT/dt and dCO2/dt, as the shift in part is caused by the slope of CO2 and thus is less than 90 deg.
Thanks for the reaction. I have followed Salby's lecture in Hamburg a few times as it is at moments difficult to follow.
I am certain that he, like Bart, is brilliant in math, but I fear that he lacks some basic knowledge in real life chemistry and physics and hasn't read the recent literature on several items he touches.
Take his:
(a) the source of the changing (atmospheric) carbon isotope ratio
The bulk of all carbon on earth in oceans, carbonate rock layers, volcanic vents (all inorganic carbon) has a δ13C ratio around zero per mil. The bulk of all fossil and current organics have a carbon ratio (far) below zero. Thus there is no possibility to make a differentiation between fossil and new organics for the firm decrease in δ13C in the atmosphere on the basis of the difference in isotopic ratio. See here the decline in δ13C over the past 600 years in the atmosphere and the ocean surface (Bermuda): http://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.gif
But there are two ways to show which is the source: - the δ14C ratio is different: fossil fuels are completely depleted of 14C as much too old and all 14C is decayed. - the oxygen balance: fossil fuel use oxygen. Based on fossil fuel use inventories and the burning efficiency for each type, one can calculate how much oxygen is used. The real amount can be measured (since about 1990 sufficient in accuracy: less than 1 in 200,000!) to make the balance for the biosphere (all together: plants, insects, bacteria, animals). That shows that there is a small deficit in oxygen use: the whole biosphere is a net source of oxygen and thus a net sink for CO2 and prefentially for 12CO2, leaving relative more 13CO2 in the atmosphere. Thus not the cause of the δ13C decline. See: http://www.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
(b) why he believes that the temperature sensitivity has been underestimated from ice-core data.
About ice cores: the same type of problem: - diffusion is quite well understood in ice cores, as that depends on factors like accumulation speed and temperature, which affect the time the pores are still open en connected with outside air and the migration speed in decreasing pore diameters. That makes that over the past history one can have resolutions ranging from about a decade (Law Dome 150 years) via 20 years (Law Dome 1,000 years) and 40 years (Taylor Dome 70 kyear) to 560 years (Dome C 800 kyear). That gives that there is an overlap of resolutions over the past 800 kyears, where all ice core measurements are within 5 ppmv for the same gas age, here for the past 1000 years: http://www.ferdinand-engelbeen.be/klimaat/klim_img/antarctic_cores_001kyr_large.jpg There is even an overlap of ~20 years between the fast accumulation ice cores of Law Dome and direct measurements at Mauna Loa: http://www.ferdinand-engelbeen.be/klimaat/klim_img/law_dome_sp_co2.jpg Gas age distribution was measured top-down in firn at Law Dome and confirmed the model calculations. Here more info over the age distribution (Fig.11) and a lot of more interesting info: http://courses.washington.edu/proxies/GHG.pdf and the 14C bomb spike distribution: http://onlinelibrary.wiley.com/doi/10.1029/96GL03156/abstract
Migration in the ice itself is unmeasurable and would flatten out the peaks over each interglacial 100 kyr back in time, which is not seen at all.
My impression is that Salby needed migration to support his theory, but that wasn't based on reality...
"However, I have yet to convince myself that the observations cannot be explained - as Ferdinand has suggested - by the high frequency variation (and derivative) being temperature dominated and the longer period change being dominated by anthropogenic addition."
At the very least, you should consider Occam's Razor - why add stuff in when it is already explained by something simpler? The contributions introduced by humans really are small in relation to total flows. We aren't at the center of everything, and it isn't always our fault.
In any case, I must go on a trip, and will not be responding further to this thread in the near future. It is only a matter of time before the divergence of human emissions and atmospheric concentration becomes glaring, so I am sanguine about the prospects for it all getting worked out in the end. Thank you, Ferdinand, for being gracious and polite as always.
Reader Comments (102)
"To the contrary..."
Sorry, no, you are wrong. You have eliminated the data which shows how bad the fit is.
"As said many times before..."
And, you were wrong many times before. It works the same as with human emissions. There is CO2 coming in from the outside, pushing its way in. If human emissions can do it, so can this. If an arbitrarily large influx of CO2 from the oceans cannot change atmospheric CO2, then nothing else can, either. Since this is obviously not the case, the proposition is false, QED.
"...but that is hardly influenced by a temperature increase..."
The rate of outward flux is modulated by the temperature.
This has all been argued before, and we are going in circles. Time will tell...
Sorry, no, you are wrong. You have eliminated the data which shows how bad the fit is.
All what I have done is plotting the same data as you have done, but using the same units for both variables, which gives a clear view of the ratio between the slopes of dCO2(emissions) and dCO2(observed). Your plot gives a completely wrong impression, because both variables are plotted in different units...
And, you were wrong many times before. It works the same as with human emissions. There is CO2 coming in from the outside, pushing its way in.
I never said that there can't be an increase in CO2 from the (deep) ocean upwelling. Theoretically it may happen. But such an upwelling must increase the total circulation through the atmosphere in the same ratio as the human emissions (a threefold since 1960) in exactly the same time frame to dwarf the human emissions and to give the same effect in the atmosphere. It is that which violates all known observations.
Thus in reality, there is no increase in deep ocean circulation (or whatever other natural cause) as the more recent estimates of the residence time of CO2 show a lengthening, which is what can be expected from a rather constant throughput in an increased atmospheric content. Neither is such an increase visible in the d13C ratio, etc...
The rate of outward flux is modulated by the temperature.
Hardly, according to Henry's law for 1 K temperature maximum 16 ppmv extra increase towards an equilibrium above the increase caused by the extra CO2 from the increased upwelling.
"But such an upwelling must increase the total circulation through the atmosphere in the same ratio as the human emissions (a threefold since 1960) in exactly the same time frame to dwarf the human emissions and to give the same effect in the atmosphere."
This is a very usual and unremarkable type of behavior for a feedback system. It is much more ordinary than CO2 tottering on the edge of a knife for centuries with no countervailing feedbacks maintaining stability.
"Thus in reality, there is no increase in deep ocean circulation..."
More meaningless narrative drivel.
"Hardly, according to Henry's law..."
Asserting this once again with no theoretical backing gets you nowhere. I have shown mathematically how it comes about. My math beats your assertion.
Bart,
I don’t think you got the gist of what I was saying w.r.t. the time-derivative of CO2, but I’m not surprised - it wasn’t exactly spelled out.
I took a couple of hours out late yesterday evening to build the model I briefly discussed in my previous post, and have tested it on synthetic data. One of its key features is that the match between temperature (as input) and the scaled time derivative of CO2 is perfect. In other words, it can match the key observations which are leading you to your conclusions, and yet this model requires no heroic assumptions at all. In fact all it requires is recognition of the fact that equilibration between ocean and atmosphere is not instantaneous. Rather than suggesting that we should be surprised to see a close relationship between the scaled time-derivative of CO2 and temperature, this model suggests that we should actually expect such a relationship, and yet it leads to a bounded solution for CO2 concentration.
For the transient behaviour, I am just using a simple response function of the form:-
τ * dCO2/dt = ΔT - f(T)* ΔCO2
where ΔT and ΔCO2 are measured from an arbitrary initial equilibrium condition. This equation is based on the assumption that the process of release of solute with temperature change starts off quickly and slows down as the concentrations adjust – a commonly observed phenomenon for the transient behavior of chemical equilibration processes.
For a fixed step change in temperature its solution yields an exponential response function of ΔCO2 in time. The temperature function, f(T), is analytically derived so that the CO2 response function at large values of t for a fixed temperature step asymptotes to the equilibrium concentration predicted from Henry's Law - based on the accepted equation for how the Henry coefficient changes with temperature. The time it takes to get to equilibrium is controlled by the parameter τ ("tau"), but is also a weak function of T via the function f(T). Note that this model is completely compatible with Henry’s Law – including the fact that for a fixed temperature change, the model does, if left alone, equilibrate at a new constant concentration value of CO2.
The model does not consider the effect of changing partial pressure. It assumes that over short timeframes, the change in atmospheric partial pressure of CO2 is sufficiently long wavelength that it has little impact on the phasing of dCO2/dt. In other words, the time derivative in the short term is dominated by the effect of temperature fluctuations.
The above equation is readily solved using a Runge-Kutta (RK4) routine. Having confirmed the numerical accuracy of the solution routine on simple step and analytic functions, I then checked out the model's behaviour on various temperature inputs involving combinations of sinusoidal cycles of differing frequencies and amplitudes and with different assumptions about the time taken to reach equilibrium.
Here is an example where, as the temperature input, 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
Note the near perfect match between dCO2/dt and Temperature.
You should mark well that it is very easy to bring the time-derivative of CO2 into exact phase with temperature inputs in all of the examples I tested, and this is the point I was trying to make in my earlier post. This is not just a “co-incidence of lag-time” as some have suggested, nor a simple integrative effect. For an assumption of instantaneous equilibration, which was what my previous post was expressly referring to, the time-derivative of CO2 should exactly lead temperature by pi/2 and be in phase with dT/dt. (This comes straight from a partial differential of the Henry coefficient w.r.t. T multiplied by dT/dt). 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.
The coincidence of amplitude variation stems from the same source. For a fixed step change in temperature, the response function (CO2 vs time) is very close to linear for durations which are short relative to the total response time of the system, and moreover the initial gradient is a function of the magnitude of the step temperature change. Hence there is an apparent simple linear relationship between dCO2/dt and deltaT if we are looking at cycles of short duration. The larger the response time of the system, relative to the periodicity of the cycles of interest, the closer this relationship appears to be.
The main message is that the observation of an approximate scale relationship between temperature and the time derivative of CO2 does not allow us to conclude that there is a simple underlying relationship of the form dCO2/dt = k(T-Te) . You cannot rule out the possibility that the actual functional relationship between CO2 and T (for an assumed invariant or long wavelength change in partial pressure) is of the form of the response equation above or something similar. In fact, it seems a lot more likely since it better fits other known science, including Henry’s Law, as well as observations.
Bart:
This is a very usual and unremarkable type of behavior for a feedback system. It is much more ordinary than CO2 tottering on the edge of a knife for centuries with no countervailing feedbacks maintaining stability.
Bart, the observations show an increase of CO2 in lockstep with human emissions. That may be the result of a response time of the sink capacity of CO2 which is slower than needed to remove all human emissions in short time (which fits all observations, including ice ages for response times of ~50 years) or it may be the result of a huge increase in natural circulation with a response time which is short enough to remove most of the human emissions, but not fast enough to remove all of the extra natural circulation (which doesn't fit any observation). In the latter case, the natural circulation must mimic the human emissions in increase ratio over the time frame 1960-current, or the increase rate in the atmosphere wouldn't mimic the exact ratio shown by human emissions.
This is not just a “co-incidence of lag-time” as some have suggested, nor a simple integrative effect.
Paul_K, I was not sure about this, as I lack the theoretical background, but was suspecting it as the coincidence between T and dCO2 was too nice. Thanks for your input, the discussion gets more interesting now...
Ferdinand,
Understanding the proof in principle only requires the equivalent of A-level maths. See if this helps.
The only complicating factor in my response equation is introduced by the f(T) term to account for the non-linearity in temperature dependence in Henry’s Law. In practice, for the small temperature changes we are considering here, the relationship between equilibrium concentration and temperature can be linearised with only small error (about 2% for a 1 degree change in temperature), so strictly speaking this feature is gilding the lily. Another way of saying this is that the f(T) term can be replaced by a constant in the response equation to a very good approximation. Let’s call this constant β. The response equation above can then be written in a much simpler form as:
τ*dCO2/dt = ΔT – β *ΔCO2
Now let’s set the (input) temperature signal equal to a sine function, ΔT = sin(ωt). The new simplified equation can be solved analytically and yields the following solution (for boundary conditions ΔCO2 = 0 at time t = 0).
ΔCO2 = Asin(ωt) – Aωτcos(ωt) + Aωτexp(-t/τ)
Where A = 1/[β*(1+(ωτ)^2)] = a constant for fixed value of τ.
.
You can confirm for yourself that this is indeed a valid solution.
The third term is a short-term transient which disappears as time goes on, and so the system rapidly "stabilises" into an oscillatory function which is the weighted sum of the first sine term and the second cosine term. The first term is exactly in phase with T. The second term is exactly in phase with dT/dt but is exactly pi/2 out of phase with T.
If we assume a small value of τ, equivalent to a near instantaneous response, the first sine term has all the weighting and so the solution for CO2 is in phase with temperature. On the other hand, with a high assumed value of τ, the second term has all the weighting and so the solution for CO2 shifts pi/2 out of phase with temperature; this brings the time derivative of CO2 exactly in phase with temperature, and that is exactly what we see in the model solution of the synthetic data as well as in the observational data from Bart's plots. This phase shift cannot be greater than pi/2 - that's mathematically impossible. Hence, any large value of tau will deliver the observation that dCO2/dt is in phase with temperature. No extraordinary coincidence is required – just a “slow” ocean response time. Since estimates of theoretical equilibration times for ocean diffusive processes include some estimates between six hundred and three thousand years, I don’t think it is too much of a stretch to assume that the theoretical equilibration time for CO2 solute in response to temperature change is going to be a lot larger than a few decades.
Paul_K,
thank you for this very clear exposition. You've elegantly put into maths the thought experiment I was trying to describe the other day. We know the response time of the ocean is slow and it is not surprising given this that dCO2/dt should be a function of Delta T.
There is a whole bunch of observational data that bart dismissed ad "narrative" that are wholly inconsistent with his model. Not least of these is the fact that the PCO2 of the atmosphere is greater than that of the surface ocean thus the dominant CO2 flux is from atmosphere to ocean despite the small temperature rise that has occurred.
Perhaps you should drop Murry Salby a line!
Ferdinand,
I managed to screw up the constants in the previous post. It should have read as follows:
Further references to τ should then equally be adjusted to be references to τ'.
My apologies for any confusion.
Paul_K,
Thanks a lot for the clear explanation! Even I could follow it with my 50 years ago (and hardly used) math...
Thus the take away message is that no matter the frequencies of the fast variations in T, with a response of the oceans (a lot) slower than the fast variations, one will always have that T is in phase with dCO2.
One remark: some of the ocean (and other natural) responses are fast, some slower and some are extremely slow:
The ocean surface responds very fast (1-3 years) to changes in the atmosphere, but that is only for 10% of the change, because of the Revelle (buffer) factor. That is the part that also is responsible for the fast reactions on temperature. Vegetation currently is a net sink for ~15% of human emissions and the deep oceans for ~25%. The total sink rate is about ~4 GtC (2 ppmv) for ~210 GtC (100 ppmv) or slightly over 50 years for all sinks together.
As the main variability in dCO2 is much shorter (1-3 years), the 50 years is slow enough to allow for the observed phase lock between T and dCO2. And more than fast enough to allow for the thight response seen over ice ages, but where also other, slower responses (land ice / vegetation area, deep ocean currents,...) are at work...
Oct 26, 2013 at 8:19 AM | Paul_K
"The main message is that the observation of an approximate scale relationship between temperature and the time derivative of CO2 does not allow us to conclude that there is a simple underlying relationship of the form dCO2/dt = k(T-Te) ."
Paul - That's fine. There are always multiple models which can mimic similar behavior over a finite interval of time. I have given you my hypothesis for how a particular model could come about. You are suggesting another one.
Either way, the important part is that they mimic similar behavior over the finite interval of time. If you match dCO2/dt as a function of temperature and integrate it, you will get the current CO2 concentration, without using any human inputs at all.
That is the important point. You cannot get a 90 deg phase shift at all observable frequencies without having an effectively integral action over the frequencies of observation. It is a necessity flowing from the Bode phase-gain requirement that the slope of the gain response function is proportional to the phase. A -90 deg phase lag always produces a -20 dB/decade gain slope, i.e., the gain response of an integrator, at least over the frequencies of observation.
And, when you integrate the temperature relationship, you will have accounted for the observed rise in CO2.
All roads lead to Rome. Humans are not responsible for the rise in CO2.
In case that is not clear enough, let me try to put it another way.
dCO2/dt integrates into CO2. This is a unique relationship, modulo an arbitrary constant offset. If you match dCO2/dt with any function and integrate it, you will get a match to the change in CO2 over that interval.
You cannot match a -90 deg phase shift without getting an effective integration. And, when you do that, the slope in the temperature record is going to integrate, too. It will account for all, or at least most, of the curvature in the accumulated CO2 plot.
The rate of human emissions also has a slope. If you try to add that into the integration, you will get too much curvature.
That is why human emissions cannot be responsible for the rise in CO2 - there is little to no additional room for them to integrate into the result.
Let me try one other tack as well.
T is coincident with dCO2/dt. What Ferdinand bascially wants to do is set
dCO2/dt = L*E + H*T
E = human emissions
L = low pass filter operator
H = high pass filter operator
The high pass filter operation is necessary in Ferdinand's paradigm because, otherwise, the scale factor which matches the variations in T already matches the slope in T to the slope in dCO2/dt.
Ferdinand considers this a fluke, and wants to eliminate the ramp in T and replace it with the scaled ramp in E. Ferdinand thinks you can do this by making H a least squares fit and subtracting the trend. But, of course, Nature has no way of doing this, as it amounts to an anti-causal filter.
In fact, in Nature, H is severely constrained. It can be no more than first or, at a stretch, second order. And, its cut-on frequency must be fairly high in order to take out the ramp in T within the given interval.
Here's the problem: any natural filtering function H satisfying these requirements is going to have serious phase distortion within plus or minus a decade of the cut-on frequency. That is going to ruin the widely observed -90 deg phase shift, and cause a lot of very observable phase distortion. Such phase distortion is not observed.
Ferdinand's paradigm is unphysical. It only exists in his mind.
Bart:
T is coincident with dCO2/dt. What Ferdinand bascially wants to do is set
dCO2/dt = L*E + H*T
As Paul_K showed, the phase lock of T and dCO2/dt is pure a result of the fast response of a few processes on T changes and a slow(er) response of the oceans on any variability, whatever the source. Thus (at least) two different processes are at work with different response times. While T is the main driver for the fast responses, it may or may not be the driver for the slope of dCO2. In my opinion, based on Henry's law and the response of CO2 on (very) long time periods (50 years to multi-millennia), T has a limited influence on CO2 levels: from 4-5 ppmv/K short term to 8 ppmv/K long term. That is all. Thus T is not responsible for the bulk (70 ppmv since 1960) of CO2, neither for the slope of dCO2.
What I wanted to show is that:
dCO2/dt = m*dCO2(emissions)/dt + n*dT/dt
minus the sink rate of CO2 for the current pCO2 difference with the equilibrium CO2 pressure.
Which can be seen in Wood for trees
But because WFT doesn't have the emissions in its database, here a plot of emissions and increase in the atmosphere where m in the above equation is 0.53 over the past 111 years (since 1900):
http://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2.jpg
and the slope of dCO2(emissions)/dt is about twice the slope of dCO2/dt:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_em3.jpg
As the slope of T is near-linear, the slope of dT/dt is near zero, thus dT/dt is not responsible for the slope of dCO2/dt and only responsible for the (lagged) variability of dCO2, and both dCO2(emissions)/dt and dT/dt are simply additive without any filtering, as good as the influence of CO2(emissions) and T is additive in the atmosphere.
Paul Dennis,
After I had gone through the above model-building process, I was seriously thinking about writing it up a little more seriously, including a full match to modern data, and bringing it to the direct attention of Professor Salby. However, I thought I should first listen to his latest thoughts on the subject.
The last time I heard him speak on his subject was over a year ago, and his position has clearly evolved. In the lecture I previously heard, he spoke about the relationship between dCO2 and T in the modern record, but did not underpin it with a complete mathematical model. Last night I watched the recent video of his Hamburg lecture – referenced by Ferdinand in a previous post. It is found here.
http://www.youtube.com/watch?feature=player_embedded&v=2ROw_cDKwc0#t=0
I would particularly draw your attention to his presentation between 16 and 23 minutes, where he describes in some detail exactly the same mathematical model which I have been describing above. I don’t think I can teach him anything!
Incidentally, the entire lecture is brilliant and his arguments are very coherent with one exception in my mind – well worth watching. Even though I remain ultimately unconvinced by his dismissal of the human addition to CO2, wherein I believe he sets up a logical paradox, he left me convinced that we have underestimated the strength of the temperature control knob on atmospheric CO2. See also my response to Bart below.
Bart,
Thanks for your responses. You, Murray Salby and I all share a common view that the modern observational data displays an approximate relationship of the form
dCO2/dt = gamma* (T-Te)
This is the only way that the modern observational data can be explained in terms of phasing, so you don’t need to pursue that argument further for me at least.
However, your position appears to be much more radical than Salby’s. His full model for atmospheric concentration (using his choice of constants) includes a dissipative term while yours does not:-
dCO2/dt = gamma*T – alpha*CO2
(Taken from his April lecture in Hamburg.) This is identical mathematically to the system I was solving above!
The response time for this system varies inversely with alpha. With a small value of alpha, (long system response time), then short term behaviour is dominated by the first term - which is what we see in the observational data.
The difference between your position (if I understand it correctly) and Professor Salby’s is extremely important. His model recognises that the CO2 response to a temperature change is bounded – it just takes a long time. Your model recognises no bounding solution. Hence you conclude that CO2 cannot have a warming effect because it would have led to a runaway feedback situation. My previous posts were trying to highlight that this is a very unsafe conclusion, which relies on the use of a short-term approximation as a full model. Professor Salby stops a long way short of drawing this conclusion, although, from his lecture, he clearly thinks that the effects of CO2 have been overestimated (as do I).
Despite my admiration for the quality of the work Salby has done, I still cannot accept his inference that most of the change in atmospheric CO2 arises from a simple temperature dependency. In my view he sets up his own unnecessary paradox to reach this conclusion. It is this. In order to explain why dCO2/dt comes into phase with temperature, he needs to postulate or demonstrate that counteracting or dissipative forces are slow (small value of alpha in his model). This takes him towards a conservative model in short timeframes, in his own jargon. However, the atmosphere doesn’t know where a molecule of CO2 comes from. They are not labelled blue and red. If there is very slow dissipation of molecules put there by temperature effect, then there has to be equally slow dissipation of molecules put there by mankind. You cannot postulate separate dissipation rates for the blue and red molecules. Hence the more reasonable explanation has to be that the CO2 profile in time is controlled by both elements.
Paul_K,
Another point where Salby goes wrong is his theoretical calculation of the migration of CO2 in ice cores. He calculated such a migration to fit his theory:
After 30 minutes in his lecture, he looks at the suppressing of high frequency variations in the ice core. While that is true, that highly depends of the resolution of the ice core in combination with the frequency of the variations, but his interpretation of a 10 fold suppression on time scales of 10 kyrs is completely out of reality for the higher resolution ice cores like Taylor Dome (resolution of ~40 years over 70 kyears).
That all is based on some calculated estimate of a huge CO2 migration in the ice (shown after 32 minutes) which is not seen in any ice core. If that would be the case, the ice core CO2 record in the far past would get flatter and flatter for every interglacial back in time, which is not measured at all: the CO2/temperature ratio remains the same for all glaciations/deglaciations over 800 kyears at around 8 ppmv/K, showing no measurable CO2 migration in the coldest (-40°C) ice cores like Vostok (420 kyears of data) and Dome C (800 kyears of data).
If there was a real 10-fold suppression of peaks over 10 kyrs, then the measured peak at 100 kyr of 300 ppmv would have been 3000(0) ppmv (on another time in his speach he says a 10-fold suppression over 100 kyr), but while ice cores filter out the high frequency data over the resolution period, that doesn't change the average over that period, which implies that the CO2 levels during the (90% of the time) cold periods would be negative...
BTW, any chance that you can be in London at Salby's speach on November 6th?
Oct 26, 2013 at 8:11 PM | Ferdinand Engelbeen
"What I wanted to show is that:
dCO2/dt = m*dCO2(emissions)/dt + n*dT/dt"
Doesn't work. dT/dt is out of phase with dCO2/dt. There is no way around this. It is in phase with T. It follows that CO2 itself must be essentially proportional to the integrated temperature anomaly with respect to a particular baseline, at least over the timeline of interest.
Oct 27, 2013 at 9:13 AM | Paul_K
"However, your position appears to be much more radical than Salby’s. His full model for atmospheric concentration (using his choice of constants) includes a dissipative term while yours does not:-
dCO2/dt = gamma*T – alpha*CO2."
Not so much. I am simply more interested in the short term behavior. As I said above, over a finite interval of time, many models can produce virtually indistinguishable results. What I am most interested in is establishing that human inputs are NOT the driver. And, that fact is established by the fact that a temperature dependent model can explain virtually the entire behavior of CO2 since 1958, the year in which precise measurements of CO2 in the atmosphere began. That model does not allow human inputs to be a significant player, because it produces a slope in dCO2/dt which matches essentially perfectly, and there is little room for the slope in human rate of emissions to have additional impact.
"Hence you conclude that CO2 cannot have a warming effect because it would have led to a runaway feedback situation."
It doesn't matter so much. Your "alpha" above is small (long time constant), and hence cannot stabilize the system unless the sensitivity of temperature to CO2 is very weak, if not precisely zero.
"...I still cannot accept his inference that most of the change in atmospheric CO2 arises from a simple temperature dependency."
The process is quite apparently temperature dependent. That does not mean, however, that temperature is the only player. Going back to what we will now, in deference to your concerns, dub the "short term model",
dCO2/dt = k*(T - Teq)
Let's suppose that Teq is more or less equal to the global temperature anomaly in say 1945, and it had been at that level for some time, so that atmospheric CO2 more or less stayed in the neighborhood of a constant level. Then, at roughly that time, there is an abrupt shift in the CO2 content of upwelling ocean waters which knocks Teq down a few notches. This establishes an increasing trend in CO2. Over the next 53 years to about 1998, temperatures rise, and the atmospheric rate of change accelerates. Then, temperatures settle out at a plateau, and the rise in atmospheric CO2 decelerates in lockstep, with the rate of rise becoming nominally constant.
That is a pretty accurate description of what we observe in the modern temperature and CO2 records. If temperatures decline, as they appear poised to do for the next 20 or so years, we should see additional deceleration in the accumulation of CO2. This is my prediction of what is in store for us. Watch, and we will see what happens.
It is important to point out that the terms k and Teq are not necessarily constant. They just appear to have been fairly constant over at least the past 68 years. But, gradual evolution, or even sudden shifts, are not precluded.
Oct 27, 2013 at 11:52 AM | Ferdinand Engelbeen
"If that would be the case, the ice core CO2 record in the far past would get flatter and flatter for every interglacial back in time, which is not measured at all: "
It does not follow. A low pass filter filters out frequency components until they reach the corner frequency, and then does not filter out anything else.
Bart:
Doesn't work. dT/dt is out of phase with dCO2/dt. There is no way around this. It is in phase with T. It follows that CO2 itself must be essentially proportional to the integrated temperature anomaly with respect to a particular baseline, at least over the timeline of interest.
Yes, dCO2/dt lags dT/dt, as good as CO2 lags T on all time frames. And as Paul_K showed, there is always a pi/2 shift between short term T variability and CO2 variability, which makes that T variability and dCO2 variability always align as result of the lag between CO2 variability and short term T variability. How does that prove that dT/dt is not the cause of the lagged variability of dCO2/dt?
Further the fact that the trend of dT/dt is essentially flat shows that there is not the slightest influence of dT/dt on the slope of dCO2/dt. That means that the influence of T on some CO2 producing process must be extremely non-linear to increase the total CO2 circulation through the atmosphere a threefold in the period 1960-current. Or a sevenfold if the deep ocean upwelling were the only cause and that all as result of an only 0.5 K temperature increase... Such a process, if it exists at all, would violate all known observations...
It does not follow. A low pass filter filters out frequency components until they reach the corner frequency, and then does not filter out anything else.
Filtering of the high frequency atmospheric CO2 changes in ice cores only happens during the open pore times between surface snow layers and fully closure of the air bubbles in the compacted ice. The filtering time and thus the resolution of the ice core depends of the yearly snow accumulation and average temperature and varies between less than a decade (Law Dome) and 600 years (Vostok).
Migration in the ice itself (as Salby alludes) only ends (in dynamic equilibrium) when there are no CO2 level differences anymore...
You just don't get it, Ferdinand. You don't understand what Paul did and what he was claiming. There's no point in going further.
Bart, what I got from what Paul_K did is that the short term variability in CO2 and CO2 rate of change is from the short variability of temperature and that you can only get the variability of T and dCO2 in phase if the removal of CO2 out of the atmosphere is slower than the slowest of the fast variability (which is not more than 2-3 years).
That is completely contrary to what you expect: a very fast response of the sinks so that only temperature is responsible for all variations, short term and long term together. But the slower response of the sinks excludes temperature as the main cause of the longer term response, as we have human inputs which are more than sufficient to explain the whole trend.
If the variability and the trend of CO2 was caused by one and only one process, then you are right, but as Paul_K effectively decoupled the variability and the trend (as good as dT/dt and dCO2/dt show), there is no reason to expect that both are caused by temperature alone...
No, Ferdinand, that is not what he was saying. He was not disagreeing with me on the substance, he was simply suggesting that it cannot be (he believes) an open ended integration, and must have some sort of limiting feedback.
And, as I stated, he may well be right, but the question is moot as far as attribution is concerned. Over the timeline of interest, the open-ended integral model is just fine. Significant human culpability for measured atmospheric CO2 is still not in the cards.
Bart - You assert that your climate system is "unstable", using the equations:
dCO2/dt = a*T
dT/dt = b*CO2 - c*T^4
Given these equations, of course it is. Your first equation says that CO2 levels will always increase with a>0, because T must be greater than 0 (3rd law and all that).
How would you propose that CO2 levels decrease in falling temperatures (like going into glacial periods) in your model?
OK Bart, let us repeat the attribution with a simple model I did make some time ago, where 95% of the increase in the atmosphere is caused by "human" input (slightly quadratic) and 5% by a linear temperature increase + a higher frequency sinusoid, no sinks involved:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sim_co2_temp_95.jpg
According to Paul_K, the temperature sinusoid causes a CO2 sinusoid with a pi/2 lag, if the sink rate is slow enough, which is anyway the case here.
Now have a look at the derivative:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sim_dco2_dT_Tanom_95.jpg
There is a perfect match in timing of the short term variability between T anomaly and dCO2/dt and a pi/2 lag between dT/dt and dCO2/dt, just like Paul_K proved. And there is a (near) perfect match between the slopes of T and dCO2/dt, but also a perfect match between dCO2(emissions)/dt and dCO2/dt
According to your thesis, the perfect match in timing of the variability and similar slope between T anomaly and dCO2/dt proves that T is the only cause of the variability and slope of dCO2/dt and thus of the increase of CO2 in the atmosphere.
But there is a problem: we know that the model used 95% human and 5% temperature induced CO2 in the atmosphere.
Which proves that the perfect match of the variability and slope between T and dCO2/dt doesn't say anything about the attribution of the origin of the increase in the atmosphere, but only proves that T is the origin of the short term variability.
Oct 28, 2013 at 7:47 PM | Curt
I apologize that I muddied the waters here trying to get across a simple concept, but it was intended that this be a perturbation model, and a vastly simplified one at that. We can take it up one level of simplification by simply adding the equilibrium temperature and input Sun source as
dCO2/dt = a*(T - Teq)
dT/dt = b*CO2 - c*T^4 + Sun
This, again, is unstable for a and b both greater than zero. Assuming it is stable, If Sun dips down, such that the temperature decreases below Teq, then CO2 levels start to trend downward.
Oct 28, 2013 at 8:51 PM | Ferdinand Engelbeen
"There is a perfect match in timing of the short term variability between T anomaly and dCO2/dt and a pi/2 lag between dT/dt and dCO2/dt, just like Paul_K proved."
That is what happens with the open integral in my model, too. Paul's model changes nothing, because it is the same as my model if you take the time constant approaching infinity. Over a short time period of observation, the models are indistinguishable. His model is still going to produce a significant slope, which is going to integrate into the curvature of the total CO2 plot. His model does not filter out that low frequency signal. It cannot, because it is a low pass filter model - it passes low frequencies. It will pass the ramp up in temperature, which is a low frequency phenomenon.
For your model to work, you need a high pass filter mechanism acting on the temperature signal. There is no physical basis for such a high pass natural response, and it could not preserve the phase characteristics which are clearly preserved if there were such a mechanism.
Paul had a very narrow objection, and you interpreted it to mean what you wanted it to mean. But, you have misapprehended it.
What you have done here and here is bizarre. You seem to be saying that, if you can match the temperature to the CO2, then take the derivative of the temperature and scale it so the amplitude of its cycles matches the amplitude of the cycles in actual temperature, then integrate it, you get something insignificant, and this somehow proves that the slope in temperature does not integrate into the observed CO2. Mathematically, that makes no sense at all.
Just integrate the temperature signal, scaled for the variations, and it accounts for everything, no human inputs required.
You must integrate the variable which matches dCO2/dt, and no other. The integral is a unique relationship, modulo only an initial offset constant, between the derivative of CO2 and its integral. If you integrate something other than that which matches the derivative of CO2, then of course you will not get anything resembling CO2 as output.
T matches the derivative of CO2, therefore you must integrate T, appropriately scaled and baselined, to match the CO2. There is a slope in T. That gets integrated, too. That slope accounts for the curvature in the CO2 plot. You cannot add in additional human forcing to any level of significance because that will increase the curvature beyond that observed.
It is really very simple. Stop resisting the obvious. It is only going to be that much more painful for you when you have to face reality.
Because of the unique relationship between the derivative and the integral, you do not have to even look at the integrated signal. All the information needed is in the dCO2/dt plot.
You have to match what is in that plot. You cannot do it with dT/dt - it is 90 degrees out of phase with the variations in dCO2/dt. You must use T. T has a slope, which matches the slope in dCO2/dt when it is scaled to match the variations, and those variations are perfectly in phase (or at least, as perfectly as you can expect with stochastic data).
Adding in human inputs also produces a slope, but now the slope is too high. The conclusion is necessarily that, human inputs cannot be significantly affecting things.
Bart, you still are convinced that one and only one (temperature controlled) process is controlling the increase of CO2 in the atmosphere. That is where it goes wrong: there are a multitude of processes at work, some mostly temperature controlled, some pressure (difference) controlled and some human controlled.
You have to match what is in that plot. You cannot do it with dT/dt - it is 90 degrees out of phase with the variations in dCO2/dt. You must use T.
As the short term variations of CO2 lag the variations of T, the short term variations of dCO2/dt lag the short term variations of dT/dt. The variations of CO2 are caused by variations of T with a lag, which gives that the variations of dCO2/dt are caused by variations of dT/dt with a lag, not by variations of T, even if these exactly matches dCO2/dt in timing because of the differentiation.
And as there is no trend in dT/dt, only a small offset, the integral of dT/dt gives a small increase of CO2 in the atmosphere for a small increase in temperature, as can be seen over many millennia. As the effect of the variability of dT/dt on dCO2/dt is shifted pi/2, the integral of the variability is shifted pi/2 too.
The slope of dCO2/dt is entirely the result of the slope in dCO2(emissions)/dt, which gives integrated the slightlly quadratic increase in the atmosphere.
The real increase in the atmosphere is thus the sum of the integral of the slope of dCO2/dt + the lagged integral of dT/dt and has nothing to do with any scale and offset of T.
The conclusion is necessarily that, human inputs cannot be significantly affecting things.
Have you already found the source of the 3-fold increase in natural circulation that doesn't violate all known observations?
"The variations of CO2 are caused by variations of T with a lag, which gives that the variations of dCO2/dt are caused by variations of dT/dt with a lag, not by variations of T, even if these exactly matches dCO2/dt in timing because of the differentiation."
"Lag" is not some arbitrary quantity which you can simply dismiss at leisure, to be filled in by some climatological God of the Gaps. The phase lag is an intrinsic quality of a unique process. That process has a 90 deg phase lag and, consequently, a -20 dB/decade gain slope. There is one, and only one, process which possesses those qualities, and that is an integration.
It does not matter if, as Paul suggested, it is not a pure integration over all time. Any feedback which would tend to produce deviation from a pure integral at very low frequencies is negligible over the bandwidth of observation.
"As the effect of the variability of dT/dt on dCO2/dt is shifted pi/2, the integral of the variability is shifted pi/2 too."
And that, of mathematical necessity, means that it is the integral of dT/dt, i.e., T, which is affecting dCO2/dt.
"The slope of dCO2/dt is entirely the result of the slope in dCO2(emissions)/dt, which gives integrated the slightlly quadratic increase in the atmosphere. "
Mere assertion on your part. It is not physically possible. You are just arranging things as you would like them to be. But, there is no physical or mathematical basis for it.
"The real increase in the atmosphere is thus the sum of the integral of the slope of dCO2/dt + the lagged integral of dT/dt and has nothing to do with any scale and offset of T."
Mere assertion on your part. It is not physically possible. You are just arranging things as you would like them to be. But, there is no physical or mathematical basis for it.
"Have you already found the source of the 3-fold increase in natural circulation that doesn't violate all known observations?"
Nothing I have stated violates any observations. Your narratives are not observations. They tell a story based on the observations, but they are not the only explanations.
In years gone past, the leaders of The Church of Rome told Galileo that the Sun went around the Earth. That was a narrative, which was consistent with all observations to date. But, it was not, itself, an observation. Your measurements of CO2 isotopes and such are observations. Your claim for how they arise is a narrative. It is not proof of anything.
Bart:
And that, of mathematical necessity, means that it is the integral of dT/dt, i.e., T, which is affecting dCO2/dt.
And that is where you go wrong:
- As Paul_K showed, as the increase/decrease of CO2 with T is a linear process for small changes of T, CO2 variability follows high frequency T variability with a pi/2 lag.
- The derivative of T and CO2 shifts the high frequency changes back with pi/2, still with a difference of pi/2 between dCO2/dt and dT/dt.
- That gives that T and dCO2/dt now are synchronized as can be seen in Wood for Trees
- The transformation of T into CO2 gives a lag of pi/2. The transformation of dT/dt into dCO2/dt also gives a lag of pi/2.
So far so good.
- Integrating dT/dt shifts T forward pi/2. Adding the transformation shift from T to CO2 (or equally from dT/dt to dCO2/dt before integration) shifts the result for CO2 forward pi/2 again, which was the original shift.
- Integrating T as surrogate for dCO2/dt shifts the variability forward with pi/2, synchronizing the integral of T with CO2. Adding the transformation shift from integrated T to CO2 adds another pi/2 shift, thus a shift of in total 180 deg.
integrating T for dCO2/dt leads to a 90 deg. shift of the calculated CO2 variability with the real CO2 variability
Thus your calculated CO2 variability based on T is 90 deg. out of phase with reality...
Moreover, have a view of what happens if you have a simple linear temperature increase with a high frequency sinusoid around it, without any other influence:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sim_co2_temp_00.jpg
The reaction of CO2 is supposed to be linear, as well as for the high frequencies as for the very low frequencies, as can be seen over 800 kyr in ice cores.
For the derivative, we have a problem:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sim_dco2_dT_Tanom_00.jpg
As both the slopes of dT/dt and dCO2/dt are zero, one need to use a factor of 0 to align the slope of T and dCO2, but that makes that the amplitude of the calculated CO2 variability based on T variability also is zero.
The only escape is that the reaction of CO2 on temperature is highly non-linear, which isn't seen in any time frame.
Your measurements of CO2 isotopes and such are observations. Your claim for how they arise is a narrative. It is not proof of anything.
Bart, you are a genius in math, but you have little knowledge of the behavior of isotopes in nature. The observations of the 13C/12C ratio (expressed in per mil δ13C) in all oceans (deep and surface) indicates that any substantial increase of CO2 coming from the oceans, including the isotopic changes at the sea-air border, would increase the current δ13C level of CO2 in the atmosphere.
For your theory to work, you need an increase in deep ocean - atmosphere circulation from ~40 GtC in 1960 to ~290 GtC in 2010. That would give an increase in δ13C, not the firm decrease we see over the same period:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_increase_290.jpg
It seems that you are at the side of the Church of Rome instead of Galileo in this case...
This is absurd. I'm not going to dignify this nonsense with any further response. You have no idea of what you are talking about, and there is no point. You will see...
Bart, I have not the slightest problem with admitting that I am wrong if you have good arguments which show where I am wrong.
Al what I have done is showing where the problems with your theory are, while I don't see any problem with the simple theory that temperature is responsible for the bulk of the variability around the trend, while human emissions are responsible for the bulk of the trend itself. That fits the observed increase of CO2 in all aspects.
That there is a shift between the integrated variability of T and CO2 is the result of the physical reaction of CO2 on temperature changes which causes a time delay and must be taken into account when integrating. Thus there is not the slightest problem with the timing of the integral of dT/dt and CO2.
The problem is with your timing of the integral of T (as far as that has a physical meaning), which doesn't take into account the delay of changes of CO2 after changes in T.
That all besides the troubles you have to get the slope and the amplitude of T variability equal to the slope and amplitude of the variability of dCO2/dt.
Oct 30, 2013 at 9:32 AM | Ferdinand Engelbeen
"...while I don't see any problem with the simple theory that..."
I know you do not see it. That is because you are not familiar with the math. I have given up hope, or am very close to it.
"Thus there is not the slightest problem with the timing of the integral of dT/dt and CO2."
There absolutely is. If you take your CO2 so derived and differentiate it, it will be out of phase with the actual dCO2/dt.
You are not even remotely in the ballpark, Ferdinand. The way you are trying to incorporate the temperature into the CO2 has no mathematical basis whatsoever.
You have to match the dCO2/dt. Once you have done that, you cannot do anything else to manipulate the integration which results in CO2. CO2 and dCO2/dt are not free to be specified separately. The change in CO2 from the beginning of the integration interval to the end is uniquely determined by dCO2/dt.
When dCO2/dt is in phase with T, then CO2 will not also be in phase with T, but with the integral of T. The games you are playing, trying to specify these two functions independently, are wrong on the most elementary level of calculus one could imagine. Your recipe is a Tower of Babble. It is not even math. It is magic. It is an incoherent ramble of the first order. It is not even possible to be more wrong. There is not even a glimmer of fact to it.
Bart, you say:
"We can take it up one level of simplification by simply adding the equilibrium temperature and input Sun source as
dCO2/dt = a*(T - Teq)
dT/dt = b*CO2 - c*T^4 + Sun
This, again, is unstable for a and b both greater than zero."
******************
Sorry, not even remotely true. The "-C*T^4" term is a powerful stabilizing influence, both in your equations and in real life.
Plugging in almost any set of plausible numbers gave me a stable response.
Oct 30, 2013 at 7:28 PM | Curt
I suggest you recheck your work. You most likely have a sign error, and have gotten either the a or b feedback negative. At the unique equilibrium point, the characteristic equation is
s^2 + (4*c*Teq^3)*s - a*b = 0
One of the roots of this equation is always positive if a and b are positive. Hence, the equilibrium is unstable, and there is no other.
Bart, as my math indeed is too long (mostly some 50 years) ago, but I remember some of the basics, here a few questions where I like to have a clear answer from you:
- does a sinusoidal change in temperature without any increase over time give a sinusoidal change in CO2 with a 90 deg lag?
- does the derivative of a sinusoidal variation as above lead to a 90 deg lead of both T and CO2 in the derivative, compared to the original values?
- does that still show a 90 deg lag between dCO2/dt and dT/dt?
- does the shift between the derivative and the original values make that T and dCO2/dt synchronize?
- does the integration of dT/dt shift the sinusoid again forward with 90 deg?
- does one need to add another 90 deg lag to reflect the influence of the integrated dT/dt variation on the CO2 variation of the original values?
and finally:
- can you match the slope and amplitude of T variability with the slope and amplitude of dCO2/dt variability in this case?
Yes, yes, yes, yes...
"- does the integration of dT/dt shift the sinusoid again forward with 90 deg?"
Integration always induces a 90 deg phase lag from the quantity being integrated.
"- does one need to add another 90 deg lag to reflect the influence of the integrated dT/dt variation on the CO2 variation of the original values?"
Let me restate that for you:
"- does one need to integrate once again to reflect the influence of the integrated dT/dt variation on the CO2 variation of the original values?"
The statements are equivalent. If you add a 90 degree phase lag, you are integrating. There is no other way to add precisely 90 deg of phase lag in a natural, minimum phase system. You cannot just add and subtract arbitrary phase variables as you please without changing other properties of the time series.
The answer is "yes". And, when you integrate again, you are doubly integrating dT/dt, which is thus the integral of T. And, that integral will have the curvature which results from integrating the slope in T. And, that curvature accounts for all of the curvature in CO2. As adding in human inputs would again increase that curvature, there is no room for them.
"- can you match the slope and amplitude of T variability with the slope and amplitude of dCO2/dt variability in this case?"
Perhaps with better data. When your data are uncertain, however, it is a fool's game to try to match everything perfectly.
Even then, these data are bulk quantities, and the true relationship is only broadly represented by them. To get variables with a precise relationship, we would need to know precisely the global distribution of temperatures, and of CO2 upwelling and downwelling, and the full solution of a set of coupled partial differential equations to weight accordingly. And, even then, there are other external forcings which can cause deviations between the variables, notwithstanding their underlying relationship.
This is a complex problem, and our data limited. But, that is how science works. None of the equations of our great theories hold perfectly. Even F = m*a fails in microscopic systems and in large, rapidly evolving ones. But, we can still manage a level of skill with them which allows us to determine, at least to some level of approximation, how particular systems will evolve.
I mean, the various temperature sets themselves do not agree with one another to the level you are demanding. Which one would I even choose? What if none of them are exactly right?
"- does that still show a 90 deg lag between dCO2/dt and dT/dt?
- does the shift between the derivative and the original values make that T and dCO2/dt synchronize?"
I may have missed the meaning here, and answered hastily, so let me lay it out carefully.
dCO2/dt lags dT/dt by 90 degrees. If you integrate dT/dt to get T, then you are lagging dT/dt by 90 degrees, so now T and dCO2/dt will be synchronized in phase.
What I have been reading from you is that you want to have
CO2 = a*HA + b*T
for HA being the accumulated human inputs, T being the temperature, and a and b being constants.
But, in that case,
dCO2/dt = a*dHA/dt + b*dT/dt
dT/dt is not in phase with dCO2/dt, so this model fails. To get it into phase, you would need to lag dT/dt by 90 deg, which is equivalent to saying you would need to integrate it. The model is then
dCO2/dt = a*H + b*T
where H = dHA/dt. Then
CO2 = CO2(0) + a*HA + b*integral(T)
where CO2(0) is the initial value of CO2 and HA(0) = 0 and the integral of T starts at 0.
And, if you choose b to match both the trend and variation in dCO2/dt, then there is very little room left for a to be anything significant.
There is also an offset needed to get a good fit
dCO2/dt = a*H + b*(T - Teq)
with Teq being nominally constant. This is OK because A) T being temperature anomaly has an arbitrary baseline to begin with B) H is not even approximately a constant, so it is not just substituting an arbitrary extraneous variable to take the place of H.
The conclusion that human inputs have little effect is not dependent on that offset, either. It follows from the fact that, to fit both the trend and the variability of dCO2/dt, b has to be such that a is necessarily insignificant.
Bart, the essence of our dispute is in:
The statements are equivalent. If you add a 90 degree phase lag, you are integrating. There is no other way to add precisely 90 deg of phase lag in a natural, minimum phase system. You cannot just add and subtract arbitrary phase variables as you please without changing other properties of the time series.
As Paul_K showed (Oct 26, 2013 at 8:19 AM and Oct 26, 2013 at 2:34 PM), the exact 90 deg shift of CO2 after T is the result of a (near linear) response function of CO2 to changes in T. But that is a response function that with a finite temperature increase will give a finite increase of CO2 in the atmosphere (according to Henry's law), not a continuous, indefinite increase.
This response function is seen on all time scales from decades to multi-millennia and is quite fixed around 8 ppmv/K.
Thus calculating the integral of dT/dt and adding a 90 deg shift * 8 ppmv/K for the response of CO2 on temperature changes is as valid as using the integral of T anomaly with an offset and a factor which fits the trend and amplitude of dCO2/dt.
The difference is that in the former case there is plenty of room for human emissions to cause the trend in CO2, while in the latter case there is no room for human emissions.
Which is the right one? All observations show that it is the former...
Again, you misapprehend what Paul_K was saying. Please see his note to me at Oct 27, 2013 at 9:13 AM:
Over a very long period of time, constant values for gamma and Te in Paul_K's nomenclature, k and Teq in mine, may be inappropriate. We could always adjust these values over time to match current conditions. Or, perhaps a global model such as Paul_K suggested at 8:19 would require less maintenance in the long term, producing a more continuous fit and allowing greater insight with additional conclusions to be reached.
But, it is a moot question as far as our discussion here is concerned. For the timeline of interest reaching back to at least 1958, either model will produce essentially indistinguishable results. And, the ineluctable conclusion from those results is that there is very little room for significant influence of human inputs to atmospheric CO2.
One last thing, Ferdinand... We do not disagree that temperature alone cannot explain the rise in CO2. However, if there is a continuous influx of CO2 from a temperature dependent source, such as outgassing from the oceans of upwelling CO2 rich waters, then there will be a temperature modulated, continuous accumulation of atmospheric CO2. That is the type of behavior which is, in fact, observed.
Ferdinand,
My apologies for the delay in response. I have been off the air for a while. In answer to your question, I cannot attend the Salby lecture unfortunately. I don't live in the UK and can't make the time for the trip.
I would urge you in light of some of your comments to watch Salby's Hamburg lecture a couple of times. Although I still do not agree with his final conclusions, his points are not trivial. In particular, you should try to follow his reasoning closely regarding (a) the source of the changing (atmospheric) carbon isotope ratio and (b) why he believes that the temperature sensitivity has been underestimated from ice-core data. His arguments in both cases are coherent and not to be lightly dismissed. W.r.t. (a) this doesn't prove his theory as such, but it removes one possible objection to it. W.r.t. (b) you need to note that he talks about two different phenomena which affect the measurements of CO2 in ice cores - one of which (diffusion) affects predominantly the high frequency changes and the second of which (attenuation from variation in depth of burial) affects the long period changes. This leaves maximum coherence in the mid-period changes, where the degree of underestimation of actual atmospheric CO2 levels is minimised. I have no expertise in this area, but these parts of Salby's story make sense to me, and would seem to merit a considered response.
Oct 31, 2013 at 4:35 PM | Unregistered CommenterBart
Bart,
I think we are generally speaking the same language. However, I have yet to convince myself that the observations cannot be explained - as Ferdinand has suggested - by the high frequency variation (and derivative) being temperature dominated and the longer period change being dominated by anthropogenic addition.
I understood exactly what you meant by the above in context, but just to be pedantic, I consider this model to be at best a partial model to explain (only) the temperature contribution while holding partial pressure constant. I am still trying to figure out what a more general model needs to look like.
It simply is impossible that the oceans are a net source of CO2. They are a net sink. You can't have a continuous increase of CO2 in the atmosphere from the oceans and at the same time no influence on any observation, while all observations show the human influence.
Thus what is wrong?
It is certain that the short time variability is caused by temperature changes and it is pretty sure that the increase of 70 ppmv over the past 50 years is not caused by temperature changes.
While looking at possible problems, I encountered one which I didn't expect: if the CO2 increase lags T, it lags more if it is on a slope than without a slope for T, while T on the slope is synchronized with T without slope:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sim_sin_slope.jpg
That gives a similar change in lag in the derivative:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sim_dsin_dslope.jpg
while the two temperatures are fully synchronized...
I suppose that the steeper the slope, the larger the extra lag will be. But I suppose that you can solve that with the right math...
Anyway, that gives doubts over the necessary integral to synchronize dT/dt and dCO2/dt, as the shift in part is caused by the slope of CO2 and thus is less than 90 deg.
Nov 1, 2013 at 10:53 AM | Paul_K
Thanks for the reaction. I have followed Salby's lecture in Hamburg a few times as it is at moments difficult to follow.
I am certain that he, like Bart, is brilliant in math, but I fear that he lacks some basic knowledge in real life chemistry and physics and hasn't read the recent literature on several items he touches.
Take his:
(a) the source of the changing (atmospheric) carbon isotope ratio
The bulk of all carbon on earth in oceans, carbonate rock layers, volcanic vents (all inorganic carbon) has a δ13C ratio around zero per mil. The bulk of all fossil and current organics have a carbon ratio (far) below zero. Thus there is no possibility to make a differentiation between fossil and new organics for the firm decrease in δ13C in the atmosphere on the basis of the difference in isotopic ratio. See here the decline in δ13C over the past 600 years in the atmosphere and the ocean surface (Bermuda):
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.gif
But there are two ways to show which is the source:
- the δ14C ratio is different: fossil fuels are completely depleted of 14C as much too old and all 14C is decayed.
- the oxygen balance: fossil fuel use oxygen. Based on fossil fuel use inventories and the burning efficiency for each type, one can calculate how much oxygen is used. The real amount can be measured (since about 1990 sufficient in accuracy: less than 1 in 200,000!) to make the balance for the biosphere (all together: plants, insects, bacteria, animals). That shows that there is a small deficit in oxygen use: the whole biosphere is a net source of oxygen and thus a net sink for CO2 and prefentially for 12CO2, leaving relative more 13CO2 in the atmosphere. Thus not the cause of the δ13C decline. See:
http://www.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
(b) why he believes that the temperature sensitivity has been underestimated from ice-core data.
About ice cores: the same type of problem:
- diffusion is quite well understood in ice cores, as that depends on factors like accumulation speed and temperature, which affect the time the pores are still open en connected with outside air and the migration speed in decreasing pore diameters. That makes that over the past history one can have resolutions ranging from about a decade (Law Dome 150 years) via 20 years (Law Dome 1,000 years) and 40 years (Taylor Dome 70 kyear) to 560 years (Dome C 800 kyear). That gives that there is an overlap of resolutions over the past 800 kyears, where all ice core measurements are within 5 ppmv for the same gas age, here for the past 1000 years:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/antarctic_cores_001kyr_large.jpg
There is even an overlap of ~20 years between the fast accumulation ice cores of Law Dome and direct measurements at Mauna Loa:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/law_dome_sp_co2.jpg
Gas age distribution was measured top-down in firn at Law Dome and confirmed the model calculations. Here more info over the age distribution (Fig.11) and a lot of more interesting info:
http://courses.washington.edu/proxies/GHG.pdf
and the 14C bomb spike distribution:
http://onlinelibrary.wiley.com/doi/10.1029/96GL03156/abstract
Migration in the ice itself is unmeasurable and would flatten out the peaks over each interglacial 100 kyr back in time, which is not seen at all.
My impression is that Salby needed migration to support his theory, but that wasn't based on reality...
Paul_K
"However, I have yet to convince myself that the observations cannot be explained - as Ferdinand has suggested - by the high frequency variation (and derivative) being temperature dominated and the longer period change being dominated by anthropogenic addition."
At the very least, you should consider Occam's Razor - why add stuff in when it is already explained by something simpler? The contributions introduced by humans really are small in relation to total flows. We aren't at the center of everything, and it isn't always our fault.
In any case, I must go on a trip, and will not be responding further to this thread in the near future. It is only a matter of time before the divergence of human emissions and atmospheric concentration becomes glaring, so I am sanguine about the prospects for it all getting worked out in the end. Thank you, Ferdinand, for being gracious and polite as always.