Arguments
Recent Comments
Prev 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 Next
Comments 45701 to 45750:
-
Daniel Bailey at 14:15 PM on 13 May 20132013 SkS Weekly Digest #19
Chris, this type of thing happens occasionally on large lakes in northern climes. I can recall several instances over the past few decades on Lake Erie, Lake St. Claire and Lake Huron here in North America. A wind-driven occurence. Extreme, yes. Rare, also.
The term "tsunami" is inapplicable, however.
-
chriskoz at 14:02 PM on 13 May 20132013 SkS Weekly Digest #19
What's the the SkS team take on this news:
Tsunami of ice plows into dozens of Canadian homes; no one injured in freak disaster
I don't know much about iceshet dynamics or how the insignifficant wind without any earthquake can cause such tsunami waves on the inland lake.
Further, is it just a "freak event" or can warming in the arctic together with jetstream pattern change, result in more frequent such events in sub-arctic lakes ?
-
bill4344 at 12:15 PM on 13 May 2013The evidence for climate change WITHOUT computer models or the IPCC
Potholer has released a sources video for this one - it's currently his most recent. I'm sure he'd be happy to have any errors pointed out.
-
Rob Painting at 11:04 AM on 13 May 2013The evidence for climate change WITHOUT computer models or the IPCC
If that's the case Tom, it would place the timing hundreds of millions of years before the evolution of Scleractinian (reef-building) coral.
-
Tom Curtis at 10:10 AM on 13 May 2013The evidence for climate change WITHOUT computer models or the IPCC
Oriolus Traillii @3, I think Potholer may have made a mistake in this case. He cites a solar luminosity of about 0.94 of the current value at the time of the purported near polar coral reefs. That places the event at around 700 million years before the present, or over 100 million years before the evolution of the first corals in the Cambrian. In the precambrian, the most probable reefs to be formed would have been stromatolite reefs, although there were other forms of precambrian reefs.
You should really contact Potholer for the source of that claim, and the basis for claiming the reef as evidence of warm water. I am sure he will be able to provide you with a suitable scientific referrence that will get the facts straight (and possibly prove me wrong).
-
Steve J at 07:29 AM on 13 May 2013Dueling Scientists in The Oregonian, Settled by Nuccitelli et al. (2012)
Talking of Fulks, just sat through this:
http://blip.tv/jim-karlock/climate-orthodoxy-perpetuates-a-hoax-5924187
Painful viewing; my knowledge of climate change is mostly limited to Potholer's videos and browsing New Scientist, but even with that I was thinking "that doesnt seem right". You can see how convincing it would seem with no prior knowledge though.
Can anyone bring themselves to review this talk?
PS Sorry if this is off topic, new to this site and didn't know whre else to put it - this thread is all that came up when I searched for Fulks. -
goonobear at 07:21 AM on 13 May 2013Muller Misinformation #3: Al Gore and polar bears
Am I incorrect, or is your quote from the film inaccurate? You say in the film Gore says:
"That’s not good for creatures like polar bears, who depend on the ice. They’re now, actually, looking for other ecological niches. It is sad what’s going on in the Arctic ecosystem."
In actuality, at approx 45:30, he states:"That’s not good for creatures like polar bears who depend on the ice. A new scientific study shows that for the first time they’re finding polar bears that have actually drowned, swimming long distances up to 60 miles to find the ice. They didn't find that before. What does it mean to us to look at vast expanse of open water at the top of our world that used to be covered by ice? We ought to care a lot because it has planetary effects."
While the overall truth of your point about Gore and Cicerone may hold, this inaccurate quotation should be corrected. Where did you find that particular line?Thanks.
-
Rob Painting at 07:12 AM on 13 May 2013The evidence for climate change WITHOUT computer models or the IPCC
Also note that the equatorial oceans would have been extremely warm during the "Greenhouse Periods" on ancient Earth. Too hot for reef-building coral similar to modern-day to have survived.
-
Rob Painting at 05:49 AM on 13 May 2013The evidence for climate change WITHOUT computer models or the IPCC
The oceans only become corrosive when CO2 is added to the atmosphere in a geologically-rapid manner such as today. This is because the chemical weathering of rock is able to supply alkalinity back to the oceans over tens to hundreds of thousands of years.
There is an upcoming rebuttal on this - it's one oversight that needs to be fixed.
-
Oriolus Traillii at 03:04 AM on 13 May 2013The evidence for climate change WITHOUT computer models or the IPCC
Dear Dana,
Great summary! One thing got me frowning, though. Do you know why there were coral reefs at the poles (at 8:05) although CO2 was 25 times higher than it is today? Did the ocean have a higher pH or were they a different type of coral or what was different when compared to todays coral reefs dissolving in highly diluted carbonic acid?
Regards
-
mcooke at 02:49 AM on 13 May 2013The evidence for climate change WITHOUT computer models or the IPCC
On observation of this video, at 3:45 - 3:53 we are told that "a doubling of Co2 from pre-industrial levels will lead to a rise in average global temperatures of about 1 degree Centrigrade". And that at 5:30 - 5:39 - "for a doubling of CO2 concentrations we should see a rise in global temperatures of between 2 and 4.5 degrees" This might cause some confusion.
-
Nick Palmer at 01:12 AM on 13 May 2013What you need to know about climate sensitivity
Rob. I'm pretty sure I was initiating a comment thread...
-
CBDunkerson at 01:07 AM on 13 May 2013Dueling Scientists in The Oregonian, Settled by Nuccitelli et al. (2012)
Dana commented on the D&K response here. Basically, the claims D&K made (e.g. massive unexplained 'step change' shifts in global energy levels) are so ridiculous that they refute themselves.
-
Rob Painting at 19:42 PM on 12 May 2013What you need to know about climate sensitivity
Nick - perhaps you are responding to a particular comment that has been deleted? Any replies on that chain are likely to be deleted too.
-
Rob Painting at 19:23 PM on 12 May 2013Dueling Scientists in The Oregonian, Settled by Nuccitelli et al. (2012)
What is there to respond to? What do you think they have refuted?
-
KK Tung at 17:59 PM on 12 May 2013The anthropogenic global warming rate: Is it steady for the last 100 years? Part 2.
In reply to post 3 by Kevin C. El Chichon erupted in 1983, and Pinatubo in 1991, during the most recent period of accelerated warming 1980-2005. This is also the warm phase of the AMO. Volcanic aerosol cools. Tambora, arguably the largest volcano eruption in 300 years, was followed by a warm phase in N. Atlantic. "The year without summer" was only temporary until the ashes were washed out.
-
Doug Hutcheson at 17:57 PM on 12 May 2013What you need to know about climate sensitivity
Earth System Sensitivity (in the ballpark of 6–8°C for doubled CO2)
Yikes! That's the first I've heard of ESS and its 6–8°C. I have been stuck in my own little world, thinking the 3°C bandied about would be the end of the matter (barring methane amplification, which I didn't think was quantified as yet). Big wake-up call to whoever is asleep at the wheel. Thanks for cheering me up. Not.
-
KK Tung at 17:51 PM on 12 May 2013The anthropogenic global warming rate: Is it steady for the last 100 years? Part 2.
In reply to post 11 by Tom Curtis: Most variance of climate data is usually in the high frequencies, and the AMO is in the low frequency. If we judge the significance of a signal by its variance, then one would have arrived at the conclusion that the 100 year long term trend of global warming, which is only 0.8 degrees C, much less than the seasonal, annual, and ENSO variations, must not be significant. Then we would all be wasting our time debating its cause.
The statistical significance of the AMO in the CET data was shown to be at the 95% confidence level, as compared to a red noise model at those frequencies.
-
Doug Hutcheson at 17:34 PM on 12 May 2013Climate change will raise the sea level in the Gulf of Finland
<pedantry>'Missippi'should be 'Mississippi'.</pedantry>
Sigh: old age has many pitfalls ... "8-/
-
FrankShann at 16:27 PM on 12 May 2013Dueling Scientists in The Oregonian, Settled by Nuccitelli et al. (2012)
I repeat my question of 14th April. Nuccitelli et al 2012 (Physics Letters A 376 (2012) 3466-3468) is often cited on Sceptical Science, but this paper has been "refuted" by Douglass and Knox in Physics Letters A 376 (2012) 3673–3675. Has there been a response to Douglass and Knox? If not, are there any plans to respond? Without a response, it is inappropriate to keep citing Nuccitelli 2012.
-
bill4344 at 14:11 PM on 12 May 2013The evidence for climate change WITHOUT computer models or the IPCC
More great work from Potholer.
No 'skeptic' appears to be doing well in taking up his challenge in the comments below the video. Perhaps one of the locals will do better? Unlikely...
-
Tom Curtis at 10:09 AM on 12 May 2013The anthropogenic global warming rate: Is it steady for the last 100 years? Part 2.
KK Tung @9, I do not think you can say so blithely that the AMO has been "observed". What has been observed is temperature variation in the North Atlantic, and it has been conjectured that that variation is the continuation of a persistent oscillation.
You purport that a persistent AMO has been observed by showing us "Fig 4:, ie, the seventh (and second last) figure in the article above. That compares the fifth Reconstructed Principle Component from MBH98 to the AMO index, and various 50-80 year band signals of various instrumental records. However, the fifth RPC of MBH98 explains only (approx) 3% of the variance of what is, afterall, a NH temperature reconstruction. That low percentate of variance explained almost certainly indicates that the RPC is not significant; and if you are seriously taking it as the AMO signal then you are commiting yourself to the idea that the AMO explains less than 5% of the variance in NH temperatures, an idea I am sure you would reject.
What we have observed in MBH98 RPC 5, then is not the AMO but just some random noise.
What is worse, the actual temperature signal of the CET, which presumably follows that of the North Atlantic very closely, is misrepresented by the "50-80 year band signal" of the CET that you show. This is easily seen in the figure below, which overlays your "figure 4" with the CET temperature series. The blue bars are annual values, while the thin red line is a 21 point binomial smooth of the annual data. It is evident that the "50-80 year band signal" must represent only a small component of the total CET signal; and hence that your "observed" AMO signal is just a small component of North Atlantic temperature variation prior to 1880. If that is the case, either the AMO is not a persistent feature of the NA, or it is a very minor factor in global and NH temperature variation. In either case you have a major problem explaining why it suddenly should appear so dominant in the twentieth century.
-
Nick Palmer at 09:49 AM on 12 May 2013What you need to know about climate sensitivity
Dana. The comments policy on your Guardian articles is so draconian - or one of the moderators is so over the top - that it seems impossible to have a robust intelligent discussion at all. You may recognise my user name and, if so you may recall that I am not one for wild offensive tirades against climate "sceptics" yet my comments are being consistently deleted, as are those of many others. What gives?
-
KK Tung at 08:29 AM on 12 May 2013The anthropogenic global warming rate: Is it steady for the last 100 years? Part 2.
Reply to post 4 by K.a.r.S.t.e.N.: Thank you for pointing out the proper credit of the Figure 5, which I attributed to you.
Currently the debate in peer reviewed literature is about whether the AMO is forced by anthropogenic (tropospheric) aerosol or by the AMOC as a natural oscillation. What you are referring to is a third possibility, that the AMO is forced by the stratospheric aerosol from volcano eruptions. It is possible, though I think it is unlikely ( Please see my comment in post8). But I can be persuaded.
-
KK Tung at 08:21 AM on 12 May 2013The anthropogenic global warming rate: Is it steady for the last 100 years? Part 2.
Reply to post 6 by KR: By "the upward trend of the AMO" I assume you are referring to the North Atlantic mean SST, because AMO is supposed to be detrended. I agree that anthropogenic forcing can force an upward trend in the N. Atlantic mean SST. In fact I am quite certain of it. In addition I think it is entirely possible that anthropogenic forcing can also force an oscillatory N. Atlantic mean SST. It is just that no credible model has been able to simulate it without contradicting some other aspect of the observation. Furthermore it is difficult to have this theory explain more than two cycles of the observed AMO.
-
grindupBaker at 06:08 AM on 12 May 2013What you need to know about climate sensitivity
eschwarzbach @ 6 Another way to view situation when "CS target remain stable". If, say, +2.8 degrees required to balance TOA in/out, I see no logical reason why 80% lowest ocean, now at ~6 degrees avge, will not need to be ~9 degrees avge before all is stable in centuries/millenia.
-
grindupBaker at 05:43 AM on 12 May 2013What you need to know about climate sensitivity
Should add @10 "thin veneer" for surface temp includes top ocean veneer. Need to study to decide a reasonable few metres depth in which thermal conductivity & local mixing significant. It's most significant because each ~6.5m ocean depth = all land+air heat. Land is significant for radiation balance only, not heat content, because it's mostly quite dark albedo.
-
grindupBaker at 04:47 AM on 12 May 2013What you need to know about climate sensitivity
eschwarzbach @ 6 "Global Warming" is an increase in the ocean heat content. I suggest a lay person will have endless difficulty contemplating land-air & ocean surface temperature unless they start by understanding it's just heat moving through into ocean, has 97.5%, freshwater=2.3%, land+air=0.2% of ecosystem heat content. Land solid has no currents so thin veneer only involved (I read ~6.5m deep somewhere), ocean liquid so heat mixes ~6km deep (ex. trenches) ~4km avge, but over centuries-to-millenia. Equator to poles top veneer takes heat, warms poles, saltier, drops, returns at depth. Tiny bits of ocean heat like ENSO sucking in & burping out seem really big to us on/in the negligible 0.2% land+air bit. Surface temperature is (1) a proxy (2) a symptom (3) what determines heat in/out balance at TOA. Example: if ocean mixing slowed to stop for few years (just fantasy for example) land+air reaches TOA balance quickly at "final" temp & AGW pauses. Ocean mixing resumes in (unrealistic) example, surface temp drops & AGW resumes. Humans now see "global cooling" when it's the exact opposite - AGW now resumed. Exaggerated example shows why must understand ocean mass, depth, heat capacity (572 yrs for +1C @ +0.9 wm**-2 is what I computed), currents before can hope to understand surface temperature changes.
-
KK Tung at 04:25 AM on 12 May 2013The anthropogenic global warming rate: Is it steady for the last 100 years? Part 2.
Reply to post 3 by Kevin C:The relationship between large volcano eruptions and each of the cooling periods for the past 400 years was examined in our PNAS paper. They don't quite line up. Also one needs a series of very large volcano eruptions to have a cooling period that lasts 30 years. Volcanic aerosols do not stay in the stratosphere for more than a year in substantial amount, and ocean inertia may prolong the cooling effect by up to seven years but with diminishing cooling. The time profile is very different than the observed cooling. One can also see in historical data large volcanoes eruptions that did not lead to a cooling period.
-
KK Tung at 04:16 AM on 12 May 2013The anthropogenic global warming rate: Is it steady for the last 100 years? Part 2.
Reply to post 1 by Bob Tisdale: Thanks!
Reply to post 2 by IanC: Sorry for the late reply; I didn't know my post was finally published online after a long wait, and so I am late catching up with all the good comments.
I mentioned in part 2 the result of using different AMO index, in particular the index by Trenberth and Shea. It is towards the end of that long post.
-
dana1981 at 01:41 AM on 12 May 2013What you need to know about climate sensitivity
eschwarzbach @6 - equilibrium climate sensitivity refers to the warming in response to any CO2 doubling on century timescales. In reality the exact amount of warming will differ at different temperatures, because some different feedbacks will probably apply, but it's a pretty good approximation.
Most equilibrium warming occurs within several decades. About two-thirds happens almost immediately (the transient response). Within a century after reaching a stable equilibrium state, just about all equilibrium warming should have occurred. However, there is also Earth System Sensitivity (in the ballpark of 6–8°C for doubled CO2), which acts on millennial timescales. This is due to very slow feedbacks, mainly large bodies of ice that take a very long time to melt.
If you scroll over the words climate sensitivity, our glossary will pop up and give you the IPCC definition of the term.
-
dana1981 at 01:35 AM on 12 May 2013What you need to know about climate sensitivity
Sam martin @3 - sensitivity isn't assumed, it's an output of climate models based on their simulations of the Earth's climate. And of course estimates from past climate changes (paleoclimate) are based on observations, not models. I'm not sure about the exact cloud feedback uncertainty, but it's pretty large.
-
meher engineer at 01:02 AM on 12 May 2013What you need to know about climate sensitivity
Re. eschwarzbach @ 6, as Andy Lacis said, "In the Hansen et al. (1988, JGR, 93, 9341–9364) paper we derived the logarithmic type formula
F(X) = log [ 1 + 1.2 X + 0.005 X2 + 0.0000014 X3 ]
where X is the atmospheric CO2 concentration in ppm. This formula gives the radiative forcing in terms of equivalent temperature change rather than in W/m2. Thus, for 350 ppm, F(350) = 7.0 °C (or 7.0/33.0 = 21.2% of the total (emphasis added_ terrestrial greenhouse effect), while for doubled CO2 (emphasis added) the formula yields ΔTo = F(700) – F(350) = 1.23 °C". That quote appears as a comment in http://chriscolose.wordpress.com/2010/08/27/adding-up-the-greenhouse-effect-attributing-the-contributions/. It should take care of your first question. Re the others, Climate sensitivity usually refers to the equilibrium state. It takes a long time to reach that state because of the Ocean's huge thermal inertia. How long? Close to a thousand years, if slow feedbacks are taken on board. Finally, the CS does not depend onthe rate at which you add CO2 to the air. The article by Colose is a good place to understand the subject.
-
eschwarzbach at 23:24 PM on 11 May 2013What you need to know about climate sensitivity
Please, help me understand some points on Climate Sensitivity. Does it refer to doubling of CO2 concentration from preindustrial times, the doubling from the present 400 ppm or for any doubling of CO2 concentration? After how much time after the doubling will the temperature reach the value idicated by CS? Does CS depend on how fast the CO2 concentration raises? And will the temperature after reaching the CS target remain stable or rise further? Where can I find the exact definition of CS?
Erik
-
rugbyguy59 at 17:54 PM on 11 May 2013Nuccitelli et al. (2012) Show that Global Warming Continues
Thanks Rob.
-
shoyemore at 17:15 PM on 11 May 2013What you need to know about climate sensitivity
Peter Gleick has an excellent post here about the Pliocene climate with a lot of links.
-
Paul W at 16:38 PM on 11 May 2013Who is Paying for Global Warming?
While I agree with the comments above. There has not been a mention of the GE Toshiba nuclear battery that is designed to be a small 4th generation replacement for the coal burning part of a coal fired power station. The remainder of the power station remains just the heat source changes.
Most of the opposition to nuclear is to teh old Cold War vintage 2nd generation with all it's melt down, waste plutonium production, very large size, very large water use, very high cost.
The 4th generation GE Toshiba design is waiting on regulatory approval and can be roled out in a modular form to a very large number of sites. The design is unstaffed after instalation and has passive control mechanisms.
It could change the coal trajectory and the CO2 levels would not have to risk civilisation.
Sustainables may be more workable than only rewnewables.
-
Rob Painting at 16:33 PM on 11 May 2013Nuccitelli et al. (2012) Show that Global Warming Continues
Rugbyguy59 - No. There's basically nothing to respond to. Their 'step-change' claim is nonsensical though, and is easily appreciated by looking at the sea level trend over the period of 2004-2008, a period which Douglass & Knox claim the Earth's radiative balance was negative . The ocean is by far the Earth's largest reservoir of heat (around 93% of global warming goes into it), and a negative radiative balance would imply the thermal expansion component of sea level rise was also negative during that period. Sea level rise should have seen a dramatic plunge, but no such thing happened.
Then there's the problem of the Earth undergoing instantaneous net loss and gain of heat. How would it be possible to instantaneously mix heat into the ocean, and then lose it again? How could that heat escape the ocean without warming the ocean surface, and cooking the atmosphere, on its way out to space?
Drawing lines on a graph, as they did, does not deflect attention away from the physical impossibilty of it all.
-
rugbyguy59 at 12:24 PM on 11 May 2013Nuccitelli et al. (2012) Show that Global Warming Continues
Dana, did you, or anyone else on the team, respond to the Douglas and Knox reply published online in Nov 2012? It seems to me they are just saying they prefer their noisy data. Is there any substnce to their claims?
-
Bert from Eltham at 10:50 AM on 11 May 2013What you need to know about climate sensitivity
Many years ago I had a lecturer in Mechanical Engineering who described the first building that had a comprehensive centrally controlled air conditioning system that he had designed. Complaints from the new occupants were thick and fast. Rooms were 'too hot' or 'too cold'. His solution was to put a 'thermostat' that people could adjust in every room. These 'thermostats' were not connected to the system! All complaints stopped!
Control is either illusory or real. Sometimes the illusion is more real.
How long will people ignore the realities? I am afraid that when only New York is flooded it may happen.
Bert
-
Riduna at 09:39 AM on 11 May 2013Who is Paying for Global Warming?
Mikeh 1
Thank you for referencing Galilee Basin coal development which notes capital investment in the Galilee Basin by Hancock Coal and two major Indian interests – Adani and GVK Enterprises - for development of what will be the largest coal mine in the world. Its product is destined for India and tends to weaken the argument put forward by Justin Guay.
Rinehart and Adani are far too shrewd to be putting their money into coal on spec or without assurances of demand and a market.
I agree with Guay that it is absurd for India to build all of the proposed coal fired power plants. However until technology development enables similar-scale generation of electricity from renewable sources at a cost below that of coal, it seems likely that the present building program will be implemented, though hopefully never completed.
-
Riduna at 09:32 AM on 11 May 2013Who is Paying for Global Warming?
Sceptical Wombat … You correctly note that China increased its wind power by more than it increased its coal fired electricity production. Commendable - but coal fired production nevertheless expanded.
I agree with you when you say that “it is misleading to simply quote the number of new power plants”. That is why I also included Table 4 which shows domestic production and consumption of coal and the figures for China speak for themselves.
The decision of the Chinese government to close dirtier power stations is to be applauded since this should reduce coal use and CO2 emissions. To-date the opposite has occurred. In 2010 China was a net coal exporter but by 2012 had become a net importer of >200,000,000 tonnes. In 2013 consumption of coal is reported as exceeding 4 billion tonnes for the first time. This shows that coal consumption, at present, continues to grow.
-
Sam martin8679 at 08:28 AM on 11 May 2013What you need to know about climate sensitivity
Thanks very much for a good article. If warming due to CO2 doubling is 1.2 degrees and most models have lower sensitivity values of 1.5 degrees with means of around 3 C presumably the models all assume some overall positive feedback. How much uncertainty is there about cloud feedback?
-
KR at 05:56 AM on 11 May 2013The anthropogenic global warming rate: Is it steady for the last 100 years? Part 2.
Dr. Tung - "The Granger test with annual data will fail to show the lag of the atmosphere, thus showing the global temperature to be causal."
If you examine the correlation of monthly data, as Tamino did here, the AMO has a 2-3 month lag behind global temperatures. It may be that annual data is a bit coarse for this analysis.
I continue to feel that the upward trend of the AMO is an effect, not a cause, of global warming, that the linear AMO detrending retains part of the GW signal and inappropriately removes it in the regression analysis, decreasing the apparent anthropogenic GW signal. The linear detrended AMO is not (as per Trenberth and Shea 2006) an independent variable.
In addition, I would again point to Anderson et al 2012, who find from a strictly energy conservation point of view (ocean heat content versus surface temperatures) that:
"...results indicate that less than 10% of the long-term historical increase in global-mean near-surface temperatures over the last half of the twentieth century could have been the result of internal climate variability"
[Emphasis added]
Arguments over regression order and detrending aside, there is sufficient evidence to show that the AMO is not capable of causing large portions of recent warming through internal variations (it would have greatly changed the observed OHC values), indicating that results pointing to large AMO contributions suffer from issues.
-
KR at 05:34 AM on 11 May 2013The anthropogenic global warming rate: Is it steady for the last 100 years?
Dr. KK Tung - You stated that "atmospheric CO2 has been measured to increase almost exponentially".
This is incorrect, CO2 is increasing more than exponentially over the last century, and the CO2 portion of forcings is therefore increasing faster than linearly.
-
KR at 05:29 AM on 11 May 2013The anthropogenic global warming rate: Is it steady for the last 100 years?
jdixon1980 - What DS said:
Notice that CO2's radiative forcing increases faster after 1950, because increasing CO2 faster also increases its logarithm faster. That's what makes the forcing "slightly more curvy than linear".
Now if CO2 were increasing in a polynomial fashion, its log (while still increasing with CO2 - the log of a larger number is larger than the log of a smaller number), would by definition have a positive first derivative, but would have a negative second derivative - less than exponential growth, less than linear forcing increase. If that polynomial grew larger (faster growth curve), the log would increase faster than it would otherwise have, with a higher (although potentially still negative) second derivative.
In the case of actual CO2 measures, the growth of CO2 is higher than exponential, the log of CO2 has positive first and second derivatives. DS did skip a step, though, and did not mention that CO2 growth is faster than exponential.
But no matter what, if the rate of growth of a value increases, the growth of the log of that value (always with a positive first derivative under growth) will grow faster than it would without that increase.
-
jdixon1980 at 05:01 AM on 11 May 2013The anthropogenic global warming rate: Is it steady for the last 100 years?
For a reality check, I asked my friend Lucas about it (a math professor and a Climate Reality Leader with the Climate Reality Project). Some of his reply went a little over my head on a quick reading, but the gist of it is that whether increasing the first derivative of a function will also increase the first derivative of its logarithm depends on what the function is:
"J: Just because a function's derivative is increasing doesn't mean the derivative of the log of the function is increasing. For a function's log to have increasing derivative, it must satisfy a certain differential equation: d^2(ln(f))/dt^2 = (f(t)f''(t)-(f'(t))^2)/f^2(t) > 0 <=> f(t)f''(t) > (f'(t))^2. This is never true for lines (f''(t) = 0) and typically not true for polynomials (for a polynomial with leading term x^n, the leading term on the left is n(n-1)x^(2n-2) and the leading term on the right is n^2x^(2n-2), so the right always eventually dominates).
However, I'm not sure that's what DS meant. DS might mean that if you increase the first derivative of f then you also increase the first derivative of ln(f). More formally, if f(0) = g(0) and f'(t) > g'(t) for t > 0 then (ln(f(t)))' > (ln(g(t)))' for t > 0. Even this might not be true though. For it to be true, we would need the following differential equation to hold: (ln(f(t)))' = f'(t)/f(t) > g'(t)/g(t) = (ln(g(t)))', or equivalently f'(t)g(t) > f(t)g'(t). This now holds true for lines (if f(t) = at+f(0) and g(t) = bt+f(0), the differential equation is abt+af(0) > abt+bf(0), which is true exactly when f'(t) = a > b = g'(t)). It is also true for pure exponential functions (if f(t) = a^t and g(t) = b^t then the diff eq becomes ln(a)a^tb^t > ln(b)b^ta^t, which is true iff a > b iff f'(t) > g'(t)). But for more complicated functions, the exact relationship depends on the functions involved."
-
jdixon1980 at 04:28 AM on 11 May 2013The anthropogenic global warming rate: Is it steady for the last 100 years?
KR @45 "Abrupt or not, if CO2 concentration shows a faster increase over time, the Ln(CO2) will also show a faster increase over time." This broad mathematical proposition is false, as I showed above by the counterexample in which CO2 = t^2. But the point is moot because, as you point out, we can see from observation that ln(CO2) actually is increasing faster over time. I know that now, because you pointed it out to me, though it wasn't clear to me from DS's statement at 7. The reason why the mathematical proposition holds true in for the particular case of CO2 as a function of time is that CO2 apparently is not proportional to t^2, or for that matter even to e^t (the second derivative of ln(N*e^t) being zero, not positive), but to something even higher order than that.
SkS is good for people like me who are technically literate (I'm a patent attorney with a mechanical engineering degree, which is admittedly growing stale after ten years) but lack broad climate knowledge, precisely because of instances like this: I read something that confuses me by contradicting what I remember from first-semester calculus, I comment about it, and someone like you can straighten me out by explaining the context that makes sense of the confusing statement, in this case by showing me that the confusing statement wasn't intended as broadly as its literal reading.
-
KR at 02:32 AM on 11 May 2013The anthropogenic global warming rate: Is it steady for the last 100 years?
jdixon1980 - While I used N and N+1 for illustration, there hasn't been a sudden abrupt shift, but rather (as seen in the CO2 data) an increase in the rate of CO2 increase rising over time, a positive second derivative. And a fairly simple check on this, taking the ln(CO2) and looking at its behavior over time, shows that forcing is actually increasing greater than linearly, that CO2 is increasing greater than exponentially.
Abrupt or not, if CO2 concentration shows a faster increase over time, the Ln(CO2) will also show a faster increase over time.
-
jdixon1980 at 02:15 AM on 11 May 2013The anthropogenic global warming rate: Is it steady for the last 100 years?
KR @42, 43 - thanks for the clarification that time is a multiplier in the exponent. I don't think that's a sign of my needing to check my "math" per se, so much as my (lack of) knowledge of the actual relationship of CO2 rise to time. My math is consistent with what you are saying - in your example where a function that is initially e^(T*N) subsequently becomes e^(T*(N+1)), it may be that the constant term in the exponent changed from N to N+1 because it is not actually a constant, but a linear function of time, which would give you something that acts like e^(t^2), an example that I mentioned of a situation in which a function "increases faster" as its logarithm also "increases faster."
However, I assume you are suggesting that the second term is not actually a linear function of time, but rather a step function that abruptly shifted being a constant N to a constant N+1, at some precise moment or over some short interval, because of some historical event causing an abrupt shift in the emissions trend? As you illustrate, DS's statement would hold true for that case as well, because as you illustrated the first derivative of the logarithm would change from N to N+1.
I hadn't considered this kind of abrupt shift when trying to understand and evaluate DS's statement. I still would contend that not all abrupt transformations of a function resulting in a transformed function having a larger first derivative would also result in a logarithm of the transformed function having a larger first derivative; for instance it wouldn't hold true if CO2 = (N)t^2 suddenly became CO2 = (N+1)t^2, but that's just a quibble with his wording that I wouldn't have brought up had I initially understood the context, which I do now thanks to your clarification.
Prev 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 Next
