Friday, December 23, 2016

Updates and Various Things I'm Thinking

We've all heard that the warming for a CO2 doubling, absent feedbacks, is 1.2 K. What calculation does this number come from? Does it come from a logarithmic dependence on CO2/CO2_initial? I'm asking, because if it does, then clearly, since the change in temperature with CO2 just 1.45*CO2_initial is 0.8-1.0 K, feedbacks have already started to kick in.  

John Fasullo et al wrote a paper published in August saying that an accelerating sea level rise is imminent. That's what my calculations show, fitting AVISO and CU sea level to a quadratic. 

acceleration of AVISO SLR = 0.052 ± 0.009 mm/yr2
acceleration of CU SLR = 0.034 ± 0.015 mm/yr2

where the error bars are 2-sigma, without autocorrelation.

Jo Nova has deleted this odious comment. As well she should have. Thanks.

And this trash from "Phil Jourdan"

I'll take this as a victory.

Still working on suyts, who thinks I "cyber stalked" him when his real name was, in fact, available months beforehand on this document. And he had already written he lived in Topeka, Kansas.

Suyts likes to insult everyone, while using a fake name himself. I resolved to show him how that felt. Clearly I made that clear to him, and it stung.

The December issue of Scientific American has an very interesting article on the climate impacts of permafrost melt, by Ted Schur of Northern Arizona University.






7 comments:

David in Cal said...

Yes, it might be feedbacks, or perhaps there's some natural temperature rise which combined with some anthopogenic temperature rise to produce more warming than anthropogenic alone. Either way, the actual rate of warming since the 1970's is probably the best basis we have for forecasting the rate of future warming.

Cheers

David Appell said...

David in Cal: What is responsible for this "natural temperature rise" you hypothesize?

David Appell said...

David in Cal wrote:
"Either way, the actual rate of warming since the 1970's is probably the best basis we have for forecasting the rate of future warming."

Why?

Feedbacks are kicking in now, not then.

David in Cal said...

I don't know what is responsible for the natural temperature rise, but the planet has been warming since the end of the Little Ice Age.

We've had anthropogenic global warming for over 40 years. Why is the positive feedback greater today than it has been?

cheers

David Appell said...

David in Cal wrote:
"I don't know what is responsible for the natural temperature rise, but the planet has been warming since the end of the Little Ice Age."

Gee, and you don't know why?

And nobody else does, either???

Amazing!!

Paul Skeoch said...

We've all heard that the warming for a CO2 doubling, absent feedbacks, is 1.2 K. What calculation does this number come from?

The simplest derivation comes from finding through radiative transfer modeling that doubled CO2 level would change the effective/average height of energy emission out to space by about 150m. Using the standard current lapse rate (6.5K/Km) that means the temperature at this effective height is about 1K lower than it was before, due to doubled CO2. Given that there is no change in lapse rate without feedbacks you can then see a 1K warming is required through the whole atmospheric column, including the near-surface, in order to bring energy emission out to space back to the required equilibrium emission temperature. You can also use Stefan Boltzmann law to note that the difference between emission at 255K (initial effective temperature of emission) and 254K is about 3.7W/m-2. (See page 446 through 447 in Held and Soden 2000)

That's the simple zero-dimensional view. The 1.2K figure comes from GCMs, finding the Planck feedback in conditions of fixed specific humidity. The global average feedback quantity strongly clusters around -3.1 W/m-2/K across models. Given CO2x2 forcing of 3.7W/m-2 that translates to Planck feedback, or "no feedback" warming of 1.2K (e.g. Shell 2013).

So, yes, these calculations implicitly depend on the logarithmic forcing relationship. Though that occurs within the 1-2xCO2 increase as well, so 1.5xCO2 = about 0.8K rather than 0.6K. However, these are equilibrium numbers, which we would expect to be 1.5-2x greater than warming to date.

JoeT said...

I'm going to approach David's question in a slightly different manner. Gunnar Myhre 1998 gives the radiative forcing as 5.35 ln(CO2/CO2i). For a doubling of CO2 that yields 3.7 w/m2. But where does that number come from? I think the best simple model is given by Modtran (this is one of many models on David Archer's website) that gives the emission spectrum as a function of wavenumber. If you integrate the area under the curve you get the upward IR heat flux. However, the flux is very much dependent on the altitude, the locality and whether you include clouds or not. Supposedly Myhre et al took all this into account when they came up with their radiative forcing. Modtran won't give you the exact result Myhre gave, but you can come close. Also I think the forcing is usually calculated at the tropopause, not 70 km up which is the default setting. The one thing you can understand better is the logarithmic dependence of the forcing on the CO2 concentration. At very low concentrations of CO2 you can see the hole in the emission spectrum get deeper and deeper. Above a certain value it stops getting deeper, but continues to get broader. This is the band saturation effect. You can always plot the IR flux versus CO2 concentration to show this logarithmic dependence.

Now to get from the forcing to the temperature change, you can derive a simple estimate of the Planck response to the forcing without feedbacks. Incoming solar radiation is about 240 w/m2. Then epsilon*sigma*T^4 = 240, where epsilon is emissivity. Then dI = 4*eps*sigma*T^3 dT = 4 I/T dT. Hence dT = T/(4*I) dI, where T = 288 K, I = 240 w/m2 (note here epsilon is around 0.62). Therefore dT = 0.3 * dI without feedbacks. For dI = 3.7 w/m2, dT =1.1 C. Close enough.

Finally, it is clear that feedbacks do exist and have for quite a while. I think the best demonstration of that is to plot the temperature versus log2(CO2) and do a linear regression to find the slope. In fact, you can use the Berkeley Earth global temperature versus the Law Dome ice core + Keeling curve data to find a slope of 2.2 C per doubling of CO2, dating back to 1850. That's a pretty good back of the envelope estimate of the transient climate sensitivity, which is twice as large as the Planck response. The equilibrium climate sensitivity would be even larger.