tag:blogger.com,1999:blog-7612793.post112940864052592896..comments2024-03-18T18:14:34.278+00:00Comments on Stoat: Butterflies: notes for a postWilliam M. Connolleyhttp://www.blogger.com/profile/05836299130680534926noreply@blogger.comBlogger20125tag:blogger.com,1999:blog-7612793.post-1130528796535390112005-10-28T19:46:00.000+00:002005-10-28T19:46:00.000+00:00Ah Lubos, I take this as a confession of failure o...Ah Lubos, I take this as a confession of failure on your part: unable to stuff wiki with your POV by fair means, you resort to foul. But, my prediction is that wiki will shrug you off as it did before.William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1130525682847456892005-10-28T18:54:00.000+00:002005-10-28T18:54:00.000+00:00Hi William!If you want to simplify the work for In...Hi William!<BR/><BR/>If you want to simplify the work for Interpol, you may list your numerous crimes yourself at:<BR/><BR/><A HREF="http://en.wikipedia.org/wiki/Wikipedia:Requests_for_arbitration/Admin_enforcement_requested" REL="nofollow">WMC investigation at Wikipedia</A><BR/><BR/>Have you written your last will yet? ;-)<BR/><BR/>All the best<BR/>LubosLuboš Motlhttps://www.blogger.com/profile/17487263983247488359noreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1130517336878072012005-10-28T16:35:00.000+00:002005-10-28T16:35:00.000+00:00Its Michael "no sense of history" Sirks! Hello and...Its Michael "no sense of history" Sirks! Hello and welcome, err, or are you? To be honest, no, you aren't really. Had any luck with JG or C yet, ho ho? [Please dont take this as an invitation to post further irrelevancies.]<BR/><BR/>Meanwhile: CR: yes: I agree, trying a tropical perturbations would be a good idea. Also because it would be out of the fourier filtering zone so watching the growth over the first few timesteps might be more interesting. Trying bigger/smaller perts is also an interesting idea. I *have* just tried it with 1/8 and 1/16th timesteps (so sloooooow) and the "first stage plateau" *doesn't* monotonically decline... which is good, I think.<BR/><BR/>But there are so many other things to try: for example, the convective code is called every timestep... but I could call it every 1/2 hour instead... doing this properly is a research project in itself, not an evening job!William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1130514869129805892005-10-28T15:54:00.000+00:002005-10-28T15:54:00.000+00:00Your Wikipedia account will probably have to be di...Your Wikipedia account will probably have to be disabled because you have violated the parole - for example on the page of Bjorn Lomborg. This hurts the Wikicommunity. <BR/><BR/>WikipediansAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1130070138376199022005-10-23T12:22:00.000+00:002005-10-23T12:22:00.000+00:00From my comment on sci.environment:James Annan wro...From my comment on sci.environment:<BR/><BR/>James Annan wrote:<BR/>>Well, they do not deal in momentum directly, but velocity and pressure. <BR/>>A small enough perturbation could in theory be rounded out, but we can <BR/>>always compile the model at higher precision, and as wmc already showed, <BR/>>in practice it tends to grow fairly rapidly due to convective instability:<BR/><BR/>>(the results are entirely routine and characteristic of small <BR/>>perturbations in GCMs)<BR/><BR/>I think your last comment says it all. "Perturbations in GCM's" are not the real world. How do you know for sure that the different trajectories are NOT due to the internal workings of the model, where there are numerous truncations and quantizations, such as the 48/day time step and the relatively <BR/>large grid size? <BR/><BR/>I think WMC should try the same experiment with a smaller grid and smaller time step and see if the difference between the two runs produces the same level of divergence with time. I suggest four cases, actually, one one with smaller grid, one with smaller grid and smaller time step, one with smaller grid, large time step but perturbed and last, one with both small grid, smaller time step <BR/>and perturbed.<BR/><BR/>ESAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1129890340779184222005-10-21T10:25:00.000+00:002005-10-21T10:25:00.000+00:00Fair enough, but I think you have miscalculated my...Fair enough, but I think you have miscalculated my score. I made two predictions; that the points were ten points apart, and if they were less than ten points they would not diverge. Since the second depends on the first I deserve double points for that one, and so my score should be -3!<BR/><BR/>The actual question was: "Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?" See http://www.cmp.caltech.edu/~mcc/chaos_new/Lorenz.html so the answer seems to be yes.<BR/><BR/>That doesn't answer my two questions though :-(<BR/><BR/>Cheers, Alastair.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1129837073637878732005-10-20T19:37:00.000+00:002005-10-20T19:37:00.000+00:00Alistair: I did put the perturbation point next to...Alistair: I did put the perturbation point next to each other. As I expected, they don't cancel.<BR/><BR/>The x axis is in days, just like the post days, not time steps.<BR/><BR/>The y axis is given in the post too. You just have to read it carefully.<BR/><BR/>The blue and black lines are non-identical immeadiately, but diverge obviously after 10 days. No, they aren't 10 pts apart.<BR/><BR/>Score 1 for my prediction ability but -1 for yours :-)William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1129823233080206152005-10-20T15:47:00.000+00:002005-10-20T15:47:00.000+00:00Right! I had been thinking about the that experim...Right! I had been thinking about the that experiment before I saw the result. It occured to me that if you put the second point diametrically opposite the first on the world stage, then the first point would behave in the same manner as it did in the first experiment, until eventually the effect of the second point had spread far enough for it to interfere with the first. By that time there would be no prospect of the two points giving the same result as no point.<BR/><BR/>OTOH if you placed the two points adjacent to each other, they could eliminate each others effect. If this elimination does happen, then there must be a maximum distance at which this elimination would happen, and let's call the locus of this distance in the phase space the edge of the basin of attraction. (The phase space in this case is in fact a physical distance! well virtual really.)<BR/><BR/>In your figure you have not labelled the axes, and so I am assuming that the x axis is in time steps of the model. I am also assuming that the y axis is the error distance of the first point from its value in the unperturbed run. If this is true then since the black line and the blue line diverge only after the tenth time step, am I correct in deducing that the two perturbing points were placed 10 points apart? <BR/><BR/>If so, it would be interesting to see what would happen it the points were placed closer together. Judging by the shape of the black line which suddenly "takes off" at around ten steps, it could be that ten points is the distance to the edge of the basin of attraction!<BR/><BR/>So I have two questions: why does the the black line (and the blue line) take off after 10 timesteps, and why do the blue and black lines coincide for ten time steps, and is the ten timesteps in both my questions a coincidence?<BR/><BR/>Hoping you can find time to answer these questions,<BR/><BR/>Cheers, Alastair.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1129756483953937102005-10-19T21:14:00.000+00:002005-10-19T21:14:00.000+00:00OK, I did try it, it did make very little differen...OK, I did try it, it did make very little difference, as I predicted (hurrah, a prediction coming true...).<BR/><BR/>See it at: http://www.antarctica.ac.uk/met/wmc/butterfly-2.png if you like (the blue line is the new run).William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1129751214117371812005-10-19T19:46:00.000+00:002005-10-19T19:46:00.000+00:00I'll paste in here a quote from Raymond Arritt to ...I'll paste in here a quote from Raymond Arritt to sci.env, which helps (perhaps):<BR/><BR/>>The chaos argument isn't that one particular small vortex grows into<BR/>>another particular large vortex. Rather, the initial disturbance<BR/>>creates small changes to the atmosphere that cause it to evolve in a<BR/>>different way. The overall statistical properties of the system remain<BR/>>the same, but the specific events happen in a different way -- tornado<BR/>>alley is still tornado alley, and the tornados still happen mostly in<BR/>>the spring, but the individual storms don't happen in exactly the same<BR/>>place and time as if the butterfly hadn't flapped its wings.William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1129741651047356652005-10-19T17:07:00.000+00:002005-10-19T17:07:00.000+00:00Hi Alistair. I see your point, but I can tell you ...Hi Alistair. I see your point, but I can tell you the result without doing it: it will simply generate a different trajectory. Energy conservation down to that level is, I think, not important. But... I might get round to trying it.William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1129736770545456362005-10-19T15:46:00.000+00:002005-10-19T15:46:00.000+00:00I have pointed this out in James's Blog, but it is...I have pointed this out in James's Blog, but it is being ignored so I am reposting my idea here, where it is more appropriate.<BR/><BR/>IMHO, your experiment has a flaw which can be easily corrected. By alterering the pressure in only one cell your are contravening the law of conservation of energy. The air pressure at a point on the surface of the Earth is determined by the weight of the column of air above it. It you reduce the pressure, then you are in effect altering the mass of air in the column. In the case of a butterfly flapping its wings global mass remains constant. To simulate a butterfly's flap you need to alter the pressure in two cells with equal and opposite effect. In that case, with the mass effectively being rtransfered from on cell to another, it would be possible to see if the model converged, or diverged as a result of the butterfly's flap, rather than due to a change in mass.<BR/><BR/>Very curious to know the result,<BR/><BR/>Cheers, Alastair.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1129539315612240432005-10-17T08:55:00.000+00:002005-10-17T08:55:00.000+00:00CIP - ah; are the graphs still too small when you ...CIP - ah; are the graphs still too small when you click on them? The top one is 3 different time periods (you can tell that if you look closely at the shape of the graph).<BR/><BR/>On the first one, the top is days 0-5, and the y axis is 0-40. The mid one is to day 15, and the y axis to 300. The bottom one is to day 90, and the y axis to 1200 (Pa).<BR/><BR/>I may get round to redrawing them tonight.William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1129516179974112812005-10-17T02:29:00.000+00:002005-10-17T02:29:00.000+00:00Belette - Very interesting, but the graphs were t...Belette - Very interesting, but the graphs were too small for me to read. Also, what are the three different top graphs? Is there any way you could show this with some legends, on a slightly larger scale?CapitalistImperialistPighttps://www.blogger.com/profile/17523405806602731435noreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1129485800114015362005-10-16T18:03:00.000+00:002005-10-16T18:03:00.000+00:00Cr - glad you liked it. There may be more to come ...Cr - glad you liked it. There may be more to come but I don't promise.<BR/><BR/>Arun: yes, its repeatable (and indeed restartable in mid run too).William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1129483822199645652005-10-16T17:30:00.000+00:002005-10-16T17:30:00.000+00:00Just to make sure: HadAM3 (64 bit version) gives b...Just to make sure: HadAM3 (64 bit version) gives bit-identical runs when started with the same initial conditions on the hardware that you're using?Arunhttps://www.blogger.com/profile/03451666670728177970noreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1129456699288193562005-10-16T09:58:00.000+00:002005-10-16T09:58:00.000+00:00Grid is 2.5 (lat) x 3.75 (long), ie about 300 km. ...Grid is 2.5 (lat) x 3.75 (long), ie about 300 km. The perturbation was to change the surface pressure frm 99424.80078124999 to 99424.80078125009 at a certain point. So I could have made it smaller, and perhaps will.<BR/><BR/>How that relates to butterfly-flaps I'm not sure. As far as the model is concerned, it doesn't matter I think: the behaviour is about scale-indep.William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1129431454960033312005-10-16T02:57:00.000+00:002005-10-16T02:57:00.000+00:00So how big are your grids/timesteps and how many b...So how big are your grids/timesteps and how many butterfly wing flaps does it take to equal the pressure pertubation you put in.CapitalistImperialistPighttps://www.blogger.com/profile/17523405806602731435noreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1129418894406651282005-10-15T23:28:00.000+00:002005-10-15T23:28:00.000+00:00The two phase growth is nice. If I remember the NW...The two phase growth is nice. If I remember the NWP stuff correctly, the initial growth in the perturbation is due to local convective instability, which takes some time to influence the mesoscale. This is exactly why NWP centres look for meteorologically interesting perturbations (for ensemble forecasts) rather than just adding random noise. In the infinitesimal limit, it is the convective instability that grows fastest, so searching for perturbations requires some careful treatment when singular vector methods are used.<BR/><BR/>I'm a little surprised that it kicks off so quickly on the global scale. I wonder if the pertubation spreads at a meteorologically plausible rate, or is it diffusing at a "numerical" rate of one grid point per time step? Anyway, it all looks very pretty.James Annanhttps://www.blogger.com/profile/04318741813895533700noreply@blogger.comtag:blogger.com,1999:blog-7612793.post-1129411459034191492005-10-15T21:24:00.000+00:002005-10-15T21:24:00.000+00:00Peter: Of course you're right: there is only one w...Peter: Of course you're right: there is only one world. To make the butterfly effect thingy work, we have to do a thought experiment: what if we had a copy world, identical except for one butterfly's flap.<BR/><BR/>All of these things, if any one were different, would send the *weather* off on a different course. But the climate would be unchanged.William M. Connolleyhttps://www.blogger.com/profile/05836299130680534926noreply@blogger.com