What is the correct value of Climate Sensitivity?

[eyeball]

You can't get a job that affords you a car with your apparent math skills? In light of all that is expended extolling the virtues of the knowledge-based economy we live in, I just don't get that. You should be earning 17000 times the average income or something.

[-1=e^ipi]

@ eyeball - This isn't the appropriate thread to discuss my financial situation.

[eyeball]

You're the one who raised it.

[Bonam]

Perhaps he's a student? You can have plenty of "math skills" while in university and yet still not have any money until after you graduate.

[eyeball]

That's one possibility alright.

[On Guard for Thee]

Okay, after reading up on non-linear regressions I think I got it now. I'll spare you guys the calculations but basically,

Perform OLS regression without the 3 restrictions.

Modify OLS coefficients to satisfy the 3 restrictions such that the increase in the sum of squares of error is minimized.

Apply Guass-Newton method for estimating non-linear regression.

Ive done all that. It confirms: GW is real and that human cell aspiration does not contribute to CO2 content.

[-1=e^ipi]

Okay, derived everything and implemented the code into matlab. I also figured out a way to 'sharpen' the volcanic aerosol data to remove the time delay.

I would like to correct a mistake from earlier. Even after I calculate everything, it won't be possible to get the characteristic temperature of the Earth's heat sink because the factor C cannot be evaluated. However, I can still get C*(T-Ts), which means I can get the temperature difference between the heat sink temperature and the surface temperature up to a scalar constant. It is still useful. For example, if this value has decreased rapidly in the past 15 years compared to the 90's, then that would suggest that more heat has 'gone into the oceans' which would help explain the slowdown in global warming. It would also be interesting to see how this parameter compares to length of day oscillations, the El Nino Southern Oscillation, the Pacific Decadal Oscillation and the Atlantic Multidecadal oscillation. Of course I can use the computed C*(T-Ts) in a linear regression to explain temperature increase (since a transfer of heat from the surface to the heat sink corresponds with a reduction in surface temperature). Using that coefficient, I could compute the characteristic heat sink temperature provided I make an assumption about the heat capacities of the surface vs the heat sink (say by comparing the quantity of air in the troposphere with the amount of water on Earth). But what is ultimately relevant is the rate of heat transfer.

The factor D, which is the characteristic decay rate of the heat sink to the surface temperature gets computed from the regression though, which is very useful.

[-1=e^ipi]

Ive done all that. It confirms: GW is real and that human cell aspiration does not contribute to CO2 content.

That's strange. I was under the impression that such a conclusion would be impossible regardless of the results of the regression because the regression being referred to (that you are quoting) is about explaining changes in atmospheric CO2 over time, not changes in temperature due to increased atmospheric CO2. That's sort of like doing a study on the effects of eating ice cream and then concluding that alligators cause cancer.

[On Guard for Thee]

That's strange. I was under the impression that such a conclusion would be impossible regardless of the results of the regression because the regression being referred to (that you are quoting) is about explaining changes in atmospheric CO2 over time, not changes in temperature due to increased atmospheric CO2. That's sort of like doing a study on the effects of eating ice cream and then concluding that alligators cause cancer.

Alligators can cause lacerations, but no increase in CO2. Id rather eat ice cream though.

[Bonam]

-1, have you done the calculation to show how much the Earth's temperature would change for a doubling of CO2 using only basic radiative physics? Or know of a reference to such a calculation? That would seem to me to be the true lower bound.

I just tried to do this quickly and discovered it is not trivial because once you calculate the mean free path for infrared radiation leaving the Earth's surface is just a few meters at existing greenhouse gas concentrations, meaning all the thermal radiation emitted from the surface is already absorbed. So it's a process of many scatterings out to some height in the atmosphere, from which photons can finally escape because water vapor concentrations become low enough to allow a sufficiently long mean free path. It is essentially the interplay between the atmospheric temperature gradient and the atmospheric water vapor partial pressure gradient that determines how sensitive the Earth system is to concentrations of CO2 in the atmosphere (to zeroth order, ignoring any kind of feedback effects).

Edited February 11, 2015 by Bonam

[-1=e^ipi]

-1, have you done the calculation to show how much the Earth's temperature would change for a doubling of CO2 using only basic radiative physics? Or know of a reference to such a calculation? That would seem to me to be the true lower bound.

See post #14. It gives a link. That value is ~1.15 C.

So it's a process of many scatterings out to some height in the atmosphere, from which photons can finally escape because water vapor concentrations become low enough to allow a sufficiently long mean free path.

You are definitely on the right path. With water vapor it comes to around 1.74 C (see link in post 14).

It is essentially the interplay between the atmospheric temperature gradient and the atmospheric water vapor partial pressure gradient that determines how sensitive the Earth system is to concentrations of CO2 in the atmosphere (to zeroth order, ignoring any kind of feedback effects).

Definately. Obviously it gets more complicated with lapse rate feedbacks, polar amplification effects, etc. The link in post #14 is obviously a simplification.

[Bonam]

Thanks for pointing me to the link, will take a look.

[eyeball]

I wonder if the boys will still remember us when they're rich and famous? It'll be fun to reminisce about when we knew them back in the day.

Will MLW our any of its members be listed as co-authors?

[On Guard for Thee]

It must be recess time.

[-1=e^ipi]

I've tried to sharpen / remove the exponential decay of the Volcanic Aerosol data to get a better approximation of Volcanic CO2 emissions. Using data from 1876 to 2009 I estimate that the 95% confidence interval for the decay time for Volcanic Aerosols is (2.04 +/- 0.42) years. Of course I used a 6 month lag so this might be a slight underestimate. It agrees with the literature, which suggests that the decay time is 2-3 years for volcanic aerosols.

Removing the exponential lag allows you to see volcanic eruptions such as Mount Tarawera (1886) that were hidden in other eruptions (in this case Krakatoa (1883)).

Edited February 11, 2015 by -1=e^ipi

[TimG]

I wonder if the boys will still remember us when they're rich and famous?

Your attempts at sarcasm only expose your own inadequacy. Climate science is not that hard as far as scientific disciplines go and anyone with a scientific background who wants to spend the time to get up to speed can learn enough to talk rationally about the topic. The fact that -1 has the inclination to do the math himself makes him much more informed that the scores of people like you who think that press releases from Greenpeace are all you need to understand the issue. Edited February 11, 2015 by TimG

[eyeball]

Your attempts at sarcasm only expose your own inadequacy. Climate science is not that hard as far as scientific disciplines go and anyone with a scientific background who wants to spend the time to get up to speed can learn enough to talk rationally about the topic. The fact that -1 has the inclination to do the math himself makes him much more informed that the scores of people like you who think that press releases from Greenpeace are all you need to understand the issue.

I have absolutely no doubt people with exceptional math skills are more capable of understanding the science. What I don't understand is how such vast vast numbers of other exceptionally gifted scientists and experts are still as apparently convinced as ever of the need to act. That these numbers are only increasing across several scientific disciplines appears to support what you say about it not being that hard to understand.

I can still subtract 97 or so from 100 as easily today as ten years ago and see the clear virtually unequivocal consensus on the need to act, so why do I need to understand much more than that?

[TimG]

I can still subtract 97 or so from 100 as easily today as ten years ago and see the clear virtually unequivocal consensus on the need to act, so why do I need to understand much more than that?

Well, that statement is simply NOT true. The 97% percent that gets repeated by brain dead media simply refers to the number of scientists that agree that humans are causing some warming. If you ask the question of whether this is a concern the consensus drops to 84% with less than 50% believing it is a major concern.

Your example actually proves how badly misinformed you are.

[eyeball]

Just a mere 84%?

So if an infinitesimal 3% were able to hold up progress for so many decades how many centuries will a colossal 16% be able to trip us up?

[TimG]

Just a mere 84%?

A "moderate" concern which does not imply they think we need to remake our society nor does it imply they even believe that reducing fossil fuel use is practical or possible. Only 41% believed that the climate change is a "serious" concern while 13% believed it was no concern at all.

As I said, you are basing your opinion on known falsehoods and misrepresentations.

Edited February 12, 2015 by TimG

[-1=e^ipi]

I want to correct a claim that I made in my last post. (2.04 +/- 0.42) years for Volcanic Aerosol decay time is incorrect. I should have performed the transformation k -> -ln(1-k) on the inverse of the decay time, so the actual decay time is (1.48 +/- 0.31).

I'll explain my method to get this value because it is relatively simple.

I am using two data sets.

One is optical aerosol depth at 550 nm (550 nm corresponds to the peak frequency of the sun. i.e. yellow light).

http://data.giss.nasa.gov/modelforce/strataer/tau.line_2012.12.txt

The second is a list of the list of largest eruptions in recent history.

http://en.wikipedia.org/wiki/List_of_large_volcanic_eruptions_of_the_20th_century

I look at the period 1876-2009 because that is the period during which all my data sets overlap.

The basic idea is that aerosols in the atmosphere will decay at a particular rate, but new aerosols will be released via volcanoes.

My differential equation is dA(t)/dt = C + B(t) - k*A(t), where t is time, A is the amount of volcanic aerosols, k is the decay rate of Aerosols, C is the volcanic emissions from weak volcanic eruptions and B is the volcanic emissions from strong volcanic eruptions.

The reason I separate weak volcanic eruptions from strong volcanic eruptions is because weak volcanic eruptions are relatively frequent (so the emissions are roughly constant) so most of the variability will be due to the few major eruptions (I use the 88 eruptions of Volcanic Explosivity greater than 3).

To represent the magnitude of emissions from strong volcanic eruptions, I define a variable, call it J, which for a given year is equal to the number of volcanic erruptions of Volcanic Explosivity 4, plus 10 times the number of volcanic erruptions of Volcanic Explosivity 5, plus 100 times the number of volcanic erruptions of Volcanic Explosivity 6 (I do this because the Volcanic Explosivity Index is logarithmic with a base of 10).

Then I can just estimate k by regressing dA(t)/dt = C + D*J(t) - k*A(t) + error, where D is a constant.

Then I can get volcanic emissions since C + B(t) = dA(t)/dt + k*A(t)

This gives a much 'sharper' function than the original volcanic aerosol data. But with the current value I get a few years where there are negative volcanic emissions; this is most likely due to the fact that I am lagging the change in aerosols by 6 months relative to aerosols to avoid reverse causality and also due to error.

If I want to ensure that all emission values are positive, I would have to drop the decay time to 1.02 years.

Also, the claim I made in my last post that the literature suggests decay times of 3 years is inaccurate. Rather the 3 years corresponds to roughly the time it takes to get back to roughly background levels (http://link.springer.com/article/10.1007/BF02839287). So a decay time of 1.02 years isn't inconsistent because the decay time corresponds to the time it takes for excess aerosols to shrink to 1/e = 36.8% of the original value (and (1/e)^(3/1.02) is approximately 5%).

What I don't understand is how such vast vast numbers of other exceptionally gifted scientists and experts are still as apparently convinced as ever of the need to act.

The scientific method does not tell people what to do.

[eyeball]

As I said, you are basing your opinion on known falsehoods and misrepresentations.

Only according to a minuscule number of scientists which are and always have been dwindling. Billions of voters and lay people all over the planet have perfectly adequate math skills for logically determining what that implies - they don't need to know advanced calculus or rocket science.

[Bonam]

-1, what's the goal of your calculations regarding volcanic aerosols?

In post 94, you mentioned that you wanted to know CO2 emissions from volcanoes and so wanted to scale from better known volcanic aerosol emissions since the CO2 emissions should be proportional. But as far as I know, average annual CO2 emissions from volcanoes are already fairly well known, at about 200 million tons / year (in comparison to about 35 billion tons from human emissions).

Also, can you explain what you mean regarding calculating a characteristic heat sink temperature for Earth? Quickly googling around, I can't find much about this term. Articles that talk about a heat sink for Earth are mostly referring to the ocean heat sinks, where heat from the surface is subducted to the deep oceans. If this is the heat sink you are referring to, it's temperature is also known.

Edited February 12, 2015 by Bonam

[TimG]

Only according to a minuscule number of scientists which are and always have been dwindling.

There you go again: making crap up. There is no evidence that a majority of climate scientists support your views on policy. All we really know is a majority think that CO2 is a "moderate" concern. And even if they did support your views on policy their opinion is largely irrelevant since they are not qualified to comment on the science of energy production. Edited February 12, 2015 by TimG

[-1=e^ipi]

Okay, so I went through with the non-linear regression of the change in CO2 on a constant, CO2, Human emissions, Volcanic emissions, the integral of Human emissions, the integral of Volcanic emissions, time, and the integral of atmospheric CO2. I used the data from 1876 to 2009.

Basically I did the regression

dCO2/dt = (A - D*CO2(0)) + (B + D)*CO2(t) + E*CO2_emissions + F*Volcanic_Aerosols + E*D*Integral(0 to t; CO2_emissions*dt) + F*D*Integral(0 to t; Volcanic_Aerosols*dt) - (AD)*t - (BD)*Integral(0 to t;CO2(t)*dt))

The 95% confidence intervals for the coefficients A, B, D, E, and F are: (262233 +/- 10191481), (-874 +/- 361), (2.98 +/- 0.0000018)x10^-4, (0.141 +/- 0.000025) and (1.95 +/- 0.000011)x10^-3. Though I will point out that I got the error message 'Matrix is close to singular or badly scaled' when doing the Gauss-Newton method.

Only the constant is not statistically significant, which isn't that relevant. E and F are highly significant, which suggests that both volcanism and human emissions are significant at explaining changes in CO2 concentrations over time.

Most relevant is the estimate of D, which if you invert it suggests that the characteristic temperature of Earth's heat sink has a decay time of 3355 years.

Edit: sorry I made a mistake in my code. These parameters are nonsense. Please do not trust them.

Edited February 12, 2015 by -1=e^ipi