The butterfly flap
James Annan
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
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
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
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
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!!!
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
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
> 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
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
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
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
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
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
> 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
> for a situation where the real world displays laminar flow :-)
;-)
raylopez99
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
>>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
"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
James Annan wrote:
> Recently, Roger Pielke Snr has been making comments on his blog about
> 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
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
> 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
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
>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
larger other differences.
James Annan
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
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
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.
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
> 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
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
>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
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
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
"infinitesimals" sensibly, thanks.
mt
James Annan
> 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
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
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
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
> 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
@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
> "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
>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
>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
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
>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
> 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
>
>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
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
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
>
> 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
But even at that point, it does not vanish but has only decayed into heat.
w...@bas.ac.uk
>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
>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
>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
>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
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
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
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...
>>>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
> 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
>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
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
news:1129685739.6...@o13g2000cwo.googlegroups.com:
>
> 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.
The net momentum of a butterfly flapping its wings is zero. Just as much
air is pushed down as is moved up and you can dissipate the energy without
having to violate conservation of momentum. Pielke doesn't have to assume
momentum is dissipated, and that he does is mysterious.
What also surprises me is that no one reacted to Pielke's "I do agree that
both weather and climate are chaotic". I thought it was generally agreed
that climate isn't chaotic.
James Annan
Thomas Palm wrote:
> The net momentum of a butterfly flapping its wings is zero.
Except if it takes off, or lands, or changes direction. Or flaps its
wings while sitting on a twig.
> Just as much
> air is pushed down as is moved up and you can dissipate the energy without
> having to violate conservation of momentum. Pielke doesn't have to assume
> momentum is dissipated, and that he does is mysterious.
>
> What also surprises me is that no one reacted to Pielke's "I do agree that
> both weather and climate are chaotic". I thought it was generally agreed
> that climate isn't chaotic.
I don't think his position has any consistent basis whatsoever, other
than the insistence that the models must be wrong. Chaotic _means_
sensitive to small pertubations (more strictly, that is not the
technical definition, but an immediate consequence).
James
w...@bas.ac.uk
>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.
Still not right! Butterflies "cause" (in the sense I expounded) weather at
all scales up to the largest.
>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?
Of course not. Imagine: we take the original run. Then run2, where butterfly
A causes tornado B. Then run3, where butterfly C causes tornado D. Then
run4, where we add the tiny perturbations from runs 2 and 3. Chances are
that neither tornadoes B or D will form.
>If not, then there is no direct cause and effect relationship.
I know what you mean, but this is the wrong statement of it. There *is*
a direct c-and-a.
w...@bas.ac.uk
>He's starting to sound like he's "gone emeritus" on the subject, IMO.
:-)))
Alastair McDonald
"Thomas Palm" <Thoma...@chello.removethis.se> wrote in message
news:Xns96F4580823105T...@212.83.64.229...
> "James Annan" <still_th...@hotmail.com> wrote in
> news:1129685739.6...@o13g2000cwo.googlegroups.com:
> What also surprises me is that no one reacted to Pielke's "I do agree that
> both weather and climate are chaotic". I thought it was generally agreed
> that climate isn't chaotic.
The Tiamat Hypothesis is that the climate is chaotic. It is a hypothesis
because it has not been proved. However it seems that Pielke Snr. buys into
it, so it does not seem to be a such crackpot idea.
Cheers, Alastair.
Thomas Palm
wrote in news:dj53a4$cj0$1...@news7.svr.pol.co.uk:
> The Tiamat Hypothesis is that the climate is chaotic. It is a
> hypothesis because it has not been proved. However it seems that
> Pielke Snr. buys into it, so it does not seem to be a such crackpot
> idea.
Try posting your theory on his website. Maybe your support will finally
cause Pielke to change his mind :-)
Phil Hays
<still_th...@hotmail.com> wrote:
>
>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,
If I left you with a different impression, I was not being clear. The
reason why I think the mythical butterfly doesn't matter is that
multiple "weather systems" (some with and some without the mythic
butterfly) will always diverge before the perturbation from the
butterfly could get large enough to make a measurable difference
between the systems.
>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 rather different.
Phil Hays
>The Tiamat Hypothesis is that the climate is chaotic.
Most of the pages I found with Google having to do with this seemed
rather crackpot. Do you have a suggested reference, or could you
start a topic with a reasonable overview?
Eric Swanson
>
>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)
One of my favorite quotes. Just before the usual sad ending for a rebel.
>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's a long discussion on Pielke Sr.'s blog by Dan Hughes discussing the
fact that shear forces tend to damp motions in the atmosphere. That was what
I was refering to in that the flap of a butterfly's wing or the trailing
vortex shed by the jumbo jet during landing both tend to dissipate rapidly.
As far as numerical simulations are concerned, these effects may or may not
influence the forcast of the future weather patterns, as they are too small
to have any impact on the other parameters at grid scale.
>>>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.
So does discretization of the equations of motion and the limited resolution
and accuracy of available data to use as inputs to the model. That's why
there is so much effort going into improving the available data, including
the AMSU, more ground stations and sonde launches, IMHO. Saying that weather
is chaotic is wonderful, but the modeling process introduces other variations
which can appear to be due to chaos, even though that's not what's actually
happening in the atmosphere.
James Annan
> On 18 Oct 2005 22:13:14 -0700, "James Annan"
> <still_th...@hotmail.com> wrote:
>
>
>>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,
>
>
> If I left you with a different impression, I was not being clear. The
> reason why I think the mythical butterfly doesn't matter is that
> multiple "weather systems" (some with and some without the mythic
> butterfly) will always diverge before the perturbation from the
> butterfly could get large enough to make a measurable difference
> between the systems.
In that case, I certainly agree - butterflies have no direct effect on
the current weather forecast. But that wsn't the point in dispute.
James Annan
>
> There's a long discussion on Pielke Sr.'s blog by Dan Hughes discussing the
> fact that shear forces tend to damp motions in the atmosphere.
I see it more as a bunch of irrelevant cut and paste, buch each to his
own...
> That was what
> I was refering to in that the flap of a butterfly's wing or the trailing
> vortex shed by the jumbo jet during landing both tend to dissipate rapidly.
> As far as numerical simulations are concerned, these effects may or may not
> influence the forcast of the future weather patterns, as they are too small
> to have any impact on the other parameters at grid scale.
Jusst to be clear on this, are you actually agreeing with RP's absurd
claim that small momentum pertubations within the atmosphere are
internally dissipated into heat?
Frankly, I can't believe that a debate based on this premise is being
sustained. This is not just a matter of "perspective" as RP keeps
saying. It's a professor of atmospheric physics saying something that is
utterly risible. He might as well have claimed that 10 is a prime or pi
is rational.
Eric Swanson
says...
>
>Eric Swanson wrote:
>
>>
>> There's a long discussion on Pielke Sr.'s blog by Dan Hughes discussing the
>> fact that shear forces tend to damp motions in the atmosphere.
>
>I see it more as a bunch of irrelevant cut and paste, buch each to his
>own...
So, you doubt that the air has viscosity?
>> That was what
>> I was refering to in that the flap of a butterfly's wing or the trailing
>> vortex shed by the jumbo jet during landing both tend to dissipate rapidly.
>> As far as numerical simulations are concerned, these effects may or may not
>> influence the forcast of the future weather patterns, as they are too small
>> to have any impact on the other parameters at grid scale.
>
>Jusst to be clear on this, are you actually agreeing with RP's absurd
>claim that small momentum pertubations within the atmosphere are
>internally dissipated into heat?
>
>Frankly, I can't believe that a debate based on this premise is being
>sustained. This is not just a matter of "perspective" as RP keeps
>saying. It's a professor of atmospheric physics saying something that is
>utterly risible. He might as well have claimed that 10 is a prime or pi
>is rational.
Well, that says it.
I admit that I don't fully understand the debate, having not attempted to
read the comments on RP Sr's blog. However, next time you sit down to your
morning cup of coffee (tea?), give it a stir to induce rotational motion
and watch what happens. The motion eventually damps out. Now, even though
the shear forces are much smaller in a gas, I submit that the same damping
process occurs. If not, hurricanes would not slow down, but keep spinning
along as they moved away from their oceanic feeding grounds. As I understand
from the discussion, please remember that conservation of momentum is true
only so far as there is no frictional forces. Friction tends to cause
heating to occur, which I think is the basis of RP's comments.
James Annan
> In article <3ro0ksF...@individual.net>, still_th...@hotmail.com
> says...
>>
>>Eric Swanson wrote:
>>
>>>
>>> There's a long discussion on Pielke Sr.'s blog by Dan Hughes discussing the
>>> fact that shear forces tend to damp motions in the atmosphere.
>>
>>I see it more as a bunch of irrelevant cut and paste, buch each to his
>>own...
>
> So, you doubt that the air has viscosity?
No, of course not. What a bizarre question!
First, I think you should have a look at RP's actual comments to
see if you want to try to defend what he actually said, rather
than try to invent a hpyothetical interpretation which is inconsistent
with his comments.
Secondly, I agree that a purely tubulent perturbation will dissipate
into heat. However, heat isn't the end of the matter. It is only
once the heat is fully lost that the perturbed state can be
considered to have converged to the unperturbed state. That
gives it a substantial time to hitch a ride on a growing mode.
But the case of momentum is altogether more fundamental than this.
As a momentum perturbation diffuses through the atmosphere, it is
precisely conserved. As the affected mass grows, the corresponding
velocity perturbation drops, but their product remains the same.
The friction you talk about is at the boundary, and this friction
exists both in models and reality. But RP explicitly claims that
momentum is destroyed by molecular dissipation within the
atmosphere, and this is utter crackpottery. Read what he wrote!
It is precisely the nature of chaotic systems that small
perturbations grow. This isn't directly a matter of energy at all, and
friction doesn't stop it from happening (unless you add enough
to completely change the nature of the system). The perturbation
doesn't directly turn into an energetic subsystem, it just leads
to the overall pattern being different (eg see wmc's blog post).
James
--
James Annan
see web pages for email
http://julesandjames.blogspot.com/
http://www.ne.jp/asahi/julesandjames/home/
NobodyYouKnow
> 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
If I might introduce a small measure of intelligence to this discussion...
The pardigm of the butterfly wings flapping and causing a hurricane is
poorly understood.
Chaos theory is about 'sensitivity to initial conditions' which means that a
small change in the starting point will build to a major change in the
outcome over time and as the effect is usually larger than the 'cause' (
relatively large positive feedbacks). But the effect of the butterfly flap
is not USUALLY amplified past a limited and local change. Dismissing the
flap as a 'local event, quickly dissipated' is as wrong as saying that it
will inevitably create a hurricane.
It is possible that this change will create a larger change and that change
will ... until you create a hurricane that would not normally have occured,
but that is VERY UNLIKELY.
Chaos theory is about the fact that it is POSSIBLE for that single flap to
change the future such that a hurricane that would NOT have formed, WILL
form, not that every flap of a butterfly wing will create a hurricane down
the road.
HTH.
w...@bas.ac.uk
>If I might introduce a small measure of intelligence to this discussion...
Sounds good...
>The pardigm of the butterfly wings flapping and causing a hurricane is
>poorly understood.
Indeed...
>Chaos theory is about 'sensitivity to initial conditions' which means that a
Yes.
>It is possible that this change will create a larger change and that change
>will ... until you create a hurricane that would not normally have occured,
>but that is VERY UNLIKELY.
No. There is just about a 100% chance that the atmos will switch to a state
in which a hurricane which would other wise not have occurred, will occur.
I refer you to:
http://mustelid.blogspot.com/2005/10/repeatability-of-gcms.html
and the comments.
Eric Swanson
still_th...@hotmail.com says...
>
>On 2005-10-20, Eric Swanson <swa...@notspam.net> wrote:
>> In article <3ro0ksF...@individual.net>, still_th...@hotmail.com
>> says...
>>>
>>>Eric Swanson wrote:
I think I understand what he said. His statement is a bit confusing, but
I do agree with his conclusion that conservation of momentum can does not
apply in the butterfly flap case. At the very least, the butterfly is
infact applying an "external" force on the air, though a very small one.
>Secondly, I agree that a purely tubulent perturbation will dissipate
>into heat. However, heat isn't the end of the matter. It is only
>once the heat is fully lost that the perturbed state can be
>considered to have converged to the unperturbed state. That
>gives it a substantial time to hitch a ride on a growing mode.
Hitch a ride? To re-phrase the famous movie line, "Show me the Energy!"
>But the case of momentum is altogether more fundamental than this.
>As a momentum perturbation diffuses through the atmosphere, it is
>precisely conserved. As the affected mass grows, the corresponding
>velocity perturbation drops, but their product remains the same.
>The friction you talk about is at the boundary, and this friction
>exists both in models and reality. But RP explicitly claims that
>momentum is destroyed by molecular dissipation within the
>atmosphere, and this is utter crackpottery. Read what he wrote!
Pielke uses the phrase "external force" to discribe the internal frictional
effects, as a way of extending the basic statement about momentum:
"In the absence of external forces, a system will have constant momentum"
Momentum is precisely conserved only in systems without friction or
dissipation. The classic case of the collision of 2 billard balls is often
used as an example of an elastic collision, however, in the real world some
energy is lost to heating. The event happens very fast, but a closer look
reveals that at the initial contact, the force is zero, but grows as the first
ball hits the second. The contact patch is not a point, but an area, as the
matrerial in each ball compresses slightly. The force between the two grows
as the compression increases until the two balls have equal velocity, then the
second ball begins to move faster than the first as the material begins to
release the stress stored in the first half of the impact period. Finally,
the two balls separate and the velocity of the second is nearly the same as
that initially of the first, while the first stops. Because of hysteresis,
some energy is lost during the compression and rebound phase, appearing as
heat. Thus, momentum is lost.
In the case of multiple collisions or viscosity in a fluid, some of the
kinetic energy is converted to thermal energy. When a faster flow of
a gas mixes with a slower flow, again, momentum is lost. The fact is
that the energy is not lost, but changes form from kinetic to thermal,
ie, heat. Of course, if you are only interested in a mathematical model
which ignores the smaller scale processes, such as friction or small scale
vorticity, then your claim may be correct.
>It is precisely the nature of chaotic systems that small
>perturbations grow. This isn't directly a matter of energy at all, and
>friction doesn't stop it from happening (unless you add enough
>to completely change the nature of the system). The perturbation
>doesn't directly turn into an energetic subsystem, it just leads
>to the overall pattern being different (eg see wmc's blog post).
Small perturbations may spread out to a larger volume, but they can
not grow in intensity, without the extra energy available to produce
that intensification. The entire circulation of the atmosphere is
the result of the energy which flows into the atmosphere from the Sun
thence back out again into deep space. I submit that the energy flow
is the more important consideration, than simply momentum, for without
the energy flow, there would be no motion at all.
James Annan
But Eric, I already explained this...the perturbation is not a separate
entitity that requires energy to grow. I suspect this iss also why RP it
so badly confused. The perturbed state is simply a different initial set
of initial conditions, which (due to the chaotic nature of the system)
evolves on a diferent - and diverging - trajectory. There _is_ _no_
_extra_ _energy_ _involved_. This is absolutely fundamental to all
chaotic systems, there is no justification for treating the atmosphere
as some special case.
>
>
>>But the case of momentum is altogether more fundamental than this.
>>As a momentum perturbation diffuses through the atmosphere, it is
>>precisely conserved. As the affected mass grows, the corresponding
>>velocity perturbation drops, but their product remains the same.
>>The friction you talk about is at the boundary, and this friction
>>exists both in models and reality. But RP explicitly claims that
>>momentum is destroyed by molecular dissipation within the
>>atmosphere, and this is utter crackpottery. Read what he wrote!
>
>
> Pielke uses the phrase "external force" to discribe the internal frictional
> effects, as a way of extending the basic statement about momentum:
> "In the absence of external forces, a system will have constant momentum"
Pielke can pretend words mean what he wants, but it is patently obvious
that the internal molecular dissipation is not an "external" force on a
fluid. Consider the action and reaction, Eric. What is the reaction on?
How he can say such things as this is a complete mystery to me:
---
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).
---
He even acknowledges that molecular dissipation is internal!
What is really scary is that he apparently intends to use these ideas in
his teaching. I hope some students have the nous and guts to tell him
he's exposing himself in public on this.
> In the case of multiple collisions or viscosity in a fluid, some of the
> kinetic energy is converted to thermal energy. When a faster flow of
> a gas mixes with a slower flow, again, momentum is lost.
No, Eric, this is completely wrong. Energy is lost as heat. Momentum is
conserved.
>
>
> Small perturbations may spread out to a larger volume, but they can
> not grow in intensity, without the extra energy available to produce
> that intensification.
Eric, it's a nonlinear system, so separating into "perturbation" and
"unperturbed system" is fundamentally invalid, and no extra energy input
is required. Do you believe your ideas apply to all chaotic systems?
Because they are trivially proved wrong in all experimentally-accessible
systems.
James
--
James Annan
see web pages for email
http://www.ne.jp/asahi/julesandjames/home/
http://julesandjames.blogspot.com/
NobodyYouKnow
> NobodyYouKnow <TheVoice...@nowhere.com> wrote:
>> If I might introduce a small measure of intelligence to this
>> discussion...
>
> Sounds good...
>
>> The pardigm of the butterfly wings flapping and causing a hurricane
>> is poorly understood.
>
> Indeed...
>
>> Chaos theory is about 'sensitivity to initial conditions' which
>> means that a
>
> Yes.
>
>> It is possible that this change will create a larger change and that
>> change will ... until you create a hurricane that would not normally
>> have occured, but that is VERY UNLIKELY.
>
> No. There is just about a 100% chance that the atmos will switch to a
> state in which a hurricane which would other wise not have occurred,
> will occur.
>
> I refer you to:
>
> http://mustelid.blogspot.com/2005/10/repeatability-of-gcms.html
>
> and the comments.
Do not confuse the reproduciblity of GCMs with the analog world. The
quantitization error is what controls the reproducability of GCMs. This is
NOT the math. As they say, the results on different machines will change
because of slight differences in the roundoff etc. The points I made hold in
the real world or in mathematics.
Raymond Arritt
> w...@bas.ac.uk wrote:
>> NobodyYouKnow <TheVoice...@nowhere.com> wrote:
>>> If I might introduce a small measure of intelligence to this
>>> discussion...
>>
>> Sounds good...
>>
>>> The pardigm of the butterfly wings flapping and causing a hurricane
>>> is poorly understood.
>>
>> Indeed...
>>
>>> Chaos theory is about 'sensitivity to initial conditions' which
>>> means that a
>>
>> Yes.
>>
>>> It is possible that this change will create a larger change and that
>>> change will ... until you create a hurricane that would not normally
>>> have occured, but that is VERY UNLIKELY.
>>
>> No. There is just about a 100% chance that the atmos will switch to a
>> state in which a hurricane which would other wise not have occurred,
>> will occur.
>>
>> I refer you to:
>>
>> http://mustelid.blogspot.com/2005/10/repeatability-of-gcms.html
>>
>> and the comments.
>
> Do not confuse the reproduciblity of GCMs with the analog world.
Good so far...
> The
> quantitization error is what controls the reproducability of GCMs.
"Quantitization error" is not a concept I've run across in atmospheric
modeling. Do you mean roundoff error, or perhaps truncation error?
> This is NOT the math.
It *IS* the math (assuming your "quantitization" error means either
truncation or roundoff). There is no exact solution for the set of
coupled nonlinear PDEs that we have to solve, so we have no choice but
to use numerical methods and accept their limitations.
> As they say, the results on different machines will change
> because of slight differences in the roundoff etc.
True.
> The points I made hold in
> the real world or in mathematics.
I assume you mean from one of your earlier posts:
"Chaos theory is about the fact that it is POSSIBLE for that single flap
to change the future such that a hurricane that would NOT have formed,
WILL form, not that every flap of a butterfly wing will create a
hurricane down the road."
The butterfly flap (or any other stimulus) causes the system to evolve
toward a different specific realization of the same climatology. The
two realizations will include different specific events, with hurricanes
being examples of such events.
All this brings up one of my curmudgeonly notions: everyone says
climate is the average of weather, but I often try to convince people to
think in the other direction -- weather is the day-to-day manifestation
of a particular climate.
Alastair McDonald
"Raymond Arritt" <raymon...@hotmail.com> wrote in message
news:1jY5f.451214$_o.140176@attbi_s71...
> All this brings up one of my curmudgeonly notions: everyone says
> climate is the average of weather, but I often try to convince people to
> think in the other direction -- weather is the day-to-day manifestation
> of a particular climate.
That fits with what I wrote;
"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."
But re-reading it, it is not surprising that it received no comments :-(
What I was trying to say was that if you think of the climate as a
strange attractor in a multi phase space, then weather is a segment
of one path taken through that attractor (not a point as I wrote above.)
In other words climate is the butterfly diagram. Weather is a short
segment of a path in that strange attractor.
If you linearize the butterfly diagram, then you can have an average
temperature, and a max and min temperatures etc. But interestingly,
since there are no fixed bounds, in fact you can only have an expected
max which on average is exceeded every hundred years, just like the
real climate.
If this analysis is correct, and if the weather is chaotic, then since it is
only a segment of the complete path that is climate, then climate must
also be chaotic. It certainly looks that way :-)
Cheers, Alastair.
Alastair McDonald
"Phil Hays" <Spampos...@comcast.net> wrote in message
news:62rcl15r0kkb1pva4...@4ax.com...
> "Alastair McDonald" wrote:
>
> >The Tiamat Hypothesis is that the climate is chaotic.
>
> Most of the pages I found with Google having to do with this seemed
> rather crackpot. Do you have a suggested reference, or could you
> start a topic with a reasonable overview?
I really must post a proper description of the Tiamat hypothesis. I had not
realised that google would yield any hits for two such unusual words.
However here is the earliest proposal of the one of the ideas behind it,
that I know of;
http://www.columbia.edu/cu/pr/96_99/18899.html
Cheers, Alastair.
Eric Swanson
says...
I think one source of of "quantization error" as the effects of grid size in a
GCM vs. the fact that the real world has much smaller scales. As you pointed
out in another post, changing the resolution of a GCM produces differing
results in overall climate, such as more storms, if I understand your post.
The relatively large size of the grid forces many variables to be aggrigated,
as they can not be explicitly calculated at the fine scales within which
they are determined in the real world..
I'm NOT refering to chaos theory, but to the simulation problem.
Alastair McDonald
news:djamli$hji$1...@news3.infoave.net...
> I think one source of "quantization error" as the effects of grid size in
> a GCM vs. the fact that the real world has much smaller scales. As you
> pointed out in another post, changing the resolution of a GCM produces
> differing results in overall climate, such as more storms, if I understand
> your post. The relatively large size of the grid forces many variables to
> be aggregated, as they can not be explicitly calculated at the fine scales
> within which they are determined in the real world..
>
> I'm NOT referring to chaos theory, but to the simulation problem.
But see;
'In 1961, an accident cast new light on the question. Luck in science comes to
those in the right place and time with the right set of mind, and that was
where Edward Lorenz stood. He was at the Massachusetts Institute of
Technology, where development of computer models was in the air, and
intellectually he was one of a new breed of professionals who were combining
meteorology with mathematics. Lorenz had devised a simple computer model that
produced impressive simulacra of weather patterns. One day he decided to
repeat a computation in order to run it longer from a particular point. His
computer worked things out to six decimal places, but to get a compact
printout he had truncated the numbers, printing out only the first three
digits. Lorenz entered these digits back into his computer. After a simulated
month or so, the weather pattern diverged from the original result. A
difference in the fourth decimal place was amplified in the thousands of
arithmetic operations, spreading through the computation to bring a totally
new outcome. "It was possible to plug the uncertainty into an actual
equation," Lorenz later recalled, "and watch the things grow, step by step." '
That was the birth of meteorological Chaos Theory. For the full story see the
source of the above at;
http://www.aip.org/history/climate/chaos.htm
Cheers, Alastair.
Eric Swanson
alas...@abmcdonald.leavethisout.freeserve.co.uk says...
>
>"Eric Swanson" <swa...@notspam.net> wrote...
I agree that round-off or truncation error is a problem. I used to build
and run simulations of large scale (at the time) dynamical systems. To minimize
round-off problems, we did our computations in double precision. I'm also
concerned with the other problem, which is the effects of grid size on the
results. Both effects are the result of the way the model is structured, not
necessarily the actual physical reality.
Eric Swanson
>
>Eric Swanson wrote:
>> still_th...@hotmail.com says...
>>>On 2005-10-20, Eric Swanson <swa...@notspam.net> wrote:
>>>>In article <3ro0ksF...@individual.net>, still_th...@hotmail.com
>>>>says...
>>>>
>>>>>Eric Swanson wrote:
>>
>> [cut]
>>
I think I see the problem. To me, "Growing" means "Intensification".
whereas, you seem to think it means just spreading to a larger volume
but with reduced intensity and thus different conditions later.
>>>But the case of momentum is altogether more fundamental than this.
>>>As a momentum perturbation diffuses through the atmosphere, it is
>>>precisely conserved. As the affected mass grows, the corresponding
>>>velocity perturbation drops, but their product remains the same.
>>>The friction you talk about is at the boundary, and this friction
>>>exists both in models and reality. But RP explicitly claims that
>>>momentum is destroyed by molecular dissipation within the
>>>atmosphere, and this is utter crackpottery. Read what he wrote!
>>
>>
>> Pielke uses the phrase "external force" to discribe the internal frictional
>> effects, as a way of extending the basic statement about momentum:
>> "In the absence of external forces, a system will have constant momentum"
>
>Pielke can pretend words mean what he wants, but it is patently obvious
>that the internal molecular dissipation is not an "external" force on a
>fluid. Consider the action and reaction, Eric. What is the reaction on?
>
>How he can say such things as this is a complete mystery to me:
The butterfly may be considered an source of external force, as it is not
part of the atmosphere, even though it is completely surrounded by air
during flight. That it derives its energy indirectly from some of the same
solar energy input as the atmosphere, thus it is part of nature is a whole
other can of worms.
>---
>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.
It's almost true in the case of solid matter, if one ignores the energy lost
in the collision. I suggest it is not true for fluids with internal frictional
effects, although there are situations where it is reasonable to neglect the
dissipation of the energy because of the different scales being investigated.
The atmosphere is not an ideal gas, incompressable or invicid, even though it
is sometimes convenient to write the equations as if it were that way.
>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).
>---
>
>He even acknowledges that molecular dissipation is internal!
I don't disagree that the dissipation, ie, the conversion of kinetic energy
to thermal (randon kinetic) energy is internal. He adds the qualifier "in
this context" and notes that the "internal force" idea is more appropriate.
>> In the case of multiple collisions or viscosity in a fluid, some of the
>> kinetic energy is converted to thermal energy. When a faster flow of
>> a gas mixes with a slower flow, again, momentum is lost.
>
>No, Eric, this is completely wrong. Energy is lost as heat. Momentum is
>conserved.
I think you better go back and check out the Laws of Thermodynamics. Energy
is neither created nor destroyed (absent nuclear processes). The internal
conversion from kinetic to thermal energy implies a loss of momentum. The
energy remains within the atmosphere, eventually exiting as part of the overall
loss to deep space thru the TOA or into the ocean's thermal mass.
>> Small perturbations may spread out to a larger volume, but they can
>> not grow in intensity, without the extra energy available to produce
>> that intensification.
>
>Eric, it's a nonlinear system, so separating into "perturbation" and
>"unperturbed system" is fundamentally invalid, and no extra energy input
>is required. Do you believe your ideas apply to all chaotic systems?
>Because they are trivially proved wrong in all experimentally-accessible
>systems.
I don't claim any expertise in chaos theory. My comments started with WMC
comparing two computer runs, each with slightly different initial conditions,
as in one "control" case and the other a "perturbed" case.
James Annan
> I agree that round-off or truncation error is a problem.
The shadowing lemma suggests otherwise:
http://julesandjames.blogspot.com/2005/10/shadowing-and-chaos.html
James Annan
> I think I see the problem. To me, "Growing" means "Intensification".
> whereas, you seem to think it means just spreading to a larger volume
> but with reduced intensity and thus different conditions later.
>
This probably explains part of it. I like to think of it as a
perturbation in the phase space of the system. If this perturbation is
decomposed into its projections onto the lyapunov vectors, then the
projection onto the growing modes will grow, and decaying mode will
shrink. In practice, this will mean that the absolute magnitude of a
random perturbation will initially shrink (the bulk of it projects onto
decaying LV), but later on it will inevitably grow as the proportion
aligned with the growing LV comes to dominate.
If you wish to think of the pertubation as a (roughly) separable
component, then its growth can be seen as being fuelled by taking energy
from the rest of the flow. There may be situations where that
description is also useful.
>>---
>>Regarding the question on the conservation of momentum, from the web
>>site http://en.wikipedia.org/wiki/Momentum, it states 的n the absence of
>>external forces, a system will have constant momentum・ This certainly
>>is true, of course.
>
>
> It's almost true in the case of solid matter, if one ignores the energy lost
> in the collision. I suggest it is not true for fluids with internal frictional
> effects, although there are situations where it is reasonable to neglect the
> dissipation of the energy because of the different scales being investigated.
> The atmosphere is not an ideal gas, incompressable or invicid, even though it
> is sometimes convenient to write the equations as if it were that way.
>
Sorry Eric, this is rubbish. First work out where your boundary is for
your system of choice, be it a small parcel of air or the whol
atmosphere. Internal friction implies equal and opposite forces within
the body.
>
>>The key condition is 妬n the absence of external forces・ Molecular
>>dissipation into heat is an 兎xternal force・in this context (the term
>>妬nternal force・would be more appropriate).
>>---
>>
>>He even acknowledges that molecular dissipation is internal!
>
>
> I don't disagree that the dissipation, ie, the conversion of kinetic energy
> to thermal (randon kinetic) energy is internal. He adds the qualifier "in
> this context" and notes that the "internal force" idea is more appropriate.
>
>
And this absolutely cannot destroy momentum, with or without
transforming it to heat. Which is in direct contradiction to what he
claimed.
>>>In the case of multiple collisions or viscosity in a fluid, some of the
>>>kinetic energy is converted to thermal energy. When a faster flow of
>>>a gas mixes with a slower flow, again, momentum is lost.
>>
>>No, Eric, this is completely wrong. Energy is lost as heat. Momentum is
>>conserved.
>
>
> I think you better go back and check out the Laws of Thermodynamics. Energy
> is neither created nor destroyed (absent nuclear processes). The internal
> conversion from kinetic to thermal energy implies a loss of momentum. The
> energy remains within the atmosphere, eventually exiting as part of the overall
> loss to deep space thru the TOA or into the ocean's thermal mass.
>
Don't be a prick.
Joshua Halpern
> Eric Swanson wrote:
>>>
>>> No, Eric, this is completely wrong. Energy is lost as heat. Momentum
>>> is conserved.
>>
>>
>>
>> I think you better go back and check out the Laws of Thermodynamics.
>> Energy is neither created nor destroyed (absent nuclear processes).
>> The internal conversion from kinetic to thermal energy implies a loss
>> of momentum. The
>> energy remains within the atmosphere, eventually exiting as part of
>> the overall loss to deep space thru the TOA or into the ocean's
>> thermal mass.
>>
> Don't be a prick.
Let me take a shot at this. Energy is conserved, momentum is diffused
into such large a volume that it disappears for practical purposes.
josh halpern
James Annan
"for practical purposes" implies you have a purpose in mind. When the
purpose is to make weather forecasts, of course you are right, because
we have much bigger things to worry about. But note that the momentum
perturbation isn't actually disappearing at all as it diffuses - the
velocity pertubation drops as the affected mass grows, but the momentum
perturbation is unchanged. Pielke claims that the mometum pertubation
actually disappears (is internally dissipated into heat) which is
fundamentally, horribly wrong.
Alastair McDonald
"James Annan" <still_th...@hotmail.com> wrote in message
news:3ru4s1F...@individual.net...
James,
Since Roger Pielke, Joshua ,and other are too polite to tell you, it falls to
me to say "You are talking crap!"
Momentum is not conserved in the same way as mass and energy.
HTH,
Cheers, Alastair.
Alastair McDonald
"Joshua Halpern" <vze2...@verizon.net> wrote in message
news:T5i6f.10074$Io4.426@trnddc06...
> James Annan wrote:
> > Don't be a prick.
>
> Let me take a shot at this. Energy is conserved, momentum is diffused
> into such large a volume that it disappears for practical purposes.
Josh,
Perhaps you could confirm this, as it seems to be an answer to James'
problem.
In the Maxwellian model of gases, the molecules collide and momentum is
conserved, but in quantum mechanics the molecular collisions can result in
momentum being lost, because energy from the collision is conversed into
the internal energy of the molecules.
At STP the loss of momentum will only occur when the collision involves a
greenhouse gas molecule. In a pure atmosphere of nitrogen and oxygen,
sound waves would travel forever because their momentum would be
conserved.
Is this correct?
Cheers, Alastair.
Eric Swanson
>
>Eric Swanson wrote:
[cut]
>>>---
>>>Regarding the question on the conservation of momentum, from the web
>>>site http://en.wikipedia.org/wiki/Momentum, it states 的n the absence of
>>>external forces, a system will have constant momentum・ This certainly
>>>is true, of course.
>>
>>
>> It's almost true in the case of solid matter, if one ignores the energy lost
>> in the collision. I suggest it is not true for fluids with internal frictional
>> effects, although there are situations where it is reasonable to neglect the
>> dissipation of the energy because of the different scales being investigated.
>> The atmosphere is not an ideal gas, incompressable or invicid, even though it
>> is sometimes convenient to write the equations as if it were that way.
>>
>
>Sorry Eric, this is rubbish. First work out where your boundary is for
>your system of choice, be it a small parcel of air or the whol
>atmosphere. Internal friction implies equal and opposite forces within
>the body.
A vortex is the result of rotation within a fluid. Thus, frictional forces which
appear due to the shear component appear with the same magnitude around the
entire vortex, thus they add to zero velocity in any single direction. The
resulting internal dissipation results in additional thermal energy , IMHO.
>>>The key condition is 妬n the absence of external forces・ Molecular
>>>dissipation into heat is an 兎xternal force・in this context (the term
>>>妬nternal force・would be more appropriate).
>>>---
>>>
>>>He even acknowledges that molecular dissipation is internal!
>>
>>
>> I don't disagree that the dissipation, ie, the conversion of kinetic energy
>> to thermal (randon kinetic) energy is internal. He adds the qualifier "in
>> this context" and notes that the "internal force" idea is more appropriate.
>>
>>
>
>And this absolutely cannot destroy momentum, with or without
>transforming it to heat. Which is in direct contradiction to what he
>claimed.
Sure it can. See the above comment about vortex forces. The simple idea of a
"parcel" of air moving in a stream tube is meaningless, as the walls of the
tube are in direct contact with more air and there is no real boundary between.
Turbulent flow involves multiple vortexes, which form at the intersection of
two different volumes of fluid moving in different directions.
>>>>In the case of multiple collisions or viscosity in a fluid, some of the
>>>>kinetic energy is converted to thermal energy. When a faster flow of
>>>>a gas mixes with a slower flow, again, momentum is lost.
>>>
>>>No, Eric, this is completely wrong. Energy is lost as heat. Momentum is
>>>conserved.
>>
>>
>> I think you better go back and check out the Laws of Thermodynamics. Energy
>> is neither created nor destroyed (absent nuclear processes). The internal
>> conversion from kinetic to thermal energy implies a loss of momentum. The
>> energy remains within the atmosphere, eventually exiting as part of the overall
>> loss to deep space thru the TOA or into the ocean's thermal mass.
>>
>
>Don't be a prick.
OK, I won't. However, I will side with Josh on this one.
You two experts can duke it out.
Joshua Halpern
> "Joshua Halpern" <vze2...@verizon.net> wrote in message
> news:T5i6f.10074$Io4.426@trnddc06...
>
>>James Annan wrote:
>
>
>>>Don't be a prick.
>>
>>Let me take a shot at this. Energy is conserved, momentum is diffused
>>into such large a volume that it disappears for practical purposes.
>
> problem.
>
> In the Maxwellian model of gases, the molecules collide and momentum is
> conserved, but in quantum mechanics the molecular collisions can result in
> momentum being lost, because energy from the collision is conversed into
> the internal energy of the molecules.
Good point, and one that I purposely avoided because
a. It broke my head thinking about it
b. I wanted a simple argument good to first approximation
but finally
c. I realized that momentum is also conserved in collisions that excite
or de-excite vibrational/rotational modes of motion.
If you have had a first class in physical chemistry/modern physics or
above, you realize that the decomposition of motion into
vibrational/rotational/translational motion is arbitrary, but very
convenient.
>
> At STP the loss of momentum will only occur when the collision involves a
> greenhouse gas molecule.
No, Oxygen and nitrogen can be rotationally and vibrationally excited,
and de-excited by collisions, they just cannot be excited or deexcited
by radiation
In a pure atmosphere of nitrogen and oxygen,
> sound waves would travel forever because their momentum would be
> conserved.
>
Try helium
> Is this correct?
>
No, see above.
josh halpern
Joshua Halpern
Just as it is fundamentally, horribly wrong in a general chemistry class
to say that mass is conserved . The intellectual frission generated by
the students' remarks on relativity are quite enjoyable. Brings new
meaning to the words teachable moment.
On the other hand, what do models do when the average momentum/whatever
disappears into the least significant digit?
My approach to this all is to say that science is based on models that
can be used to understand nature. There are nests of models, that the
most basic are the most correct, but often the most difficult to use,
while there are also very simple but useful models which are incorrect
in many regards (e.g. valence). The most important thing about a model
is to learn the limits within which it is useful. This goes to a term
that Michael Tobis used frequently, the skill of the model, ie, that is
models can be very important for understanding without being perfect.
On another level, the sensitivity of models to particular changes of
inputs/parameterizations determines the accuracy with which those inputs
must be understood.
I will now ignite a conflagration: Intelligent design is NOT a useful
scientific model. Evolution is.
josh halpern
Michael Tobis
> that Michael Tobis used frequently, the skill of the model, ie, that is
> models can be very important for understanding without being perfect.
I'm not dead yet!
I'm also sure I didn't coin this usage. Credit my thesis advisor at the
least, John R Anderson, who long ago had the good sense to bail out of
climate and go to work commercially in visualization in the
entertainment industry. (He's now at Pixar.)
I think the applicability of chaos theory to climate prediction,
especially on time scales shorter than a Milanlovic cycle, is so close
to nil that talking about it is pointless. Rebutting Pielke on the
grounds that he doesn't understand chaos theory attends to the wrong
question.
Whether he understands it or not, there isn't the remotest sign that it
is relevant. Even if one could meaningfully say that the climate system
is not chaotic and the models are, that really says absolutely nothing
of consequences, Models of interest in the usual climate debate
empirically have stable statistics, and that is hardly surprising and
probaby provable. The real world is not perfectly known and is thus
best treated as a realization of a stochastic process whether it is
"chaotic" or not. The models wander about the model phase space
constrained by physics that models how the real world models around the
real phase space. Empirically, the models are successful at doing so.
Not only has nobody come up with any reason why the statistics that
process can't be modelled, any such argument is trivially refuted by
understanding what the models in fact do. So I think the whole argument
is misguided on both sides.
mt
Eric Swanson
>
>Alastair McDonald wrote:
>> "Joshua Halpern" <vze2...@verizon.net> wrote ...
Oh darned, this is getting messy.
But Josh, the MSU/AMSU senses mivrowave emissions from oxygen molecules in the
atmosphere, which is claimed to be related to the temperature. The O2 molecules may
not be emitting in the IR, but, they apparently are emitting at lower frequencies.
Saying more would only illuminate my lack of understanding.
NobodyYouKnow
Those are only one example of quantitisation error. Quantitisation error is
a more general term for the loss of precise knowledged in any reduction of
the real world to data. It includes the sparsity of measurement, the
limitations of analog converters, the limitaitons of computer models, etc.
>
>> This is NOT the math.
>
> It *IS* the math (assuming your "quantitization" error means either
> truncation or roundoff). There is no exact solution for the set of
> coupled nonlinear PDEs that we have to solve, so we have no choice but
> to use numerical methods and accept their limitations.
But computers are NOT chaotic. Do not confuse the limitations of computer
simulations with chaotic systems in the real world. Chaos is real. If
computer simulations do not model them, that does not make them less real.
NobodyYouKnow
> NobodyYouKnow wrote:
>> The points I made hold in
>> the real world or in mathematics.
>
> I assume you mean from one of your earlier posts:
>
> "Chaos theory is about the fact that it is POSSIBLE for that single
> flap to change the future such that a hurricane that would NOT have
> formed, WILL form, not that every flap of a butterfly wing will
> create a hurricane down the road."
>
> The butterfly flap (or any other stimulus) causes the system to evolve
> toward a different specific realization of the same climatology. The
> two realizations will include different specific events, with
> hurricanes being examples of such events.
Exactly. Note that the arguments against the 'butterfly effect' based on the
limiations of computer models ( which are not examples of chaos theory ) or
'dissipation' ( which is irrelevant since the momentum or conversion of
energy is NOT the issue, so much as the difference in the outcome which
STILL progresses in a 'different path'). Many arguments here are based on
the outcomes being 'similar' which is NOT the point of chaos theory. Chaos
theory holds that they will be different BECAUSE of the butterfly flap, NOT
that the overall constrainst on the climate system will change.
It is like the ultimate example of chaos theory. A pool table with a
frictionless surface and perfectly elastic bumpers. The *exact* angle of the
pool cue strike may be so slightly different that there is no perceptible
difference in the balls direction or position for the first hundred bumps,
but the *difference* will keep adding up at each impact and while later, the
ball is moving in a totally different direction and at a totally different
place.
Dissipation in the climate system are irrelevant. Whether the momentum of
the initial wind, or the convection currents created by a *slightly*
different temperature, the changes will accumulate.
>
> All this brings up one of my curmudgeonly notions: everyone says
> climate is the average of weather, but I often try to convince people
> to think in the other direction -- weather is the day-to-day
> manifestation of a particular climate.
Which means that the overall climate outcome will probably be about the same
while the exact outcome changes, which MAY in rare cases make a major
difference in EVENTS ( i.e. the extra hurricane ). And both ways of looking
at it are valid.
One point to note is that some weather systems are 'more chaotic' (
sensitive to minor differences ) than others which is why the weather
forecaster can sometimes give probabilities of a particular outcome and
sometimes just has to say that wild weather is approaching.
Joshua Halpern
in oxygen are forbidden, but there can be much weaker magnetic dipole
transitions between the fine structure elements of the ground triplet
state. For much much much more than you want to know (well maybe not
Eric) http://mls.jpl.nasa.gov/data/eos_polarized_atbd.pdf. My sense is
that the probability of exciting these things in a collision is very
small because they would require a spin flip and the energy differences
are really small so they would not play an important role.
josh halpern
James Annan
>
> James,
>
> Since Roger Pielke, Joshua ,and other are too polite to tell you, it falls to
> me to say "You are talking crap!"
>
> Momentum is not conserved in the same way as mass and energy.
>
> HTH,
>
> Cheers, Alastair.
>
>
>
You just broke my...
+--------------------------------------------+
\ 1 2 3 4 5 6 7 8 9 /
\ 0 10 / /
\ / /
\ CRACKPOT METER / /
\ / /
\ / /
\___________________________/___/
\ /
\.........................../
James Annan
Well, they do not deal in momentum directly, but velocity and pressure.
A small enough perturbation could in theory be rounded out, but we can
always compile the model at higher precision, and as wmc already showed,
in practice it tends to grow fairly rapidly due to convective instability:
http://mustelid.blogspot.com/2005/10/butterflies-notes-for-post.html
(the results are entirely routine and characteristic of small
perturbations in GCMs)
> I will now ignite a conflagration: Intelligent design is NOT a useful
> scientific model. Evolution is.
But what about conservation of momentum (within the context of butterfly
flaps and atmospheric physics)? How about "Intelligent Slowing"?