EPA document supports ~3% of atmospheric carbon dioxide is attributable to human sources

Ferdinand Engelbeen says:
August 3, 2014 at 1:31 am
“Bart, the reduction of the rate of change compared to the emissions is of little interest: as long as there is a positive rate of change, it is human induced.”
It certainly makes it easier, to assume the answer before you look at the data, and then focus on the evidence which tends to support that answer. That is classic confirmation bias.
It does not, however, make the answer correct.
“Can you explain to me in reasonable terms why the Bode Gain Phase Theorem which is about a one variable gain/feedback system would be applicable to a two variable system largely without feedback?”
The theorem says that 90 deg phase lag = integration. You cannot shift the data in time via a natural process which would not affect the amplitude and, moreover, the change in amplitude has a specific frequency dependence, that of an integrator. It says that the model must be, at least for the period of observation 1958-present and its observable frequency range, dCO2/dt = k*T + constant. It says that the sensitivity is measured in ppmv/K/unit-of-time.
“Or do you think that all is caused by one and the same process?”
I think there is a dominant process involved, which is some form of temperature dependent pumping into the atmosphere.
Samuel C Cogar says:
August 3, 2014 at 10:45 am
Well, Ferdinand does have a lot invested in it, but not professionally. When the truth becomes known, he will be chagrined, but he will not suffer any real injury. Which is good, because he really is a very nice fellow.

Bart says:
August 3, 2014 at 10:57 am
It certainly makes it easier, to assume the answer before you look at the data
I did first look at the data: the increase in the atmosphere is less than the human contribution. As my wife knows (and I often forget) if that happens with our household budget, that means that our expenses are higher than our income if you add more to you bank account each month than it gains at the end of the month…
As long as the increase in the atmosphere is smaller than what humans emit, then humans are responsible for the increase. No matter if that is 1% or 99% of the human emissions.
Except for an enormous increase in natural CO2 circulation in lockstep with the 4-fold increase of human emissions, for which is not the slightest indication.
The theorem says that 90 deg. phase lag = integration.
The theorem is for a one-variable gain/feedback system. I don’t see any integration in the case of the two-variable T-CO2 system with a fixed gain and no appreciable feedback. You still haven’t explained that.
In my opinion, based on practical experience:
In first instance, if T goes up (as is the case for the oceans), then the CO2 flux out immediately goes up (and the flux down decreases), but the CO2 levels themselves lag the increase in T.
If T changes with a sinusoid, CO2 will follow wit 90 deg. That is all that happens. The amplitude may increase with longer frequencies, up to a maximum of 17 ppmv/°C, according to Henry’s Law (assuming constant deep upwelling and constant CO2 concentration in the upwelling).
If there is zero average temperature increase of a T sinusoid, there is zero average CO2 increase, but still a 90 deg. lag of CO2 after T.
The derivatives show the same sinusoids which are shifted 90 deg. back in time. As both the T slopes and dCO2/dt slopes are zero the factor needed to match the slopes is not definable.
If there is a stepwise increase in temperature, CO2 will follow with the same time constant as for the sinusoid, until 17 ppmv/°C is reached. Then it stops. Simply because there is a new equilibrium reached between input and output fluxes (caused by delta pCO2 oceans-atmosphere) and the CO2 pressure in the atmosphere. There is no continuous constant net CO2 influx from a stepwise T increase.
The step change will show up in the derivatives, but will give a short offset from zero for T and a stepwise, decreasing offset from zero for CO2. Again almost zero slopes, no definable factor.
If there is a continuous increase in T, CO2 will follow with the same time constant as for the sinusoid, thus a lag of the CO2 increase after T increase, but again with maximum 17 ppmv/°C T increase.
In the derivatives, that shows up as two sinusoids with a 90 deg. lag for dCO2/dt after dT/dt. Both with zero slope and an offset from zero. A slope in T, but no slope in dCO2/dt, that is a factor zero, thus zero amplitude, if the theorem is applicable. Which makes the theorem quite questionable in this case…

Bart says:
August 3, 2014 at 3:29 pm
This is not at all remarkable. It is how feedback systems work. It is how this system works.
I think I do see the problem: I did think that you meant by “feedback” the feedback from the carbon cycle, but you mean the feedback from the whole system on temperature. As that is what the theorem implies.
But there is hardly any feedback from the carbon cycle / level on temperature. The (negative) feedback from the carbon cycle is on the increased CO2 levels, not on temperature.
I still don’t see any reason to imply the theorem rules on a two-variable lead-lag system with no appreciable feedback on the first variable.

Ferdinand Engelbeen says:
August 3, 2014 at 4:26 pm
I am speaking of the relationship between temperature and atmospheric CO2. There is a 90 degree phase lag. That means that the model must be, at least for the period of observation 1958-present and its observable frequency range, dCO2/dt = k*T + constant. It means that the sensitivity is measured in ppmv/K/unit-of-time. It means you have to integrate the whole T, including the slope in T, to get CO2. When you do that, there is little to no room for human inputs to have a significant effect.

Ferdinand Engelbeen says:
August 4, 2014 at 3:11 am
“All what happens is that the amplitude of the CO2 variability is smaller for higher frequencies than for lower frequencies, a 90 deg. lag …”
Exactly. I.e., it is an integral relationship. You are dancing around the issue, and apparently do not realize that you are stating an equivalence relationship. You are trying to argue that 2+2 is not equal to 4. Sorry, no. There is no getting around it. The sensitivity is in ppmv/K/unit-of-time.

“Which varies with the…”
Maybe it does, and maybe it doesn’t. It’s been remarkably stable since 1958. Since that covers most of the era in which we are interested, it is enough.
“But still: why would a theorem based on a gain/feedback system be applicable on a simple unidirectional gain system without feedback?”
The result is widely applicable, and holds for any linear (or linearized) system with minimum phase (no right half plane zeros) rational transfer function, and natural systems generally fall into this category. It is the bedrock of control theory, governing how the open loop response must be shaped in the vicinity of the crossover frequency in order to achieve stability.

Ferdinand Engelbeen says:
August 4, 2014 at 12:49 pm
Nonsense. It tracks perfectly, for all practical purposes. You are drawing a secant line on an essentially quadratic function, and calling it a derivative. No dice.
I think the language “R” people go on about is open source. Good luck proving Bode wrong. You might try tackling Einstein and Bohr, and exposing them as frauds, while you’re at it.

Ferdinand Engelbeen says:
August 4, 2014 at 1:55 pm
dCO2/dt = k*(T – To)
T has had a more or less linear trend, so its integral is essentially quadratic, as total CO2 is essentially quadratic.
You are drawing a secant line on an essentially quadratic function, and calling it a derivative. That is invalid. If you match here (and, we do), then there is a match. The sensitivity factor k is, indeed, remarkably well represented by a very stable parameter value since 1958.
For the rest, have at it. Any frequency at which you have a 90 deg phase lag, you will find the gain rolling off at -20 dB/decade in a band enclosing that frequency. A -20 dB/decade roll-off is the signature of integration taking place over the frequency band. If you try to put in a feedback parameter to limit the integration, you will get observable phase distortion near the corner frequency, of which we have none evident in the CO2 record.