What is the correct value of Climate Sensitivity?

[On Guard for Thee]

Are you mocking a mathematical genius?

Is that who I am mocking....

[eyeball]

I've had a pack of 35 cm. of global warming in my backyard for more than a month. And it got to -15C last night.

I've already got the first coat of paint on the hull and sunburned arms. It got to +15C.

I'd probably say bring it on except I saw how low the biggest river hereabouts was the other day - I've certainly commented on it being that low before but usually in August.

Judging by the lack of snow pack this late in the season I imagine I'll be speechless regarding the river this August.

[-1=e^ipi]

Looking at the variability indices, I think that I will go with this for a while:

- Use a 3 sinusoidal model to detrend AMO from temperature.

- Use a 5 sinusoidal model to detrend PDO from temperature.

- Use SOI instead of MEI, since ENSO is too chaotic to predict and SOI should be temperature detrended.

Perhaps I need to determine the optimal number of sinusoids using Akaike's Information Criterion.

Doing this gives me a 95% confidence interval of [0.71, 3.79]C with a best estimate of 2.00 C. This is a slight reduction in uncertainty from the earlier estimates. However, the residual from this estimate still shows some features of the above 3 climate oscillations.

One possibility is that there is a lagged response in global temperatures to these climate oscillations. One solution is to impose an exponential lagged effect of the climate oscillations on global temperatures. Using a decay time of half a year gives a 95% confidence interval of [0.80, 2.97]C with a best estimate of 1.79 C. This gives an even smaller confidence interval. Perhaps I should have this decay time as a free parameter in the model, or I should treat changes in these climate oscillations as forcings. But having a lagged effect of climate indices seems to be a good idea.

One possible explanation for my low estimates is that I'm not fully taking human emitted aerosols into account. So I will need to look into this.

Edited March 7, 2015 by -1=e^ipi

[On Guard for Thee]

I've already got the first coat of paint on the hull and sunburned arms. It got to +15C.

I'd probably say bring it on except I saw how low the biggest river hereabouts was the other day - I've certainly commented on it being that low before but usually in August.

Judging by the lack of snow pack this late in the season I imagine I'll be speechless regarding the river this August.

Vancouver is warning of water restrictions I hear. No snow in the hills means no water in the Fraser. I think its to do with 1+2.5=?*over&y7

[Bonam]

I've had a pack of 35 cm. of global warming in my backyard for more than a month. And it got to -15C last night.

The heavy snow on the east coast is getting a lot of news coverage but what most people don't seem to hear about is that out west, we have the lowest snowpack on record. I've checked back through the data in WA state myself as far back as it goes, and no other winter even comes close to having this little snow. The precipitation levels are normal, but the temperatures are just too high... it all comes down as rain instead of snow.

[cybercoma]

The heavy snow on the east coast is getting a lot of news coverage but what most people don't seem to hear about is that out west, we have the lowest snowpack on record. I've checked back through the data in WA state myself as far back as it goes, and no other winter even comes close to having this little snow. The precipitation levels are normal, but the temperatures are just too high... it all comes down as rain instead of snow.

It's as if weather is not climate. Amazing.

[Michael Hardner]

I've had a pack of 35 cm. of global warming in my backyard for more than a month. And it got to -15C last night.

You're like a poster child for incorrect thinking on this subject. So much so that I wonder if you're not actually trolling for climate change...

[TimG]

You're like a poster child for incorrect thinking on this subject. So much so that I wonder if you're not actually trolling for climate change...

Nope. He is just using alarmists propaganda techniques which you are perfectly fine with. You only object when skeptics use them. It's looking like it will be a dry, hot summer on the west coast. I will see if you will be as diligent calling out alarmists who claim hot weather is evidence of climate change.

[Michael Hardner]

Nope. He is just using alarmists propaganda techniques which you are perfectly fine with.

You only object when skeptics use them. It's looking like it will be a dry, hot summer on the west coast. I will see if you will be as diligent calling out alarmists who claim hot weather is evidence of climate change.

I have already done that on here, so you're clearly not up to date.

[eyeball]

The heavy snow on the east coast is getting a lot of news coverage but what most people don't seem to hear about is that out west, we have the lowest snowpack on record. I've checked back through the data in WA state myself as far back as it goes, and no other winter even comes close to having this little snow. The precipitation levels are normal, but the temperatures are just too high... it all comes down as rain instead of snow.

That seems odd to me as precipitation levels out on the WCVI are way below normal. What little wet weather we have had the last few months now seems to come at us from the NW as opposed to the usual direction SW. Of course the remarkable thing about the NW direction is how mild it is.

The Ridiculously Resilliant Ridge is back.

As readers here know, the hottest debate in atmospheric science is not whether man is causing climate change – that was settled decades ago. The debate is, HOW is that change going to manifest, as increasing global heat content drives changes to circulation patterns that have been consistent for millennia. This past winter’s “ridiculously resilient ridge”, which brought drought to the west, and arctic cold to the eastern US, is looking more and more as if it is at least partially a product of climate change.

I just can't help but fell that if this is a new state of normal it could turn into a real windfall in my property's value. I mean, it's just been freaking gorgeous out here.

The Pacific Ocean is certainly living up to its name too, this time of year we're usually often dealing with 5 - 7 meter seas on a regular basis but it's been basically calm and almost flat on occasion. The surfers are whining almost as loudly as the skiers.

[-1=e^ipi]

So apparently human emitted SO2 has a ridiculously fast decay time of like half a day. http://www.sciencedirect.com/science/article/pii/0004698175901286 Therefore, human emitted SO2 forcing should be roughly proportional to SO2 emissions.

Finding global SO2 emission data is fairly difficult. However, I managed to find historic SO2 emission data (http://sedac.ciesin.columbia.edu/data/set/haso2-anthro-sulfur-dioxide-emissions-1850-2005-v2-86/data-download) and recent SO2 emission data (http://iopscience.iop.org/1748-9326/8/1/014003/media/erl441620suppdata.pdf). Both data sets are constructed by the same people (Smith et al) although there is a slight discrepancy from 2000-2005 during the overlap. I can assume that the 2000-2011 data set is more accurate and simply increase the 2000-2011 data by 541 GgS/y to make them comparable. For a rough value of 2012 SO2 emissions, I can estimate this using the linear trend between 2010-2011.

SO2 emissions are the only thing that can explain my low estimates of climate sensitivity (other than climate sensitivity actually being low) since they have a significant cooling effect. However, if I put SO2 as a climate variability index or if I use SO2 directly as a forcing (and either treat it as a free parameter or fix it to something reasonable such as -0.005 W/m^2 per TgS/y http://onlinelibrary.wiley.com/doi/10.1029/2007JD008683/pdf) I get a higher climate sensitivity, but the uncertainty becomes ridiculously large (example: 95% confidence interval of [0.05,184.93]C with best estimate of 4.25C). It looks like I'll either need more data or better model specification if I want a reasonable estimate of climate sensitivity.

- - - - -

One more thing, I was looking over the Van Hateren 2012 paper again and I think it both underestimates climate sensitivity and underestimates the uncertainty for a number of reasons:

- To get the relative effect of changes in solar irradiance in W/m^2 and greenhouse gas forcing in W/m^2, Van Hateren takes 1 - 0.3 (which he/she assumes to be the albedo of the earth) and divides by 4 (which is the ratio of the surface area of a sphere to the area of a circle of equivalent radius). However, as I mentioned earlier, changes in solar irradiance affect equatorial regions more due to receiving more direct sunlight. And due to the Stefan-Boltzman law, the temperature change due to changes in solar irradiance should be less than what Van Hateren is assuming (I explained this in more detail in post #269, where I gave a lower bound of 0.0441). Not to mention 0.3 for the Earth's albedo is likely an underestimate. Although there is also the effect of cosmic rays. Overall, this assumption about the relative strength of solar activity vs greenhouse gas activity should cause an underestimate of climate sensitivity.

- Van Hateren allows for the coefficients of his impulse response function to be negative, which as I explained earlier can give a nonsense impulse response function that underestimates climate sensitivity. Although this doesn't seem to be an issue by the results of figure 6 in Van Hateren's paper.

- Van Hateren detrends data with the Multivariate ENSO index (MEI) but doesn't take into account the issue of reverse causality. If global warming causes MEI to increase, then this means that Van Hateren is underestimating climate sensitivity.

- There is a lot of model specification error in what Van Hateren does, which is not taken into account. I'm not going to go into all the details, but some of the stuff I have done earlier in this thread is comparable with what Van Hateren has done and if I relax my assumptions to try to take into account specification error, my uncertainty increases by quite a bit. Also, there are a lot of coefficients that Van Hateren assumes to be true without much justification that he uses in detrending and in other things (and the uncertainty of these coefficients is not taken into account).

[-1=e^ipi]

Perhaps I should use monthly data from 1876-2012 instead of annual data. That might help reduce the uncertainty. In addition, perhaps I should weight months by the inverse square of their standard errors (which I can get from http://www.metoffice.gov.uk/hadobs/hadcrut4/data/current/time_series/HadCRUT.4.3.0.0.monthly_ns_avg.txt).

Another option is to use reconstructed temperature data from earlier points in time. Mann et al. 2008 seems to be the best reconstruction for 500-1850 AD, and Marcott et al. 2013 seems to be the best reconstruction over the Holocene (both are shown in the image below). If I want to get really crazy I can use Pleistocene reconstructed temperatures by Shakun and Carlson 2010. Note that the blue area is the 1 sigma uncertainty for Marcott et al., so don't put too much confidence in it. The Marcott et al. data has far less time resolution (20 years at best) and more uncertainty. Also, if I were to use data for the entire holocene then I would have to take into account Milankovitch cycles (which explain why Holocene temperatures have been decreasing for the past 8000 years). There are also more reconstructed data sets available for the Mann et al. time period than the Marcott et al. time period.

Also, I want to retract an earlier claim I made about current global temperatures relative to the medieval warm period. Current global temperatures are warmer than the majority of the medieval warm period, but based on the uncertainty of Mann et al. chances are that at least 1 year in the medieval warm period was warmer than 2014.

[On Guard for Thee]

Phew. Hopefully thats over.

[TimG]

Mann et al. 2008 seems to be the best reconstruction for 500-1850 AD

Mann 2008 is complete and total garbage that uses proxies with an orientation opposite to what their physics requires in order to make its conclusions (i.e. the primary proxy needed for the period prior to 1500 decreases with temperature but that did not give the "right" answer so Mann flipped it and arbitrarily claimed this proxy now increases with temperature). You can find a much more technical discussion of the numerous flaws in this paper here:

http://climateaudit.org/tag/mann-2008/

Here is a link to the comment that PNAS published on the paper:

http://www.pnas.org/content/106/6/E10.full?ijkey=6054afc9aeb848de052d626d7d74d9d42eb8291f&keytype2=tf_ipsecsha

PNAS limits the size of comments which makes it hard to make a case. The blog linked above has more in depth explanation. More importantly, PNAS allowed Mann to publish a response that simply ignores the criticisms.

This paper should have had a correction/reaction published but the ideologues run the journals don't want "undermine the cause" by acknowledging that critiques of climate science can be right. This is unfortunate because people like you come along and are tricked into believing it has merit years later. The failure of the climate science establishment to police itself in this matter is one of the reasons why I have nothing but contempt for the field.

Edited March 16, 2015 by TimG

[eyeball]

In the vast vast global conspiracy that you believe surrounds climate science how do you explain the contemptible failure to bring any charge whatsoever against a climate scientist anywhere with fraud? Climate data and the reports the data generated have been compared to the Bre-X scandal. I mean c'mon, you guys can't come up with one charge of fraud to back up the most fundamental tenet of your case?

[TimG]

In the vast vast global conspiracy that you believe surrounds climate science how do you explain the contemptible failure to bring any charge whatsoever against a climate scientist anywhere with fraud?

This line of argumentation simply shows that the person that is using it has no clue what the issues are and is really just an mindless ideologue spouting talking points and really has no interest in discussing the substance.

People who are not mindless ideologues understand that scientific fraud is near impossible to prove because one must show that the motivation for any error was deliberate (a feat that requires mind reading). That said many things can be dishonest and deceptive without amounting to fraud. In this case, the problem is not one scientist with a bad paper but the scientific institutions that refused to correct an egregious error after it was pointed out. By refusing to even acknowledge the egregious error the climate science establishment has shown it is more interested in politics than science which makes every piece of science produced by these people suspect.

Edited March 16, 2015 by TimG

[bush_cheney2004]

In the vast vast global conspiracy that you believe surrounds climate science how do you explain the contemptible failure to bring any charge whatsoever against a climate scientist anywhere with fraud?

That's the beauty of the climate change scam....no matter how outrageous the "settled science" claims, it is no more important than research on the mating habits of snapping shrimp.

[cybercoma]

Has -1 come full circle yet?

[On Guard for Thee]

Has -1 come full circle yet?

Must be a formula for a circle somewhere I guess.

[cybercoma]

I just want to know if Euler has come to agree with the literature yet.

[-1=e^ipi]

@ TimG

How about Marcott et al. is that reasonable to use or not?

I can take into account the issues of the reconstructed temperatures having a lower time resolution and greater uncertainty (by simply doing a weighted regression that takes measurement error into account). But if the temperature estimates are biased or the uncertainty is underestimated then that is a concern.

Two reasons why using reconstructed data may be useful are because it can give an idea of the long term temperature responses (that may occur due to a change in CO2 levels) and it can help me better distinguish between temperature changes due to solar activity and temperature changes due to greenhouse gases. If there is only 130 years of empirical data then it becomes difficult to estimate temperature changes over a longer time scale than this. Also, since solar activity, greenhouse gas forcing and SO2 levels are very correlated over the last 130 years, there isn't enough data (or data of good quality) to be able to give a good estimate of climate sensitivity if I allow the temperature response to solar activity or SO2 levels to vary freely with respect to the temperature response to changes in CO2 levels. I could impose restrictions such as Van Hateren did, but then I will have greater specification error and the estimate may be biased.

Anyway, I don't mind giving the benefit of the doubt to the climate alarmists for the sake of argument. As far as I can tell, I don't see evidence of high climate sensitivity estimates from the empirical data. The instrumental data seems to support an equilibrium climate sensitivity between 1.5 C and 3 C. So I'm seeking alternative 'explanations' as to why my estimates are consistently low.

Also, if Mann is biased downward, then that will mean that the estimate of the temperature response to a change in forcing will be low for longer response times, which may actually lead to an underestimate of climate sensitivity. So the climate alarmists can't have it both ways. If the temperature variation before industrial times is small, then this suggests that the long-term temperature response to a change in forcing is small (but at the same time would suggest that a greater percentage of the warming observed over the past 130 years is due to greenhouse gases).

[-1=e^ipi]

Must be a formula for a circle somewhere I guess.

e^ix gives you a circle on the complex plane if you vary x from 0 to 2*pi.

[-1=e^ipi]

I just want to know if Euler has come to agree with the literature yet.

The literature is in disagreement with itself. That's one of the reason's the IPCC's uncertainty range for climate sensitivity (1.5 C - 4.5 C) is so large.

Instrumental climate sensitivity estimates (and to a lesser extent the paleo estimates) consistently give low climate sensitivity estimates (1.5 C - 3.0 C), where as the general circulation computer models are consistently giving high climate sensitivity estimates (3.0 C - 4.5 C). Of course, a lot of this perceived uncertainty is partly due to individuals not analyzing the data properly and making gross oversimplifications (the Loehle paper in the original post is a good example, but I would argue that even individuals like James Hansen do this). In addition, many people are underestimating the uncertainty of their estimates because their models may have a lot of specification error (this is especially true for GCMs). Also, the definition of 'equilibrium climate sensitivity' is somewhat ambiguous, which adds to the uncertainty of the estimates.

I'm trying to do time series analysis of the empirical data properly to see if I can get a decent estimate of climate sensitivity (and the impulse response function) without making oversimplifications that give large specification error. Are the empirical estimates in the literature low because of specification error? Or are the GCM estimates in the literature high because of specification error? I don't know.

Edited March 16, 2015 by -1=e^ipi

[-1=e^ipi]

Update:

My earlier claim that the AMO and the PDO can be modeled as 3 and 5 sinusoids respectively may not be correct. These oscillations may not have any periodic features at all; they may simply be random noise + autocorrelation and the observed cyclical behaviour is a result of this. If I take the AMO data, detrend a temperature response, a constant and autocorrelation, and then take the fourier transform of the residual, only the peak period of ~70 years remains. If I do the same thing with the PDO data, the PDO residual has no clear periodic tendencies.

- - - - -

I think I have a solution to a problem I was having earlier on how to detrend the El Nino Southern Oscillation (ENSO) from the temperature data set. The problem is that temperature change due to ENSO may be a lagged response. However the functional form of this response is unknown. If I assume a functional form, then I run the risk of unaccounted for specification error. Also if the functional form is difficult to estimate (even a simple exponential lag may be difficult) then it adds to the non-linearities of my model and makes it more difficult to have a convergent solution.

Van Hateren assumed that temperature response to ENSO is exponentially lagged with a decay time of 4 months. Kevin Cowtan uses a simple lag of 4 months (http://www.ysbl.york.ac.uk/~cowtan/applets/nbox/nbox.html). This suggests that the time scale of response is much less than 1 year. So if I simply have both an ENSO term and an ENSO term lagged by 1 year in my model (or if I am using monthly data, maybe 12 ENSO terms with lags varying between 0 and 1 years) then this should give a good approximation of the temperature response to ENSO. Because of the a priori information and the fact that my degrees of freedom is reduced by adding in extra lagged terms, I shouldn't have significant unaccounted for specification error. It also enters the functional form linearly, which makes it easier to estimate.

I can probably do the same thing for the temperature response to AMO or PDO since the natures of these responses are similar. Also, when I try to detrend temperature from AMO, PDO or MEI in order to avoid reverse causality, perhaps I should have lagged temperature terms (up to 1 year) to account for the possibility of a lagged temperature response.

- - - - -

I managed to construct a monthly data set from 1866-2012 and accounted for all of the issues associated with unequal days in each month + more accurate data at later times (plus seasonally detrending and removing temperature response from AMO, PDO and MEI). It didn't really improve the estimates by much (even after I varied the model a few times), probably because even though I do have more data points, the variation in the parameters in data is still small (solar irradiance, greenhouse gas forcing and SO2 are all strongly correlated over this period). The biggest uncertainty seems to be with how strong solar activity is relative to greenhouse gas forcing. Another issue is that if I use monthly data, convergence to a unique estimate is a lot harder (since my model is nonlinear) and it takes far more computational time.

- - - - -

I found reconstructions of 5 more long-lived greenhouse gases (CFC-11, CFC-12, CFC-113, CCl4, SF6) http://cdiac.ornl.gov/oceans/new_atmCFC.html. I can calculate their radiative forcing effect using https://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch2s2-10-2.html. Including these factors should give a better estimate of greenhouse gas forcing than just using CO2, CH4 and NO2. In particular, since CFC concentrations have been decreasing since the 90's, this can help explain some of the slowdown in global warming over the past 2 decades.

[TimG]

How about Marcott et al. is that reasonable to use or not?

If you want to compare with measured temperatures it is useless as well since the data in the modern period is too sparse to have statistical relevance. If you want a reconstruction that gives you relative changes in the past then it is OK. The trouble is everyone quoting the paper does not use it that and focuses on the comparisons to modern temperatures which are basically fiction.

Specifics of the criticisms can be found here: http://rogerpielkejr.blogspot.ca/2013/03/fixing-marcott-mess-in-climate-science.html

and here: http://climateaudit.org/2013/03/31/the-marcott-filibuster/

But if the temperature estimates are biased or the uncertainty is underestimated then that is a concern.

The trouble is it is often no possible to compare past temperatures with today. All the proxies can show is how temperatures changed in the past. The step of translating a change in a proxy value into a number of degrees if often difficult and subject to bias.

Anyway, I don't mind giving the benefit of the doubt to the climate alarmists for the sake of argument.

A reasonable starting point. My cynicism is based on years of observing climate scientists react to criticism. They may be not that different from other scientists if other scientists were faced with the same level of outside scrutiny, however, that does not excuse their failure to put science ahead of politics.

At this point the field is so politicized that only "true believers" will waste their time with the field which will only serve to exaggerate the bias in the literature. Note that this does not mean they are completely wrong. It just means the envelop will be pushed as far as possible in the direction of alarm given the data available. So finding the actual sensitivity at or below the low end of the literature comes as no surprise and you should not second guess yourself too much.

Also, if Mann is biased downward, then that will mean that the estimate of the temperature response to a change in forcing will be low for longer response times, which may actually lead to an underestimate of climate sensitivity. So the climate alarmists can't have it both ways.

I think you need to look at climate as a chaotic system where there are natural long term variations that are not a result of any "forcing". Obviously, external forcings will add to the long term variations and cause the system boundaries to move. IMO, it is wrong to assume that every wiggle over periods of 100-1000 years is "caused" by something. Edited March 16, 2015 by TimG