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Re: [Phys-L] some climate concepts, numbers, and references



John,

I'm trying to get a grip on precisely how you arrive at your 4 degree
estimate (based on .91 doubling of CO2 conc). Do you mean beginning with the
industrial revolution? Also, from where does the 504 GT figure come (or
have you answered that somewhere?). Is it to do with burning all currently
known fossil fuel reserves?

What do you think of applying transient climate response (TCR), which is a
measure of the magnitude of transient warming while the climate system is
not in equilibrium (particularly wrt the deep ocean). TCR = the increase in
20-year mean global temperature over a 70 year timeframe during which CO2
concentrations, rising throughout at 1% p.a. compound, double.

TCR estimates in IPCC's AR5 averaged roughly 1.8 degrees C. An increase from
400 to 526 ppm by, say, ~2085 (70 years) would give Temp change = 1.8 x
ln(526/400) / ln(2) = approx. 0.7 degrees increase. If I've got the gist of
things right in my first paragraph, would you agree with this figuring, or
is the burn time (70 yrs) for known fossil fuel reserves too fast


-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of John Denker
Sent: Thursday, 9 October 2014 6:36 PM
To: Phys-L@Phys-L.org
Subject: [Phys-L] some climate concepts, numbers, and references

Here are some useful concepts and numbers. Tracking them down was more
laborious than I expected it to be.

1) Concept: The incremental amount of energy per unit time is only
/logarithmic/ in the amount of CO2 in the atmosphere. That's because the
atmosphere is more-or-less optically thick at the relevant wavelengths
already. So, adding more CO2 cuts down on what's coming in, not just on
what's going out.

If it were linear instead of logarithmic, all our gooses would be cooked
already.

This is why people talk about the number of "doublings"
of the CO2 level.

2) More particularly, they talk about the number of doublings relative to
the pre-industrial level.

Most practitioners take the pre-industrial level to be 280 ppm. There are a
few papers, mostly on the NASA site, that take it to be 275 ppm. The
difference is sufficiently small that I'm not going to worry about it.

As a corollary, people talk about the 2xCO2 level i.e. double the
pre-industrial level, namely 560 ppm.

3) In the climate business, the concentrations are measured in terms of v/v
(not w/w) i.e. volume per unit volume (not weight per unit weight).

4) The canonical 2xCO2 level i.e. 560 ppm corresponds to adding a "forcing
term" of 3.7 W/m^2 to the global energy-balance equation.


http://www.pik-potsdam.de/~stefan/Publications/Book_chapters/Rahmstorf_Zedil
lo_2008.pdf

That is a humongous number. As a point of reference, the solar constant
is on the order of 1300 W/m^2.
That's the incoming energy at the top of the atmosphere, at normal
incidence.

As a corollary, if you wanted to tolerate the CO2 in the atmosphere (and
in the ocean!) and only wanted to balance the energy equation, you could
set up a reflector. Alas, it would need to have a humongous area.

5) Current CO2 level: For several months in mid-2014, the CO2
concentration was just over 400 ppm. There's a ± 5 ppm seasonal variation
superimposed on that.
We're in the trough right now, namely 395 ppm, but
400 is a good number if you average over the year.
It keeps going up.

https://scripps.ucsd.edu/programs/keelingcurve/
http://climate.nasa.gov/400ppmquotes/

https://scripps.ucsd.edu/programs/keelingcurve/wp-content/plugins/sio-bluemo
on/graphs/mlo_one_year.png
http://scrippsco2.ucsd.edu/images/stories/home/mlo_front_plot.png

6) One gigaton of CO2 /in the atmosphere/ corresponds to 0.5 ppm. This
doesn't depend on anything except the total mass of the atmosphere.

http://spacemath.gsfc.nasa.gov/Calculus/6Page51.pdf

7) One gigaton of CO2 /released into the environment/ produces only about
half a gigaton of CO2 in the atmosphere. Most of the other half partitions
into the ocean fairly quickly. OTOH I have zero confidence that this
ratio will remain unchanged over time. The solubility of CO2 decreases
strongly as pH goes down and/or temperature goes up.

There's also some monkey business with deforestation in the southern
hemisphere and reforestation in the northern hemisphere. For
back-of-the-envelope calculations these can be neglected /for the moment/
but I have zero confidence that they will remain negligible. For one
thing, there is a lot of frozen peat in the northern tundra, and if that
thaws and rots, it will release huge amounts of CO2.

8) The exciting number is the /sensitivity/ i.e. the response of the global
temperature to a change in the energy input rate.

The key concept here is that this number is defined so as to include the
effects of all negative and positive feedback loops. These are only rather
poorly understood, which means there is a lot of uncertainty attached to
the sensitivity number.

Quoting Holden:

We estimate climate sensitivity as likely (66% confidence) to lie in
the range 2.6–4.4  °C, with a peak probability at 3.6 °C.


http://www.mucm.ac.uk/Pages/Downloads/Other_Papers_Reports/RW%20clim%20dym%2
0probabilistic%20calibration%20GENIE%201%20rcvd%20082009.pdf

9) Let's talk about the cost of the problem.

For some purposes, to a first approximation, we might be interested in the
/expectation value/ of the cost, i.e. weighted average of the possible
costs, weighted according to the probability of incurring that cost.

To a better approximation, we should compute the net present value (NPV)
by discounting the costs according to /when/ they are incurred.

10) Let us examine the process of calculating the aforementioned
expectation value.

Very hypothetically and temporarily, consider the case
where the sensitivity numbers were narrowly clustered
around the peak value, and the cost was a smoothly
varying function of temperature. Then we could treat
the sensitivity-distribution as a delta function. The
only thing that would matter would be the center of the
sensitivity distribution.

Non-hypothetically, we have a rather broad distribution of sensitivity
numbers. Furthermore, the cost of dealing with the problem is a very
strong function of temperature. It is /at least/ exponential. At some
point it becomes even worse than that; it becomes an ultra-steep step
function, i.e. a life-or-death function, literally survival-or-extinction.

Now consider what happens when you convolve a Gaussian with an exponential
... in this case a Gaussian probability distribution with an exponential
cost model. The resulting integrand is just a shifted Gaussian.

Therefore the upper end of the sensitivity distribution contributes to the
expectation value more than the lower end. This is not some Chicken-Little
over-reaction; it is not even an opinion. It is required by the
mathematics.

11) A temperature rise of 2 °C is considered "dangerous".
Anything more than that is considered "extremely dangerous".

http://rsta.royalsocietypublishing.org/content/369/1934/20.full

The analysis suggests that despite high-level statements to the
contrary, there is now little to no chance of maintaining the global
mean surface temperature at or below 2°C. Moreover, the impacts
associated with 2°C have been revised upwards, sufficiently so that
2°C now more appropriately represents the threshold between
‘dangerous’ and ‘extremely dangerous’ climate change.

That's from a book chapter; the larger book is indexed at:
http://rsta.royalsocietypublishing.org/content/369/1934.toc

12) Anybody who doesn't like these numbers is cordially invited to come up
with other numbers, and to explain why the other numbers are better.

13) Current climate science is directed toward building new models that
describe /regional/ rather than global changes.
All regions will be affected, but not all in the same way.

Similarly, there's more to the story than average temperature.
We need to model regional precipitation. We need to model regional
/extremes/ in temperature and precipitation, so as to predict the chance of
droughts, floods, crop failures, et cetera.

====================
Putting all the numbers together, consider what would happen if we stopped
all man-made CO2 emissions tomorrow: We have already emitted enough CO2 to
push the temperature rise well past 2 °C (using the weighted expected value)
... i.e. well into "extremely dangerous" territory.

Next, consider the effect of burning enough additional carbon to make 504
gigatons of CO2:

504 Gt released into the environment
--> 252 Gt in the atmosphere
--> 126 ppm on top of what we have now
--> 526 ppm total
--> 0.91 doublings relative to pre-industrial 280 ppm
--> 4.00 °C temperature rise,
(using the weighted expected value)

That's so far beyond what is considered "extremely dangerous"
that I don't even have a name for it.

It could be less than that, or it could be more, but that seems like a
reasonable number for planning purposes.

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