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).

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)

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.

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...

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.

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.

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]
________________________________________________________________________

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.

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.