Joel Shore (13:28:45) :
But, just one thing more: Whatever conclusion Knorr draws from his analysis, I am not required to reach the same conclusions. He has provided information. If you free your mind from the dogma, you will be able to draw independent conclusions from available information, too.

Correction:
I have shown that the sensitivity of CO2 to yearly global temperature variation is about 189 ppmv/degC. With a time constant of 2 years, this provides direct correspondence between the yearly temperature variation of about +/- 0.1 degC to the +/- 3 ppmv observed variation in CO2 levels at Mauna Loa.

Bart says:

I have shown that the sensitivity of CO2 to yearly global temperature variation is about 189 ppmv/degC.

You have shown no such thing because there is no evidence that it is the temperature variation that is responsible. Besides which, your prediction is high by at least an order order of magnitude in what it predicts for the glacial – interglacial transitions (despite the fact that the longer times for equilibration would lead to the expectation of even a larger effect). And, your data is completely incompatible with year-to-year variability in global temperatures and CO2 growth rates.

In a sane world, that would just about settle the entire argument, and show that CO2, as always in the historical record, follows temperature, and not the other way around.

In a sane world, your notions would be completely dismissed by the scientific community. (Well, I am glad to see that at least in one respect, this world isn’t too crazy!)

philincalifornia:

This is essentially the same as saying that the sink (side B in your analogy) has become effectively saturated in the short time period under discussion, which is in apposition to Knorr (as well as the laws of science).

Actually, my little analogy predicts what Knorr et al. see exactly: What Knorr et al. say is we consistently see the same fraction of the additions (~45%) remaining in the atmosphere with the rest going into the other parts of the system. In my analogy, whatever is added to Side A will be rapidly partitioned between the two sides in a definite ratio (in the ratio of their volumes to be precise for the analogy), just like what Knorr et al. see. Of course, I don’t claim this to be any evidence that Knorr et al. is correct or that the real system will continue to operate this way. My analogy is, after all, just an analogy. And, while I think it captures a fair bit of the physics (at least for such a simple analogy), I certainly wouldn’t expect it to capture all of it.

Willis Eschenbach (17:10:23) :
You can agree with him if you like, but his notion of atmospheric dynamics is pure fantasy. The natural CO2 emissions and the anthropogenic emissions must be treated equally by the sinks. There is no plausible argument which can be made otherwise.
The sensitivity is pretty clear. Look at the CO2 charts I linked to – do you not see a +/- 3 ppmv once per year harmonic? Look at the temperature charts. Do you not see a +/- 0.1 degC variation? Look at my calculations. Do they not all fit the data?
Joel Shore (16:19:48) :
“Besides which, your prediction is high by at least an order order of magnitude in what it predicts for the glacial – interglacial transitions (despite the fact that the longer times for equilibration would lead to the expectation of even a larger effect).”
A different operating point. The equations have to be linearized about the current equilibrium. The equilibrium conditions a long time in the past were likely different.
“And, your data is completely incompatible with year-to-year variability in global temperatures and CO2 growth rates.”
In general terms in recent history, no. That is how I reached the conclusions. Once again, as Ferdinand appears wont to do, you assume data with significant error bars is “truth”.
Look, I’m done here. I have no illusions that I will turn around entrenched specious reasoning which has been reinforced over many years. Maybe, you will all give it another thought when the CO2 concentrations reverse course, which I claim they are very likely to do within some lag interval after temperatures show a definite decline. That lag interval is affected by the dominant time constant such as I have calculated (and which must, perforce, have significant error bars, too), as well as the lag associated with what I am sure is significant confirmation bias between the time the people taking the measurements stop throwing out measurements which do not agree with their expectations, and the time they start accepting them as truth.

Willis, I am not a huge fan of Vostok because there is so little snow there that the CO2 readings are made up to 1000’s of years apart (see data ftp://ftp.ncdc.noaa.gov/pub/data/paleo/icecore/antarctica/vostok/co2nat.txt). The impulse response of the natural system (e.g. http://unfccc.int/resource/brazil/carbon.html) is in the neighborhood of 10’s of years. Therefore a big slug of CO2 (e.g. 100’s of ppmv) landing on earth during the Vostok record would be invisible. Note that I can’t speculate where that slug of CO2 would come from, just that it would not show up in the ice core. Bottom line is I don’t like relying on a sensitivity that is calculated from temperature and CO2 curves that are very highly smoothed.
Ferdinand has ice core data that he showed me once a while back (somewhere in Greenland, forgot where) but it had something like 10’s of years resolution thanks to lots of snow causing the air pockets to lock up a lot faster. Maybe he can dredge up a temperature sensitivity estimate from that data. Also would be interesting to see a C13/C12 ratio sensitivity to temperature from the ice cores.
Considering the impulse response graph linked above, and if we dumped the whole human carbon emission from 1970-2006 (ftp://cdiac.ornl.gov/pub/ndp030/global.1751_2006.ems) of 217Gt of C (800Gt of CO2) into the atmosphere back in 1970, that would have caused the CO2 to pop from 325ppmv to 425ppmv roughly. From eyeballing the graph we would have about 40% left in 2006 or about 365ppmv. The actual in 2006 was 380. Makes sense that it is more since we didn’t dump it all back in 1970 but have trickled it in since. But it seems to me that it should be even higher (just intuition). Also the model doesn’t have any ability to do annual variations. OTOH, it should have reasonable fidelity for the major fluxes.

It seems to me the problem with using global seasonal temperature change is that it doesn’t capture the hemispheric bias (peak CO2 is just before NH growing season, but also near the peak of SH ocean warmth). Using a single global temperature can’t capture that effect.

By the way, I should add that the “conception” of AGW skeptics that I discussed in the last sentence of the last post is not one that I personally subscribe to in the absolute terms that I put it (i.e., without a qualifier like “some” or “many”). And, I am in fact happy to see some skeptics like Willis and Ferdinand take on those with more extreme views.
If there is going to be a debate about scientific issues, it ought to be about issues where there is at least some legitimate grounds for debate (such as what the climate sensitivity is).

There are also obvious harmonics in the CO2 data with periods of 1/3 year, 1/4 year, and 1/5 year, but they are much smaller in comparison.

Found my problem with the GISS data – I was reading the data in column-wise rather than row-wise, so the data stream was January each year, then February each year, etc… Using absolute temperatures here, I am getting +/- 0.057 degC variation at the 1 year harmonic, and +/- 0.042 degC variation at the 1/2 year harmonic, which is roughly 2/3 of the amplitude of the first harmonic.
The time constant of the CO2 system is rolling off frequencies at the usual -6 dB/octave, so it stands to reason the CO2 signature at the 1/2 year period would be attenuated by a factor of 2. Hence, CO2 at the second harmonic would be expected to vary at 1/3 of the first harmonic, just as has been recorded at MLO.
I am reasonably assured this is on the right track, and if I were able to put the man-hours into it, I could gin up a reasonable case based on real world physical mathematical constraints. Not all the values should be expected to be precisely what they need to be – there are significant error bars on everything, but they are close enough, and based on actual physical constraints, and I am content. I mean, WTH, who’s going to listen to me anyway? But, maybe this will serve as inspiration for someone who understands the development, and is willing to put in the time to flesh it all out.

Bart (21:11:47) :
Yeah, I just wanted to make sure you had all bases covered (although, given that this doesn’t really address the biosphere and deforestation, there probably are other bases to cover). I have no vested interest in whether it’s 20, 40, 60, 80 or 108 (as in 388 minus the magic 280) ppm of anthropogenic CO2 in the atmosphere. My only interest, which is not particularly vested, but more instilled, is the truth, if it can be established mathematically.
As you know, however, if it were to be established that levels over 280 ppm were only 20 ppm, 40 ppm or even 60 ppm anthropogenic, this is devastating to AGW alarmism, so this is an important line of discussion. For example, let’s say that in 150 years, we have only elevated CO2 by 60 ppm, with the rest being natural and temperature-related, the future doubling, in addition to looking extremely lame regarding climate catastrophe, is also looking extremely far away too. This, as a stand-alone fact, obviously negates the immediate need for “climate crisis” political action.
I don’t need to tell you this. I guess I’m suggesting that you don’t give up on this thread just yet.
My qualitative prediction for atmospheric CO2 levels in a cooling world is the same as yours. CO2 levels will go down, despite anything that happens in India and China, and Gordon Brown will have a photograph of a wind turbine on the front cover of his autobiography in … 2016.

Two more comments.
Willis Eschenbach (18:55:35) :
“According to HadCRUT, the actual global average temperatures (1961-1990 avg) are:
Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec
12.1, 12.2, 12.9, 13.9, 14.9, 15.6, 15.9, 15.7, 15.1, 14.1, 13.0, 12.4”
I think the GISS data is an “anomaly” whereby the base period variation is taken out. So, would that invalidate my thesis? Not necessarily. What I have written as S*dT is kind of like my value of Ko, where I have assumed S is the dc gain of a linear operator. However, it was justified for the operation K[adot] ~ Ko*adot because adot is very low frequency. However, since dT has strong components at dc, as well as at the frequency of one cycle per year and its higher harmonics, that is not generally the same, and I really do need S to be a frequency dependent operator.
So, the model has to be more like
Cdot = (Co-C)/tau + (1+Ko)*adot + So*dTo + S1*dT1 + S2*dT2 + …
where dT0, dT1,dT2… is the harmonic expansion of dT, and So, S1, S2,… are constants representing the gain of the operator at the specific frequency.
In estimating the 1st harmonic sensitivity, I found S1 to be about 189 ppmv/deg_C. However, it may be more on the order of 1/20th of that, which would give it the required sensitivity to the absolute variation in dT. Is it possible for such convenient happenstance to occur?
Actually, yes it is. It is well know in systems theory that, to precisely compensate and regulate a known disturbance, it is necessary to have an internal model in the loop. This internal model varies in such a way as to cancel out the disturbance precisely. For example, a PID controller is insensitive, in the steady state, to a constant disturbance, because the “I” part of the controller is an integral, which is an internal model of a constant. (What I define as “the steady state” here is a time interval which depends on the gain of the internal model.)
Do we have an internal model of yearly variation in the CO2 loop? Yes, we do, at the very least in the yearly cycle of biomass growth and decay. This internal model could act to compensate the yearly variation precisely, so that the net sensitivity to temperature variation could be to temperature anomaly, rather than to the absolute variation, and the manifestation of this regulation could be an effective degaining of S1 by precisely the ratio of temperature anomaly amplitude to absolute temperature variational amplitude at that frequency. It would be no accident – an internal model in a stable control loop naturally converges to the correct offset for exact compensation. But, if the effective gain is low, it would take a while to reconverge to a changed input, and the system would then effectively be disturbed only by the anomaly.
Sound far fetched? Admittedly, it is only conjecture at this time. But, it is on far firmer ground than the idea of decoupled dynamics for anthropogenic and natural CO2 emissions. It is actually a well worn concept in control theory, as to which the ubiquity of the “PID” control loop attests.
I want to make it clear, though: There are two threads running here. One is, can we attribute the rise in CO2 solely to anthropogenic sources? I am convinced we cannot, and that the attempts to do so by arbitrarily decoupling the dynamics of the anthropogenic and natural CO2 are so much blowing smoke.
The other thread is, can we reasonably extend the model I have put forward to explain the rise in CO2 as a result of the rise in temperature? I believe we can, but my efforts to do so have not progressed nearly so far, and the mechanism by which it does so may not be immediately apparent. Stay tuned, probably on another board sometime. This one is well past its “sell by” date.