## Friday, July 28, 2017

### Original Climateball

Andy Dessler set off a bit of a tweetstorm asking where the definition of climate sensitivity as 2xCO2 came from.

Turns out the answer is Arrhenius in 1896
but, to meander to the point of this post for another reason Eli was guided to an old favorite, Through the Looking Glass, and the Original Climateball dialog between Alice and Humpty Dumpty.  To just pull a few lines out of the mouth of the egg:
'You don't know what you're talking about!' cried Humpty Dumpty. 'How many days are there in a year?'

'Three hundred and sixty-five,' said Alice.

'And how many birthdays have you?'

'One.'

'And if you take one from three hundred and sixty-five what remains?'

'Three hundred and sixty-four, of course.'

Humpty Dumpty looked doubtful. 'I'd rather see that done on paper,' he said.

David Appell said...

Are there other useful choices?

David B Benson said...

David Appell, not really. All are proportions of one another.

David Appell said...

What's wrong with dT/dF, where T = surface temperature and F = manmade radiative forcing?

dT/dF = lambda = climate sensitivity when CO2 = 2x CO2_0, but there's no reason to expect lambda to be a constant over any range of CO2, whether it's doubled, +50%, +150%, or whatever.

In other words, lambda is a function of both CO2 and temperature. So it isn't fundamental.

David Appell said...

In other words, the problem with defining climate sensitivity as dT(2x CO2_0) is that dT(4x CO2_0) is not 2*dT(2xCO2_0), as one would naively expect. The temperature feedbacks in the first doubling of CO2 are likely larger than the feedbacks in the second doubling.

In any case, the respective feedbacks are certainly not equal. It's clear that

dT/dF = lambda = lambda(T, CO2)

and not equal to a constant.

Even worse, lambda is sure path dependent (the path being CO2(time)).

izenmeme said...

Interesting assertion.
What evidence do you have to support the idea that ice albedo loss and methane increases (along with many other factors) will not be larger feedbacks as temperatures increase ?
What current feedbacks do you envision reducing as temperatures rise ?

Russell Seitz / Bright Water said...

2.2 cheers for feedback mitigation.

If we knew more about ocean albedo variability arising from marine biology, I might make it 2.3.

David B Benson said...

David Appell --- Yes, climate sensitivity, as usually defined, is dubiously useful. For example, in the mid-Pliocene the carbon dioxide concentration was about the same as now while the global temperature was 2--3 °C warmer than now. Of course the climate system is currently far from equilibrium so the warming will come as the climate equilibriates. So what, then, is the climate sensitivity?

EliRabett said...

It's a weakness of all simple parameterization, but also the strength. As long as there is a single overwhelming driver and the system has not been driven too far from it's equilibrium point 2x CO2 does a decent job.

lifeisthermal said...

Since we are talking about a thermodynamic system it should be described with the first law. Which part is "forcing"? Is it Q or W? It has to be one of them.
Why is "forcing" unique for gh-theory? Otherwise we have either a force or we don't.
We know "forcing" doesn't add any energy, and the heat flow is constant and limited(TSI), then how can Q increase without adding either work or energy?

Try this for effective temperature:

TSI-4g²=4T(effective)

That is ∆U=Q-W. If you don't have the first law, you have nothing.

David Appell said...

thermal: as I previously told you at Roy Spencer's blog, the terms in your equation don't even have consistent units. So right away it's obviously wrong.

David Appell said...

OpenID izenmeme said...
"What evidence do you have to support the idea that ice albedo loss and methane increases (along with many other factors) will not be larger feedbacks as temperatures increase ?"

Well, I'm not going to present much evidence in a comment. The ice-albedo feedback will be mostly done after we reach 2xCO2. I don't know about melting methane clathrates, except that most scientists seem to think now they won't occur before 2100, but you may be right about them.

Increasingly I am beginning to think we won't get to 2xCO2. That's still a long-ways off, +150 ppm, less than we're at now. I don't really know though.

What do you think?