## Steve Koonin and the small percentage fallacy

Steve Koonin had an op-ed in the Wall Street Journal a while ago called Climate science is not settled. He was also involved in initial attempts by the American Physical Society to draft a statement on climate science that Judith Curry discussed in a post a day or so ago. Judith seemed to think that his departure from the committee drafting the statement meant noone left understood things properly.

I pointed out that this seemed unlikely given how poor his article was. What I highlighted was the following.

For example, human additions to carbon dioxide in the atmosphere by the middle of the 21st century are expected to directly shift the atmosphere’s natural greenhouse effect by only 1% to 2%. Since the climate system is highly variable on its own, that smallness sets a very high bar for confidently projecting the consequences of human influences.

Interestingly, Steve Koonin has now authored a guest post on Judith’s blog, trying to explain what he meant. It all seems a little odd to me.

Typically the natural greenhouse effect is regarded as increasing effective surface temperatures by 33K, or producing a radiative forcing of 120Wm-2 (or 150Wm-2 depending on how you measure it). By the middle of the 21st century, temperatures will be expected to have risen by between 1.5oC and 2.5oC, and the net change in radiative forcings plus feedbacks will be between 6.5Wm-2 and 9.5Wm-2. So, by a standard measure the enhanced greenhouse effect will have amplified the natural greenhouse effect by between 4.5% and 7.5%, much more than the 1% to 2% claimed by Koonin.

Now, it seems that he’s decided to measure relative to a base temperature of 288K, or relative to a net downward flux at the surface of 503Wm-2. These numbers may be right, but neither would typically be regarded as a normal way to quantify the natural greenhouse effect. So, yes, relative to these numbers, it is a small change, but this isn’t the standard way to quantify the greenhouse effect and these small numbers don’t really tell you anything as to the significance of this. I did try to point this out in the comments and then made a rookie ClimateballTM mistake by trying to illustrate that even an extreme change would be regarded as small relative to these quantities. For example, a 10oC increase in surface temperature would probably make the planet uninhabitable for mammals, but would only be a 3% to 4% shift according to Koonin’s metric. Of course, I then got accussed of exaggerating etc. and everything went downhill from there.

Anyway, I’ve rambled as I normally do. What I really wanted to do was highlight an exchange, between Steve Koonin and Isaac Held, in the minutes (starting on page 433) from the Climate Change Review Workshop – held last year – of the American Physical Society (H/T Willard – I don’t know how he finds these things). It’s an interesting exchange in it’s own right, but is also relevant to this discussion (the bolds are mine).

DR. HELD: …..Some of the questions that came through in your background document I thought were a little off, if I can be frank —

DR. KOONIN: That’s fine. We are not experts.

DR. HELD: — in the sense that they don’t conform to my picture of how the climate system works. So, I have my null hypotheses. And I have been doing this for over 30 years, so I have developed a lot of hypotheses. Some of them turn out to be wrong. I don’t like this argument from complexity saying oh, it’s a chaotic system. There is all sorts — you can get a nonlinear system to do nything you want. That just doesn’t tell me anything. But whenever I look at the forced response of the climate system, it looks linear to me. And what is the best example we have of forced responses? The seasonal cycle. Seasonal cycles are remarkably linear-looking.

I grew up in Minneapolis which is why I plotted Minneapolis here. [next page] I just repeated it twice for clarity. This is just the seasonal cycle. It’s almost perfectly inside the squiggle. There is an awful lot of nonlinear fluid dynamics and cloud formation stuff going on underneath this. My analogy here is the thermodynamic limit of statistical mechanics. The smaller response, you seem to worry about the fact that the external forcing is so small, but that just makes it more likely to be linear.

DR. KOONIN: Although, in real thermodynamics, since you have a good separation of scale, there is a small parameter or a big parameter, right? The size of the atoms or the number of atoms or something?

DR. HELD: I am not saying it is as good as thermodynamics, but that’s my underlying picture. One other example of forced response that Dick referred to, we have Milankovitch. We don’t have anything really in between — I mean, we have the sunspots, but that’s hard to see, it’s so small. So, we have the seasonal cycle and Milankovitch. Those are both changes in our orbit. And that looks pretty linear, too, at least in the sense that you see the periods of the orbital changes coming out.

DR. KOONIN: If you take a given model, one of the ones in the middle of the pack, and start doing the linear study on one or several of the forces, start cranking up the solar constant or the aerosol loading or CO2, does it behave in a linear way?

DR. HELD: Yes.

DR. KOONIN: Over the range of what we are talking about?

DR. HELD: A lot of people looked at that. It’s very linear.

DR. COLLINS: Yes, it is very linear.

DR. HELD: The whole language, the whole forcing-feedback language we look at is assuming that this linear picture is useful. Otherwise, what is forcing and what is feedback? I don’t even know where to start.

DR. COLLINS: At the risk of breaking protocol, may I?

DR. KOONIN: Yes.

DR. COLLINS: You can force the model separately with different forcing agents, look at the separate response, add the response and then add the forcings and compare the total response to the total forcings. That has been done ad nauseam, not a problem.

DR. HELD: The models look pretty linear. The observed seasonal cycle, that looks linear. Even if in the Ice Age times, things look pretty linear. We don’t know that much about it. So, why should I assume that things are, gee, the anthropogenic CO2 pulse is going to interact in some exotic way with internal modes of variability? Well, it’s conceivable. But I am not convinced. I don’t think that is particularly relevant.

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### 106 Responses to Steve Koonin and the small percentage fallacy

1. This post got rather convoluted (as usual) so I’ll add a comment to point something out. What Isaac Held says in the exchange seems fairly obvious to me. If I have a complex, dynamical systems and then apply an external force, the system will respond to that force through $F = ma$. It doesn’t matter that the underlying dynamics is complex, or chaotic. So, if the forcing/feedback paradigm has merit – in the sense that we can regard external influences as applying a force to the system – then the underlying chaotic nature shouldn’t have much impact on how the overall system responds to that force. It will clearly influence the internal dynamics, but not the overall response.

As Isaac Held points out, our seasonal variations are a great example of this. We’re very confident about the typical weather at different times of the year at any location on the planet, despite the fact that the underlying dynamics of the climate system is very complex.

2. GSR says:

Do we know from the transcripts if these discussions were part of the proceedings in which Curry was involved? If she was present then it appears that she has misrepresented to the tenor of the discussions.

3. GSR,
Yes, she was involved.

4. John Hartz says:

ATTP: If you are from Minneapolis, why do you spell the word, “rookie” as “rooky.”? 🙂

5. Willard says:

It came from Hank Roberts at Eli’s, AT. His own quote:

DR. HELD: I think you [Koonin] are getting the concept of radiative forcing wrong.

http://rabett.blogspot.com/2014/02/like-lambs-to-slaughter.html

***

Another interesting bit:

DR HELD: No — well, yes, they are. I’m sorry. They are both in chapter 10 of AR5. In fact, they are both right next to each other in the summary of chapter 10. And so, for people who read chapter 10, these are two different statements. And it’s discussed in some detail in chapter 10.

DR. CURRY: The issue is what showed up in the summary for policymakers.

DR. LINDZEN: And the press release.

DR. CURRY: And the press release, yes.

DR. KOONIN: That’s not science, but it’s important.

Judy, Dick, and Steve talk about press releases while Isaac would rather stick to the science.

You can’t make this up.

***

Compare and contrast with:

Unfortunately, the necessary brevity and non-technical nature of a newspaper article has created some confusion about what I meant and how I arrived at the 1-2% figure.

http://judithcurry.com/2015/04/08/are-human-influences-on-the-climate-really-small/

6. John Hartz says:

ATTP: Are you or Willard responible for the bolded sentences of the section of committee minutes you have included in the OP?

7. JH,
Yes, it was me. I did say “(bolds are mine)” in the OP.

8. John Hartz says:

9. Willard says:

Open the damn document, JH. Search for the damn quote. Scratch your own damn itch.

It’s a transcript. It’s in monotext.

Searching for “Held:” with the “:” might be fun

10. Joshua says:

I light of the discussion with Judith at her crib about how to define “expertise,” I found this kind o’ interesting:

DR. KOONIN: That’s fine. We are not experts.

Now that there seems to me like something that you couldn’t make up.

11. John Hartz says:

Willard: You might want to remove that bur from underneath your saddle. If you do, it will be easier for you to ride your high horse.

12. jsam says:

It strikes me as a variation of the “but it’s just a trace gas” meme.

13. izen says:

Quantifying the metric of AGW as a percentage in the way that Kooning favour seems vaguely analogous with minimising the problem of weight gain in middle age by comparing the change with the total change in weight over a lifetime from birth to adulthood.

14. If I ever get a speeding ticket, I will simply argue that compared to the speed of the Earth around the Sun, I was barely moving.

15. John Hartz says:

The analysis presented in the following article directly relates to the positions espoused by Held and Collins in the above OP.

If We Dig Out All Our Fossil Fuels, Here’s How Hot We Can Expect It to Get by Michael Greenstone*, The Upshot, News York Times, Apr 8, 2015

Here’s the operative paragraph about methodology from Greenstone’s article,

To understand the scope of this challenge, I’ve tallied the projected warming from fossil fuels extracted so far and the projected warming capacity of various fossil fuels that can be extracted with today’s technology. This accounting was done by taking the embedded carbon dioxide in each energy source and using a standard model for the relationship between cumulative carbon emissions and long-run temperature changes based on a 2009 Nature article. (More detail on the method is available here.)

*Michael Greenstone, the Milton Friedman professor of economics at the University of Chicago, runs the Energy Policy Institute there. He was the chief economist of President Obama’s Council of Economic Advisers from 2009 to 2010.

16. Eli Rabett says:

In Koonin World there is zero CO2 in the atmosphere and the Sun don’t shine. His baseline is beneath contempt

17. Brandon Gates says:

ATTP,

Typically the natural greenhouse effect is regarded as increasing effective surface temperatures by 33K, or producing a radiative forcing of 120Wm-2 (or 150Wm-2 depending on how you measure it).

150 W/m^2 is the number I have mesmerized from the RC post “The CO2 Problem in Six Easy Steps”: http://www.realclimate.org/index.php/archives/2007/08/the-co2-problem-in-6-easy-steps/

I was not aware of alternative measurements/calculations. Pointers to where I could read up?

18. Brandon,
Okay, I think the two numbers come via this. If you consider the surface (which would be the TOA in the absence of an atmosphere) then the outgoing flux is about 150W/m^2 higher than it would be in the absence of a greenhouse effect. On the other hand, today, a 1K increase in surace temperature produces about a 3.7W/m^2 increase in outgoing flux (or, alternatively, a 3.7W/m^2 radiative perturbation would be associated with about a 1K increase in surface temperature). So, 33 x 3.7 = 120 W/m^2. Therefore, I think it depends on whether you quantify it in terms of the increase in surface flux relative to there being no greenhouse effect, or quantify it relative to the radiative forcing that would produce a 33K increase in surface temperature, relative to the TOA today. Or, I could be confused myself, as I have struggled a bit with this myself at times.

19. From the transcripts:

DR. KOONIN: Clarification: the models don’t get the timing of ENSO?
DR. CURRY: Yes, even with initialization and the decadal simulations, it looks like there is
some predictability of the Atlantic multidecadal oscillation, maybe out to ten years, but Pacific
DR. KOONIN: It’s not in the model?
DR. CURRY: Yes, just fell apart. So, apart from ENSO, I mean, the other modes, the longer modes, the Atlantic multidecadal oscillation, Pacific decadal variability are important ones on time scales that we were concerned about, and also the stadium wave, which I will mention in a minute.

#WHUT the ? is Curry talking about? Is that pure gibberish?

The fact of the matter is that ENSO is a easily understood as a solution to a perturbed wave equation. The last 130+ years of ENSO behavior as characterized by the Southern Oscillation Index is trivially modeled with the known forcings applied.

20. pbjamm says:

Wow. That exchange read like a very long round-about way of saying “And there is physics…”

“So, why should I assume that things are, gee, the anthropogenic CO2 pulse is going to interact in some exotic way with internal modes of variability? Well, it’s conceivable. But I am not convinced. I don’t think that is particularly relevant.”

Beauty

21. Brandon Gates says:

ATTP,

Thanks, I think that gives me enough search terms to ask Google. My maths aren’t the best in the world, but even I can see that a 30 W/m^2 difference wants explanation. Since log CO2 graphs are topical today, here is my all-time favourite numbskull plot from the small-number fallacy crowd:

The underlying function is 0.5 ln(CO2) with a little calculus thrown in to make the numbers itty bitty.

22. afeman says:

For a real treat in that transcript, search for “magnet”.

23. The Very Reverend Jebediah Hypotenuse says:

…and Then There’s Physics says:
April 9, 2015 at 1:37 pm

If I ever get a speeding ticket, I will simply argue that compared to the speed of the Earth around the Sun, I was barely moving.

Compared to the speed of stupid, you were stationary.

24. Of course since Held and I are both from the progressive state of Minnesota, we agree with his optimistic statement ” I don’t like this argument from complexity saying oh, it’s a chaotic system. “. Resigning to the argument of the intractability of chaos is equivalent to punting the football on first-down — you don’t even give yourself a fighting chance.

A group of us over at the Azimuth Project forum are making real progress in isolating the deterministic components of the seeming chaotic El Nino Souther Oscillation system. It’s eye-opening basic physics, simple to formulate, but you need to be able to numerically solve a differential equation.

25. Brandon Gates says:

Too Right Rev. Hippocampus,

I believe you’ve inspired me to change the y-axis of the graph I just posted to IQ.

26. Brandon sussed it out:

The underlying function is 0.5 ln(CO2) with a little calculus thrown in to make the numbers itty bitty.

Whichever skeppy drew that graph knows the fine art of lying through visualization.
#WHUT the FUD ?

27. Brandon,
Here’s one way to get the numbers. If you consider the full greenhouse effect, then you can determine the radiative effect as

$\sigma(288^4 - 255^4) = 150$ Wm-2.

So, that gives you the number that Realclimate quote. An alternative way to estimate the relationship between radiative forcing and temperature is to use

$\dfrac{dF}{dT} = 4 \sigma T^3 \Rightarrow dF = 4 \sigma T^3 dT$.

So, if you assume that TOA temperature is $T = 255$ K and use $dT = 33$ K, then you get 124Wm-2.

28. So, if you assume that TOA temperature is T = 255 K and use dT = 33 K, then you get 124Wm-2.

Good, but with one modification: not the ‘TOA temperature’ but the ‘Effective Radiating Temperature’. ( TOA temperature is much closer to 0K )

Also, the 288K is what we observe, but that includes, as you’ve noted, the effects of atmospheric motion, so the radiative surface temperature, for radiative comparison would be closer to 345K:

These numbers are calculable but hypothetical because the atmosphere won’t sit still.

That’s also why the concept of Radiative Forcing is also hypothetical.
That’s why the AR5 introduced a new concept ‘Effective’ Radiative Forcing, meaning what’s actually happening but that we can’t measure:

29. Damn it, here you go ‘ERF’:

30. Eddie,

Good, but with one modification: not the ‘TOA temperature’ but the ‘Effective Radiating Temperature’.

Okay, fine.

Also, the 288K is what we observe, but that includes, as you’ve noted, the effects of atmospheric motion, so the radiative surface temperature, for radiative comparison would be closer to 345K:

Yes, true.

That’s also why the concept of Radiative Forcing is also hypothetical.
That’s why the AR5 introduced a new concept ‘Effective’ Radiative Forcing, meaning what’s actually happening but that we can’t measure:

As I understand it, the difference is whether or not you let the stratosphere adjust.

31. Regarding Isaac Held’s comments on linear response, particularly with respect to seasons, there are two points.

1. The LOCAL seasonal response would seem to be ( excluding the tropics, of course ) quite liner ( the long nights of winter are colder ). But the global average temperature of earth is out of phase with global seasonal radiative forcing. Earth warms up as it is emitting more energy than it receives and cools down as it receives more energy than it emits through the course of the seasons. Now, the reason for this, the low heat capacity of the Northern Hemisphere compared to the Southern Hemisphere, is understood and not a changing factor for millenia, but if one is using seasonal response as an analogy, one should compare global to global response, and not local to global.

2. More importantly, Held seems to downplay the significance of dynamic variation. More cold fronts pass in one year, fewer pass in the next, but they average out. Perhaps this is so, perhaps not ( there do seem to be some longer term variations in circulation ). But the chaos is not limited to this synoptic variability. It permeates the GCMs in their ability to faithfully reproduce what happens in the real world. ( a small error in how well convection is actually accounted for multiplied by every thunderstorm that will occur between now and 2100 can compound greatly and is not necessarily reverted to the mean ).

I have modeled the ‘Radiative Forcing’ ( the RF, not the ERF ) as defined for 2xCO2 and a given days’ atmosphere here:

The value at the tropopause is close to what the nominal value.
But examine the value of difference in net radiance at the tropopause and the ‘middle of the troposphere’. Notice that they are very nearly the same. Most of the RF is exerted below 600millibars. You can see that by comparing the top half and bottom half:

Now, here is the resulting RF for the same atmosphere with 2xCO2 everywhere, Warmed 2.4C, and humidified such that the relative humidity remains constant uniformly throughout the troposphere:

The difference between the upper and lower troposphere for this case:

For both cases, the forcing of the lower troposphere is greater than the forcing for the upper troposphere, suggesting that even the same amount of mass exchange will increase the amount of heat conveyed by convection.

For the warmed and humidified troposphere, the upper troposphere actually loses more energy than it would for the base preindustrial case, suggesting that convection in such an atmosphere would actually become more effective at ultimately sending energy to space.

Convective response is locked in a struggle with radiative changes and the results appear to indicate a reduction, though not an elimination of those radiative changes.

32. As I understand it, the difference is whether or not you let the stratosphere adjust.

That one’s the ‘Adjusted’ RF as opposed to ‘Instantaneous’ RF before strat adjustment.

I set out to see this for myself in an exercise you might be interested in here.

33. Steven Mosher says:

“. So, why should I assume that things are, gee, the anthropogenic CO2 pulse is going to interact in some exotic way with internal modes of variability? Well, it’s conceivable. But I am not convinced. I don’t think that is particularly relevant.”

I’m unclear here. Is he suggesting that anthropogenic forcing cannot project onto modes of internal variability?

34. Eddie,
I’m actually not quite sure what you’re getting at. That we don’t know for certain what will happen if we apply an external forcing? Sure, I don’t think Isaac Held was saying that we did. I think his point was that the response to a change in external forcing is likely to be linear and that the response to a change of atmospheric CO2 today is unlikely to be wildly different to a comparable change in forcing in the past, simply because the system is non-linear and chaotic.

I must admit, that you confuse me somewhat in that you seem to understand the topic quite well and yet your view appears to be either: “everything might be fine”, or “we don’t know enough yet”. I guess each to their own, but that’s not an obvious way to consider the likely consequences of increasing anthropogenic forcings – well, to me at least.

35. Steven,

Is he suggesting that anthropogenic forcing cannot project onto modes of internal variability?

No, I don’t think so. I think he is simply suggesting that it’s not going to connect in a way that differs wildly from what we think has happened in the past and is not going to produce something that will be wildly different to what we broadly expect.

36. BBD says:

I must admit, that you confuse me somewhat in that you seem to understand the topic quite well and yet your view appears to be either: “everything might be fine”, or “we don’t know enough yet”.

Is this actually the same guy who doesn’t understand the carbon cycle at all? This uneven topic knowledge is really strange.

37. JCH says:

Just to head this off, I have it on good authority that should the sun go out, it will not overwhelm the stadium wave.

38. David Young says:

I believe there are two consequences of Koonin’s observation:

1. Measuring these small relative changes is challenging.
2. Modeling these changes is also very challenging. Typical truncation errors are order deltaX ^-2 times the second derivative of the function.

39. DY,
Yes, apart from the slightly inconvenient point that we’ve rejected (at the 95% level) that natural variability can explain the observed warming since 1950. Challenging doesn’t mean impossible.

For your amusement, this is the best description of what Steve Koonin is suggesting

The effect of a doubling of CO2 is small compared to the effect of the bloody sun going out. No sh*t Sherlock!

So, yes, if you choose to compare one number with another number that happens to be large, the relative effect is clearly going to appear small. That doesn’t mean that the apparently small number cannot be detected or that this apparently small number cannot have some kind of measureable/significant effect. If you can’t get this basic point, I think I shall ignore most of what you say from now on. This – I should add – is not something that bothers me in the slightest. It’s kind of what I do already.

40. dhogaza says:

David Young:

“1. Measuring these small relative changes is challenging.”

Therefore, measuring a 1C change in the temperature of something is much easier if the baseline is 0C degrees rather than 273K ?

41. dhogaza,
I hadn’t thought of that. Attribution studies would be so much easier if climate scientists worked in Celsius, rather than Kelvin. Brilliant.

42. dhogaza says:

ATTP:

“I think he is simply suggesting that it’s not going to connect in a way that differs wildly from what we think has happened in the past and is not going to produce something that will be wildly different to what we broadly expect.”

That’s clearly correct, no need for the “I think”. He’s saying there’s no reason to expect forcing due to adding anthropogenic CO2 to the atmosphere to act differently than the CO2 already in the atmosphere due to natural sources. Ditto changes in forcing due to other causes.

43. BBD said:

Is this actually the same guy who doesn’t understand the carbon cycle at all? This uneven topic knowledge is really strange.

It is not strange at all in the world of talking-point science. Yesterday, Eddie lifted a chart that Lucifer had made and was arguing like it was settled science. So it is either that Eddie and Lucifer are the same person, or it is the blind leading the blind. If the latter, for a pseudo-skeptic to “understand” something, all he has to do is borrow the argument of another pseudo — then polish it up so it is not pure plagiarism, and voila, he can start to engage with ATTP.

Unfortunately, I ain’t buying #WHUT they are selling. Lapse rate is fixed to first-order, it is a negative feedback to second order, and the value of this perturbation will come out of observational data.

44. David Young says:

2. Modeling these changes is also very challenging. Typical truncation errors are order deltaX ^-2 times the second derivative of the function.

I recall that you are another one of those first-down punters that thinks that the complexity of hydrodynamics makes modeling of climate numerically intractable. I don’t have much use for your negativity and I imagine neither does Held based on the the quote that ATTP cited.

#WHUT’s the point of focusing on problematic artifacts of the math details when the first-order physics itself doesn’t work that way ? Take a look at recent papers on sloshing. Sorry to inform you but the results are quite stable, and straightforwardly reduce to a formulation that is readily numerically calculated.

45. Meow says:

Take a look at recent papers on sloshing. Sorry to inform you but the results are quite stable, and straightforwardly reduce to a formulation that is readily numerically calculated.

This is interesting. Do you have some handy cites?

46. John Hartz says:

ATTP: Isn’t a “stadium wave” what Judith Curry’s accolytes do when she posts a comment on her website?

47. Willard says:

> Now that there seems to me like something that you couldn’t make up.

Of course Judy can make things up:

Koonin is humble and doesn’t claim primary expertise, but he definitely has synthetic expertise with regard to climate change

http://judithcurry.com/2015/04/07/draft-aps-statement-on-climate-change/#comment-691841

This seems to be an extension of what Judy said earlier:

Andrew Montford’s expertise is more in the area of providing context and synthesis (different from McIntyre the auditor).

http://judithcurry.com/2015/04/07/draft-aps-statement-on-climate-change/#comment-691497

Therefore we have at least three boxes: primary expertise, synthesis expertise and auditing expertise. Since Koonin is an expert in climate synthesis, I suggest we add another box for our Beloved Bishop: True Scot expertise. Another box for Matt King Coal, David Rose, and James Delingpole might also be needed. I hesitate between synthetic synthetic expertise and interpretative expertise.

INTEGRITY ™ — Free Boxes Inside!

48. Meow says:

@Willard: I think that primary obfuscatory rhetorical expertise would fit most of them.

49. MMM says:

I like measuring sea level rise as a percent of increase compared to the Marianas Trench to surface distance. So don’t bother me about sea level rise problems until we see at least 300 feet of rise.

50. MMM says:

More seriously: I actually think a somewhat relevant comparison is between the anthropogenic increase in forcing, and the forcing from the non-condensible gases. E.g., since water vapor and clouds are feedbacks, they shouldn’t be included in the comparison.

51. Willard says:

One of the reasons why I read Judy’s is because sometimes Andy Lacis drives by with comments such as this one:

Steven,

Physicists should take the time to understand their physics better.

Only 1% to 2% . . . that may sound small and insignificant . . . but it isn’t.

It is well known that the normal human body temperature is about 310 K. Furthermore, it is also well known that a seemingly small change (up or down) in absolute body temperature by only 1% (3.1 K, or 5.6 F) would make one sicker than a dog, and, that a 2% change in body temperature (up or down by 6.2 K, or 11.2 F) will virtually guarantee a dead body. From this, it should be sufficiently clear that, when viewed in absolute energy terms, the viable margin between life and death in the Earth’s biosphere is remarkably narrow – so much so that a seemingly insignificant 1% to 2% change in the total energy of the global environment will invariably result in serious disruption of the established infrastructure of life in the biosphere.

There is no substitute for appealing directly to basic physics for physical insight and better understanding of the ongoing global warming problem. And I do recall one particular case in the 1970s (in which you might have participated) when the JASON group of physicists was tasked to weigh in on the then open question of radiative forcing due to doubled CO2. At that point in time, the JASONs had available the computational resources to calculate one of the earliest line-by-line radiative forcing determinations for doubled CO2. They found the downward flux change at the ground surface to be less than 1 W/m2, from which they erroneously concluded that the radiative forcing caused by the doubling of atmospheric CO2 was “not all that significant”.

While the JASON group’s radiative calculations were numerically on target, the JASONs were clearly mistaken in their interpretation of the calculated results. Radiative forcing takes place over the entire atmosphere, and not just at the ground surface. If they had to select a single point on the vertical profile that best describes the radiative forcing by CO2, they should have selected the tropopause point, where the instantaneous flux change due to doubled CO2 is nearly 5 W/m2 for a clear-sky atmosphere. Moreover, the JASONs did not take into account the additional radiative magnification that is invariably contributed by the longwave opacity from water vapor and cloud feedbacks, which are several times larger than the radiative forcing due to CO2 alone, and therefore should have been included in their analysis.

In simple terms, the basic essence of the global warming problem is best understood as a straightforward problem in global energy conservation, as was first noted by Joseph Fourier in 1824. Specifically, the global-mean surface temperature of the Earth is about 288 K, which implies that the Planck emission from the ground surface must be about 390 W/m2. Furthermore, the global-mean solar energy absorbed by the Earth is observed to be about 240 W/m2 (with about 100 W/m2 reflected directly back to space).

Given that the Earth should be in near-global energy balance, this implies that the Earth must radiate about 240 W/m2 of longwave energy out to space (as has also been verified by satellite measurements). Absent the greenhouse effect, the 240 W/m2 of absorbed solar energy can only support a surface temperature of 255 K. This “missing energy” circumstance led Joseph Fourier to conclude that there must be thermal heat energy radiated downward from the atmosphere to supply the additional heating of the ground surface.

The flux difference of 150 W/m2 between the 390 W/m2 emitted by the ground surface and the 240 W/m2 of LW flux going out to space at the top of the atmosphere is a direct measure of the strength of the terrestrial greenhouse effect. Greenhouse action builds up the surface-emitted flux to 390 W/m2 and creates the ensuing reduction by 150 W/m2 of the outgoing longwave flux to space – all accomplished by radiative energy transfer means (via sequential emission, absorption, and re-emission interactions).

Physicists should also appreciate the nature of the Clausius-Clapeyron relation, and the fact that it is exponential in temperature. Undisturbed, with a source of liquid water, the atmosphere is always striving to reach an equilibrium 100% relative humidity. In simple terms this means that the holding capacity of the atmosphere for water vapor doubles for every 10 K increase in atmospheric temperature. And, there is no doubt that water vapor is a very potent greenhouse gas.

Detailed radiative attribution calculations show explicitly that water vapor accounts for about 50% of the 150 W/m2 of greenhouse effect, and that longwave cloud opacity accounts for 25%. Both of these radiative effects are due to the climate system’s fast feedback processes. The remaining 25% of the greenhouse effect comes from the radiative forcings by the non-condensing greenhouse gases (which incidentally also act to sustain the terrestrial greenhouse effect at its present strength). Of the non-condensing greenhouse gas contributions, CO2 is by far the strongest contributor accounting for about 20% of the 150 W/m2 greenhouse effect, with the remaining 5% due to minor GHGs like CH4, N2O, O3, and CFCs.

A key point to keep in mind is that it is these non-condensing greenhouse gases that act as the principal radiative forcing agents of the climate system. Because of their thermodynamic, chemical, and radiative properties, CO2 and the minor GHGs are chemically slow-reacting with atmospheric lifetimes ranging from decades to many centuries. Once they are injected into the atmosphere these gases effectively remain there indefinitely by not condensing or precipitating at prevailing atmospheric temperatures as they continue to exert their radiative forcing.

Since CO2 is the strongest and most effective of these non-condensing radiative forcing gases, it then follows that CO2 can be identified as the principal LW control knob that governs the global climate of Earth. The fact is that the other forms of radiative climate forcing (e.g., changes in solar irradiance, surface albedo, and aerosol forcing) are small by comparison. This makes the case for recognizing CO2 as the principal climate control knob that much more compelling.

Atmospheric water vapor, on the other hand, has the role of principal fast feedback process in the climate system by condensing and precipitating from the atmosphere in response to changes in local meteorological conditions (constrained by the exponential temperature dependence of the Clausius-Clapeyron relation), meaning that the atmospheric distribution of water vapor (and clouds) can change rapidly on a time scale of hours and days in response to changing weather conditions.

Applied radiative forcings that heat (or cool) the atmosphere cause more (or less) water vapor to evaporate, which generates more (or less) longwave opacity, which then contributes more (or less) radiative greenhouse effect. Such changes in water vapor cause big changes in radiative heating or cooling, but the changes are limited in magnitude by how much change the water vapor undergoes in reaching its new equilibrium distribution.

Because of this, water vapor and clouds act to magnify the initial radiative perturbation, but cannot on their own initiative manufacture or impose a warming or cooling trend on global climate, even though they contribute more strongly to the atmospheric radiative structure than the radiative forcing gases that actually drive and control the global temperature trend.

The physics cause-and-effect nature of the global warming problem is not all that complicated. The basic “cause” component of global warming has been clearly identified and understood for many decades, and has been accurately quantified by precise measurements of atmospheric CO2 (e.g., the Keeling curve).

This is fully corroborated by the latest annual data report of fossil fuel extraction that now approaches 10 gigatons of carbon/yr (roughly equivalent to 10 cubic km of coal/yr, which when burned, adds about 5 ppm CO2 to the atmosphere, half of which remains there for many centuries). The radiative effects of CO2 are fully known from well-established understanding of greenhouse gas radiative properties and radiative transfer modeling of the atmospheric structure.

How can a physicist not comprehend that it is atmospheric CO2 that is the principal radiative forcing agent for the ongoing global warming? . . . and not be concerned that water vapor, as the climate system’s principal feedback agent, has an exponential dependence on temperature?

To be sure, there are other factors that contribute to climate change. But decades of measurements and analysis have shown that variations in solar irradiance, land use, aerosols, ozone, and other minor greenhouse gases, while making a contribution, are small by comparison to CO2.

Of greater interest is the “unforced” variability of the climate system on decadal time scales that arises from changes in ocean circulation patterns that are effectively un-influenced by changes in atmospheric radiative forcing. The deep ocean is a very large cold storage reservoir. An upwelling blob of cold ocean water can put a “pause” in the ongoing global warming, temporarily diverting the greenhouse “heat” to warming the ocean. But once that cold blob of ocean water has been warmed up to its equilibrium temperature, it is back to the business of continued global warming. And also note that the ocean cannot cause a decadal warming spurt – the deep ocean is colder than the surface biosphere, so it cannot be a source of heat.

Significantly, the key climate system components (water vapor, clouds, ocean) are not configured to respond to radiative and/or temperature perturbations on a sufficiently small enough incremental scale that would permit a monotonic approach to global energy balance equilibrium. Instead, there is always over-reaction such as when water vapor condenses en mass to produce storms, coupled with the similarly over-reactive responses by atmospheric and ocean dynamics to pressure-temperature and salinity differences, to produce the quasi-chaotic weather and the longer-term climate noise that characterizes the climate system.

Physicists should not be confused by these random-looking quasi-chaotic fluctuations about the local climate equilibrium point, and should instead focus more on the changing energy balance equilibrium point of the climate system. They should also pay attention to the geological record that points to an atmospheric CO2 level of 450 ppm as being incompatible with polar ice caps, a level that is expected to be reached by the end of this century. While it may take a thousand years for the polar ice to melt, the future course is being prepared for a 70 meter rise in sea level.

http://judithcurry.com/2015/04/08/are-human-influences-on-the-climate-really-small/#comment-691948

Looks like commentary expertise to me.

52. MMM,
I think one problem is that estimating the forcing from CO2 in the greenhouse effect is non-trivial. Do you do define it as single factor addition, or single factor removal. It’s explained quite well here.

53. Willard,
Eli beat you to it.

54. MMM says:

“And also note that the ocean cannot cause a decadal warming spurt – the deep ocean is colder than the surface biosphere, so it cannot be a source of heat”

I like almost everything about Andy Lacis’ comment except the above quote: because to me, slowing a heat sink looks a lot like a source of heat. So if the deep ocean can slow heating by burping a mass of cold water, why can’t it accelerate heating by slowing the rate of cold water moving to the surface? There’s an upper limit on rate (trivially defined as the current heat uptake of the ocean, but probably rather less than that), but I would be surprised if you couldn’t get something pretty impressive. After all, we do see ENSO events with pretty big heat spikes…

-MMM

55. MMM,

So if the deep ocean can slow heating by burping a mass of cold water, why can’t it accelerate heating by slowing the rate of cold water moving to the surface?

Yes, I think it can. Andy Lacis’s point is – I think – that the oceans can’t be the source of the energy. They can influence that rate which we warm/cool due to some change in external forcing, but cannot produce a long-term (multi-decade) warming/cooling trend by themselves.

There may be some caveats. Dansgaard-Oeschger events are thought to be internally forced due to a change in a major deep ocean current that triggers sudden NH ice sheet retreat. However, given that we don’t currently have large ice sheets, there isn’t really a known mechanism through which changes in ocean circulation can produce some kind of major warming event.

56. David Young says:

I read quite a bit on the Ringberg conference and it seemed to me one of the themes was that constant feedback factors (as used in energy balance methods) were perhaps significantly inaccurate. It would be interesting to see if ice albedo feedback during an ice age was a constant feedback factor. I kind of doubt it. Clearly a 2 box model cannot explain an ice age. So this would seem to support Koonin’s thought that the climate is not linear. There is also the whole field of sudden climate change. I’m not completely sure what Held is getting at above, but linear response to forcing seems to me obviously limited to special situations.

Ice ages according to what I have read are caused by large changes in summer insolation at high Northern latitudes and corresponding decreases in southern latitudes. The total forcing is pretty much constant except for feedbacks– its the distribution of the forcing that changes. I seem to remember a figure of 50 W/m2 or even 80 W/m2 locally which is once again very large in Koonin’s world.

Climate is not completely unpredictable, but our ability to simulate the complexities seems to me to be pretty uncertain. I tend to prefer simple models based on 35 years of experience in fluid dynamics.

It also seemed to me even though perhaps I missed something that Nic Lewis’ presentation was very thorough in dealing with previous work on observationally constrained energy balance methods. Maybe I missed it but I didn’t see any other careful work with this model. Anyway, if I missed it, could someone point me to some recent work on energy balance models?

57. “This is interesting. Do you have some handy cites?”

These studies are scaled to volumes the size of storage tanks. These are what are called boundary value problems, not initial value problems, which are much different beasts.

Frandsen, Jannette B. “Sloshing motions in excited tanks.” Journal of Computational Physics 196.1 (2004): 53-87.

Shao, Yan-Lin, and Odd M. Faltinsen. “A harmonic polynomial cell (HPC) method for 3D Laplace equation with application in marine hydrodynamics.” Journal of Computational Physics 274 (2014): 312-332.

Bai, W., X. Liu, and C. G. Koh. “Numerical study of violent LNG sloshing induced by realistic ship motions using level set method.” Ocean Engineering 97 (2015): 100-113.

PDFs available from ResearchGate. Faltinsen has a book on the subject, titled”Sloshing”.

58. Brandon Gates says:

ATTP,

There’s a potential issue that residual heat from prior warm periods throws off OHC trend estimates. Can’t recall if this paper has been discussed here or not:

Liang, et al. (2015), Vertical Redistribution of Oceanic Heat Content: http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-14-00550.1?af=R
Preprint: http://www.mit.edu/~xliang/resources/liang2015a.pdf

Subtly different from heat burbling up from the abyssal deep and causing warming at the surface, which I don’t believe is plausible. The usual suspects have been observed to conflate the two in unholy ways.

59. Yes, I think it can. Andy Lacis’s point is – I think – that the oceans can’t be the source of the energy. They can influence that rate which we warm/cool due to some change in external forcing, but cannot produce a long-term (multi-decade) warming/cooling trend by themselves.

That’s true for the tropics and mid-latitudes where the average temperature of the atmosphere is higher than the average temperature of the oceans. For the poles, where the average temperature of the air is less than the average temperature of the oceans beneath, the ocean is at different times, a source of warming. That rate of warming varies with the sea ice coverage which itself varies. In addition to the latent heat of freezing/melting, that seems to provide the fingerprint of Arctic warming
– when sea ice grows, colder autumn through spring as it was 1945-1975:

– when sea ice shrinks, warmer autumn through spring as it was 1910-1945, and 1975-present:

How much of the recent Arctic Sea Ice decline is from ‘global warming’ and how much of recent warming is from a waving stadium remains to be seen.

60. DY,
You do realise that when estimates of ECS are made using paleo evidence, the ice-albedo feedback is actually normally treated as an external forcing, rather than as a feedback, partly to counter what you seem to be suggesting.

“Why did the JASONs only get a 1W/m^2 change in flux at the surface?”

Turns out the 1W/m^2 is correct, the problem is they were looking at the surface, not the tropopause:

One of the confusions is that the atmosphere is not a single ‘layer’ but many overlapping layers which partially absorb and emit. Early papers considered the forcing at the surface as Lacis notes until Manabe and Ramanathan pointed out the meaning of using the tropopause.

The rational for the tropopause is the ‘top of the convection’ and the equation for heating rate is
H = (constants ) * dF/dz where H is the heating rate ( K/day ) and F is the net radiative flux.

This is typically applied to much thinner layers than the whole atmosphere,.
But by considering the troposphere as a whole, the term dF should relate to the heating rate of the troposphere.

It’s interesting to note that doubling CO2 doesn’t change the heating rate of the individual layers within the troposphere very much ( as opposed to the individual layers of the stratosphere which show such a strong cooling ). But the dF at the tropopause is significant.
I’ll post the Heating Rate changes I found later.

62. Willard says:

Turbulent One,

Please be advised that one does not simply comment in Mordor using many nicknames. It is called sock puppetry. Peddling the same pet graphs over and over again in every thread is also suboptimal.

W

63. anoilman says:

I invite anyone who thinks ‘small can’t be serious’ to breath in a nice deep 300PPM of H2S and call me in the morning.

64. anoilman says:

Willard… stop playing with Lucifer the Father of Lies.

65. Next time your child is runs a temperature, can we expect the doctor to say, “nothing to worry about; only 1 or 2% above normal…”?

66. john,
Eli has a Twitter hashtag called #Kooninisms. You could enter the contest 🙂

67. I just realised that your next post, aTTP, makes the same point I did above. I didn’t read it there first: honest. Body temp is an analogy I’ve used in the past.

68. …aTTP. Done.

69. Arthur Smith says:

What perhaps should really be pointed out here is that Koonin’s use of an apples / oranges ratio to come up with a small percentage is most directly illustrating his utter unfamiliarity with the basic science of climate. I just read his response at Judy’s, and he is taking the ratio of forcing, defined at the TOP of the atmosphere, to downward thermal radiative flux at the surface (“the greenhouse effect”). But it is fundamental to understanding this that a small imbalance at the tropopause necessarily leads to a much larger surface flux change, as both upward and downward flows are greater there due to the higher temperature of the surface relative to the tropopause, not even worrying about feedback effects. Yes they are measured in the same units, but the flux at TOA and at the surface are very different things and simply cannot be compared in this way. If you did the same sort of comparison for Venus, for instance, any forcing change at the top would be a really tiny fraction of the surface downward IR flux, but it would lead to a far greater flux change at the surface. The ratio of the two is simply not meaningful.

And his second example is similarly inept. He looks at total absorption – smacking of the old “saturation” argument. Suppose we started at 99% – a 1% increase would mean all IR from the surface was completely blocked, and we would warm up to the maximum temperature entropically allowed, about 5000 degrees! Radiative transfer is not terribly complicated, but anybody thinking just looking at absorption gives you any substantive intuition about it has simply not understood the fundamentals of radiative transfer. Pierrehumbert’s book, or even his Physics Today article, gives a great intro – Koonin clearly hasn’t read them or at least not absorbed the basics there.

70. BBD says:

Thank you, Willard.

71. Arthur,
I agree. It’s quite a remarkably ill-informed set of comments by Koonin. It’s actually hard to know how to interpret it. Hubris would seem to be a rather generous way of describing it.

72. Being a bit of dummy myself, I’m always looking “climate change for dummies” types of explanations.

That is why I’m a fan of using seasonal change to illustrate a range of concepts that are relevant to global warming. I’ve actually used this a couple of times with environmental politics students.

In my home town of Melbourne, the 23.4 degree ‘axial forcing’ that cycles between winter and summer changes the length of each day by a maximum of 2:27 minutes at the time of the equinoxes, and by less than 1 second at the solstices. In percentage terms, the length of day and the sun’s azimuth varies between just 0.17% and 0.001% per day. (I wonder what Steve Koonin thinks about all of those ‘sunrise and sunset’ charts for every city on the planet? Are they even possible?)

Everyone knows Melbourne weather can swing 15 degrees C just from day to day; everyone also knows that the average temperature for January is higher than for July. The point I make to the students is that this seasonal forcing is far weaker than the weekly and daily variations in weather -all but undetectable- but it is the only cumulative influence throughout the year.

I also like to use this analogy because a lot of the people who claim to dismiss global warming -if they are to be logically consistent- should also be calling for an end to the idea of…well, summer.

73. Joshua says:

Why did the poster formerly known as Lucifer (that is Eddie’s previous name, is it not?) start using a sock?

74. BBD says:

Perhaps he gave in to temptation?

75. JCH says:

For the ams reason Chef Hydro did. Actually, I’m confused. I made up that sock for him because I knew he could do at least one thing: boil water. Am I the only person who suspected Lucifer was the Chef, and that Divid Blake was… socks galore.

76. John Hartz says:

Joshua:

“Who knows what evil lurks in the hearts of men? The Shadow knows” – Lamont Cranston

77. Joshua says:

==> “Am I the only person who suspected Lucifer was the Chef,”

The thought occurred to me, but I haven’t seen any reference to himself as a noble hero vanquishing an evil enemy or any unintentional irony. Makes it less likely it’s Chief. He could have changed his style to hide his identity – but Chief never struck me as having that level of self-control over his more endearing characteristics.

78. JCH says:

That’s the doubt. Could the Chef and the David exercise such amazing self-restraint? But they appeared just as the Chef disappeared, and the David bloomed into multiple personalities all over the place. Like the Victor at RC who used Australian slang, but was the smartest kid from New York. For a time I wondered if it was one in the same person. Maybe somebody who invented a character who was borrowing from both.

But having a new graph of the stadium wave cinched it for me. Nobody but a truly spurned judy believer carries around a graph of the stadium wave.

79. I thought the Chief was Rob Ellison?

Also, is someone now sockpupetting David Springer? This comment seems moderately sensible, which seems rather out of character.

80. Joshua says:

Anders –

That’s him. The level of bombast is the equivalent of a notarized signature.

81. JCH says:

He is RE. He’s disappeared, and suddenly new people with some traits in common have appeared.

On RC a weird combo of Chef Hydro and DS showed up. He ended up boreholed.

82. Joshua says:

RE?

83. Robert Ellison.

84. Joshua says:

Oh, Robert Ellison. Could be.

If so, I’d be impressed with the level of self-control displayed in hiding his more typical attributes.

I never expected that he could stay away and that he’d inevitably reemerge. He has promised to quit many times in the past only to cave, although I think that he did hold out longer this time than he ever has before.

85. Joshua says:

We’ll know for sure it’s him if he ignores any uncertainties to confidently predict cooling for “a decade or three.” The other signal would be if Eddie and WHT get involved in an epic handbag fight.

86. Willard says:

> He is RE.

I doubt he is, JCH, for many reasons. Let’s wait until Eddie owns his schtick.

87. Harvey says:

@Brandon Gates, way above, at this comment: https://andthentheresphysics.wordpress.com/2015/04/09/steve-koonin-and-the-small-percentage-fallacy/#comment-52738

I had that same chart thrown at me by a denier recently. Seemed way off, but I’m a long way from calculus, natural logs, and such. Can you (or anyone else in this thread) give me a plain language explanation?

88. Brandon Gates says:

Harvey,

I think it is quasi-correct to describe the function of that plot as the first derivative of 0.5 ln(CO2) with respect to CO2. In plain language, they multiplied the natural log of CO2 concentration by one half, and then calculated the change in that value from bucket to bucket. The intent being to “show” the incremental change of temperature for every 20 ppmv CO2 rise.

In rebuttal to that plot the first time I saw it, I ginned up this:

Of course the idjuts aren’t interested in what “the models” say, however it’s perfectly fine for one of their own to pull random coefficients out of their wazoo and jigger things to make stuff look less “alarming”.

89. Brandon Gates says:

@ATTP April 9, 2015 at 3:58 pm,

Understanding how the two values are calculated helps me a great deal. I will do some reading to better understand why. Other questions I’ve had may be starting to gel into something resembling a synthesis. Thanks for your help.

90. Brandon Gates says:

Web,

#WHUT the FUD ?

I’ve become somewhat a collector of shonky plots: http://climateconsensarian.blogspot.com/p/hall-of-shame.html

I’ve been rather lax about updating it and have missed some really awful ones. Like poor cooking, I’m sure they’ll resurface at some point.

91. The other signal would be if Eddie and WHT get involved in an epic handbag fight.

I don’t think Lucifer or Turbulent Eddie is actually Rob Ellison aka Chef Hydro, General Skippy, Capt. Kangaroo, etc as Lucifer actually knows how to draw a graph. Last I heard from the Chef, he was in a typhoon shelter hiding out from cyclone Marcia.

I would like to rub his nose in the results of the ENSO modeling project, simply nailed it 🙂 It’s hilarious to ask him how a land-locked Minnesotan can figure out the dynamics El Nino 🙂 Say #WHUT ?

92. I’m pretty sure Eddie is not Rob Ellison, so maybe we could end this surmising as to who he might be.

93. anotheralionel says:

Why did the poster formerly known as Lucifer (that is Eddie’s previous name, is it not?) start using a sock?

He was slipped one in a book by Lucifer Malfoy and being the good little house-elf he is succumbed to temptation.

94. Steven Shumak says:

For a less Earth-bound perspective, the Red Spot on Jupiter is another example of a stable system existing and perstsing in a planet’s atmosphere yet has emerged from chaotic underlying processes (a multiplicity of them, in fact). Any sun has a similar stability.

As an interested layman, then, I am curious. What is unique about our earth’s four-season cycle? Why is it such a telling observation?

95. Steven Shumak said:

“For a less Earth-bound perspective, the Red Spot on Jupiter is another example of a stable system existing and perstsing in a planet’s atmosphere yet has emerged from chaotic underlying processes (a multiplicity of them, in fact). Any sun has a similar stability.

As an interested layman, then, I am curious. What is unique about our earth’s four-season cycle? Why is it such a telling observation?”

Significant recent news thanks to Cassini. Saturn and Jupiter’s oscillating winds (i.e. rings) are likely synchronized to the seasonal obliquity of the orbit. Definitely Saturn as it is a semi-annual cycle. Jupiter is more weakly synchronized to the seasonal but potentially more to the gravitational pull of it’s moons.

https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2018JE005625

Also this has significance for our understanding of the earth’s oscillating winds.

96. Steven Shumak says:

At the risk of revealing even more about the depths of my ignorance about such matters, I realize now that I probably missed the key point(s) in your comments about Koonin. In particular, I am not sure if the most salient point of your (and others) criticism of his ‘thesis’ is the demonstration that 1) small changes CAN and DO have large downstream effects, or, 2) linearly evolving systems can emerge from underlying chaotic processes/regimes, or, 3) periodic systems, in particular, can be affected (if not controlled) by small inputs, or, 4) none of the above (!)

s

97. Steven,

What is unique about our earth’s four-season cycle? Why is it such a telling observation?

I think this is making a fairly simple point. The dynamics is non-linear and, hence, chaotic. This means we can’t make predictions about the exact state more than a few days in advance. However, despite this, there clearly are patterns that tell us how the average state of the system responds to changes. So, the seasons tell us how the system respond to the change in solar insolation as the Earth orbits the Sun. Essentially, even though the system is chaotic, we can still understand how it will respond – on average – to changes, even if we can’t predict the exact state at some distant point in the future.

98. Steven Shumak says:

Indeed. Thank you.

I guess I was surprised to learn that the seasons are the first and only example of such a phenomenon in climatology (and, of course, apologies if I have misunderstood). I say that because many other physical systems possess that same property (e.g. the orbits of some planets are ultimately chaotic, but are still eminently predictable in their long-term behaviour).

99. The most significant point I believe is that equatorial behaviors (such as the rings of Saturn) are likely the least chaotic features, as they are constrained by topological considerations and thus more amenable to forcing along boundary paths.

1) small changes CAN and DO have large downstream effects, or, 2) linearly evolving systems can emerge from underlying chaotic processes/regimes, or, 3) periodic systems, in particular, can be affected (if not controlled) by small inputs, or, 4) none of the above (!)

1) is operable

The issue with 3) is that one always has to determine whether the observed climate cycle is a natural resonance or a forced response. Seasonal responses are almost certainly forced, as is probably the case with the periodic reversal of the Saturn ring velocity. Yet, as Peter Read notes in the article, it can be perturbed (see your point #1 regarding small changes) but then will eventually re-synchronize to the prevailing forcing.

The Red Spot on Jupiter is off the equator and thus has a more complex set of boundary conditions and may indeed be chaotic and a natural resonance.

The way that science proceeds in the absence of controlled experiments is that one first understands the systems with the fewest states and boundary conditions and then go from there. So I would look at the equatorial behavior such as the rings before the red spot. I have no idea if Koonin would agree with this approach.

100. Steven Shumak says:

PP: Very helpful, thank you. Especially:

‘. . . one first understands the systems with the fewest states and boundary conditions and then go from there. So I would look at the equatorial behavior such as the rings before the red spot’.

Thank you

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