Continuation of Exponential Growth # 2.

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208 Comments
lucia (#551),
Humorous. 🙂
Jerry
I urge everyone to read the Murray Duffin post here, and the reference cited in the link.
It’s dynamite, if true (and the Physics seems good)!
Sorry, here:
http://www.climateaudit.org/?p=2378#comment162710
The article itself is at:
http://www.arxiv.org/PS_cache/arxiv/pdf/0707/0707.1161v3.pdf
The Wood experiment, described in section 2.5 on P. 32 of that document, needs to be repeated under controlled modern conditions, in my humble opinion.
Funded by Mobil no doubt.
Looks interesting to me, even with my grip of physics being limited.
Regards
Peter Bickle
Re #4 – this ms does not seem to have been published, and I doubt that it can ever be. It is a verbose, chaotic ramble, dwelling on obscure AGWsceptic movies (sec 3.2), MHD, etc. For 18 pages, it demolishes laboriously the proposition that real greenhouses work by the greenhouse effect, as if that strikes at a pillar of climatology. Wikipedia disposes of that far more effectively in a paragraph.
I have continued looking at some ODE systems that are important relative to the basis of ‘chaotic response of complex dynamical systems’. I am working on posts of the results of my calculations and will get them posted Real Soon Now.
One almost certain conclusion is that convergence has yet to be demonstrated for any such system.
Come on over and let me know what you think. All comments and corrections are appreciated.
Article by A. Robinson, N. Robinson, and W. Soon in Journal of American Physicians and Surgeons (2007):
http://nzclimatescience.net/images/PDFs/gwreview_oism150.pdf
Words fail me to describe the brilliancy of this summary, addressing ALL issues of AGW and beyond.
ooops
over = http://danhughes.auditblogs.com
or click my name above
Nobody else will ask this, so is there a generally agreed upon definition of “chaos” in the modeling context? Just looking at the discussion, I don’t think it means the same thing to everyone.
chaos = deterministic nonperiodic flow resulting from nonlinear dynamics, leading to extreme sensitivity to initial conditions
I will let Dr Browning judge whether chaos is OT. I will let Steve M judge whether there is any useful auditing function to be fulfilled by discussing weather vs climate. Myself, I don’t think so. Too easy to go OT.
11, Dr. Browning specifically brought the chaos issue up in this thread, so I presume that it’s ontopic. Your definition is what I think most of us understand, and would include, for example, the pressure effects of turbulence. A very small pressure sensor placed in a turbulent flow field would measure a chaotic pressure, which, to the best of my understanding, would yield a Gaussian distribution of pressures if measured over a reasonably long period. This, due to the nonlinearity of the NS equations, and the nonuniqueness of solutions.
The last statement the Dr. Browning made, however, seemed to imply that it had to do with the convergence of models. That’s something else, completely. That’s why I ask.
No convergence. Thank you, Dan.
=====================
Larry, thanks for clarifying the link to an auditing function (that being model convergence). You can imagine how a topic like this could spiral into irrelevance very quickly if the focus on auditing is lost.
chaos = existence of Smale’s horseshoe.
Here’s the tiein to climate modeling:
http://www.climateaudit.org/?p=1335#comments
Specifically,
Dr. Browning seems to be suggesting that this won’t be possible no matter how many terraflops we can throw at it.
Chaos is not on topic. The convergent numerical solutions of the incompressible NavierStokes equations are an indication that turbulent flow is not chaotic when properly resolved. Please ask Steve M. to start another thread on chaos if you want to discuss that topic. This thread
is about the exponential growth that appears in the continuum systems (unbounded in a finite time interval in the case of the hydrostatic system or bounded in a finite time interval in the case of the nonhydrostatic system) that are approximated in weather prediction and climate models and the impact of those growths on the associated numerical models. Thank you
for keeping your focus on the topic of this thread.
Jerry
With regard to the central point of this topic, exponential functions in nature, may I add the Beta function? At the moment I have been looking at the movement of small gasses within proteins molecules. The kinetics of which follow KohlrauschWilliamsWatts (KWW) kinetics.
The KKW function shows that N(t) = Amp*EXP(1/Tau)^Beta, where Tau is the halflife of the process (ln(2)/k) and the Beta function is between 0 and 1. In a normal exponential, Beta is TAKEN, as 1; but is generally not proven to be the case. The stretching function give you quite a headache at first and the lineshapes of KWW functions look like more complex mixed exponential processes. The easiest way to identify a KWW process is to look for a linear plot using N vs. Log(t) plot. Wikipedia has a picture of what the beta function does to exponentials, which I have reproduced.
KWW type processes are everywhere, they are typically found in systems where there are a number of stable states, with largish activation barriers in between.
Larry (#16),
That is exactly what I am “suggesting” as long as the inviscid NavierStokes equations with gravitational and Coriolis forces added (or the corresponding viscous system with the appropriate small atmospheric viscosity) is the system of equations approximated in a numerical weather or climate model. These problems have nothing to do with chaos, but to a bad continuum physical approximation (in the case of the hydrostatic system) and to problems with numerical approximations of fast exponential growth (in the case of the nonhydrostatic system).
Jerry
19, here’s a dumb question, but has anyone ever determined that the continuum model implied by NS is even valid for numerical solutions? Is it not possible that you may not get a solution to the continuum equations until you get to the scale where it’s no longer a continuum?
Is this an obtuse question?
Larry (#20),
No, it is not an obtuse question. But the NS equations have been the standard system used for almost all 3D fluid dynamics. And the problems mentioned above show up with grid sizes around 510 km, i.e. a fairly crude mesh in terms of physical features properly resolved.
Jerry
@Larry–
That’s actually an excellent question.
We actually have good ways of understanding when the continuum model breaks down. This is a scaling issue. If, at the scale you examine things, a “very small volume” contains a huge number of molecules, the continuum model applies. So, if you like calculate how many air molecules there are in a 0.1 mm cube. You’ll probably think that number is pretty big.
There are more clever things one can do, and more precise definitions, but they really come down to: How many molecules are in something that seems like a “fluid point” in the problem I’m considering.
Right. When you get to the “Brownian motion” (not to be confused with our Dr. Browning) scale, it’s not a continuum. But I wasn’t sure if they are even in the same order of magnitude to where it could be a potential issue. I think we’re many orders of magnitude from that point, but the thought crossed my mind that we may never be able to solve some types of fluid mechanical problems with NavierStokes, regardless of the terraflops we have on our desktops, because it may be necessary to descend into the Brownian scale to get the kind of detail necessary.
Doing the entire atmosphere that way would be a big job, to say the least.
@Larry– There are transport problems that are solved using representations other than Navier Stokes. However, when the continuum assumption breaks down, it’s no longer, strictly speaking fluid mechanics. Fluid mechanics is a subset of continuum mechanics. Recognizing when the continuum assumption breaks down is important.
I’ve had friends work on nanoscale problems where you can’t use NavierStokes. Also, if you reach the edge of the atmosphere, NavierStokes can’t be used.
I’m looking at scale issues related to gas dynamics at:
http://iecfusiontech.blogspot.com/2007/11/gasvalvedesign.html
The comments by Brent are especially useful.
Scale is actually quantified as a Knudsen number which relates the mean free path of the gas molecules to the scale of the object in question. At Knudsen numbers around 1 treating the gas as a continuum fails.
I plan to get around that in my case by experiment. I will use the continuous gas formulas to get me in the ball park and then adjust until the system works. Unfortunately the problems climate researchers have can’t be solved that way. The best you can do with climate is predict. Look for the divergence. Work back to see if there is a better solution. You can also check to see if your “improvement” made other past predictions better or worse.
Larry (#20),
I should add that in the case of fast exponential growth near jets
(for the nonhydrostatic system), the phenomenon has been seen in reality, e.g. clear air turbulence, and in the neighborhood of decaying storms (gravity wave ripples). Thus the NS equations seem to correspond quite well to reality.
Jerry
I might also mention that if the exact exponential growth rate is known, a change of variable can remove that growth from the problem by the corresponding exponential change of variables. Unfortunately, in the 3D
case the growth depends on spatial wave numbers so a simple change of variables will not work.
Jerry
lucia (#24),
As you mentioned, as you move further out into the earth’s atmosphere the fluid becomes a plasma and magntohydrodynamics should be used. That is another entire can of worms, e.g. continuum approximations were made in that system that are ill posed.
Jerry
M Simon (#25),
You are talking tuning and that is a very dangerous game, i.e. the
resulting numerical solution may be far from reality (as in Sylvie’s Gravel’s manuscript).
Jerry
Gerald,
In engineering it only has to work. The theory need not be correct. It just needs to bring you in the vicinity of a solution.
Second, a feed back system properly designed will cover up a lot of misunderstanding. I know the valve will be highly nonlinear. Its components will have serious hysteresis and material creep problems. The gas flows will be probabilistic. You servo the system to the desired results and it doesn’t matter. Which is why some of the companion articles deal with feedback. Detectors. Instrumentation. There is also a bit about having sufficiently large tanks inserted in the system at convenient places in order to reduce rates of change possible. It is ALL about scale. Try doubling the size of the oceans to slow down the dT/dt for a given energy input. An exercise best left to the reader.
A very bad way to do basic science. A good way to do engineering. The fact that this is engineering in service of basic science is even better.
Of course if your system response is exponential to change and your feedback loop is longer than the system response time you are farklempt. Nuclear reactors would be uncontrollable for this reason if it wasn’t for the approximately 1% delayed neutrons. Even then there is a narrow range of reactivity where the delayed’s help. Get above that range and the reactor self controls – i.e. melts down.
Re # 4 Pat Keating,
No one seemed to pick up your point. I dont know if its because this is the wrong thread but, without knowing of Prof Woods note, this was an area that I have thought was worth looking at for some time. I realise that the results should be predictable from the physics but then they say that GCMs are based on physics. I think it would be interesting to do several variations on the Wood test with air including varying concentrations of water vapour and carbon dioxide and also with varying height. I had in mind a slowly revolving carousel tracking the sun on which one could mount a control column and others of differing atmospheres.
I didnt understand Plinys point. I thought it would be interesting to see experimentally how much more heat the IR gives to the air at varying concentrations. Am I missing something rather simple that makes this a waste of time?
31 David
I think the main reason it received a limited number of comments is that it appears that there is acceptance of the validity of the Wood experiment, even among AGW believers.
Ironically, I have come to wonder if the Wood experiment should not have been done as a cooling experiment at night, rather than a warming experiment in daytime.
Let me add that what usually happens in these cases is that if you can get a lashup to work and it has high utility a lot of people get assigned to understanding and improving on the original design and correcting the bad theories.
Read some of Tesla’s work. Brilliant in general, but he had some serious and glaring misunderstandings – according to what we know now. The thing is his misunderstandings lead him to dead ends. OTOH he made things work. Like radio controlled boat models in the very late 1800s. An amazing accomplishment for its time.
Now it is good to have so many people studying climate. What is unfortunate is that our minuscule understanding has given rise to orthodoxy that pretends to more understanding than it actually has. This is easy to hide because the time scales are so long and the system itself is chaotic with strange attractors (You want to know the most likely weather for tomorrow? Same as yesterday). Even when the time scales are short (electricity) understanding is some times decades in coming. The real crime in all this is not this prediction or that prediction. It is confidence intervals that do not match the quality of the data and its analysis.
One must take this as a common human failing because we see it in all fields. Predicting the future gains one prestige. Tarot reader or climate scientist. Doesn’t matter.
M. Simon,
In the process control systems you describe, the errors in the control loop are continually corrected by feeding measurements back into the control loop. Because of this continuous response to actual measurements, the errors in the system can be corrected for. Short term weather forecasting shares this kind of correction mechanism because new weather measurements are also fed back into the system. With climate forecasting we have a loop that has to run without these constant corrections from external measurements and thus cannot get away with this kind of ad hocery. Unlike in your three term controller, you can’t assume that Dx = dx and that integral x = sigma x.
Sorry, I simply cannot help myself, I guess I am just a “rub the hound’s face in it” kind of guy! 😆
Here is sure evidence of the forecasted killer AGW signal superimposed on seasonal norms (ref. scorecard of NWS meteo runs from last week):
Wow, what a radical Super Santa Ana, we should be having fire reports and all time record high temps any minute now (sarcasm off).
#34 >> With climate forecasting we have a loop that has to run without these constant corrections from external measurements and thus cannot get away with this kind of…
There are 2 situations here: 1) a physical system, like M Simon’s nuclear reactor, and 2) an analytical prediction/simulation of a physical system.
While it may be true that climate forecasting does not run as a closed loop system with constant corrections from external measurements and may be numerically instable, all indications are that the climate itself does operate as a closed loop system, with constant corrections.
Therefore, analyzing & simulating the closed loop system may be a lot easier than simulating the system from the bottom up.
Jerry, I don’t think you and Simon are on the same wavelength at all. He’s talking about a feedback controller, like an autopilot or a cruise control. Not anything like simulating the NS equations. Apples and rutabagas.
# 32 Pat,
Nighttime would be interesting too. Anecdotally – I am not the gardener – this is what was called, ironically, a cold frame which was widely used to grow on things that would not have survived day or night in the open.
Chris Harrison (#34),
You are bang on. The insertion of new wind obs into short term weather prediction models redirects the numerical model’s track that has O(1) errors in the matter of 24 – 36 hours. Without the new obs, the errors
from the inaccurate parameterizations would destroy the accuracy of the model. This is the danger of tuning. The model can be completely unphysical in a very short time. I am amazed how after all of the
discussion, numerical examples, and references on this thread, the same irrational arguments are repeated. RTFM people. And quit getting off the topic of this thread and using it for unsupported arguments. This is a quantitative thread.
Jerry
Larry (#25),
Not entirely. He has assumed that the tuning keeps the solution accurate,
i.e. close to reality. That is not the case with the parameterizations
in short term weather models. The boundary layer in general should be a turbulent flow, but because it can’t be adequately resolved, it is parameterized by a very crude approximation. The results in Sylvie
Gravel’s manuscript are quite clear on how the errors in this approximation propagate vertically and would destroy the accuracy of the solution without the obs update.
Jerry
@ M. Simon
Engineers also don’t like illposed systems of equations, because they don’t work. Look for “ill posed” a lot with names like “Prosperetti” or “Drew” and you’ll see discussions about illposed problem in the multiphase flow literature. The problem of practical significance was trying to use codes to predict what happened in Loss of Collant Accidents in nuclear reactors.
Ill posedness sounds like a nitpicky mathematical issue. Unfortunately, it’s such a truly horrible one that it results in systems of equations that don’t work. At all.
@Larry in 37. I suspect apples to rutabagas too.
PID control bears some superficial resemblance to iterative numerical solutions, but it’s a different thing. “Tuning” a loop doesn’t affect where the loop ends up, it affects how fast it gets there and whether it oscillates (or possible goes entirely unstable) in the process. Not the same thing as model tuning at all.
lucia (#41),
Heinz once mentioned to me that the equations used to describe nuclear reactor safety were ill posed. I wonder if the ones you are describing are that system. Scary.
Jerry
Larry (#42),
So the process bears little resemblance to tuning the NS equations as done in weather and climate models. I guess the obvious question is why was it brought up on thread.
Jerry
Given that the parameterizations in short term weather prediction models become inaccurate so quickly (2436 hours as would be expected from the fast exponential growth term) and are overcome only by new wind obs, can someone prove that the parameterizations in coarser mesh climate models perform better that those in global weather prediction models on a day to day basis? If not, then the climate model solutions will diverge from reality in just as short of time period (or even shorter) as in weather prediction, but are not able to correct with obs as discussed above. Even if the climate models resolve the largest scales of motion (but obviously do not compute the correct forcings at the largest scale), they do not resolve features with length scales O(100 km) or forcing of that scale, both of which are very important in obtaining the actual atmospheric spatial spectrum.
As has been proved on this thread, the forcings can always be chosen so that the desired solution or spectrum is produced even with the wrong system of equations or incorrect large dissipation. There is a manuscript by Dave Williamson et al. at NCAR that shows that the parameterization in the NCAR climate model diverged from reality very quickly (with no credit given to Sylvie). I see no possible scientific explantion for how a climate model might be close to reality . And in fact if one looks at the output
closer, one sees all sorts of day to day flaws in a climate model as expected from the arguments here.
Jerry
Jerry– There were quite lively arguments over the correct formulation of the pressure term.
Yes. I’d suspect Heinz was bringing up the precise problem I am discussing. It was (and is) taken quite seriously. It’s not a quibble. It doesn’t have to do with chaos, or sensitivity to initial conditions or anything of the sort.
I understood from my advisor that things were sometimes thrown around at meeting. . .
lucia (#46),
An interesting problem, especially given the significance of the
implications.
Jerry
Chris Harrison,
Total agreement! It is the continuous comparison against reality that makes controllers work.
As you point out short term forecasts do that.
Climate science has no such feedback mechanism on reasonable time scales. Which is why if you follow previous climate hysterias they tend to peak very near the peak of the cycle. Based on that heuristic I’d say that we are at an inflection point.
Larry,
It is not entirely different from model theory either. When you want very tight control you want to match the control algorithm to the plant algorithm. Too much damping in the control and your response is slow. Not enough and your solution diverges.
Some processes are integrating and these are easy to control. They would be things like filling a tank from the bottom. At fixed pressure the flow decreases as the tank fills up. Systems that have an exponential response to change are much more difficult to model or control. In an integrating system errors damp. In an exponential one they multiply.
We know weather is exponential in many respects. Is climate? Are the models? Do the models match the real climate. Do we have a good handle on the real climate? Such an open ended problem.
Lucia,
I’m very familiar with the Loss Of Coolant Accident (LOCA). Of course it is ill posed. The number of significant variables is enormous. Just two related ones: Hours of continuous operation since last shut down. Total operational history since last core replacement. etc. Two more: is the coolant boiling out (breech at a high point) or is it being forced out by steam pressure (breech at a low point).
Then you have instrument failure associated with a core breech i.e. the instruments show a rising water level when it is actually falling. That one happened at Three Mile Island. In the Navy it is drilled into you that a core meltdown will lead to erroneous level readings. I’m told a Navy man was on duty at the time. The training must not have stuck. Or he was misled by other indications. Or he stopped thinking rationally in the emergency.
So yes – very ill posed indeed. It is why we have containment vessels.
The thing is we know the integrator in our system: the earth and the oceans. We also get help from the fact that a 1% rise in temperature causes a 4% increase in radiation. So what gets the most attention? The system with the lowest thermal mass – the atmosphere.
#36 Gunnar,
There are all kinds of tricks you can play even with a system you do not understand. As long as the system is continuous and your control system can operate at a much higher frequency than the controlled system and you can assume over a short enough segment of operation the response is linear you can control the system even if you don’t understand how it works. Of course you may have to do things like adjust the gain of the system and the time constant of the integrator to keep things under control (depending on how tight the control has to be).
I think that is Jerry’s point. Good feedback will correct bad models. Engineers depend on it because the real world is full of disturbances. So the model never can match reality. The question then is how close? A lot closer if there are fewer principles involved. I can tell you how fast a car will accelerate if you tell me force vs time. Telling me how much force a given engine puts out based on first principles is harder.
Hehe, the entire reason for the existence of adhoc automaticgaincontrol circuits.
Mark
I suggest that there is a fundamental naivety in the Wood experiment, in that the onset of cellular convective instability is highly dependent upon boundary conditions. I have only worked on the electrohydrodynamic instability of liquids, and have shown experimentally that the theoretical criteria obtained for effectively infinite parallel electrodes do not readily translate to the small testcells used by experimenters. I have no idea how the numbers pan out for air, but it seems likely that a small box, with tight boundary constraints, would differ considerably from a glasshouse, which would in turn differ considerably from the whole atmosphere.
Re #31 and #32
Yes, as per #32, the fact that the greenhouse effect is inexactly named is just a nonissue, and has no relevance to the validity of climate science. But if you really want to know about greenhouses, there is practical greenhouse science. In that linked study of glazing materials, you’ll find a paper cited on p 13 that said IRblocking glazing material reduced heating costs by 13%. Significant, but not dominant. Noone anywhere, that I am aware of, has suggested that IR absorption by GHG within a greenhouse is other than totally negligible.
Lucia, interesting that you in the fluid mechanics modeling field were looking at what happened at TMI. IIRC, the way it boiled over did surprise a lot of people, keeping a water level in the overhead drum while the reactor was going dry. I suppose that it’s a case of “if you’re a hammer, all your problems look like nails”. Most instrumentation types looking at what happen concluded that the “cause” was under instrumentation. Both are right, just in different ways.
@Larry–
I never looked at TMI myself. I mostly did gassolid and solidliquid flows– but the illposed issue is important to the whole field! 🙂
I think the multiphase flow conversation has two (or three) discussions going on in parallel.
To be more precise, the fluid dynamics crowd were trying to model what happens to fluid in pipes during many types of hypothetical LOCA accidents, not strictly speaking just TMI. This is as much to try to design things so they will work should accidents of various sorts happen. There were also people running a variety of experiments mimicing various accident scenarios.
The modeling question is: Can the computer models predict what happens during a bunch of hypothetical accidents? What if a pipe breaks in a particular spot and no one does anything, can we predict what happens? Or a valve gets stuck there? Or imagine other things that might go wrong, can we predict what happens?
Mr. Simon seems to be addressing another issue which is: given the range of what might happen, can the operators and their control systems handle the issue.
Both sets of questions get asked, and of course, information gets communicated back and forth between them.
However, they aren’t quite the same problem. The illposed issue addresses the fluid dynamic modeling question directly: can we predict what happens?
The answer to that issue only impacts the control question in so far as we do use information about the system response to design a control system. So… if we can’t model the flow system at all, then we can’t use the output of models to design the control system the operators might use.
(In reality, design of reactors involved modeling and experiments. After all, you can build scaled experiments and test stuff. So, a great deal of information required to model control systems was available even if there was quite a bit of uncertainties in model prediction. Also, numerical models aren’t totally pathetic– some things can be modeled, but the uncertainties and limitations need to be explored, and documented. Then, the control systems need to be designed to consider all plausible outcomes. )
lucia,
In the Navy we spent a lot of time on hypotheticals similar to those you mention. I don’t see how you can address those problems except in the most general way. Aside from the fluid dynamics problems which have to be horrendous with the steep pressure drops and phase changes.
At the time I was only an operator so of course I didn’t get deeply into fluid mechanics. I did get deeply into “if xxx breaks this way what will happen to the plant? What should you do about it?” Surprisingly one of those what ifs covered exactly the TMI scenario years before it happened. The idea of that particular tank with only one indicator was in some outbuilding where it couldn’t be conveniently eyeballed was considered the height of stupidity by the Navy instructors. It was the general consensus that the plant was poorly designed. If fact we even covered the backwards reading level gauge and the fact that a poorly trained operator would prematurely turn off the emergency cooling water when the proper thing to do was to maintain flow.
I think all that caused the NRC to tighten up on training requirements.
Well, this may be interesting to some but it is way OT, so I’ll shut up.
On a more general note: so much of what we know is a patchwork. You use these equations here and those equations there and this equation to decide which is which. If you are on the boundary between the two regimes – good luck and God bless. The particle guys would like some kind of unified field theory. It is not just the particle guys who need that. It is all of physics. The difficulty is that if we had something like that it would be too difficult to use unless we made the usual simplifying assumptions.
You can cover up a lot of ignorance with the usual simplifying assumptions. Not that I’m complaining mind you. I know where some of the skeletons are buried. The difficulty is that once you produce miracles people think you are omniscient instead of understanding that you have just narrowed your focus enough to accomplish something. You have bounded the problem.
I was specifically referring to the fact that as the reactor boiled itself dry, the steam drum above it kept it’s level, and the level instrument gave the operators warm fuzzies that everything was copasetic as the relief valve was puking its guts out all over the floor of the containment structure. Better instruments would have indicated a problem, but the 2phase fluid mechanics that caused the level to just sit there surprised a lot of the design engineers at B&W. For obvious reasons, they’d never done any experimental work with boiling a reactor dry. And from what I’m gathering (here’s the ontopic part), modeling probably wouldn’t have done them any good.
Okay, party people let’s get this exponential growth in physical systems party started!
A hundred parts per million by volume of carbon dioxide in the atmosphere has resulted in a seventh of a degree centigrade rise in the trend of the global mean temperature anomaly in the last hundred and twentyfive years or so, taken as a fact.
Regardless if you agree or not with that postulation or not.
The question is posed to you thusly: How many years will it take to add another one hundred, and what global mean temperature anomaly rise will it result in?
.
.
.
.
To not leave anyone hanging, I say within eight years it will go up another one hundred, and that will result in an additional anomaly of a sixth of a degree, resulting in an anomaly of plus one point three percent, all things considered.
What say you?
RE: #58 – I say it will be an additional (0.7 deg C)^(0.5) or thereabouts.
RE 58. You used fractions. now I have to math. right before thanksgiving when I am calculating the radiative
balance of heating a turkey, which is not a black body… CRAAPPP. now I have to start all over. TANKS FUR NUTIN.
NO SWEET POTATO for you!
@Larry– You’re right (as you so often are). The problem at TMI wasn’t fluid dynamics modeling.
The only reason I bring up the thermohydraulics modeling issue is issue of illposed equations rears its ugly head in many approximate models. Jerry is correct that illposed equations that have been patched up using unphysical fixes are suspect. Suggesting that the problems of illposedness or unphysical patches will be fixed up by averaging is bizarre. You can flip till the cows come home but averaging the results from a biased coin would result in a biased average.
So, if Jerry is correct and the systems of equations in GCM’s are a set of illposed equations that have been patched with an unphysical patch, then that puts predictions in some doubt.
Normally, that means that we turn to improving the models and collecting new data to test the new models. (The problem with postdiction in place of prediction is that tweaking is always possible with postdiction. )
Of course, Steve M’s discovery of the errors in the US temperature record gives us some pause. After all, while it is true that the US is only a small amount of the land mass, one must wonder a bit about the accuracy of other temperature records. This is particularly true if other records were corrected or processed same person or agency or method as the American record, or if methods were shared.
Now… I need to go bake pie.
@Steve– when you tent bits with foil, the turkey is really not a black body!
Sorry, quantity of less than one … (0.7)^2 deg C. Less than 1/2 a degree.
Sorry MOshPiT. Dang, and I wanted that yam. And it’s not a black body either. Dang the luck.
Sadlov, so you say .35 C in 8 years? Just as good as a guess as any. What’s the model say, and what’s the margin of error? I want error bars!!!! Or some ice cream.
Ain’t going up 100 ppm in 8 years.
Sorry, can’t resist yet another jab at meteo models. Last week at this time killer AGW fueled “late” statewide Santa Anas and warth were prog’d for the current period. Reality? Frost. Tonapah Low a distinct possibility. On the topic of frost in this CWA (SFO) – I believe that the past couple of nights’ frost advisories for substantial portions of the CWA may have set a record. The shortest frost free period within a given year. We had late frost and now are having frost somewhat on the early side. Yet another abject meteo failure for time frames beyond 72 hours.
RE 66.
My heating bill is gunna be through the roof this year. I prefered 98 with the sunnyvale F2.
Dude, that was like blocks away from me. Being from the midwest I smelt that twister before
it ever formed. Awesome weather day.
LOL. This is one of the things that drives me nuts. The NWS can’t predict 72 hours out, but the elite climate modelers can predict 100 years. I know they think they see more order, because they think they see the “big picture,” but I don’t see any proof that they have any clue about the “big picture.” They can’t even factor clouds and humidity into those models. And to those who believe in climate models, I would refer them to P.T. Barnum. I keep thinking this is just a bad dream.
RE: #68 – both meteo models and GCMs are un physical and have incorrect boundary conditions. Both also require ongoing “adjustments” in order to prevent singularities and other non convergent behavior. I also note that both meteo and GCMs assume things like 2XCO2 and 2.5 deg C rise. They assume the AGW signal they claim to predict as a sort of recursive boundary condition. Snake oil …
I have just rediscovered that while I was away , this (my preferred) thread on CA grew by several hundreds posts .
Have read everything and chaotically oscillated between the states of posting and not posting – yes , no , no , yes , no , yes , yes …
The summary :
– No significant progress with regard to the old thread (small disappointment)
– Gunnar is still slow and mostly wrong
– excellent quote of Mandelbrot by Steve M that nobody picked up (actually Dan Hughes should have)
– 2 links by Spence UK to very good papers
– a REALLY boring debate if climatology is the same thing as meteorology (nobody cares anyway)
– many confusions as to what means mathematically deterministic chaos in dynamical systems (largely non limited to NS)
I’d like to comment on one particular point in the whole “averaging business” .
Somebody I forgot who , implied somewhere that RANS (Reynold Averaged Navier Stokes) was meaningful .
It is not and in any case it makes the NS problem worse and not better .
Once you have the original NS that you can’t solve , you can of course always ask the question of averages instead of the instantaneous values , try to get answers about “average” flows .
Nothing easier than that – similar to the perturbation treatment a parameter can always be decomposed in a sum of its average and a “perturbation” term .
However this transformation has a price and the price is the apparition of the Reynold stress tensor which adds 6 aditionnal unknowns and not one equation more .
That’s the closure problem of RANS .
As there are obviously not additional and hitherto unknown natural laws concerning this stress tensor , you are free to invent your own closures as you like – noise hypothesis , stochastic hypothesis , turbulent viscosity , reynolds diffusivity … not one of them physical .
Of course depending on your creativity you’ll get in some cases a more or less good fit even if what fits here , wouldn’t fit there .
Is that a solution of NS ?
Clearly not but you can get a “model” that will work for a specific case and as long as you strictly stay in the specified conditions which the closure was fitted for and don’t pretend that you have a solution of NS , you are OK .
At this occasion I’d like to also get rid once for all of this too often used argument regarding the aeronautical engineering .
People say what’s the problem with NS when the planes can fly .
Well if we should resolve the NS up to the Kolmogorov scale for a flow around a wing , we’d need some 10^18 nodes .
That is clearly far above anything we can do and wil be able to do in any foreseeable future .
Yet the planes fly . Why ?
Because the flow model people are interested in is in a steady state for all practical purposes .
Almost everything is supposed constant (in terms of chaos theory the phase space has a ridiculously small number of dimensions) and spatially we are looking at an extremely restricted region .
Should we use the same model to compute the velocity field some 500 m behind the plane , it would be hopelessly wrong and with little relationship whatsoever to the real velocity field .
That’s why being able to make planes fly says nothing about our ability to solve NS in the general case (be it DNS , RANS , LES etc) .
For Jerry :
Because you mentioned it somewhere so here is the answer .
Yes the Earth’s orbit is chaotic as well as all the orbits in the general Nbody gravitationnal system .
And it is even not out of topic because the Lyapounov time which measures the exponential divergence of orbits initially
beginning at the same point is in the ordre of magnitude of 5 – 20 millions years which is well within the time scales on which
the climate is contemplated 🙂
However that doesn’t mean that the orbits will do anything very strange anytime soon – it only means that the orbits are not
computable over more than some 100 millions years .
In other words if you go back 100 millions of years or more , you have no idea what the Earth’s orbit was and will never have one .
Why didn’t the Earth already leave the Solar System in those 4.5 billions years ?
Well pure luck – it is probable that at the birth of the solar system there were many more bodies than today but the most gravitationnaly unstable have already been eliminated by collision or ejection .
I probably was the only one to use the term RANS. I know it sure wasn’t Gunnar! 🙂
I doubt I said “RANS is meaningful” (although.. who knows? These are blog comments.)
I know that whatever I said, it was in the framework of the conversation here. One of the issues is:
Is eddy viscosity just some absolutely totally unphysical patch stuffed in to damp the illposedness issue?
The answer is: not necessarily. Eddy viscosity has some physical basis in the analytical framework that supports RANS. Reynolds stresses don’t vanish with small grid size, so eddy viscosity doesn’t vanish as the grid cell size vanishes. Eddy viscosity, for all its many deficiencies isn’t just an unphysical patched stuffed in to prevent the illposedness issue Jerry describes. It’s stuffed in to describe something real within the Reynolds decomposition. If you don’t stuff in something to capture the action of the Reynolds stresses, your model will definitely be “unphysical”.
Everything else you say about the closure problem is true. Whatever eddy viscosity is we know both analytically and empirically that
a) it’s not a constant.
b) it’s hellaciously difficult to figure out it’s magnitude (and everyone tunes for different flows) and
c) as you try to ‘improve’ RANS solving directly for higher order moments, you realize eddy viscosity isn’t even a scalar!
d)Problems ensue and
e) You decide to that LES sounds like a wonderful idea.
But, with regard to the problem Jerry is discussing in this thread, the eddy viscosity isn’t entirely unphysical, and, in the framework of RANS, eddy viscoisty doesn’t vanish as the grid size gets small. It’s magnitude is unaffected by grid size. (The problem then is: eddy viscosity is crap and if you use it, you can’t even begin to pretend you aren’t tuning. Everyone knows you are tuning a lot,.)
In contrast, for LES, what ever eddy viscosity is, “eddy viscosity” must vanish as the grid size gets small. So, in principle, you can claim you won’t tune, or the tuning problem will vanish as the grid size gets small enough.
So, we are left with: RANS has the same problems it always had. They aren’t aggravated by Jerry’s illposedness issue.
LES is proposed as the solution to RANS problems– but it would be destroyed by Jerry’s issue.
So…. ?
PS: I agree about the airplanes. I don’t know why nonengineers, or students who did summer projects think solving flow around airplanes is more difficult that other engineering flows. Yep– predicting the wake behavior is much more difficult that determining lift on an airplane. Undergraduates taking their first aero course can code a simple panel method in excel to calculate lift on an airfoil at small angle of attack. (We’re prefer they wrote a real program, but it can be done in excel.) That’s more or less from first principles.
Suggest undergraduates determine pressure drop in a straight pipe from first principles and engineers will explode with laughter! From a computational point of view, getting a decent answer for the pressure drop in a straight pipe without tuning a model is harder than getting lift on an airfoil!
>> I know it sure wasnt Gunnar!
Interesting that you feel compelled to say this.
>> From a computational point of view, getting a decent answer for the pressure drop in a straight pipe without tuning a model is harder than getting lift on an airfoil!
See, we agree after all. Two different purposes, two different methodologies.
@gunnar– I mentioned you in my response to Tom Vonk because you were one of the people he named. In contrast, while he seems to be responding to something I wrote, he failed to mention me. 🙂
>>Two different purposes, two different methodologies.
Ehrmmm… I don’t have any clue how that relates to what I said to Tom, but if you think we agree, I guess that will have to do.
Eddy (or turbulent) viscosity is for me only one rather subordinate point in RANS .
Already on the fundamental level , if I use an operator to transform a physical law and the result of applying this operator is that I finish by getting an additional tensor full of unknowns that don’t represent any relevant physical quantity and therefore don’t appear in any additional equations then I know that I did something stupid .
In that sense the Reynolds stress tensor is unphysical – it is a monstrous child of a misguided operator .
I can understand why it was done historically at a time when people still wanted to find randomness at the core of the turbulence , but it is strange that it appears even today in fluid mechanics textbooks without the appropriate caveats .
Since the beginning of this thread I have considered the Jerry’s issue as being a subset of a larger issue that is connected to the computability of NS solutions .
LES is interesting insofar that it compels people to really look at the whole scale spectrum because a subgrid closure is necessary .
And by doing that they necessarily encounter self similarity which leads to fractal closures (see f.ex Scottti , Menevau and Hylin & al) .
That’s why the deterministic chaos theory that is best suited to deal with computability and convergence problems is
always strongly correlated to any discussion about computability of NS solutions but of course covers a field of dynamical systems that is vastly larger than only fluid mechanics .
@Tom Vonk–
If your argument is that RANS is often crappy: Yep! It’s often crappy and has major problems in many types of flows.
But I think the great “Just how crappy his RANS” debate is somewhat off topic with regard to this thread. The questions I’m wondering about is:
Do GCM’s claim to use RANS? Or Do GCM’s claim to use LES?
If GCM’s use RANS, then stuffing in a turbulent viscosity isn’t a total fiction picked out of nowhere. It’s got some basis, and the magnitude should be grid independent and not vanish as the grid size gets smaller.
If GCM’s use LES, stuffing in a grid independent turbulent viscosity smacks of total fiction used to patch up the illposedness that Jerry says exists in the continuum equations.
But, even though I’m discussing turbulence models, I should stress that the illposedness of the equations has nothing to do with turbulence. But where illposedness exists, it can, oddly enough, cause a bigger problem for the better turbulence model, LES because LES captures large scale behavior and medium scale behavior. The illposedness exists at what would be called the large scales.
RANS smears everything except the mean and so, can in some circumstances, hide out the illposedness.
From a purest point of view, the best way to solve this issue is to DNS the planet. But we know we can’t do that. If Jerry is correct about the illposeness (and I suspect he is ) next best approach is probably to drop the hydrostatic assumption and use an LES based code to model the planet.
This is computationally intensive, and evidently, hasn’t been done.
Carnac predicts the hydrostatic assumption will be dropped soon. After all, Jerry says the GISS models seem to be showing symptoms of the illposedness as the grid size drops. Solutions are blowing up; that’s the one thing that always convinces all numericists they have a problem.
Carnac predicts dropping the hydrostatic assumption will result in many journal articles but have little effect on the estimate of climate sensitivity to CO2.
Tom (#70),
I agree with everything you say in the first part about any artificial closure scheme.
In the second part, I stated that chaos is off topic on this thread.
Do you have any mathematical proof that any of the motions you mentioned are chaotic? If not, then these are not quantitative statements, just assumptions.
Jerry
Jerry
lucia (#71),
I did not state that eddy viscosity was stuffed in to hide the ill posedness of the hydrostatic system. I did state that with sufficient unphysically large dissipation, many flaws (continuum or numerical)
can be masked. And unphysically large dissipation, e.g. eddy viscosity,
is always added to numerical models that cannot resolve the real scales of motion that appear in a continuum solution with the real Reynold’s number because otherwise the model would blow up. Thus the model is not physical,
but patched to allow computation. In the latter case, the accuracy of the computation is in question.
Also please distinquish between the hydrostatic continuum system (ill posed, unbounded exponential growth in a finite time interval) and the nonhydrostatic continuum system (well posed, bounded fast exponential
growth in a finite time interval) when discussing my statements. Thank you.
Jerry
How is the closure problem of RANS (ontopic) related to GCM tuning & performance (offtopic)? References on the former, comments in unthreaded on the latter, would be welcome.
Q: “hydrostatic” and “nonhydrostatic” are distinct classes of equations/behaviors thought (or intended) to apply to oceans and atmospheres, respectively?
RE 71. My father in law would love you. Pressure drop in a pipe.
http://www.komax.com/
airfoils are easy.
The atmosphere is hydrostatic. Otherwise it wouldn’t be held to the earth. Over short elevation changes, you might be able to ignore it, but over significant vertical distances, it’s very significant. And in the atmosphere, it not only affects pressure, it also affects density. You can’t ignore it in general.
80, airfoils are easy because you can make the assumption of no permanent pressure drop. It’s wrong, but close enough, and makes life a lot simpler. Can’t do that in a pipe. Friction becomes the governing thingy.
@Jerry
What magnitude of eddy viscosity are people putting in the models?
If GCM’s are based on RANS,you can’t neglect Reynolds stresses without creating at truly unphysical model. That’s the way RANS (crappy or not) is constituted. One may certainly complain about the shortcomings of using a turbulent (eddy) viscosity to close the model– everyone does. On can hate RANS — many do.
But people I know would rarely call either eddy viscosity itself or RANS unphysical. That’s a very strong term, and if simply used to mean “an approximation that often fails a lot”, we’re going to start calling an awful lot of things “unphysical”.
That said, if the correct value of eddy diffusivity based on a turbulent length and velocity scale (nu ~ u^2/l) was estimated to be 103 m^2/s, and a code were using 101 m^2/s, or if you used a negative value of eddy viscosity, accusations of unphysical would abound.
So, I now have to ask, how large is the large is the value of eddy viscosity used in GCM’s? Can you compared the magnitude to what one might estimate based on say, an eddy diffusivity based on say a reasonable characteristic length scale “L” and a reasonable characterisitc velocity “V”? (Not a rhetorical question for effect. I don’t know what the characteristic velocity or length might be for your problem.)
On the mentioning “illposed & etc. I agree that your illposed issue exists only when the hydrostatic assumption is used, and Coriolis forces matter. Sorry if anything I the way I worded comment 75 failed to repeat those ideas. I believe if you scroll back you will see that I have noted the importance of those two features to your analysis in earlier comments.
@Bender:
>>How is the closure problem of RANS (ontopic) related to GCM tuning & performance (offtopic)? References on the former, comments in unthreaded on the latter, would be welcome.
Historically, computational models based on Reynolds decompositions contain “constants” that are tuned, or tweak, or what have you. So, RANS has at least something to do with accusations of tuning. (The problem is: the tweaking isn’t limited to the NS. It’s also in the heat equations, in cloud models etc..)
I could explain more about RANS if you like.. but I don’t think it’s specifically germain to Gerry’s thread. (Except in so far as we are having a difference of opinion of whether or not eddy viscosity is “unphysical”. )
>>Q: hydrostatic and nonhydrostatic are distinct classes of equations/behaviors thought (or intended) to apply to oceans and atmospheres, respectively?
For most practical engineering applications, the pressure, p, in of motionless water varies hydrostatically. So, the change in pressure with depth only varies as a function of the weight of water above it.
dp/dz = ro G. where z points “up”, ro is density and G is a positive value. (So, P decreases as you go “up”.)
This statement says: “the sum of the forces are zero” when bodies do not accelerate. So, as you can see, that equation describes conservation of momentum in motionless water. (If water were truly motionless, you’d get dp/dy=0 and dp/dx=0. Pressure doesn’t vary orthogonally to gravity.)
However, just as we get F=ma for billiard balls, we get more complicated transport equation when fluid flows. We get inertia terms (the accelerations.) We also get some viscous terms that can be explained several ways.
You can see these equations various places. The full set are the Navier Stokes Equations.
When we do certain fluid problems, we might say we use the hydrostatic assumption. By this we mean we will use
dp/dz = ro G. to describe conservation of momentum in the vertical direction.
Since it’s a flow problem, we include the acceleration and viscous terms in the other directions.
We don’t always use that approximation. For example, if solving for lift on an airfoil, we would never use it. We keep all the inertial terms, set gravity to zero and then, depending on the specific problem either keep the viscous terms or drop them out. In that flow, pressure certainly does not vary hydrostatically.
And despite the word “hydro” in there, we we don’t use the hydrostatic assumption when solving for flow of water around an airfoil. If we don’t make the hydrostatic assumption, pressure does not vary hydrostatically. The decision is based on the relative magnitude of terms in the full NS equation and what goes wrong if you use the hydrostatic assumption.
Bender,
I thought I understood the use of the term hydrostatic in this thread, but Larrys comment in #81 has me confused. So I am going to purposely expose my ignorance by replying to your #79 in order to get it fixed.
I believe hydrostatic refers to an approximation made to the equations of fluid dynamics wherein it is assumed that the vertical component of fluid motion is completely dominated by the gravity term. That is, the rate of change in fluid pressure is determined solely by gravity (and other accelerations are negligible). This has the effect that pressure depends only on vertical position in an equilibrium solution to the equations. I dont know how the modelers handle vertical mixing in this case (since the hydrostatic approximation would seem to change the types of vertical fluid motion the equations would predict), but perhaps they parameterize it? Perhaps they ignore it? Perhaps the differences arent important?
There is no reason that the hydrostatic approximation should apply solely to atmospheres, or oceans. You can make the same approximation in either case.
No offense intended to the obvious experts here. All flames graciously appreciated
@steve mosher. Ok.. we’re totally OT now. Is your father in law ‘Komax?’ Or does he just like static mixers?
@Neil– no flames for either you or Larry.
I’m trying to think of an easy example that many people would have read. Are you familiar with Bermouilli’s equation in it’s full form?
1/2 ro U^2 + P + ro G H = Po where Po is the total pressure and ro is the density of air. (Applies under blah, blah blah conditions?)
Suppose you are dealing an engineering problem where air is flowing at a rate of 100 m/s around an airfoil with a chord that is 0.1 m. You plan to measure the pressure at locations around the airfoil surface. Does gravity matter much compared to velosity changes.
Well… Velocity is going to vary from 0 to 100 m/s. (Zero is achieved when air stagnates on the front of the airfoil) So, that will make a difference of DP1 = 1/2 * ro * 100m/s.* 100m/s.
In contrast, the difference in height across the airfoil is 0.1 m. So, that will make a difference of DP2= ro* 9.8 m/s * 0.1m
If we take the ratio, we can cancel the density of air and get DP1/DP2~ 1/2 U^2/gH ~ 5000.
The changes in velocity affect the pressure 5000 times as much as the change in height. What matters is U^2/gH.
There end up being other more sophisticated reasons we can remove gravity from the airfoil analysis. But you can see that in general,
if H is small or U is large, we often can neglect gravity.
If U is small and H is large we can say pressure is affected by gravity only. That’s the hydrostatic assumption– static because U is small.
So, Larry focused on the magintude of “H”– elevation change You focused on “zero acceleration”. What matters is the Froude number U^2/gH — also sometimes called Richardson number.
I went into ecology to avoid engineering. Thanks guys.
Lucia, and these dimensionless “numbers” are all actually ratios; usually ratios of forces in fluid mechanics. So your Froude number would be the ratio of inertial to gravitational forces, just like the Reynolds number is the ratio of inertial to viscous. It’s easier to understand their significance if you look at them that way.
Then the hydrostatic assumption comes down to a fight between inertia and gravity.
@Larry– Yep. The Froude number is a dimensionless parameter. But I’m figuring bender might feel more comfortable if I just call it a “ratio” and let him notice it has no dimensions. 🙂
@Bender– What? You don’t want to read about engineering? But you asked about RANS! 🙂
So tell me, do you prefer “ratio” or “dimensionless parameter”?
No. I DO want to read about engineering. I’m just making sure y’all know what level I’m operating at!
Lucia,
Thanks for the explanation. Now I (think I) understand what Larry was saying.
So does using the “Hydrostatic Equations” refer to dropping the momentum/inertia/kinetic energy term in the vertical dimension entirely, or does it refer to something like assuming it is small and using it as a perturbation?
Do the “NonHydrostatic Equations” add back viscous forces, too?
Jerry tells us the hydrostatic equations are illposed, and he has showed us the graphs to prove it in a certain case involving a jet causing vertical shear. I can imagine that the simplifying hydrostatic assumption leads to unphysical results when significant things are happening in the vertical dimension, and I take Jerry’s word for it that unbounded exponential growth occurs in such models. I don’t have a feel for why the nonhydrostatic equations handle the jet better, though. Is there any intuition or analysis you could share?
I take that as a Nussult on engineering numbers. I think he must think they’re a Froude. I’ll just Mach him…
Meteorological Tutorial: Hydrostatic versus Nonhydrostatic Systems.
All of the scale analyses that I will discuss here is present in a number of our manuscripts (references cited before but I will be happy to cite them again if anyone wants the details), but here I will provide a brief discussion to clarify the terms.
One can think of the unmodified, inviscid NavierStokes equations
as the starting system for the discussion. The equations in the system include the conservation of mass (density rho), the conservation of momentum (3 velocity components u,v,w) that include the gravitational and Coriolis forces, and a pressure (p) equation. This system provides five equations for the 5 unknowns rho, u, v, w, and p. The ideal gas law provides a connection between the pressure, density, and temperature. The density and pressure equations can be combined to eliminate the 3D divergence and form an entropy (potential temperature) equation that is a
3D advection (convection) equation.
Now if scales for the independent variables (x,y,z,t) and corresponding
scales for the dependent variables (rho, u, v, w, and p) are chosen
that correspond to the largest motions in the atmosphere (more about the other scales in comment that follows), then dimensionless parameters (ratios of scaling coefficients) appear in
the transformed (dimensionless or scaled) system. Such a scaled system was first derived by Charney. In the scaled system the vertical acceleration
(dw/dt) is 6 orders of magnitude smaller than the vertical pressure gradient and gravitational terms. Thus Charney neglected the vertical acceleration term and the resulting system is called the hydrostatic system. Then various forcing terms (parameterizations
of dubious accuracy) and ad hoc dissipative terms of various types were added to the basic system. This system has been the standard one used in all global weather and climate models and many limited area models until very recently.
Unfortunately, just because a term is small in a scaled system does not necessarily mean that it can be neglected without mathematical consequences. (Similar mistakes have been made in the oceanographic and plasma equations).
The system above without the hydrostatic approximation is called the
nonhydrostatic system.
I will discuss other atmospheric scales in thecomment to follow.
Jerry
Before I discuss the other scales of motion for the atmosphere, I will allow some time to elapse so that the above tutorial can be read by everyone interested in this topic. Then I will answer any questions related to that tutorial before proceeding to the next step. Hope the tutorial
and discussions to follow are helpful.
Jerry
@Neil:
>>So does using the Hydrostatic Equations refer to dropping the momentum/inertia/kinetic energy term in the vertical dimension entirely,
No. It means using an approximate relation for conservation of momentum in the vertical dimension. There can still be motion in the vertical direction. For example, the classic problem of “long gravity waves” involves up and down motion of the surface of a liquid (like water). However, the momentum equation uses the hydrostatic assumption.
If you see examples of these solutions, you’ll see the final wave equation describes vertical displacement of a surface. But the first derivative of displacement is velocity, so there is vertical velocity . So, as you see it’s not neglected. (Note: even with the hydrostatic assumption, you still retain that momentum equation. So, u,v,w, p unknowns. Three momentum equations plus conservation of mass. One momentum equation is approximated — but you are good to go there. )
As to perturbations– there are no doubt problems where the hydrostatic equations are used to get a solution to leading order. Then, there could be some small parameter that you use to get the next set of equations. But, that’s not inherent in the hydrostatic assumption. The leading order is hydrostatic– the next set of equation in the perturbation is something else.
>> Do the NonHydrostatic Equations add back viscous forces, too?
Not necessarily. Account for anything other than gravity in the momentum equation and it’s nonhydrostatic. You could add inertia only, or viscous diffusion only or both, the “z” momentum equation is no longer hydrostatic.
On intuition… I never have intuition about illposedness. But, if a set of equations involving approximations are illposed, something needs to be fixed. If the issue only happens when the hydrostatic approximation is used, one way to fix that is don’t make the hydrostatic approximation.
That approximation is made to obtain a set of equations that is less computationally intensive to solve, so you can see the difficulties for those running GCMs which already suck up a lot of computer resources.
Fascinating. Keep it coming. Once a day, once a week, whatever works for you. Popcorn time.
RE: 93
Do you have a reference for the derivation?
Thanks.
Lucia, thankyou for your patient explanations.
Jerry, thankyou for the summary tutorial.
I will gnaw the bone and (horrors!) crack a book or two.
Jerry
Because you asked , then turbulence is chaotic and I provided already several arguments on this thread .
As I know that you like mathematical proofs (I do too) , perhaps the most famous is the Ruelle , Takens paper
“On the nature of turbulence” (http://projecteuclid.org/Dienst/Repository/1.0/Disseminate/euclid.cmp/1103857186/body/pdf) .
Of course this proof has been elaborated end developped since this time but the Ruelle&Takens paper is as mathematical as mathematical proofs can go and is considered as one of the foundations of the study of turbulence .
Btw it is sensibly the same kind of proof that demonstrates that the orbits of the 3 body problem are chaotic .
That’s why it is today impossible to discuss turbulence or existence of 3D NS solutions without discussing computability and deterministic chaos .
As for the ergodicity of the NS solutions , the jury is still out – personnaly I’d incline more to the side of non ergodicity .
I don’t know if it was here or somewhere else that somebody (not Jerry) mentioned the 2D and 3D NS .
Completely different beasts .
Almost nothing can be inferred from the 2D case that would be useful for the 3D case .
Existence of smooth solutions is proven for the 2D case while it is not the case for the 3D and it is not tomorrow that some breakthrough will take place .
The energy and enstropy cascades work completely differently for the 2D and 3D cases .
For obvious reasons the eddy is orthogonal to the the velocity gradient in the 2D case while it is not so in the 3D case .
The only thing that the 2D has in common with 3D is that both are chaotic .
Caveat for those who would still confuse chaotic with random :
Chaotic systems impact basically only the computability , they are anything but random .
For instance quantities like energy are computable and boundaries can be rather easily obtained by using f.ex Fourier transforms – in that sense the system doesn’t do anything and everything .
Unfortunately boundaries on energy (v squared) or vorticity (in the 2D case) are not enough to infer boundaries on the system’s orbit in the phase space and that’s the reason why this exact orbit is not computable for a time exceeding a limit T depending on the system .
David Elmer (#97),
The reference is
Browning G., and H.O Kreiss, 1986:
Scaling and Computation of Smooth Atmospheric Motions.
Tellus 38A
295313
Tom (#99),
Did you ever read the Henshaw, Kreiss, and Reyna manuscripts on the minimal scale estimates for the incompressible NS equations like I asked you to do?
Jerry
Watch meteo models versus actuals for the West Coast over the next 72 hours. Watch also the changes in model runs during that time. Key CWAs to observe: Oxnard, Hanford, Monterey, Sacramento, Eureka, Reno. Even at the moment, forecasters are frustrated, things are not resolving. He he he!
Mathematical Tutorial for Hyperbolic Systems
One of the first questions that someone might ask after the above tutorial
on the hydrostatic and nonhydrostatic systems is what went wrong with what seems like an extremely accurate approximation (the neglect of the vertical acceleration term, i.e. the hydrostatic assumption)
that was based on a comprehensive scaling analysis of large scale atmospheric flows?
This is the question that started Heinz and me down the path of determing what went wrong and how to determine if there was an alternate accurate and well posed continuum system that could be used instead.
The nonhydrostatic system as described above is a quasilinear hyperbolic system and the mathematical theory for these systems is well developed. When neglecting the vertical acceleration term, the hydrostatic system is no longer a hyperbolic system and is ill posed for both the initial, boundary value problem (IBVP) and the initial value problem (IVP).
The discovery of the first problem was by Browning, Oliger, and Kreiss at NCAR over three decades ago (later published in a manuscript by Oliger and Sundstrom). This problem arose in a practical attempt by Klemp (MMM)
to develop a limited area model based on the hydrostatic system. The second problem was discussed in the manuscript by Browning and Kreiss cited earlier and the consequences demonstrated in (non)convergence tests
of the hydrostatic system in the earlier version of this thread.
A new hyperbolic system of equations was introduced by Browning and Kreiss
that could be proved mathematically to accurately describe all scales of motion in the atmosphere. Because the new system is hyperbolic, it is well posed for both the IBVP (with appropriate lateral boundary conditions)
and the IVP. This system will converge to the correct solution of the unmodified nonhydrostatic system as the mesh is refined.
References are available that show the distinct differences between the IBVP for the hydrostatic system with unphysical dissipation (Tribbia et al.) and the multiscale system with no dissipation (Browning and Kreiss).
It has also been shown that when a standard accurate and stable semiimplicit scheme is applied to the mesoscale problem for the nonhydrostatic system, the same solution as for the multiscale system introduced by Browning and Kreiss is produced.
As I have stated earlier, when unphysical heating terms are added to a hydrostatic model, the model must maintain hydrostatic balance by artificially redistributing the heating in a manner to prevent overturning.
This is not a physical process, nor a scientific one.
Jerry
Jerry:
Sure. Generally speaking, if you add one unphysical thing “A” to any model and that thing matters at all, the addition will often cause the model to predict clearly unphysical behavior. You can sometimes ‘fix’ that particular problem by doing something else that has no sound physical basis. The result is dubious.
But…. maybe I jumped into the thread too late. Where do you discuss adding heating terms (be they physical or unphysical)? I’ll take a wild guess and assume the artificial redistribution of heating arises by including eddy diffusivity to close terms in a heat equation. Is that a reasonable guess?
Anyway: what are the artificial heating terms? And the artificial redistribution is done how?
RE 85. He was the man. Sold it off a couple years back. We are OT
Lucia (#104),
Heating terms were added to the hydrostatic system after the derivation (as were the unphysically large dissipative terms), e.g. they appear in the potential temperature (entropy) equation. Because of the crudeness of the mesh in large scale models, things like convective heating are parameterized over an entire grid box and the amount of heating determined by an arbitrary fraction of that box. As that heating is artificial,
so is the impact on the hydrostatic system. Also note that in Sylvie’s manuscript, the most important parameterization in the first 36 hours was that of the lower boundary layer. That led to O(1) errors within 36 hours. Not very physical. As I have said before, the forcings can be tuned to produce any solution one wants. That does not mean they are physically realistic.
One other point. If a climate model’s lid is at infinity, then the hydrostatic system is not appropriate at high altitudes (the plasma equations are more appropriate in the ionosphere). And if they have an artificial lid at lower altitudes, then they must correctly determine the inflow variables at that altitude which they certainly do not. In fact, usually at the upper levels they use a sponge layer to absorb the outgoing gravity waves . A sponge layer is exactly how it sounds, increased dissipation near the upper lid – a gimmick to prevent reflection of gravity waves.
Jerry
Lucia (#104),
There was an extensive discussion about tuning parameterizations with Jimy Dudhia from NCAR on the previous version of this thread. One only peruse the documentation for the NCAR climate model or WRF model to see just how many different parameterization versions there are for the same physical process and how many games have been played at lateral and vertical boundaries.
Jerry
Tom (#99),
I find it amusing that you say nothing is known about the NS equations and then you turn around and claim they are chaotic. Dynamical systems usually refer to systems of ODE’s and PDE’s are a very different animal.
Can you have an ill posed system of ODE’s? That requires unbounded growth
in any small finite time interval and as far as I know requires an infinite set of wave numbers for that to happen, i.e. it is not a finite number of ODE’s that will lead to this behavior.
Tom (#99),
The reference you cited is over 30 years old. I think we have come a long way since then. The HKR minimal scale estimates are for the full nonlinear incompressible NS equations. No approximations made.
Jerry
lucia, re #107: see comments #104#130 on exponential growth #2
@Jerry–
I’m having a little difficulty knowing precisely what is being argued over, and I need specific details.
1) The chapter of the book you referenced in 100 is money walled. Is there someplace we can get it quickly for free? That will help us all know precisely which system and which equations you consider those of Charney, and called “the hydrostatic system”. I certainly know what the hydrostatic assumption is, but if this term is being used as a very, very specific system, I’d like to read that set of equations.
If there is no easily available reference, can you just type them into whatever you use when you write manuscripts, save it as a pdf and make the pdf available for downloading? Or scrawl then on a sheet of paper, take a scan it, save as pdf and I’ll squint at them?
2) Do you have a specific reference that shows the specific heating terms and dissipiaton terms so I can know precisely what sorts of terms are bothering you in the AGCMs?
Once again, writing the terms down would be great!
3) What is “Silvie’s manuscript”, and where is it available?
4) Is this the browning and kreiss paper? Is a nonmoney walled version available at your work web site? Or Kreiss’s?
lucia, this harkens back to post ~#60 in #2.
The relative contributions of data sources and forcing components to the largescale forecast accuracy of an operational model
Lucia (#111),
1) The reference in 100 is a standard library journal and can be copied
for free by anyone with access to a university or scientific library.
I can also make a copy of a reprint and if Steve M. is willing, post it on his web site just as I did with Sylvie’s draft manuscript. You might also
want to look at the manuscript on microphysics by Lu et al. cited on the previous thread and freely available. Some journals also will alow a single copy for a small fee.
2) Read the documentation for the NCAR hydrostatic climate model or the nonhydrostatic WRF model that is freely available on the NCAR CGM and WRF web sites.
3) As Bender has stated, Sylvie’s manuscript is available on this site on the previous thread.
4) No. This manuscript was published as part of a proceedings and is only available in that book. A newer version of the manuscript was in
preparation when I retired out of disgust with the modelers who rejected valid mathematical manuscripts based on nonsensical political reviews. That is the reason I started to comment on Steve M’s site where the truth could not be buried.
Jerry
Lucia (#111),
1) The reference in 100 is a standard library journal and can be copied
for free by anyone with access to a university or scientific library.
I can also make a copy of a reprint and if Steve M. is willing, post it on his web site just as I did with Sylvie’s draft manuscript. You might also
want to look at the manuscript on microphysics by Lu et al. cited on the previous thread and freely available. Some journals also will alow a single copy for a small fee.
2) Read the documentation for the NCAR hydrostatic climate model or the nonhydrostatic WRF model that is freely available on the NCAR CGM and WRF web sites.
3) As Bender has stated, Sylvie’s manuscript is available on this site on the previous thread.
4) No. This manuscript was published as part of a proceedings and is only available in that book. A newer version of the manuscript was in
preparation when I retired out of disgust with the modelers who rejected valid mathematical manuscripts based on nonsensical political reviews. That is the reason I started to comment on Steve M’s site where the truth could not be buried.
Jerry
lucia (#111),
Can you imagine trying to publish the result that the hydrostatic system is ill posed for the IVP and will not converge (all current global climate and weather prediction models) and that the nonhydrostatic system has fast exponential growth so is sensitive to any small error given all of the gas we took on our previous rigorous mathematical manuscripts? Heinz stated early on that it takes ~ 10 years for things to change. I retired in 2002 and we are at the 5 year period now and the atmospheric “scientists” still don’t get it. I prefer not to wait around for them to catch up. 🙂
Jerry
Jerry
I can’t remember having said somewhere that “nothing was known about NS” and I certainly don’t think that .
However what I did say was that existence and smoothness of 3D NS equations was not established what is a quite another issue .
You asked for a mathematical proof that turbulence was chaotic and I provided it even if it is not me who claims that but Ruelle&Takens .
It is indeed 30 years old and if it is still widely quoted today (and has of course been refined since the 1970ies) it is because it is still valid as mathematical proofs usually are unless an error is found .
Do you want much more recent ?
Try I.C. Li (f.ex http://arxiv.org/pdf/math/0507254) .
Not surprisingly reference is again given for … Ruelle&Takens 🙂
Yes I read not only the paper you referenced but several more Henshaw and Kreiss papers (3 of them) and commented on them already in thread #1 .
I won’t comment again on the 2D case because as I already said and as the HKR paper also says , both energy and enstropy are conserved what is not the case for 3D .
The paper aims to correlate the “minimal” eddy size to the kinematic viscosity and the global bound for velocity gradients .
That can be done exactly for the 2D case where the global bound is proven to exist thanks to enstropy conservation and can be estimated .
For 3D the paper shows that IF the global bound exists (the proof doesn’t exist yet) and the initial/boundary conditions are suitably regular THEN a relationship can also be computed .
Finally this minimum scale (3D case) is found to be consistent with the chaotic Kolmogorof scales and related to the decay rate of the energy spectrum .
While the HRK paper is indeed interesting by providing estimators for energy dissipation under certain conditions , it is completely irrelevant for the Ruelle&Takens paper .
Specifically HRK doesn’t claim anywhere having shown RT invalid nor is it relevant for the nature of the attractors in the considered flows .
I have difficulty to understand why you seem to avoid the chaos theory like if it was a dirty word or stood somehow in contradiction with the classical fluid dynamics .
Actually the chaos theory is a tool to study non linear dynamical systems of which fluid dynamics (and NS) is a particular case .
That’s why I agreed with everything you said and it can be easily expressed also in the frame of chaos theory while I agreed with nothing that J.Dudia said and that was wrong in any frame be it chaos theory or otherwise .
However if what you want to say is that the chaos theory is not necessary to prove that the hydrostatic assumption has deadly flaws for for climate/weather modelling then I agree too .
Tom Vonk–
I’m not quite sure what point you are trying to make with that Li paper. As far as I can tell Li pretty much :
* says ‘people’ have been trying to use the concept of chaos to understand turbulence and cites reference 17– the R&T paper. (I think we would all agree that R&T were trying to link turbulence and chaos.)
* shows that several pdes that are not the NS are chaotic.
* shows that one pde that describes Faraday water waves is chaotic. (This is a flow. I don’t think anyone would call it “turbulent”.)
* tells us there is no mathematical proof that turbulence is not chaotic.
*says any flow that is not laminar is turbulent.
* says that spot turblence is not chaotic. (So, evidently, at least some nonlaminar flows are not chaotic!)
* muses and predicts that someone, someday will prove turbulence is chaotic. He advises using Fourier Series.
* says some quaint things about the state of engineering including “Fluid engineers gradually gave up all these Reynolds type models and started directly computing the original Navier Stokes”. Fluid engineers gave up RANS? Past tense?! Hah!
So, it would appear:
Mathematicians are still trying to figure out if turbulence is chaotic. Turbulence has not been proven chaotic. Turbulence has not been proven not chaotic. Some mathematicians have odd notions about what engineers do and think.
This is an interesting chaos tangent, but I can’t say it tells me anything about Jerry’s issue or how it affects GCM’s!
@Jerry — My questions aren’t pointed.
I’m hoping for answers with links that send me directly to the resource (chapter, book, manuscript). There are now one bajillion comments spread over three threads. I sincerely can’t find the link to “Silvie’s manuscript”. Because these are blog comments, many references say things little more than R&T 19xx, and I often can’t figure out the precise title or journal to request from the library.
I was hoping that an article we are all discussing on this thread was more easily available to those trying to follow the conversation. I know I can get a chapter of a book from the library, but that’s slow for web conversations. When I can click and download, I can read immediately.
If your goal is to prevent the findings being buried, making it easy for curious people to read would be in your interest. Otherwise, they will while away their time going off on tangents reading the Dr. Li’s musings on chaos, which TomV linked. 🙂
Both: I agree with some things JimD said but also recognize the dangers of averaging, parameterizations or tuning. I also find many things things he said to vague to either agree with or dispute. It appears he vanished months or years ago.
That’s too bad– I’d like to ask him some specific questions so I understand more about the modeling framework and parameterizations in GCM’s. (I don’t want to do this by inferring modeling assumptions from lines of Fortran! )
lucia #112
Thanks bender, I’d done this:
Your search – Silvie’s manuscript – did not match any documents.
And read “Silvie’s manuscript“, on comment 62 of thread # II! and I’m dropping the link here to make it easier for future lurkers to find.
Which looks looks like a nice paper comparing how various closure models affect accuracy of weather forecasts. It seems to say the model for the boundary layer is important, and in particular, the model predicting diffusion of heat is important. For short range forecasting, the simpler model without counter gradient diffusion worked better.
But… I was able to identify a parameterization for heat flux… but nothing that was obviously unphysical. Argueable unphysical maybe, but obviously? No.
Telling me to read NCAR documents, find the modeling assumptions, and heating terms and guess which ones bug Jerry isn’t quite going to work for me! Scrawling an equation on a piece of paper, circling the bad approximation, scanning and putting the scanned page on line would.
Don’t like crossword puzzles, do you?
I would second Lucia’s request for ready links. I won’t be back to campus for a while, and Tellus is only online from 2002, the proceedings aren’t available, etc.
@larry — 120: Nope! I hate jigsaw puzzles even more.
Maybe we should speculate about whether the process of finding references cited on blogs is chaotic?
Lucia
Ruelle&Takens is not some musing or a “try” . It is a mathematical proof .
I don’t know of a paper proving an error in this proof . Do you ?
As for Li , look better , despite the (partly) strange remark about engineering , he knows what he is talking about and clearly knows the RT paper .
What Li may think or not think about engineers is irrelevant .
On a particular note I was not commenting on anything you posted , I was answering Jerry who asked for a proof relating turbulence to chaos .
That’s why it is not strange that it doesn’t answer your wonderings about hydrostatic approximations and GCMs .
As you seem to think that Li is also musing (so not only R&T) I assume that you are not familiar with the chaos theory and it’s importance to understanding of dynamical systems in general and fluid dynamics in particular .
Right ?
Tom (#116),
Enstrophy (integral of square of vertical component of vorticity) is not conserved in 2D. The dissipation rate of enstrophy is part of the theory and that dissipation rate is due to the dissipative terms of the NS equations. I think you did not read the manuscript very carefully.
If I recall correctly, the maximum theorem for 2D vorticity was used to bound the 2D vorticity, but that is a different result. And in 3D there is no known bound for the velocity, but if one assumes that is the case, then the estimates follow there too. Has anyone ever seen unbounded velocity components in 3D NS computations when the minimal scale is correctly resolved? If so, please provide a reference.
Jerry
RE 122. You hate jigsaw puzzles?
Dang. OT, Whenever I did Jigsaws by myself I always segregated the edge pieces and interior pieces
into two piles. And then of course one works logically from the outside to the in, finishing the border first
before assembling any inner pieces. Logical.
Then After finishing the border, you segregate interior pieces into Inies and outies. Does a piece have 4 outies:
3 outies, 2 outies, 1 outie. This improves your search for matching..
So, sort by edge, then sort by protrusions, then color match. Logical
My SO is an artist. She HATES my approach. She looks at Color matching FIRST and is constantly pulling
edge pieces from my edge pile because the have some silly color match.
Endless debates.
Lucia (#119),
I think you missed the point of Sylvie’s manuscript. It does not help to provide manuscripts or references if people do not read them carefully.
The main result in Sylvie’s manuscript was that she could shut down all
of the forcing terms (physical parameterizations) in the Canadian global hydrostatic model and the same quality forecast was obtained up to 36 hours. The most important (unphysical) parameterization was the lower boundary layer parameterization (not any of the water cycle terms). Because the velocities near the surface are smaller than in the jet stream, it takes awhile for that unphysical parameterization to destroy the accuracy of the forecast, but it will do so within 36 hours. This is a clear example of how tuning a model with artificial gimmicks can make things look better while in fact being completely unphysical. (You might want to look at the corresponding boundary layer parameterization in the NCAR climate model).
And the only reason that the global NWP model stays on track over time is that the observational winds (especially the jet level values) are updated every 612 hours (mathematical reference on updating cited). I mentioned on the previous thread that Sylvie also ran a case where only satellite
data was inserted with no radiosondes to provide information to help
the satellite retrieval problem and the result was a disaster. Are there radiosondes over the oceans, especially in the southern hemisphere?
I find these results quite pathetic given all of the hoopla about the accuracy of weather models, the need for more computing power,and the trial and error approach used by tuners. Note that the new theory was developed by 2 people using mathematics and a PC.
Jerry
Steve (#125),
If we keep things OT the thread would be much reduced and easier for people to find the essential comments. Lucia has made this point quite clear.
Jerry
@Tom V–
First, I didn’t say R&T were musing. I think Li muses at the top of page 5 of his paper.
R&T is a successful mathematical proof of something. It is cited when explaining transition to turbulence rather than real, honest to goodness turbulence. (It is cited in Landau and Lifshitz). Why their work is cited frequently in discussions of transition to turbulence and not those discussing full blown turbulence itself can be understood by reading the narrative in their section 4.
If you have an actual argument that explains why you think their paper proves what you say it does, make it. Gerry asked you to, but instead you wished to to “prove” their paper proves turbulence is chaotic by telling us that Li cites it.
Sure Li cites it. But Li absolutely, positively does NOT say R&L prove turbulence is chaotic in that particular peer reviewed paper. He says they tried.
After saying that he sets about trying to find a way to develop such a proof .
Now, let’s look at what the Li paper actually does.
The stuff before page 3 is entirely prefatory– but in this prefatory material, he tells us ‘people’ have been trying to use the concept of chaos to understand turbulence and cites reference 17. So, the ‘people’ who Li thinks were trying were Ruelle and Takens.
He then tells us that “low dimension chaos is the starting point of a long journey toward understanding turbulence.” He then seems to set off on the yellow brick road to the emerald city discussing several mathematical problems that are not the NS and which, in all cases, lack features contained the full NS.
He discusses the SineGordon equations. (Note: not full NS.)
He discusses the complex GinzburgLandau equation. (Not: not full NS.)
He mentions the modified KdV equation and says it should — in principle– share some features with the GinzburgLandau equation. However, he does nothing more with the KdV equations.
By the end of page 4 the LI begins musing — yes musing about similarities these various sets of equations share with NS. Even those who no no math can flip to the bottom of page 4 and see that once Li starts to actually discuss the NS, he stops doing any mathematical proofs. In fact, all math disappears.
His argument change to entirely nonmathematical statements that could be understood by even the truly math averse and include sentences like: “One should hope that turbulence should share some of the features of chaos in the perturbed sineGordon equation”… “In principle, ….” and “So, I think….” He even argues by simile involving marbles and diamonds.
While I respect verbal arguments, and the use of marble/diamond analogies, these are not mathematical proofs. They are musings.
Li’s paper is interesting paper, but it falls short of proving turbulence is chaotic. Moreover, he doesn’t claim to have proven that. Instead, he simply suggest that since NS shared features with these other equations one might expect the NS shared the feature of chaos.
@Jerry—
Yes. I skimmed Silvie’s paper. I did so because it contains a lot of information, which, by itself could be used to support a wide variety or arguments. I’m trying to figure out what argument you are trying to make.
I was skimming the paper when I saw benders link. But, I was not yet sure that was the paper.
FWIW, I caught the bit on the boundary layer parameterization being the most important.
I’ll ask you more later– probably monday. But, I already know that
a) it would help me if I had links to articles and
b) it would help if you would come right out and say which terms you believe are unphysical.
I can’t say whether I agree or disagree if I have to guess based on what I think is unphysical. I’d just guess any intelligent person would think what I think, decide you must agree with me, and then agree with you.
You do see the dilemma?
lucia (#128),
Your response to Tom was quite illuminating.
In discussions about Sylvie’s draft manuscript on the earlier version of this thread, I gave some background for the reason the study was initiated.
As you have aptly pointed out, there is much extraneous material
on this and every thread and it is difficult to sort thru to obtain the pertinent material. Unfortunately I cannot control that problem – it is part of an open forum and has both advantages and disadvantages as discussed earlier.
Also on the earlier thread I presented a very simple proof that when unphysically large dissipation is used, only by using unphysical forcing can the spectrum be made to look realistic. I would be happy to reproduce
that proof if you are unable to find it. It only involves about 3 lines of mathematics and there is also a simple one that shows that any solution one desires can be obtained when appropriate forcing terms are added to any well posed system.
I cannot provide links to articles that are in books or journals because of copyright infringement. Many libraries now have electronic journal access so even if you are not at work, you can access the articles from home. That is what I do.
I will be happy to answer any questions that you have.
I will also see if there is a way to access the Tellus article, but our more recent article on multiscale initialzation in JAS might be adequate
for your purposes.
Jerry
All,
As lucia seems not to comprehend the importance of Sylvie’s results,
I will provide a summary of their importance and the implications for climate models. (Hopefully this will be the last time.)
In Sylvie’s manuscript, the same forecast accuracy is obtained over the most data dense region in the world with or without any parameterizations
for a period up to 36 hours. The unphysical parameterization that had the most impact in that time period was the lower boundary parameterization and initially it only impacted the accuracy of the small velocities near the surface, but eventually also led to O(1) errors within 36 hours in the jet
where most of the kinetic energy resides (as did the full set of parameterizations). The lower boundary layer parameterization is an attempt to overcome the problem of resolving the turbulent boundary layer that properly should be modeled using the full 3D nonlinear
turbulent NS equations. The parameterization is clearly unphysical (lucia – this answers your question) and Sylvie’s results show that it could be replaced with an even simpler parameterization (gimmick) without any degradation in the forecast accuracy. It is important to note that Sylvie chose a consecutive number of winter forecast days to test the robustness of her results. That suite of forecasts is routinely used to test the global Canadian model for forecast accuracy.
Now the obvious question is what role do the parameterizations play
if they are not physical and do not help the accuracy of the forecast in the first 36 hours (and after that time the forecast errors are O(1)). The answer is not much. They are used to tune the results (force the model in an unphysical manner) and the impact of such unphysical forcing has been revealed by Sylvie’s results. It has also been proved mathematically
that one can always obtain any solution one wants by adding appropriate
forcing terms. Of course whether they are realistic is another story.
As stated in my earlier comment, it is not the parameterizations that keep the model on track, but the wind observations that are inserted every 612 hours. The new observational wind data overwhelms the large parameterization errors as expected from the mathematical theory (BK updating manuscript). Just how important the updating is to the forecast accuracy was revealed when Sylvie made a small change to the Canadian
data assimilation scheme based on the Bounded Derivative Theory (BDT) (BK multiscale manuscript). Suddenly the Canadian model outperformed the NOAA global weather prediction model by an unprecedented amount (not my words).
The plot I included at the end of Sylvie’s manuscript illustrates this result.
Before discussing the implications for climate models, I will respond to
an argument by Jimy Dudhia that things are different in the summer.
Yes, they are different, the results are worse. In the summertime, there are smaller scale storms. It has been proved mathematically
and illustrated numerically with convergent solutions (BK multiscale manuscript) that for smaller scales of motion, the vertical component of velocity is directly proportional to the total heating. This has also been shown in a more practical setting by Fillion, Page, and Zwack (MWR). Thus if there are any errors in the total heating or any errors in the initial vertical component of the vorticity, the corresponding storm will not be correct in intensity or location. And any error in the total heating will lead to incorrect long gravity waves that are not handled properly by
limited area models. It is convenient that there is little data to check the accuracy of the smaller scale forecasts. That is why Jimy Dudhia will not compute relative forecast errors (nor run the analytic test in the multiscale manuscript that would reveal all of these problems). In an earlier comment, I mentioned that NCAR was now considering a global version of the nonhydrostatic limited area WRF modls because there were a few problems with open boundaries.
Now climate models use the hydrostatic system and same (or cruder) boundary layer approximation as the Canadian global model. The corresponding parameterizations are included in documentation on the physics (not Fortran code) on the NCAR web site. I have asked and will ask again how can parameterizations that deviate from reality within 36 hours provide a realistic climate forecast.
The answer is that with unphysically large dissipation (required to prevent the computational solution from blowing up because it cannot properly resolve the minimal scale for the atmosphere or ocean), a realistic spectrum can only be achieved by using unphysical forcing.
Jerry
Jerry,
This explanation was clear in earlier threads. But thanks for spelling it out again for the benefit of lucia.
lucia,
In the future you may want to spend a bit more time reading the earlier comments. These three threads are really not that polluted with noise. Not like the other threads. Also, be aware that Jerry does not have a secretary, is retired, and does not have easy access to all the technologies which we take for granted.
[Definitely OT, but it sure would be nice if Steve M had a secretary to help him with data files and references and whatnot. As Jerry points out, you don’t want to breach copyright by posting papers for widespread distribution.]
Jerry–
I still need to get you to spit a few things right out because you are calling the closure unphysical, and I’m honestly trying to figure out precisely how you use this word. (I’ve know various people to use it differently, but I reserve it for things like: “Your model predicts raindrops fall ‘up’. Wouldn’t you agree that’s a bit unphysical?”. In contrast velocities off by an order of magnitude I would call really poor.
So, I’m simultaneously trying to calibrate for semantics, figure out what’s bothering you, and figure out what’s going on in these GCMs.
So, specifically:
1) I equation (2) in Silvie’s manuscript the “unphysical parameterization”?
I’ll pretty much go ahead and assume the answer to this is “yes” as I can’t see how the answer could be “no”. 🙂
2) Assuming the answer is yes, what do you consider unphysical about 2:
(a) The whole idea of Reynolds averaging which always results in our need to close. (This seems to bug Tom Vonk and those in the “Everything about RANS is cr*p camp.”)?
(b) You’re ok with Reynolds averaging in principle, but you dislike the counter gradient transport term in (2) regardless of magnitude. (For readers who are wondering why I am asking: This has the effect of causing heat to flow in the direction most people call backwards on average. Jerry and Silvie already know this. 🙂 Also: this term provides at least one tuning knob, called gamma subscript Y.)
(c) You’re ok with a and b but hate ordinary eddy diffusivity K term period, regardless of magnitude or how it is estimated? (Nontransport savvy readers might wish to know that As long as K is positive definite least makes heat flow from hot to cold. This is at least the correct direction, and the simplest type of closure may only provides one knob, K, depending on the type of closure.)
(d) Or are you willing to accept K or gamma in principle, but you magnitude of K climate modelers and weather forcasters’ use? (Example: Is the magnitude of K so clearly much, much larger than one might guess based by scaling u’l where u’ is some arguably rational characteristic velocity for the eddies and l is some arguably rational length scale for the eddies? Or suffers from some other flaw that would make you call it unphysical? Do they use a negative value for K? )
(e) Other? (EG. We can’t do this beause turbulence is really chaos? 🙂 )
I’ve read the threads. I know people who would hate equation (2) for any of these reasons; I know people who would accept (2). I’m trying to figure out which thing you dislike!
4. Is your main concern that results deviate from reality within 36 hours? (Though clearly, using unphysical closures, or even just bad ones, could cause this, I see this as a separate from the accusation of “unphysical”. By my definition of “unphysical” a term could be physical, yet totally inadequate and even flat out wrong. )
5. I’m also wondering what precisely you consider unphysical eddy viscosity the weather models use and also find out precisely what they use for eddy visosity. But I think we should defer this until I understand what you think is unphysical about parameterization (2) in Silvie’s paper.
bender– I’ve read the threads. My questions are not answered. I’m trying to ask them more precisely.
Jerry– Is this the NCAR document you think I should read
http://www.ccsm.ucar.edu/models/atmcam/docs/description/ ?
ok. just making sure. (you did miss the earlier link i provided.)
am learning lots from your questions. much appreciated.
lurk /on
Oh–on equation 2, in Silvie’s manuscript, I was saying ‘gamma’ would make heat go backwards based on the word she used “counter gradient diffusion”. However, if the transport quantity y is thought to be heat, it would appear to be a heat addition term.(I could guess at motiations, but I’d rather Jerry confirmed this is a term that bugs him.)
lucia (#133),
Yes, but I think you would find that the Tellus manuscript and the JAS Multiscale manuscript would be a better way to spend your time.
I do not like any ad hoc dissipation terms or parameterizations because of the dangers involved in any conclusions drawn from models involving such terms.
There is a reason that modelers do not run convergence tests, i.e.
the runs won’t converge.
Jerry
@Jerry–
In response to 136. Since exact modeling with no parameterizations is impossible, I respect the idea of trying to get estimates using parameterizations. But,
a)each parameterizations and any tuning constants must be justified and explained. (There are ways to do this.)
b) full model predictions must be viewed with caution.
c) full model predictions must be tested against empirical data. Flaws must not be waved away.
d) proven forecasting ability beats hindcasting any day.
e) modelers should admit that parameterizations can, and do introduce uncertainty, and this can matter.
If you are in the “no parameterization” camp and you appear to be, that’s fine. But, I’m not really going to get information to help me make up my mind about the strengths of weaknesses of GCM’s. Because I don’t consider the answer ‘never use parameterizations reasonable’. That said, I am often suspicious about parameterizations particularly when modelers dodge questions about them. I also know what tricks people can do to get models to look good. But, in that regard, I would wish to learn more details regarding what parameterizations are actually used.
I’ll get the chapter from the library. With luck it will provide the sort of information I seek. 🙂
Yet another abject failure of the NWS meteo model derived forecasts for multiple CWAs on the West Coast, over the past 72 hours. So what’s new.
lucia (#137),
Just because one can add unphysically large dissipative terms to a
continuum system of equations so that the numerical solution looks smooth and stays bounded without resolving the minimal scales of the real solution with the correct Reynold’s number does not mean the solution is accurate.
This is exactly one of the problems with soft “science” – too much computing and not much science.
I would hope that you would want the basic (homogeneous or unforced) differential system to be well posed and without fast exponential growth so that the system can be accurately approximated by numerical methods that are convergent before adding ad hoc parameterizations whether they be realistic or not.
That is not the case for the ill posed hydrostatic system of meteorology or the nonhydrostatic system of meteorology that has fast exponential growth.
Numerical solutions have been shown to converge for the 2D incompressible NS equations with very large Reynold’s numbers (small kinematic viscosities) and for the 3D incompressible NS equations for Reynold’s numbers that are currently computable. You might also want to peruse the manuscripts by Heinz and his students on these topics.
Jerry
Steve (#138),
There is very little observational data over the ocean off the coast of California. That is why the forecasts over California are less accurate than the ones over the east coast. This could be clearly seen when
Sylvie broke up the forecasts over the US into regions.
Jerry
140 Jerry
It’s petty easy to do forecasting if you know what’s happening 2500 miles to the west of your location. Even Ben Franklin, without instruments or models, was able to note that rain in Phillie on Tuesday was usually followed by rain in Bean Town on Wednesday.
lucia (#139),
So if a climate model (or a short term NWP model) fails to be realistic in 12 days (Williamson et al manuscript), doesn’t that mean that it does not satisfy one of your requirements?
Jerry
Pat (#141),
Exactly. And it is my belief that the visual images from satellites (not the “quantitative” retrieval data) are one of the main reasons for somewhat improved forecasting. Also the local Doppler radars are good at seeing moisture coming over shorter time periods.
Jerry
Yes, the satellite images show the fronts quite clearly, and the Doppler radar is great for shortterm local forecasting re precipitation.
BTW, I have the impression that the fronts tend to move in a direction normal to the frontal line — is that generally true?
Pat (#144),
We seem to be in complete agreement. 🙂
Your hypothesis seems reasonable, but I have not looked at that issue mathematically.
Jerry
RE: #140 Real world demonstrations of Syvlie’s thesis continue apace. The elephant in the room vis a vis both meteo models and GCMs.
lucia (#137),
>>This is exactly one of the problems with soft science – too much computing and not much science.
FWIW, my Ph.D involved doing real honest to goodness experiments. 🙂
On 142– Being in accurate in 12 days is a matter of great concern and I assume that is in regards to my question 4. And if that were all you were saying this discussion would not be taking this long. If all you are saying is the results diverge from reality for some unknown reason and you think that’s mysterious unsettling problem for GCMs that modelers must explain, then I agree with you. That’s an unsettling problem and modelers must agree.
But you seem to be bandying around explanations for the disagreement, and it’s your explanation I am finding opaque..
I’m trying to figure out precisely what you are describing as “artificial gimmics” or “unphysical parameterizations” in your comment #126. I’m not necessarily disagreeing they exist, but you won’t seem to come right out and say what things you believe to be artificial and why. (I have no doubt you think you are answering, but you aren’t.)
So, in that regard, back to 137:
>>Just because one can add unphysically large dissipative terms to a continuum system of equations so that the numerical solution looks smooth and stays bounded without resolving the minimal scales of the real solution with the correct Reynolds number does not mean the solution is accurate.
Sure. You’ve said this. I agreed long ago. I’d go further, adding unphysically large dissipative terms to a continuum equations would result in inaccurate solutions.
But you are begging the question, I’ve been asking: where are these unphysically large terms. (To be unphysically large, they must both large and unphysical. Mere existence is not enough.)
>>I would hope that you would want the basic (homogeneous or unforced) differential system to be well posed and without fast exponential growth so that the system can be accurately approximated by numerical methods that are convergent before adding ad hoc parameterizations whether they be realistic or not.
Sure. But I have no clue what claim you are trying to support with this. Whatever you do, you want a set of equations that would be computable and is illposed if you gridded them down to capture the Kolmogorov scale.
So, in that vein, are you now implying that that you can not get smooth bounded numerical solutions to:
a) The hydrostatic system (full NS) when molecular viscosity is included?
b) The nonhydrostatic system when molecular viscosity is included?
Based on the earlier threads and reading some of your manuscripts, I thought I knew your answer to these. But I am beginning to think I don’t know your answers. So, please say yes or no, not “Read Browning and Kriess”.
These questions are not attempts to back you into a corner and have yes or no answers. (FWIW, I think we agree on the answer to at least one of these questions. ) That said, your to these questions will affect what I ask next.
lucia (#147),
You continue to assert that you have read our manuscripts, but continue to ask questions that seem to indicate that you have not read them very carefully. It is time that you start to answer some questions so I can see
what you have learned from the manuscripts.
Before we continue, have you or have you not read
the multiscale manuscript and if so please describe the system of equations cited in (2.1) so we can both agree on the system described in the earlier comment (inviscid, compressible NS with Coriolis and gravitational forces). What are the horizontal, vertical, and time scales and dependent variable scales.
What does the S_1 scaling parameter mean. Where is the heating term?
Why is dissipation left off of these equations?
Jerry
Jerry:
No. I did not assert I had read all your manuscripts.
I said I read the comments in these three threads. I said I read Silvies Manuscript (once I was able to identify which manuscript you meant by this.) I told you Kress and Browning 1984 is money walled (see above). I dont have it. I have not read it. (I read the abstract)
I said I have not read the book chapter you advised I read after I asked you for a reference that might list the full set of the equations you call the hydrostatic system and the nonhydrostatic system. I wanted a reference so I can be certain I know precisely what set of equations you mean when you use these terms. (I can guess, but wouldnt it be better if you told me?
That chapter is also money walled. I plan to get it from the library, as there appears to be no other way to get you to specify the precise specific set of equations you use these terms to describe. (Why you cant scan the page with the equations, and ask Steve to upload the page is beyond me. It would fall well within fair use of copyright. But, for now, until I get the chapter, I am somehow left to guess. )
As to any other manuscripts, you will need to be more specific about their titles authors dates etc. Otherwise, neither I, nor anyone reading this thread, is likely to read the manuscripts.
1) I have no clue which manuscript you have given the nickname the multiscale manuscript. I know this is a blog, and we dont have formal citations rules, but, since I dont know which paper that is, I cant answer your question.
2) When you say the earlier comment which specific earlier comment do you mean?
Are you asking me where the heating term is in equation 2.1 or the multiscale manuscript? Beats me! Even if I have read the manuscript, I still don’t know which manuscript you call the multiscale manuscript. So, clearly, I cant know which is equation 2.1.
If you mean to ask if there is dissipation in inviscid compressible NS with Coriolis and gravitational forces: No. Viscosity is neglected. Consequently this set of approximate equation has no viscous dissipation. ( That said, Im not sure I would ever use the term inviscid NS. Why not say Euler equations? )
Did I answer the question you meant to ask?
If not, ask your question more clearly, and Ill try to answer it. If showing the equation is necessary, then get a scanner, scan the equations, and upload the pdf. Doing that wouldnt violate copyright, and its easy. I could answer more quickly.
Now, that I tried to answer the question I think you meant to ask, will you answer the ones I asked?
Are you saying that that one can or one cannot get smooth bounded numerical solutions to:
a) The hydrostatic system (full NS) when molecular viscosity is included?
b) The nonhydrostatic system when molecular viscosity is included?
These are simple questions/ The answers to these questions are either yes one can, no one cant, or I dont know.
I already asked these questions, and I know you can answer them without saying Please read my manuscripts. These questions can be answered without regard to your manuscripts because you are not the only person in the world who has done DNS either in 2D or 3D!
lucia (149),
The manuscripts were written for a reason, i.e. to mathematically quantify
the problems with the various meteorological systems.
You said you don’t know which system of equations. I provided an exact reference (Tellus) and you haven’t read it. I mentioned another reference many times on this site, but you can’t find it. You might try using google scholar to find all manuscripts written by Heinz and me. That is what Steve
M. did when I first started to post.
But just to make sure I don’t hear any more whining, here it is again:
Browning, G.L., and H.O. Kreiss, 2002:
Multiscale Bounded Derivative Initialization for an Arbitrary Domain.
Journal of the Atmospheric Sciences (00224928)
Vol. 59, no. 10,
pp 16801695
I was able to access this manusscript on line from the CSU library
and print it. Do some homework and quit trying to have me rewrite results that are in print. I believe the phrase is “spoon feed me”.
Jerry
lucia,
Steve M has a copy of the paper. Maybe he can post it in the CA literature database?
Steve. Done – http://data.climateaudit.org/pdf/others/Browning&Kreiss2002.pdf
A Browning literature dump from above paper. Some may find this helpful.
Multiscale Bounded Derivative Initialization for an Arbitrary Domain available for download at: http://ams.allenpress.com/perlserv/?request=getabstract&issn=15200469&volume=059&issue=10&page=1680
Here’s what I got. In terms of definitions. Based on this: “unphysically large dissipative terms” and this: “To be unphysically large, they must both large and unphysical.”
I take it Jerry considers a physical term that is beyond the bounds of reality unphysical.
I take it lucia doesn’t consider an unrealistic physical term unphysical.
I would define a physical process that is unrealistic as unphysical. For example, water not freezing until 0 F or not boiling until 400 F is unphysical, because it’s false.
I would define a process that is not physical at all as nonphysical.
So, raindrops falling up is unphysical, as is needing winds of 1,000,000 miles an hour to make a model work. An algorithm is nonphysical. Something like that.
Bender,
Thanks for the list of papers with titles. SteveM sent me the paper.
I will now write the link in a way that will permit future readers can use their browser tools or google to find this paper when Jerry is refers to it either by a) nickname , b) title and author only or c) full title :
The multiscale manuscript (AKA Multiscale Bounded Derivative Initialization for an Arbitrary Domain
Browning, G.L., and H.O. Kreiss, 2002, AKA Browning and Kreiss 2002)
Jerry:
I know the manuscripts written for reasons. I also know that ordinarly, people don’t provide citations with nothing more than nicknames for a reason. As you can see, once you stated the title people were able to find the paper.
You have mentioned many references quite vaguely using no titles, no publications dates frequently. I think asking you to state the title of a manuscript you wrote for clarity is reasonable.
If you continue to suggest you showed something in the “whatchamacal it paper” or “some paper I wrote with my advisor sometime during the ’90s” or “one of the several manuscripts I have mentioned a long time ago in comments”, or even “the multiscale manuscript”, I will continue to ask you to provide enough information for me to know precisely which paper you mean. Given a title, I can use google scholar. I am not going to sift through the numerous references on which both you and Heinz appear and guess which of these corresponds to the “whatchamacal it manuscript”.
On to the question you asked me
It now appear that your question refers to equations 2.1 (a) – 2.1 e) in “Multiscale Bounded Derivative Initialization for an Arbitrary Domain”
You ask:
‘
Because you asked stating no particular motivation for this series of questions, but seem to think it is useful to use the Socratic method, I will now answer your specific questions as you posed them. I will avoid going even one wit further, and providing nothing in addition to the answers to your questions as I understand them:
please describe the system of equations cited in (2.1) so we can both agree on the system described in the earlier comment (inviscid, compressible NS with Coriolis and gravitational forces).
This appears to be a set consisting of an approximate version of
conservation of mass (2.1e),
momentum (2.1 bd) and
energy (2.1 a) (At least this looks like conservation of energy.)
Written for air (gamma = 1.4)
Viscosity is neglected. Flow is assumed adiabatic (that is, you assume no heat addition). Coriolis forces are retained. The effect of gravity is retained. Compressibility of air is retained. Since I see no second law of thermodynamics, likely you have assumed there are no irreversible effects.
The narrative before this equation indicates the equations are written to apply when most of the energy exists at low wave numbers only (for example a decaying energy spectrum.) The impact of small scales of motion (which in your case happens to be storms) is neglected.
What are the horizontal, vertical, and time scales and dependent variable scales.
Characterisitic scales are provided in 2.2.
Horizontal and vertical velocities ~ 10 m/2 Vertical W= 0.1 m/s,
Horizontal length scales are: L= 10^6 m The vertical length scale D – 10 Km.
From this, in text, you state the typical length scale describing this large scale disturbance is on the order of a day– which matched
T= L/U = 10^6 m/ 10 m/s = 10^5 S. (Other time scales could be concocted. Example D/U is of the order of a hour, which could be important should we eventually describe the situtations where the set of equations descried by 2.1 breaks down.)
You have not specified which dependent variables. One can concoct an infinite number (e.g. cceleration, dynamic pressure, whatever.) You later ask for S, so I will wait. If you want some other dependent variable, please tell me which.
Why is dissipation left off of these equations?
The short answer is: Viscous dissipation is left of these equations because you are neglecting viscous effects.
The long answer,
Neglecting dissipation is appropriate for certain physical systems characterized by large Reynolds number, based on length scales and velocity scales of interest. In the system you are studying, you have previously assumed there is little energy in the small scale motion and developed the set of equations 2.1 this flow. Nneglecting viscosity is consistent with your previous assumption that there is little energy in small scale motions.
In short: You first assumed away small scales (possibly justifyably for the problem you are studying.) Once you assumed them away, viscous dissipation vanishes. It’s a consequence of an underlying assumption (simplification, what have you.)
What does the S_1 scaling parameter mean?
In words your manuscript states S1 in 2.2b
“represents the maximum size of the deviation of the pressure at a given height from the horizontal mean of the pressure on that height divided by the mean.”
You say this has a value of 0.1 for a flow case you are considering. This means variations in pressure in the horizontal plane may be as much as 10% of those from the top to the bottom of the atmosphere. This would suggest that, when studying a flow where there are only large wave number components, assuming pressure varies hydrostatically might be ok for some problems, but it may be a problem for other problems. (I note: equations 2.1 (a)(e) includes nonhydrostatic effects, as seen in the pressure gradient terms in 2.1e and 2.1 b)
Where is the heating term?
There is none, as one would expect when someone assumes adiabatic flow — which you said you assumed in the paragraph just before writing equtaion 2.1a.
I answered all the questions you asked
So, there you go. I answered the every questions you asked! I have no idea where you are trying to go with this but I am fervently hoping I can eventually extract answers to the questions I have asked you in comments.
Now, if you could be so kind:
Please answer these two which I asked in 149 and 147. As you will recall, these questions were motivated by your comments 130 and 129. You previously were alluding the idea that one might wish to use a system of equations that gives smooth bounded numerical solutions and seemed to suggest someone somewhere is not.
I have many questions which you resist answering– but for now, I just want you to answer these two. “Yes”, “No” or “I don’t know” will do.
Are you suggesting that that one can or one cannot get smooth bounded numerical solutions to:
a) The hydrostatic system (full NS) when molecular viscosity is included?
b) The nonhydrostatic system when molecular viscosity is included?
bender and Steve M. (#151),
You both have considerably more patience than me. 🙂
Now that the manuscript is posted, anyone can ask questions about the details.
In agreement with the mathematics, the numerical example shows that a short term forecast can be run without any form of dissipation and that a mesoscale storm can be recreated within a balanced large scale flow without any numerical accuracy problems (the numerical method used was only a second order accurate numerical method). But care must be taken to use a well posed continuum system, well posed continuum open boundary conditions, a numerical method that is accurate and stable for the initial boundary value problem (this is not a trivial analysis problem), a continuum balancing scheme that will provide the correct balance for the initial conditions in a limited area, the initial vertical component of the vorticity, and the actual heating. And even then one can see that long gravity waves can be generated from the mesoscale heating that can conflict with the largescale boundary conditions. The balancing scheme minimizes this problem, but it still occurs as expected from theory.
From this manuscript it can be seen why the WRF (or any other current limited are weather prediction model) has problems.
1. Anthes model was based on the ill posed hydrostatic system. Yet 100’s of NCAR manuscripts were published using that model.
2. The WRF model uses the nonhydrostatic (well posed) system.
But the time split method is not stable and the boundary conditions
are an ad hoc sponge layer type of treatment at both the lateral and vertical boundaries. Initial conditions for the small scale vorticity are not known and instead computed by an ad hoc iterative method. The real heatings are not known and instead approximated by ad hoc parameterizations that are more often than not discontinuous. Discontinuous (rough) forcings have been shown to have a very detrimental impact on multiscale systems (reference available).
As one starts to read this manuscript, the problems with correctly forecasting smaller scale storms even under ideal conditions becomes clear.
And the obvious questions of what is done under less than ideal circumstances can be answered.
Jerry
Shoot! Underlines work only in preview.
I underlined the specific questions before my answers and they vanished. 😦
No more patient, Jerry. Maybe just a little quicker on the keyboard. I’m generally against spoonfeeding too; but lucia’s responses are worth the effort.
You know how this younger generation is. 🙂
lucia (#155),
When you are finished reading the manuscript all the way thru, you will see where the heating term is added and the impact of smaller scale heating on the equations. The manuscript and its predecessors include both rigorous mathematics and illustrative examples so that a reader can better understand the mathematics.
At the scales indicated in the manuscript, the real atmospheric dissipation terms play little or no role and that is why they were neglected. The ensuing hyperbolic theory has been shown to be extremely accurate (additional reference available by Fillion, Page, and Zwack in MWR if requested).
Jerry
bender (#158),
lucia has asked some very good questions, but needed to do some reading so
we can communicate better. Now that she has a copy of the multiscale manuscript and is proceeding thru it, hopefuly it will be instructive for all of us.
Jerry
John (#153),
Thanks for your effort to obtain the reference. You have saved me more than once!
Jerry
RE: #144 – ever seen a cold front do the chachacha, then slide left off the stage? Got one of them right now on the West Coast. The thing literally came in, backed off then repeated about 3 times prior to really moving past Pac NW. Now its sliding toward the NE almost along rather than normal to its boundary.
First, I think it’s worth putting down some breadcrumbs because as far as I can tell, we are off on a tangent that is irrelevant to questions I have been asking about claims Jerry made when both
a) when writing his synopsis of Silvie’s Manuscript which is about boundary layers. and
b) when Tom V and I were discussing RANS (which has deficiencies, but is a way to model general flows.0
My repeated questions sprung up during Jerrys discussion of Silvie’s manuscript. Silvie was modeling a boundary layer. During this conversation, Jerry began to say that viscous dissipation and eddy viscosity are unphysical when used in the flow Silvie describes– see for example #126 and #130.
Saying these are unphysical during a conversation about boundary layers is nonsense.
But, knowing blog conversations can be confusing, I began asking Jerry to clarify what he meant– asking in the context of a boundary layer ( I had previously asked him to clarify the same claims which he interjected while Tom and I were discussing RANS.) I asked Jerry a series of questions in 132, which were not answered and remain unanswered.
Then, after posting several nonanswers, suddenly in 148, Jerry decides I must be quizzed.
But I am not quizzed on the content of Silvie’s manuscript which we were discussing. I am suddenly quizzed on the contents and a heretofore unmentioned manuscript he called “The multiscale manuscript”.
Nope, I had not read this paper prior to discussing Silvies paper! And guess what? This paper is entirely irrelevant to the questions I was had been Jerry.
How?
The flows have entirely different energy spectra
* The “Multiscale Manuscript” looks at a flow with a decaying turbulence energy spectrum. Not only is it decaying, it is almost totally, completely decayed. So– what turbulence there is came from elsewhere,has been dying has a quite low magnitude..
* In contrast, the boundary layer is created in the boundary layer. It is the place in the flow where turbulence is most vigorously produced.
* RANS, for all it’s faults, is general. So, in principle it applies to both flows. (In practice, it often fails.)
The magnitude of viscous dissipation and or turbulent diffusion are totally different in the two flows.
* The “Multiscale Manuscript” looks at a flow were both viscous dissipation and and turbulent diffusion are quite low.
* In contrast, in the boundary layer flow: which we were discussion when I asked Jerry the questions in 132, the viscous effects are as important as inertial effects. Moreover, turbulent diffusion is as more important than mean advection in the direction normal to a flow surface (That surface would be our planet earth.)
* RANS: this is supposed to handle both types of flows. (But for various reasons, codes often fail.)
So:
Boundary layer: turbulent diffusion is the most important term.
Gravity Wave : turbulent diffusion utterly unimportant.
RANS: supposed to do both.
I could go on and one, but basically, Jerry made some specific statements with regard to eddy diffusivity, viscous dissipation, in boundary layers He said they were unphysical. I have been asking him about that, and I will continue to pose questions with regard to that.
Possibly Jerry thinks I am asking questions that one should not ask– but those were the questions I am asking.
My comments on comment # 156
So now, I will comment on bits of his paragraphs, with my reaction visavis, the questions that I asked. I am doing this because it seem to me that Jerry thinks he is in the process of answering questions that I began to pose back around comment 132. (Which were posed during a discussion of modeling boundary layers.)
Yep. Got that.. You appear to be saying you have shown that you can get reasonably decent answers when neglecting viscosity in a flow where viscous effects don’t matter. You can do this provided you are careful and don’t make other approximations.
Now for my rhetorical question answer pairs:
Q: But what does this have to do with your apparent claim that viscous dissipation and/or eddy viscosity are unphysical in general or more specifically in a boundary layer where diffusion and dissipation terms are large or dominant?
Answer: What you are discussing has nothing to do with your repeated claims about eddy viscosity or dissipation in general and certainly does not apply to a boundary layer.
I have repeatedly concurred that an illposed system should not be used. If it’s the hydrostatic assumption that makes it illposed, they should try including hydrostatic effects. I said this long ago in comments. If it’s some other assumption that makes the problem illposed, relax that assumption. If it’s only illposed when two assumptions are made, relax one assumption, the other or both.
So, I think we both agree on this, right? (And we agreed before you felt the need to make me read this paper in you attempt to answer my question about parameterizations used in boundary layers?
rhetorical question
Qs” But what does this have to do your apparent claim that viscous dissipation and/or eddy viscosity are unphysical in general and in boundary layers?
Answer: Nothing!
Glad to hear, this system is well posed!
Evidently, according to comment 156, you don’t like some of their bc or ic approximations. You say here in comments that some of parameterizations used are ad hoc (i.e. special purpose– just like your system of equations 2.1 or 2.3 which applies to a special idealized flow, but would fail if applied elsewhere).
Yeah, well, boundary layers are ad hoc– they apply to the special case where boundary layers exist.
Your flow is ad hoc: it applies to the special case where the pile up of assumptions you invoked apply.
These are two completely different flows, and you are trying to match them at the boundaries. Yes, it’s difficult. No argument.
So, back to rhetorical question
Q: But, once again, what does this difficulty have to do your claims that viscous dissipation and/or turbulent diffusion are unphysical in general or in the boundary layer itself. And how does it answer my repeated questions with regard to your clam about this?
Answer: Nothing!
Dandy.
But, this has nothing to do with the questions I have been asking you, which I posed back when we were discussing boundary layers, and which you have not answered.
And as for this: #160
BINGO Jerry! At the scale indicated in this multi scale manuscript dissipation is utterly unimportant. This paper doesn’t support your claim that viscous dissipation is “unphysical” in general or in boundary layers.
It just discusses a particular flow where viscous dissipation happens to be nearly equal to zero.
For this reason, discussing this flow has nothing to do with any question I asked you on and around comments 120140.
You previously said viscous dissipation and turbulent diffusion are unphysical in the general case (RANS) and more specifically in a boundary layer which has entirely different scales. In those a boundary layer, those terms are large. That is why I asked you to justify your claim when you made it in regard to a boundary layers.
So…not to put words in your mouth, but given the question I actually asked, and given the fact that you seem to be thinking you are patiently answering my question, it would appear you are saying:
“Viscous dissipation is unphysical everywhere including boundary layers because I , Jerry, can find a special case where it is nearly zero. In that special case, where it is zero, I can get good results by setting it to zero.
Hence, since this to viscous dissipation is zero in this one particular flow, you must decree it unphysical in general (RANS) and even a boundary layer (or RANS)! ”
Surely, you do not think this? (I think we only got here because you are not actually reading my question, particular in the context in which they are asked. Rather, blogs being what they are, you are answering some question that exists in your own mind.)
Surely, you see that you have not shown turbulent diffusion or viscous dissipation to be unphysical in general or in a boundary layer?!
So,… now that t he diversion is over
This has been long. It has involved forcing me to read the multiscale manuscript. Sigh. . .
========
Now, because I can’t help myself:
#160:
Well…. I didn’t ask you where it was added, did I? You asked me where the heating term was in the set of equations set 2.1! I answered they weren’t there, They aren’t. There are heating terms in many other places. If you wish to expound on them, do so.
But, once again, would this discussion be relevant that viscous dissipation and/or turbulent diffusion are unphysical in general or in the boundary layer itself. A
Answer: Nope.
Do conversations between two scientists not talking about the same thing happen often at cocktail parties? Or is it just on blogs? 😀
What are we going to do with all these broken chairs?
Maybe we ought to take the good chairs out the back of the bar. This thing aint over yet.
C’mon, guys, Jerry’s retired and can’t stand the noise and lucia’s already having troubles locating files amidst the traffic. You’re not helping. Take it to “unthreaded” and leave it there.
lucia (#164),
Let us review your statements.
The title of this thread is exponential growth in physical systems.
It was meant to show that in the presence of shear, e.g. the jet stream,
the exponential growth in any small time interval for the hydrostatic
system used in global weather and climate models is unbounded, i.e. the hydrostatic system is ill posed. This has a direct impact on climate models and the topic of this site is climate audit. The thread was also meant to show that the nonhydrostatic system for meteorology is well posed, but has fast exponential growth near a jet so will be very sensitive to any error ( observational, forcing, numerical, or otherwise). This also has a direct impact on climate models.
You claimed to have read the thread comments, but somehow managed to miss the discussion about Sylvie’s manuscript and when it was referred to someone else had to find it for you.
The boundary layer approximation in Sylvie’s manuscript was the parameterization that was the dominant one in keeping the growth of the velocities at the surface under control (but is not physically accurate)
and the growth of the forecast errors due to this parameterization is clearly shown in Sylvie’s plots). And a simpler gimmick worked just as well. You asked for more information about the parameterizations and I provided a reference at NCAR that describes the continuum equations and forcing terms of their model in detail. You complained that you had to read Fortran code which meant that you didn’t look very hard. And I doubt you have read the manuscript yet.
You also continue to miss the point that the weather model was kept on track by new wind obs every 612 hours, i.e. not by the inaccurate parameterizations. This is not possible in a climate model prediction
and again has a direct bearing on climate studies.
You specifically asked to see the equations for the hydrostatic system and the nonhydrostatic system. The Tellus reference was provided, but you did not take the time or effort to obtain the article and read it. The multiscale manuscript contains a summary of the unscaled equations,
the scaling values, and the scaled system for both large scale and mesoscale motions in the atmosphere. From there it is trivial to define the hydrostatic system based on my earlier comment about the neglect of the vertical acceleration term (given that you read the thread).
And then you made a big mess of the simple boundary layer argument in Sylvie’s manuscript and are confusing it with the unphysically large dissipation used in computer models to allow computation, but not necessarily an accurate solution. The damage done by such games has been demonstrated using convergent numerical solutions for the viscous incompressible NS equations based on the minimal scale estimates of Henshaw, Kreiss, and Reyna (reference cited earlier and available on request but I doubt you will read it).
Pardon me if I seem to find problems with your whining.
Jerry
@Sam– I have never had this level of misunderstanding discussing modeling during happy hour. Most people understand that “The guy you seek lives in Boston” is not “giving an address”. Those who do know that Jerry provides are not references. I do not plan to explain this to him further. Should he ever understand this, he may then understand why no on on the thread (other than me) seem to read his papers!
Yep, the reason I’m the only one “whining” for halfway complete citations is I was getting them and reading them. But hey! 🙂
@TheDuke — Nope, it’s done.
@Bender– The problem wasn’t the OT stuff.
@Jerry — Clearly, we are done. I will not attempt to explain the full ridiculousness of individual statements your response; it’s pointless.
I beg to differ .
I have read them (at least some) as well as several Henshaw, Kreiss, and Reyna papers that are quite interesting even if very classical – bounding Fourier transform expansions is a current technical stuff , doesn’t work for all cases but when it works it is nice .
Actually everything useful has already been more or less said in threads 1&2 (references included) when discussing with Dudia .
Most agree now that for climate modelling : the hydrostatic assumption is wrong and the non hydrostatic assumption has a
problem with exponential error propagation – what I sum up by saying that both are a manifestation of the fact that NS gives raise to deterministic chaos in most (not all !) physical cases .
Personnaly I didn’t see much added value in #3 because obviously it has been a ping pong game where the players were playing on different tables but , well , it is not my problem .
#170 Done? lucia! I was hoping to learn from you! I understand that Jerry’s treating you like he would a graduate student, and I know that can be very annoying. I, for one, am impressed with your patience in tracking his assertions line by line. I am impressed that you are reading the papers and understanding them, and calling him to task. I see how he is being vague and that this is the ultimate barrier to communication. Is it not possible to be more patient with him? I really enjoy your comments.
Perhaps Tom #171 is right and this thread – as Jerry has narrowly defined it – is over for now. That doesn’t mean the topic shouldn’t be broadened, perhaps shifted to a new thread.
For the record, Tom, I got a lot out of #3, because I now understand what the “hydrostatic assumption” is. In turn, threads #1 and #2 now make a lot more sense to me – as do the Browning papers (which I scanned, but was incapable of “reading” = understanding). It was *lucia* that precipitated this understanding.
The moral of the story being that sometimes a knockdown dragout has great teaching value. I think this principle has been known for a long time in politics and law, it’s less common in science. But if you read about some of the flame wars Newton engaged in, you realize that it’s not unheard of.
# 174
Then all the power to you Bender 🙂
Welcome to the club of people who are playing with viscous dissipation in boundary layers and dissert about enstropy casades during breakfeast .
Actually I think that you are right .
Jerry is the boss in this thread and he defined very clearly and accurately its purpose and as far as I am concerned this purpose has been fulfilled somewhere in the #2 .
What I would like now would be a thread where would be discussed the existence of regular Navier Stokes solutions , the validity of numerical simulations of the same and the ergodicity problem .
But for that we’d need somebody like a Dan Hughes coupled to a Terry Tao to sponsor the thread and that’s not easy to find 🙂
To give an idea about what I have in mind , have a look at http://terrytao.wordpress.com/2007/03/18/whyglobalregularityfornavierstokesishard/ .
I am in absolute admiration for that “reflexion” (it is not a paper) because to express very complicated questions in such a clear way understandable to (almost) everybody is not given to many .
And since you are now also a convert to scale invariance , you will find more interesting stuff about this issue on his website too .
Conflict in science follows a power law; calm most of the time, occasional squabbles, rarely casualties. When there’s intense combat, it’s time to pay attention, because you know the scientists are engaged on an assumption or assertion that is supercritical for some hulking logical structure that is known to them, but not the people around them. The hydrostatic assumption in weather & climate modeling appears to be one of these things. Who knew?
Thanks for the links, Tom. I will investigate. I’ve always liked Dan Hughes’ comments, but have never had the time to spend more than a minute on his site. Maybe now is the time, as this subject is a little far from the auditing function of CA.
OTOH there is also lucia’s new blog:
http://rankexploits.com/musings/2007/newclimateblog/
I suggest you post your idea there.
Tom– I would never claim Jerry provides no referenes. Jerry constantly volunteers traceable references for for papers he is eager for us to read. Sure, one must google, but at least they can be found.
If you read that paper, more power to you. So did I. I agree with your assessment. I also agree noone is disagreeing on the nonhydrostatic issue or the jet issue etc. As far as I can tell, on these issues: Consensus has been reached. The topic is past debating. Lack of questions is not an indication that anyone fails to understand their significance. With regard to those issues, we are in the “What’s to discuss?” phase.
I’m also not saying thread 2 contains no references to anything at all. JimD in particular dropped references, often providing actual links! Thread 2 as some interesting not to mention fascinating debates. (I particularly like the evidently on topic debate over whether JimD is commenting on government time.)
That said, thread 2 just doesn’t have references to the questions I was asking. Evidently, these questions, and their assiated topics are today decreed off topic. Maybe that’s why there are no relevant references on thread 2? 😉
Now at the risk of venturing off into the forbidden territory, CHAOS! TomV said:
You may be right — or not.
My only point on R&T is that their mathematical treatment is not thought to prove turbulence itself is chaos. It is a highly respected paper and certainly proves some solutions to the NS correspond to deterministic chaos. Practitioners consider those case to be transition to turbulence and not turbulence. The problem isn’t the math; it’s that R&T only prove that some solutions are deterministic chaos and many practitioners don’t consider those cases real turbulence. Deterministic chaos is variously called ‘transitional’, ‘soft’, or even ‘not turbulence’.
You will note that Li, in the paper you studied says that no one has proven that real turbulence is not chaos. Entirely true. (The Li paper also contains some howlers about RANS.)
So as I see it it seem equally reasonable reasonable to root for “turbulence is chaotic” or for “turbulence is not chaotic”. Neither has been proven.
But, that’s not the topic of this thread.
So, I’ll move onto bender and Tom’s suggestion: More general modeling issues have evidently been decreed off topic; we can’t discuss them here. If we want to discuss them, we must do so elsewhere. 🙂
Lucia, yes, “Most people understand that ‘The guy you seek lives in Boston’ is not ‘giving an address’.” But if the purpose is to give the person asking about the guy some practice at using the phone book and finding out really how interested the person asking the question is about locating the guy, well. (Not that I’m saying that’s what Jerry was doing, I’m just sayin’) I probably would have given you a link, but I’m not Jerry, and it’s not that hard to find a paper by two specific people on mulitscale issues. Whatever.
I saw it as a lot of talking around each other. Cross purposes? Mistaken attributing of motives? Somewhat vague and circular? Whatever, it seems that it would be more productive if:
1. Before starting, the specific exact topic should be clarified, as well as the key terms.
2. One question was asked/dealt with at a time.
3. The discussion was not treated as either a debate or a competitive endeavor.
That said, perhaps this is why it takes 12,000 people and 5 years to come out with a 30,000 page document that says basically “Climate is changing and humans have a role in it.” 😀
In any case, both commonly used meteo and GCMs are ill posed and we see the results of that.
@Sam– Interesting analogy.
I would be happy to use the phone book if given a name. I don’t know about other people, but I can’t look up “The guy you seek” in the phone book. I need a name like “Joe Smith”. Jerry’s most recent reference was “The multiscale manuscript”. Jerry did not provide the title or authors names until after I explained that I had not read this previously unnamed paper because he had provided no names, no title and no journal.
Possibly, I should be patient and guess Jerry is one of the authors of the paper, google and guess. Possibly not.
As soon as Jerry grudgingly provided the information I requested, it became possible for people to use Google scholar. It happened to be the middle of the in my time zone, but bender ask steveM to put the paper in the data based and provide the link. Others googled and found it. When I logged on in the morning, the information was available to me.
Of course, the most idiotic thing about this is the paper was clearly sitting on Jerry’s desk. He was demanding that I pass a quiz that involved providing explanations of various terms in equations 2.1 and then read and regurgitate the value of the characteristic scales listed in the paper.
I do not speculate as to Jerry’s goals, motives, suspicions, issues or what not. For all I know, he doesn’t like to type out full titles for fear of wearing out his finger tips. Either way, if I am to pass a quiz to explain equations 2.1(a)(e), I expect to be given a citation that assures I answer the question I am being asked.
Gerald Browning, #113:
I love that line. If anyone was ever to write the definitive story of this blog, the phrase in bold would be a perfect title.
Lucia; I didn’t say it was unreasonable of you to ask that, but you didn’t go about it in a very good way, and more than Jerry being so terse was helpful. But I agree with bender about the grad student thing. (I don’t consider a link to be spoonfeeding, but I ain’t gonna go to the library for you.)
As far as the phone book analogy, it depends on the question; I would have thought the name of the person would have been in the question: “Where does Joe C. Bloe live?” “The guy you seek lives in Boston.” or some such. You could have assumed that he meant a paper he wrote that had multiscale in the title, just like he assumed you knew that. (Or if my assumption he’d already mentioned it was faulty, I could have been on the same path.)
Here on this thread:
If you search for “multiscale” on this site, the first link that pops up lists it in post 674:
References:Browning and Kreiss, 1986: Scaling and Computation of Smooth Atmospheric Motions
Tellus, 38A, 295313 (and Charney reference therein)
Browning and Kreiss, 2002: Multiscale Bounded Derivative Initialization for an Arbitrary Domain, JAS, 59, 16801696 CMC Website
I’m not blaming you for not searching for it (I didn’t think of it myself until right now) and it is rather curious he just didn’t list it, but the information is there, so….
From the outside (I try not to get involved in these types of discussions) I give you both an A+ for patience, and both an F for your ability to communicate effectivly with each other.
That should have been “any more” not “and more”
Hopefully we all learn a lesson from this, even if it’s not what effect wind shear has on airplane wings. 🙂
All,
lucia has claimed that I have not provide exact citations and
that she read the previous versions of this thread.
Just to prove that the two statements are contradictory, I went back to thread 1 and request that lucia look at the following :
Introductory comments for thread 1 (2 references)
comments 43, 44, 103, 133, 144, 163, 168, 186, 207, 217, 348, 351, 395.
I also included the comments that contain the simple proofs I mentioned on thread 3 and the model convergence plots so lucia could find them.
Jerry
All,
It does not help to provide references if people do not at least read the nonmathematical part of the text. I continue to be willing to answer questions about the mathematics, but not when someone has not even obtained a copy of the reference and at least read something other than the abstract.
The multiscale manuscript is a very thorough presentation of the relationship between different solution components and scales of the atmosphere. There is much to be learned about the free atmosphere
if one reads the manuscript. And the mathematical technique of splitting up the solution into its component is a very powerful tool.
Jerry
Sheesh Jerry: I didn’t say you never,evern provided any references at all or ever. See my comment 137 above.
I said what you provide me when I ask for references are not references, and the reference in your “pop quiz” was vague. I was not here when you posted thread 1; so clearly, those reference were not given in answer to questions I asked.
I did say I read the thread; I did indeed read it.
I never said I had obtained and read every paper on the thread. I have not. I don’t intend to do so, and never intended to obtain every paper you have recommended to answer every in the past 9 months. Though you may feel I absolutely must read them, many are clearly unrelated to anything I have asked questions about.
Let’s look at your list
For what it’s worth, I will begin with the list you are now providing:
This paper is money walled:
Jerry, please carefully reread this thread; you will find I said this paper is moneywalled and I was getting it from the library. This may not fast enough for you, but I so be it.
I read this paper:
It’s interesting.
As to the comments in which you provide references:
Comment 43 on thread 1.
a) This is not a reference.
b) I don’t have any idea why you think I haven’t read that comment.
Comment 44 According to the thread, it describes a microphysics package Willis was curious about. According to the keywords in the abstract, it appears to be about cloud physics. I have asked nothing about clouds. Going backwards, the reference does not appear to be related to anything I have asked about
Maybe the paper is about something other than clouds, maybe it contains information I seek. But given the evidence, I have no idea why I would read that paper, cited in thread 1, in the course of trying to get answers to the questions I asked you in thread three. In any case, like many papers, it’s money walled and costs $32. Should I order it from my library?
Comment 103: Tom asked a question I did not ask. FWIW I have read Henshaw Kreiss Reyna .
In the HKR paper, they compute the 2D NS down to the smallest scales. Since 1989, computations in 3D have been done by others. Similar computations have been done in much more complex flows, including some containing particles. (See Squires papers.
Just prior to your little quiz, one of my two questions were motivated by my total consternation, when, in the context of the previous discussion, you suddenly, seemed to be suggesting that the full NS, would not give smooth solutions if gridded down to the the Kolmogorov scale.
Based on your constant references to HKR in the thread, I had assumed your answers to my questions would be “Yes, you can get smooth solutions to the full NS when viscosity is included.)
But, you didn’t answer those simple yes/no questions, though I reposted them 3 times.
And then, you decided to assign your pop quiz.
I could continue through the list of comments. But I’d rather summarize
Summary
a) I read the thread.
b) I read some of the papers cited. I selected the ones that appeared relevant to the question I asked and which were not money walled.
c) I did not read others for various reasons which I have described.
d) I said you often give vague references like “read the thread” when I ask you for papers. Some are so vague as to not be references. This is particularly true given the specificity of some of my questions.
lucia (#188),
Your comment in #170 :
Yep, the reason I’m the only one “whining” for halfway complete citations is I was getting them and reading them. But hey
I am not “eager” nor do I care if you read our manuscripts. I will let history judge the quality of our work. I do care when you claim I have not provided complete citations when asked.
If you read my comment thru, you will see that I said that I also included comments that contained the simple mathematical proofs referred to in thread 3. That is exactly what #43 is about. And I highly suggest you read the proof that using an unphysically large dissipation leads to an error equation with large damping and can destroy the accuracy of the computed solution relative to the true solution very quickly.
The reference to comments in thread 1 were to indicate that when asked I provided full citations. Nothing more deep than that. But the Lu (#44) reference does provide a very good scaling of parameterizations used in mesoscale models. You mentioned that you were curious about unphysical forcings and this manuscript certainly demonstrates the tuning knobs that are available.
Has any other DNS manuscript provided miminal scale estimate theory for the incompressible NS equations or just run some more code? The HKR estimates are a very elegant and unique piece of complex mathematics. Give credit where it is due and please don’t tell me about other computer runs unless there are some rigorous mathematical results that precede the runs. I have seen enough “garbage in, garbage out” for my lifetime.
Jerry
*sigh*
I’ve been reporting on the progress of this cold season on the middle West (US) Coast. I had a suspicion that the climatic seasonal transitions were all running early. Such a situation is certainly out of whack with NOAA long term outlooks published during early 2007. So now we have the start of climatic autumn July 19, and the start of climatic winter on or around Oct 20. This last bit may be controversial. Here is the retrospective. We got our normal late autumn weather during the period Sept 20 – Oct 20. Then, a little over a month of a typical early winter “halcyon days” pattern kicked in. After that, a slow build up to the current, unmistakably mid winter climatic seasonal situation. And sure enough, as we roll into what would normally be “halcyon days” there are storms lined up which will give us early February in late December. Good job NOAA modelers!
re 191. could you repeat that again in French so I dont understand it twice.
http://www.islandnet.com/~see/weather/almanac/arc2002/alm02dec2.htm
I would add that I doubt that Spring will come early. Bottom line, not quite a year withou a summer, but definitely a long cold season.
“Researcher: Basic Greenhouse Equations “Totally Wrong””
http://www.dailytech.com/Researcher+Basic+Greenhouse+Equations+Totally+Wrong/article10973.htm
Re #194
Well those of us on the East coast can compensate since we really didn’t have a winter.
re 194. Ya, spring is coming fast here.
MarkR (#195),
The historical assumption discussed in the cited manuscript that the standard equations are valid all the way to infinity is clearly not realistic. The author’s result in the manuscript is that if this assumption is relaxed, then boundary information must be entered from above and the result is very different.
Note that I have indicated a similar problem with climate models. Usually there is an artificial lid at a given altitude with no information input from altitudes above the lid where the equations eventually change their nature (plasma equations). The belief by modelers in such an assumption over long periods of time (as in climate simulations )should indicate the level of credibility one should have in a climate model.
Jerry
In the March 2008 issue, Mathematical Association of America’s Focus magazine, is an interesting article entitled Mathematicians Recruited for Climate Change Research (pg. 14), wherein it’s reported that Inez Fung, awardwinning professor of atmospheric science at the University of California at Berkeley, said this in her SIAM (Society for Industrial and Applied Mathematics) plenary address at the Joint Mathematics Meetings in San Diego, January 2008:
“Mathematicians are needed to formulate better ways of modeling both planetwide and local interactions as well as to devise better approaches for understanding uncertainty and risk. We also need faster computers and more and better observations. Unfortunately, as the ‘grid’ of observations becomes more dense, the current mathematical models diverge more in their local predictions, in contrast to what we would hope for.”
So, nothing new in the climate modeling world.
The journal of Computational Physics has a Special issue that might be of interest to many here, Predicting weather, climate and extreme events, http://tinyurl.com/6phbc5 .
This is a review article, http://tinyurl.com/6kgswc
And Elsevier, aka Big Science Publishing, has kindly provided links to 8422 related articles, http://tinyurl.com/5t3oh4
Trying to make Links turned into a major pain, so I gave up.
Climate Science takes RC to task on Climate Models:
http://climatesci.org/2008/11/28/realclimatemisunderstandingofclimatemodels/
Re: John Baltutis (#201),
There seems to be a pattern in which Real Climate oversells any point that they are trying to make. Selling is about building trust. any exaggerations that they make will only revert to injure the Real Climate brand
never made the cut:
Tsonis et al. (2007):
Wang et al. 2009:
Kyle Swanson, at RC, on Much ado about natural variaiblity
Jerry, wrt
The hyper viscous layer in model E, besides being unphyical, does it not fit the description of an ad hoc and inaccurate attempt to add a boundary layer, for the same or similar reasons, or perhaps being unphysical, even worse reasons?
John F Pittman (#207),
If one believes that the viscous, compressible, forced Navier Stokes equations are correct everywhere in the lower atmosphere, then sufficient numerical resolution near the surface would be required to resolve the thin turbulent boundary layer and the forcing terms near the surface would have to be accurate. Neither of these has ever been accomplished and any replacement of either of these physical processes with any ad hoc method is suspect.
Sylvie’s manuscript clearly shows this conclusion.
Jerry