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Discussion > Murry Salby: Relationship Between Greenhouse Gases and Global Temperature

Missy - your questions are useful in making me think about things. I'm away from home at the moment and so don't have notes etc to hand but I'm in the process of composing what I hope will be answers to your questions. In the meantime, I hope the following will be helpful, rather than confusing.

I think Prof Salby said two things:

[A] Atmospheric CO2 level is proportional to the integral of temperature. .. .. (1)

[B] Atmospheric CO2 level is given by the solution of the differential equation.. .. (2)
dC(t)/dt = -alpha . C(t) + gamma . T(t)

How can both be correct? The answer is that (1) is an approximation to (2) which holds under some circumstances.

If the temperature T were to jump up by a fixed amount and then stay at that constant level:

Equation (1) (or rather its solution) says temperature will increase in a ramp-fashion, with constant increase per year.

Equation (2) (or rather its solution) says temperature will increase in a ramp-fashion, with constant increase per year at first.

Equation (2) (or rather its solution) says that eventually, when the system reaches equilibrium, atmospheric CO2 will no longer increase but will remain constant, with the increase over what it was originally being proportional to the jump in T.

To reiterate:

Over short timescales, atmospheric CO2 is proportional to integral of temperature.
Over long timescales, atmospheric CO2 is proportional to temperature.

Equation (2) explains why CO2 lags temperature. It's the same equation that describes a lowpass resistor-capacitor filter. Anyone familiar with electronics knows that the output of such a filter lags its input.

I hope that the above makes some sort of sense (and that in typing it in on the fly, I haven't got something back to front).

Jul 14, 2013 at 2:59 PM | Registered CommenterMartin A

Hmm looks like I need to watch them video again, I though he said CO2 varies with the integral of temp over the longer periods, humph wrong again .

Jul 14, 2013 at 3:42 PM | Registered CommenterDung

Dung I wrote the post above without being ab le to check conveniently (my transcript of his talk is at home)

But a quick look at Utube (1:04:20) confirms he says that the CO2/integral of temperature applies over short timescales (< 1 century)

Jul 14, 2013 at 4:48 PM | Registered CommenterMartin A

Much attention has been focussed on the lag between temperature rising and CO2 levels picking up.
It is interesting to look the past. especially at the other end of the cycle. When the last interglacial, the Eemian, started to cool CO2 levels were around 270 ppm. They stayed at approx that level for about the next 8000 years while the temperature dropped by over 10 degrees.
Also the Eemian was 3 - 5 degrees warmer at its peak than the earth is today yet CO2 levels were only around 280 ppm. (And there was much less, if any, Arctic ice but the Polar bears survived).
Those facts make it clear that CO2 does not have the powerful influence claimed by the AGW proponents.

Jul 15, 2013 at 12:05 AM | Registered Commentermikeh

DeSmogBlog has done a search on Murry Salby's past and turned up a load of stuff that does not show him in a favourable light. They have published it on their website. They seem to have pulled no punches, even posting messy divorce details.

In brief, Murry Salby left his previous university (Colorado) under a cloud, having been banned from using university facilities and with issues about his teaching activities. Some similarities to the deterioration of employee/employer relationship that seems to have happened at Macquarie University.

There are also details of NSF investigation that determined there had been financial irregularities.

I can now see that an idea I had of nominating Murry Salby as the Met Office's next Chief Scientist has even less likelihood of success than I had previously thought. But it's always worth looking on the positive side of things.

Let's suppose that Salby had been a model employee at Colorado University. No doubt, he would have still been there, doing research on esoteric aspects of climate physics of interest to specialists but with no prospect of ending the catastrophe of CAGW "climate science".

In that case, he would not have moved to Australia and Macquarie University, where he found himself "waiting for resources". As he recounts in his Hamburg presentation, it was the need to do something during the wait that caused him to produce his textbook. And his finding that the information available on the physics of greenhouse gases was inadequate triggered his investigations - which he summarised in the Hamburg talk.

I think that, in years to come, Salby's work is likely to become the new foundation of a rigorous climate science. It is ironic that his employee/employer problems, which now look likely to hinder the acceptance and further development of his ideas, were, in a sense, the cause of his developing the ideas in the first place.

Jul 15, 2013 at 1:25 PM | Registered CommenterMartin A

Bit of an own goal, like the Creationists popping up on WUWT at the moment. They may have done nothing wrong, but they are definitely a credibility hit for us, and Salby seems the same - a credibility liability in the short term.

Jul 15, 2013 at 1:49 PM | Unregistered CommenterTheBigYinJames

Salby's recent fate was what I alluded to in the last sentence of my Jul 13, 2:11 PM post. I had thought his past behaviour was widely known.

Anyway, 'mikeh' seems to propose that because temperatures can change without any apparent change in CO2 levels, CO2 _therefore_ has no powerful influence on temperature. That is like saying that because I can light a fire without matches that matches cannot light fires. As if there can only be one mechanism for changing the temperature. I had thought that the greenhouse effect of CO2 was fairly universally understood and accepted.

Salby says he doesn't believe the ice core CO2 records that 'mikeh' quotes - do his figures come from other evidence or is there a conflict here? On the other hand, Salby says there is a relationship on the order of a hundred years (see Martin above) between CO2 levels and temperature, so the 8000 years is challenging.

The comment that Polar bears survived a lack of ice is rather sweeping given the apparent scientific uncertainty over the evolution of Polar bears.

For some background on this discussion, I found some interesting articles that pin CO2's rise quite firmly to anthropogenic causes. One is by a fellow sceptic. Possibly these are not as new to you all as to me.

http://www.ferdinand-engelbeen.be/klimaat/co2_measurements.html

http://www.skepticalscience.com/anthrocarbon-brief.html

Is Salby really overturning these analyses?

Jul 15, 2013 at 2:15 PM | Unregistered CommenterMissy

Missy, it might have the word skeptic in the name, but that's as far as that site goes towards that ideal.

Jul 15, 2013 at 2:18 PM | Unregistered CommenterTheBigYinJames

That is like saying that because I can light a fire without matches that matches cannot light fires.
No, Missy, what you are implying is that the presence of CO2 sometimes affects temperature and sometimes doesn't.
Can you provide any sort of scientific references that might support that. I know CO2 is a Magic Gas as far as the eco-worriers are concerned but I don't think magic is a reliable source somehow.

Jul 15, 2013 at 3:29 PM | Registered CommenterMike Jackson

TBYJ

Having read the NSF reports about Salby I still wait to have my faith in him shaken. You do not make a report as to why someone is sacked by including the fact that he supplied superior computer equipment to the campus without permission unless you are bloody desperate.

Jul 15, 2013 at 4:16 PM | Registered CommenterDung

Missy

Please be accurate in telling people what I said. You said

On the other hand, Salby says there is a relationship on the order of a hundred years (see Martin above) between CO2 levels and temperature, so the 8000 years is challenging.

In fact, I said:


But a quick look at Utube (1:04:20) confirms he says that the CO2/integral of temperature applies over short timescales (< 1 century)
Jul 14, 2013 at 4:48 PM Martin A

If you go back and re-read what I said I think you'll see that Salby's differential equation says that, over short timescales, CO2 is proportional to integral of temperature. Over long timescales, then it's proportional to temperature.

BTW, I think Salby *does* believe ice core records - just that they smearing they do to the detailed history has to be allowed for.

More to follow...

Jul 15, 2013 at 6:09 PM | Registered CommenterMartin A

Missy (con'td...)

You refer to the so-called Skeptical Science website. They give a shopping list of arguments as to why the increase in atmospheric CO2 is due to fossil fuel use. I remember that previously you said you found their "Mass Balance" argument convincing. This is one of the items in their shopping list.

They say

3) The mass balance

Over the course of the twentieth century, the increase in CO2 in the atmosphere measured in tonnes has been less than anthropogenic emissions in every year, and has averaged only 44% of anthropogenic emissions over the period from 1850-2005. Indeed, growth in atmospheric emissions probably has not exceeded anthropogenic emissions since the early 1880s, approximately the time anthropogenic emissions reached the equivalent of 0.45 ppmv of atmospheric concentration. It is interesting to note that the airbourne (sic) fraction, ie, the atmospheric increase divided by total emissions, has increased slightly in recent times. This means that natural carbon reservoirs have acted as a net sink over the course of the 20th century, and strongly indicates that the source of the increase in CO2 concentration is anthropogenic.

I mentioned that although it sounds plausible in a way, I could not see how it provides logical proof that the increase in CO2 is due to fossil fuel burning. I thought at first it was just my slow-wittedness but I now think that they are simply wrong - on this item at least.

If you go through the rest of their shopping list, I think you'll find that one or two of them are dealt with by Salby. If you were to do that and report your results, it would be really interesting and useful.

On the "mass balance" argument, if you have a system of two reservoirs (atmosphere, ocean+land) in dynamic equilibrium, with equal flows in both directions between the reservoirs, then perturbations of the equilibrium need to be analysed by looking at differential equations. Even if you want to understand simply a new equilibrium, with everything in steady state, you need to set the time derivatives to zero and find the new algebraic equation whose solution gives the equilibrium condition. SkS does neither of these, so I can't see how what they conclude can possibly be correct.

Especially since what they claim gives completely different results from a simple analysis of the equilibrium between atmosphere <-> ocean+land, with large and equal transfers (150GtC/yr) in both directions, with a large (750 GtC) reservoir in the atmosphere*. The only way to get results like theirs would be to have CO2 being hoovered out of the atmosphere at constant rate, independent of how much is in the atmosphere. (And likewise, to have ocean+land emitting at precisely the same constant rate, independent of temperature or anything else.) Systems in dynamic equilibrium just don't work like that, though SkS seem to think they do so far as I can make out.

If I am suffering from misconceptions on any of this, please put me right - I'm keen to be on the right track.

* Numbers similar to those on Salby's slide, presumably of IPCC origin.

Jul 15, 2013 at 7:20 PM | Registered CommenterMartin A

James, wrong link.

Mike Jackson, no I don't believe so. It is nearly universally accepted that CO2 in the atmosphere always affects temperature. What is not so accepted is that it is the _only_ thing that influences temperature, which 'mikeh' implies is believed be climate science.

Dung, does your 'faith' in Salby derive solely from his saying something you would dearly like to be true? What would it take for you to lose faith in him?

Martin, I don't really follow your arguments. I think you need someone with a better grasp of mathematics as a sparring partner :-) But this puzzles me: if we stopped emitting CO2 tomorrow completely, there would be 5-10GT of CO2 less entering the atmosphere. Am I understanding you/Salby correctly that such a change would have no effect on the levels measured at Muana Loa - the measurements would still rise at their current rate because of existing historic influences?

Jul 15, 2013 at 9:59 PM | Unregistered CommenterMissy

if we stopped emitting CO2 tomorrow completely, there would be 5-10GT of CO2 less entering the atmosphere. Am I understanding you/Salby correctly that such a change would have no effect on the levels measured at Muana Loa - the measurements would still rise at their current rate because of existing historic influences?
Jul 15, 2013 at 9:59 PM Missy

Roughly speaking, yes. Although I'd say "...the measurements would still rise at their current rate because of existing historic influences current high global temperature".

But I can see how to SkS (and to you, perhaps) that would seem to make no sense at all, if the "mass balance" argument is convincing to you.*

What Salby says is that, since rate of emission is proportional to temperature, and temperature is now higher than since records began, emission is also now higher than it has been since records began. Since the rate of increase of atmospheric CO2 = net rate of emission of CO2, the rate of increase of CO2 will continue to rise at the same rate as it was rising before the hypothetical stop of human emission.

What Salby implies, and what a calculation from the equation for a system in equilibrium seems to confirm, is that human CO2 emission plays a very small part in the total rise in atmospheric CO2.

* I'd really like someone to explain the mass balance argument to me in detail. It's clear that it seems obvious to the SkS people and the authjor of the other website you pointed to. And to you too. But it's not what the equations tell me and I can't get my mind around how statements like the following apply to systems in dynamic equilibrium:

"...the natural CO2 sinks were larger than the natural CO2 sources... Thus it is impossible that natural sources were responsible for (a substantial part of) the increase of CO2 in the past 50 years. This proves beyond doubt that human emissions are the main cause of the increase of CO2"

But as I said, maybe it's just my slow-wittedness.

Jul 15, 2013 at 10:38 PM | Registered CommenterMartin A

CO2 tracks the integral of temperature very well during the satellite record.

Jul 15, 2013 at 11:22 PM | Unregistered Commentermichael hart

..the natural CO2 sinks were larger than the natural CO2 sources..

This seems a straightforward argument to me so I find it odd that you don't follow it. It is like representing atmospheric CO2 with a bath. The blue tap (natural sources) is turned on, the plug is out (natural sinks) and the water also just dribbling from the overflow. If the drain plus the overflow-dribble can take the flow rate of the cold tap, then there is equilibrium. If we turn on the red tap (anthropogenic sources) then more water exits the overflow (increased natural sinks, eg. ocean uptake, extra plant growth) but if the red flow is too fast the level starts rising beyond the overflow.

It is not a perfect analogy, I know. In particular the water that has flowed from the drain and overflow does not just disappear but can return into the bath in some circumstances.

All the same, you seem to be saying that the bath level is rising not because the red tap is turned on but because although all of the red water is flowing out of the overflow some green water is coming in from a third tap that is not part of the model (or returning through the drain and overflow). Turning off the red tap will make no difference - the bath will just continue filling.

I find that baffling. If you hadn't started the thread I would be worrying that you were pulling my leg.

It is such a shame that we cannot try turning off the red tap :-)

Jul 16, 2013 at 2:07 PM | Unregistered CommenterMissy

1. If the temperature rises the flow from the blue tap increases and the drain hole gets smaller.

Jul 16, 2013 at 5:15 PM | Registered CommenterDung

Missy

Let me try and express what Salby said in its bathtub analogy. Let's suppose that we have:

- the blue tap (=natural sources) turned on at 100 pints/hour [representing 100 GtC/yr]

- the plug is out, representing natural sinks. The flow out from the plughole is proportional to the volume of water in the bath. Currently, there are 500 pints in the bath (it's a big bath) and the flow through the plug hole is 100 pints an hour. (The 500 pints in the bath represent 500GtC in the atmosphere.) Outflow = inflow, so the system is in equilibrium ie the volume of water in the bath is not changing.

_________________________________________________________________________
Illustrating how a system reaches a new equilibrium...

The following is to establish the idea of the system finding a new equilibrium...

- I now turn the blue tap to increase the inflow to 150 pints/hour. (ie 50% increase) The volume of water in the bath starts to increase, and the flow out through the plughole increases in proportion.

- When there are 750 pints in the bath (50% increase), the outflow through the plughole is now 150 pints per hour (50% increase to match). Outflow matches inflow and the system is again in equilibrium (ie the volume of water in the bath is once again constant but now at 750 pints).

The numbers used here are approximately those on the IPCC slide.
____________________________________________________________________

Fossil fuel arrives...

- now let's also add some fossil fuel CO2 water from a small hosepipe - say a constant flow of 10 pints per hour.

- So the total input to the bath is now 160 pints/hour. The volume will rise [to (160/150)*750 = 800 pints, at which point the output via the plughole is now 160 pints/hr and the system is again in equilbrium. So the 10GtC/yr pints/hour has caused an increase of (800-750)/750 = 6.7% CO2 volume of water in the bath.

Does the foregoing make sense - especially the idea of a system being in equilibrium?

It illustrates how (using the model above, at least) a quantity of CO2 released per year, bigger per year than anything released by civilisation to date, causes only a moderate (~6%) increase in atmospheric CO2, which then remains at constant level when the system reaches equilibrium.

[SkS will disagree with the details, especially they would disagree with outflow being proportional to atmospheric CO2 content but not with the principle of equilibrium]
________________________________________________________________________

Jul 16, 2013 at 7:38 PM | Registered CommenterMartin A

Martin

Can you explain something to me? Sinks change their behavior and in particular, the oceans are both a sink and a source. If the temperature goes up the oceans hold less CO2 and therefore are not such a big available sink at the new temperature.

Jul 16, 2013 at 8:44 PM | Registered CommenterDung

Dung,

You'd be better off asking someone who actually knows. But here is my guess...

The ocean works as both CO2 source, emitting more as temp goes up, and as CO2 sink, absorbing more as airborne CO2 concentration goes up.

I am guessing that it acts mainly as a source in regions such as the Gulf of Mexico, where cold water, rich in CO2, rises to the surface, is warmed, and releases CO2.

In cold Northen regions where the Gulf Stream finishes up, having given up its heat, you now have cold, CO2-depleted water. Solubility of CO2 in seawater is higher at lower temperatures. I am guessing that the ocean acts mainly as sink in those regions.

This cold, CO2-hungry water happily sucks up (with some probability, I imagine) each airborne CO2 molecule that comes into contact with it. The rate of molecules contacting the water will be proportional to the atmospheric CO2 concentration.

Just because oceanic CO2 emission in warm regions goes up, I don't see why that should significantly affect the ability of cold ocean regions to absorb CO2.

That's my guess as to what happens - nothing more than that. Better to ask someone who knows.

Jul 16, 2013 at 9:46 PM | Registered CommenterMartin A

Martin

on Jul 15th you said:

What Salby says is that, since rate of emission is proportional to temperature, and temperature is now higher than since records began, emission is also now higher than it has been since records began. Since the rate of increase of atmospheric CO2 = net rate of emission of CO2, the rate of increase of CO2 will continue to rise at the same rate as it was rising before the hypothetical stop of human emission.

When you say "since records began" you must be talking about thermometer records because the geological records show temperature has been far higher in the past.
The ice core records also show that previous interglacials just a few hundred thousand years ago were warmer than this one (various papers give various actual temperatures but somewhere between 3 and 10 degrees warmer) and strangely levels of CO2 were a lot lower?
SO! if you have correctly interpreted what Salby said then Salby is wrong ^.^

Jul 16, 2013 at 10:01 PM | Registered CommenterDung

Dung

I should have been specific. By "since records began", I meant in the same sense used by Salby (and the Met Office).

Since around 1850 (I think) for temp and since around 1960 for CO2.

I think I should have said "What Salby's work implies..." rather than "What Salby says...". I don't now think he actually said those things - although I think they do follow from that he said.

Jul 16, 2013 at 11:05 PM | Registered CommenterMartin A

Thanks TBY et al for the utter caving-in to non-specific legalia spread by John Mashey (of all people), on a website run with funds from someone prosecuted by US govt for online gambling-related fraud.

Jul 17, 2013 at 2:53 AM | Registered Commentershub

shub, I haven't caved in to anything, that's why you're giving me a hard time here. It's very easy to cave in and join in the cheer-leading.

Jul 17, 2013 at 8:53 AM | Unregistered CommenterTheBigYinJames

Yes, I understand equilibrium and your description is very nice, but nevertheless the analysis does not explain how removing the hose pipe (halting CO2 emissions) would make no difference to the rise in the level.

Your numbers and assumptions are chosen to make the model work, but they are somewhat arbitrary. As such the percentage increase you calculate seems rather meaningless. There is no particular reason to believe that sinks are directly proportional to the atmospheric volume of CO2 or that they adjust rapidly to changes. The equilibrium that existed (before anthropogenic emissions) developed over thousands of years. It may be that 120GtC circulated between land and air and that 90GtC circulated between ocean/air but this was an equilibrium in a relatively closed system, no doubt dependent upon temperature too. (Numbers from
https://en.wikipedia.org/wiki/File:Diagram_showing_a_simplified_representation_of_the_Earth's_annual_carbon_cycle_(US_DOE).png)

Adding 9GtC annually to this closed system is going to have an effect, in all likelyhood increasing photsynthesis and ocean uptake but is the response immediate and is it linear all the way up? We've now emitted how much, perhaps 500GtC? (60 years at 9GtC/a) half of it absorbed. That compares to the 800GtC currently in the atmosphere. Rather more than 7%, no?

By the way you say later that "cold, CO2-hungry water happily sucks up (with some probability, I imagine) each airborne CO2 molecule that comes into contact with it". That is nice anthropomorphism of the continual interchange of CO2 molecules in each direction across the air/water boundary that, depending upon the conditions, results in a flow in one direction or the other :-)

--

I know nothing more of Salby's dismissal at either CU or MU than what has been made public recently, so I'm interested in people defending him, seemingly unconditionally. Do people have information not publicly available that indicates he was wrongfully dismissed by either university?

Jul 17, 2013 at 8:10 PM | Unregistered CommenterMissy