Murry Salby responds to critics

Jo Nova writes:

Murry Salby was sacked from Macquarie University, and Macquarie  struggled to explain why, among other things, it was necessary to abandon, and strand him in Paris and hold a “misconduct” meeting in his absence. Since then he has been subject to attacks related to his previous employment. I’ve asked him to respond, which he has at length in a PDF (see below). The figures listed below refer to that PDF, which encompasses 15 years of events.

I don’t have the resources (unlike the  National Science Foundation, the NSF) to investigate it all, but wanted to give Murry the right of reply.

On closer inspection the NSF report used by people to attack Salby does not appear to be the balanced, impartial analysis I would have expected. Indeed the hyperbolic language based on insubstantial evidence is disturbing to say the least. Because of the long detailed nature of this I cannot draw conclusions, except to say that any scientist who responds to a question about Murry Salby’s work with a reference to his employment is no scientist.

Remember the NSF report was supposedly an inhouse private document. It was marked “Confidential”, subject to the Privacy Act, with disclosure outside the NSF prohibited except through FOI. Desmog vaguely suggest there “must have been an FOI”, but there are no links to support that. In the end, a confidential, low standard, internal document with legalistic sounding words, may have been “leaked” to those in search of a character attack.

My summary of his reply:

See: http://joannenova.com.au/2013/08/murry-salby-responds-to-the-attacks-on-his-record/

The PDF:

Click to access re_nsf_r.pdf

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August 20, 2013 1:09 pm

richardscourtney says:
August 20, 2013 at 4:39 am
And your calculations of O2 change assumed to be a result of plant growth are trumped by the empirical data Allan MacRae provided (empirical data always trumps theory).
I do agree that human emissions are small compared to the diurnal change of CO2 by vegetation. But that says next to nothing about the influence of these changes over the whole globe over a full seasonal cycle. That can be calculated from the oxygen use or production by the whole biosphere. That is land and seaplants, bacteria, insects and animals. That includes vegetation growth and decay and forest fires, droughts and floods… The observed data show a net O2 production by the biosphere, which is the result of ~1 GtC/year uptake as CO2.
Thus the biosphere doesn’t take all human induced CO2 away in the next available tree. Far from it…
About Salby and ice cores:
Not only the ice cores, also in the firn in the years prior to sealing of the ice. Mixing of gases in the firn (i.e. a material with open porosity open to the atmosphere) is certain to occur as weather varies atmospheric pressure so pumps air in-and-out the firn.
The diffusion in firn is well known and can be calculated, as that is a matter of pores diameter, which is reverse proportional to firn densitiy. That physical “model” is confirmed by direct measurements top-down in firn at Law Dome, published in 1996 by Etheridge e.a.
But Salby did go a step further:
According to his calculation (model?), the measurements in ice of 100 kyr old might be a factor 10 too low, thus the measured 300 ppmv during the Eemian might have been 3000 ppmv. But then there is a problem: ice cores may smooth out the differences by diffusion (for which is no proof), but that doesn’t change the average over the period of resolution. As 90% of the time the earth is in a glacial state, to give an average of ~200 ppmv, the glacials should be below zero CO2…
You (and others) make the theoretical assumption that bubbles in the ice act as containers for ice because they are sealed. But the bubbles are not closed containers because the ice is permeated by liquid water that differentially dissolves gases.
Ice at -20°C has a liquid-like layer of unordered watermolecules at the ice-air border and virtually none at the crystal borders, except for dust/salt inclusions. But nevertheless there were attempts to calculate a possible diffusion in the Siple Dome ice core from increased CO2 levels near a remelt layer. That did give a broadening of the resolution at mid-depth from 20 to 22 years and at full depth to 40 years. That is all.
For the much colder (-40°C) Vorstok and Dome C ice cores that is not measurable. If there was some substantial migration, that would result in a flattening of the CO2/temperature ratio for each interglacial back in time, each some 100 kyr apart.

August 20, 2013 2:04 pm

Bart says:
August 20, 2013 at 9:56 am
…but the increase over the past decades doesn’t follow temperature…”
Absurd. Of course it does.

It doesn’t:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_co2_acc_1900_2011.jpg
the integrated function of the temperature anomaly of yours (whatever that represents) shows a nice fit with the CO2 increase, but it has little resemblance of the real temperature increase.
Why is it so hard for you people to understand??? A change in the linear portion STILL DOES NOT MAKE ROOM FOR HUMAN INPUTS!!! There is a quadratic factor which is necessarily produced by the human inputs BUT WHICH IS ALREADY ACCOUNTED FOR BY THE TEMPERATURE RELATIONSHIP!!!
No reason to shout…
In your assumption of what happens in nature, there is no place for human emissions. But that is only the result of curve fitting, which matches the SH temperature anomalies (thus there should be your upwelling source?), but the increase is in the NH first, not in the SH…
Further, that should lead to an increase of over 100 ppmv/°C, completely out of range for what nature shows over seasons, a few years and multi-decades to multi-millennia. Moreover, according to some more assumptions, the increase in the atmosphere has not the slightest impact on the CO2 releases from the oceans, neither on the sinks in polar waters or in vegetation, no impact on the 13C/12C or 14C/12C ratio’s, neither on the turnover/residence time of CO2 in the atmosphere…
In my assumption of what happens in nature, there is full room for human emissions (around 50%) and a litttle room for the temperature increase: some 4.5 ppmv/°C over the past 5 decades, completely in line with the 5 ppmv/°C over the seasons, 4-5 ppmv/°C over a few years (Pinatubo, El Niño) and 8 ppmv/°C over multi-decades to multi-millennia. It fits the isotope ratio’s, the oxygen balance, the residence time and I don’t know more to mention…
Maybe there is something wrong with your basic assumption?

Bart
August 20, 2013 2:32 pm

Ferdinand Engelbeen says:
August 20, 2013 at 2:04 pm
“…but it has little resemblance of the real temperature increase.”
Looks pretty good to me.
Thank you for showing me the integral function of WFT. I did not know it had that.

August 20, 2013 3:29 pm

TO ALL – i’ve posted this message previously.
Please examine the 15fps AIRS data animation of global CO2 at
http://svs.gsfc.nasa.gov/vis/a000000/a003500/a003562/carbonDioxideSequence2002_2008_at15fps.mp4
It is difficult to see the impact of humanity in this impressive display of nature’s power.
In the animation, does anyone see the impact of industrialization? USA? Europe? India? China? Anything related to humanity? I don’t.
I do see evidence of natural seasonal fluxes on land, and also evidence of deep ocean currents.
The animation does make it look like we Canadians and the Russians have lots of heavy industry emitting megatonnes of CO2 in the far northern Arctic. Not so.
This is no proof, but it appeas that atmospheric CO2 flux and CO2 concentration are overwhelmingly natural.

Nick Stokes
August 20, 2013 3:36 pm

Bart
“The value of k is set. The value of a1 is set. So, the curvature k*a1 is set, and it matches observations.”
“k and a1 are not arbitrary. We have no room for alpha1 to add in to any level of significance.”

This is arm-waving. You have nothing quantitative to back it up. You should at very least determine k by regression, so you would have error estimates. Then you should test your claims about α1. Your talk about level of significance is just hot air.
Your argument comes down to saying that a second derivative of CO2 can predict the slope of the temperature. This is where your cherry-picking of the SH stands out. In that case it works not too badly. For SST, or global SAT, it is not good at all. It is obscured because you compare by eye on a differentiated plot – ie one which greatly emphasises short term fit vs trend failings.
And it all comes unstuck when you do try to demonstrate a prediction in the integrated domain. You can’t do better than simple polynomial regression.
k is poorly determined. For example, you use 0.3 to show a SH fit, 0.2 for global. When I pointed out the bad performance of your global approx, you said that it hadn’t been optimised. But I did that, regressing in the undifferentiated domain. The optimal value of k came down to nearly 0.1, vs your 0.2. It is not well determined at all. The reason it came down is that, when trying to meet a LS in a domain that had not been aggressively high-pass filtered, it sacrificed HF fit to get the trend right.

Bart
August 20, 2013 4:20 pm

Nick Stokes says:
August 20, 2013 at 3:36 pm
“This is where your cherry-picking of the SH stands out.”
You keep making this bizarre claim. It isn’t cherry picking – that’s where the action is, as indicated by the coherence of the fit. This is like me saying that child molestation by adults is correlated with sexual abuse which the perpetrators, themselves, suffered as children, and you demuring that children who become addicted to drugs don’t generally end up as child molesters.
This is a non-argument. It is irrelevant. There should be no more requirement for fitting every temperature set perfectly than there should be for matching the stock exchange indices.
“You can’t do better than simple polynomial regression.”
You cannot connect low order polynomials to the variations in the rate of CO2. You can do so with the temperature. Come ON Nick, what in the world are you thinking?
“The optimal value of k came down to…”
Optimal based on what criterion? You have no way to truly optimize this without knowledge of the autocorrelation. And, you don’t need to. You can see the goodness of the fit with your own eyes.
These data are not perfect. There is no one-to-one mapping. When you get a good fit which is consistent with commonly observed natural behavior, you know you’ve got it.
Look, just watch and see what happens. The human inputs are already diverging from the atmospheric concentration. The divergence will accelerate as temperatures stagnate and even decline. Before too many more years, you will know I am right.

jimmi_the_dalek
August 20, 2013 5:07 pm

My what a lot of comments. I will just comment on that of Bart 20th Aug 9:56 am where he is discussing the graph that dbstealey keeps showing.
“The “isolate” function is basically a high pass filter. His plot shows that the variational parts of CO2 generally lag the temperature by 90 degrees in phase (1/4 wavelength for the ups and downs)”
Yes, precisely. Though I prefer WFT’s description that ‘isolate’ subtracts the mean and leaves the noise, as that gives a better idea of what has been done. But no matter what it is called Bart agrees that the graph shows that the variational parts (a.k.a. ‘noise’) of the CO2 growth lags temperature, and of course since the low frequency part (a.k.a. the trend)has been omitted it follows that nothing has been said about whether this part follows, leads, or has no connection whatsoever to the temperature. Yet this type of graph is used to support the claim that CO2 lags temperature on all time scales (I am not going to wade back through this thread to see who claims that, but I know it has been claimed). So can we now take it that Bart agrees that this particular graph does not say anything at all except about the brief one or two year fluctuations that occur?
Bart also says “People who are not familiar with control systems seem to find it exotic”. I think part of the trouble is that Bart is so familiar with that, that he thinks that everything can be analysed in those terms.
At some stage I point out that physics was quantitative, not purely qualitative. So here (if it works) is WFT with the CO2 curve (12 month average), the linear trend, the CO2 curve subjected to an isolate calculation (subtract the mean to leave the noise) and the first derivative of the CO2 curve.
http://www.woodfortrees.org/plot/esrl-co2/mean:12/trend:60/plot/esrl-co2/mean:12/plot/esrl-co2/mean:12/isolate:60/plot/esrl-co2/mean:12/derivative
They are plotted on the same graph to make a point – the CO2 curve and its trend are up the top, and on the same scale the ‘isolate’ curve, and the derivative curve are hardly distinct from zero. So why exactly are we spending so much time analysing the residuals and ignoring the main data?

Bart
August 20, 2013 6:16 pm

jimmi_the_dalek says:
August 20, 2013 at 5:07 pm
“So can we now take it that Bart agrees that this particular graph does not say anything at all except about the brief one or two year fluctuations that occur?”
It’s not my graph. That is why I do not present it. I favor one such as this, which shows that the trends match up pretty closely, too. When the derivative is in phase, or coincident if you prefer, with the temperature, then it is a given that absolute CO2 lags temperature, as integrating the derivative imparts an inherent 90 degree phase lag.
The low frequencies flow into the high frequencies smoothly, without any apparent phase distortion. This is why Ferdinand’s idea that the temperature is responsible for short term behavior, but human inputs are for the long term, is untenable.
“I think part of the trouble is that Bart is so familiar with that, that he thinks that everything can be analysed in those terms.”
Everything can. It is quite a general discipline.
“So why exactly are we spending so much time analysing the residuals and ignoring the main data?”
Because the residuals indicate what driving force is responsible for at least the great majority of increasing CO2 concentration. And, what they indicate is that humans are not responsible.

Nyq Only
August 21, 2013 2:23 am

Bart: “You keep making this bizarre claim. It isn’t cherry picking – that’s where the action is, as indicated by the coherence of the fit.”
Perhaps but it does change the meaning of the relationship you are showing. You are demonstrating a relationship between CO2 and the southern hemisphere concentration. That in itself is an interesting claim but obviously not the same claim as a relationship between global temperature and CO2.

August 21, 2013 4:55 am

Bart:
I have now considered your maths. Thankyou for providing them.
Firstly, I considered your logic and it seems sound. Alternative models may be possible, but I did not develop any because my purpose was – as I said – to evaluate your analysis.
Then I put your model into a spread sheet and – as I said I would – I started to play with it by adjusting variables. This is the model I assessed
CO2 = A00+r*A0+C0 + (k*a0+d0+r*alpha0)*t + 0.5*(k*a1+r*alpha1)*t^2 + (h(t)+r*m(t))
It seems that, as you said, you have provided the best fit by adopting the values for parameters which you have adopted. However, in itself that is merely a curve-fitting exercise because your model has 6 possible variables (remember Neuman’s elephant).
It would require all your variables to have defined physical meanings which can be empirically checked for your model to be completely grounded in reality.
And I do not understand your statement that

k and a1 are not arbitrary.

I can vary them on my spreadsheet and they do not represent any physical parameter that I can determine. What are they in terms of physical reality?
You say

b0 = k*a0 + d0
b1 = k*a1
g(t) = k*f(t)
It is because the same value of k scales a1 to b1 as well as f(t) to g(t) that we have corroboration of k.

I fail to understand what you are saying there, too.
Since the values of a0, d0, a1 and b1 are arbitrary it seems to be mere curve fitting to find a relationship between them.
In other words, I fail to see how your model represents physical reality except as mere curve fitting because it includes arbitrary and adjustable non-physical terms.
And, importantly, if your model does not represent physical reality then it cannot be used as a valid tool to deduce anything about physical reality.
Please tell me what I am missing here because it seems very likely that I have failed to understand something important.
And I request that you understand I am trying to ‘get to grips’ with what you are claiming. If you think I am being unusually harsh with you then I suggest you ask Ferdinand about some of my disagreements with him in the past.
Richard

jimmi_the_dalek
August 21, 2013 7:09 am

Bart,
Your entire piece of maths amounts to circular argument. You write down some forms for T and dCO2/dt, do some manipulation involving a trivial integration, then produce an anthropogenic term and say it cannot be added because the result is already fixed. But you have not specified the possible physical origins of the parameters in your equations.
So lets just add some qualifications.
You are really using temperature anomalies rather than temperature, but that’s no big deal,
anomaly = (T-a0) = a1.t + f(t)
(not a very good approximation, but that’s secondary). The important point is that since you are going to use the experimental data, you have to allow for the possibility that a1 is determined by a mixture of natural and anthropogenic causes in proportions which are unclear.
Then with dCO2/dt = b0 + b1.t + g(t) you have to recognise that b0 and b1 may (or may not ) have been influenced by human input, because you are using the experimental data, which may include anthropogenic effects – I mean that’s the question are looking at isn’t it – so you cannot assume implicitly that there is no contribution from the start and then attempt to add it in later.
So you do your integration, and get an expression,
CO2 = b0.t +(1/2)b1. t^2 + higher terms +integration constant
(yes that is all it is)
to which I am compelled to ask, so what? Every single term has “constants” to which you have to add the qualification “may contain anthropogenic factors”. What have you proved?

GregM
August 21, 2013 8:49 am

Nyq Only says:
August 20, 2013 at 11:59 am
“Neat. Fun game – swap Hadcrut for “Random noise test pattern”
Tried that. No similarity whatsoever. What is your point?
Try DTdt vs CO2 instead . Should match if T highly depends on CO2?
http://www.woodfortrees.org/plot/esrl-co2/from:1959/mean:13/detrend:-0.10/normalise/plot/hadcrut3gl/from:1959/mean:12/derivative/detrend:-0.10/normalise/mean:13/normalise
Doesn´t match at all. How come?
D(CO2)dt follows T fairly well , DTdt doesn´t follow CO2 at all.
Means that CO2 depends on temperature, not the other way around.

Bart
August 21, 2013 9:01 am

richardscourtney says:
August 21, 2013 at 4:55 am

“And I do not understand your statement that
k and a1 are not arbitrary.
I can vary them on my spreadsheet and they do not represent any physical parameter that I can determine. What are they in terms of physical reality?”

The variables a0, a1, b0 and b1 are fixed by the observations, as are the variations f(t) amd g(t). You can determine them by analyzing the plots of T and dCO2/dt.
The variable k is fixed by the necessity that b1 = k*a1 and g(t) = k*f(t) for affine similarity. The remarkable properties are that the variational terms f(t) and g(t) are essentially scale similar in the first place, and that there exists a value of k for which both equations are satisfied (within reasonable margins of error).
“If you think I am being unusually harsh…”
No, not at all. I appreciate your trying to “get to grips” (we generally use the phrase “come to grips”, at least in the US) with what I am saying. I try to limit my frustrations to when people are being either abusive or intentionally obtuse.
jimmi_the_dalek says:
August 21, 2013 at 7:09 am
“…you have to allow for the possibility that a1 is determined by a mixture of natural and anthropogenic causes in proportions which are unclear…you have to recognise that b0 and b1 may (or may not ) have been influenced by human input…

No, b0, b1, and a1 are merely observational parameters. You can estimate them directly from the plots. The only assumption I am making is that the remarkable affine similarity between the two series, dCO2/dt and T, is no accident, and indicates a causal relationship. Based on the quality of the fit, I find that reasoning to be on solid ground.
That the arrow of causality flows from temperature to CO2 is settled by the fact that assuming temperatures respond to the rate of change of CO2 leads to absurd conclusions, such as that we could increase CO2 arbitrarily, and the temperature would only respond while we were increasing it, and revert to its former equilibrium level when we reached steady state at an arbitrary level. Changes in temperature would lead the level of absolute CO2 by 90 degrees in phase. This is untenable in that the effect would precede the cause.

Bart
August 21, 2013 9:10 am

jimmi_the_dalek says:
August 21, 2013 at 7:09 am
“But you have not specified the possible physical origins of the parameters in your equations.”
Actually, I have, in previous posts. There are no doubt other possibilities, but my hypothesis is that upwelling CO2 rich waters constitute a pumping action of CO2 into the atmosphere. This pumping action is modulated by temperatures, and there is some equilibrium level of temperatures for which the pumping action will cease. This leads directly to an equation of the form
dCO2/dt = k*(T – Teq)
As I suggested earlier:

A more complete toy system which mimics the full system would be
dCO2/dt = (CO2eq – CO2)/tau + H
dCO2eq/dt = k*(T – Teq)
where tau is a time constant, and H is the rate of human inputs. In this system, sinks are represented by the time constant tau. If tau is “short” (sinks action is powerful), then H will be severely attenuated, not effectively integrated, and CO2 will track CO2eq. This is a fairly ordinary and common-type control action.

August 21, 2013 11:30 am

Bart says:
August 21, 2013 at 9:10 am
There are no doubt other possibilities, but my hypothesis is that upwelling CO2 rich waters constitute a pumping action of CO2 into the atmosphere. This pumping action is modulated by temperatures, and there is some equilibrium level of temperatures for which the pumping action will cease.
As said many times before, the hypothesis of a sustained increase of CO2 from upwelling rich waters combined with the temperature increase is physically impossible, because it violates some basic laws and about all available observations.
A sustained increase in temperature of 1 K induces an increase of CO2 influx of the oceans (about 5% of the current influx from the equatorial upwelling places) and a decrease in outflux into the deep oceans at the cold polar sink places (again about 5%). That gives an increase of CO2 in the atmosphere. But the increase of CO2 in the atmosphere will give the opposite reaction: a decrease in influx and an increase of outflux. According to Henry’s law, an increase of ~16 ppmv in the atmosphere fully compensates for 1 K temperature increase, restoring the fluxes of before the increase.
Thus a sustained temperature increase doesn’t lead to a sustained extra influx of CO2 in the atmosphere, but leads to a assymptotic increase with a decay rate of a few years.
Any increase in CO2 from upwelling (either quantity or concentration) will show the same behaviour, except if the CO2 concentration at the sink places would have increased with 140 ppmv in the far past (double the recent increase), for which there is not the slightest indication.
But even if that was the case, then the cause of the recent increase would be the increased upwelling and temperature has only the 16 ppmv extra as effect. Thus anyway, there is no sustained effect from a sustained difference in temperature and the correlation found (for the trend, not for the short term variability) is pure coincidence…
About the possibility of an increase in (deep) ocean upwelling:
– An increase of deep ocean upwelling will give an increase of the 13C/12C ratio in the current atmosphere (including the change in isotopic ratio between ocean and atmosphere). Human emissions give a strong decrease. As from a process viewpoint the near 3 times increase of human emissions and a near 3 times net sink rate since 1960 must be mimicked by a near 3 times increase of natural carbon circulation, that would give following trend in d13C since 1960:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_increase_290.jpg
– Such an increase in throughput would reduce the residence time of CO2 in the atmosphere again with a near threefold, for which there is no evidence, to the contrary, it seems that the residence time slightly increased over recent decades…

Bart
August 21, 2013 11:46 am

Ferdinand Engelbeen says:
August 21, 2013 at 11:30 am
“As said many times before, the hypothesis of a sustained increase of CO2 from upwelling rich waters combined with the temperature increase is physically impossible, because it violates some basic laws and about all available observations.”
This is mere assertion on your part, and is not tenable. If upwelling waters continually pump CO2 into the system, then the waters will trend upward in CO2 content. Part of that upward trend will outgas to the atmosphere. Atmospheric concentration will keep rising as the CO2 rich waters diffuse into the surface system over time.
“An increase of deep ocean upwelling will give an increase of the 13C/12C ratio in the current atmosphere…”
The ratio argument is full of holes. It is mere speculation.

Nyq Only
August 21, 2013 12:07 pm

Bart: d0 was arbitrary, so the linear trend term alpha0 does not negate the possibility of significant human influence (are you listening, Nyq?)
Thanks for the maths. Some questions if I may just to clarify what you are saying. There seems to be two ways of reading your final statements there:
1. there is room for in the linear trend term (and constant term) for human influence but not in the other two. (i.e. you are leaving open the possibility of human influence)
or
2. there appears to be room in the linear trend term for human influence but by examination of the other terms that human influence can be dismissed (i.e. you are saying there cannot be any human influence of any significance)
Putting that issue aside you suggest the quadratic term cannot be human influenced. Hence it must be some natural phenomenon. What is your physical interpretation of that term?
You presented an argument earlier regarding the 90 degree phase shift of an integral to show that CO2 must lag temperature. I was wondering if you could sketch out the implications of that argument for the linear and quadratic terms of your model. Was your argument primarily pertaining to g(t) and f(t) in your model?
Genuine questions.

Nyq Only
August 21, 2013 12:19 pm

GregM says: August 21, 2013 at 8:49 am
“Tried that. No similarity whatsoever. What is your point?”
Not much similarity in the bumps and wobbles and some similarity in the linear trend. It is the linear trend in CO2 that is the issue that needs explaining. Everybody seems to agree that temperature does drive CO2 (or common parameters drive both) at shorter time periods.
There are various methods by which we can show remove or add arbitrarily linear trends to graphs. If we use your method we can add a positive slope to some random noise so that it rises in tune with CO2 over longer time scales. We could tweak the number to get a better match. The rise will be there because we put it there (in a graph sense).

Bart
August 21, 2013 1:01 pm

Nyq Only says:
August 21, 2013 at 12:07 pm
“1. … but not in the other two.”
I don’t think we have enough info on the variational part of the anthropogenic input. It may be small enough not to make a big dent either way.
But, my position is door #2. It is not that “…the quadratic term cannot be human influenced.” It could but, as the temperature relationship already accounts for it, there is no more room for significant human influence to add to it. Because the temperature influence on this term is corroborated by the match between the variations in temperature and the rate of change of CO2, the dominance of the temperature dependent impact is confirmed.
“What is your physical interpretation of that term?”
I believe it is simply the integrated trend in temperature. There is a flow of CO2 being pumped into the surface system which, if temperatures were constant, would be at a more-or-less steady rate. But, because the temperatures have been increasing, the input rate has been increasing, too. That accumulated increase begets a quadratic curvature in the absolute atmospheric concentration.
“I was wondering if you could sketch out the implications of that argument for the linear and quadratic terms of your model. Was your argument primarily pertaining to g(t) and f(t) in your model?”
Consider a sinusoid
x(t) = A*sin(w*t)/w
If w is “small”, over a finite interval, this approaches
x(t) := A*t
the integral of which is
y(t) := 0.5*A*t^2
The integral, considered as a network device, has a gain of 1/w and a phase shift of – 90 degrees, so the true integral of x(t) is
y(t) = A*(sin(w*t – pi/2) – sin(-pi/2))/w^2 = A*(1-cos(w*t))/w^2
Of course, we could have gotten this result with the usual formulas for integration of trig functions, but this shows how the integral can be represented as a frequency dependent gain and a phase shift of -pi/2 radians which is, of course, -90 degrees.
In the limit as w approaches zero, that becomes
y(t) := A*((w*t)^2/2)/w^2 = 0.5*A*t^2
as before. Hopefully, that elementary example shows how the phase shift manifests itself in the lower frequency regime.

August 21, 2013 1:26 pm

Bart says:
August 21, 2013 at 11:46 am
This is mere assertion on your part, and is not tenable. If upwelling waters continually pump CO2 into the system, then the waters will trend upward in CO2 content. Part of that upward trend will outgas to the atmosphere. Atmospheric concentration will keep rising as the CO2 rich waters diffuse into the surface system over time.
Maybe, maybe not. The increase of 70 ppmv CO2 over the past 50 years needs an increase of 140 ppmv at the downwelling side 800-1200 years ago, without any mixing in of the rest of the deep oceans. But that is not the point.
The point is that a sustained increase in temperature, whatever the changes in upwelling might be, doesn’t give a sustained extra influx of CO2 in the atmosphere, only 16 ppmv/K extra at maximum with a short decay rate towards the result of the changes in upwelling (or the changes caused by the human emissions or whatever other source…).
The ratio argument is full of holes. It is mere speculation.
You have obviously not read the rest of the discussion. Dr. Spencer was wrong on that point. And you may explain to me how outgassing of the deep oceans (at 0 to +1 per mil d13C) or the mixing in of surface waters (at +1 to +5 per mil) may DEcrease the d13C of the atmosphere at -8 per mil (including the water-air border fractionation):
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.gif
or over the period 1978-2002 (for the atmosphere, need to make an update for the more recent years):
http://www.ferdinand-engelbeen.be/klimaat/klim_img/d13c_trends.jpg
Again, the SH lags the NH, which points to a source of low 13C in the NH, as the CO2 levels in the SH also lag the increase in the NH. Thus the source can’t be from the high 13C CO2 emissions out of the oceanic upwelling places in the SH…

Bart
August 21, 2013 2:22 pm

Ferdinand Engelbeen says:
August 21, 2013 at 1:26 pm
“The point is that a sustained increase in temperature, whatever the changes in upwelling might be, doesn’t give a sustained extra influx of CO2 in the atmosphere…”
Without conceding your calculation, which I believe is based on questionable ice core data, this isn’t what I am claiming anyway. I am not claiming the atmospheric increase is temperature driven, but rather temperature dependent.
“Dr. Spencer was wrong on that point. “
Says you.
“And you may explain to me…”
It is speculation, Ferdinand. It is a storyline. A narrative. It may sound plausible to you, but plausibility is not proof. There are any number of possibilities to explain the phenomenon. Just because you cannot think of any does not mean the subject is closed.

jimmi_the_dalek
August 21, 2013 2:23 pm

Bart
“No, b0, b1, and a1 are merely observational parameters. You can estimate them directly from the plots. ”
Precisely!
From the plots of experimental data! Which may (or may not) contain human induced components, and thus cannot be used to prove that they do (or do not)

Bart
August 21, 2013 5:52 pm

jimmi_the_dalek says:
August 21, 2013 at 2:23 pm
No, jimmi. That’s not how it works. Please think it over some more.

August 22, 2013 2:08 am

Thank you Gail Combs for your informative post of August 20, 2013 at 1:13 am
I suggest everyone readi it again.

August 22, 2013 3:05 am

In Gail Combs post of August 20, 2013 at 1:13am she correctly states that there are many natural sources of atmospheric CO2 that are far greater than the humanmade CO2 component.
Yet the global warming alarmists continue to blame humankind for the observed increase in atmospheric CO2 concentration since systematic measurements began circa 1958, and also blame humankind for the minor global warming observed from ~1975 to ~2000
– notwithstanding the fact that we do not have accurate measurements of pre-1958 atmospheric CO2 measurements and there is considerable contradictory evidence in the pre-1958 CO2 data;
– and notwithstanding that the atmospheric CO2 data signature is overwhelmingly natural at annual, seasonal and daily time scales, even in urban environments near the sources of humanmade CO2;
– and notwithstanding that atmospheric CO2 lags temperature al all measured time scales, from about 9 months in the modern data record to about 800 years in the ice core record; [Note to Warmists: The future CANNOT cause the past.]
– and notwithstanding that atmospheric CO2 continues to increase but global warming ceased about 10-20 years ago, and Earth may now be entering a natural global cooling period;
– and notwithstanding that atmospheric CO2 increased from 1940 to 1975 during a previous period of global cooling;
– and notwithstanding that the global warming alarmists have failed in every major scientific prediction they have attempted; Contrary to IPCC projections, there has been NO net global warming for 10-20 years, and no evidence of wilder weather, more hurricanes, or tornados. “Green energy“ technologies have failed to produce significant amounts of useful net energy;
– and notwithstanding that the leading proponents of global warming alarmism have been proven in the Climategate emails to be guilty of reprehensible behaviour including scientific misrepresentation, vicious academic intimidation, and criminal misbehaviour. Warmist scientific and ethical failures included the Mann hokey stick, the Divergence Problem, Mike’s Nature Trick, Hide the Decline, the intimidation of the editors of scientific journals and the firing of skeptics from universities – a long history of thuggery.
Every dire prediction by the global warming alarmists has proven to be unsubstantiated and some of their conclusions and recommendations were clearly fraudulent, and yet our political leaders continue to pander to global warming hysteria and have squandered over a trillion dollars of scarce global resources on global warming nonsense.
All this real-word evidence fails to support the hypothesis of catastrophic humanmade global warming, and further suggests that global warming alarmism is destructive irrational cult hysteria, lacking both ethics and scientific merit.

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