Chris @599: “You need to take the log sooner I think.” I understand you now. It’s an easy enough change to make so I’ll try it and we’ll see what happens. But otherwise does the iterative summing method I described seem reasonable?
wilisays
Thanks for the link, wayne. It’s a complex process, but the near-term net effect of more tall bushes and trees in the tundra does seem to be more local warming.
On permafrost feedback in general, here is another fairly recent article:
One thing the full article makes clear is just how much carbon is available to the atmosphere from that one source:
“Cumulative CO2 emissions under RCP8.5 are 26PgC (12-52PgC) by 2100. By 2300, the majority of the permafrost carbon stock could be already released to the atmosphere, with cumulative CO2 emissions being 529 PgC (362-705PgC)”
Chris Dudley: I made the “log sooner” change you proposed, and here are some results. I’m holding off on all the permutations until confidence is higher, I just enclose the ones that were most symptomatic. Here’s RCP3-PD, now and before. Here’s RCP8.5, now and before. And lastly here’s the triangle burst diagnostic, now and before. For RCP3-PD I don’t see much difference, but for RCP8.5 it’s obvious. I would describe it as a larger “spread” between the response functions. If nothing else this change makes the algorithm much simpler: it’s now reduced to a single step instead of two.
Slightly off-topic, but still relevant. Italian seismologists are going to jail for not being able to predict an earthquake (http://www.theatlanticwire.com/global/2012/10/italian-seismologists-are-going-jail-not-being-able-predict-future/58203/). This news is full of irony. Earthquakes are not predictable while climate change is. So maybe all climatologists will be going to jail 20 years from now for not being able to predict the future? Sounds bizarre, but you never know.
Chris Dudley @606: “I’m not quite sure why you have taken the derivative of the CRF.”
Hmm, I thought that was the whole idea: to model inertia by distributing each year’s instantaneous temperature change over the next 2000 years, in unequal slices the sizes of which are determined by Climate Response Function percentages. But I could be grossly misunderstanding this! I’m usally OK once I have derivatives to work with, but math analysis gives me terrible headaches. Anyway here’s the pseudo code.
for (int iSamp = 0; iSamp < RCP_YEARS; iSamp++) { // for each yearly CO2 concentration sample in ppm
// compute instantaneous change in average global surface temperature, relative to baseline
InstantTemp = log(Concentration[iSamp] / Concentration[0]) / log(2) * ClimateSensitivity;
// distribute instantaneous temperature change over next 2000 years according to climate response function
PrevRespPct = 0;
for (int iYear = 0; iYear < 2000; iYear++) { // for each response function year
RespPct = gRespPct[iYear].Pct[RespFuncIdx]; // get this year's percentage from the response function
TempSlice = InstantTemp * (RespPct - PrevRespPct) / 100; // compute this year's slice of temperature
OutputTemperature[iSamp + iYear] += TempSlice; // add slice to appropriate temperature bucket
PrevRespPct = RespPct;
}
}
Dansays
re: 609
I wish I could say I am being sarcastic when I say this but I suspect anti-science Ken Cuchinelli, the Virginia Attorney General, may be taking notes about the Italian seismologists case.
Did anyone has more info into the following ongoing research?
ESTIMATING THE PERMAFROST-CARBON FEEDBACK ON GLOBAL WARMING
A key uncertainty is the fraction of carbon that might be decomposed under anaerobic conditions – resulting potentially in methane emissions to the atmosphere. Given the high warming potential of methane, the overall magnitude of the permafrost-carbon feedback will depend strongly on this fraction. http://www.pik-potsdam.de/~anders/publications/schneider_meinshausen11.pdf
Schneider-Meinshausen (per Scholar) is cited by 5; of those, one is cited by 15, and others have several cites apiece, so the paper “has grandchildren” — you’ve looked those up? I didn’t check the other one.
A – I think they call it a ‘swamp ocean’, or maybe a slab ocean – heat capacity may be modelled (I won’t write it in computer code exactly; T is temperature, ECS is equlibrium climate sensitivity here expressed as K per doubling of CO2, y = year number):
Noting an analytical solution for constant forcing:
Teq – T = (Teq-T0)*exp(-t/time_constant)
dT/dt = (Teq-T0)*exp(-t/time_constant) / time_constant
@ t = 0, dT/dt = (Teq-T)/time_constant
which can be converted to an iteratable form:
T(y) = T(y-1) + 1 year * [Teq(y-1) – T(y-1)]/time_constant
or if time_constant is a dimensionless number that happens to be equal to the number of years of the time constant:
T(n)
=
T(n-1) + [Teq(n-1) – T(n-1)] * time_step / time_constant
+ [ average (j = n-5000 to n-1 or whatever works) of ( T(j) * exp[-(n-j) * time_step / mix_time]) – T(n-1) ] * time_step / mix_time
… I’m not sure if that last part entirely makes physical sense – it makes some qualitative sense but I’d have to do some more work to see if it ought to be changed – does it violate energy conservation? … I haven’t actually tried doing this.
Patrick 027says
re wili (re Chris Colose) @ 594 “You seem to think of the point when feedbacks exceed human forcing is just an arbitrary point. Chu and many others don’t.” – I missed that point earlier. What I meant (what I thought you meant) by Chuvian runaway was a runaway of an extent more limited (covering a smaller range of temperatures that can’t be at equilibrium) than the big ice-albedo and H2O-vapor greenhouse runaway feedbacks of snowball and ‘steamball’ conditions. (non-Planck) Feedbacks in W/m^2 exceeding forcing is I think already expected just from the fast feedbacks.
Re Chris Korda – (last part of my third-to-last comment) – it will be much easier if the deep ocean temperature (or multiple such thermal reservoirs)is explicitly computed iteratively. More on that later…
Re wili – “Feedbacks in W/m^2 exceeding forcing is I think already expected just from the fast feedbacks.” – at least when equilibrium is approached; not sure offhand about right now.
Patrick: Thank you! It seems like we’re on the same page. Your simplified equation @617 looks very similar to the pseudocode I gave @610 no? I’m just applying Hansen’s response functions to this equation. Or maybe I’m missing your point, if so please forgive my obtuseness!
Well, it looks as though it reproduces the Heaviside response. And, is also seems like a term in an integration by parts expansion of equation 3. But, why not follow equation 3 instead?
wilisays
The guys on “The Climate Show” seem pretty concerned about the permafrost feedback study (covered at about the 11 minute mark):
“So maybe all climatologists will be going to jail 20 years from now for not being able to predict the future? Sounds bizarre, but you never know.”
Maybe if they fail to warn people and politicians with sufficient clarity.
On the other hand, those people who have been trying (with some success) to minimize the perceived risk from climate change might find themselves with a case to answer
The Atmospheric Chemistry and Physics discussion page for “Earth’s Energy Imbalance and Implications” makes for surprisingly interesting reading. Hansen et al. took a few punches but I guess that’s par for the course. Apparently Hansen originally had photos of his grandkids in the paper, but both anonymous referees upbraided him for that, understandably. The first referee also accused the paper of “excess verbosity”, ouch. More interestingly, in response to the second referee’s objection that older SRES scenarios were used instead of the new RCP scenarios, Hansen replied: “Our paper compares observations (thus the past) and models, thus only deals with the past. It is of interest to see how the real world changes compare with the past projections. In a future paper when we replot Figure 16 in conjunction with our simulations for the future we can use the new RCP scenarios, but for this paper the old SRES scenarios are more relevant.” So it seems my wish for RCP temperature projections might someday be granted.
But the most entertaining critic is one Nabil Swedan, who lobs such gems as “The subject paper is based on other flawed papers that were challenged. Authors of the subject paper have not addressed the comments of challengers yet,” and “The subject paper is based on the greenhouse gas effect science that is unrecognized by Russians, Chinese, Indians, and much of the west.” Holy smokes! And the crescendo: “… the subject paper … does not follow the scientific methodology of proof, it disagrees with observations, it is based on flawed referenced papers, and it utilizes a flawed science that is unrecognized by most of the world.” What happened here? Do the Koch brothers have a mole in the European Geosciences Union?
Chris Dudley @621: Despite considerable effort I still haven’t figured out how to apply the interpolated Climate Response Functions directly to equation 3. If you feel sufficiently inspired to offer up some pseudocode of your own I would gladly give it a shot. But what’s your response to the results I gave at @607 using your “log sooner” fix? With respect to the “electric burner” analogy we were discussing, are the new results better or worse? Heaviside is a type of Green’s function so that’s encouraging. Between you and Patrick I get the impression that I’ve implemented something functionally equivalent to equation 3, by differentiating the Climate Response Functions. It might be the hard way but that’s OK with me if it gives acceptable results.
Dan H.says
Kevin,
It appears that climate change was the third rail in this year’s election. Both candidates could not get far enough away from it. When was the last time you heard two candidates vying for the title of “Oil King.”
Patrick 027says
re Chris Korda – including a deep ocean
non-conveyor belt version
C is the more immediately accessible heat capacity of the near-surface climate system, including (largely made from) some upper portion of the ocean
Cdeep is the heat capacity of the deep ocean
Cexchange is a measure of the rate of exchange between the upper and deeper ocean
generalize to a surface thermal reservoir C(0) and multiple other reservoirs C(j), j = 1 through ?, C_step(j,k,n) = time_step*C(j,k,n) is the reservoir size that is transfered from reservoir j to reservoir k in the time step going from n-1 to n. C(j,k,n) may be larger than C(k,j,n), hence one can have a conveyor-like aspect
(although having each transfer being dumped and mixed into the reservoir still provides a mixing like aspect. A true conveyor would have reservoirs being produced from surface water and then being stored and then brought back to the surface at some time… etc..)
However, in order for all C(j) to stay constant over n (otherwise use C(j,n), for each j, the sum of all C(j,k,n) over k must equal the sum of all C(k,j,n) over k. Otherwise, maybe this would work:
C(j,n) = C(j,n-1) + sum over k of [C(k,j,n) – C(j,k,n)]
Then … (in isolation of the climate forcing+feedback):
T(j,n) = T(j,n-1)*(1 – sum over k of C_step(k,j,n)/C(j)) + sum over k of T(k,n-1)*C_step(k,j,n)/C(j)
A little algebra and adding the climate forcing+feedback term:
T(j,n)
=
T(j,n-1)
+
sum over k: [T(k,n-1) – T(j,n-1)]* C_step(k,j,n)/C(j)
+
if j=0: [Teq(n-1) – T(0,n-1)]*time_step/time_constant
else, 0.
SecularAnimistsays
Could be an interesting week next week …
Will soon-to-be Hurricane Sandy hit the northeastern USA as a super-storm of historic proportions, like Katrina and Irene rolled in to one — perhaps inundating New York City with the massive storm surge that Irene almost delivered last year …
While at the same time, hyperactive sunspot region AR1598 unleashes a gigantic coronal mass ejection directly at the Earth, triggering a Harrington-class geomagnetic storm that shuts down the entire North American electric grid for days or weeks .. or months …
… just days before a presidential election?
wilisays
Please check my maths to see if I am at least roughly in the right ball park. Hansen has claimed (in his TED talk and elsewhere) that our emissions of ghgs are adding energy to the atmosphere equivalent to 400,000 Hiroshima bombs every day.
If we multiply that over ten years, and figure that the top billion or so of world population is responsible for the lion’s share (say 80%) of the emissions, could we then conclude that, on average, every member of that top billion (presumably including all on this forum) had contributed the energy equivalent of one Hiroshima bomb (or more) toward atmospheric global warming over the last decade?
Thanks ahead of time for corrections, tweaks, reactions, thoughts…
(reCaptcha has gone French, sort of: licyeen sevire)
T(j,n)
=
T(j,n-1)
+
sum over k (forgot this earlier: k=0 to ?, except for k=j): [T(k,n-1) – T(j,n-1)]* C_step(k,j,n)/C(j)
+
if j=0: [Teq(n-1) – T(0,n-1)]*time_step/[C(j)*ECS]
else, 0.
making 1/[C(0)*ECS] analogous to ‘C(space,j,n)’/C(0);
let k=-1 denote ‘space’, so C(-1,0,n) is the ‘heat capacity’ that is transfered from ‘space’ to the surface per unit time, where ‘space’ is at Teq. Maybe I should replace ‘space’ with ‘TOA’ … well, it’s an interesting mathematical analogy. Anyway, with that,
C(-1,0,n) = 1/ECS (units work out; ECS is in K/(W/m^2) and C is in J/(K*m^2*s), a heat capacity per unit area per unit time)
And then just make the second term in the T(j,n) equation a sum over k from -1 to ….
C(0) would vary if latent heat uptake varies over T or t (thus n), but we can let C(0) be constant and just have some additional C(k) with variable C(k,j,n) values to take care of that (but wouldn’t the temperature of those reservoirs always be equal to T(0,n) anyway?); the actual time constant of the response will be slower than the stated value due to the other reservoirs.
PS T is a temperature anomaly; hence in such a simplified model at equilibrium all T(j) are equal even though the actual temperatures vary. Of course this isn’t necessarily the case, but it’s a simple model.
re 626 Chris Korda
“Apparently Hansen originally had photos of his grandkids in the paper, but both anonymous referees upbraided him for that, understandably. The first referee also accused the paper of “excess verbosity”,”
3) The authors claim that the earth is warming, which is not. Surface is warming but the upper atmosphere is cooling equally to surface warming, and there is no energy imbalance.
not quite the whopper of the last point, but has he ever heard about the heat capacity of the ocean, or for that matter, the height of the tropopause (does he think it’s at 500 mb globally?). (I have encountered this misunderstanding elsewhere, including – or at least it could be understood that way – in Bryson and Murray’s “Climates of Hunger”)
In the hope that science precedes the bulldozers yet again:
“We had coffee with a self-effacing chap who’d discovered a number of hydrothermal vents in the North Atlantic (he fears the imminent deep-sea mining of polymetallic sulfides in international waters — says we’re “right on the edge” of that tech taking off).” A Land Where Even the Vomit Is Courteous
Anything the scientists would like to learn from that real estate before it’s leveled and scraped? Last call, last call.
Hm … Last Call
There’s a ring to it.
Anyone seen an open source journal of gone or going ecosystems?
Patrick 027says
re 627 Chris Korda – clarifications: I haven’t actually looked at the Hasen paper you were refering to. I’ve only been offering equations that are essentially a numerical integration of the differential equation that describes how a radiative disequilibrium will tend to decay with time. It’s a very, very simplified physics-based model.
Setting aside the effects of the deep ocean, etc, – ie just using a single unified reservoir’s heat capacity – and using only fast feedbacks (I didn’t introduce any slow feedbacks anywhere in this particular series of comments), the expectation based on physics is that each delayed response T curve (each of which must correspond to a different value of heat capacity, for the same ECS) must have a maximum or minimum when it intersects the instantaneous response curve (my Teq value) – maximum if it was below Teq before, minimum if it was above – because it is always going toward Teq. T is declining if greater than Teq, increasing if less than Teq. The slope of T is independent locally of the slope of Teq but is proportional to Teq-T.
#633–Oh, I don’t know, Patrick–I think that point is at least in training for the Golden Horseshoe. Certainly it is wildly wrong.
dhogazasays
Dan H:
It appears that climate change was the third rail in this year’s election. Both candidates could not get far enough away from it. When was the last time you heard two candidates vying for the title of “Oil King.”
Yes, Dan H, your side is winning, just as those in favor of burning witches in Salem “won”. Winning in the political arena will not stop physics, however. Enjoy it while you can, though. Personally I think we’ve passed the point of no return in the last two decades, and whatever hope there was for responding intelligently and with minimum impact has passed by. We’re in it to the end, at this point, for better or worse. And you’re emblematic of those responsible.
The way I implemented eqn. 3 was to take each year’s contribution to the instantaneous temperature (dF/dt) multiply that by the CRF (normalized to 1 rather than 100) and then add the CRF to all the remaining years as an array. Then go on to the next year’s contribution to the instantaneous temperature and do the same.
What I meant by Heaviside response is a step up in forcing, which I thought could figure in my head. For a step up, you should get the CRF back which I think you do. For the way I did it, dF/dt for the step function would be a Dirac delta function, so I would get the CRF back in one step with all future iterations adding nothing.
SecularAnimistsays
I have often imposed on the moderators’ patience by noting the rapid growth of solar and wind energy for electricity generation, which for me gives rise to optimism that we can eliminate GHG emissions from that sector much more quickly than many people believe.
For example, over the last five years, wind power has accounted for 35 percent of all new generating capacity added in the USA — second to natural gas, and more than coal and nuclear combined. Solar power is a much smaller part of new generation capacity, but is growing even more rapidly than wind, with new installations in the second quarter of 2012 increased 125 percent from the second quarter of 2011.
Now, some readers will think this is far-fetched, but I think that in the not-too-distant future the day will come when 100 percent of new electricity generation capacity added to the USA’s electric grid is wind and solar.
640 Prokaryotes , So nice to see Gavin on Frontline, his very a propos presentation was very short, like the attention he gets in the real world, while spot on precision gets overwhelmed by hysteria and fear which was fuelled by ignorance spewed by contrarians , Frontline showed that science doesn’t have a chance in the world of politics when an economic meltdown takes over the minds of many more inclined to believe in charlatans simply because they offer the peace of mind to be found in doing nothing. I guess in the end, extreme weather and climate will do all the talking while correct science the only worth while explaining.
This probably comes down to less cooling for the northern hemisphere as would occur otherwise in the instant of abrupt shutdown.
Jim Larsensays
643 SecularA said, ” when 100 percent of new electricity generation capacity added to the USA’s electric grid is wind and solar.”
Now weave that into your 15 year plan. Do the scales mesh? If so, great. If not, then you’re describing failure.
wilisays
SA wrote @ # 643: “the day will come when 100 percent of new electricity generation capacity added to the USA’s electric grid is wind and solar”
Of course, that day could come much sooner if we drastically reduced our rate of electric use, and became more flexible in when we used some of it.
But back to science–and communicating it: Hansen (in his TED talk and elsewhere) has said that the energy we add to the atmosphere through GHG’s every day is the equivalent of 400,000 Hiroshima bombs.
First, does that claim hold up?
2nd, is the energy that has been added to the oceans (equivalent to two Hiroshima bombs every two seconds for the last fifty years, according to a post at SkS) included in that calculation, or is that a separate total?
Finally, given that about 80% of the ghg’s are added as a direct or indirect result of the activities of the top billion or so consumers (am I at least in the ball park here?), wouldn’t that mean that each of those billion have added at least one-Hiroshima-bomb worth of energy to the atmosphere over the last decade? (More, perhaps, if the oceans are included?)
Thanks ahead of time for any corrections, comments, reactions…
Are these somewhat-reassuring results trustworthy? Or is the Atlantic circulation in today’s climate models intrinsically too stable? Our model intercomparison also addressed that question, using a neat little scalar metric known as Fov: the net amount of freshwater travelling from the AMOC to the South Atlantic.
The current thinking in physical oceanography is that the AMOC is more or less binary – it’s either “on” or “off”. When AMOC strength is below a certain level (let’s call it A), its only stable state is “off”, and the strength will converge to zero as the currents shut down. When AMOC strength is above some other level (let’s call it B), its only stable state is “on”, and if you were to artificially shut it off, it would bounce right back up to its original level. However, when AMOC strength is between A and B, both conditions can be stable, so whether it’s on or off depends on where it started. This phenomenon is known as hysteresis, and is found in many systems in nature.
Most observational estimates (largely ocean reanalyses) have Fov as slightly negative. If models’ AMOCs really were too stable, their Fov‘s should be positive. In our intercomparison, we found both positives and negatives – the models were kind of all over the place with respect to Fov. So maybe some models are overly stable, but certainly not all of them, or even the majority. http://climatesight.org/2012/10/24/climate-change-and-atlantic-circulation/#comments
Re Wili, regarding equivalent to Hiroshima bomb impact, imho i think this is to abstract for quantifying, mainly because of different pathways? But a good metaphor to explain the large impact from carbon footprints.
Russellsays
A propos of the consequences of fluctuating ocean currents, I was astonished to see that a recent Warner film atchive release dvd, Living on velvet features the dinner party discourse of a 1934 climate bore bent on blaming the dust bowl on the meandering of the Gulf Stream.
The way I implemented eqn. 3 was to take each year’s contribution to the instantaneous temperature (dF/dt) multiply that by the CRF (normalized to 1 rather than 100) and then add the CRF to all the remaining years as an array. Then go on to the next year’s contribution to the instantaneous temperature and do the same.
Your statement appears to fit the pseudo-code I gave in #610 very well. It seems we’re describing the same algorithm, albeit in different ways, so I’m going to assume we’re done and post the complete updated results below. Thank you Chris and Patrick for helping me with this project, which turned out to be a lot more than I bargained for! As I said in #626, Hansen et al. plan to apply their method to temperature projections in a future paper, so we’ll be able to compare to their results at some point.
This first group has one plot per RCP scenario, and shows how that RCP is affected by each of Hansen at al.’s Climate Response Functions: RCP3-PD, RCP4.5, RCP4.5-SCP, RCP6, RCP6-SCP, and RCP8.5. The second group has one plot per CRF, and shows that CRF’s effect on each of the RCPs: Slow, Intermediate, Fast, and Instantaneous. All of these plots are also available as a single PDF file. The C code can be viewed here, and a zip file containing the VC++ project and all input and output data is here.
Finally, to revisit the question originally posed @203: Assuming the IEO2011 Reference case of “1 trillion metric tons of additional cumulative energy-related carbon dioxide emissions between 2009 and 2035”, and given that this case equates to following RCP8.5 until 2035 as previously demonstrated @408, what increase in average global surface temperature relative to pre-industrial would result by 2035? Depending on CRF choice, the (updated) answers are 1.2ºC (slow), 1.5ºC (intermediate), or 1.7ºC (fast).
#594–Well-pointed, Wili. And there’s also some empirical data here:
http://www.sel.uaf.edu/manuscripts/069_beringer05.pdf
So you seem quite correct!
A video with Prof Jonathan Overpeck – Abrupt Climate Change “India special”
https://www.youtube.com/watch?v=pJlQPEswq8k
Chris @599: “You need to take the log sooner I think.” I understand you now. It’s an easy enough change to make so I’ll try it and we’ll see what happens. But otherwise does the iterative summing method I described seem reasonable?
Thanks for the link, wayne. It’s a complex process, but the near-term net effect of more tall bushes and trees in the tundra does seem to be more local warming.
On permafrost feedback in general, here is another fairly recent article:
http://www.biogeosciences.net/9/649/2012/bg-9-649-2012.html
(Thanks to prokaryotes for pointing it out on his new and excellent blog: http://climatestate.com/pure-climate-science/item/estimating-the-permafrost-carbon-feedback-on-global-warming.html)
One thing the full article makes clear is just how much carbon is available to the atmosphere from that one source:
“Cumulative CO2 emissions under RCP8.5 are 26PgC (12-52PgC) by 2100. By 2300, the majority of the permafrost carbon stock could be already released to the atmosphere, with cumulative CO2 emissions being 529 PgC (362-705PgC)”
Per Espen Stoknes possible new climate policies http://climatestate.com/images/Blog/2012/october/Per%20Espen%20Stoknes_possible_new_climate_policies.jpg
Full lecture on climate change and psychology http://climatestate.com/climate-state-blog/videos/item/why-climate-and-psychology-2.html
Chris (#603),
I’m not quite sure why you have taken the derivative of the CRF. Maybe pseudo code would help.
Chris Dudley: I made the “log sooner” change you proposed, and here are some results. I’m holding off on all the permutations until confidence is higher, I just enclose the ones that were most symptomatic. Here’s RCP3-PD, now and before. Here’s RCP8.5, now and before. And lastly here’s the triangle burst diagnostic, now and before. For RCP3-PD I don’t see much difference, but for RCP8.5 it’s obvious. I would describe it as a larger “spread” between the response functions. If nothing else this change makes the algorithm much simpler: it’s now reduced to a single step instead of two.
I get kind of tired of symbolic actions, but what the heck. Facebook users–especially American ones–may want to do this:
http://twibbon.com/support/end-climate-silence
Slightly off-topic, but still relevant. Italian seismologists are going to jail for not being able to predict an earthquake (http://www.theatlanticwire.com/global/2012/10/italian-seismologists-are-going-jail-not-being-able-predict-future/58203/). This news is full of irony. Earthquakes are not predictable while climate change is. So maybe all climatologists will be going to jail 20 years from now for not being able to predict the future? Sounds bizarre, but you never know.
Chris Dudley @606: “I’m not quite sure why you have taken the derivative of the CRF.”
Hmm, I thought that was the whole idea: to model inertia by distributing each year’s instantaneous temperature change over the next 2000 years, in unequal slices the sizes of which are determined by Climate Response Function percentages. But I could be grossly misunderstanding this! I’m usally OK once I have derivatives to work with, but math analysis gives me terrible headaches. Anyway here’s the pseudo code.
for (int iSamp = 0; iSamp < RCP_YEARS; iSamp++) { // for each yearly CO2 concentration sample in ppm
// compute instantaneous change in average global surface temperature, relative to baseline
InstantTemp = log(Concentration[iSamp] / Concentration[0]) / log(2) * ClimateSensitivity;
// distribute instantaneous temperature change over next 2000 years according to climate response function
PrevRespPct = 0;
for (int iYear = 0; iYear < 2000; iYear++) { // for each response function year
RespPct = gRespPct[iYear].Pct[RespFuncIdx]; // get this year's percentage from the response function
TempSlice = InstantTemp * (RespPct - PrevRespPct) / 100; // compute this year's slice of temperature
OutputTemperature[iSamp + iYear] += TempSlice; // add slice to appropriate temperature bucket
PrevRespPct = RespPct;
}
}
re: 609
I wish I could say I am being sarcastic when I say this but I suspect anti-science Ken Cuchinelli, the Virginia Attorney General, may be taking notes about the Italian seismologists case.
Did anyone has more info into the following ongoing research?
ESTIMATING THE PERMAFROST-CARBON FEEDBACK ON GLOBAL WARMING
A key uncertainty is the fraction of carbon that might be decomposed under anaerobic conditions – resulting potentially in methane emissions to the atmosphere. Given the high warming potential of methane, the overall magnitude of the permafrost-carbon feedback will depend strongly on this fraction. http://www.pik-potsdam.de/~anders/publications/schneider_meinshausen11.pdf
QUANTIFYING CLIMATE FEEDBACKS OF THE TERRESTRIAL BIOSPHERE UNDER THAWING PERMAFROST CONDITIONS IN THE ARCTIC http://climatemodeling.science.energy.gov/projects/quantifying-climate-feedbacks-terrestrial-biosphere-under-thawing-permafrost-conditions
Thermokarst Lakes as a Source of Atmospheric CH4 During the Last Deglaciation http://www.sciencemag.org/content/318/5850/633.abstract
Schneider-Meinshausen (per Scholar) is cited by 5; of those, one is cited by 15, and others have several cites apiece, so the paper “has grandchildren” — you’ve looked those up? I didn’t check the other one.
Climate Disruption: Are We Beyond the Worst Case Scenario?
Michael Jennings
Article first published online: 3 SEP 2012
DOI: 10.1111/j.1758-5899.2012.00193.x
© 2012 London School of Economics and Political Science and John Wiley & Sons Ltd
Re 610 Chris Korda –
A – I think they call it a ‘swamp ocean’, or maybe a slab ocean – heat capacity may be modelled (I won’t write it in computer code exactly; T is temperature, ECS is equlibrium climate sensitivity here expressed as K per doubling of CO2, y = year number):
Noting an analytical solution for constant forcing:
Teq – T = (Teq-T0)*exp(-t/time_constant)
dT/dt = (Teq-T0)*exp(-t/time_constant) / time_constant
@ t = 0, dT/dt = (Teq-T)/time_constant
which can be converted to an iteratable form:
T(y) = T(y-1) + 1 year * [Teq(y-1) – T(y-1)]/time_constant
or if time_constant is a dimensionless number that happens to be equal to the number of years of the time constant:
T(y) = T(y-1) + [Teq(y-1) – T(y-1)]/time_constant
or a bit more accurately, I think:
T(y) = T(y-1) + [Teq(y-1) + Teq(y) – T(y-1) – T(y)]/(2*time_constant)
which can be rewritten as
T(y)*[1 + 1/(2*time_constant)] = T(y-1) + [Teq(y-1) + Teq(y) – T(y-1)]/(2*time_constant)
or (if I did the algebra correctly)
T(y) = ( T(y-1)*2*time_constant + [Teq(y-1) + Teq(y) – T(y-1)] ) / [2*time_constant + 1]
where:
Teq(y) = ECS * log( CO2concentration(y) )/log(2)
Alternative – (where n is the number of time steps – time_step could be less than a year; time_step must be in same units as time_constant):
T(n) = T(n-1) + [Teq(n-1) – T(n-1)]*time_step/time_constant
Now add a deep ocean (a very simple one)
T(n)
=
T(n-1) + [Teq(n-1) – T(n-1)] * time_step / time_constant
+
[ average (j = n-5000 to n-1 or whatever works) of ( T(j) * exp[-(n-j) * time_step / mix_time] ) – T(n-1) ] * time_step / mix_time
… I’m not sure if that last part entirely makes physical sense – it makes some qualitative sense but I’d have to do some more work to see if it ought to be changed – does it violate energy conservation? … I haven’t actually tried doing this.
re wili (re Chris Colose) @ 594 “You seem to think of the point when feedbacks exceed human forcing is just an arbitrary point. Chu and many others don’t.” – I missed that point earlier. What I meant (what I thought you meant) by Chuvian runaway was a runaway of an extent more limited (covering a smaller range of temperatures that can’t be at equilibrium) than the big ice-albedo and H2O-vapor greenhouse runaway feedbacks of snowball and ‘steamball’ conditions. (non-Planck) Feedbacks in W/m^2 exceeding forcing is I think already expected just from the fast feedbacks.
correction for second-to-last comment:
Teq(y) = ECS * log[ CO2concentration(y) / CO2concentration(baseline) ]/log(2)
Re Chris Korda – (last part of my third-to-last comment) – it will be much easier if the deep ocean temperature (or multiple such thermal reservoirs)is explicitly computed iteratively. More on that later…
Re wili – “Feedbacks in W/m^2 exceeding forcing is I think already expected just from the fast feedbacks.” – at least when equilibrium is approached; not sure offhand about right now.
Patrick: Thank you! It seems like we’re on the same page. Your simplified equation @617 looks very similar to the pseudocode I gave @610 no? I’m just applying Hansen’s response functions to this equation. Or maybe I’m missing your point, if so please forgive my obtuseness!
Antarctic land ice loss rate refined:
http://www.sciencedaily.com/releases/2012/10/121022093146.htm
Slow, but steady.
Chris (#610),
Well, it looks as though it reproduces the Heaviside response. And, is also seems like a term in an integration by parts expansion of equation 3. But, why not follow equation 3 instead?
The guys on “The Climate Show” seem pretty concerned about the permafrost feedback study (covered at about the 11 minute mark):
http://www.theclimateshow.com/the-climate-show-29-if-the-sun-dont-come-you
Bojan #609
“So maybe all climatologists will be going to jail 20 years from now for not being able to predict the future? Sounds bizarre, but you never know.”
Maybe if they fail to warn people and politicians with sufficient clarity.
On the other hand, those people who have been trying (with some success) to minimize the perceived risk from climate change might find themselves with a case to answer
Was I disappointed?
Oh, yeah. Elections are about important issues–well, some of them, anyway:
http://doc-snow.hubpages.com/hub/Not-One-Word
re 619 Chris Korda – yes, that part is exactly the same.
The Atmospheric Chemistry and Physics discussion page for “Earth’s Energy Imbalance and Implications” makes for surprisingly interesting reading. Hansen et al. took a few punches but I guess that’s par for the course. Apparently Hansen originally had photos of his grandkids in the paper, but both anonymous referees upbraided him for that, understandably. The first referee also accused the paper of “excess verbosity”, ouch. More interestingly, in response to the second referee’s objection that older SRES scenarios were used instead of the new RCP scenarios, Hansen replied: “Our paper compares observations (thus the past) and models, thus only deals with the past. It is of interest to see how the real world changes compare with the past projections. In a future paper when we replot Figure 16 in conjunction with our simulations for the future we can use the new RCP scenarios, but for this paper the old SRES scenarios are more relevant.” So it seems my wish for RCP temperature projections might someday be granted.
But the most entertaining critic is one Nabil Swedan, who lobs such gems as “The subject paper is based on other flawed papers that were challenged. Authors of the subject paper have not addressed the comments of challengers yet,” and “The subject paper is based on the greenhouse gas effect science that is unrecognized by Russians, Chinese, Indians, and much of the west.” Holy smokes! And the crescendo: “… the subject paper … does not follow the scientific methodology of proof, it disagrees with observations, it is based on flawed referenced papers, and it utilizes a flawed science that is unrecognized by most of the world.” What happened here? Do the Koch brothers have a mole in the European Geosciences Union?
Chris Dudley @621: Despite considerable effort I still haven’t figured out how to apply the interpolated Climate Response Functions directly to equation 3. If you feel sufficiently inspired to offer up some pseudocode of your own I would gladly give it a shot. But what’s your response to the results I gave at @607 using your “log sooner” fix? With respect to the “electric burner” analogy we were discussing, are the new results better or worse? Heaviside is a type of Green’s function so that’s encouraging. Between you and Patrick I get the impression that I’ve implemented something functionally equivalent to equation 3, by differentiating the Climate Response Functions. It might be the hard way but that’s OK with me if it gives acceptable results.
Kevin,
It appears that climate change was the third rail in this year’s election. Both candidates could not get far enough away from it. When was the last time you heard two candidates vying for the title of “Oil King.”
re Chris Korda – including a deep ocean
non-conveyor belt version
C is the more immediately accessible heat capacity of the near-surface climate system, including (largely made from) some upper portion of the ocean
Cdeep is the heat capacity of the deep ocean
Cexchange is a measure of the rate of exchange between the upper and deeper ocean
Thus, in isolation
Let
C_step = time_step*Cexchange
T(n) = T(n-1)*(1 – C_step/C) + C_step/C * Tdeep(n-1)
= T(n-1) + [Tdeep(n-1) – T(n-1)] *C_step / C
The second term of that can simply be added to the formula for T(n) that includes climate forcing+feedback effects, so that
T(n)
=
T(n-1)
+
[Teq(n-1) – T(n-1)]*time_step/time_constant
+
[Tdeep(n-1) – T(n-1)] *C_step / C
and the temperature of the deep ocean
Tdeep(n) = Tdeep(n-1)*(1 – C_step/Cdeep) + C_step/Cdeep * T(n-1)
or
Tdeep(n) = Tdeep(n-1) + [T(n-1) – Tdeep(n-1)]* C_step/Cdeep
Conveyor model:
generalize to a surface thermal reservoir C(0) and multiple other reservoirs C(j), j = 1 through ?, C_step(j,k,n) = time_step*C(j,k,n) is the reservoir size that is transfered from reservoir j to reservoir k in the time step going from n-1 to n. C(j,k,n) may be larger than C(k,j,n), hence one can have a conveyor-like aspect
(although having each transfer being dumped and mixed into the reservoir still provides a mixing like aspect. A true conveyor would have reservoirs being produced from surface water and then being stored and then brought back to the surface at some time… etc..)
However, in order for all C(j) to stay constant over n (otherwise use C(j,n), for each j, the sum of all C(j,k,n) over k must equal the sum of all C(k,j,n) over k. Otherwise, maybe this would work:
C(j,n) = C(j,n-1) + sum over k of [C(k,j,n) – C(j,k,n)]
Then … (in isolation of the climate forcing+feedback):
T(j,n) = T(j,n-1)*(1 – sum over k of C_step(k,j,n)/C(j)) + sum over k of T(k,n-1)*C_step(k,j,n)/C(j)
A little algebra and adding the climate forcing+feedback term:
T(j,n)
=
T(j,n-1)
+
sum over k:
[T(k,n-1) – T(j,n-1)]* C_step(k,j,n)/C(j)
+
if j=0:
[Teq(n-1) – T(0,n-1)]*time_step/time_constant
else, 0.
Could be an interesting week next week …
Will soon-to-be Hurricane Sandy hit the northeastern USA as a super-storm of historic proportions, like Katrina and Irene rolled in to one — perhaps inundating New York City with the massive storm surge that Irene almost delivered last year …
While at the same time, hyperactive sunspot region AR1598 unleashes a gigantic coronal mass ejection directly at the Earth, triggering a Harrington-class geomagnetic storm that shuts down the entire North American electric grid for days or weeks .. or months …
… just days before a presidential election?
Please check my maths to see if I am at least roughly in the right ball park. Hansen has claimed (in his TED talk and elsewhere) that our emissions of ghgs are adding energy to the atmosphere equivalent to 400,000 Hiroshima bombs every day.
If we multiply that over ten years, and figure that the top billion or so of world population is responsible for the lion’s share (say 80%) of the emissions, could we then conclude that, on average, every member of that top billion (presumably including all on this forum) had contributed the energy equivalent of one Hiroshima bomb (or more) toward atmospheric global warming over the last decade?
Thanks ahead of time for corrections, tweaks, reactions, thoughts…
(reCaptcha has gone French, sort of: licyeen sevire)
note: time_constant = C*ECS or (with the last version above) C(0) * ECS, the 0 refering to j. But for this, it is best to give ECS in terms of K per W/m^2 rather than per doubling of CO2. (C would be in terms of J/(K*m^2), a heat capacity per unit area (global average). See https://www.realclimate.org/index.php/archives/2012/07/unforced-variations-july/comment-page-8/#comment-241456
Let the forcing per doubling of CO2 be ECSdoubling ~= (from memory) 3.7 W/m^2 * ECS, then:
Teq(y) = ECSdoubling * log[ CO2concentration(y) / CO2concentration(baseline) ]/log(2)
T(j,n)
=
T(j,n-1)
+
sum over k (forgot this earlier: k=0 to ?, except for k=j):
[T(k,n-1) – T(j,n-1)]* C_step(k,j,n)/C(j)
+
if j=0:
[Teq(n-1) – T(0,n-1)]*time_step/[C(j)*ECS]
else, 0.
making 1/[C(0)*ECS] analogous to ‘C(space,j,n)’/C(0);
let k=-1 denote ‘space’, so C(-1,0,n) is the ‘heat capacity’ that is transfered from ‘space’ to the surface per unit time, where ‘space’ is at Teq. Maybe I should replace ‘space’ with ‘TOA’ … well, it’s an interesting mathematical analogy. Anyway, with that,
C(-1,0,n) = 1/ECS (units work out; ECS is in K/(W/m^2) and C is in J/(K*m^2*s), a heat capacity per unit area per unit time)
And then just make the second term in the T(j,n) equation a sum over k from -1 to ….
C(0) would vary if latent heat uptake varies over T or t (thus n), but we can let C(0) be constant and just have some additional C(k) with variable C(k,j,n) values to take care of that (but wouldn’t the temperature of those reservoirs always be equal to T(0,n) anyway?); the actual time constant of the response will be slower than the stated value due to the other reservoirs.
PS T is a temperature anomaly; hence in such a simplified model at equilibrium all T(j) are equal even though the actual temperatures vary. Of course this isn’t necessarily the case, but it’s a simple model.
re 626 Chris Korda
“Apparently Hansen originally had photos of his grandkids in the paper, but both anonymous referees upbraided him for that, understandably. The first referee also accused the paper of “excess verbosity”,”
Just imagine the new one they would of torn G&T!
… wow, point 3 of Nabil Swedan
http://www.atmos-chem-phys-discuss.net/11/C11464/2011/acpd-11-C11464-2011.pdf
not quite the whopper of the last point, but has he ever heard about the heat capacity of the ocean, or for that matter, the height of the tropopause (does he think it’s at 500 mb globally?). (I have encountered this misunderstanding elsewhere, including – or at least it could be understood that way – in Bryson and Murray’s “Climates of Hunger”)
In the hope that science precedes the bulldozers yet again:
“We had coffee with a self-effacing chap who’d discovered a number of hydrothermal vents in the North Atlantic (he fears the imminent deep-sea mining of polymetallic sulfides in international waters — says we’re “right on the edge” of that tech taking off).”
A Land Where Even the Vomit Is Courteous
Anything the scientists would like to learn from that real estate before it’s leveled and scraped? Last call, last call.
Hm … Last Call
There’s a ring to it.
Anyone seen an open source journal of gone or going ecosystems?
re 627 Chris Korda – clarifications: I haven’t actually looked at the Hasen paper you were refering to. I’ve only been offering equations that are essentially a numerical integration of the differential equation that describes how a radiative disequilibrium will tend to decay with time. It’s a very, very simplified physics-based model.
Setting aside the effects of the deep ocean, etc, – ie just using a single unified reservoir’s heat capacity – and using only fast feedbacks (I didn’t introduce any slow feedbacks anywhere in this particular series of comments), the expectation based on physics is that each delayed response T curve (each of which must correspond to a different value of heat capacity, for the same ECS) must have a maximum or minimum when it intersects the instantaneous response curve (my Teq value) – maximum if it was below Teq before, minimum if it was above – because it is always going toward Teq. T is declining if greater than Teq, increasing if less than Teq. The slope of T is independent locally of the slope of Teq but is proportional to Teq-T.
#633–Oh, I don’t know, Patrick–I think that point is at least in training for the Golden Horseshoe. Certainly it is wildly wrong.
Dan H:
Yes, Dan H, your side is winning, just as those in favor of burning witches in Salem “won”. Winning in the political arena will not stop physics, however. Enjoy it while you can, though. Personally I think we’ve passed the point of no return in the last two decades, and whatever hope there was for responding intelligently and with minimum impact has passed by. We’re in it to the end, at this point, for better or worse. And you’re emblematic of those responsible.
Biologists Record Increasing Amounts of Plastic Litter in the Arctic Deep Sea
http://www.sciencedaily.com/releases/2012/10/121023101029.htm
Need a plastic which decomposes in seawater.
Oxygen’s Ups and Downs in Early Atmosphere and Ocean
http://www.sciencedaily.com/releases/2012/10/121023134812.htm
Paleoclimate more complex than earlier thought.
Frontline: Climate of Doubt #public #opinion #denial https://www.youtube.com/watch?v=A5GVHqlnPAc&feature=vmdshb
I wrote (#630): “… a Harrington-class geomagnetic storm …”
Oops, sorry, that should be Carrington.
Chris (#627),
The way I implemented eqn. 3 was to take each year’s contribution to the instantaneous temperature (dF/dt) multiply that by the CRF (normalized to 1 rather than 100) and then add the CRF to all the remaining years as an array. Then go on to the next year’s contribution to the instantaneous temperature and do the same.
What I meant by Heaviside response is a step up in forcing, which I thought could figure in my head. For a step up, you should get the CRF back which I think you do. For the way I did it, dF/dt for the step function would be a Dirac delta function, so I would get the CRF back in one step with all future iterations adding nothing.
I have often imposed on the moderators’ patience by noting the rapid growth of solar and wind energy for electricity generation, which for me gives rise to optimism that we can eliminate GHG emissions from that sector much more quickly than many people believe.
For example, over the last five years, wind power has accounted for 35 percent of all new generating capacity added in the USA — second to natural gas, and more than coal and nuclear combined. Solar power is a much smaller part of new generation capacity, but is growing even more rapidly than wind, with new installations in the second quarter of 2012 increased 125 percent from the second quarter of 2011.
Now, some readers will think this is far-fetched, but I think that in the not-too-distant future the day will come when 100 percent of new electricity generation capacity added to the USA’s electric grid is wind and solar.
I don’t think it’s far-fetched — because actually, that day has already come.
640 Prokaryotes , So nice to see Gavin on Frontline, his very a propos presentation was very short, like the attention he gets in the real world, while spot on precision gets overwhelmed by hysteria and fear which was fuelled by ignorance spewed by contrarians , Frontline showed that science doesn’t have a chance in the world of politics when an economic meltdown takes over the minds of many more inclined to believe in charlatans simply because they offer the peace of mind to be found in doing nothing. I guess in the end, extreme weather and climate will do all the talking while correct science the only worth while explaining.
Abrupt shutdown of Atlantic Meridional Overturning Circulation due to global warming seems unlikely http://www.agu.org/pubs/crossref/2012/2012GL053763.shtml
This probably comes down to less cooling for the northern hemisphere as would occur otherwise in the instant of abrupt shutdown.
643 SecularA said, ” when 100 percent of new electricity generation capacity added to the USA’s electric grid is wind and solar.”
Now weave that into your 15 year plan. Do the scales mesh? If so, great. If not, then you’re describing failure.
SA wrote @ # 643: “the day will come when 100 percent of new electricity generation capacity added to the USA’s electric grid is wind and solar”
Of course, that day could come much sooner if we drastically reduced our rate of electric use, and became more flexible in when we used some of it.
But back to science–and communicating it: Hansen (in his TED talk and elsewhere) has said that the energy we add to the atmosphere through GHG’s every day is the equivalent of 400,000 Hiroshima bombs.
First, does that claim hold up?
2nd, is the energy that has been added to the oceans (equivalent to two Hiroshima bombs every two seconds for the last fifty years, according to a post at SkS) included in that calculation, or is that a separate total?
Finally, given that about 80% of the ghg’s are added as a direct or indirect result of the activities of the top billion or so consumers (am I at least in the ball park here?), wouldn’t that mean that each of those billion have added at least one-Hiroshima-bomb worth of energy to the atmosphere over the last decade? (More, perhaps, if the oceans are included?)
Thanks ahead of time for any corrections, comments, reactions…
Some analysis discussion…
Climate Change and Atlantic Circulation
Are these somewhat-reassuring results trustworthy? Or is the Atlantic circulation in today’s climate models intrinsically too stable? Our model intercomparison also addressed that question, using a neat little scalar metric known as Fov: the net amount of freshwater travelling from the AMOC to the South Atlantic.
The current thinking in physical oceanography is that the AMOC is more or less binary – it’s either “on” or “off”. When AMOC strength is below a certain level (let’s call it A), its only stable state is “off”, and the strength will converge to zero as the currents shut down. When AMOC strength is above some other level (let’s call it B), its only stable state is “on”, and if you were to artificially shut it off, it would bounce right back up to its original level. However, when AMOC strength is between A and B, both conditions can be stable, so whether it’s on or off depends on where it started. This phenomenon is known as hysteresis, and is found in many systems in nature.
Most observational estimates (largely ocean reanalyses) have Fov as slightly negative. If models’ AMOCs really were too stable, their Fov‘s should be positive. In our intercomparison, we found both positives and negatives – the models were kind of all over the place with respect to Fov. So maybe some models are overly stable, but certainly not all of them, or even the majority. http://climatesight.org/2012/10/24/climate-change-and-atlantic-circulation/#comments
Re Wili, regarding equivalent to Hiroshima bomb impact, imho i think this is to abstract for quantifying, mainly because of different pathways? But a good metaphor to explain the large impact from carbon footprints.
A propos of the consequences of fluctuating ocean currents, I was astonished to see that a recent Warner film atchive release dvd, Living on velvet features the dinner party discourse of a 1934 climate bore bent on blaming the dust bowl on the meandering of the Gulf Stream.
Chris Dudley (#642):
Your statement appears to fit the pseudo-code I gave in #610 very well. It seems we’re describing the same algorithm, albeit in different ways, so I’m going to assume we’re done and post the complete updated results below. Thank you Chris and Patrick for helping me with this project, which turned out to be a lot more than I bargained for! As I said in #626, Hansen et al. plan to apply their method to temperature projections in a future paper, so we’ll be able to compare to their results at some point.
This first group has one plot per RCP scenario, and shows how that RCP is affected by each of Hansen at al.’s Climate Response Functions: RCP3-PD, RCP4.5, RCP4.5-SCP, RCP6, RCP6-SCP, and RCP8.5. The second group has one plot per CRF, and shows that CRF’s effect on each of the RCPs: Slow, Intermediate, Fast, and Instantaneous. All of these plots are also available as a single PDF file. The C code can be viewed here, and a zip file containing the VC++ project and all input and output data is here.
Finally, to revisit the question originally posed @203: Assuming the IEO2011 Reference case of “1 trillion metric tons of additional cumulative energy-related carbon dioxide emissions between 2009 and 2035”, and given that this case equates to following RCP8.5 until 2035 as previously demonstrated @408, what increase in average global surface temperature relative to pre-industrial would result by 2035? Depending on CRF choice, the (updated) answers are 1.2ºC (slow), 1.5ºC (intermediate), or 1.7ºC (fast).