The butterfly flap

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James Annan

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Oct 14, 2005, 6:58:38 PM10/14/05
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Recently, Roger Pielke Snr has been making comments on his blog about
chaos theory and how it affects the real climate system. Myself and
William Connolley have commeented on his blog and ours, but frankly all
this blog ping-pong is getting a bit tedious and perhaps a few more
perspectives might help to clarify things.

The relevant URLs are:

http://climatesci.atmos.colostate.edu/?p=68
http://climatesci.atmos.colostate.edu/?p=70
http://julesandjames.blogspot.com/2005/10/butterfly-effect.html
http://julesandjames.blogspot.com/2005/10/more-on-butterfly-flap.html
http://mustelid.blogspot.com/2005/10/repeatability-of-gcms.html

Now, as far as I can make it out, RP's position seems to be that
although the models are demonstrably sensitive to small pertubations at
all scales (limited only by numerical resolution, which is of course a
movable threshold), the real world actually is not sensitive in this
way. Of course this is fundamentally unfalsifiable since we cannnot
carry out perturbed pair experiments with the real world, only
models...but he hasn't suggested what physics the model are missing,
except to say that in the real world, all sorts of pertubations (even
momentum) will simply dissipate.

I'm wondering if anyone can suggest any way to make progress.

James
--
James Annan
see web pages for email
http://www.ne.jp/asahi/julesandjames/home/
http://julesandjames.blogspot.com/

Roger Coppock

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Oct 14, 2005, 10:13:30 PM10/14/05
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Gee! I was going to post something, but Dr. Connolley beat me to it:
He said, "
Um, that was pretty weird. "The information from the butterfly is
quickly lost on scales close to the size of the butterfly, as the
atmosphere is a dissipative system such that only particularly
significant powerful forcings, or small climate forcings near a climate
transition (but certainly not as small as a butterfly's flapping
winds) can upscale (i.e., teleconnect) to the global scale." is
wrong. Its provably wrong in climate models, and generally believed to
be wrong in reality."


When we're talking gloabal mean temperatures, a pair of butterfly wings
has zero effect.
Just like the effect of a single supermodel in a thong bikini has on
one male's member.
Tho that human male's member dissipates heat, it doesn't add much to
the global mean
temperature.

Science Cop

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Oct 15, 2005, 12:15:03 AM10/15/05
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Yeah. Grow UP! That would be progress.

SCIENCE has no jails to put science hoaxers in. Science has no armed
law enforcement. Science has only one punishment for science fraud:
complete ostracism. Once a science hoaxer has been identified his
publications are dumped and never mentioned again. Nobody engages the
criminal in arguments or discussions of any kind. Their thoughts are
not worthy of listening to.

THe evidence for Global Warming is conclusive. If you are not familiar
with all the evidence, that is where you ought to be spending your
time. Dragging the lie-filled words and links to Pielke makes you his
accomplice. Stick with him, get punished same as him.

Scientific Death Penalty has no forgiveness, no time limit, no appeals
process. The first serious deliberate science fraud costs you for ever
and ever and ever. Now make a clean separation between you and Pielke
or join him in disgrace.

raylopez99

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Oct 15, 2005, 12:24:06 AM10/15/05
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I suggest you look into the Reynolds number
(http://en.wikipedia.org/wiki/Reynolds_number)

Basically for laminar flow your 'butterfly wings' will dampen out.

For turbulent flow your 'butterfly wings' _may_ increase in value,
depending on what the Navier-Stokes theory predicts.

RL

RayLopez99 @evilfucker.com

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Oct 15, 2005, 12:34:17 AM10/15/05
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raylopez99 wrote:

> I suggest you look into the Reynolds number
> (http://en.wikipedia.org/wiki/Reynolds_number)
>
> Basically for laminar flow your 'butterfly wings' will dampen out.
>
> For turbulent flow your 'butterfly wings' _may_ increase in value,
> depending on what the Navier-Stokes theory predicts.

What does that have to do with 114 oil platforms sunk? Global Warming
is KILLING your Oil Billionaires. I have armies of trained butterflies
flapping their wings on my command. Bwahahahah!!!

http://today.reuters.com/investing/financeArticle.aspx?type=bondsNews&storyID=2005-10-14T192609Z_01_N142817_RTRIDST_0_HURRICANES-PLATFORMS-DESTROYED.XML

WASHINGTON, Oct 14 (Reuters) - The U.S. government has raised its
tally of the number of oil and natural gas platforms in the Gulf of
Mexico destroyed by hurricanes Katrina and Rita to 113, according to
the Interior Department.

Interior Secretary Gale Norton said last week that 108 offshore
platforms had been destroyed by the two storms. That number was
increased to 113 in the department's latest hurricane damage
assessment.

The department also raised the number of underwater pipelines damaged
by the hurricanes to 58 from 44.

The damage to oil and natural gas infrastructure in the Gulf of Mexico
from hurricanes Rita and Katrina this year compared to Hurricane Ivan
last year, based on information from the Interior Department's Minerals
Management Service, is as follows:

Rita Katrina Ivan Platforms Destroyed 66 47 7 Platforms Extensive
Damage 32 20 20 Rigs Adrift 13 6 5 Rigs Extensive Damage 10 9 4 Rigs
Destroyed 4 4 1 Rigs Unaccounted For 0* 0 0 Number of Pipelines Damaged
28 30 102 Platform Evacuation High 754 660 575 Rig Evacuation High 107
89 NA Platforms in Storm Path 1600 1300 150 * 3 missing rigs are
counted as destroyed

Joshua Halpern

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Oct 15, 2005, 1:26:49 PM10/15/05
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Because of the walls where the velocity is zero. An amusing calculation
would be an infinite tube in space with liquid flowing through it, so
that momentum and energy can be transfered without loss to the tube from
the fluid.

Raymond Arritt

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Oct 15, 2005, 1:42:49 PM10/15/05
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James Annan wrote:

> Now, as far as I can make it out, RP's position seems to be that
> although the models are demonstrably sensitive to small pertubations at
> all scales (limited only by numerical resolution, which is of course a
> movable threshold), the real world actually is not sensitive in this
> way. Of course this is fundamentally unfalsifiable since we cannnot
> carry out perturbed pair experiments with the real world, only
> models...but he hasn't suggested what physics the model are missing,
> except to say that in the real world, all sorts of pertubations (even
> momentum) will simply dissipate.

The well-known problems with analog forecasting speak to the "real
world" aspects of sensitivity to initial conditions.

(full disclosure: RAP Sr. was my graduate advisor)

Michael Tobis

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Oct 15, 2005, 2:42:05 PM10/15/05
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The whole discussion is more subtle and interesting that at first I
expected. The clash of an information theory point of view and a
nonlinear dynamics point of view may be quite fruitful.

My take on Ray Lopez's point is that, though surprisingly on-topic for
Ray, it's wrong. In a tube with laminar flow through it, a perturbation
indeed dissipates. This is not because of the Reynolds number, but
because the information associated with the perturbation is advected
out of the tube.

However, if the flow is rapid compared to information propagation
through the fluid (wave velocity), the perturbation will dissipate even
if the flow is turbulent. In this case the real world would lose the
information and the (typical Navier Stokes) discrete model wouldn't
(because numerical noise would flow upstream).

So this seems to back up Pielke's point. It's not that the model fails
to introduce real physics, but that the model introduces false physics.
If my analysis is right then it seems at least possible to construct a
discrete model of a non-chaotic system that is itself chaotic, not
because it is missing properties of the real system but because it
introduces artifacts.

mt

RayLopez99 @evilfucker.com

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Oct 15, 2005, 4:08:14 PM10/15/05
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Raymond Arritt wrote:

> (full disclosure: RAP Sr. was my graduate advisor)

Did Pielke advise you to associate with known criminal science frauds
to enhance your income?

raylopez99

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Oct 15, 2005, 5:59:26 PM10/15/05
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Hey Mike--thanks for the backhand compliment. Idiot.

I think you are hallucenating, and making a mountain out of a molehill,
as usual. Introducing "information theory" into this problem will not
help (next we'll be hearing about the two photon diffraction problem
and information traveling faster than the speed of light). Or perhaps
you misspoke when you said "even if the flow is turbulent"; did you
mean 'even if the flow is laminar?" then the rest of your post is
thought provoking.

Here is what a Princeton science paper on Google --one of many-- says
about perturbations in laminar and in turbulent flow (they dampen in
the former and can amplify in the latter), read it carefully:

In fluid flow, we often interpret the Reynolds number as the ratio of
the inertia force (that is, the force given by mass x acceleration) to
the viscous force. At low Reynolds numbers, therefore, the viscous
force is large compared to the inertia force, and the flow behaves in
some ways like a car with a good suspension system. Small disturbances
in the velocity field, created perhaps by small roughness elements on
the surface, or pressure perturbations from external sources such as
vibrations in the surface or strong sound waves, will be damped out and
not allowed to grow. This is the case for pipe flow at Reynolds numbers
less than the critical value of 2300 (based on pipe diamter and average
velocity), and for boundary layers with a Reynolds number less than
about 200,000 (based on distance from the origin of the layer and the
freestream velocity). As the Reynolds number increases, however, the
viscous damping action becomes comparatively less, and at some point it
becomes possible for small perturbations to grow, just as in the case
of a car with poor shock absorbers. The flow can become unstable, and
it can experience transition to a turbulent state where large
variations in the velocity field can be maintained. If the disturbances
are very small, as in the case where the surface is very smooth, or if
the wavelength of the disturbance is not near the point of resonance,
the transition to turbulence will occur at a higher Reynolds number
than the critical value. So the point of transition does not correspond
to a single Reynolds number, and it is possible to delay transition to
relatively large values by controlling the disturbance environment. At
very high Reynolds numbers, however, it is not possible to maintain
laminar flow since under these conditions even minute disturbances will
be amplified into turbulence.

Cheers,

RL

King Amdo

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Oct 15, 2005, 6:29:02 PM10/15/05
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Hi, just thinking that the butterfly theory thing is observable as
karma what you do has a reaction...as you can see this reaction...if
ones awareness is sufficently tuned...and you are not meant to see this
reaction, and you are suppost to be a naive blind mad moron blundering
about trashing through your own balance and awareness and 'good
karma'...making life more difficult for yourself than should
be...hassled to fuck...into scitzaphenia...the ultimate con/blag...a
mind/reality con....which is why you (I) need a car and are unable to
generate a auspicious reality around you whereby people just offer you
lifts or whatever.


James Annan wrote:
> Recently, Roger Pielke Snr has been making comments on his blog about

> chaos theory...(etc)

<<<<<snip>>>>>

James Annan

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Oct 15, 2005, 6:44:24 PM10/15/05
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Michael Tobis wrote:

Well hey, I can create a model that is unconditionally unstable, even
for a situation where the real world displays laminar flow :-) But I'm
not sure what that has to do with the question.

As far as I can make out his position (and I hope I am not
misrepresenting it), RP agrees that the atmosphere displays "chaotic"
type sensitivity to adequately large perturbations. However, he claims
that it is not at all sensitive to small perturbations, which are
instead simply dissipated (even perturbations to the momentum field). I
put "chaotic" in quotes because of course chaos is _defined_ with
respect to infinitesimal perturbations...

Michael Tobis

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Oct 15, 2005, 6:58:24 PM10/15/05
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> Well hey, I can create a model that is unconditionally unstable, even
> for a situation where the real world displays laminar flow :-)

;-)

My point is that the sensitivity to initial conditions may be peculiar
to the models and conceivably not relevant to the real system. Not that
I actually believe it, but that dismissing the idea isn't trivial.

I don't know if it really means anything to say that a real system is
sensitive to initial conditions. Initial conditions are a mathematical
abstraction, and chaos applies to the model. So waxing philosophical it
may be difficult to resolve the butterfly question, which in any case
is unfalsifiable as you point out.

In my experience, it *is* possible to build models that are
sufficiently strongly forced and dissipative that they track each other
indefinitely even though they have complex eddy dynamics and modestly
different parameters. So I suppose this may be true of some physical
systems, including the weather. It's an interesting question, but of
course weather is not climate.

mt

Michael Tobis

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Oct 15, 2005, 6:58:24 PM10/15/05
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> Well hey, I can create a model that is unconditionally unstable, even
> for a situation where the real world displays laminar flow :-)

;-)

raylopez99

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Oct 15, 2005, 11:45:50 PM10/15/05
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Good point. With a model you can create anything, whether or not it
makes physical sense. Thus for laminar flow you can create a unstable
model where a butterfly wing perturbation creates a hurricane, which
defies real life. Which raises the question posed by Essex & McKitrick
in their book: why should anybody believe the GCMs, which have a grid
space that cannot even approximate tornadoes and local storms, much
less hurricanes? When these storms are what dissipate heat and spread
it all over the earth, and create aerosols and cloud cover which
affects solar energy absorbed by the earth? Perhaps these storms even
change the adiabatic lapse rate, which the same authors claim is
usually modeled by GCMs (incorrectly) as a constant 6.5 C/km.

These are the questions you should be asking, not trivial ones that are
already known.

Modeling is tough work, but models can always be and should be
challenged. That is the stuff of real scientists.

RL

James Annan

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Oct 16, 2005, 2:37:28 AM10/16/05
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Michael Tobis wrote:

>>Well hey, I can create a model that is unconditionally unstable, even
>>for a situation where the real world displays laminar flow :-)
>
>
> ;-)
>
> My point is that the sensitivity to initial conditions may be peculiar
> to the models and conceivably not relevant to the real system. Not that
> I actually believe it, but that dismissing the idea isn't trivial.

It seems that it can be dismissed as non-science, if its proponent
cannot outline any possible experiment to falsify the belief, nor any
alternative model which simulates the atmosphere plausibly without
showing chaotic sensitivity.

As far as I can make out, his arguments about the supposed insensitivity
of reality to small perturbations could apply equally to the existing
models. Indeed, I presume that such intuition was widespread, prior to
Lorenz. Of course in the case of models, such intuition can easily be
proved wrong.

Alastair McDonald

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Oct 16, 2005, 6:34:52 AM10/16/05
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"James Annan" <still_th...@hotmail.com> wrote in message
news:3rarb3F...@individual.net...

> Now, as far as I can make it out, RP's position seems to be that
> although the models are demonstrably sensitive to small pertubations at
> all scales (limited only by numerical resolution, which is of course a
> movable threshold), the real world actually is not sensitive in this
> way. Of course this is fundamentally unfalsifiable since we cannnot
> carry out perturbed pair experiments with the real world, only
> models...but he hasn't suggested what physics the model are missing,
> except to say that in the real world, all sorts of pertubations (even
> momentum) will simply dissipate.
>
> I'm wondering if anyone can suggest any way to make progress.

This may help, but it not the final solution :-(.

The point to remember is that chaos is caused by positive feedback.
A butterfly flapping its wings will have no effect unless its effects are
amplified. If so, they could end up as a tornado. But you need an
additional factor to produce this amplification.

In the atmosphere the amplification is usually provided by instability.
The instability is due to the water vapour in the air, which can provide
the positive feedback to the air as it rises. If the air was conditionally
unstable, and the butterfly flapped it wings then the tornado could be
triggered, but not on the other side of the world. This agrees with
what RP has pointed out.

One point to note is that there is a common misunderstanding about
cause and effect. An effect is generally the result of several causes,
not just one. If a brick falls and breaks your toe, is the cause Newton's
gravitation, your carelessness in dropping it, your curiosity in picking it
up,
or my indolence in not putting the spare bricks back on the pile after
building your patio wall? In fact if your wife had not demanded that wall,
your toe would not now be swollen.

Similarly, a butterfly flapping its wings in Brazil will not be the sole cause
of a tornado in the USA.

The other butterfly effect, the strange attractor which looks like a butterfly
raises another issue. With the effects that cause it, the initial conditions
determine its path. Since it never passes through the same point twice,
the initial conditions describe a unique path. However, this path is bound
by the shape of the strange attractor, i.e. it is always inside the outline
of the butterfly, therefore it is possible to predict approximately where
it will be, but not exactly. In other words weather it the point at which
the path is, day to day. Climate is the shape of the butterfly.

NB. This is a slightly different description of climate. It is no longer a
linear average of weather. It is the strange attractor described by
weather. I.e.. weather is a point of the curve, climate is the curve
itself. But sometimes we use the term weather to describe a short
segment of the curve, such as when we ask "What will the weather
be like over the weekend?" Actually, we never, in common parlance,
use weather to describe a point on the curve because that would
be infinitely small, which would be meaningless to the average layman.

There another point, but I do not know the answer to it. If you increase
the amount of positive feedback, you move from strange attractors
into white noise. White noise appears to be random, but it also has
a maximum bound. I would be interested to know how you calculate
that upper bound, because I believe that the weather is not random.
It is white noise.

Ray Lopez is associating chaos with turbulence. As the volume
of water passing through a tube increases, the water flow changes
from laminar to turbulent flow. I am not sure where positive feedback
fits into that scheme of things. But I will now try to explain it. The
friction against the walls of the tube prevents the flow there reaching
the maximum because it is made turbulent. As the flow increases,
the turbulent layer next to the wall thickens exponentially, forcing the
water in the centre of the tube to flow faster and so widen the layer
of turbulent flow, until this positive feedback has converted the total
width of the tube to be turbulent.

The above could probably be described more eloquently proving
that positive feedback is necessary. But it would seem that
unless the butterfly in Brazil could flap its wings so strongly that
it created a wind which created turbulence against the Earth's
surface, Reynolds's number does not apply in these circumstances,
and Ray Lopez is talking nonsense as usual :-)

HTH,

Cheers, Alastair.

peroxisome

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Oct 16, 2005, 7:30:40 PM10/16/05
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James Annan wrote:
> Recently, Roger Pielke Snr has been making comments on his blog about
> chaos theory and how it affects the real climate system. <snip>

> Of course this is fundamentally unfalsifiable since we cannnot
> carry out perturbed pair experiments with the real world, only
> models...

errr, not to put too fine a point on it, models in themselves are not a
verification of anything. You have to match model predictions against
experimental data, to find out if the model is good.

If you have a (hidden) assumption in your model, you cannot simply say
that a contrary assumption is wrong, because it cannot be tested ! The
assumption in the model can equally be wrong.

yours
per

James Annan

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Oct 16, 2005, 9:19:02 PM10/16/05
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A moment's reflection has shown that it is trivial to build models
where the chaos is purely an artefact of the numerical solution, and
the underlying continuum equation is non-chaotic.

Consider

x'=2.6x-3.6x^2

(x' is the derivative of x wrt time)

Clearly for any positive initial condition x0>0, this system converges
to teh stable solution x=2.6/3.6. Forward time-stepping with a small
time step will yield essentially the same result. However, with a time
step of dt=1, we get the famous discrete logistic map

x+ = 3.6x(1-x)

(x+ is the successor to x in a discrete series)

which is chaotic. I expect that the Lotka-Volterra equations etc will
behave similarly. However, it's hard to see this being relevant to
atmospheric physics - it is a form of numerical instability, which is
easily ruled out for atmospheric models. Anyway, RP's argument is not
that the continuum equations of the model are themselves non-chaotic,
he appears to be claiming that the real atmosphere is non-chaotic, and
therefore any continuum equations or model that exhibits chaotic
behaviour must necessarily be doing so due to its incomplete
representation of the real physics.

James

Raymond Arritt

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Oct 16, 2005, 11:21:21 PM10/16/05
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James Annan wrote:

> Anyway, RP's argument is not
> that the continuum equations of the model are themselves non-chaotic,
> he appears to be claiming that the real atmosphere is non-chaotic, and
> therefore any continuum equations or model that exhibits chaotic
> behaviour must necessarily be doing so due to its incomplete
> representation of the real physics.

Ensembles of numerical simulations that begin with different initial
conditions tend to be under-dispersive. That is, the range of outcomes
in the model tends to be smaller than the range of outcomes in the real
world. Perhaps this under-dispersiveness implies that the real
atmosphere is even more chaotic than model atmospheres. But I'm not a
dynamical systems jock -- so, does anyone know if this is a reasonable
inference?

James Annan

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Oct 17, 2005, 12:57:56 AM10/17/05
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I think the most common inference from this is that the model has a
drift due to model error, so the whole ensemble diverges from reality.
People try to compensate for this by adding more spread, but this is
essentially because they do not know the direction of the drift, rather
than because the model doesn't show adequate chaotic sensitivity.

(One way to check on the relative importance of model error [drift] v
chaotic sensitivity to initial conditions in real forecasting is to
look at the growth of forecast error over time. IIRC it is generally
linear rather than exponentional at first, indicating that the former
dominates. Nevertheless, the behaviour of rapidly-growing perturbations
is a useful guide to forecast skill.)

As a further thought on the matter, although we cannot of course do
perturbed-pair experiments with the real world, we can do so with
smaller chaotic systems such as some electrical circuits and the
thermally-forced rotating annulus. If Roger's theory is a general one,
then he should be able to give sufficient conditions for replicated
experiments to give identical results in these cases too (ie, so long
as the initial conditions in the replicated experiment are everywhere
within some delta of the original, the states will converge and the
output will replicate indefinitely).

James

Phil Hays

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Oct 17, 2005, 2:09:25 AM10/17/05
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"James Annan" wrote:

>As a further thought on the matter, although we cannot of course do
>perturbed-pair experiments with the real world, we can do so with
>smaller chaotic systems such as some electrical circuits and the
>thermally-forced rotating annulus. If Roger's theory is a general one,
>then he should be able to give sufficient conditions for replicated
>experiments to give identical results in these cases too (ie, so long
>as the initial conditions in the replicated experiment are everywhere
>within some delta of the original, the states will converge and the
>output will replicate indefinitely).

Why limit this challenge to just real world experiments? Is there a
mathematical system that is chaotic in the large scale, but for which
most differences in state less than some delta would converge and
replicate the output indefinitely?

It would seem to me that such systems exist. I think that many fairly
trivial examples could be generated. What would be more interesting
is a system that was more like the atmosphere and still had such
behavior.

I'm rather less than sure that the real weather/climate system is such
a system. But there is a different effect that may well be worth
thinking about. If the mythical butterfly did flap, it injects a
certain amount of energy into the system. This energy will grow with
time (assuming a Lyapunov exponent of > 1). However, if random noise
from other sources (radioactive decays, cosmic inputs to the
atmosphere, anything else) was larger, in total, than the energy from
the butterfly, then even if we could run controlled experiments for
all but these random factors, with and without the mythical butterfly,
the runs would diverge before the butterfly's energy could matter due
to the large other differences

So isn't there a minimum sized event of interest? For the weather
system, it is probably rather larger than a butterfly.


--
Caution: Contents may contain sarcasm.
Phil Hays

Phil Hays

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Oct 17, 2005, 2:20:06 AM10/17/05
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larger other differences.

James Annan

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Oct 17, 2005, 2:50:25 AM10/17/05
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Phil Hays wrote:
> "James Annan" wrote:
>
> >As a further thought on the matter, although we cannot of course do
> >perturbed-pair experiments with the real world, we can do so with
> >smaller chaotic systems such as some electrical circuits and the
> >thermally-forced rotating annulus. If Roger's theory is a general one,
> >then he should be able to give sufficient conditions for replicated
> >experiments to give identical results in these cases too (ie, so long
> >as the initial conditions in the replicated experiment are everywhere
> >within some delta of the original, the states will converge and the
> >output will replicate indefinitely).
>
> Why limit this challenge to just real world experiments? Is there a
> mathematical system that is chaotic in the large scale, but for which
> most differences in state less than some delta would converge and
> replicate the output indefinitely?
>
> It would seem to me that such systems exist. I think that many fairly
> trivial examples could be generated. What would be more interesting
> is a system that was more like the atmosphere and still had such
> behavior.

Since chaotic behaviour is defined with reference to infinitesimal
perturbations, I think you'd have to tighten up your definition of
"chaotic in the large scale" for the premise to make sense. OTOH, one
can certainly construct conditionally stable systems that are
insensitive to small perturbations but react to large ones. Eg consider
a ball bearing rolling around in a local minimum, until it is pushed
hard enough to roll to a new one. But that is not chaotic. Computer
models are also insensitive to perturbations below their numerical
resolution, but then again, they are not strictly chaotic anyway (for
precisely that reason).

The chaos in atmospheric models arises directly from the fundamental
equations that govern all fluid flow, so one would have to overturn
quite a lot of well-established physics to generate a qualitatively
different model.

James

James Annan

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Oct 17, 2005, 7:21:45 AM10/17/05
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peroxisome wrote:

I didn't say his assumption was wrong because it could not be tested. I
said it was unfalsifiable as it cannot be tested.

peroxisome

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Oct 17, 2005, 8:09:31 AM10/17/05
to

James Annan wrote:
>
> I didn't say his assumption was wrong because it could not be tested. I
> said it was unfalsifiable as it cannot be tested.
> It seems that it can be dismissed as non-science,..."
correct; my bad.
surely if it is unfalsifiable, neither the assumption for or against
can be held to be true ?

You are in the position where you have a hidden assumption in your
model, and you are saying that this assumption cannot be tested. Your
assumption is that the models are sensitive to perturbations at small
scales; but you can't test this either.

slightly confused
per

James Annan

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Oct 17, 2005, 8:29:11 AM10/17/05
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peroxisome wrote:

> James Annan wrote:
>
>>I didn't say his assumption was wrong because it could not be tested. I
>>said it was unfalsifiable as it cannot be tested.
>>It seems that it can be dismissed as non-science,..."
>
> correct; my bad.
> surely if it is unfalsifiable, neither the assumption for or against
> can be held to be true ?

Assumptions against it may be (potentially) held to be scientific in
nature, assuming they are subject to testing.

I should make clear that my suspicion that RP's position is
unfalsifiable is by no means set in stone. It remains possible that he
will provide a clearer description of his position such that it can be
tested.

> You are in the position where you have a hidden assumption in your
> model, and you are saying that this assumption cannot be tested. Your
> assumption is that the models are sensitive to perturbations at small
> scales; but you can't test this either.

One can certainly test the proposition that a model is susceptible to
small perturbations. It has been repeatedly demonstrated.

peroxisome

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Oct 17, 2005, 9:00:09 AM10/17/05
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James Annan wrote:

> peroxisome wrote:
>
> > You are in the position where you have a hidden assumption in your
> > model, and you are saying that this assumption cannot be tested. Your
> > assumption is that the models are sensitive to perturbations at small
> > scales; but you can't test this either.
>
> One can certainly test the proposition that a model is susceptible to
> small perturbations. It has been repeatedly demonstrated.

yes; that would be an assumption of the model. Whether that has
anything to do with the real world, according to you, is something that
cannot be tested.

yours
per

Phil Hays

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Oct 17, 2005, 10:39:28 AM10/17/05
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"James Annan" wrote:
>Phil Hays wrote:

>> Why limit this challenge to just real world experiments? Is there a
>> mathematical system that is chaotic in the large scale, but for which
>> most differences in state less than some delta would converge and
>> replicate the output indefinitely?
>>
>> It would seem to me that such systems exist. I think that many fairly
>> trivial examples could be generated. What would be more interesting
>> is a system that was more like the atmosphere and still had such
>> behavior.
>
>Since chaotic behaviour is defined with reference to infinitesimal
>perturbations, I think you'd have to tighten up your definition of
>"chaotic in the large scale" for the premise to make sense. OTOH, one
>can certainly construct conditionally stable systems that are
>insensitive to small perturbations but react to large ones. Eg consider
>a ball bearing rolling around in a local minimum, until it is pushed
>hard enough to roll to a new one. But that is not chaotic. Computer
>models are also insensitive to perturbations below their numerical
>resolution, but then again, they are not strictly chaotic anyway (for
>precisely that reason).

Computer models, or more correctly some thoughts on digital signal
processing, is what that started this thought. Behavior near the
numerical resolution can be rather different than large scale
behavior.


>The chaos in atmospheric models arises directly from the fundamental
>equations that govern all fluid flow, so one would have to overturn
>quite a lot of well-established physics to generate a qualitatively
>different model.

Other than the passing thought that the atmosphere has a "numerical
resolution" at around 6*10^-23. Navier-Stokes is true for large
collections of atoms, not for individual atoms. This might mean that
the atmosphere is not strictly chaotic in the mathematical sense as
well. Which is why such a model would be more interesting.

If one could show that the mythical butterfly's wing flap would decay
to less than this "atmospheric numerical resolution", then again
experiments, with and without the mythical butterfly, would not be
meaningfully different. They diverge for other reasons (noise inputs
from all other sources).

Michael Tobis

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Oct 17, 2005, 12:07:19 PM10/17/05
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I think the idea (Reid B's (Bryson's?) position) that one can't model a
system with a chaotic model is ludicrous.

That said, I don't think the question of whether the real world is
chaotic is well-posed. So I agree with Phil here (if I'm understanding
him correctly). To put it another way,while "the mathematics that
describe fluid flow" are an excellent and fascinating approximation, in
mathematical questions dealing with inifitesimals it's not at all clear
that they apply. I'm not even

I think the information theoretic point of view advocated by the
Colorado State people (my advisor was a CS grad, btw) does have
something to offer.

While there are constant "innovations" (in the statistical sense) the
amount of information in the system is constant. Therefore some
information must constantly be lost.

This is why we will never be able to obtain a very high resolution CGCM
of the Devonian, for instance. Topographic information is irrecoverably
lost. As a consequence, one might feel that it is reasonable to say
that the continental configuration of the Devonian has no influence on
today's weather. Even though misplacing a pebble (there having been no
butterflies then) would have led to a different trajectory, there is no
way to establish that causality going backwards.

You and RP, it seems to me, are using similar words to describe
different things.

Causality is tricky business in continuum dynamics. Pinatubo caused a
global cooling in a meaningful sense that is much more robust and of
much more practical interest than the way a butterfly "causes" a
tornado.

mt

D.H. Gottlieb

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Oct 17, 2005, 12:32:25 PM10/17/05
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Hi,

The issue here is the type of model you are creating: statististical,
numeric, queue, non-linear, and the level of granularity you can
reasonably expect. At what level of granularity do we all agree we have
a "real and reliable model"?
Granularity and reality in a model are tied to computing power--still.
The deterministic nature of Chaotic systems add a complexity that
requires a very high level computing--read here sophisiticated software
and lots of power. We are not yet up to the task because there is an
issue with non-graceful failure in unbounded sets (and models) which
require us to reason over them over time.
Models are not the answer. They weren't the answer 20 years ago and
they are still not up to the task of modeling large Chaotic systems.


D.H. Gottlieb
www.thegalileosyndrome.com

Michael Tobis

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Oct 17, 2005, 1:15:51 PM10/17/05
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Gee I thought I'd proofed that... drop the sentence fragment and spell
"infinitesimals" sensibly, thanks.

mt

James Annan

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Oct 17, 2005, 7:01:02 PM10/17/05
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Michael Tobis wrote:

> I think the idea (Reid B's (Bryson's?) position) that one can't model a
> system with a chaotic model is ludicrous.
>
> That said, I don't think the question of whether the real world is
> chaotic is well-posed. So I agree with Phil here (if I'm understanding
> him correctly). To put it another way,while "the mathematics that
> describe fluid flow" are an excellent and fascinating approximation, in
> mathematical questions dealing with inifitesimals it's not at all clear
> that they apply. I'm not even
>
> I think the information theoretic point of view advocated by the
> Colorado State people (my advisor was a CS grad, btw) does have
> something to offer.

Do you have any explanation of how the "information theoretic" point of
view fails to be valid for the models? Even a vague guess would be a
start...

Of course, such a view is easily proven false with models, but I'm
asking if one can see how the cases of models and reality could be
distinguished a priori. After all, the models contain representations of
friction and dissipation, which one might expect to cause "information"
to be lost (indeed, this seems to be the entire basis of RP's claim that
the real world is not chaotic).

I find it hard to accept that the information theoretic argument also
allows momentum to dissipate, as RP claims will occur.

> You and RP, it seems to me, are using similar words to describe
> different things.

Well, RP seems to be specifically using the language of standard chaos
theory, and he is using the result that the models are chaotic as (one
more) reason for rejecting them.

James Annan

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Oct 17, 2005, 7:12:03 PM10/17/05
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Phil Hays wrote:

But one can change the numerical resolution at will, thus any scale can
be accurately modelled.

>
>
> Other than the passing thought that the atmosphere has a "numerical
> resolution" at around 6*10^-23. Navier-Stokes is true for large
> collections of atoms, not for individual atoms. This might mean that
> the atmosphere is not strictly chaotic in the mathematical sense as
> well. Which is why such a model would be more interesting.
>
> If one could show that the mythical butterfly's wing flap would decay
> to less than this "atmospheric numerical resolution", then again
> experiments, with and without the mythical butterfly, would not be
> meaningfully different. They diverge for other reasons (noise inputs
> from all other sources).

Certainly all I have written is based on a clasical continuum view of
the world, which breaks down eventually. Nothing that RP has written
indicates that he is talking about perturbations at the molecular or
smaller scale. I guess at the quantum scale it might be better to talk
about the probabilities of future outcomes changing or something. I
don't know if and where this has been discussed.

Michael Tobis

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Oct 17, 2005, 7:09:00 PM10/17/05
to
I'll revisit the conversation. I'm certainly not saying modeling is
pointless. My opinion is more that chaos theory itself is pointless.

I am saying that "chaos" is a mathematical property of continuous
systems, and if you start splitting hairs neither the computer model
nor the system modeled is a continuous system. Of course,
hair-splitting is what chaos is all about.

The "butterfly" is a mathematical abstraction. Real butterflies causing
real tornados strikes me more as unverifiable philophical meandering
than as anything with any practical importance.

mt

Raymond Arritt

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Oct 17, 2005, 7:48:13 PM10/17/05
to

It's worth pointing out that chaotic behavior is a result, not an
assumption, of the equations used in the model. The primitive equations
of fluid motion were well known long before their chaotic nature was
appreciated.

James Annan

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Oct 18, 2005, 7:29:32 AM10/18/05
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Michael Tobis wrote:

> I'll revisit the conversation. I'm certainly not saying modeling is
> pointless. My opinion is more that chaos theory itself is pointless.
>
> I am saying that "chaos" is a mathematical property of continuous
> systems, and if you start splitting hairs neither the computer model
> nor the system modeled is a continuous system. Of course,
> hair-splitting is what chaos is all about.
>

That seems like rather too determined a cop-out. Yes, chaos is a
propertly of mathematical systems. At some level, the continuum view of
fluid flow breaks down. However, it seems to me that chaos theory tells
us that the reality is also susceptible to small perturbations at
least so long as we do not get too close to the threshold at which the
continuum description breaks down, and every experimentally-accessible
system confirms this view to the level that we can initialise and
measure them. A butterfly is still many many orders of magnitude removed
from a molecule. If there is a threshold below which a perturbation does
not matter, it is below our abilities to measure and control even in
simple systems such as electrical circuits.

> The "butterfly" is a mathematical abstraction. Real butterflies causing
> real tornados strikes me more as unverifiable philophical meandering
> than as anything with any practical importance.

No-one is talking about actually tracing cause to effect over such
scales. RP is apparently using the chaotic behaviour of models as
evidence that they are unrealistic, because it contradicts his intuition
that the real world isn't!

Thomas Palm

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Oct 18, 2005, 9:49:29 AM10/18/05
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"Michael Tobis" <mto...@gmail.com> wrote in news:1129590540.714354.44490
@g44g2000cwa.googlegroups.com:

> I'll revisit the conversation. I'm certainly not saying modeling is
> pointless. My opinion is more that chaos theory itself is pointless.
>
> I am saying that "chaos" is a mathematical property of continuous
> systems, and if you start splitting hairs neither the computer model
> nor the system modeled is a continuous system. Of course,
> hair-splitting is what chaos is all about.

Chaos can be found in pretty simple systems such as a double pendulum. In
no way do you need a continous system.



> The "butterfly" is a mathematical abstraction. Real butterflies causing
> real tornados strikes me more as unverifiable philophical meandering
> than as anything with any practical importance.

The only real importance seems to be that it puts a theoretical upper limit
to how accurate weather forecasts can ever become.

Another interesting question is how far up in scale chaos is important. A
butterfly may be able to change the path of a hurricane, but can it change
an El Niño? Can it move the start of an ice age?

Michael Tobis

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Oct 18, 2005, 10:50:17 AM10/18/05
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Thomas Palm wrote:
> "Michael Tobis" <mto...@gmail.com> wrote in news:1129590540.714354.44490
> @g44g2000cwa.googlegroups.com:
>
> > I'll revisit the conversation. I'm certainly not saying modeling is
> > pointless. My opinion is more that chaos theory itself is pointless.
> >
> > I am saying that "chaos" is a mathematical property of continuous
> > systems, and if you start splitting hairs neither the computer model
> > nor the system modeled is a continuous system. Of course,
> > hair-splitting is what chaos is all about.
>
> Chaos can be found in pretty simple systems such as a double pendulum. In
> no way do you need a continous system.

If I understand you correctly this is a lumped system, but one which is
modeled by parameters with coninuous rather than quantum states. Both
the model and the real world are quantized. But I think this is a
quibble.

> > The "butterfly" is a mathematical abstraction. Real butterflies causing
> > real tornados strikes me more as unverifiable philophical meandering
> > than as anything with any practical importance.
>
> The only real importance seems to be that it puts a theoretical upper limit
> to how accurate weather forecasts can ever become.

Well, there was already an upper limit based upon how well we can
identify the initial conditions. It's not clear this interesting
theoretical abstraction adds anything much in practice, since we have
no hope of actually finding out what the predictability limit due to
chaos, or to unresolved phenomena, or to poorly resolved boundary and
initial conditions. I agree that is the main importance of it, and it
just doesn't seem to matter much.

I think what James and William are exercised about is how Pielke and
Bryson conclude anything about climate and climate modeling from this.
On this point I have to agree with them. I think we need to frame the
argument carefully, sionce if even professionals miss the point we can
hardly expect the lay public to resist misuse of the concept.

However, they are saying that what Pielke is saying is meaningless. I
do find some of what he is saying a bit wrongheaded. On the other hand,
I agree with Pielke that it's doubly wrong (both incorrect and
counterproductive) to be saying that butterflies cause tornados.
Perhaps I go further because I think it's equally wrong whether in the
real world or in dynamical models.

It's wrong because it uses a sense of causality that is useless, and
it's counterproductive because this delicate and lovely but essentially
sterile piece of mathematics is being used to confuse and misdirect
public debates of matters of great import.

> Another interesting question is how far up in scale chaos is important. A
> butterfly may be able to change the path of a hurricane, but can it change
> an El Niño? Can it move the start of an ice age?

Is El Nino weather or climate?

Is it fair to say that chaos is essentially unforced?

El Nino is an unforced variability, and is hard to predict, as are some
of the other interannual and decadal modes of the ocean. Culturally
speaking prediction of these phenomena is considered climate
prediction, but formally they are better considered as weather.

Nevertheless, tides and seasons remain predictable on very long time
scales. These are forced variations.

Anthropogenic climate change is forced and hence predictable, or at
least, in no way fundamentally limited by chaos theory properly
understood. All this talk of chaos is a red herring, and I'm
discouraged to see everyone picking at it, rather than explaining that
it's more interesting than it is important.

mt

Phil Hays

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Oct 18, 2005, 10:55:41 AM10/18/05
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James Annan wrote:

>Phil Hays wrote:

>> Other than the passing thought that the atmosphere has a "numerical
>> resolution" at around 6*10^-23. Navier-Stokes is true for large
>> collections of atoms, not for individual atoms. This might mean that
>> the atmosphere is not strictly chaotic in the mathematical sense as
>> well. Which is why such a model would be more interesting.

>> If one could show that the mythical butterfly's wing flap would decay
>> to less than this "atmospheric numerical resolution", then again
>> experiments, with and without the mythical butterfly, would not be
>> meaningfully different. They diverge for other reasons (noise inputs
>> from all other sources).

>Certainly all I have written is based on a clasical continuum view of
>the world, which breaks down eventually. Nothing that RP has written
>indicates that he is talking about perturbations at the molecular or
>smaller scale.

If the mythical butterfly's wing flap swirled 0.2 liters of air, that
is 10^-3 moles, or 6*10^20 atoms. While it is not exactly correct to
decay the swirl by numbers of atoms, I'm going to do so. An
alternative might be to track energy of atoms with numbers of such
groups, to which I'm going to wave my arms and declare that will give
a roughly similar result. Small swirls of air have a short lifetime,
I'm going to use a time constant of 5 seconds. On the other end,
large scale disturbances in the atmosphere grow at varying rates, some
on the scale of weeks, and others grow in hours. If our mythical
butterfly was in stable air lasting a few hours, the swirl might have
~2000 time constants of decay before it would have a chance to start
growing, and would have ~10^-580 atoms involved at the time it started
growing. I would venture that this is enough to break the classical
continuum view of the mythical butterfly.

w...@bas.ac.uk

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Oct 18, 2005, 12:09:09 PM10/18/05
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>mt


--
William M Connolley | w...@bas.ac.uk | http://www.antarctica.ac.uk/met/wmc/
Climate Modeller, British Antarctic Survey | Disclaimer: I speak for myself
I'm a .signature virus! copy me into your .signature file & help me spread!

Michael Tobis

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Oct 18, 2005, 12:10:34 PM10/18/05
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Maybe that's what RP is trying to say. It's wrong. I think you said it
better, so now it can be refuted easily enough.

Yes, the perturbation would settle into undetectable noise long before
it made a measurable difference. But it would be *different* noise.
What chaos theory shows is that in principle, this may suffice to cause
the perturbed and unperturbed systems to diverge.

On the other hand, it's absolutely right. The butterfly doesn't cause
the divergence. The difference in the uncontrollable noise difference
between the two realizations causes the divergence. In any realizable
sense, just having two physically distinct realizations is sufficient
for them to diverge, No butterfly is necessary. If there are three
realizations, one with butterfly and two without, there is no way to
distingush between the two without a butterfly and the one with. So
it's hard to say the butterfly caused anything at all.

These are two different, equally valid, ways of looking at the problem.
I think the latter way is more useful, especially since we don't need
to appeal to butteflies in a quantum universe to get non-predicatbility
anyway.

mt

w...@bas.ac.uk

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Oct 18, 2005, 12:16:48 PM10/18/05
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Michael Tobis <mto...@gmail.com> wrote:
>I think what James and William are exercised about is how Pielke and
>Bryson conclude anything about climate and climate modeling from this.

Somewhat unusually, I disagree with you pretty thoroughly about all
this. This probably means that someone is using words in different ways.

As far as I'm concerned this is nothing to do with climate. We're
talking about weather. I've said before (blog; elsewhere) that I
don't think the climate is chaotic, but that it changes smoothly
wrt to perturbations (in most cases).

>On this point I have to agree with them. I think we need to frame the
>argument carefully, sionce if even professionals miss the point we can
>hardly expect the lay public to resist misuse of the concept.

Probably. RP's point is that small perturbations don't grow, they
decay. This is WRONG, as far as I'm concerned. Certainly in GCMs,
its provably wrong: small perturbations amplify.

>However, they are saying that what Pielke is saying is meaningless.

No. Its potentially meanginful, but wrong.

>I
>do find some of what he is saying a bit wrongheaded. On the other hand,
>I agree with Pielke that it's doubly wrong (both incorrect and
>counterproductive) to be saying that butterflies cause tornados.

In GCMs, there is a sense in which butterflies can cause tornados. It
is this:

Take a GCM run. Record its output. Now, impose a minor perturbation
to the initial conditions and re-run. After a month, the weather will
be different. Select a day when there is a tornado (well, a mid-lat
cyclone will have to do because they don't have the rez for tornadoes)
in run 2 but not in run 1. There you have it: a tornado caused by a
minor perturbation.


> It's wrong because it uses a sense of causality that is useless,

true, but thats not the point. And in attempting to defned that kind
of view, RP has stepped well over into making completely false
statements.

>Is El Nino weather or climate?

Weather

-W.

Thomas Palm

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Oct 18, 2005, 12:55:20 PM10/18/05
to
"Michael Tobis" <mto...@gmail.com> wrote in
news:1129647017.5...@g44g2000cwa.googlegroups.com:

> Thomas Palm wrote:
>> "Michael Tobis" <mto...@gmail.com> wrote in
>> news:1129590540.714354.44490 @g44g2000cwa.googlegroups.com:
>>
>> > I'll revisit the conversation. I'm certainly not saying modeling is
>> > pointless. My opinion is more that chaos theory itself is
>> > pointless.
>> >
>> > I am saying that "chaos" is a mathematical property of continuous
>> > systems, and if you start splitting hairs neither the computer
>> > model nor the system modeled is a continuous system. Of course,
>> > hair-splitting is what chaos is all about.
>>
>> Chaos can be found in pretty simple systems such as a double
>> pendulum. In no way do you need a continous system.
>
> If I understand you correctly this is a lumped system, but one which
> is modeled by parameters with coninuous rather than quantum states.
> Both the model and the real world are quantized. But I think this is a
> quibble.

It's a lumped system: one pendulum attacked to the end of another. You
happen to be right that since this is angular motion it is quantized even
in reality, but the quanta will be absurdly small and for any
perturbation large enough to shift between them motion is chaotic.

>> > The "butterfly" is a mathematical abstraction. Real butterflies
>> > causing real tornados strikes me more as unverifiable philophical
>> > meandering than as anything with any practical importance.
>>
>> The only real importance seems to be that it puts a theoretical upper
>> lim
> it
>> to how accurate weather forecasts can ever become.
>
> Well, there was already an upper limit based upon how well we can
> identify the initial conditions. It's not clear this interesting
> theoretical abstraction adds anything much in practice, since we have
> no hope of actually finding out what the predictability limit due to
> chaos, or to unresolved phenomena, or to poorly resolved boundary and
> initial conditions. I agree that is the main importance of it, and it
> just doesn't seem to matter much.

If Pielke is right and small perturbations decay there would be hope that
we one day can measure the system good enough to make essentially perfect
weather forecasts. If he is wrong it is a waste of resources to even try
since adding more data will give diminishing returns. Sometimes knowing
what problems you can't solve is quite useful.

> However, they are saying that what Pielke is saying is meaningless. I
> do find some of what he is saying a bit wrongheaded. On the other
> hand, I agree with Pielke that it's doubly wrong (both incorrect and
> counterproductive) to be saying that butterflies cause tornados.
> Perhaps I go further because I think it's equally wrong whether in the
> real world or in dynamical models.

I would say it is trivially right, however at that level of detail there
will be trillions of other causes to a tornado so it may not be useful.
It's something that can be fun to talk about among scientists, but I
agree that the public debate is rather pointless and often misleading.
It's like people talking about everything being relative, which drove
Einstein nuts.

Under some conditions you can control chaotic systems in a very elegant
way using little energy by pushing them from one attractor to another. I
don't know if this has been applied in any practical application yet, but
there has been theoretical suggestions that seem sound for making
mechanical systems that can be controlled with little energy. I doubt
this is realistic for weather since it is so horribly complicated, but it
is at least a possibility. I wouldn't entirely dismiss the possibility
that one day chaos theory will help us change the track of a hurricane
without having to use nukes or other brute force methods.

> Nevertheless, tides and seasons remain predictable on very long time
> scales. These are forced variations.

Talking about useless knowledge: the solar system itself is chaotic,
which means the orbit of the moon is it to some extent on long enough
timescales. This will mean that you can't predict tides arbitrarily long
into the future.



> Anthropogenic climate change is forced and hence predictable, or at
> least, in no way fundamentally limited by chaos theory properly
> understood. All this talk of chaos is a red herring, and I'm
> discouraged to see everyone picking at it, rather than explaining that
> it's more interesting than it is important.

At least it is too technical to attract the loonies so it is a scientific
discussion, which isn't too common in this group nowadays :-(

While anthopogenic climate change probably isn't chaotic it is non-
linear, and it may be sensitive so that small changes in forcing will
end up in very different final states. I suspect this sensitivity is
limited to certain thresholds though, not as in chaos where a small
initial change always causes huge differences after a while.

Eric Swanson

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Oct 18, 2005, 1:08:42 PM10/18/05
to
In article <4355...@news.nwl.ac.uk>, w...@bas.ac.uk says...

>
>Michael Tobis <mto...@gmail.com> wrote:
>>I think what James and William are exercised about is how Pielke and
>>Bryson conclude anything about climate and climate modeling from this.
>
>Somewhat unusually, I disagree with you pretty thoroughly about all
>this. This probably means that someone is using words in different ways.
>
>As far as I'm concerned this is nothing to do with climate. We're
>talking about weather. I've said before (blog; elsewhere) that I
>don't think the climate is chaotic, but that it changes smoothly
>wrt to perturbations (in most cases).
>
>>On this point I have to agree with them. I think we need to frame the
>>argument carefully, sionce if even professionals miss the point we can
>>hardly expect the lay public to resist misuse of the concept.
>
>Probably. RP's point is that small perturbations don't grow, they
>decay. This is WRONG, as far as I'm concerned. Certainly in GCMs,
>its provably wrong: small perturbations amplify.
>
>>However, they are saying that what Pielke is saying is meaningless.
>
>No. Its potentially meanginful, but wrong.

But, in the real world, small vortices exist. They form often in high
energy flows over mountains and around valleys. They form as dust devils
over hot surfaces. They form at the tips of wings of large jet aircraft.
All seem to damp out rather quickly, unless the underlying conditions can
couple in enough energy to allow them to grow. If perturbations as small
as the shed vortex from a jumbo jet caused tornados in the real world,
then we would likely have seen a measurable increase in the number over the
past 50 years, the result of more jet flights and a steady trend toward
heavier aircraft.

>>I
>>do find some of what he is saying a bit wrongheaded. On the other hand,
>>I agree with Pielke that it's doubly wrong (both incorrect and
>>counterproductive) to be saying that butterflies cause tornados.
>
>In GCMs, there is a sense in which butterflies can cause tornados. It
>is this:
>
>Take a GCM run. Record its output. Now, impose a minor perturbation
>to the initial conditions and re-run. After a month, the weather will
>be different. Select a day when there is a tornado (well, a mid-lat
>cyclone will have to do because they don't have the rez for tornadoes)
>in run 2 but not in run 1. There you have it: a tornado caused by a
>minor perturbation.

But, tornados are sub-grid phenomina in climate change GCM's, I think. The
weather model guys work with higher resolutions, but a tornado is an intensly
local affair. I think you are really saying that the conditions for a tornado
appear in the models on one day in the run, but not in the same day of a run
with slightly different initial conditions. Are you thinking of initial
conditions strictly limited to a change in what we called "vorticity" when I
was trying to learn fluid dynamics (it was my worst subject)? Do all such
small changes lead to increases in tornados, or are there other portions of the
initial conditions for model runs which produce the other factors which feed
energy into the tornado? When this sort of experiment is repeated with finer
resolution, does the same result emerge, ie, is the result simply due to
quantization error?

--
Eric Swanson --- E-mail address: e_swanson(at)skybest.com :-)
--------------------------------------------------------------

raylopez99

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Oct 18, 2005, 1:40:55 PM10/18/05
to
Dr. Bill - you are aware of the stepwise jump shown by the Great
Pacific Climate Shift of the 1970s? Hence your clever use of the
phrase "in most cases" below. So we are quibbling over semantics.

RL

Thomas Palm

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Oct 18, 2005, 2:28:14 PM10/18/05
to
swa...@notspam.net (Eric Swanson) wrote in
news:dj3a6o$27cg$1...@news3.infoave.net:

> In article <4355...@news.nwl.ac.uk>, w...@bas.ac.uk says...
>>
>>Michael Tobis <mto...@gmail.com> wrote:

>>>However, they are saying that what Pielke is saying is meaningless.
>>
>>No. Its potentially meanginful, but wrong.
>
> But, in the real world, small vortices exist. They form often in high
> energy flows over mountains and around valleys. They form as dust
> devils over hot surfaces. They form at the tips of wings of large jet
> aircraft. All seem to damp out rather quickly, unless the underlying
> conditions can couple in enough energy to allow them to grow.

The vortices disspate as individual, visible structures, but that doesn't
mean they haven't caused changes further away that keep propagating.

> If
> perturbations as small as the shed vortex from a jumbo jet caused
> tornados in the real world, then we would likely have seen a
> measurable increase in the number over the past 50 years, the result
> of more jet flights and a steady trend toward heavier aircraft.

This is a good example on why it is bad to talk about butterflies causing
tornadoes to people who don't understand the exact meaning. It's not that
a butterfly flapping its wing will cause a more tornadoes. What
butterflies, or jets, do is reshuffle the deck. You will statistically
have the same number of tornadoes, you will just have them in different
places.

(In the same way the question if the two tornadoes that hit USA badly
this year was caused by global warming has a trivial answer of yes.
Without global warming there may have been other hurricanes, but there
certainly wouldn't have been any taking exactly those paths)

>>In GCMs, there is a sense in which butterflies can cause tornados. It
>>is this:
>>
>>Take a GCM run. Record its output. Now, impose a minor perturbation
>>to the initial conditions and re-run. After a month, the weather will
>>be different. Select a day when there is a tornado (well, a mid-lat
>>cyclone will have to do because they don't have the rez for tornadoes)
>>in run 2 but not in run 1. There you have it: a tornado caused by a
>>minor perturbation.
>
> But, tornados are sub-grid phenomina in climate change GCM's, I think.
> The weather model guys work with higher resolutions, but a tornado is
> an intensly local affair.

Then take a hurricane, a low pressure zone or any larger structure and
you will see the same thing. Look at wmc:s blog for pictures of the
differences.

> I think you are really saying that the
> conditions for a tornado appear in the models on one day in the run,
> but not in the same day of a run with slightly different initial
> conditions. Are you thinking of initial conditions strictly limited
> to a change in what we called "vorticity" when I was trying to learn
> fluid dynamics (it was my worst subject)? Do all such small changes
> lead to increases in tornados, or are there other portions of the
> initial conditions for model runs which produce the other factors
> which feed energy into the tornado?

There will be exactly as many changes that lead to less tornadoes that
lead to more ones. What wmc suggested was just that you pick one that
didn't exist without the perturbation. You could equally well have done
the opposite and said that the perturbartion caused the absence of a
tornado.

> When this sort of experiment is
> repeated with finer resolution, does the same result emerge, ie, is
> the result simply due to quantization error?

It's a fundamental part of the equation that governs the atmosphere so it
will remain no matter how small grid you use.

James Annan

unread,
Oct 18, 2005, 6:22:45 PM10/18/05
to
w...@bas.ac.uk wrote:

>
> true, but thats not the point. And in attempting to defned that kind
> of view, RP has stepped well over into making completely false
> statements.
>

Including, most remarkably, his latest comment on the (non) conservation
of momentum, which I reproduce here in full:

http://climatesci.atmos.colostate.edu/?p=70#comment-413
-----------------
Regarding the question on the conservation of momentum, from the web
site http://en.wikipedia.org/wiki/Momentum, it states “In the absence of
external forces, a system will have constant momentum”. This certainly
is true, of course.

The key condition is “in the absence of external forces”. Molecular
dissipation into heat is an “external force” in this context (the term
“internal force” would be more appropriate). Perhaps it is the word
“external” that is causing confusion. The phrase could more clearly be
written as “In the absence of unbalanced forces or in the presence of no
forcing, a system will have constant momentum” (of course, a balance of
forces can also produce constant momentum).

We can use a sea breeze as an example. A sea breeze often starts from
calm conditions in the morning. Clearly, momentum is not conserved since
there are forces (i.e. from the heating of the ground surface by the
sun) which initiates wind. Later in the evening, the sea breeze weakens
to zero speeds. The momentum is lost as the kinetic energy is
dissiapted. Momentum is clearly not conserved for this weather feature,
or any other atmospheric circulation.

-----------------

Describing molecular dissipation within the system as an "external
force" is....well, words fail me. He even points out that "internal
forcing" would be a better term! Anyway, this level of complete nonsense
appears to be necessary to defend his viewpoint that small enough
perturbations will simply vanish.

(As an aside, a thermal perturbation will kick off instability in a GCM
anyway, so I don't see how dissipation into heat can be assumed to make
everything go away anyway).

James Annan

unread,
Oct 18, 2005, 6:41:58 PM10/18/05
to
Phil Hays wrote:

But even at that point, it does not vanish but has only decayed into heat.

w...@bas.ac.uk

unread,
Oct 18, 2005, 7:00:48 PM10/18/05
to
Eric Swanson <swa...@notspam.net> wrote:
>If perturbations as small
>as the shed vortex from a jumbo jet caused tornados in the real world,
>then we would likely have seen a measurable increase in the number over the
>past 50 years, the result of more jet flights and a steady trend toward
>heavier aircraft.

Sorry Eric. This is the wrong sense of causation. Its a very easy mistake
to make, but you need to try to avoid making it. Or I need to be
clearer that this isn't what I mean.

>>In GCMs, there is a sense in which butterflies can cause tornados. It
>>is this:
>>
>>Take a GCM run. Record its output. Now, impose a minor perturbation
>>to the initial conditions and re-run. After a month, the weather will
>>be different. Select a day when there is a tornado (well, a mid-lat
>>cyclone will have to do because they don't have the rez for tornadoes)
>>in run 2 but not in run 1. There you have it: a tornado caused by a
>>minor perturbation.

*This* is the sense of causation that I mean.

>But, tornados are sub-grid phenomina in climate change GCM's, I think. The
>weather model guys work with higher resolutions, but a tornado is an intensly
>local affair.

Err yes, thats why I said "(well, a mid-lat
cyclone will have to do because they don't have the rez for tornadoes)".
Come on, lets stick to the important bits...

> I think you are really saying that the conditions for a tornado
>appear in the models on one day in the run, but not in the same day of a run
>with slightly different initial conditions.

Yes.

> Are you thinking of initial
>conditions strictly limited to a change in what we called "vorticity" when I
>was trying to learn fluid dynamics (it was my worst subject)? Do all such
>small changes lead to increases in tornados, or are there other portions of the
>initial conditions for model runs which produce the other factors which feed
>energy into the tornado? When this sort of experiment is repeated with finer
>resolution, does the same result emerge, ie, is the result simply due to
>quantization error?

*any* change in the initial conditions will do. I used a change in the
surface pressure (vorticity isn't a model variable) but a pert to the p*
does imply an effective change in the vorticity.

It isn't easy to re-run the model at different rez. But the same
effects would emerge, what might change is the length of the growth
phase.

http://mustelid.blogspot.com/2005/10/butterflies-notes-for-post.html

if you missed it.

w...@bas.ac.uk

unread,
Oct 18, 2005, 7:04:34 PM10/18/05
to
Thomas Palm <Thoma...@chello.removethis.se> wrote:
>This is a good example on why it is bad to talk about butterflies causing
>tornadoes to people who don't understand the exact meaning. It's not that
>a butterfly flapping its wing will cause a more tornadoes. What
>butterflies, or jets, do is reshuffle the deck. You will statistically
>have the same number of tornadoes, you will just have them in different
>places.

Agree completely. (Aside: changes in the *number* of tornadoes would
be climate. Small changes to the initial conditions *don't* affect
the climate (certainly of atmos-only runs).

-W.

(sorry to TP for accidental personal-send too)

w...@bas.ac.uk

unread,
Oct 18, 2005, 7:11:57 PM10/18/05
to
James Annan <still_th...@hotmail.com> wrote:

>Including, most remarkably, his latest comment on the (non) conservation
>of momentum, which I reproduce here in full:

>http://climatesci.atmos.colostate.edu/?p=70#comment-413

That is getting pretty weird. What he seems to be missing (and what CIP
missed initially, then realised he had) is that while total moment
is conserved, total-amount-of-moving-around (effectively, kinetic
energy) isn't. So why RP is branching off on this weird tangent
I don't know.

On a slightly different topic... but still momentum... total atmos
angular momentum has to be conserved (on the long term). And therefore
surfaec wind stress has to integrate to zero. And in the tropics
there are ?easterlies? (I can never remember the sign conventions...)
from the trade winds / hadley circulation. And this therefore
*implies* westerlies in the higher latitudes, even though its not
dynamically obvious why there should be westerlies there.

Phil Hays

unread,
Oct 18, 2005, 8:50:16 PM10/18/05
to
"Michael Tobis" wrote:

>Yes, the perturbation would settle into undetectable noise long before
>it made a measurable difference. But it would be *different* noise.

Noise is always different. If it wasn't, it wouldn't be noise. Not
to say that noise might not have stable statistics, a fact I've used
in digital signal processing. But the magnitude and phase of the
noise at any given point can not be known, or controlled.


>What chaos theory shows is that in principle, this may suffice to cause
>the perturbed and unperturbed systems to diverge.

Yet all copies of the system are perturbed by noise. The noise level
can't be ignored, other than by an idealized model of the system, or
for a short enough term with large enough perturbation.


>On the other hand, it's absolutely right. The butterfly doesn't cause
>the divergence. The difference in the uncontrollable noise difference
>between the two realizations causes the divergence. In any realizable
>sense, just having two physically distinct realizations is sufficient
>for them to diverge, No butterfly is necessary. If there are three
>realizations, one with butterfly and two without, there is no way to
>distingush between the two without a butterfly and the one with. So
>it's hard to say the butterfly caused anything at all.
>
>These are two different, equally valid, ways of looking at the problem.
>I think the latter way is more useful, especially since we don't need
>to appeal to butteflies in a quantum universe to get non-predicatbility
>anyway.

I fail to see how the first way is valid, other than an approximation
useful for large enough signals for short enough periods of time.

BTW: I think the most important point of all this was made by WMC in
his blog:

"All of these things, if any one were different, would send the
*weather* off on a different course. But the climate would be
unchanged."


--
Phil Hays

James Annan

unread,
Oct 18, 2005, 9:35:39 PM10/18/05
to

w...@bas.ac.uk wrote:
> James Annan <still_th...@hotmail.com> wrote:
>
> >Including, most remarkably, his latest comment on the (non) conservation
> >of momentum, which I reproduce here in full:
>
> >http://climatesci.atmos.colostate.edu/?p=70#comment-413
>
> That is getting pretty weird. What he seems to be missing (and what CIP
> missed initially, then realised he had) is that while total moment
> is conserved, total-amount-of-moving-around (effectively, kinetic
> energy) isn't. So why RP is branching off on this weird tangent
> I don't know.

Well he has little choice, since an arbitrary pertubation will have a
non-zero momentum commponent, so if the momentum can't be simply
"dissipated" then it will spread throughout the atmosphere. But if his
prior belief in a non-chaotic atmosphere is so strong that it leads him
to reject the law of conservation of momentum as a consequence, then it
seems that there is little chance of further rational consideration of
the subject. He's starting to sound like he's "gone emeritus" on the
subject, IMO.

(Of course, momentum will be exchanged with the Earth via surface
friction, in both reality and models, but a pertubation at a finite
height will spread upwards too - at least, according to all standard
views of physics...)

James

raylopez99

unread,
Oct 18, 2005, 10:29:19 PM10/18/05
to
You're an idiot. As I have stated elsewhere, you're an idiot squared.

As for butterfly wings--in the real world, it depends on the Reynolds
number. Laminar flow dampens perturbations, while turbulent flow can
allow them to grow. Where the jetstream is, because of the Reynolds
number, you have a rarified atmosphere and you can get turbulence. Jet
stream can affect lower atmosphere, all the way down to the surface
(where it's laminar the last X meters).

So a butterfly flapping its wings 1 meter off the ground (laminar
field) cannot cause a hurricane, but, a big ass butterfly (like a 747)
that's at 10k m (turbulence), might create a vortex that might create a
perturbation that affects weather.

I knew this from way back when and I don't even work in this field.
You people call yourselves "scientists". Sheez.

RL

Eric Swanson

unread,
Oct 18, 2005, 11:09:09 PM10/18/05
to
In article <Xns96F3D017C46CET...@212.83.64.229>,
Thoma...@chello.removethis.se says...

>
>swa...@notspam.net (Eric Swanson) wrote in
>news:dj3a6o$27cg$1...@news3.infoave.net:
>
>> In article <4355...@news.nwl.ac.uk>, w...@bas.ac.uk says...
[cut]

>>>In GCMs, there is a sense in which butterflies can cause tornados. It
>>>is this:
>>>
>>>Take a GCM run. Record its output. Now, impose a minor perturbation
>>>to the initial conditions and re-run. After a month, the weather will
>>>be different. Select a day when there is a tornado (well, a mid-lat
>>>cyclone will have to do because they don't have the rez for tornadoes)
>>>in run 2 but not in run 1. There you have it: a tornado caused by a
>>>minor perturbation.
>>
>> But, tornados are sub-grid phenomina in climate change GCM's, I think.
>> The weather model guys work with higher resolutions, but a tornado is
>> an intensly local affair.
>
>Then take a hurricane, a low pressure zone or any larger structure and
>you will see the same thing. Look at wmc:s blog for pictures of the
>differences.

No, a hurricane is much bigger than a tornado and can not form unless the
conditions in the atmosphere and ocean are right. The small perturbations
are not likely to produce those large scale conditions, IMHO, therefore the
notion of a butterfly flapping it's wings causing a tornado (or hurricane)
is likely to be wrong, especially as the kinetic energy introduced into the
air is damped to heat rapidly. The much larger wing vortex from a jumbo jet
during landing can tear apart a small plane flying close behind, but are of
little concern to another craft a few miles further behind.

>> I think you are really saying that the
>> conditions for a tornado appear in the models on one day in the run,
>> but not in the same day of a run with slightly different initial
>> conditions. Are you thinking of initial conditions strictly limited
>> to a change in what we called "vorticity" when I was trying to learn
>> fluid dynamics (it was my worst subject)? Do all such small changes
>> lead to increases in tornados, or are there other portions of the
>> initial conditions for model runs which produce the other factors
>> which feed energy into the tornado?
>
>There will be exactly as many changes that lead to less tornadoes that
>lead to more ones. What wmc suggested was just that you pick one that
>didn't exist without the perturbation. You could equally well have done
>the opposite and said that the perturbartion caused the absence of a
>tornado.

But, then there is no repeatable cause and effect, ie, take several runs with
several other perturbations. Then add the one perturbation for which you
postulate to cause a tornado. Does a tornado always occur in these modified
cases? If not, then there is no direct cause and effect relationship. If you
want to get into chaos or statistics, then maybe tornados might be said to
appear more (or less) frequently as a result of the last change. But, you
can't simply pick two cases, one which does have a tornado as a result, and
make a solid cause-and-effect claim, IMHO.

>> When this sort of experiment is
>> repeated with finer resolution, does the same result emerge, ie, is
>> the result simply due to quantization error?
>
>It's a fundamental part of the equation that governs the atmosphere so it
>will remain no matter how small grid you use.

But the equations are set to discrete grid points with the conditions within
the grid "box" averaged. You can not know where in the "box" a small scale
event, such as a tornado, might happen, even though you think your larger
"box" exhibits the conditions suitable for tornado formation. Halve the grid
spacing and the tornado may still be sub-grid, however, there are now 4 "boxes"
instead of one in which to place the tornado. Only one of the four boxes now
exhibits tornado like conditions. As a result, the impact on adjacent grid
boxes will be different, for example, the tornado's motion might move it from
one small grid box to another in a few time steps, while in the coarser grid
model, the tornado would still be within the larger grid box, with little
impact on the adjacent grid boxes. I submit that the resulting fine scale
simulation will give different results compared to the results from the coarse
simulation. I think this is quantization error, which can produce unstable
conditions in a model, which APPEAR to be chaotic behavior.

As an example, I recall learned that early GCM's could not simulate fog over
the ocean. That was the result of the relatively coarse vertical resolution
in these early models, which tended to switch from clear to full cloud
conditions in the first layer over warm ocean waters, oscillating back and
forth on successive time steps. Adding a relatively thin boundary layer
allowed the model builders to simulate fog.

Raymond Arritt

unread,
Oct 18, 2005, 11:57:06 PM10/18/05
to
Eric Swanson wrote:

> No, a hurricane is much bigger than a tornado and can not form unless the
> conditions in the atmosphere and ocean are right. The small perturbations
> are not likely to produce those large scale conditions, IMHO, therefore the
> notion of a butterfly flapping it's wings causing a tornado (or hurricane)
> is likely to be wrong, especially as the kinetic energy introduced into the
> air is damped to heat rapidly. The much larger wing vortex from a jumbo jet
> during landing can tear apart a small plane flying close behind, but are of
> little concern to another craft a few miles further behind.

"What we have here is a failure to communicate." (Cool Hand Luke,
starring Paul Newman)

The chaos argument isn't that one particular small vortex grows into
another particular large vortex. Rather, the initial disturbance
creates small changes to the atmosphere that cause it to evolve in a
different way. The overall statistical properties of the system remain
the same, but the specific events happen in a different way -- tornado
alley is still tornado alley, and the tornados still happen mostly in
the spring, but the individual storms don't happen in exactly the same
place and time as if the butterfly hadn't flapped its wings.

>>There will be exactly as many changes that lead to less tornadoes that
>>lead to more ones. What wmc suggested was just that you pick one that
>>didn't exist without the perturbation. You could equally well have done
>>the opposite and said that the perturbartion caused the absence of a
>>tornado.
>
> But, then there is no repeatable cause and effect, ie, take several runs with
> several other perturbations. Then add the one perturbation for which you
> postulate to cause a tornado. Does a tornado always occur in these modified
> cases? If not, then there is no direct cause and effect relationship.

Bingo. That's the point (or one of the points, anyway) -- chaotic
behavior means you *can't* identify a direct cause and effect
relationship between the initial conditions and a specific later event
beyond a certain time in the future. Chaos causes deterministic
forecasting to break down.

Phil Hays

unread,
Oct 19, 2005, 12:41:59 AM10/19/05
to
James Annan wrote:

>Phil Hays wrote:

Sure. And this tiny amount heat is spread out over a large and
growing mass of air, and is being slowly radiated off to space. And
what is the random variation in heat deposited by meteors in a similar
mass of air? For that matter, what is the variation in rate of heat
transfer from the surface to a similar mass of air? Not even to
mention heat variations from the fleets of aircraft, assorted passing
sailboats, flocks of birds, ocean wave variations, volume setting of
boom boxes, baseballs, baseball bats, mosquitoes, footballs, rugby
players, loudmouth politicians, hang gliders, slings and arrows,
energy from earthquakes, neutrinos from distant supernovas and lot of
other heat sources, all not completely predictable, and all (I think)
are rather larger than the mythical butterfly's tiny heat trail. For
that matter, what is the quantum variation in the thermal radiation
from this volume of air? Very small in percentage, yes, but is it
small in comparison to the mythic butterfly's heat trail?

The real atmosphere, like any other real physical system, will have a
"noise floor", probably rather higher than set by quantum effects.
Any perturbation below this noise floor is just going to be lost in
the noise, or in other words is not going to have a predictable effect
regardless of how carefully I repeat the experiment. Models, on the
other hand, are designed and built carefully to be repeatable, and
deal with scales, at the smallest, that are rather larger than that of
the mythical butterfly. WMC's example has a grid of ~300 km. 300 km
* 300 km * 1km (how thick? DNKSWAG=1km). This is about 10^16 moles
of air, or 10^19 times the air moved by the mythical butterfly.

I don't know what this noise level is at. I feel sure that it is
rather higher than the mythical butterfly, and is probably rather
below the realistic accuracy of current weather models.

It would be interesting to find ways to measure the noise floor of the
atmosphere on different time and spatial scales.

James Annan

unread,
Oct 19, 2005, 1:13:14 AM10/19/05
to

Phil Hays wrote:


> The real atmosphere, like any other real physical system, will have a
> "noise floor", probably rather higher than set by quantum effects.
> Any perturbation below this noise floor is just going to be lost in
> the noise, or in other words is not going to have a predictable effect
> regardless of how carefully I repeat the experiment.

Now you're onto the "predictable" track, which is similar to how I
originally misunderstood Richard Ekyholt's comments (also now on
RPSnr's blog). The only way I could see his comments being correct and
relevant was to link them to the insignificance of the effect as far as
practical prediction goes. I of course agree that the effect of a
butterfly flap is not predictable, and that weather forecasters have no
need to account for them.

But in fact neither of them is talking about prediction. They are
claiming that the basic chaotic sensitivity of the system is purely an
artefact of the numerical model, and that any small enough perturbation
will actually converge back to the unperturbed case for the system
itself. That's just flat-out wrong as far as chaotic mathematical
systems are concerned (and Prof Eykholt makes no special case out for
the atmosphere, as far as I can see - his comments are broad ones
concerning chaotic systems in general).

As far as I am aware, the standard approach to chaos theory has been
shown to be valid in all experimentally-accessible chaotic systems, to
the limits of experimental ability. In the case of chaotic electrical
circuits, that probably sets an upper limit for the hypothetical
"perturbation threshold" at a pretty low level.

James

Thomas Palm

unread,
Oct 19, 2005, 2:39:24 AM10/19/05