An interesting and determinative (to me) result is contained in a recent paper in Science magazine (https://www.science.org/doi/10.1126/science.adg8269). Here Alexakis and his collaborators show that there are two energy cascades in their model atmosphere. For turbulent energy at scales below 10km the 'normal' energy cascade dissipates energy to smaller scales. But, for turbulent energy at larger scales there is an inverse cascade which can generate large scale self-organization.
It seems that it would require a very large butterfly to cause a tornado.
Do you mind if I leave a question from your father's paper on ocean heating? I missed it first time round, have asked this question now but I guess he is no longer monitoring the comments section (or the question is too dumb - understandable). He derives a figure of 0.66 +/- 0.5 W/sqm of downwelling LWIR from the increase in ocean warming from the Argo data source in the last twenty years. Are we able to extrapolate this to give a figure for the doubling of CO2?
I apologize for being pedantic. I tend to believe in the butterfly effect not necessarily in the context of butterflies, but in casual chains like, white papers, books, innovation, Rosa parks, MLK, Buddha, Jesus, Gandhi and the little choices we make like a repost/like or transformative conversation that happens half way around the world. 🙏
I was greatly enlightened by an excellent letter from Dr. Pielke Sr to the editor of the Bulletin of the American Meterological Society in 1998, (pp2743 to 2745. Dr. Pielke explained that there were two schools of thought; advocates of global circulation models maintain that "in the context of prediction, weather is considered an initial value problem while climate is assumed to be a boundary value problem." However,, "another perspective holds that both climate and weather prediction are initial value problems." Climate modelers must assume climate is a boundary value problem to justify predicting future climate based on anthropogenic gas increases, However, "weather prediction is a subset of climate prediction, and both are, therefore, initial value problems in the context of nonlinear geophysical flow." Since climate prediction is an initial value problem, deterministic nonlinear differential equations meant to model it fall into the instabilities explained in Edward Lorenz's landmark paper "Deterministic Nonperiodic Flow" (J. Atm. Sci., 1963, Vol 20, pp 130-140.) By the way, Lorenz himself was quite humble about his key insight; he noted that, as early as 1950, the British meteorologist Eric Eady published a paper pointing out that "any forecast is just one member of a large ensemble of possible forecasts, and we have no real reason for selecting among those."
If we are arguing over the flutter of butterfly wings shouldn’t there be some serious studies on wind turbine kinetic energy disturbance and its impact on weather and climate before we cover the earth and fill the oceans with them?
An issue I see here is the lack of a common understanding of 'cause.' There seems to be an implicit assumption (actual?) that cause means 'but for' the named event - here, a butterfly flapping its wings - and all else being equal (of course, it never is! everything is in motion at some pace, albeit sometimes that pace is not discernable by humans), the event -- here, a tornado -- would not have happened. I think the math is all very fine but remain unconvinced that there may be some chain of events that link butterflies to tornadoes. I don't know. But the math does not convince me this is not possible.
I have always thought that the butterfly effect was almost certainly nonsense. I'm glad to see a good analysis of why it doesn't happen. Chaos and complexity theory became "cool" but largely untested.
It's been about 20 years since I spent some time analyzing and publishing on the onset of turbulence in transient flows. I appreciate and agree with the point about the dissipation scale and the idea that the butterfly wing is not large enough to have an impact. But the single chain of cause and effect discussed at larger scales does not make sense to me and the reason is that the system of interest involves the coupled, strongly nonlinear interactions within a fluid system. This creates the "extreme sensitivity to initial conditions" mentioned below. It also produces a phenomenon called "baskscatter", whereby small (but large enough) scale motions are nonlinearly coupled back into larger scale motions. One of the main research questions about computational models is (or at least was) the degree to which backscatter below the scales they capture can alter the large-scale results. Simple energy flow arguments about scales above the dissipation scale miss the boat. The physics involved is in no sense a simple, linear system.
R Paul Drake, Professor Emeritus, University of Michigan
I've always taken the Butterfly Effect to just be a statement about the unpredictability of chaotic systems due to their sensitivity to perturbations on all scales. Whether literal butterflies could be involved seems like a fanciful question that could never be answered in practice.
But since Pielke Sr. et al. address that specific question, I have to say I didn't really understand what seems to be their central point, to wit:
"In order for a kinetic energy disturbance to grow in size and/or travel large distances, production of kinetic energy needs to exist at a rate larger than the loss of this energy into heat (called dissipation). The length scale where dissipation dominates in the atmosphere is about 0.1 to 10 millimeters, although it occurs on all spatial scales. At and below this scale, nonlinear turbulent motions essentially do not exist."
I'm not seeing why energy dissipated as heat couldn't be a source of instability. Convective instability refers to the behaviour of an air mass whose temperature differs from its surroundings (see Convective Instability on Wikipedia). The magnitude of the difference determines whether vertical motion will be damped or amplified. Why isn't it possible that a tiny amount of kinetic energy dissipated as heat could push the temperature of an air mass that is already at the edge of instability over the threshold? We're talking about something on a hair trigger -- all you need is a hair.
Like I said, I think the scenario is fanciful because how could we ever know. But I'm not seeing how we can rule it out as a physical impossibility.
I have just read Sr. et al [more correctly: R.A. Pielke Sr., Bo-Wen Shen, and Xubin Zeng] and they really take a simple approach to the physical reality of the effect caused by a butterfly wing flap across real atmosphere, space and time. and, of course, their answer is absolutely correct.
But weather and climate models are clever but, alas, s t u p i d . If one changes the input, say for a value like "global average surface temperature this time step" by as little as 1/100th of a degree, that change may either disappear in the future iterations, or grow and grow and create a physically unrealistic prediction of future temperatures. and no, it does not "average out", neither in the mathematical models or in the real world. .
The spaghetti graphs of climate models predictions, for any future value, show that chaotic effect even after programmatic guardrails are used to hide chaotic results.
The problem seems confusing because we look at a single butterfly, ignoring that at the same time there may be millions of over butterflies, sparrows and crows flapping their wings as well, reinforcing and/or canceling possible effects at distance. Perhaps the effect more closely resembles dither in a digital recording, reducing "noise" and allowing unexpected patterns to emerge from "chaos".
Kip, I think that’s what might not be clear to many of us not in the biz.. does wing flapping actually cause something (which is what it sounds like) or are the models people use extraordinarily sensitive to initial conditions such that a butterfly or an ant scratching its face can change the outcomes? One is about the models, and the other is about physical reality.
Sr. et al are perfectly right. But, like many who read about Chaos and its effects, they are off-base. They are far far too literal in the quip about butterfly wings flapping. It is an interesting uber-academic exercise, but not pertinent to anything.
I will have to read their paper to see if they are really being silly about this flapping business, or if they are pulling our legs.
The Butterfly Effect is the reason that numerical weather prediction has a narrow time limit -- 7 to 10 days. It is the reason that hurricane landfall predictions are only generally valid out 72 hours.
Neither Lorenz or Smagorinsky meant that quip literally. It is meant to illustrate the inescapable fact that small, even infinitesimal, changes to initial inputs can and do have huge effects over many iterations of weather/climate model processes -- those that involve non-linear mathematical equations. This can be referred to as "extreme sensitivity to initial conditions".
Sr. and Shen have indeed explored this idea before... “Is Weather Chaotic? Coexisting Chaotic and Non-Chaotic Attractors within Lorenz Models” and found both types of attractors within Lorenz models (so did Lorenz, by the way).
However one views the butterfly wing's power, it remains that for weather and climate model any difference, no matter how small, can and will generate large difference in model output after many iterations -- that is the primary cause for the huge spread in models predictions we see after 100 years or so. That spread exists despite specific coding to control chaotic effects by limiting results that soar off to infinity and dive to zero.
Should be easy to test. Plot number of hurricanes vs butterfly habitat destroyed in the Amazon. The two should be correlated. If it is true, we can control hurricanes by killing butterflies.
It all depends on the scale of the disturbance.
An interesting and determinative (to me) result is contained in a recent paper in Science magazine (https://www.science.org/doi/10.1126/science.adg8269). Here Alexakis and his collaborators show that there are two energy cascades in their model atmosphere. For turbulent energy at scales below 10km the 'normal' energy cascade dissipates energy to smaller scales. But, for turbulent energy at larger scales there is an inverse cascade which can generate large scale self-organization.
It seems that it would require a very large butterfly to cause a tornado.
Do you mind if I leave a question from your father's paper on ocean heating? I missed it first time round, have asked this question now but I guess he is no longer monitoring the comments section (or the question is too dumb - understandable). He derives a figure of 0.66 +/- 0.5 W/sqm of downwelling LWIR from the increase in ocean warming from the Argo data source in the last twenty years. Are we able to extrapolate this to give a figure for the doubling of CO2?
https://www.washingtonpost.com/weather/2020/02/02/butterfly-effect-is-not-what-you-think-it-is/
I apologize for being pedantic. I tend to believe in the butterfly effect not necessarily in the context of butterflies, but in casual chains like, white papers, books, innovation, Rosa parks, MLK, Buddha, Jesus, Gandhi and the little choices we make like a repost/like or transformative conversation that happens half way around the world. 🙏
I was greatly enlightened by an excellent letter from Dr. Pielke Sr to the editor of the Bulletin of the American Meterological Society in 1998, (pp2743 to 2745. Dr. Pielke explained that there were two schools of thought; advocates of global circulation models maintain that "in the context of prediction, weather is considered an initial value problem while climate is assumed to be a boundary value problem." However,, "another perspective holds that both climate and weather prediction are initial value problems." Climate modelers must assume climate is a boundary value problem to justify predicting future climate based on anthropogenic gas increases, However, "weather prediction is a subset of climate prediction, and both are, therefore, initial value problems in the context of nonlinear geophysical flow." Since climate prediction is an initial value problem, deterministic nonlinear differential equations meant to model it fall into the instabilities explained in Edward Lorenz's landmark paper "Deterministic Nonperiodic Flow" (J. Atm. Sci., 1963, Vol 20, pp 130-140.) By the way, Lorenz himself was quite humble about his key insight; he noted that, as early as 1950, the British meteorologist Eric Eady published a paper pointing out that "any forecast is just one member of a large ensemble of possible forecasts, and we have no real reason for selecting among those."
If we are arguing over the flutter of butterfly wings shouldn’t there be some serious studies on wind turbine kinetic energy disturbance and its impact on weather and climate before we cover the earth and fill the oceans with them?
An issue I see here is the lack of a common understanding of 'cause.' There seems to be an implicit assumption (actual?) that cause means 'but for' the named event - here, a butterfly flapping its wings - and all else being equal (of course, it never is! everything is in motion at some pace, albeit sometimes that pace is not discernable by humans), the event -- here, a tornado -- would not have happened. I think the math is all very fine but remain unconvinced that there may be some chain of events that link butterflies to tornadoes. I don't know. But the math does not convince me this is not possible.
I have always thought that the butterfly effect was almost certainly nonsense. I'm glad to see a good analysis of why it doesn't happen. Chaos and complexity theory became "cool" but largely untested.
It's been about 20 years since I spent some time analyzing and publishing on the onset of turbulence in transient flows. I appreciate and agree with the point about the dissipation scale and the idea that the butterfly wing is not large enough to have an impact. But the single chain of cause and effect discussed at larger scales does not make sense to me and the reason is that the system of interest involves the coupled, strongly nonlinear interactions within a fluid system. This creates the "extreme sensitivity to initial conditions" mentioned below. It also produces a phenomenon called "baskscatter", whereby small (but large enough) scale motions are nonlinearly coupled back into larger scale motions. One of the main research questions about computational models is (or at least was) the degree to which backscatter below the scales they capture can alter the large-scale results. Simple energy flow arguments about scales above the dissipation scale miss the boat. The physics involved is in no sense a simple, linear system.
R Paul Drake, Professor Emeritus, University of Michigan
I've always taken the Butterfly Effect to just be a statement about the unpredictability of chaotic systems due to their sensitivity to perturbations on all scales. Whether literal butterflies could be involved seems like a fanciful question that could never be answered in practice.
But since Pielke Sr. et al. address that specific question, I have to say I didn't really understand what seems to be their central point, to wit:
"In order for a kinetic energy disturbance to grow in size and/or travel large distances, production of kinetic energy needs to exist at a rate larger than the loss of this energy into heat (called dissipation). The length scale where dissipation dominates in the atmosphere is about 0.1 to 10 millimeters, although it occurs on all spatial scales. At and below this scale, nonlinear turbulent motions essentially do not exist."
I'm not seeing why energy dissipated as heat couldn't be a source of instability. Convective instability refers to the behaviour of an air mass whose temperature differs from its surroundings (see Convective Instability on Wikipedia). The magnitude of the difference determines whether vertical motion will be damped or amplified. Why isn't it possible that a tiny amount of kinetic energy dissipated as heat could push the temperature of an air mass that is already at the edge of instability over the threshold? We're talking about something on a hair trigger -- all you need is a hair.
Like I said, I think the scenario is fanciful because how could we ever know. But I'm not seeing how we can rule it out as a physical impossibility.
I have just read Sr. et al [more correctly: R.A. Pielke Sr., Bo-Wen Shen, and Xubin Zeng] and they really take a simple approach to the physical reality of the effect caused by a butterfly wing flap across real atmosphere, space and time. and, of course, their answer is absolutely correct.
But weather and climate models are clever but, alas, s t u p i d . If one changes the input, say for a value like "global average surface temperature this time step" by as little as 1/100th of a degree, that change may either disappear in the future iterations, or grow and grow and create a physically unrealistic prediction of future temperatures. and no, it does not "average out", neither in the mathematical models or in the real world. .
The spaghetti graphs of climate models predictions, for any future value, show that chaotic effect even after programmatic guardrails are used to hide chaotic results.
The problem seems confusing because we look at a single butterfly, ignoring that at the same time there may be millions of over butterflies, sparrows and crows flapping their wings as well, reinforcing and/or canceling possible effects at distance. Perhaps the effect more closely resembles dither in a digital recording, reducing "noise" and allowing unexpected patterns to emerge from "chaos".
Kip, I think that’s what might not be clear to many of us not in the biz.. does wing flapping actually cause something (which is what it sounds like) or are the models people use extraordinarily sensitive to initial conditions such that a butterfly or an ant scratching its face can change the outcomes? One is about the models, and the other is about physical reality.
Sr. et al are perfectly right. But, like many who read about Chaos and its effects, they are off-base. They are far far too literal in the quip about butterfly wings flapping. It is an interesting uber-academic exercise, but not pertinent to anything.
I will have to read their paper to see if they are really being silly about this flapping business, or if they are pulling our legs.
The Butterfly Effect is the reason that numerical weather prediction has a narrow time limit -- 7 to 10 days. It is the reason that hurricane landfall predictions are only generally valid out 72 hours.
Neither Lorenz or Smagorinsky meant that quip literally. It is meant to illustrate the inescapable fact that small, even infinitesimal, changes to initial inputs can and do have huge effects over many iterations of weather/climate model processes -- those that involve non-linear mathematical equations. This can be referred to as "extreme sensitivity to initial conditions".
Sr. and Shen have indeed explored this idea before... “Is Weather Chaotic? Coexisting Chaotic and Non-Chaotic Attractors within Lorenz Models” and found both types of attractors within Lorenz models (so did Lorenz, by the way).
However one views the butterfly wing's power, it remains that for weather and climate model any difference, no matter how small, can and will generate large difference in model output after many iterations -- that is the primary cause for the huge spread in models predictions we see after 100 years or so. That spread exists despite specific coding to control chaotic effects by limiting results that soar off to infinity and dive to zero.
The first tornado graphic appears to show clockwise rotation. Was this intentional?
Should be easy to test. Plot number of hurricanes vs butterfly habitat destroyed in the Amazon. The two should be correlated. If it is true, we can control hurricanes by killing butterflies.
Glad to see Roger Sr. still in the game!