Water Vapour: The Big Wet Elephant In The Room

Guest opinion: Dr. Tim Ball

clip_image002

In my last two articles I examined what we know, but more importantly what we don’t know, about the three main greenhouse gases (GHG). The first examined methane (CH4) and the second CO2. The fluster of responses about data and accuracy of measurements is essentially irrelevant because combined CH4 and CO2 represent only four percent of the GHG. It didn’t matter whether Beck was right or wrong about actual CO2 measures, what was important was the degree of variability the data showed, such as with the stomata data. This variability was deliberately eliminated in other measures to achieve a smooth, with no splinters, ‘hockey stick’ because it contradicted the well-mixed scenario essential to the Anthropogenic Global Warming (AGW) agenda.

The articles about CH4 and CO2 illustrate the modus operandi of the creators and proponents of the AGW hypothesis. They designed them to prove the hypothesis rather than disproving, as is the proper scientific method. This includes selecting and adjusting the start and end points of records, ignoring those that don’t fit or worse contradict the hypothesis. There is inadequate temperature data for construction of the computer models, and there is even fewer data for every other variable. Data is created mathematically, such as the use of parameterization for temperatures. As the Intergovernmental Panel on Climate Change (IPCC) explain parameterization as follows,

“…the technique of representing processes that cannot be explicitly resolved at the spatial or temporal resolution of the model (sub-grid scale processes) by relationships between model-resolved larger-scale variables and the area- or time- averaged effect of such subgrid scale processes.”

Figure 1 shows the current percentages of greenhouse gases as a part of total atmospheric gases. The challenge for the IPCC and its promoters was to create a different set of percentages and images for the public. This required amplifying one side, as I explained about CO2 and CH4 while downplaying the other side.

clip_image004

Figure 1 (After Heartland.org)

The first and most important device was the definition of climate change Article 1 of the UNFCCC, a treaty formalized at the “Earth Summit” in Rio in 1992, defined Climate Change as:

a change of climate which is attributed directly or indirectly to human activity that alters the composition of the global atmosphere and which is in addition to natural climate variability observed over considerable time periods.

This allowed them to limit the variables considered in their investigation, which is depicted by the forcing diagrams. Figure 2 shows those for the 2001 IPCC Report.

clip_image006

Figure 2

LOSU stands for Level of Scientific Understanding. Notice only two are rated “High” but we know that is not accurate. Stratospheric water vapour is included, but tropospheric water is not. This is interesting because the 2007 Report says,

Due to the computational cost associated with the requirement of a well-resolved stratosphere, the models employed for the current assessment do not generally include the QBO.

It appears they knew little and did not have the data or the ability to resolve what was going on. The level of knowledge is the same in the 2013 AR5 Report (Figure 3). The changes are telling. Now “Long-lived greenhouse gasses” are “Well-mixed greenhouse gasses.” This is because they switched the narrative. The early story said that CO2 residency time was 100 years, but that was challenged and corrected. The new, false, narrative was that CO2 was well mixed. The “Very High” assessment doesn’t fit the increasing divergence between the CO2 level and the temperature.

clip_image008

Figure 3

The confidence level for well-mixed greenhouse gasses is now “Very high”. This is simply not possible because, as the satellite data from OCO2 shows, CO2 is clearly not a well-mixed gas. The problem is similar to the objective of the IPCC to determine human causes of climate change. It is only possible if you know how much climate changes without the human effect. You can only determine the CO2 effect if you know the effect of the predominant greenhouse gas – water vapor.

The IPCC acknowledges that water vapor is the most important and abundant greenhouse gas. In the 2007 Report they wrote

“Water vapour is the most abundant and important greenhouse gas in the atmosphere.

They then explain why they are going to ignore it.

However, human activities have only a small direct influence on the amount of atmospheric water vapour.”

The 2013 IPCC Report FAQ 8.1 responds to criticism about not including water vapour as a greenhouse. Here is the entire FAQ, which is illuminating and begs many questions. (There is no significance to the fact it is on page 666.)


 

As the largest contributor to the natural greenhouse effect, water vapour plays an essential role in the Earth’s climate. However, the amount of water vapour in the atmosphere is controlled mostly by air temperature, rather than by emissions. For that reason, scientists consider it a feedback agent, rather than a forcing to climate change. Anthropogenic emissions of water vapour through irrigation or power plant cooling have a negligible impact on the global climate.

Water vapour is the primary greenhouse gas in the Earth’s atmosphere. The contribution of water vapour to the natural greenhouse effect relative to that of carbon dioxide (CO2) depends on the accounting method, but can be considered to be approximately two to three times greater. Additional water vapour is injected into the atmosphere from anthropogenic activities, mostly through increased evaporation from irrigated crops, but also through power plant cooling, and marginally through the combustion of fossil fuel. One may therefore question why there is so much focus on CO2, and not on water vapour, as a forcing to climate change.

 

Water vapour behaves differently from CO2 in one fundamental way: it can condense and precipitate. When air with high humidity cools, some of the vapour condenses into water droplets or ice particles and precipitates. The typical residence time of water vapour in the atmosphere is ten days. The flux of water vapour into the atmosphere from anthropogenic sources is considerably less than from ‘natural’ evaporation. Therefore, it has a negligible impact on overall concentrations, and does not contribute significantly to the long-term greenhouse effect. This is the main reason why tropospheric water vapour (typically below 10 km altitude) is not considered to be an anthropogenic gas contributing to radiative forcing.

 

Anthropogenic emissions do have a significant impact on water vapour in the stratosphere, which is the part of the atmosphere above about 10 km. Increased concentrations of methane (CH4) due to human activities lead to an additional source of water, through oxidation, which partly explains the observed changes in that atmospheric layer. That stratospheric water change has a radiative impact, is considered a forcing, and can be evaluated. Stratospheric concentrations of water have varied significantly in past decades. The full extent of these variations is not well understood and is probably less a forcing than a feedback process added to natural variability. The contribution of stratospheric water vapour to warming, both forcing and feedback, is much smaller than from CH4 or CO2.

 

The maximum amount of water vapour in the air is controlled by temperature. A typical column of air extending from the surface to the stratosphere in polar regions may contain only a few kilograms of water vapour per square metre, while a similar column of air in the tropics may contain up to 70 kg. With every extra degree of air temperature, the atmosphere can retain around 7% more water vapour (see upper-left insert in the FAQ 8.1, Figure 1). This increase in concentration amplifies the green- house effect, and therefore leads to more warming. This process, referred to as the water vapour feed- back, is well understood and quantified. It occurs in all models used to estimate climate change, where its strength is consistent with observations. Although an increase in atmospheric water vapour has been observed, this change is recognized as a climate feed- back (from increased atmospheric temperature) and should not be interpreted as a radiative forcing from anthropogenic emissions. Currently, water vapour has the largest greenhouse effect in the Earth’s atmosphere. However, other greenhouse gases, primarily CO2, are necessary to sustain the presence of water vapour in the atmosphere. Indeed, if these other gases were removed from the atmosphere, its temperature would drop sufficiently to induce a decrease of water vapour, leading to a runaway drop of the greenhouse effect that would plunge the Earth into a frozen state. So greenhouse gases other than water vapour provide the temperature structure that sustains current levels of atmospheric water vapour. Therefore, although CO2 is the main anthropogenic control knob on climate, water vapour is a strong and fast feedback that amplifies any initial forcing by a typical factor between two and three. Water vapour is not a significant initial forcing, but is nevertheless a fundamental agent of climate change.

clip_image010

FAQ 8.1, Figure 1 | Illustration of the water cycle and its interaction with the greenhouse effect. The upper-left insert indicates the relative increase of potential water vapour content in the air with an increase of temperature (roughly 7% per degree). The white curls illustrate evaporation, which is compensated by precipitation to close the water budget. The red arrows illustrate the outgoing infrared radiation that is partly absorbed by water vapour and other gases, a process that is one component of the greenhouse effect. The stratospheric processes are not included in this figure.


This section is so full of misstatements and false assumptions that it requires an entire column in itself, but that is not the purpose of this column. Suffice to say that this appears to be another way of presenting the already disproven positive feedback. It is also an example of, in the vernacular, having your cake and eating it too. Their argument misses the point entirely. They don’t know how much contribution human water vapour (H2O) makes because they don’t have critical information. They don’t know how much H2O humans produce, how much H2O there is in the atmosphere, or the amount H2O varies naturally. When assessing how much the energy balance is affected by greenhouse gases, the source is only an issue if you want to point an accusatory political finger. For science, the total amount of each gas and how it varies is critical. As NASA notes,

Water vapor is a critical variable for climate studies. The absorption of infrared (IR) radiation by atmospheric water vapor and its subsequent emission at lower temperatures greatly influences the radiative energy balance of the planet.

So, the questions are how much H2O is in the atmosphere and how much does it vary?

In 1996, the challenges for measuring water vapour were explained as follows.

It is very hard to quantify water vapor in the atmosphere.  Its concentration changes continually with time, location and altitude.  To measure it at the same location every day, you would need a hygrometer, which in earlier days made use of the moisture-sensitivity of a hair, and by now of for instance condensators.  A vertical profile is obtained with a weather balloon.  To get a global overview, only satellite measurements are suitable.  From a satellite, the absorption of the reflecting sunlight due to water vapor molecules is measured.  The results are pictures of global water vapor distributions and their changes.  The measurement error, however, is still about 30 to 40%.

By 2002, according to NASA, it was no better.

Finally, water vapor plays a key role in the Earth’s hydrologic cycle. Therefore, a better understanding of its role will require long-term observations of both small and large scale water vapor features, a major goal of the National Aeronautics and Space and Administration’s (NASA’s) Mission to Planet Earth (MTPE) program.

But the IPCC is only interested stratospheric water vapour from CH4 as Figure 3 shows. Even here they don’t know much,

Since trend estimates from the cited literature are used here, issues such as data records of different length, potential lack of comparability among measurement methods and different trend calculation methods, add to the uncertainty in assessing trends.

If they were interested in tropospheric water vapour, they could use the total column water vapour measures from RSS.

We have merged the water vapor measurements from the many radiometers in operation since 1987, including SSM/I, SSMIS, AMSR-E and WindSat.  These data were all processed in a consistent manner using our radiative transfer model and careful instrument intercalibration.  The water vapor from these instruments are used to create a Total Precipitable Water (atmospheric water vapor) product that is best for use in climate study.

This means we have a 28-year record according to RSS and 19 years according to the IPCC. These are the people who demand a 30-year record for statistical significance.

The IPCC employed their standard amplification technique, known as the Global Warming Potential (GWP) to increase the effect of CO2 and CH4 while reducing the role of H2O. What is GWP?

The Global Warming Potential (GWP) is defined as the time-integrated RF due to a pulse emission of a given component, relative to a pulse emission of an equal mass of CO2 (Figure 8.28a and formula). The GWP was presented in the First IPCC Assessment (Houghton et al., 1990), stating ‘It must be stressed that there is no universally accepted methodology for combining all the relevant factors into a single global warming potential for greenhouse gas emissions.

A search for GWP values produces a bewildering range of numbers. This prompted Gavin Schmidt, now Director of NASA GISS, to write,

The relative contributions of atmospheric long‐wave absorbers to the present‐day global greenhouse effect are among the most misquoted statistics in public discussions of climate change.

How does Schmidt clarify the problem? In typical circular argument using self-generated computer model data.

Motivated by the need for a clear reference for this issue, we review the existing literature and use the Goddard Institute for Space Studies ModelE radiation module to provide an overview of the role of each absorber at the present-day and under doubled CO2. With a straightforward scheme for allocating overlaps, we find that water vapour is the dominant contributor (~50% of the effect), followed by clouds (~25%) and then CO2 with ~20%. All other absorbers play only minor roles.

The IPCC is less sure about what is going on. Here is what they wrote in Chapter 8 of AR5 Consider the number of values and subjectively related decisions in this supposedly scientific process (my bold).

Emission metrics such as Global Warming Potential (GWP) and Global Temperature change Potential (GTP) can be used to quantify and communicate the relative and absolute contributions to climate change of emissions of different substances, and of emissions from regions/countries or sources/sectors. The metric that has been used in policies is the GWP, which integrates the RF of a substance over a chosen time horizon, relative to that of CO2. The GTP is the ratio of change in global mean surface temperature at a chosen point in time from the uncertainties related to both GWP and GTP, and the relative uncertainties are larger for GTP. There are also limitations and inconsistencies related to their treatment of indirect effects and feedbacks. The values are very dependent on metric type and time horizon. The choice of metric and time horizon depends on the particular application and which aspects of climate change are considered relevant in a given context. Metrics do not define policies or goals but facilitate evaluation and implementation of multi-component policies to meet particular goals. All choices of metric contain implicit value-related judgements such as type of effect considered and weighting of effects over time.

Water vapour is the giant wet elephant in the IPCC laboratory. The definition of climate change they received allowed them to ignore anything that didn’t fit their hypothesis. As a result, the IPCC focus is on eliminating, ignoring, and creating false narratives to enhance the role of CO2. This has the effect of pushing the elephant of water vapour under water so that like an iceberg the public only see about 10 percent of the mass.

clip_image012

Get notified when a new post is published.
Subscribe today!
5 1 vote
Article Rating
427 Comments
Inline Feedbacks
View all comments
October 31, 2015 5:33 pm

OK Bart, you say:
Think of it in a series of steps in a continuous loop:
1) as you say, atmospheric CO2 increases, so ocean pCO2 decreases
2) less CO2 downwells
3) new CO2 laden waters upwell, so ocean concentration rebounds
4) atmospheric CO2 increases
5) go to step 1 and repeat

I have a quite different opinion…
Assuming that the ocean upwelling didn’t change in mass or CO2 concentration and no human emissions, a step response in temperature will have this following steps:
At the upwelling side:
1) pCO2 of the ocean increases.
2) pCO2 difference with the atmosphere increases.
3) CO2 flux out of the ocean surface increases.
4) CO2 concentration in the ocean surface decreases, CO2 depleted water flows towards poles.
5) New water is upwelling from the deep oceans.
6) CO2 influx from the oceans increases pCO2 in the atmosphere.
7) pCO2 difference between ocean surface and atmosphere decreases.
8) CO2 flux out of the oceans decreases.
9) CO2 concentration in the ocean surface is less depleted, CO2 depleted water flows towards poles.
10) Go to step 5 and repeat until pCO2 difference and thus CO2 influx in the atmosphere is restored as was before the step increase in temperature.
At the sink side:
1) pCO2 of the ocean increases.
2) pCO2 difference with the atmosphere decreases.
3) CO2 flux into the ocean surface decreases.
4) CO2 concentration in the ocean surface is less enriched, CO2 enriched water sinks into the deep.
5) New waters flow in from the tropics.
6) Less CO2 outflux into the oceans increases pCO2 in the atmosphere.
7) pCO2 difference between ocean surface and atmosphere increases.
8) CO2 flux out of the oceans increases.
9) CO2 concentration in the ocean surface is more enriched, CO2 enriched water sinks into the deep.
10) Go to step 5 and repeat until pCO2 difference and thus CO2 outflux into the deep oceans is restored as was before the step increase in temperature .
Steps 5-10 will give an asymptotic increase of CO2 towards a new steady state between oceans and atmosphere (without other disturbances). The final end of the temperature step is when the original in/out fluxes are restored (and equal without other disturbances). That is at a change of 16 ppmv/°C in the atmosphere…

Reply to  Ferdinand Engelbeen
October 31, 2015 5:49 pm

Bart,
Some part may need clarification:
By higher temperatures the pCO2 of the upwelling waters increases, which gives more CO2 out the ocean surface, and that gives less CO2 concentration in the remaining waters, but still with a pCO2 at least as high as in the atmosphere. Most releases are in the tropics (and other upwelling zones), while during the transport to the poles the waters slowly change from net CO2 emitters to net CO2 absorbers, due to colder temperatures. Another important factor is bio-life, but in general tropical waters may have a high pCO2, despite lower CO2 concentrations (after degassing of the upwelling) than near the poles. pCO2 is the main driving source, with temperature and concentration as main components.

afonzarelli
Reply to  Ferdinand Engelbeen
October 31, 2015 7:32 pm

Ferdinand, very well, you managed to get a similar amplitude and trend using the NH data set by simply adjusting the scale…
My guess is that bart uses the SH data because the satellite data doesn’t cover the whole MLO data set. One shouldn’t discount the similarity between the global satellite data and the southern hemisphere data. Perhaps the southern hemishpere data is a better reflection of global temps (than the northern hemisphere).
The thing about bart’s graph is that at ALL times amplitude and trend match using the same scale. In other words, if one were to go back in time ten years and plot the same graph using the same scale, one would get the same result. (or 20 years or 30 or 40…) For that matter, if the past is any indicator of the future, then one should be able to get the same result 10, 20, or even 30 years from now. This shouldn’t happen if the temperature trend is entirely unrelated to the carbon growth rate trend. Getting back to points that i made earlier, whenever the temperature trends flat so also does the carbon growth rate. Whenever you see step rises, you see them in both data sets. Sooner or later bart’s graph will need an adjustment in the scale (and thus the amplitudes won’t match) if the temperature trend is unrelated to the carbon growth rate trend. It has yet to happen after 57 years in defiance of the odds…

Reply to  Ferdinand Engelbeen
November 1, 2015 2:53 am

Fonzie,
Still a huge discrepancy between NH temperature trend and SH CO2 variability. The T to CO2 factor nearly halves. Further it is proven (from both the O2 and 13C/12C balances) that all the variability is from vegetation, while any long term (> 3 years) natural increase in the atmosphere is from the oceans. The real trend of the influence of temperature on vegetation is essentially zero, thus the T-CO2 factor for the amplitudes is independent of the slopes, whatever causes the slopes. That are independent processes…
And the “fit” of the integral doesn’t hold for the period before 1960, if one accepts the CO2 values as measured in high resolution ice cores (less than a decade):
http://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_T_dT_em_1900_2011.jpg
For every period in time, Bart’s formula needs a different k factor to translate temperature into CO2 rate of change. From near zero over the Holocene to extremely small during glacial – interglacial transitions and reverse to quite large in modern times. If one simply uses Henry’s law as base and the observed sink rate for any excess CO2 in the atmosphere above steady state, that shows a nice correlation over all periods…

Reply to  Ferdinand Engelbeen
November 1, 2015 3:04 am

Bart,
An error in point 8) of the sink side:
8) CO2 flux out of the oceans increases.
must be:
8) CO2 flux out into the oceans increases.

Reply to  Ferdinand Engelbeen
November 1, 2015 5:30 am

Sorry again:
8) CO2 flux into the oceans increases.
Never just copy and paste without rereading every single sentence…

Bartemis
Reply to  Ferdinand Engelbeen
November 1, 2015 11:04 am

Ferdinand Engelbeen October 31, 2015 at 4:34 pm
“But why did Bart choose the SH temperatures?”
Because the NH temperatures are clearly bogus. Here, as you see, after more than 100 years of lockstep between SH and NH, the NH suddenly diverges around 2000. The SH continues to match the satellite record.
http://woodfortrees.org/plot/hadcrut4nh/plot/hadcrut4sh/plot/rss/plot/uah
Too many “adjustments” have been made to NH temperatures. They are unreliable.
afonzarelli October 31, 2015 at 7:32 pm
“My guess is that bart uses the SH data because the satellite data doesn’t cover the whole MLO data set. One shouldn’t discount the similarity between the global satellite data and the southern hemisphere data. Perhaps the southern hemishpere data is a better reflection of global temps (than the northern hemisphere).”
Exactly. Ferdinand is grasping at straws. You’re a sharp dude, Fonzie.
Ferdinand Engelbeen October 31, 2015 at 5:33 pm
“8) CO2 flux out of the oceans increases.
9) CO2 concentration in the ocean surface is more enriched, CO2 enriched water sinks into the deep.”

How cam flux out of the oceans enrich the ocean waters?
“That is at a change of 16 ppmv/°C in the atmosphere…”
As much as you want that to be the case, there is no such requirement.
Think of what happens without any atmosphere at all. A general, global step increase in temperatures causes less downwelling, and the pCO2 of the surface oceans steadily increases.
Then, put in the atmosphere. With steadily increasing pCO2 of the surface oceans, the atmosphere also gets a steadily increasing concentration.
Ferdinand Engelbeen November 1, 2015 at 2:53 am
“For every period in time, Bart’s formula needs a different k factor to translate temperature into CO2 rate of change.”
A) Uses ice core reconstruction, which I reject as insufficiently validated
B) So what? Even if true, systems change over time, sometimes abruptly.
“If one simply uses Henry’s law as base and the observed sink rate for any excess CO2 in the atmosphere above steady state…”
… one gets a lousy reconstruction, such as the one you have shown. The longer you choose your time constant, the better the fit in the modern era. And, the more the trend in dCO2/dt comes to be seen as being driven by the trend in temperature.
Trying to extend the model to speculative data over the long ago past is unnecessary. For the past 57 years, we know that dCO2/dt = k*(T – T0). That is the era of the greatest rise observed over the past century.
Ferdinand Engelbeen November 1, 2015 at 5:30 am
“8) CO2 flux into the oceans increases.”
Does the cart pull the horse? The oceans are the horse, pulling the cart, which is the atmosphere. That is because the source is the upwelling waters, as the source of energy in the cart-horse system is within the horse. The atmosphere is subordinate to the oceans.
Again, think of what happens without any atmosphere at all. A general, global step increase in temperatures causes less downwelling, and the pCO2 of the surface oceans steadily increases.
Then, put in the atmosphere. With steadily increasing pCO2 of the surface oceans, the atmosphere also gets a steadily increasing concentration.

Bartemis
Reply to  Ferdinand Engelbeen
November 1, 2015 11:11 am

The important part of the above is this:

Think of what happens without any atmosphere at all. A general, global step increase in temperatures causes less downwelling, and the pCO2 of the surface oceans steadily increases.
Then, put in the atmosphere. With steadily increasing pCO2 of the surface oceans, the atmosphere also gets a steadily increasing concentration.

Reply to  Bartemis
November 1, 2015 4:27 pm

Bart:
“8) CO2 flux out of the oceans increases.
9) CO2 concentration in the ocean surface is more enriched, CO2 enriched water sinks into the deep.”

How cam flux out of the oceans enrich the ocean waters?
Which I said was in error from copying the points 1-10 from the upwelling.
Point 8 must be reverse at the sinks:
8) CO2 flux into the oceans increases,
9) CO2 concentration in the ocean surface is more enriched, CO2 enriched water sinks into the deep.
Which is logical.
A) Uses ice core reconstruction, which I reject as insufficiently validated
Of the same level as someone who object against CO2 measurements in the atmosphere, as these were never validated, for the simple reason that the old chemical methods were a factor 100 less accurate than the NDIR method used by Keeling Sr.
B) So what? Even if true, systems change over time, sometimes abruptly.
Don’t want to argue that one again and again. Sufficient to say that the simple application of Henry’s law fits all variations over the past 800,000 years, including human emissions up to today. If that doesn’t fit the +/- 1 ppmv current noise around the trend, so what? That noise has no connection with the trend at all…
Think of what happens without any atmosphere at all. A general, global step increase in temperatures causes less downwelling, and the pCO2 of the surface oceans steadily increases.
Without an atmosphere, the ocean waters (as far as not boiling) at the upwelling would expel CO2 until the newly formed CO2 atmosphere (with some water vapor) has the same CO2 pressure as in the oceans for the temperature at the equator. That is up to 700 μatm within mostly full vacuum, in equilibrium with the 700 μatm of the ocean waters. Henry’s law is for each gas/liquid equilibrium own partial pressure in the atmosphere independent of other constituents in the same atmosphere or lack thereof.
The sinking waters near the poles do the same, but at a lower pressure: ~150 μatm.
If there is sufficient circulation of the near pure CO2 atmosphere, the 700 μatm CO2 at the equator will be mixing with the 150 μatm at the poles, which gives an about 290 μatm global CO2 pressure for the current global average seawater temperature. With sufficient mixing speed, that gives about the same gas pressure in the newly formed near 100% CO2 atmosphere over the full globe.
Which makes that at steady state the 700-290 μatm difference at the upwelling sites will emit ~40 GtC/year CO2 out of the oceans into the atmosphere and the 290-150 μatm difference at the sink sites will sink ~40 GtC/year out of the atmosphere into the deep oceans…
You see, for Henry’s law, it doesn’t matter if there is an atmosphere or not, the same CO2 pressure differences and fluxes are at work…
Next step:
8) CO2 flux into the oceans increases.
Does the cart pull the horse? The oceans are the horse, pulling the cart, which is the atmosphere. That is because the source is the upwelling waters, as the source of energy in the cart-horse system is within the horse. The atmosphere is subordinate to the oceans.
Well Bart, you have a rich fantasy.
For any gas and any liquid, the ratio between the gas in the atmosphere and in the liquid is fixed for a fixed temperature. That is what Henry’s law says. If there is more partial pressure of that gas in the atmosphere than in the liquid the gas flux is from the atmosphere into the liquid and reverse. The resulting flux is directly proportional to the partial pressure difference between atmosphere and liquid, one way or the other.
The driving force is the partial pressure difference between atmosphere and oceans. At the sink places, the partial pressure in the atmosphere is higher than in the sinking waters, thus CO2 is pushed into the oceans. How much is directly proportional to the partial pressure difference between atmosphere and oceans. If CO2 increases in the atmosphere, the pCO2 difference between atmosphere and ocean surface increases and more CO2 is pushed into the oceans waters…
The CO2 sink rate thus is not static as you seem to think, it is dynamic and influenced both by temperature and pressure difference.
A general, global step increase in temperatures causes less downwelling, and the pCO2 of the surface oceans steadily increases.
The first part is true but only temporarily, the second is nonsense: the pCO2 of the ocean surface increases with 16 μatm/°C, which gives an initial increase in CO2 influx and a decrease in CO2 outflux. That increases the CO2 level/pressure in the atmosphere. Once the CO2 increase in the atmosphere matches the temperature caused average pCO2 increase in the ocean waters, the steady state is re-established again with the same CO2 in/out fluxes as before the temperature increase…

Reply to  Ferdinand Engelbeen
November 1, 2015 5:47 pm

Not to get into the middle of this, but I had a question about a supposition I’ve had, and maybe it’s something you can comment on.
On a snowball (or partial snowball) earth, I’ve thought that the ice would reduce the oceans ability to sink Co2, and with the majority of the surface frozen the air would dry out, and at some point if it got cold enough, start a Co2 cycle (snowing dry ice), such as a snowball planet might have, and that vulcanism would over time pump Co2 into the atm leading it to start melting the tropical ocean, water would start to accumulate leading to a water (ish) world.
Thoughts?

Bartemis
Reply to  Bartemis
November 1, 2015 6:34 pm

“8) CO2 flux into the oceans increases”
It doesn’t increase. You have the cart drawing the horse.
“Of the same level as someone who object against CO2 measurements in the atmosphere…”
You haven’t seen me make that argument. I think older measurements are questionable because they were influenced by local environments.
“Without an atmosphere, the ocean waters (as far as not boiling)…”
This is a thought experiment. No need to consider this.
You are getting confused because you are trying to imagine what would happen in a complicated scenario. I am trying to un-complicate it for you.
What would happen is that the gradient of CO2 in the oceans would become shallower versus latitude, and the oceans would have to increase their average pCO2 significantly to overcome the decline in downwelling. It could take centuries for this to settle out.
“At the sink places, the partial pressure in the atmosphere is higher than in the sinking waters, thus CO2 is pushed into the oceans.”
The pp in the atmosphere has to increase substantially in order to overcome the reduction in capacity due to temperature change. Again, this could take centuries.

Reply to  Bartemis
November 2, 2015 2:11 am

Bart:
8) CO2 flux into the oceans increases”
It doesn’t increase. You have the cart drawing the horse.

Bart, I did work a few years in a cola bottling plant (Royal Crown Cola Cy), because of lack of better work at that time.
To press the CO2 in the sugared liquid, the cola was cooled down to about 5°C and with a thin film over a large surface, the cola got carbonated under several bar CO2 pressure.
After being bottled, samples were taken by pressing a combined thermometer – pressure meter through the cork, shaking the bottle a few minutes and observing temperature of the liquid and pressure above the liquid. With some conversion table, one could see if the carbonation was within limits.
Now in (seldom here) real hot summers, the cooling couldn’t maintain the 5°C and temperatures of the liquid went up. All we had to do was increase the CO2 pressure in the carbonating part to maintain the carbonization.
Thus if the ocean waters at the sink places increase in temperature, that gives an immediate drop in atmosphere – ocean surface flux and thus in sink rate.
That gives an increase of CO2 in the atmosphere.
The increase of CO2 in the atmosphere again increases the outflux from the atmosphere into the ocean surface waters. Thus that increases the sink rate.
When the pressure difference between CO2 in the atmosphere and the pCO2 in the liquid is again the same as before the temperature increase, the same sink rate will be obtained.
It doesn’t matter at all if the atmosphere or the oceans are leading: the pCO2 difference is the driving force for any flux between atmosphere and ocean surface.
What would happen is that the gradient of CO2 in the oceans would become shallower versus latitude, and the oceans would have to increase their average pCO2 significantly to overcome the decline in downwelling. It could take centuries for this to settle out.
Bart, you have a complete wrong idea of what happens in the oceans, no matter if there is an atmosphere or not.
If we may start at steady state, influx and outflux between “atmosphere” (even if that is 100% CO2 at 0.000290 bar) and oceans are equal.
At every part of the oceans, the flux between atmosphere and oceans is a matter of local pCO2 difference. With an increase of 1°C everywhere in all ocean surfaces, the pCO2 of the oceans everywhere increases with ~16 μatm.
The result is that where the ocean waters are upwelling, the influx into the atmosphere increases and so does that everywhere (in ratio to the local pCO2 difference), as long as the pCO2 in the oceans is higher than in the atmosphere due to local temperatures. Some parts of the water flow from equator to poles even may become net sources where they were small net sinks before the warming up.
Where the temperature of the waters still is cold enough, the sink rate is reduced by the temperature uptick.
Both increased influx and reduced outflux increase CO2 in the atmosphere.
To overcome the increased pCO2 of 16 μatm in the oceans everywhere, all you need is an increase of 16 ppmv in the atmosphere. That is really all you need.
The 10 ppmv increase for a 0.6°C increase in temperature over the past 57 years was reached about 15 years after Mauna Loa started, the rest of the 70 ppmv thus is not from a temperature increase…
The pp in the atmosphere has to increase substantially in order to overcome the reduction in capacity due to temperature change. Again, this could take centuries.
Only with 16 ppmv/°C: the reduction in sink capacity is due to the 16 μatm increase in ocean pCO2 for 1°C temperature increase. A 16 ppmv increase in the atmosphere restores the pCO2 difference between atmosphere and oceans and thus the outflux from atmosphere into the deep oceans…

Bartemis
Reply to  Bartemis
November 2, 2015 9:19 am

Ferdinand, your cola bottles were not recirculating oceans. We are talking about massive quantities and flows, and very slowly evolving diffusion processes.
The proof that you are wrong is that, under your scenario, human inputs would cause a pressure change which would drive the CO2 down faster, too. In that case, human inputs could not produce a rise proportional to themselves.
Take, for example, your equation
τ * dCO2/dt = ΔT – f(T)* ΔCO2
You’ve got to put the human inputs in there, too. Forget the temperature related parts for now and focus on these portions
τ * dCO2/dt = τ*H – ΔCO2
where H is the anthropogenic input (with appropriate units per unit time). In steady state for τ short, the solution is approximately
ΔCO2 := τ*H
So, ΔCO2 would not be proportional to the total accumulated H, but to H itself. You go one polynomial order down with a system like this. So, you don’t get a quadratic curve due to H, you merely get a linear trend.

Bartemis
Reply to  Bartemis
November 2, 2015 9:38 am

Someday, after I have worked out some puzzles, I will give you my full model. But, it is shaping up to be something like this:
d(ΔCO2)/dt = k1*H + k2*ΔT – ΔCO2/tau
This is very simplified, because k1 and k2 are the dc gains of specific system responses. But, basically, k1 is small and tau is large, such that the impact of k1*H – ΔCO2/tau is negligible compared to k2*ΔT over decades long time spans.

Reply to  Bartemis
November 2, 2015 12:10 pm

Bart,
Henry’s law is as good for the oceans as for pressing CO2 in cola… Even if it is a one-way process. In the oceans an increase of CO2 in the atmosphere changes both the influx and outflux. Thus even if it is a circulation, an increased pressure in the atmosphere gives more sink into the oceans and less source from the oceans… Thus for 16 ppmv extra in the atmosphere, there is no CO2 increase in the atmosphere anymore caused by 1°C temperature increase…
tau for ΔT, the variability, is very short (possibly less than a year), as that is the fast reaction of vegetation on temperature changes.
tau for ΔT, the ocean warming – CO2 reaction is already slower, more in the order of a few years for the ocean surface and up to hundreds of years for the deep oceans.
tau for ΔpCO2 between oceans and atmosphere caused by human emissions (or volcanoes) is slightly over 50 years, not really fast and completely independent of the other two reactions.
Again you think of all CO2 exchanges as one process, while that all are separate processes with their own decay rates to a new steady state, independent of the other processes…
τ * dCO2/dt = τ*H – ΔCO2
With a long tau, H builds up in the atmosphere and as human emissions are linear increasing over time, the increase is slightly quadratic in CO2 with a linear increase in dCO2/dt.

Bartemis
Reply to  Bartemis
November 2, 2015 12:56 pm

“…while that all are separate processes with their own decay rates…”
Sorry, no. You cannot treat them separately like that. If tau is long for H, then it is long for ΔT. All contributions go into the same bucket.

Reply to  Bartemis
November 2, 2015 2:17 pm

Bart,
Again, you don’t understand what happens in nature: different processes are at work, where the CO2 change in the atmosphere is from different, separate processes which nearly don’t influence each other. Two of them are temperature dependent (vegetation and oceans), where vegetation is hardly pressure dependent and oceans more, each with their own time constants. The third one, human emissions is not temperature dependent and the removal is mainly pressure dependent without much influence of temperature and its own decay rate.
Different processes, different decay rates, different effects in the atmosphere…

Bartemis
Reply to  Bartemis
November 2, 2015 3:40 pm

No, Ferdinand. Any mechanism of removal, whether pressure dependent or temperature dependent, acts exactly the same no matter the source.

Bartemis
Reply to  Bartemis
November 2, 2015 3:45 pm

To clarify, it acts exactly the same regardless of the source. Either way, you get an increase in pressure. Either way, the mechanism that reacts to pressure, reacts to that pressure.
You can’t have it both ways, and what you are suggesting is profoundly unphysical.

Reply to  Bartemis
November 3, 2015 2:27 am

Bart,
Temperature changes the setpoint of the ocean-atmosphere equilibrium.
Human emissions are above the setpoint for each year of emissions.
A temperature change in the vegetation gives a fast transient response of extra CO2 into the atmosphere with a tau of less than a year (seasonal changes much larger and shorter).
A temperature change in the oceans gives a slower transient response with a tau of a few years (seasonal changes much larger and shorter).
A pressure change above equilibrium over the oceans gives a quite slow response with a tau of over 50 years back to equilibrium. In vegetation a tau of ~170 years (Bern model, not sure of that).
Both oceans and vegetation react extremely fast (seasonal) to fast (1 to a few years) on temperature changes. Temperature is the driving force for pressure changes in the atmosphere in that case. Both oceans and vegetation react a lot slower on pressure changes. That is the whole point…

Bartemis
Reply to  Bartemis
November 3, 2015 8:25 am

The is a “Just So” story, Ferdinand. It is the way you want things to be. It has no evidentiary value.

Reply to  Bartemis
November 3, 2015 12:13 pm

Bart:
The is a “Just So” story, Ferdinand. It is the way you want things to be. It has no evidentiary value.
Sigh.
Steady state level for the current area weighted average ocean temperature per Henry’s law:
290 ppmv
Observed CO2 level:
400 ppmv
Observed CO2 increase above steady state level:
110 ppmv
Observed net CO2 sink rate:
2.15 ppmv/year
Observed tau for a response of any linear process to a disturbance equals disturbance / effect:
110 ppmv / 2.15 ppmv/year = ~51 years
Observed tau in 1988 ( http://www.john-daly.com/carbon.htm ):
130 GtC / 2.4 GtC/year = 62 ppmv / 1.14 ppmv/year = ~54 years
Seems quite linear and quite long to me.
Conclusion:
CO2 responses of ocean surfaces and vegetation to pressure changes in the atmosphere above steady state is much slower than for temperature changes.

Bartemis
Reply to  Bartemis
November 3, 2015 12:28 pm

Double sigh.
Data clearly show dCO2/dt = k*(T – T0).

Bartemis
November 1, 2015 6:48 pm

Let’s keep the focus where it should be, though. I say this is a mechanism which can lead to a dynamic of the form
dCO2/dt = k*(T – T0)
You do not agree.
But, the relationship is dCO2/dt = k*(T – T0), no matter what the explanation for it is, and humans are having very little effect on atmospheric CO2.
So, get busy finding your own explanation if you find mine wanting. But, dCO2/dt = k*(T – T0) is a given, and any explanation which does not recognize that is wrong.

Reply to  Bartemis
November 2, 2015 2:28 am

Bart,
No Bart:
τ * dCO2/dt = ΔT – f(T)* ΔCO2
both ΔT and ΔCO2 assumed starting from steady state. It is a transient response of only 1-3 years in vegetation, which levels off to below zero after a few years and a transient response of the ocean surface waters at about 16 ppmv/°C in equilibrium with the atmosphere at steady state. The rest is from human emissions.
All variability is from the influence of temperature variability on vegetation, ~10% of the increase is from the higher ocean temperatures and ~90% is from human emissions.
Your formula doesn’t include the response of the CO2 in/out fluxes to the increased CO2 pressure in the atmosphere. That is where you go wrong…

Bartemis
Reply to  Ferdinand Engelbeen
November 2, 2015 9:21 am
Bartemis
Reply to  Ferdinand Engelbeen
November 2, 2015 9:26 am

Your inability to fit prominent features is a manifestation of the phase distortion I have been speaking of, BTW. This is what I have meant by that. You will not get a good fit until you extend your time constant to be much longer, with f(T) becoming quite small, so that you effectively have an integration.

Reply to  Ferdinand Engelbeen
November 2, 2015 12:26 pm

Bart,
My reconstruction is a first attempt to fit the variability. In fact the variability around the trend is of little interest, as that is not more than +/- 1 ppmv around the trend of over 70 ppmv and caused by a process that integrates to below zero after 1-3 years.
The fit of the calculated increase of CO2 in the atmosphere based on human emissions and the decay rate of any extra CO2 in the atmosphere with a tau of over 50 years, is middle of the noise caused by temperature variability, except for the Pinatubo, but that too is gone after a few years.
Again, variability and slope are from completely independent processes which don’t influence each other.

Bartemis
Reply to  Ferdinand Engelbeen
November 2, 2015 12:53 pm

“In fact the variability around the trend is of little interest…”
That’s like saying the fingerprints at a crime scene are of little interest.
If you don’t match the fingerprints, you’ve got the wrong culprit.

Reply to  Ferdinand Engelbeen
November 2, 2015 1:59 pm

Bart,
If the process that causes the variability is proven not the cause of the trend, it is of no interest at all in finding the cause of the trend…

Bartemis
Reply to  Ferdinand Engelbeen
November 2, 2015 3:41 pm

It is not “proven”, and your fit is lousy.

Reply to  Ferdinand Engelbeen
November 3, 2015 2:06 am

Bart, it is proven beyond doubt that the short-term variability in CO2 rate of change is from changes in vegetation. That can be seen in the opposite changes of CO2 and δ13C. If it was from the oceans, CO2 and δ13C changes would parallel each other. The opposite changes are only possible either by vegetation or fossil fuel burning/land clearing. The latter are quite monotonic increasing, thus vegetation is the cause:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_dco2_d13C_mlo.jpg
On the other side, vegetation is a net, increasing sink for CO2 over longer periods, at least since 1990 when the oxygen measurements were accurate enough to measure the small changes in oxygen use/release:
http://www.sciencemag.org/content/287/5462/2467.short
and
http://www.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
Thus whatever your theory says, the process that causes the short-term variability is not responsible for the long-term increase in CO2 or CO2 rate of change, to the contrary. If the long term trend is caused by temperature (effect on the oceans) or human emissions or a mix, is independent of the cause of the short term variability. That variability is only +/- 1 ppmv around the trend of 70 ppmv, negligible.
The “fingerprint” found in the room is from the housewife, not from the burglar…

Bartemis
Reply to  Ferdinand Engelbeen
November 3, 2015 8:35 am

“That can be seen in the opposite changes of CO2 and δ13C.”
That is not proof. There are any number of reasons that these could appear to be out of phase with one another.
“That variability is only +/- 1 ppmv around the trend of 70 ppmv, negligible.”
Yet, my reconstruction matches it, while yours does not.

Reply to  Ferdinand Engelbeen
November 3, 2015 11:46 am

Bart,
That is not proof. There are any number of reasons that these could appear to be out of phase with one another.
Bart, the CO2 rate of change and δ13C rate of change are exactly synchronized and opposite to each other. No hand waving from your side can change that. That is full proof that all the variability is from changes in vegetation and not from the oceans, as human emissions (the only other possibility) are too smooth without much variability.
Yet, my reconstruction matches it, while yours does not.
So what? You can match the variability which integrates to zero in the real world on longer term, while in passing by arbitrarily attributing the slope to temperature, which has nothing to do with the variability and in the real world is not more than 16 ppmv/K, not 120 ppmv/K…

Bartemis
Reply to  Ferdinand Engelbeen
November 3, 2015 12:26 pm

“That is full proof that all the variability is from changes in vegetation and not from the oceans…”
Sorry, no. That is just a guess, which is contradicted by the data.
“You can match the variability which integrates to zero in the real world on longer term…”
Begging the question. The data show it matches both long and short term since at least 1958.
You fingerprints don’t match. You’ve got the wrong culprit.
Match your hypothesis to the data, not the data to the hypothesis.

Bartemis
Reply to  Bartemis
November 2, 2015 3:41 pm

It is not “proven”, and your fit is lousy.

afonzarelli
Reply to  Bartemis
November 2, 2015 4:39 pm

Yeah, bart, i would think those step rises in temps (circa 1980 & 2000) which correspond exactly with the step rises in the carbon growth rate, especially when all else trends flat, ARE definitive proof that temperature (for whatever reason) drives the trend in carbon growth…

November 2, 2015 12:56 am

micro6500,
As far as I remember, still some waters around the equator were unfrozen, where the last remains of life could survive. Indeed volcanoes did remain active and without sufficient sinks, the CO2 levels increased enormously, ultimately increasing the temperatures around the equator high enough to start the melting, which itself was self sustained up to near the poles by increasing water vapor in the atmosphere.
At least that is the story I heard. No guarantee of exactness…

afonzarelli
Reply to  Ferdinand Engelbeen
November 2, 2015 6:04 pm

Ferdinand, i’ve been trying to stay out of y’all’s way (because, like the back side of a horse, i have a tendancy to get in the way…), but i’ve been waiting patiently for a while to ascertain where you get your figure of 16 ppm per 1 degree celsius for your (henry’s law) rise in CO2. I know in the past that you’ve derived that figure from ice cores. Is there any other basis for the use of that (16 ppm) figure?

Reply to  afonzarelli
November 3, 2015 1:42 am

Fonzie,
Henry’s law for the atmosphere – ocean surface waters equilibrium in the literature gives values of 4-17 ppmv/°C in equilibrium with each other.
The correction factor used to calculate the real pCO2 at equilibrium of ocean waters at the temperature of the water intake vs. the pCO2 measured at the measurement device uses a similar correction factor:
http://www.ldeo.columbia.edu/res/pi/CO2/carbondioxide/text/LMG06_8_data_report.doc shows the formula for the temperature influence:
(pCO2)sw Tin situ = (pCO2)sw Teq x EXP[0.0423 x (Tin-situ – Teq)]
The non-linearity is less than 3% of the linear calculation for small changes (less than 1°C) in temperature.

Bartemis
Reply to  afonzarelli
November 3, 2015 8:43 am

The literature is, unfortunately, often driven by a perceived need to match the data with a preconceived hypothesis. We have seen how badly the literature has projected temperatures forward based on the AGW hypothesis.
Even if the calculation is correct, it does not hold in the long term for this dynamically changing system of reservoirs. The match of the rate of change of CO2 with temperature is conclusive. We have the fingerprints. We know the culprit. And, it is not humans.

Reply to  afonzarelli
November 3, 2015 11:32 am

Bart,
Henry’s law was established in 1803 and since then, up to today, confirmed by millions of direct measurements of seawater pCO2. That has nothing to do with “dynamic changing reservoirs”, as the law applies to every moment of the day for every place of the ocean surface…
One can discuss the results of the law, which indeed depends of dynamic changing reservoirs, but the law itself holds everywhere every time.

Bartemis
Reply to  afonzarelli
November 3, 2015 12:22 pm

This isn’t a question about whether Henry’s law is generally valid, it is a question of how it is applied. Again, you have a mental block when it comes to the analysis of dynamic systems. I don’t know what more I can say.

November 3, 2015 12:44 pm

Bart,
OK, it ends here (again)…
It seems to no avail to try to convince you, as you don’t accept any observation that may even remotely contradict your theory. All you have is an arbitrary match of two curves, where the variability is certainly caused by temperature variability, but for the rest a false attribution of the slopes to temperature which violates all known observations, including Henry’s law…
I hope that Anthony will publish my guest contribution soon, so that we will have a last discussion. If that doesn’t help, then there is no hope left that we can match our opinions…

Bartemis
Reply to  Ferdinand Engelbeen
November 3, 2015 1:20 pm

“…as you don’t accept any observation that may even remotely contradict your theory.”
You don’t accept the fundamental observation that shows your hypothesis is wrong. Your favored observations have many potential explanations. The dCO2/dt to temperature relationship has only one interpretation.
“All you have is an arbitrary match of two curves…”
It is not arbitrary. It matches both the trend and the variability exquisitely.
“…but for the rest a false attribution of the slopes to temperature…
The trend is a natural outcome of the relationship which matches the variation. It happens to match the trend in dCO2/dt. You claim, bizarrely, that is mere coincidence. It is not.
“… which violates all known observations, including Henry’s law…
It is you who wants to violate Henry’s law. Increasing pCO2 of the surface oceans necessarily results in increasing concentration in the atmosphere. And, a change in temperature necessarily results in increasing pCO2 of the surface oceans.
“If that doesn’t help, then there is no hope left that we can match our opinions…”
It’s not going to “help”, if by “help” you mean persuading me to your point of view. I know what this plot means. There is no doubt about it.
http://i1136.photobucket.com/albums/n488/Bartemis/temp-CO2_zpsnp6z3jnq.jpg

afonzarelli
Reply to  Bartemis
November 3, 2015 6:00 pm

“All you have is an arbitrary match of two curves…”
The probability of getting a match of these two curves at all is slim to none. If the temperature trend was a quarter of what it is, no match. If it was just half, no match. Just three quarters, no match either. The step rises also show an exact match in “amplitude”. There is no reason that this should happen even once (let alone twice) if there is no relationship between the trend in temperature and the trend in carbon growth rate…
“…but for the rest a false attribution of the slopes to temperature…”
Ferdinand has done nothing whatsoever to prove this statement except to say that such attribution is falsified by the theory. (the data doesn’t fit the theory, so the data must be wrong…) One thing that i’ve noticed about ferdinand is that if he sees something he doesn’t like, he just flat out ignores it. And he ain’t gonna touch this baby with a ten foot pole…

Reply to  Ferdinand Engelbeen
November 4, 2015 1:29 am

OK,
I can match all variability where you can’t match the slopes, whatever arbitrary factor you try to use (part of my guest contribution):
http://www.ferdinand-engelbeen.be/klimaat/klim_img/trans_2sin_slope.jpg
Any mix of sinusoids in temperature is followed by a transient response of CO2 in the atmosphere with a similar mix in sinusoids with a pi/2 lag for responses of sufficient duration (2 years in this case).
If temperature besides the sinusoids has a linear slope, the CO2 increase in the atmosphere also has a near-linear slope with a very small non-linear extra (maximum 3% for small changes in temperature).
If you take the derivatives, both dT/dt and dCO2/dt shift pi/2 back in time and both have zero slope, except for dCO2/dt which has an extremely small slope due to the small non-linearity.
The offset of dCO2/dt caused by temperature in the past 57 years is 0.015 ppmv/month with a “slope” of maximum 0.00045 ppmv/month at the end of the 57 years.
The shift back of dCO2/dt makes that both T and dCO2/dt are completely synchronized in timing, as can be seen in the lowest plot, but T has a slope and dCO2/dt has no appreciable slope…
No arbitrary factor in the world can match the two slopes except near zero, which does erase all variability…
Here theoretically but also in the real world, all the variability in the derivatives is from the influence of temperature and any slope in the derivatives is not from temperature. The slope in the derivatives is from a slightly quadratic increase of CO2 in the atmosphere by an external factor: human emissions.
Factors used can be seen in the table in between upper and middle plot, but “emissions” were not plotted in this case.
I rest my case…

Reply to  Ferdinand Engelbeen
November 4, 2015 4:36 am

That looks to me that CO2 is following temps..

Bartemis
Reply to  Ferdinand Engelbeen
November 4, 2015 8:47 am

A) These are heavily smoothed data with very smudged out detail
B) You don’t really match the phase very well, it wanders in and out of phase, as the changing phase delay for lower frequencies distorts the output
C) You don’t match the amplitude very well
D) This is only over 30 years, so you don’t observe the lower frequencies in the full 57 year CO2 record. Use the HADCRUT4SH data and see what you get.
Occam’s Razor: Why torture the data so, when all you have to do is integrate? This is a much better fit
http://i1136.photobucket.com/albums/n488/Bartemis/temp-CO2_zpsnp6z3jnq.jpg
and, it took hardly any processing at all. This is a quite good fit, too, over a longer period, though the data are not as good:
http://i1136.photobucket.com/albums/n488/Bartemis/temp-CO2-long.jpg_zpsszsfkb5h.png
Again, the odds of the trend AND the variability matching up like this simultaneously by happenstance are vanishingly small.

Bartemis
Reply to  Ferdinand Engelbeen
November 4, 2015 9:07 am

There’s nothing wrong with being wary of the conclusion, Ferdinand. Though I say the odds are “vanishingly small”, they are not zero (nothing ever is absolutely zero probability). And, you have other observations which, in your mind, suggest an inconsistency.
But, to utterly dismiss what is right in front of your nose… This I do not get, and I do not consider scientifically responsible. You must allow that dCO2/dt = k*(T – T0) is at least a possibility. Once you do, you can consider all the evidence even-handedly, without confirmation bias driving you to a premature conclusion.
I would advise you back off, and more thoroughly consider the problem, before you commit yourself even further to a narrative which, frankly, is unlikely to stand the test of time.
The rate of change of CO2 decelerated at precisely the time that temperatures reached their recent plateau. This, at a time when human emissions were accelerating. And, we have just gotten word that the Chinese have been underreporting their inputs, so emissions actually were accelerating even faster than anyone believed.
If temperatures continue their stasis or, as is likely, start trending down once this El Nino has passed, the divergence is going to get even worse, as the rate of change of CO2 declines further. Should that be the case, the hypothesis you favor will be falsified, after you have invested every ounce of your personal credibility in it. Do you really want to take that chance?
If you start out with the assumption that temperatures are driving the rate of change of atmospheric CO2 as a given, I am quite sure you will be able to come up with reasons that your other observations can be made consistent with that assumption. Right now, you are stopping at a result which appears consistent with your hypothesis, instead of delving further. That is classic confirmation bias.

Reply to  Ferdinand Engelbeen
November 4, 2015 10:33 am

Bart,
The essence of my (theoretical) exercise is that a linear increase in temperature gives a near-linear increase in CO2 and that gives a zero slope for dT/dt and a near zero slope for dCO2/dt.
The essence of the real change in the atmosphere is that the temperature increase in the atmosphere is linear and its effect on CO2 levels is near linear. That means that the slope of the derivative of the CO2 increase for the part caused by the temperature increase is near zero. Thus the slope in dCO2/dt is not caused by temperature.
The latter is also proven by observations: all the variability is from vegetation, which has a small negative offset and slope. There is a small positive offset from the warming ocean surfaces, but that too has hardly a slope.
Further, I don’t see any reason to even consider your theory as possible, as it violates all observations, not at least the fact that any CO2 increase in the atmosphere above steady state will push more CO2 into the ocean surface, not reverse and that the steady state for the current average ocean surface temperature is 290 ppmv, while the atmospheric pCO2 is 400 ppmv…
Thus I don’t worry about my credibility, I do worry about yours…
We will see what the future will bring, with China releasing ever more CO2, but I have no problems to match the slopes and variability of the above theoretical exercise, this time with “emissions”:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/trans_2sin_slope_em.jpg
You see, a near perfect match between amplitudes and slopes (with a small factor even completely perfect). Temperature matches all the variability and slope of dCO2/dt, while the real influence of temperature on the slope of dCO2/dt is near zero and all of the slope is from the “emissions”…

Bartemis
Reply to  Ferdinand Engelbeen
November 4, 2015 10:49 am

Two sinusoids + slope +… You’re just using made up data!
Good grief. And, here I was assuming good faith on your part.
The whole thing is about matching the phase across the entire observable and observed spectrum, not at a couple of specific sinusoids of selected frequency.

afonzarelli
Reply to  Ferdinand Engelbeen
November 4, 2015 11:21 am

Bartemus November 4, 2015 9:07 am
Excellant comment here bart…
I think it would be interesting for ferdinand to assume that your graph is correct just to see what he can come up with in the way of an anthropogenic rise. (that still needs to be explored) There is a school of thought out there that says warmer temps cause an inefficiency in the sinks so that anthro co2 then piles up in the atmosphere. Sounds dubious to me, but if anybody could make it work it would have to be ferdinand…
I do think the odds have gone beyond “vanishingly small”. When two data sets are in lock step for over half a century then “vanishingly small” becomes “next to nil”. By definition, either one is causing the other or something else is causing them both. At this point it’s become predictive. We know exactly what the carbon growth rate will be based on the temperature. (and based on the slightly higher carbon growth rate the last few years we can actually confirm that the warmistas are right, it has been warming!) Perhaps what is needed is a statistician who can figure out exactly what the odds are here, because it appears that we’re well beyond the point where it can be said that ferdinand’s hypothesis has been falsified…

Bartemis
Reply to  Ferdinand Engelbeen
November 4, 2015 11:39 am

“There is a school of thought out there that says warmer temps cause an inefficiency in the sinks so that anthro co2 then piles up in the atmosphere.”
The problem with that idea is that temperatures have been increasing roughly linearly, and the rate of emissions has been rising roughly linearly. So, if temperatures modulate the rate at which emissions accumulate, you have a quadratic rate of change of CO2. However, CO2 rate of change has been rising roughly linearly, too.

afonzarelli
Reply to  Ferdinand Engelbeen
November 4, 2015 11:40 am

Sorry bart, “bartemus” should read “bartemis”. (must have been thinking about that “teaching the dog latin” thing…)

afonzarelli
Reply to  Ferdinand Engelbeen
November 4, 2015 12:01 pm

I hear you, bart, i hear you… I had a warmist once tell me the same thing. He said that unless the earth was truely “gaia” then the earth wouldn’t know how much carbon to take out and therefor the data (your graph that is) must be wrong!

Reply to  Ferdinand Engelbeen
November 4, 2015 12:59 pm

Bart,
The whole thing is about matching the phase across the entire observable and observed spectrum, not at a couple of specific sinusoids of selected frequency.
You still don’t get it: I do agree and the whole world agrees and even all warmistas in the world agree with you that 100% of the CO2 and thus the dCO2/dt variability is caused by temperature variability. No matter what frequencies are involved.
What you don’t see is that the slope of dCO2/dt caused by a linear increase in temperature is (near) zero, because the main processes involved: vegetation and oceans have either a negative response (vegetation) or a near linear response (oceans) to temperature on periods of > 3 years.
All what I have shown is that you can match frequencies, amplitudes and slopes without any contribution of temperature in the CO2 rate of change and that your attribution of the slopes to temperature only is pure arbitrarily.

Bartemis
Reply to  Ferdinand Engelbeen
November 4, 2015 1:33 pm

“What you don’t see is that the slope of dCO2/dt caused by a linear increase in temperature is (near) zero, because the main processes involved: vegetation and oceans have either a negative response (vegetation) or a near linear response (oceans) to temperature on periods of > 3 years.”
No, Ferdinand. That is an hypothesis, not data. The data do not support it. The data show quite clearly that dCO2/dt = k*(T – T0).
“All what I have shown is that you can match frequencies, amplitudes and slopes without any contribution of temperature in the CO2 rate of change and that your attribution of the slopes to temperature only is pure arbitrarily.”
In your own, made-up world, sure. You can make up whatever dynamic you desire in a model. But, don’t kid yourself that you are engaged in science. You are engaged in screenwriting.
You have to match the real world data. You have to show that you can get 90 deg phase shift across all observable frequencies without getting the trend.
You cannot. It is a mathematical impossibility in a naturally evolving system. Once you have 90 degrees phase shift across all observable frequencies, you have a de facto integration over the interval of observation, and you will match dCO2/dt = k*(T – T0).
Why are you so committed to this dogma that you will follow it down in flames? Free your mind. You have learned a narrative. It is time to unlearn it, and look at what the data are telling you.

November 4, 2015 10:44 am

Micro6500,
That looks to me that CO2 is following temps…
Yes it does:
– with a few months over the seasons: T up, CO2 down, vegetation dominant.
– with about half a year for 1-3 year variability: T up, CO2 up, vegetation dominant
– with tens to hundreds of years over multi-decennia to multi-millennia: T up, CO2 up, (deep) oceans dominant.
No it doesn’t for the CO2 increase over the past 165 years: T slightly up, CO2 strongly up, humans dominant.

Bartemis
Reply to  Ferdinand Engelbeen
November 4, 2015 10:52 am

Ignore it, Micro6500. It’s just Ferdinand’s model, with no real world input.

Reply to  Bartemis
November 4, 2015 1:25 pm

Bart, just a little childish?
http://www.ferdinand-engelbeen.be/klimaat/klim_img/antarctic_cores_001kyr.jpg
and
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.jpg
The combination of both curves show an increase of CO2 with low 13C/12C ratio, which excludes the oceans, while if from vegetation, that would imply burning down – without regrowth – of 1/3rd of all land vegetation, which is highly implausible. Both curves are in exact ratio and timing with human emissions…
But you may have another theory which doesn’t violate any of the observations…

Bartemis
Reply to  Bartemis
November 4, 2015 1:46 pm

Childish? Hardly. I am appalled that you would try to pass a model off as reflective of the real world.
You can cherry pick a couple of frequencies, and produce a 90 deg phase shift, sure. That is trivial. What you cannot do is produce a 90 degree phase shift from the highest to the lowest observable frequency without effectively performing an integration.
The 13C/12C ratio is not uniquely explainable by human inputs driving the CO2 concentration. We do not have all the sources well cataloged and known, and it all depends on the diffusion dynamics, a very complicated subject with typically non-intuitive results, and extended settling times.
But, there is no alternative explanation for dCO2/dt = k*(T-T0) that leaves humans in the driver’s seat.

Bartemis
Reply to  Bartemis
November 4, 2015 1:50 pm

And, the ice core estimates are fundamentally unverifiable. I do not believe them. It is physically impossible for a system response to be both high bandwidth and low bandwidth at the same time. And, that is what is required for tight control over centuries, then sudden high sensitivity to human inputs.

afonzarelli
Reply to  Bartemis
November 4, 2015 5:24 pm

Ferdinand, along with the human emissions hockey stick, there are three other temperature related hockey sticks whose “blades” also begin in the mid 1800s…
The ipcc’s sea level rise hockey stick beginning in 1870; the mann temperature hockey stick beginning in 1860; and the university of colorado tsi hockey stick beginning in 1840. (note these are all warmist outfits, this is “their” data…) The last one is of particular interest because there is a very clear shift of the slope in your ice core record no later than 1840. At a 2 ppm per decade rate the ice core record outpaces human emissions (.2 ppm per decade) ten to one. There is also another shift in the slope of your ice core graph in the late 1800s which corresponds with a step rise in tsi…
http://lasp.colorado.edu/lisird/tsi/historical_tsi.html

afonzarelli
Reply to  Bartemis
November 4, 2015 11:50 pm

Ferdinand, i went back and read your second (?) of four 2010 pieces which was on the carbon 13 ratio. I think it’s a must read for anyone who needs a crystal clear explanation as to what it’s all about. (some times when we’re so busy throwing mud at you, it’s so easy to forget just how gifted you really are…) Of the four, i thought it was the most exquisitely written. Thanks much for sharing that gift and look forward to your upcoming essay.
Now… back to throwing mud (!). You based your conclusion that the source must be anthropogenic on deductive reasoning. It can’t be trees because they are a sink over time and not a source. It can’t be the oceans because of the carbon 13 “finger print”. My objection to this is simple: the oceans ARE a source, supplying half of all emissions. If that doesn’t affect the carbon 13 ratio (as expected), then why should an imbalance that adds more have an affect on the carbon 13 ratio?

Reply to  Bartemis
November 5, 2015 1:28 am

Bart:
What you cannot do is produce a 90 degree phase shift from the highest to the lowest observable frequency without effectively performing an integration.
What you don’t (want to?) see is that the increase of CO2 in the atmosphere from the linear increase in temperature is quasi-linear and thus its derivative is (near) completely flat. There is no direct or indirect influence of temperature on the slope of dCO2/dt, whatever caused the variability around the trend. Your “match” between the T and dCO2/dt slopes is completely bogus.
Any decrease in 13C/12C ratio is not uniquely from human emissions for certain, as vegetation could be the source (it isn’t). There may be unknown alternative natural sources, but these should then have increased in exact ratio and timing as human emissions, which is extremely unlikely. Anyway, it is really certain that it can’t be the oceans, as good as adding an acid to a solution can’t increase the pH.

Reply to  Bartemis
November 5, 2015 1:39 am

Bart:
It is physically impossible for a system response to be both high bandwidth and low bandwidth at the same time. And, that is what is required for tight control over centuries, then sudden high sensitivity to human inputs.
You still see the carbon cycle as one process, but there are many processes at work: some extremely fast (ocean surface and leave growth and wane), but limited in capacity, some slower (deep oceans and more permanent storage in vegetation debris), some are temperature-only dependent, some pressure-only dependent and some are a mix of both.
This mix of processes does react very fast ánd very slow on temperature changes and in between on pressure changes. Human emissions only affect the latter.

Reply to  Bartemis
November 5, 2015 2:20 am

Fonzie:
At a 2 ppm per decade rate the ice core record outpaces human emissions (.2 ppm per decade) ten to one.
The above graphs are direct measured data, giving real HS’s not “selected proxies” like Mann’s HS. Sea level rise is limited in time based on tide gauge measurements, but proxies show 120 m rise since the last ice age… TSI may have an influence, not very visible in recent times…
The natural variability as seen in the past 57 years is +/- 1 ppmv. Human emissions of the period 1750-1850 are within natural variability, that is undetectable. Increase 1850-2000 was indeed ~5 ppmv, but emissions were of the same order (10.8 GtC). From 1900 on, things get more interesting. We have accurate figures for 1958-current but if we may assume that ice core CO2 has some truth in the data, the ratio still is remarkable linear:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_1900_1959.jpg
My objection to this is simple: the oceans ARE a source, supplying half of all emissions. If that doesn’t affect the carbon 13 ratio (as expected), then why should an imbalance that adds more have an affect on the carbon 13 ratio?
Emissions from the deep oceans do affect the 13C/12C ratio in the atmosphere, but that are not one-way emissions, that is about as much CO2 out of the deep that goes into the deep: from the warm upwelling sites near the equator to the cold sink places near the poles. That is a near permanent flux of ~40 years, which can be deduced from the 14C decay rate after the 1950-1960 atomic bomb tests and the “diluting” of the human fingerprint to about 1/3rd to what it would be if all human emissions should stay in the atmosphere:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_zero.jpg
The discrepancy in the early years is probably from vegetation which gradually changed from a small net source to a small, but growing sink for CO2…

Reply to  Bartemis
November 5, 2015 2:24 am

Of course the deep ocean carbon cycle is not ~40 years, but ~40 GtC/year rather permanent flux between equator and poles, probably not much affected by seasonal changes…

Bartemis
November 5, 2015 8:44 am

Ferdinand Engelbeen November 5, 2015 at 1:28 am
“What you don’t (want to?) see is that the increase of CO2 in the atmosphere from the linear increase in temperature is quasi-linear and thus its derivative is (near) completely flat.”
Nonsense. dCO2/dt = k*(T-T0). A linear increase in temperature with time produces a quadratic increase in CO2.
“…but these should then have increased in exact ratio and timing as human emissions…”
Nearly affine functions are always affinely similar to one another.
Ferdinand Engelbeen November 5, 2015 at 1:28 am
“You still see the carbon cycle as one process, but there are many processes at work…”
It does not matter. Only the aggregate response matters.
Ferdinand Engelbeen November 5, 2015 at 2:20 am
“…but if we may assume that ice core CO2 has some truth in the data, the ratio still is remarkable linear…”
Not very remarkable, just two series that both happen to be trending the same way, a 50/50 proposition. This is remarkable:
http://i1136.photobucket.com/albums/n488/Bartemis/tempco2_zps55644e9e.jpg
Two series which match so closely, every bump and burble lies on top of one another, i.e., the fingerprints match.
“… that is about as much CO2 out of the deep that goes into the deep…”
But, not necessarily of the same isotopic content. This is all model world, not real world.

Reply to  Bartemis
November 5, 2015 8:53 am

Just like your model world which ignores the fact that the influx/efflux to/from the atmosphere from the ocean depends on the pCO2. The real dependence should have the following form:
dCO2/dt = fossil fuel flux +sources (CO2,T) – sinks (CO2,T)

Bartemis
Reply to  Phil.
November 5, 2015 10:50 am

Mine is strictly empirical. The data match dCO2/dt = k*(T – T0).

Reply to  Bartemis
November 5, 2015 9:54 am

Two series which match so closely, every bump and burble lies on top of one another, i.e., the fingerprints match.

But not for the reason you think. they match because the temp series you use is infilled with data that’s created based on the proposed temp/Co2 CS value, then when you use temp to calculate CS, tada they look like they match.
When you average the difference between daily rising temps, and the following night’s falling temp based on surface stations and account for uncertainty since 1940 the average derivative of daily temps change is 0.0F +/-0.1F

Bartemis
Reply to  micro6500
November 5, 2015 11:00 am

They don’t attempt to match a derivative relationship. They try to match a proportional relationship:comment image
And, it’s mostly in the NH. The SH matches the satellite data during the period of overlap, and that is what I used for the plot.

afonzarelli
Reply to  micro6500
November 5, 2015 12:30 pm

Bart, how’s your dog coming along with those latin lessons?
At what point would you guess that ferdinand will cave? (or all opposition for that matter) If ten years from now human emissions are at 6 ppm in per year (double what they were in 2000), but carbon growth is down around say 1 ppm per year, what do you think ferdinand’s response will be?

November 5, 2015 12:13 pm

Bart:
A linear increase in temperature with time produces a quadratic increase in CO2.
Since when is that? Just invented today to save your theory? What physical law is that based on?

Bartemis
Reply to  Ferdinand Engelbeen
November 5, 2015 12:24 pm

Data first, hypothesis after, Ferdinand. Don’t try to impose your physical understanding against the data. Seek the physics which explain the data, not the data which explain the physics.

Reply to  Bartemis
November 5, 2015 12:45 pm

Yes, the data show that CO2 in the atmosphere increases slightly quadratic, which human emissions do with a 4-fold increase in the past 57 years, near twice as high as the increase in the atmosphere. That is quite clear and no hypothesis needs to be invented, as that is exactly what the slope in the CO2 derivative shows, simply by applying the rules for a linear decay.
Good luck with finding a hypothesis that shows a 4-fold increase of CO2 in the atmosphere in exactly the same time span (and a similar drop in 13C/12C ratio), while getting rid of these nasty human emissions…

Bartemis
Reply to  Bartemis
November 5, 2015 12:48 pm

That model does not match the data. dCO2/dt = k*(T – T0) does.

Reply to  Bartemis
November 5, 2015 3:04 pm

Bart,
That model does fit the data. It seems that I had used sea surface data for my previous plot. Here I have used the same temperature data (RSS) as you did and dCO2/dt(obs) both from Wood for Trees. With a transient response of 12 months and a CO2:T factor of 4 that gives:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/trans_rss.jpg
The transient response of CO2 in the atmosphere to temperature is smoothed, as that is an integral towards a new steady state. If you take the derivative, all variability is back where the amplitude is a matter of the full response of in this case vegetation to temperature changes, which is smaller, but faster than for the oceans,
As one can see, the transient CO2 derivative and RSS-T are fully synchronized with exactly the same variability frequencies and amplitude changes. The main difference is that dCO2/dt from a transient response to a linear T changes has zero slope, while of course T has a slope. That means that:
There is zero influence of a transient response of CO2 to a linear temperature change on the slope of the CO2 rate of change.
Al what you need to do is add the response of the system to human emissions and you have an almost perfect match. At least as perfect as the match of RSS-T by an arbitrary factor and offset, which changes the amplitudes, depending of the difference in slopes…
Whatever you invent, this proves that your theory is not a unique solution and while my real world theory matches all observations, your theory violates them all…
Note: I just realized that there are no titles on the right axes, of course on the upper plot it is CO2 in ppmv (1.5 ppmv added since 1980 from the “bio” response, but that is in fact negative, but more that compensated by a stronger increase from the oceans). For the lower plot it is dCO2/dt in ppmv/month. For the (emissions and the) increase in the atmosphere, these start non-zero in 1980.

Bartemis
Reply to  Bartemis
November 5, 2015 3:30 pm

It still doesn’t match, Ferdinand. There’s still a phase mismatch. It’s not as good as this:
http://i1136.photobucket.com/albums/n488/Bartemis/temp-CO2_zpsnp6z3jnq.jpg
You won’t get as good as that until you move your time constant to a very large value, at which point you will be doing an effective integration.
And, you are only looking at 37 years. Take it all the way back 57 years with the SH data, and you will see even more phase distortion with the longer term frequency components.

Bartemis
Reply to  Bartemis
November 5, 2015 4:01 pm

This is what you are dealing with, Ferdinand. The phase response of the normalized transfer function tau/(tau*s+1) looks like this for various values of tau:
http://i1136.photobucket.com/albums/n488/Bartemis/gainphase_zpstjtpoqmo.jpg
You have a data record of potentially 57 years, which means the lowest frequency observable is about 0.0175 yr^-1, but you can still discern phase to somewhat lower than that.
You need 90 deg of phase lag down to perhaps 0.01 yr^-1 in order to match as well as the pure integral, which means you’re going to need a time constant North of 100 years.
If you put in a time constant of 100 years, you are going to start to see a substantial trend in your dCO2/dt, and you are going to have to substantially diminish the max possible contribution from human emissions accordingly.
But, once you’ve gone that far, you might as well go all the way, and make the time constant infinite. When you do, you will find the trend in dCO2/dt is perfectly explained by the temperature relationship.

Reply to  Bartemis
November 6, 2015 1:41 am

Bart,
The derivative from a transient response of (vegetation) CO2 to temperature variability is exactly synchronized with the temperature variability, no matter if tau for that response is 6, 12 or 24 months.
No matter if you take the RSS period or the full period. No matter the ultimate height of the response of CO2 to temperature.
There may be a small discrepancy of one month, due to back and forth calculations, but that is not the point of interest. The point of interest is that all the variability for all frequencies is exactly the same if you take the temperature as base or the derivative as base. There is no difference in phase distortion for T or dCO2/dt.
Only the amplitudes differ and the slope of the latter is near zero (the small slope in the plot is because begin- and endpoint are not equal). The latter integrates to what the change in CO2 does for a temperature change over longer term. Changing the response rate does change the amplitudes, but doesn’t change the frequencies or appearance of the derivative.
For a tau of 6 months:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/trans_rss_der_06-4.jpg
For a tau of 12 months:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/trans_rss_der_12-4.jpg
For a tau of 24 months:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/trans_rss_der_24-4.jpg
Any discrepancy of the variability for the derivative of the transient response with the real rate of change is exactly the same as for the temperature variability…
Thus sorry Bart, your theory is not a unique solution, it is all curve fitting and human emissions are the main cause of the increase in the atmosphere, as the derivative of a transient response to a linear increase in temperature has (near) zero slope…

Reply to  Bartemis
November 6, 2015 2:59 am

Bart,
If one plots a shorter time interval, it is clear that the derivative of a transient response is exactly synchronized with the temperature variability, not even a month difference. Here for 1995-2000:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/trans_rss_der_synchro.jpg

Bartemis
Reply to  Bartemis
November 6, 2015 7:59 am

“The derivative from a transient response of (vegetation) CO2 to temperature variability is exactly synchronized with the temperature variability, no matter if tau for that response is 6, 12 or 24 months.”
Where do you get such ridiculous ideas? Do you really think you can brazen this out with such nonsense?
No, Ferdinand, you need a 90 deg phase shift to get a match. The plot I have given you shows the phase response of your filtering process, and how you need to vary things to get the necessary phase shift over a given band of frequencies.
I’m sorry, Ferdinand, but your match still stinks. It gets worse the longer the record, because it is at the lower frequencies where the phase reverts to zero degrees, in accordance with the plot I have given you.

Bartemis
Reply to  Bartemis
November 6, 2015 8:28 am

These are fingerprints, Ferdinand. You have to match every loop, whorl, and arch as best you can. The more you match, the more likely you have the correct culprit.
Your match is poor. Much less good than mine. The longer you make your time constant, the better your match will be.
http://i1136.photobucket.com/albums/n488/Bartemis/disc2_zpsmowajzfa.jpg

Bartemis
Reply to  Bartemis
November 6, 2015 8:33 am

I chose your 24 month one to highlight, as it is the best of your poor fits. The fits get progressively better the longer you make tau. To get the very best fit, extend tau to a very high number.

Reply to  Bartemis
November 6, 2015 9:06 am

Bart,
I don’t know where it goes wrong in your reasoning, but I have the impression that you are talking about a complete different response than what is seen in the real world as a transient response.
If you calculate a transient response of 6, 12 or 24 months, the CO2 response in all three cases is about 90 degrees after the temperature changes. If you take the derivatives of these three CO2 curves, the timing is exactly the same as for the temperature plot itself: the same variability at exact the same place, only the amplitudes are different. The blue curve has zero lag with the red curve, see the detailed plot 1995-2000, even not for a tau of only 6 months.
Thus if there any discrepancy between the real CO2 rate of change, that discrepancy is exactly the same, no matter if you use the T curve or the flat dCO2/dt curve + a slope (human emissions).
The plot I have given you shows the phase response of your filtering process
What filtering process? Just straightforward calculation of the CO2 response, integrating towards a new equilibrium, without any feedback from CO2 on temperature. Are you again using a response based on a feedback control?

Bartemis
Reply to  Bartemis
November 6, 2015 9:33 am

“If you calculate a transient response of 6, 12 or 24 months, the CO2 response in all three cases is about 90 degrees after the temperature changes.”
This is an illusion, Ferdinand.
The signal is a sum of frequency based components, some high, some low. The very prominent spikes you see are high frequency components. The more rounded formations are lower frequency.
When you implement
dCO2/dt = k*(T – T0) – CO2/tau
you are applying a filter to the data. This filter has a response in the frequency domain as shown in my curves at November 5, 2015 at 4:01 pm.
You generally get -90 deg phase lag at the higher frequencies. But, the phase response tails off to zero degrees at low frequencies. So, your spikes (higher frequency formations) do get a -90 deg phase shift. But, your lower frequency ones do not. Thus, the spikes, which draw your eye, look reasonable, but you are missing the less prominent, lower frequency components which still fail to match very well.
This is a manifestation of phase distortion, such as I have been writing to you about for probably years now.
What we have in the dCO2/dt data is a spread of frequency components, from the lowest observable (frequency of the inverse of the observation interval) to the highest (Nyquist rate).
The correct transfer function has tau so long that it makes little difference between it and a straight integration over the time interval of observation. Anything less than this produces not-as-good a fit.
As you increase your tau, you are going to get better and better results. You can see it in the progression of plots you have provided – the tau = 24 month is better than the tau = 12 month, is better than the tau = 6 month.
Keep moving it up to longer values. You haven’t gotten the best fit, yet. Your fit is still poor.

Bartemis
Reply to  Bartemis
November 6, 2015 9:51 am

Please note the “Very low frequency component” I have indicated by the thick, slightly curved line in the plot at November 6, 2015 at 8:28 am. The curvature here is due to the “pause” in surface temperatures.
The actual rate of change of CO2 from actual data very closely resembles the T curve. It, also, settles out during the pause.
If you attempt to take your filtered dCO2/dt (red line) and add emissions to it, you will not be able to replicate this effect of the “pause” in temperatures.
http://i1136.photobucket.com/albums/n488/Bartemis/pause_zpsxfiwj6pp.png
Again, as you increase your tau, this very low frequency component will start getting the same -90 deg phase shift evident all across the frequency spectrum in the real data, as well as the gain needed to make it stand out. When you reach a tau which reasonably reproduces the “pause” effect, you will only be able to add in a tiny portion of emissions in at best.
This is a very prominent fingerprint. It shows very clearly that the culprit is not humankind.

Bartemis
Reply to  Bartemis
November 6, 2015 9:59 am

Incidentally, my highlighting where even your own plot shows a discrepancy with the pause is in no manner an acceptance or endorsement of said plot. It appears to get from the blue curve to the red curve, you subtracted an arbitrary trend line, producing a zero trend over a period when observations have an essentially zero trend. A proper calculation of the airborne fraction would be simply a scale factor, and a trend would not get arbitrarily zeroed out.

Bartemis
Reply to  Bartemis
November 6, 2015 10:07 am

I have to leave on a trip shortly. I will be gone until Saturday Nov. 14. If I do not respond to further inputs, it does not indicate acquiescence. We will just have to pick it up again at a later time.
Bottom line is: the longer you make the response, the better your fit against real world data will be, and the less you will be able to add in human emissions as a significant driver. Occam’s razor comes down solidly on the side that human emissions are not a significant driver.

Reply to  Bartemis
November 6, 2015 10:18 am

Bottom line is: the longer you make the response, the better your fit against real world data will be, and the less you will be able to add in human emissions as a significant driver. Occam’s razor comes down solidly on the side that human emissions are not a significant driver.

And from what I’ve seen of actual surface measurements (not the published junk), there is no evidence Co2 has reduced cooling over a 24 hour through the last 75 years periods.

Reply to  Bartemis
November 6, 2015 11:32 am

Bart,
The match is in the first place for the frequencies 1-3 years. After that other processes take over, which are even negative for vegetation, which is the main cause of the short term vaiability. There is simply no difference between the curves for 6, 12 or 24 months decay for dCO2/dt and all curves match the curve of T completely synchronized. Any mismatch between the two curves is a matter of adding the same slope and implying matching scales for the difference in amplitude.
If you compare both T and calculated dCO2/dt to the observed dCO2/dt, both don’t match the longer term > 3 years that good, no matter the 6, 12 or 24 month decay. Here for the years 2000-2010 where you saw tha largest discrepancy (Which doesn’t exist):
For 6 months:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/trans_rss_der_obs_06-4.jpg
For 12 months:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/trans_rss_der_obs_12-4.jpg
Only the dCO2/dt amplitude halves.
For 24 months:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/trans_rss_der_obs_24-8.jpg
Response of CO2 doubled to keep the same scales…
Thus there is no influence of any “filtering” out of lower frequencies between 6 and 24 months decay rate. Both T variability and transient dCO2/dt variability follow each other exactly synchronized and both show the same discrepancies with the observed dCO2/dt. Which is quite normal: Pieter Tans calculated that temperature and drought could explain 60% of the variability, not 100%…
That doesn’t say much about the cause of the slopes. I haven’t done that part (yet) as the emissions and the net result of the emissions are yearly, while the calculations here are monthly. If I have some spare time I will interpolate the data and add the variability of the zero-slope dCO2/dt…
Main result of this discussion: it doesn’t make any difference for the variability if you take T or the transient response as dCO2/dt. In both cases the discrepancies with the observations are exactly the same.
Rest the cause of the slopes. As proven here that the same variability can result from the transient response to temperature with zero slope, the slope can be as good from emissions as from temperature.
As emissions are twice what is observed in the atmosphere and there is no known process on earth that does increase CO2 in the atmosphere with 110 ppmv from 0.8°C warming in only 165 years and still fits all observations…

Bartemis
Reply to  Bartemis
November 6, 2015 1:50 pm

Incredible. I expressly tell you how your output is bad, and how it is worse the longer the interval over which you look at it, and you send an even shorter shorter output comparison to look at, and insist all is well.
This is just awful, Ferdinand. You’re not even close. Oh, well. No more time. Until we meet again…

Reply to  Bartemis
November 6, 2015 3:16 pm

Bart,
you subtracted an arbitrary trend line, producing a zero trend over a period when observations have an essentially zero trend.
Thanks for the insult, since when does a linear increase of CO2 (as result of a transient response to temperature) give a non-zero slope in dCO2/dt?
Incredible. I expressly tell you how your output is bad, and how it is worse the longer the interval over which you look at it, and you send an even shorter output comparison to look at, and insist all is well.
You are just diverting the attention from where your plot goes wrong: for any time span longer than 3 years, the frequencies don’t match, as good as for my plot, as these both are completely identical for the variability in timing and frequencies.
Further for the slopes, your plot has opposite slopes for T and dCO2/dt for 35 of the 57 years… So spare me from that kind of critique, as the “match” is at least as bad for your plot…

Bartemis
Reply to  Bartemis
November 6, 2015 3:37 pm

“Thanks for the insult, since when does a linear increase of CO2 (as result of a transient response to temperature) give a non-zero slope in dCO2/dt?”
Since it isn’t a linear increase. CO2 has been increasing quadratically, as a result of a linear rise in temperature, because dCO2/dt = k*(T – T0).
And, the words to which you are responding were in reference to the plot at November 6, 2015 at 9:51 am, so you’re not even arguing anything apposite.
“You are just diverting the attention from where your plot goes wrong…”
My plot doesn’t go wrong. Yours does. Your plot is a poor match. It only vaguely matches for short term, high frequency content. I’ve tried to explain why, but it just sails over your head.
We aren’t even vaguely on the same page. I do not think you understand anything I have been explaining to you. Whether that is willful or because you just don’t have the intellectual capacity to understand is something I cannot answer.
But, the bottom line is, your results do not match the data, and your obstinacy in refusing to understand why is only reflecting poorly upon your capabilities.

Reply to  Bartemis
November 7, 2015 7:39 am

Bart:
CO2 has been increasing quadratically, as a result of a linear rise in temperature, because dCO2/dt = k*(T – T0).
Of course in the real world CO2 has been increasing quadratically, because human emissions did at twice the increase in the atmosphere. There is no known physical mechanism that shows that temperature can be the cause of an unlimited quadratic increase of CO2 into the atmosphere from a fixed temperature difference. Al what you do is attributing all the increase of CO2 to temperature, which is a nice example of circular reasoning. Neither the response of vegetation (negative) or oceans (transient to a fixed increase for a fixed temperature jump) do show any appreciable non-linear behavior.
Incredible. I expressly tell you how your output is bad, and how it is worse the longer the interval over which you look at it, and you send an even shorter output comparison to look at, and insist all is well.
Not at all: I responded to your “mismatch” of the plots in an earlier message and only saw the second message later.
As I said already a few times, the short term variability is proven from the response of vegetation to short term temperatures. That levels out after 1-3 years to below zero. Thus longer tau’s have zero effect on that process. What you still don’t (want to) understand is that the response of CO2 to temperature is not one process, but several processes, each with their own response time, amplitude and maximum capacity. Looking at a curve which only shows the effect of the short term variability doesn’t show what the effect of other temperature related processes is with longer decay rates.
your results do not match the data, and your obstinacy in refusing to understand why is only reflecting poorly upon your capabilities.
Your results do not match the data either and your refusing of any observation which doesn’t fit your theory is only reflecting poorly on your capacity to understand what happens in the real world…
Like the fact that either you match the slopes or the amplitudes, not both, if the real slopes are quite different. Which is the result of two different processes in the real world: one that determines the variability, the other the slopes…

Reply to  Ferdinand Engelbeen
November 7, 2015 8:07 am

The carbon content of the atm is about 720 GigaTon https://en.wikipedia.org/wiki/Carbon_cycle
Biomass is 3 for 4 some times that much. The size of the sinks are near 100 times the size of human output, very slight changes in the biosphere could easily either emit or consume our entire output (and could be entirely responsible for all of the change in the atm).
I don’t see how there can be any declaration of the cause. And while yes we know the human isotope composition, we also know it’s getting feed right back into the biosphere, and we don’t know if any process is selective, or not.
But if more carbon enhances growth (which we know it does) you can’t neglect that sinks will increase over time. How many tons of carbon would a 3% increase in the volume of the Amazon rainforest consume? Same with the increased greening on the edges of the various deserts?
Lastly, you can’t use any of the published temperature series to do this calculation, as huge portions are entirely made up.

Reply to  Bartemis
November 7, 2015 12:49 pm

micro6500,
Biomass is 3 for 4 some times that much. The size of the sinks are near 100 times the size of human output, very slight changes in the biosphere could easily either emit or consume our entire output (and could be entirely responsible for all of the change in the atm).
Indeed it is not possible to make a distinction between recent organics and fossil organics based on the 13C/12C ratio, but it is possible for the 14C level (fossil fuels have no 14C left) and one can look at the O2 balance: both fossil fuel use and organics decay use oxygen, plant growth produces oxygen. By looking at the O2 changes in the atmosphere (with sufficient resolution since ~1990) and subtracting the oxygen use by burning fossil fuels, one can determine how much oxygen was produced or used by the biosphere as a whole: plants, bacteria, molds, insects, animals,… That shows a net production of oxygen and thus a net uptake (of ~1 GtC/year) of CO2 and preferentially 12CO2, leaving relative more 13CO2 in the atmosphere. Thus the biosphere is not the cause of the CO2 increase, neither the 13C/12C drop in the atmosphere.
See: http://www.sciencemag.org/content/287/5462/2467.short
Neither are the oceans, as their 13C/12C ratio is higher than in the atmosphere, even including the fractionation at the water-air border and reverse.
The variability in sink rate by the natural carbon cycle is surprisingly small: +/- 1 ppmv (for ~75 ppmv going in and out the atmosphere within a year) around the trend of 70 ppmv in the past 57 years. Thus it seems that the carbon cycle is rather constant…

Bartemis
November 5, 2015 12:50 pm

Here is a toy model that demonstrates why Ferdinand’s and others objections are off the mark. Let
A = atmospheric CO2 content
O = oceanic content
alpha = steady state proportionality
tau = rapid time constant to equalize proportions of oceanic and atmospheric content
H = human inputs
B = oceanic THC imbalance
dA/dt = (O – alpha*A)/tau + H
dO/dt = (alpha*A – O)/tau + B
Note that, in this model, overall net sinks are assumed negligible, and
d/dt(A + O) = H + B
i.e., the mass balance is obeyed.
These equations rapidly equalize atmospheric and oceanic content, subject to the proportionality factor alpha. It should be quite large, as the oceans can absorb vastly more CO2 than the atmosphere.
The solution for A as tau -> zero is
A = integral(H+B)/(1+alpha)
Since alpha is large, the first part is small, and we have
A := integral(B/(1+alpha))
the assumption being, obviously, that B is much greater than H.
Let B be temperature dependent such that B/(1+alpha) := k*(T – T0). Then
dA/dt = k*(T – T0)
Most of the H goes into the ocean O, which is approximately
O = alpha*A = (alpha/(1+alpha))*integral(H+B) := integral(H+B)
H contributes to oceanic acidification, but much less than the natural B.
This example shows how the result can be perfectly consistent with Henry’s law, one of Ferdinand’s recurring objections, as the alpha parameter would be related to this quantity.
I am not saying this is how things are. It is a toy model, just an example of why the objections do not hold any water.
dCO2/dt = k*(T – T0) is physically viable.

Reply to  Bartemis
November 5, 2015 3:15 pm

Bart:
Note that, in this model, overall net sinks are assumed negligible
The pea under the trimble…
Human emissions increased a fourfold in the past 57 years.
Increase rate in the atmosphere increased a fourfold in the same period.
Thus net sink rate increased a fourfold in the same period.
Which makes:
The only way that the natural carbon cycle can dwarf human emissions, is that it increased a fourfold in the same period.
For which is not the slightest indication in any observation…

Bartemis
Reply to  Ferdinand Engelbeen
November 5, 2015 3:33 pm

All it requires is that the “k” value be what it is.

Reply to  Ferdinand Engelbeen
November 6, 2015 1:49 am

Bart,
The sinks don’t make any differentiation for a reaction on an atmospheric increase between human or natural CO2. Thus if the increase in the atmosphere increased a 4-fold in the past 57 years and the net sink rate increased a 4-fold in the same period, that requires that either there was no increase in natural cycle at all, or the natural cycle increased a 4-fold too. Not a 3-fold or 5-fold.
There is zero indication that the natural cycle increased anyway, to the contrary.

afonzarelli
Reply to  Ferdinand Engelbeen
November 6, 2015 3:41 am

“Not a three-fold or five-fold”
If it’s temperature that’s driving the carbon growth-rate, then without the temperature step rises it would indeed be “a three-fold”…

Reply to  Ferdinand Engelbeen
November 6, 2015 4:45 am

Fonzie,
Even with “only” a threefold increase in the atmosphere from a natural cause (oceans as the only possibility), that would be visible in all observations, especially the residence time. A threefold increase in residual CO2 is only possible from a threefold increase in the total carbon cycle, if that was the cause. That makes that the residence time should have been reduced a threefold too.
What is observed is that if you average all different estimates of the residence time over the years in two time periods, the more recent estimates give a longer residence time, consistent with a rather constant throughput in an increasing CO2 level of the atmosphere…
BTW, thanks for reading my essay about the 13C/12C ratio. My strength was when I still was working in the chemical industry – already 10 years ago – when there were problems with a process is to eliminate the impossibilities rather than looking at the possible causes. Was several times much faster in finding the real cause than the opposite way…

Bartemis
Reply to  Ferdinand Engelbeen
November 6, 2015 8:35 am

All it requires is that the “k” value be what it is. This is not an unlikely event.
I don’t even know what your point is. The rise was what it needed to be to produce the results we observe.

Reply to  Ferdinand Engelbeen
November 6, 2015 11:42 am

Bart,
The results are only artificially valid for the increase in the atmosphere, including its variability. For the rest, that violates all other observations: human emissions just disappear in space, as if that wasn’t the case, the only possible alternative is that the natural carbon cycle increased a fourfold in exact lockstep with human emissions… For which is not the slightest indication…

afonzarelli
Reply to  Ferdinand Engelbeen
November 6, 2015 11:50 am

Yeah, ferdinand, one of the things that you offer folks is in gaining clarity on some of these arguments which are not always well understood by the masses. (things like quibbling over the validity of the MLO data set when there are scores of stations round the globe saying the same thing…) Your piece on the carbon 13 ratio was “classic engelbeen” in that it left no ambiguity as to what the argument is. And that’s a great starting point for a debate…
Another area that needs this type of clarity is a refutation of jaworowsky’s take on ice cores. It seems most skeptical thinking on ice cores is wrapped up in his theory. I actually think he made it more difficult (not less) to develop a credible argument against the validity of ice cores. I had to dig into some of your work to figure it out (and i’m really grateful for that, thanks…). It would be nice if such a refutation was readily available (as in a guest essay) for skeptics to see.
Well, it looks like the life of the party (bart…) is leaving here. I hope he gets back before anthony posts your guest essay, as the comment page won’t be the same without him (will it?!). That should be fun. Make sure to put a pot of coffee on for that one, because it’s sure to be an all nighter. (and keep plenty of antacids handy…)

Bartemis
Reply to  Ferdinand Engelbeen
November 7, 2015 6:10 am

It’s all narrative. Fonzie. It’s what the ice core champions think should happen. But, they don’t actually know, indeed, cannot know, because there are no independent means of verification.
Theories about what should happen are like battle plans before a war – they rarely survive first contact with the enemy. Nature holds all sorts of surprises for the unwary. One should not treat unverified theorizing any way but provisionally, as a means of projecting hypotheses that are verifiable.
The narrative on ice cores is fundamentally at odds with the reality of system bandwidth. Not impossible, but quite unlikely. Tread cautiously, and pay serious attention to alternatives to the narrative.
Remember, e.g., dietary fat consumption should make people fat, and prone to heart disease. They are only now waking up to the reality that the cure was worse than the disease, decades after that science was “settled” (but, unverified). I cannot tell you how many times my colleagues and I have gone into the lab expecting a particular result in an experiment, only to be stymied by secondary effects that were considered to be negligible, but turned out not to be, and had to be worked around. It is the nature of the beast.
And, now my wife is calling, and I really must go. Last word: Ferdinand’s signal processing skills are lame, and his “fit” is lousy. The data fit dCO2/dt = k*(T – T0), and none of the denial and obfuscatory tactics are going to change that.

Reply to  Ferdinand Engelbeen
November 7, 2015 11:23 am

Fonzie,
I have a page about the objections of the late Jaworowski against ice cores CO2 at:
http://www.ferdinand-engelbeen.be/klimaat/jaworowski.html
What closed the door for me is that he said that the low (pre-industrial) levels measured in the ice core are because during drilling and relaxation a lot of cracks are formed and CO2 escapes (preferentially?) to the atmosphere, while the bubble measurements show 180-300 ppmv and the outside air after drilling up to measurement day were over 360 ppmv…
Further, after an email to him about the “arbitrary shift” by Neftel to “match” the Mauna Loa data, where he used the wrong column in Neftel’s table (he used the ice age, not the average gas age), he responded that all air is immediately sealed after the snow has fallen, which makes that there is no difference between ice age and average gas age (which would be marvelous: no averaging…). Neftel did observe one (!) melt layer between 68 and 69 m depth and adjusted the average gas age below that layer accordingly.
Etheridge e.a. published the results of three Law Dome ice cores in 1996, with obviously the objections of Jaworowski from 1992 in mind, which were point by point rejected.
http://www.agu.org/pubs/crossref/1996/95JD03410.shtml
Unfortunately still behind a paywall.
Here the main findings:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/law_dome_overlap.jpg
Some more info can be found at:
http://courses.washington.edu/proxies/GHG.pdf
About any migration in relative warm (coastal) ice cores:
http://catalogue.nla.gov.au/Record/3773250
Net result, an increase of the resolution from ~20 to ~22 years at medium depth and from ~20 to ~40 years at full depth (~70,000 years)
About gas age and spread at bubble closing depth:
http://onlinelibrary.wiley.com/doi/10.1029/96GL03156/abstract
They used the 14C bomb spike to determine both average gas age and gas age spread very accurately. Which renders Bart’s remark about ice core validity completely off the mark.
As usual, everything that may remotely conquer his one-issue theory based on an arbitrary match of two slopes must be wrong, unproven or ignored… Makes it quite difficult to have a civil conversation about real world observations…

Reply to  Ferdinand Engelbeen
November 7, 2015 12:55 pm

Fonzie,
I have a page about the objections of the late J*aworowski against ice cores CO2 at:
http://www.ferdinand-engelbeen.be/klimaat/jaworowski.html
What closed the door for me is that he said that the low (pre-industrial) levels measured in the ice core are because during drilling and relaxation a lot of cracks are formed and CO2 escapes (preferentially?) to the atmosphere, while the bubble measurements show 180-300 ppmv and the outside air after drilling up to measurement day were over 360 ppmv…
Further, after an email to him about the “arbitrary shift” by Neftel to “match” the Mauna Loa data, where he used the wrong column in Neftel’s table (he used the ice age, not the average gas age), he responded that all air is immediately sealed after the snow has fallen, which makes that there is no difference between ice age and average gas age (which would be marvelous: no averaging…). Neftel did observe one (!) melt layer between 68 and 69 m depth and adjusted the average gas age below that layer accordingly.
Etheridge e.a. published the results of three Law Dome ice cores in 1996, with obviously the objections of J*aworowski from 1992 in mind, which were point by point rejected.
http://www.agu.org/pubs/crossref/1996/95JD03410.shtml
Unfortunately still behind a paywall.
Here the main findings:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/law_dome_overlap.jpg
Some more info can be found at:
http://courses.washington.edu/proxies/GHG.pdf
About any migration in relative warm (coastal) ice cores:
http://catalogue.nla.gov.au/Record/3773250
Net result, an increase of the resolution from ~20 to ~22 years at medium depth and from ~20 to ~40 years at full depth (~70,000 years)
About gas age and spread at bubble closing depth:
http://onlinelibrary.wiley.com/doi/10.1029/96GL03156/abstract
They used the 14C bomb spike to determine both average gas age and gas age spread very accurately. Which renders Bart’s remark about ice core validity completely off the mark.
As usual, everything that may remotely conquer his one-issue theory based on an arbitrary match of two slopes must be wrong, unproven or ignored… Makes it quite difficult to have a civil conversation about real world observations…
Note: I used J*aworowski, as a previous response did disappear in cyberspace, I suppose that his name is a redirection towards the moderation bin…

Reply to  Bartemis
November 6, 2015 11:38 am

Bartemis November 5, 2015 at 12:50 pm
Here is a toy model that demonstrates why Ferdinand’s and others objections are off the mark. Let
A = atmospheric CO2 content
O = oceanic content
alpha = steady state proportionality
tau = rapid time constant to equalize proportions of oceanic and atmospheric content
H = human inputs
B = oceanic THC imbalance
dA/dt = (O – alpha*A)/tau + H
dO/dt = (alpha*A – O)/tau + B
Note that, in this model, overall net sinks are assumed negligible, and
d/dt(A + O) = H + B
i.e., the mass balance is obeyed.
These equations rapidly equalize atmospheric and oceanic content, subject to the proportionality factor alpha. It should be quite large, as the oceans can absorb vastly more CO2 than the atmosphere.

The part of the ocean that exchanges readily with the atmosphere is that portion above the thermocline, which holds ~670 GT of CO2 compared with ~720 GT in the atmosphere, so alpha is ~1.
Tau should not be small given that the ocean significantly lags the atmosphere.
As for B the surface ocean loses a comparable net amount to the deep as it gains from the atmosphere so H≅-B.
So the assumptions made in your model aren’t representative of the real world.

Bartemis
Reply to  Phil.
November 6, 2015 1:53 pm

You do not understand the model.

Reply to  Phil.
November 6, 2015 8:27 pm

Bartemis November 6, 2015 at 1:53 pm
You do not understand the model.

Really, well I know that the assumptions you make don’t match the situation on this planet.

Bartemis
Reply to  Phil.
November 7, 2015 5:54 am

No, you don’t know that. You’ve just made a bunch of assertions.
dCO2/dt = k*(T – T0)
All of your and Ferdinand’s plugging your ears and shouting “Nah, Nah, Nah!” won’t change that. It is a slam dunk. There is no doubt about it.

Reply to  Phil.
November 7, 2015 10:32 am

Phil.,
All what Bart does is inventing processes which don’t or even can’t exist in the real world, as these violate one or even all observations. And ignoring all observations which refute his theory…
Like here: if the natural cycle should dwarf human emissions, that implies:
1) An extreme fast cycle
2) Huge natural quantities involved
3) A fourfold increase in natural cycle 1958-2013
1) + 2) would imply an extremely small residence time, but all empirical observations show a residence time of 3-14 years, average ~5 years, or about 150 GtC/year throughput of CO2 in 800 GtC currently in the atmosphere. Human emissions are currently around 9 GtC/year or ~6% of the natural cycle. Small but measurable in a lot of observations.
3) Needs some clarification.
Bart says:
Note that, in this model, overall net sinks are assumed negligible.
That would be a little difficult, as:
dA/dt = H + B – S
for S = ~0
dA/dt = H + B
That gives a problem, as
H + B > H > dA/dt in the past 57 years
That implies that the net sink is certainly not negligible.
The increase in the atmosphere increased a fourfold/year between 1958 and 2013. So did the human contribution and thus the net sink:
For 1958: dA/dt = H + B – S
For 2013: 4*dA/dt = 4*H + x*B – 4*S
or
(x-1)*B = 3*(dA/dt – H + S) in 2013, compared to 1958
where B = dA/dt – H + S in 1958
or x = 4
There is not one observation that confirms any increase in the natural carbon cycle over the past 57 years.
The only valid alternative is that B = 0, which matches all observations, including a small increase in residence time…