Climate Audit

James Lane

And thanks to Jerry, Jimy, Bender and others for one of the most interesting threads I’ve seen on any climate site.
It seems to me that some of the issues being debated could be readily resolved by experiment, so what about it?

Filippo Turturici

Maybe some statistic would correct me (I use statistics just to analyse data, not because I studied them deeply) but one example could be comparing, on entire periods, the functions y=0 and y=sin(x): they have the same average (and this is obvious) and I can even find a good correlation between them because of this (here a statistic could correct me) but we know they are completely different functions.

For the matter originally leading this discussion (maybe someone pointed it before, so I beg your pardon, I had lost it in the preceding 443+3 messages) there could be also the inverse problem: from a small beginning trend, we can extrapolate almost every kind of function we want; and it is very easy to demonstrate, numerically, how a line could be very near to an exponential or to a function which is now growing but will decrease at a certain point, in such particular conditions.
Computational fluid dynamics is a recent and still difficult branch of science, which still needs many “field tests” and heavy computational power for (relative) small problems; and then I find very unlikely (as much as the IPCC finds it very likely) that we can fully modelise then forecast up to a century how Earth’s atmosphere behaves – not to talk about random and out-of-control influences, like volcanoes or the same Sun. Of course, we do not need a 0.01°C gradient in 1m, neither we could complain about a 0.5°C error over 100 years for a 100km^2 area, such precision is not required for now, but I have still my doubts about.
So such a kind of errors, like forecasting an exponential growth even when it is not happening, can be easy to do: indeed what it seems to be happening: grow trend for global temperature is smaller since 1998 than in the previous 10 but also 20 years; for anyone having studied basic mechanics, it is obvious that global temperature rise is now slowing down (which does not mean it has stopped or is decreasing); so, even with an approximation, I cannot find signs of exponential growth for now; neither I can understand how someone can talk of acceleration of global warming in recent years.

jae

Steve S: Are you essentially saying that the rising hotter air in the tropics and subtropics will “suck” more cold air from the artic (and antartic)?

Steve Sadlov

RE: #6 – Rising at first, but mostly, spinning not to mention, greater turbulence. But yes, the idea would be, GW (including whatever percent is “A”) results in a larger number of more intense lows at or below 36 deg latitude. Possible corollary may be, more excursions of the jet stream into semi tropical latitudes. Seems like a possible built in negative feedback loop, right down there at the basic circulation level.

Bill F

#3, I am dealing with precisely that problem at one of my current sites. We are working in an area where rainfall is highly correlated with the ENSO state in the pacific. So while the “average” rainfall over a 30 year period is around 32 inches per year, something like 70-80& of the years have a rainfall total that is either 5+ inches above or below the average. In my case, we are trying to establish what the “typical” ecological conditions are in a creek where the flow conditions are controlled by the rainfall and by the elevation of the water table (where the level is also controlled by the rainfall). For the last 10-15 years, the rainfall has alternated between historically high and historically low annual totals, and our challenge is to determine if the creek is a intermittent stream or not. The answer is yes…and no. When there is alot of rain, it is perennial and when there isn’t alot of rain, it is intermittent. So how do you decide what the “typical” conditions in the creek are when the rainfall is very rarely “typical”? With no central tendency, how do you decide what set of conditions to evaluate the stream for?

Gerald Browning

Jimy Dudhia (#442)

I was very careful how I worded the discussion about Sylvie’s results.
The results were obtained for multiple cases over an extended period of
days and used mathematical norms of the differences between the forecasts interpolated to observational locations over North America where the observational data is most dense (as opposed to incestuously comparing to model analysis at a later time). I am amused to see that you are shocked.
One of the reviewers stated that “we knew all of this”, but obviously that is not the case (this is a standard reply by someone wanting to hide something).

I also again point out the fact that a simple change in the CMC assimilation program according to “toy” theory had a sufficient impact on the forecast to surpass the accuracy of the NOAA NWS global assimilation and model package.

Why do you think that Christial Page wrote his new manuscript supporting our balancing method for mesoscale storms. The WRF model will have
considerable difficulties using that balancing method because of all of the kluges at the boundaries.

As soon as I am able to scan the manuscript, you can read the results for yourself.

Have you read our discussion about gravity waves? Evidently not.

Where are the multiple cases on consecutive days for the WRF forecasts with errors computed as Sylvie did? Talk is cheap. Quantitative analysis speaks for itself.

Jerry

Jim D

#12 Jerry
The technique you describe, comparing against radiosondes, is a standard one. NCEP uses this
routinely to evaluate its models. I put a link to their site at the end of this post.
Could it be that when the reviewer said “we knew all this”, he/she was referring to the
finding that adding data improved the forecast, in which case I wouldn’t be surprised either.
The findings also point to major deficiencies either in the model or initialization system
used for the control run, and the CMC should have been embarrassed by such a result. Anyway, I want
to see that paper, because it just doesn’t sound right.
I don’t know the Page method you mentioned, but I don’t see how balancing storms relates to
the boundaries unless those boundaries are far too close to the area of interest for comfort.
Usually we keep domains large enough that boundary effects are reduced in the area of interest.
http://www-ad.fsl.noaa.gov/users/loughe/projects/NCEP_verif/

Steve McIntyre

may I suggest that bystanders who are unfamiliar with numerical analysis issues bite their tongues and remain bystanders on this thread? Go to Unthreaded.

Filippo Turturici

#13: Henrik Svensmark, of the Danish Space Reasearch Institute, estimated the influence of cosmic rays in recent years warming by a variation in cloud cover of about 3%, causing an heat flux increase of 0.8 to 1.7 W/m^2.
http://www.dsri.dk/~hsv/

Steve Sadlov

RE: #14 – “Usually we keep domains large enough that boundary effects are reduced in the area of interest.”

Please expound on this. Reduced by X in an area (more properly volume ) V. Do you know what X and V are? Sort of curious to see your characterization of what you think might be the range of magnitudes. Please advise.

Gerald Browning

Jimy Dudhia (#14),

The errors computed in Sylvie’s manuscript are relative errors, not absolute errors as cited in your link. Unless the general reader knows the magnitude of the fields at various altitudes, it is very difficult to determine what is actually happening. But with relative errors, it is trivial for the general reader to see the magnitude of the problem at each level (as you shall soon see). That is why we were able to diagnose the main contributors (forcing and data) to the forecast errors very quickly.

The lower boundary layer parameterization was the only parameterization that was crucial in the time frame indicated. It was quite interesting to watch the error in the lower boundary layer parameterization pollute the forecast as time proceeded.
Only because the winds at the lower boundary were small compared to the jet stream did the problem not have a faster impact.

I mention that Sylvie was quite surprised by the results, but at least
she was willing to run the tests and write an honest assessment. She also presented the results at CSU and at a Canadian conference so must have felt that there was substance to the manuscript. Clearly the results had an
influence on CMC thinking and they (Page, Fillion, Zwack) are moving forward.

I also mention that in Sylvie’s presentation, she showed that the CMC model produced as accurate a forecast as the ECMWF forecast during the period cited, i.e. the Canadian model is just as good as the often quoted best global model during the period cited. Another one of your bogus arguments.

If gravity waves are important to the mesoscale forecast and the
dscontinuous forcings that have large relative errors are generating
incorrect gravity waves, how can the forecast be correct?

And how far must you move out the boundaries. Our analytic theory shows that gravity waves generated by mesoscale storms O(100 km) are O(1000 km). The point of a limited area model is to decrease the mesh size in a smaller area to resolve the smaller scales, e.g. a thunderstorm. If you must move out the boundaries (the new method to trim the contour plots?), what has been gained in terms of computational resources. Have you parallelized the code to make up for the waste of resources.

Jerry

Steve Sadlov

FYI:

Western US 500mB T Bias and Correlation

Gerald Browning

Steve S. (#20),

I just read your excellent question after I had responded to Jimy
Dudhia’s message. Thank you for raising the issue and I hope my response to
Dudhia helps to answer that question. If a small scale storm or a squall line of storms intersects one of the lateral boundaries on the boundary of the forecast region, then there is a serious problem because it will not be present in the large scale data. Unless the forecast region is changed all the time to account for this problem (a pain and might not even be possible), the error in those storms at the boundary will have an impact on the forecast. Errors at the boundaries can be quantified in mathematical terms for the slowly evolving solution in time and a demonstration of their impact has been published.

Let me know if my answers have been sufficient.

Jerry

Gerald Browning

Steve S. (#24),

Is there a description on the RTVS site how the errors are computed?

There should be a complete description somewhere on the site discussing
that.

Why do they not plot the relative errors at all levels as a function
of time as Sylvie did? The most important variable is the vertical component of vorticity that is not mentioned.

And it should be possible to look at a particular variable at a given level
and compare it to observational variables and other models at the same time.

Then it would be a lot easier to understand the problems.

Jerry

Paul Linsay

A bit off topic, but related to boundary values. Climate is supposed to be a boundary value problem and weather an initial value problem. I’ve never understood the distinction for a fluid system like the ocean or the atmosphere. Boundary value problems always mean to me solutions that are time invariant, yet all but the simplest and most viscous fluids don’t show that. I’m slightly aquainted with Taylor-Couette flow, the flow of a fluid between two rotating cylinders. At very low rotation speeds the patterns are “static.” But turn up the angular velocity some and the flow patterns become very complicated and are history dependent, i.e., depend on initial conditions as well as the boundary conditions of rotation speed and geometry. Why shouldn’t the earth’s fluid fields behave in the same way? In some sense the ocean and atmospheric currents are Couette flow on a very rough sphere.

Steve Sadlov

May 1998, Sunnyvale-Los Altos CA, F2 and F1 – Food for thought?

A meaty case study. Approaching the current limits of understanding.

Gerald Browning

Steve S.(#31),

After seeing how the site is biased and undocumented, I did not go any further. But I will take a second look at ground level just to see what they did there. Note that Sylvie’s adjustment to the data assimilation program provided an increase over the NOAA model at ground level.
That has decreased over time as the word spread.

Jerry

Gerald Browning

Steve s. (#31)

I tried to compare the two (GFS and RUC ) at the surface. Same problem.
Are we getting suspicious yet?

Jerry

gb

Re # 19.

I still don’t get it. Why are you insisting on inviscid simulations? Neglecting eddy diffusion doesn’t seem physically correct to me. On this point I agree with Jim I think. Neglecting eddy-diffusion in a large-eddy simulation leads to bad predictions, this has been reported many times. Parameterization of eddy diffusion is thus essential.

Jim D

(note I may be not posting again for about a week as I will be on travel)
I am still confused as to what Jerry wants to show with a WRF model run.
Clearly the model is doing realistic forecasts, and it can do any idealized case too
without any tuning. What else is there to show? He seems to be casting very vague and dubious
aspersions without showing a convincing argument against the dynamics or numerical methods.
Also, if people here don’t even trust NOAA to evaluate their forecasts properly, what hope
is there? Don’t you think they have any oversight given that they provide a public
service? Why should the American weather service be any less honest than the Canadians
or Europeans?
Regarding boundaries, as you see in the link posted in my previous message, the
domain goes from the Rockies west of Utah to the east coast, but the area of interest is
Tornado Alley. Here the boundaries are sufficiently far that systems developing to the west
that might generate thunderstorms in the central US, develop mostly within the
domain rather than being fed in through the boundaries, as they would have been
if the west boundary was too far east. Boundaries are necessarily of low space and
time resolution, so we need the model to be able to develop hi-res features after
the air has come into the domain.
Finally, I am confused by all the issues that are conflated around Sylvie Gravel’s paper.
I now believe, having seen what the BDT idea is about, this is about the improvement of a poor initialization technique
that could easily have degraded a global model. Data assimilation, numerical methods, and physics are side
issues when the dynamics is poorly initialized, because you get basically a very noisy forecast
that would even be visibly rough looking at standard fields like 500 mb height. I suspect
this was the case, and the gain came from reducing the noise level.

Gerald Browning

Jimy Dudhia,

When you run some verification tests on the WRF forecasts exactly
like Sylvie did, then I will discuss the issues with you. Otherwise from now on I will ignore your comments because you are just wasting my time
with verbiage.

The great web site that you suggested is not documented and does not compute relative errors at all levels. Surprise, surprise. The humorous thing is that the group that developed that web site was formed when I was at NOAA and they still haven’t computed the right items (for the reasons I have indicated).

And you never did address the issue of gravity waves generated by forcings that are in error. If they are important as you stated (the reason that the
unstable numerical method you use is suppose to be so great), then what happens when the model generates the wrong gravity waves thru forcing errors. Oops. And those waves have been shown to have scales on the order
of 1000 km, the size of the middle portion of the US. Small problem.

Talk to you when you provide some quantitative results. Meanwhile I need to
find out how to scan in Sylvie’s manuscript for discussion.

Jerry

Gerald Browning

Jimy Dudhia (#41)

If you use your example and switch to 24 hours, the RUC model data is not available. Then switch to vector wind and the SRF data for the
NAM model (whatever that is) is worse than the global model.
As I have said many times, the models can be tuned to produce results, but how physical they are is open to question.

And the lay person can interpret relative errors (percentage error)
like Sylvie used. Then things can be understood.

I wait for your WRF relative error forecast plots (that will never appear).

Jerry

gb

Re # 43:
Jerry, the point is this: Assume the motions are governed by the Navier-Stokes equations (so we don’t have to worry about density fluctuations). In the atmosphere a broad range of spatial and temporal scales are present (be it turbulence, gravity waves etc.). Atmospheric models are never able to resolve the whole spectrum of scales (as we agree on). This implies that atmospheric models do not directly solve the Navier-Stokes (as in DNS) but in fact the filtered Navier-Stokes equations (as in LES). To see what is really solved we have to take the Navier-Stokes equations (or better the nonhydrostatic equations) and apply a spatial filter. So let us assume we have a spatial filter (I will denote it by [.]) which doesn’t touch the large scales (larger than the grid size) but takes an average over the small unresolved scales (the so called subgrid scales). The result of the filtering are the Navier-Stokes equations again in terms of the filtered velocity and pressure [u_i] and [P] plus an additional term: the partial derivative of [u_i u_j] – [u_i][u_j] which is called the subgrid stress tensor (sorry, I don’t know how to use Latex here). The filter must satisfy some conditions. All this, including the filtering, can be found in any recent text book about turbulence. The point is that the subgrid stress tensor is not zero but gives a contribution and has a clear physical meaning. It is the effect of the unresolved scales on the resolved scales. Simply putting this term to zero is not correct. It has to be taken into account, i.e. parameterized, in an atmospheric model so far I can judge. Whether or not it is parameterized in an accurate way I don’t know but it should be there in a model. Perhaps you could discuss how to deal with this term or the other unresolved subgrid motions. I can imagine that a jet in the atmosphere generates a lot of shear and commonly this produces a lot of turbulence and thus a large local subgrid contribution. Having quite high viscosities near a jet might be very realistic and physically correct.

Gerald Browning

All,

Kinkos has scanned the draft manuscript and converted it to pdf format on a CD (not perfectly, but it is possible to read the text and view the plots). I have included one extra plot to show the improvement of the Canadian global model compared to the NOAA global model at 36 hours. This is not during the period when the work was completed (the improvement was even more dramatic then and I also have that plot if interested), but it is sufficient to show how a bit of theory has a much larger impact than all of the other ad hoc tunings of the forcings in the models. Now I just have to find the best way to post the pdf file on the web so it can be accessed and discussed by those interested.

Jerry

Gerald Browning

gb (#46),

It has been shown analytically and demonstrated with convergent numerical solutions that incompressible NS turbulence models that do not properly resolve the scales of the solution will not produce the correct solution.
Any subgrid scale methods can be checked against the correct solution in 2D. I know about ad hoc dissipation and am not interested in that topic.
Please do not repeat the same argument again until reading
the references by Kreiss and his students, e.g. in the SIAM
Journal of Multiscale Modeling and Simulation. Then I am willing to discuss the issue in more detail. Thank you.

Jerry

Gerald Browning

David (#51),

Will give it a shot later this evening. I look forward to your comments
and a lively discussion with all interested parties on this thread.

Jerry

Gerald Browning

David Smith (#51),

Can a link be formed to the pdf file in a folder on esnips
or must each reader download the manuscript from that site?

How does that site compare to the google document site?

I have also asked Steve if he would like to add the copy on his web
server.

As soon as there is an acceptable solution to everyone, I can
post the manuscript.

Jerry

fFreddy

Jerry, what user name did you sign on to esnips with ? And did you use any tags on your upload ?

Gerald Browning

All,

Steve M. has graciously consented to post the manuscript on his site.
I sent him a copy this evening and hopefully it is not too large for the e-mail system. Once it is posted, I will add a bit of background and answer any and all questions. I believe the manuscript will settle a number of issues and look forward to hearing your comments.

Jerry

Gerald Browning

All,

Steve M. has kindly posted a copy of the draft of the manuscript at

Jerry

Gerald Browning

All,

The url is

Click to access browning.pdf

Jerry

Gerald Browning

All,

Strawman summary of results:

a) For short term, large-scale forecasts a very simple dynamical model suffices.

b) The radiosonde and aircraft wind data can be used in an analysis that involves only simple interpolation and provides adequate results compared with the more complicated assimilation schemes in current use.

c) Based on the above two facts, a supercomputer is not required to obtain a comparable forecast for the periods indicated.

d) Forecasts from longer time periods that depend on parameterizations are obtained from extensive (and expensive) trial and error experiments that may or may not be physical. For example, relative errors in the boundary layer parameterization grow significantly as the forecast proceeds. This particular problem and others are masked by the periodic updating of the NWP model with new observational data every 6-12 hours.

e) The large-scale forecasts can be used to provide boundary conditions for limited area models with the following caveats. The smaller scale features are not sensitive to errors in the large-scale forecast (unlikely). Gravity waves in the large-scale forecast do not have an impact on the small scale features and gravity waves produced by small scale features in the limited area model, if important in triggering other storms, are generated correctly (unlikely) and interact with the boundary data properly (unlikely).

f) This periodic updating is not possible in climate models and they use very crude parameterizations with O(1) relative errors.

Comments on any of these strawman conclusions are welcome.

Jerry

Gerald Browning

bender,

Thank you for being patient and waiting until Sylvie’s manuscript was made available for everyone. Hopefully this manuscript has made a number of issues clearer for everyone. I also hope that everyone can see the benefit of having quantitative results available to resolve issues without
the need for excessive verbiage. Steve M’s analysis of MBH results
were sufficient to hold up to criticism by the hockey team and the NAS panel for exactly the same reason. Steve M. is well aware of the backlash
when pointing out questionable claims. I admire his tenacity, sense of humor (that I lack), and his brilliance.

Jerry

Dave Dardinger

re: #67

Well I read most of the paper and skimmed the rest, but I’m not experienced in modeling so I don’t have anything partiularly to contribute. You may have to wait till Jim D gets back to get much of a response. Though you never know around here when someone will speak up.

Jim D

Jerry,
I am now back, and will take a look at the manuscript within the next day, and get back to you on that soon.
I am not sure why you don’t trust the verification page I posted, so I will see if I understand
what it is you are asking for from the paper. (the RUC forecast only runs 12 hours, so that is why
you can’t get longer verifications for that model).
As we now focus on storm scale, verification tends to be more against simulated radar echoes
than global scale RMS, and I am not in the global verification field. What I showed from NCAR is a forecast
page. Verification pages are usually set up by independent groups from the modelers.

I also want to extend the comments of gb on sub-grid parameterizations. Atmospheric models always
have sub-grid turbulence schemes. These usually activate only in turbulent areas such as the
daytime boundary layer, or highly sheared or overturning regions associated with mountain waves
or convection. Methods of handling these regions range from a turbulent kinetic energy prediction
equation to simpler diffusion coefficients based on local shear and stability. In addition,
many models have numerical diffusion schemes to keep energy from accumulating at poorly
resolved scales near the grid scale. These can be seen as a smoothing of the finer scales.
WRF has numerical methods that allow us to minimize the need for this particular type of diffusion.

Gerald Browning

Jimy Dudhia (#71)

Gee, it seems like we struck a nerve. Sylvie’s manuscript agrees with all of the “toy” theory that you have never read and I doubt can even comprehend. Her manuscript is more honest than anything you have said or done.

While you were gone I looked up your publications. Without a model to tune,
you would be in bad shape. You have never written an analytic (model independent) manuscript in your entire career. That is why you are so adamant in defending your heavily dissipated and smoothed models.
This approach has become known as soft science and is a disgrace to the great theoreticians of the past.

I await an honest assessment of the errors in your forecasts. I surmise that it will never happen.

Have you called Roger Pielke Sr. yet.

Jerry

gb

The discussion appears to be about weather forecasts now. However, the topic here should be climate modelling and climate projections. Calculating L2 norms or related quantities perhaps make sense for short term weather forecasts but are I think irrelavant for long term climate simulations because of the limited predictability of the dynamics.

Jim D

Jerry,
I gave my opinion, and would be glad if someone else in atmospheric modeling (outside NCAR, if you want)
took a look at the paper, and at my opinion, and checked for biases. I only stated
well known facts, and noticed that none of them were disputed. If I was reviewing
that paper, I would have asked for those additional plots, and the main argument of
the paper would have crumbled by itself. How can a claim be made that a model
with neither rainfall or a diurnal cycle is almost as good as one with them?
It is mind-boggling to people in NWP (and, yes, I am firmly and unapologetically in NWP),
and it is clear why an NWP-focused journal rejected it.

The data assimilation part of the paper was basically data impact tests with nothing new
proposed. I don’t see the connection with the CMC vs US scores attached at the end, or
how you claim credit for them. Surely the Canadian model uses physics to get these scores,
thus disproving the point of the paper.
For gb, the connection to climate here is the physics. Jerry seems to be saying
physics is not needed, I think, but I am not sure.

I am not sure why you keep referring me to Prof. Pielke Sr. I only raised
his name as an example of someone involved with the RAMS model, which uses the very
same NWP techniques that you seem to have rejected, and it would be more appropriate for
you to settle your differences with him than me.

Gerald Browning

After many of our theoretical manuscripts on the BDT had been rejected
by reviews quite similar to those above (but eventually published
because the mathematics could not be overcome) and with claims that
the global models and assimilation systems were doing so well, I had begun to write a global spectral model based on the multiscale system to determine how well an unforced, multiscale model would compare to the current hydrostatic spectral models. The model was already producing quite reasonable results (in particular fronts formed by the convergence of characteristics) when Sylvie came to visit
She saw some of the results and appeared quite concerned. Her visit was intended to learn more about the BDT so we started down the path
of the manuscript to determine what forcings and data should be initially added to a new model based on the BDT. There was obviously considerable concern at her organization, but Sylvie made the runs (she also met Heinz while here). At the end of the exercise, she presented the results at CSU (announcement available) and at a conference in Canada. Can someone explain to me why she would do that if the manuscript was incorrect or why her organization would pay for her meeting expenses? Or why Sylvie participated in Christian Page’s new manuscript
(available in draft on American Meteorological Society web site under
PTA and to appear shortly.) Note that Page’s manuscript was not given to an Editor at NCAR but to one at NASA and was accepted. Feel free to ask CMC or Sylvie if the manuscript is correct as stands. If not, she spent over a year running extensive tests and using considerable computing resources leading everyone on including her bosses. I don’t think that Sylvie would do that. In fact Sylvie’s significant other is Ted Shepard, the Editor of JAS. Clearly he knew exactly what we were doing and never disagreed
with any of the findings. Is he also dishonest. I think we all know where that label lies.

Jerry

fFreddy

Re #79, Gerald Browning
Yes, please. Also, a list of acronyms would be very helpful.

fFreddy

Re #81, thanks. BDT is defined in #75 as Bounded Derivative Theory. Any idea on NWP ?

Steve Sadlov

I think it has been shown (oh, dear, here we go) via social network diagrams that NCAR and The Hockey Team have massive overlap.

Gerald Browning

Steve S. (#84),

Steve M. has had considerable “interaction” with a number of the “scientists” from NCAR. His experiences have essentially been the same as mine. IMHO more about unverified modeling results than great science. And lots of fine verbiage with no substance or content.

Jerry

Jim D

Jerry,
Please read a book on mesoscale modeling (Cotton and Pielke at CSU have both written them),
and then explain to me what aspects of this kind of modeling you don’t like. Do you think they
live by tuning the physics, and inventing forcing terms? Please give your opinion on their RAMS model,
which shares a lot of the same basics with WRF and MM5 that you have been criticizing. I have a lot
of respect for these two scientists whose life’s work has been in developing the atmospheric modeling field
to where it is today.

Why do you keep saying the page I posted in #14 doesn’t verify other levels when it does?
(clue: hit the Level menu). What is wrong with verifying against soundings like it does?
As for the RUC model, they only run 12 hours because the purpose of that model is to provide
hourly analyses in real-time, and their scope is short-range to avoid overlap with the
scope of the NAM which is up to several days.

Thanks for the history of the paper, but I remain skeptical (I am allowed to here, aren’t I?),
and all my questions stand.

Gerald Browning

Jimy Dudhia (#88),

Do you believe the curves on the CMC website that compare the errors in the various international models at 48 and 120 hours for the wind data? (Figure 3d with definition of measure given in decription of plot):

How does the root mean square vector wind error compare with the l_2 error of the difference of the forecast and observations of the vector wind?

Jerry

bender

Is the percentage error a secret?

Shhhhhh!

Gerald Browning

Jimy Dudhia (#93),

Baloney. The very fact that you said that Sylvie’s manuscript would
have been rejected, but you are unable to understand the results states very clearly that the manuscript did present something new (at least to your fine group). And the fact that the “statistic” that you asked for is not even a mathematically defined measure of the error between different functions says even more. Then you have the nerve to state that the RTVS site is meaningful when a reader cannot decipher what the errors really mean, does not separate out
the main contributors (forcing and data) to the accuracy of the forecast. and does not indicate that the large-scale forecast can be done with a PC. I think you have lost your scientific credibility (if you ever had any). And I would hope that the general reader on this site starts to wonder how their taxpayer funds are being spent.

Jerry

Gerald Browning

All,

I asked Jimy Dudhia if he believed the error curves on the CMC web site not to choose the best tuned model (that is well known – it is the ECMWF model), but to explain to me how to interpret the percentage difference between the errors in the models at 48 and 120 hours using only the root mean square error. Also to explain the percentage error in any model at either times using only the root mean square error.

Jerry

bender

But gavin at RC told me that parameterizations were not an issue. That the problem of parameterization was not under-constrained. Implying that the various parameterizations are in no way overfits.

And yesterday gavin at RC pretends not to understand the need for calculating the overall error associated with an inferred parameter. He gets all huffy at a reader who suggests Hansen’s models, as good as they are, need improvement before he is convinced.

Sorry. I am way OT and ranting. I just wish someone would show how error propagates through a GCM parameterization, from the “known” physics to the unknown/inferred physics. Instead, I see denial and cover-up. “What error?” “You don’t know what you’re talking about.” Of course I don’t know what I’m talking about. That’s why I’m asking questions!

Steve Sadlov

RE: #97 – It’s been a few years (more like decades – LOL!) ….. my main use of continuum physics wayyyyy back in my own academic days, was for geophysical apps. Heat flow, seismic reflection prospecting, etc. I recall we used ERF and ERFC. I need to crack the old books. This is a fascinating thread.

Steve Sadlov

RE” #101 – “Known” should have been “know.”

Jim D

Jerry, (#94-#97)
The mathematician’s perspective (which is clearly where you are coming from) is very different
from that of the physicist in looking at model outputs. The people on your list (#95) that I had heard of
were in the field of numerical methods, but none of them did physics as far as I know.
You probably know that numerical weather prediction is a combination of numerical methods with
physics, and all your complaints seem to point to a lack of understanding how physics
is implemented in models. Physics is based on equations too (thermodynamics, radiation, turbulence,
and more complex systems associated with microphysics, cumulus parameterization and vegetation effects).
An NWP model is a combination of all these mathematical sub-systems. The reason we use computers
is because there is not way to study this interaction purely mathematically.
Why wouldn’t you want to know whether your forecasts have a cold or warm bias? This would be a
mathematical, not physical, perspective.

Percentage error is also somewhat less useful in atmospheric science. For example we prefer to
know if the temperature has a 1 degree error than a percentage error of 0.3% if you use the
absolute temperature scale. You just get more of a feel. Likewise with geopotential height there is
a very large background value making percentage errors quite small. Physicists prefer to see
errors with physical units. One area we use percentage error is in rainfall bias, where it
is useful to know if a model produces 10% too much rain over a domain.

On the subject of convergence tests, we’ve been over this before on this thread. The way
to do a convergence test is to know the correct converged solution as the scale gets smaller. The
real atmosphere has such a high Reynolds number that models can’t test all scales down to
molecular viscosity for convergence. To do that you would need a model that could
represent motion on scales over at least five orders of magnitude, which is not possible
on current computers. So what is done instead for these tests is to reduce the Reynolds number
so that convergence can be achieved with current computers. The method they choose is to
select a physical viscosity and keep it fixed as the grid length is reduced. This shows
convergence.

Gerald Browning

Willis (#99),

Exactly.

Jerry

Gerald Browning

Steve (#103),

There has been a general decline of science and I blame some of it on the misuse of computers. Code up a model and write a manuscript.
It is disheartening.

Heinz once said that we needed to start a journal called
Numerical Modeling without Tricks. 🙂

Jerry

Gerald Browning

Jimy Dudhia (addendum),

You seem to have forgotten that I worked on those “glorious” climate models at NCAR for a number of years and you might want to look at the manuscript
on microphysics that I wrote with Chungu Lu. I am well aware of the
“physics” in these models and the crudeness of the assumptions is pathetic.

Jerry

Pat Frank

#98 — right on, Bender. I’ve also been asking to see such things for a long time. I’ve searched the literature for a published study of total physical error in GCM projections, and found none. I asked Lindzen if he knew of any such study, and he replied that to his knowledge, no such study had ever been done. Everywhere in the physical sciences, errors get propagated through the relevant theory and the reliability of a prediction is judged in that light. But not in GCM science. There, prediction is latter-day divine revelation. It’s prima facie true, and you’d better believe it.

Jim D

Jerry,
#111. First of all, I do not do this in work hours. Friday was a day off, and I use my home computer.
#109-#110. I don’t know why you want a percentage error from the CMC data, and besides,
for a vector wind error, what would you use as a mean to divide by? Obviously they
don’t produce percentage errors because that is not as useful a quantity as absolute error.
This is standard in the field so that people can compare results with each other.
If you want a percentage error from RTVS, you can just find a mean from climatology and divide by it.
As far as physics goes, the models are only getting close to real weather and climate
because they have physics, and your manuscript (Gravel et el.) would have demonstrated that
if only you showed the lack of diurnal cycle and rainfall that resulted without physics,
or tried to verify the same set-up in the tropics or the US convective season where the lack
of physics would have led to more immediate dynamical errors.
If you worked in physics, you should know that the basis of physics parameterizations
is the knowledge of the processes. For this knowledge we rely on the scientists who
work in the various fields (radiation, microphysics, land-surface, turbulence and boundary layer),
and develop parameterizations. Yes, it is difficult to bring all these parameterizations
together into a model, but each modeling group has taken that on, and with success as
demonstrated by the journals that are full of verifications of these models if you just
look for them. A model that does not verify well does not survive. You are going to say
that the models are tuned to verify well, and it may surprise you that I agree, but the
disagreement is that your perception of tuning is that the physics is somehow grossly distorted,
while mine is that the tuning is minor and within the uncertainties of the processes,
requiring some physics insight, and not just blindly turning knobs. Very few parameterizations
work perfectly first time when put into a full model. So call me a tuner, but there is expertise in that,
because to get it right requires a knowledge of how everything interacts in the model, which is
50000 lines of code, as well as the counterparts in the real atmosphere, and don’t belittle the tasks
faced in developing full-physics models.

Gerald Browning

Jimy Dudhia (#1110,

I apologize for the assumption that you replied from work.

Because you have hinted that it is possible to know the percentage error from the absolute error, please provide the relative (percentage) errors for the CMC curves or the RTVS information. Is the general reader suppose to know how to translate the absolute error to a percentage error?
It is trivial to provide the percentage error – why not do so?
Clearly a case of obfuscation. Note that the percentage errors in Sylvie’s manuscript are as high as 70-75% in the winds at the lower levels
at 48 hours for the operational model. Thus the vorticity for any boundary conditions for a limited area model at these levels would be nonsense. How is the small scale vertical component of vorticity determined in your WRF initial conditions when it is clearly not present in the large-scale observational data or in the initial conditions from the large-scale model? What happens if the small scale storm is already present in the limited are domain at the beginning of the WRF forecast?

Norms do not require a mean and if the model is coded properly, the mean pressure (or geopotential) should be removed from each level in order to avoid problems with steep topography. Also if the model and obs are close, the mean should cancel out unless the model is way off. By computing the relative errors at each level, the mean is allowed to change with height, i.e. an even more compelling reason to plot the percentage errors as a function of height.

Because your model is doing so well, please provide the percentage errors for it as a function of height for multiple forecasts as Sylvie did. A simple way to resolve this.

If you read our manuscript or Page’s, you will see that you only need the vertical component of vorticity and the total heating to determine the slowly evolving solution in time. Thus no model run is needed if you have the wind data from a storm – all you need to do is play with the million parameters in the well known microphysics until the remaining variables match the observations. Of course there might be more than one set of parameters that works. How many hours of computer time would that take
you in your current mode?

The errors in the tropics are terrible because the model solution is so dependent on the total heating that is poorly parameterized and there are very few observations in that area. Sylvie states very clearly that we chose the winter time because that is when the large-scale motions are typically the most important and we chose the most observationally dense
area so the errors could be computed with some reliability. If the models are having problems in this best case scenario ….
We also provided horizontal plots of the vorticity just to ensure that the percentage errors were providing correct information (as they clearly are
just as the mathematics states they will).

I continue to wait for the percentage errors as a function of height from
your model. Anyone can publish a single case study where they can tune
the physics to provide something that looks like the obs. Let us see
how it works on a tougher “toy” case or in a predictive setting for a consecutive period of days.

Jerry

Jim D

#115 C_G_K. Thanks for your comments on tuning. I certainly concur with what you said
about weather prediction models, and we have many cases on which to base the statistics
when the models are run daily in forecast operations. For climate models, it is a valid
question that past climate represents basically one case to tune the model to, but that
case has lot of data because it covers the last century, so in some ways it is also
quite constrained. Now the question is whether by fitting past climate we can guarantee
fitting future climate. This comes down to how much we understand about the changes
occurring, particularly with greenhouse gases, and their impact on the climate system.
The consensus (and I know people here don’t like that word) is that we do know enough
of the climate feedbacks to have confidence in the projections, and the physics of
the climate system has no surprises in store for us. This is justified because in terms
of the extra energy CO2 adds to the system, the changes are incremental rather than
destabilizing in the short term (less than a century), so the predictions of even simple linear
models are not far off.

Jim D

Jerry #116,
I forgot to answer this part

Thus the vorticity for any boundary conditions for a limited area model at these levels would be nonsense. How is the small scale vertical component of vorticity determined in your WRF initial conditions when it is clearly not present in the large-scale observational data or in the initial conditions from the large-scale model? What happens if the small scale storm is already present in the limited are domain at the beginning of the WRF forecast?

We use the primitive equations, so momentum is the boundary condition, not vorticity. It is
correct that small-scale vorticity is often not present in initial or boundary analyses
if it is associated with an unresolved storm like a convective system, but usally the analysis
has enough other clues (instability, convergence boundaries) for the model to generate its own within a few hours.
This only becomes a big issue in short-term forecasting (1-6 hour range), where they
have to rely on cycling model information from previous forecasts with newer data (data assimilation).

Reid

Re #121: Jerry comments “Are we to suddenly believe this model is any better given the lack of any legitimate verification by a PDE analyst, a numerical analyst, or common sense. You aren’t fooling anyone.”

Unfortunately, he is fooling the vast majority of scientists. Willful ignorance is the order of the day.

Gerald Browning

Reid (#122),

Hopefully this thread and the one before have raised some eyebrows.
All my arguments have been backed up with mathematical proofs and supportive numerical examples using convergent numerical solutions.
Even the CMC model supports my arguments. And Jimy has done nothing but spout nonsense exactly as expected. I think you can see why the peer review system has major problems. If Jimy were able to be an anonymous reviewer
with a biased Editor, Sylvie’s manuscript would have been rejected just like many of our mathematically rigorous manuscripts would have been without major confrontations.
At least this is in a public forum where Jimy can’t make his statements without me being able to show the game he is playing.

Jerry

Gerald Browning

For those interested in the party line of the AMS see the draft statement
under the AMS web site called Weather Analysis and Forecasting.
Compare with the percentage errors in Sylvie’s manuscript.

Jerry

Gerald Browning

Sorry about the multiple signatures. I always want to make sure that
my posts are signed the same way and just didn’t see the ones below the comment before I posted.

Jerry

bender

Parameterizations are whole sets of parameter values. Some parameters are more fixed than others because there is less uncertainty about their true values. These are the ones that can be justifiably tweaked. Gavin Schmidt assures me there are only 3-4 of these. Maybe he’s talking about the assemblage of modules, as opposed to what’s available for tweaking withing individual modules. I’m not sure, but his answers are always unsatisfactory, smelling of obfuscation.

Is Gavin Scmidt honest?

MarkW

Being able to successfully hindcast historical climates (even if the models could actually do this) is not proof that the models will be able to successfully forecast future climates.

fFreddy

Re #133, Gerald Browning

you might first want to peruse the manuscript by Chungu Lu et al. that discusses the typical microphysical schemes I mentioned earlier.

Sure. Is there anywhere I can download it from without learning Chinese ?

John Baltutis

Re: #134

A google search for Chungu Lu and Browning and further digging found this: Scaling the microphysics equations and analyzing the variability of hydrometeor production rates in a controlled parameter space, a pdf file.
Hopefully, that’s the one Jerry referenced.

Gerald Browning

John (#136),

That is the correct one. If anyone has any questions about this manuscript, I will be happy to answer them. Scaling the microphysical equations is quite illuminating, especially when there are large errors in the winds coming from a global model. If a mesoscale storm is fully developed, there are only 1 or 2 terms that are important and these are related to condensational cooling and latent heating. Before then the so called triggering terms can be completely overwhelmed by errors in the large scale velocities. If you read my
recent post discusssing the lack of the vertical component of vorticity in the limited area domain and the lack of other small scale heating components, you can start to see the problems with a limited area model that is attempting to develop smaller scale features that don’t exist in the large scale initial data. There is a game that is played that I will discuss in more detail. You will be quite shocked how this has been done.

Jerry

Jim D

#131 Tom,
This site has had people showing that linear bulk (global-average) models can predict CO2 warming to
within degree of the sophisticated models, and people respond with glee saying what
is the point of a complex model? Now you contradict them and say that can’t be done.
I was trying to use language people here would agree with, but there seems to be an
internal conflict among CA posters on this point.
The linearity of these bulk models comes about because the energy balance change due to CO2 is small compared to
the energy storage in the atmosphere/ocean system, and compared to the total forcing
by solar and infrared fluxes. The storage acts like a damper, not allowing large deviations
of the surface atmospheric temperature from the ocean temperature in a global average.
Likewise the upper atmospheric temperature is constrained by the surface temperature and
physical laws.

Tom Vonk

#140 Jim

I have begun to post in this thread because the topic (exponential propagation of errors) is one but not the only one issue in the dynamics of chaotics systems such as weather and climate .
Insofar I don’t take position what kind of sophistication would be necessary for a numerical model to adequately predict long term dynamics .
Whatever the sophistication , everything is garbage or to put it in more diplomatic terms of Dan Hughes “numerical chaos” .
In the course of the discussion I realised that you don’t understand chaos dynamics so the point is becoming somewhat moot .
Apparently you can only think in linear terms such as “The linearity of these bulk models comes about because the energy balance change due to CO2 is small compared to ….” .
Such a line of thinking is hopelessly inadequate and wrong for chaos dynamics .
You could spend your life “sophisticating” numerical treatements of a simple Lorenz system (only 3 ODE !) and be flabbergasted how difficult it is to only sort out the problems of convergence , error propagation and sensibility to non physical parameters like the time and space integration step .
Forget about long term predictions time averaged or otherwise in any case .
Of course that there are damping terms in the system , there always are but they don’t make a chaotic system less chaotic .
Of course that some parameters may be bounded that’s what the strange attractors are there for .
Now proving their existence and metrics is something that nobody did and I suspect that it is not feasible for such a complex system .
Like Lindzen says , nobody is able to adequately simulate the “natural variability of the climate” so what is the point to pretend that it can be simulated when only one variable , namely CO2 concentration , changes ?

As long as you believe that a computer run and linear thinking is adequate for the climate system , you will be only dabbling in the dark untill the difference between the numerical long term “predictions” and reality grows to a point where it will be no more possible to pretend that we know everything but only need a couple of billions because we didn’t sophisticate enough .

Jim D

#140 Tom,
I agree that weather is chaotic, and this is a level of chaos that is understood
from the weather record and models. Now to make the jump that climate-scale chaos
will somehow manifest in the next century is the part I don’t go along with. The
disagreement here is the amplitude of the chaos, not whether it exists. The obvious
experiment is to run a weather model for a century with CO2 changing, and this is
what is done. Climate models are just low-resolution weather models with some
additional features to allow for ocean, sea-ice and vegetation changes.
The results show a growth in temperature against the background weather
chaos. I just state the results, and say they seem reasonable to me based on
energy considerations and the atmosphere/ocean system, where we know the primary processes.
I would be very interested if someone finds short-term chaos in the climate,
but no mechanism for such a thing has yet even been proposed as far as I know.
Bear in mind, such chaos would have to include the ocean from energy considerations,
and that has a large thermal inertia.

Jim D

#141, Jerry,
Do you mean the run you asked for in #305 on Part 1 of this thread? It mentions Lu et al.
and a hydrostatic test in #186. Yes, I am confused. I already explained that result for you.

#141 and #143, Jerry and bender,
The WRF model code is free to look at, so you can see the parameters there.
Yes, even gravity and the shape and size of the earth are approximated in models together with
physics, yet the models reproduce the key features of the weather and can be used to predict
weather. It is amazing to me how simple the model is compared to the real world, and
still is so successful. Uncertainties in the model are not as much a limitation as
uncertainties in initial conditions from data. Changing g by 0.1% or using a more ellipsoidal
earth won’t noticeably change weather forecasts, so these are not considered primary
parameters to vary. The bigger model uncertainties relate to how to deal with sub-grid convective
towers, or the fall-speed of ice crystals, or the effects of vegetation and soil on
evaporation, or the effects of cloud on radiation. These parameterizations are continually evolving.
This is where the research is. However, despite all this, when you see a blown forecast
by a global model, it is more likely due to poor initial conditions than a fault of the
model itself. So, now that the models are quite good, data assimilation has become a major
focus for the further improvement of forecasts, and that wouldn’t have been the case if
the models were severely flawed.

Gerald Browning

Jimy Dudhia (#146),

I await the percentage errors that back up any of these claims. Otherwise
you are just spouting nonsense as usual.

The parameterizations in the CMC model overwhelmed the assimilation process
in 24-36 hours (and the CMC global model does better than the NCEP global model).

I also see you didn’t discuss how the soil parameterization
is initialzed nor how the model is able to generate the correct
vertical component of vorticity several hours late in the forecast
(essentially the time scale of these motions).
Just keep sidestepping the issues. You have been well brain washed
by Klemp and Skamarock.

Trial and error to the max.

Jerry

Gerald Browning

Jimy Dudhia,

error (CMC)

Gerald Browning

Jimy Dudhia,

Did you forget to mention the site

http://www-ad.fsl.noaa.gov/fvb/rtvs/wrf/DWFE/model/model_verification_tool_user_manual.html#sect6.0

Evidently there is a site that plots the errors as a function of height.
Where are those errors plotted and why doesn’t RTVS show them?

Jerry

Gerald Browning

Jonathan (#153),

When I was at NOAA FSL, a daily forecast meeting was held in a similar manner. The forecasters tended to look at the global models that have some accuracy for 12-36 hours (because of data assimilation), then at the RUC limited area model, and then would guess. Sounds like you have had a similar experience. Thank you so much for posting.

After everything that Jimy Dudhia said about the RTVS site, I come to find out that at one time they did plot the errors as a function of height,
but that no longer is done. I wonder why.

Jerry

Tom Vonk

Jim # 144
Still more of the same .
All your arguments go like that :
1)
I run a global model for some long term prediction (never mind that it is incomplete and wrong)
2)
I change a variable and run the global model again (never mind that it is still incomplete and wrong)
3)
I look at the difference of the 2 states (never mind that it is wrong too) and if it is small I conclude that the parameter I changed has a small influence .
The above approach is not science because it is not a comparison of theory vs experience , it is a comparison of theory vs theory .
It could have a limited validity if and only if it has been proven that this particular theory (in this case a given numerical model) adequately and precisely represents the reality in all its aspects .
My point from the beginning has been that this proof has not been given and in my opinion will never be because precisely the climate is chaotic on ALL TIME SCALES .
Now as you admit that the climate is indeed chaotic , you have to unwind this thread untill its end .
First and most obviously it is not predictible on the long term (never mind Lyapounov coefficients , you can’t calculate them for this system) .
Second you have pseudoperiods at all time scales and associated thresholds .
Third you can never say when one of the multiples thresholds will be reached , so you can never say when a relatively fast transition will begin .
And with all that somebdoy would want to make a valid long term prediction ?

Short term chaos in the climate ?
All depends what you call by short term .
Top of head I can already think of several examples :
– NINO is an obvious one
– number of large scale extreme events per year is another (or in physical terms energy dissipated by such events per year)
– NAO is an interesting case that is probably interacting with Nino what would yield a certain amount of pseudo periods
– a very prominent case is the arctic ice mass variation – chaotic with badly understood multidecadal cycles superposing on shorter term variations
– average yearly cloudiness variation is not understood but certainly chaotic

To sum it up I’ll quote R.Pielke :

“The claim by the IPCC that an imposed climate forcing (such as added atmospheric concentrations of CO2) can work through the parameterizations involved in the atmospheric, land, ocean and continental ice sheet components of the climate model to create skillful global and regional forecasts decades from now is a remarkable statement. That the IPCC states that this is a “much more easily solved problem than forecasting weather patterns just weeks from now” is clearly a ridiculous scientific claim. As compared with a weather model, with a multi-decadal climate model prediction there are more state variables, more parameterizations, and a lack of constraint from real-world observed values of the state variables.”

Gerald Browning

Fox watching the henhouse,

For those that are not aware of the Developmental Testbed Center (DTC) at NCAR, it is suppose to check new models for their improvement in forecasting. The problem is that it is funded by NOAA and NCAR, i.e. the organizations that are developing the models. I now come to find out that in the website just above, there was a wintertime experiment of the WRF model (just like Sylvie did over 5 years ago). Note that Jimy Dudhia said it was wrong to check a winter case, but WRF in fact did so without reference to Sylvie’s manuscript. I call this intellectual dishonesty of the worst type. On the website I posted I come to find out that RTVS (part of NOAA that develops models) clearly listed many more statistics than on the current web site mentioned by Jimy Dudhia, including ones that shows errors as a function of height similar to what Sylvie did many years earlier. Jimy is also intellectually dishonest because he failed to mentioned he WRF test knowing full well it had been run and then had the nerve to criticize Sylvie’s manuscript for the same sort of test. He is dishonest for failing to mention that the statistic that I wanted to see (errors as a function of height) had been available before and used on the WRF model, but is no longer displayed on the RTVS site he quoted.

I will no longer respond to Jimy Dudhia given his intellectual
dishonesty. I have seen this enough times in his comments and by the same group at NCAR. Enough.

Jerry

bender

Re #147
Thanks for the reply Jim D.

You say:

I am not sure I completely understand the question

I guess I am going to have to keep working at clarifying my question, because I think you’re right. Maybe my question is still too ill-posed.

You say:

models may take some things as fixed (e.g. the Greenland ice sheet) that may actually change, or sea-level or the solar constant, etc.

But when I express concern over “things taken as fixed which are in fact variable” it’s not parameters I’m concerned about being fixed, but circulatory features/scenarios against which model predictions are validated. Tom Vonk #156 seems to understand my question because he makes reference to the kinds of features I have in mind: ENSO, NAO, etc. I’m thinking major features like the ITCZ, and the things that characterize it (vorticity, periodicity, etc.)

So, again: are these features not structurally unstable? My very limited understanding of climate dynamics suggests some of them, to some degree, are. Next, if they are structually unstable then what would this mean for the overfit parameters that are derived through the trial-and-error process that you describe (basically, a genetic algorithm)? How do these seemingly irreducible uncertainties affect estimates of key parameters such as CO2 sensitivity?

That’s about as straight as I can ask it.

bender

Re: Neil Haven #3,

It seems to me the point about the existence of central tendencies is an important one, and one on which we are in nearly complete agreement

Yes, and yes.

If this clashes with anyone’s opinion, I’d be interested in learning how.

I predict that we are about to find out how. For starters:

Finally, models don’t predict specific behavior. What they predict is a certain probability distribution of behaviors – using multiple runs with slightly different initial conditions. This helps to account for uncertainty with respect to initial conditions and determine the robustness of the results. Likewise, multiple models which may assume different parameters or take into account different mechanisms help to determine the robustness of various results.

From one Timothy Chase:
http://www.realclimate.org/index.php/archives/2007/05/hansens-1988-projections/#comment-33257

Gerald Browning

Jimy Dudhia,

Go tune your piece of junk.

Jerry

Jim D

Well, I think this thread ran its course finally. I’ll not be checking in here
so often now, as I have found it to be a drain on my free time.
Signing out.
Jim D

bender

Thanks very much for posting here, gentlemen. Hope to see you again when “Exponential Growth in Physical Systems #3” is open. Have a great weekend.

Gerald Browning

For those on this thread,

I compiled the gnu version of g95 (Fortran 95) last night and will test it on a trial case. According to the g95 group, g95 will compile WRF ( publicly available on the WRF site) and it should run on a Linux or Windows computer. So anyone that wants can run the
WRF model with all of its kluges on analytical or real cases to determine the impact on the accuracy of the numerics of all of the smoothing at the boundaries, filters, divergence damping ( numerical instability) and other games that have been played. Any takers?

Jerry

Jerry

Jerry

Tom Vonk

So, again: are these features not structurally unstable? My very limited understanding of climate dynamics suggests some of them, to some degree, are. Next, if they are structually unstable then what would this mean for the overfit parameters that are derived through the trial-and-error process that you describe (basically, a genetic algorithm)? How do these seemingly irreducible uncertainties affect estimates of key parameters such as CO2 sensitivity?

Yes they all are in reality Bender .
Once it has been admitted that the climate is as chaotic as weather is , you are in for the ride .
One has only to get through the smoke screen of temporal averages , scaling illusions and other non-resolved-yet-well-understood phenomenons to find the good old chaos with all its attributes .
If you don’t admit that what does that mean for the overfit parameters ?
That you produce numbers that show what the models makes them to show .
That means numbers that move somewhere in the phase space and LOOK like climate whereby lacking the characteristic chaotic behavior .
The interesting and absurd result is that if somebody took the pain to go for a 10 000 years “simulation” he’d probably still see a behavior without a trace of unstability or unexpected transitions .

Everybody should read what the people really do with ENSO simulations .
Actually simulation is a quite strong word – what they do is to assume a delayed oscilator (because a qualitative argument shows that such a system if it is extremely simplified would behave like a delayed oscilator) then they add an “atmospheric noise” aka assume that everything else is random and make computer runs .
As your basic model is both bounded and mathematicaly reasonable the output stays bounded and looks reasonable .
The random part creates variability and the oscilator part creates stability .
Of course both the model and the results have nothing to do with the reality but if you do , say , a 200 years run , you get a pseudo periodic curve (f.ex for the pressures) that looks like an ENSO .
Now you can infinitely vary boundary and initial conditions , the randomizing of the “noise” , couple it , uncouple it and generally publish one paper per year .
However all what such papers do is to say in a very sophisticated and costly way what a delayed oscilator with a random component does when certain assumptions are met or not met .
No chance that you ever get in unstabilities or fast transitions – a delayed oscilator doesn’t use to do that .
Now if you were to say “Hey guys but ENSO is anything but a delayed oscilator with noise .” you’d only get uncomprehending stares and a “Huh ? What are you talking about and who are you first place ?”

In a much more complicated manner the climate models are doing more or less the same thing .

bender

Tom Vonk #172
You may be interested in the hatchet job by William Connolley on my comment at this thread at RC:
http://www.realclimate.org/index.php/archives/2007/05/climate-models-local-climate/#comment-33923

I had pointed out how in his essay with James Annan he said that [paraphrase] climate is not chaotic, but then was forced to back-pedal here, in response to comment #27:
http://www.realclimate.org/index.php/archives/2005/11/chaos-and-climate#comment-5396
admitting that sometimes climate is chaotic. I’m not trying to show him up. It just seems to me he and some others may be in denial over the true nature of the global circulation. I’m not asserting this. I’m asking.

Your input in the debate there might be helpful to obtaining a resolution of the issue.

Gerald Browning

bender,

If you are not able to back up your arguments on your own, it seems to me that you should not engage in those arguments and then ask Tom to
fight your battle for you.

Jerry

Gerald Browning

bender,

I do not think anyone knows for sure if the climate is or is not chaotic.
There are certainly areas of fast exponential growth in local solutions
that would lead to large numerical errors of any numerical solution.
In the actual continuum equations those solutions are bounded – just next to impossible to compute accurately. That is why I am so skeptical of
any numerical climate or NWP model if these local areas are triggers for smaller scale storms.

The original equations that Ed Lorenz derived were an extremely simplified version of the interaction of several spectral modes of the inviscid equations of motion and could hardly be called an accurate approximation of the full system of equations. However those equations led to a strange attractor and an entire field of mathematics that analyzed ode’s with strange attractors. I do not agree that Ed’s simple example implies anything about the full system. On the other hand, if the full system
has something similar, it certainly raises disturbing issues. The
presence of large, fast exponential growth also raises serious
questions.

I look forward to hearing Tom’s thoughts on this text.

Jerry

Jerry

Tom Vonk

Bender

Sorry to disappoint you but I am almost physically allergical to “Realclimate” .
I have been there 2 times long ago and had to admit that nevermore .
It is not a place where you can lead a meaningful discussion because people like Connoley and Gavin (to mention only 2) bring out the worst in you .
Their contributions are brimming with agressivity , intolerance and dogmatism – it made me think of what an Inquisition court could have looked like with boiling lead and iron maidens included .
As my living doesn’t depend on scientific publications on the climate field but I have some knowledge about chaotic systems , I prefer to spare me the high adrenaline levels 🙂
That’s why I couldn’t read the links you provided .

As for the question if the climate is chaotic it is almost common sense .
First difficulty is to define chaos – up to now many necessary conditions are known (all of them present in the climate) but nobody can define with mathematical rigor what a sufficient condition would be .
Second difficulty is stochastics and that’s where many people make the jump from weather to climate .
Indeed chaos is all about the trajectory of a system in the phase space .
While this trajectory is continuous and unique , it can’t be foreseen beyond a certain period of time .
However some chaotic systems present one or several strange attractors that are subspaces of the phase space with the property that all trajectories may move ONLY within those subspaces .
So if those subspaces are relatively “small” then despite the unability to predict exactly the evolution of a trajectory you can bound it (in a space with several millions of dimensions) and thus separate the possible from the impossible .
Of course if you have f.ex 2 connected attractors (like an 8) then a system that is in the lower part (f.ex an ice age) can stay there a certain time and then unpredictibly move to the upper part (f.ex a warme age) by a fast transition .
Obviously the climate models don’t do anything like that but when the modellers talk about damping and averaging then without knowing it they postulate that the system is moving within a “small” strange attractor .

Typically the RANS (reynolds averaged navier stokes) is such an approach .
If you take the original N-S and make a change of variable substituting to the instantaneous variable v(t) the sum of its time average over T V(T) and a perturbation term [w(t)] what is legit if v(t) is continuous you get another set of equations .
As the original N-S is chaotic , the RANS are also chaotic so you won nothing .
But your PED has now a time independent term V(T) and the new variable is [w(t)] while v(t) = V(T) + [w(t)] .
Again and it is common sense if v(t) is chaotic then [w(t)] is chaotic too . BUT V(T) being time independent is NOT chaotic .
So you see the opening – if I can say something special about [w(t)] like it is “small” , it is “random” etc then I could get solutions where the v(t) would be the sum of a stationary solution over T and another calculated factor .
Once you have that you go from [0,T] to [T,2T] and redo the same trick .
It works in some simple systems where [w(t)] seems arguably to be more or less random .
That is also what basically the models do – hence the formulations like ENSO = delayed oscillator + noise .
So now even if this is only an analogy based on N-S , when somebody says that climate is not chaotic it translates that the time averages of all parameters are not chaotic AND that the “perturbation” terms are random or negligible or whatever .
To the first it can be said that it is rigorously true over [0,T] if and only if you have the right PEDs .
However the jump to [T,2T] is an initial condition problem and you’d have to check all that Jerry is talking about here – convergence , error propagation etc while not having the right PEDs anyway .
To the second it can be said that it is a boundary problem of the famous unresolved dimensions and their interaction with the resolved dimensions .
It is an extremely complicated problem with preciously few results – the least that can be said is that there is not a magical minimal resolution size above which things matter and below which they either don’t or can be easily parametrised (remember : we know all the physics and there are no surprises in store according to Jim) .

On top of the above what is a mathematical problem (preferably not ill posed) you get a numerical problem that is due to the fact that you can’t even begin to dream to have all the equations let alone solve them so you have to simulate the system numerically .
Wrapped up that translates that you produce numbers that are supposed to converge to an unknown exact solution of an unknown number of equations . Hardly looking like science , does it ?

Last but not least and back to chaos . Jerry has mentioned the Lorenz system that is an easy system of 3 non linear ODEs producing chaos .
Even such a system exhibits unpleasant dependence on unphysical parameters like time and space step and stays hardneckingly unpredictible .
It is not excluded and it is my belief that no physically feasible numerical resolution can converge or even approximate
the exact solution . The reason being that an infinitely small integration step would imply an infinite calculation time what is not physical .
To farther chaos reading I strongly recommend Dan Hughes site : http://danhughes.auditblogs.com/

Tom Vonk

Darn emotes .
In the above read : (like an 8 .) and not (like an 8)

Gerald Browning

Tom

Agree up to the last statement that is a leap in logic. No one knows
the answer because we do not actually know if there is a continuous system of equations that describes the dynamics, physics, etc. of the real climate at all space and time scales. And if there were, as you have stated, it would be heinously complex far beyond the simple system approximated numerically and parametrically in climate models. Over long periods of time, no one knows what simplifications, if any, would be allowed
despite the wishful thinking of the climate modelers. I think this we both are in full agreement.

Jerry

Jerry

gb

Re # 180. Tom Vonk, in # 175 Bender gave links to some very thoughtful comments by Pierrehumbert and Isaac Held, no Gavin or William involved here, so to refuse to read these comments seems a bit silly. Pierrehumbert and Isaac Held are experts in chaotic systems and climate dynamics. I have seen a number of their papers and they have clearly much more knowledge than you haveabout turbulence and the role of chaos in atmospheric and ocean flows, and climate. You might learn something from them. There is clearly chaos on short time scales and perhaps there is chaos on longer time scales, this cannot be ruled out if I understand their comments correctly. However, the key question is how large are the fluctuations? There seems little evidence that chaos will bring about a global temperature change of a degree or more in a time scale of a century, surely not of the same order as what a doubling of CO2 can bring about. Think of a turbulent flow (my field of expertise). Chaos can be present on all scales. However, measurements and simulations show that beyond certain length and time scales the fluctuations are insignificant. Furthermore, the mean variance of turbulent fluctuations is bounded and in fact shows clear scaling behaviour. This is because the chaotic system still obeys physical laws, which you easily forget if you think only in terms of Lorenz equations. Measurements and simulations of turbulent flows (DNS, LES) are possible because the statistics (mean and variance) can be reproduced, in contrast to every realization. So therefore it does not seem so odd to me that long term weather predictions are impossible (of course) but climate predictions are.

By the way Bender and Tom, how do you think that chaos can cause a change in the global mean temperature? The chaos in the ocean and atmosphere does not create or destroy heat. Take a pan of water and stir the water. It will very difficult to predict the flow but I can tell you what happens with the temperature: nothing. The chaos in the atmosphere and the ocean just redistributes the heat. The only way that chaos can change the mean global temperature is by changing the albedo of the Earth, i.e. clouds or see ice. Does that seem likely and will that cause a large temperature change within a century? I just want to mention these point because people here seem to thing that chaos can cause all kinds of magic: it doesn’t. Physical laws are still valid and physics puts some clear constrains on the chaotic fluctuations, also in the climate. That doesn’t rule out that some surprises can occur but that should be a reason to be even more careful about adding CO2 to the atmosphere, not less. However,I have to say that I am not a climate expert so perhaps some people can correct me.

bender

gb,
You, like the zealots at RC, are missing COMPLETELY my point. I, unlike IPCC, am interested in the uncertainty (i.e. error bars) surrounding the estimate of the CO2 sensitivity coefficient – which is derived through parameterizations with certain types of complex models. If those models are structurally incorrect, the error in that model specification propagates through to the parameter estimate. I am NOT saying that chaos creates global heat. Someone else might have said that at some time, but PLEASE stop attributing such sophomoric statements to me. That is an RC trick. I understand the difference between redistribution and rise.

Now, you tell me what the RCers couldn’t: what caused the Arctic warming in the 1930s-40s? Hansen et al. (2007) admit that they do not know, and are ready to give up looking for a regional-scale forcing, factor X. You will notice how that issue was dodged completely at RC? Is it possible that our estimate of the current global warming trend is exaggerated by a modern recurrence of factor X? Yes, it is.

“Where is the heat coming from?” This sounds like Steve Milesworthy. Remember: you have not censused the temperature field. You have sampled it. Incompletely (and highly inefficaciously, I might add). Now, what if the heat bounces around chaotically from areas where you’ve sampled accurately (precious few) to areas where you’ve not sampled or sampled inaccurately (the great majority of land surace, sea surface, ocean depth, earth depth, upper atmosphere, etc.)? What will that do to your search for “global” forcings and your “global” parameter estimates? It will bias them. In short, I am suggesting the CO2 sensitivity parameter may be over-estimated because of SEVERAL reasons, inappropriate model choice and faulty parameterization being just one of these.

None of these issues are on the table however – because the issue of uncertainty surrounding parameter estimates has been taken off the table from day one. If the “experts” would put the statistical issues on the table, it could be discussed by people more qualified than myself. So why is it off the table? Why is it the unmentionable topic? Why is it left to the “unqualified” people to do what the qualified should be doing?

In conclusion: climate chaos is not a hypothesis designed to discredit the models. It is just one of the reasons why climatologists might be hooked on overfitting ad hoc models. Overfit, ad hoc models are error-prone models. Maybe there is some error in the estimation of the CO2 sensitivity coefficient? It is just a question. Why can this question can not be asked without stirring a witch-hunt?

Dan Hughes

Viscous Dissipation of Fluid Motions and Conversion to Thermal Energy

In the previous discussions of chaos, dissipation, and ill-posedness in the comments listed above in this post, there was little mention of the thermal effects of physical dissipation in the fluid motions of interest. I have been looking for information on this subject without much success. I have contributed these notes to a thread at Climate Science (the site appears too be down at this time, I’ll add a link later). Viscous dissipation has also been the subject of this post. To date I have gotten very little feedback of any kind. Maybe all this is incorrect, but no one has said that either. All pointers to literature relating to the following will be appreciated.

To be clear I am referring to the conversion of fluid motions into thermal energy via the viscous shear-stress terms in momentum balance equations. These are momentum diffusion contributions to the momentum balance equations. The thermal energy due to viscous dissipation appears as a positive-definite contribution to the various forms of the thermal energy conservation equation. Viscous dissipation always acts to increase the thermal energy of the fluid. If a temperature representation is used as the thermal energy equation, it always acts to increase the temperature.

Viscous dissipation is a volumetric process occurring at all times so long as fluid motions are present. The process is constantly acting to increases the thermal energy content of the fluid and thus increase its temperature.

In contrast I am not referring to the explicit and implicit viscous-like terms that arise from, and sometimes added to, the discrete approximations to the continuous form of the momentum equations. Somewhat ironically, these terms seem to be frequently labeled as ‘momentum dissipation’. The label momentum dissipation seems to be used in the GCM world more than in other computational fluid dynamics applications. I think it is a good assumption that the viscosity-like coefficients that are used for momentum dissipation are not used to calculated the viscous dissipation contributions to thermal energy equations.

It is of course true that these momentum dissipation additions to the momentum balance equations have an indirect effect of the viscous dissipation to the extent that they modify the velocity distributions and gradients in the flow. These latter are the correct terms for calculating the viscous dissipation.

Modeling and calculation of the viscous dissipation and consequent thermal energy addition in GCM models has a somewhat checkered history. This is due in part to the evolutionary nature of the models and changing application areas. More nearly complete and comprehensive accounting of the components of, and physical phenomena and processes occurring in, the climate system have generally developed over decades of time. Applications to calculations of the thermal history of the planet over hundreds of years has required that the energy-conservation aspects of the modeling be fundamentally sound and theoretically correct. However, a large contribution to addressing the fundamentally sound and theoretically correct model has been the approximations made at the continuous-equation level of the modeling. The momentum balance equations used in the models are simplified versions of the complete equations. More specifically, the thin-atmosphere approximation on a spherical surface, the representation of surface drag, the no-slip condition at land-atmosphere interfaces, the corresponding boundary condition at ocean-atmosphere interfaces, and the decomposition of the velocity into horizontal and vertical fields has also contributed to the problem. While calculations and analyses with the GCM models/codes have been carried out over four or five decades, it seems that only late in the 20th century and early in the 21st century have the problems with the modeling and calculations of the viscous dissipation been corrected in some of the models/codes. Two somewhat recent discussion have been given by ,Boville and Brethron and Becker.

Again this situation is most likely a reflection on the interests in carrying out calculations for 100s of years of time.

It is my understanding that the global-average volumetric viscous dissipation in the atmosphere is calculated to be equivalent to about 2W/m^2 of energy; and I have seen much higher values. I do not know if there are estimates available from measured data in the atmosphere. A very wide spread has appeared in the literature over the years. This conversion of fluid motions into thermal energy has occurred for as long as the present composition and motions in the atmosphere have been roughly equivalent to the present-day conditions.

The standard argument is that this is a small number relative to the other energy-addition contributions to an energy balance for the planet. However, the radiative-equilibrium argument means to me that, as equilibrium is approached few energy additions can be consider to be a small number and neglected. Almost all finite numbers will not satisfy attempts to make 0 = 0. As I understand the situation, the effect of doubling of CO2 in the atmosphere is equivalent to about 1.6 W/m^2 and that the effects of the consequent changes in the thermal-energy state for the planet will be easily measured and observed in time spans of only 100s of years. How can an equilibrium-based approach to descriptions of the thermal-energy state of the planet neglect internal volumetric sources such as the viscous dissipation if they are of the same order as assigned primary imbalances?

I think another important issue is related to the development of the continuous equations used in CGM models/codes. Taken as a whole these equations are known to be incomplete. The basic-equation models for the fluid motions and thermal state are not the complete equations that describe the motions and energy conservation. The all-encompassing parameterizations, many of which deal with mass and energy sources and sinks and interchanges across sub-system interfaces, are ad hoc/heuristic, best-expert-approximations (EWAGs) and thus cannot be assured of complete accounting of the mass and energy balances for the processes that are parameterized. In summary, the continuous equations very likely do not accurately account for the mass and energy conservation that actually occur in the physical system. I suspect it is easily possible for the lack of completeness and complete understanding to be responsible for several W/m^2 difference between the model equations and physical reality.

Is it not possible that the differences between the model equations and the actual physical phenomena and processes incur errors on the order of a few W/m^2. Again this might be a small number relative to the macroscopic energy balance for the planet, but as equilibrium is approached, and the imbalance is accumulated over 100s years of time in a calculation, significant differences are very likely possible. It is an important issue that the level of incompleteness and imbalances in the modeling at the continuous-equation level, relative to physical reality, must be significantly less than the physical imbalances that are driving the planet toward a new equilibrium state.

Finally we come to, as we always do, the fact that the numbers are the results of numerical solution methods. In order to ensure that strict accounting and conservation of the energy distributions within the system requires extremely close attention to how the numerical methods are developed and implemented. An example of how easily it is to overlook important details is given by the usual practice of numerically integrating different parts of a model system using different time steps. A related issue is calculations using parallel-computing capabilities by various approaches to domain de-compositions. Exchanges of mass and energy at interfaces between subsystems presents another opportunity to overlook mass and energy conservation requirements. Generally these must be evaluated at the same time-step level in order to ensure strict conservation.

It is important to note that while there are many ways to account for the mass and energy conservation of a given calculation, this process in no ways ensures that the calculations are in accord with and reflect the actual mass and energy balances and conservation in the physical phenomena and processes. However it is an important issue that the numerical imbalances must be significantly less than the physical imbalances that are driving the planet toward a new equilibrium state.

As a stable equilibrium state, the radiative equilibrium state for example, is approached, no imbalance can be counted as small and dismissed. The imbalance between physically reality and the continuous model equations is almost certain to be a genuine problem. The effects of the viscous dissipation, constantly acting to increase the thermal energy of the atmosphere is physical reality. I am uncertain of the actual physical value. The imbalances introduced by numerical solution methods is very likely a problem in some GCM models/codes. This problem has been discussed as recently as 2003. Small imbalances acting constantly over long periods of time cannot be ignored as equilibrium states are approached.

Here is a curious side issue that was discussed in this olde paper by H. A. Dwyer from 1973 located here. The results given in the paper indicate that the effects of his estimate of the power generation activities by humans can easily be seen in the calculations with his model. He used 15.0 x 10^18 BTU/yr (1.58 x 10^22 Joules/yr) as the ‘heat generation’ by mankind over a period of 100 years. Energy conversion activities by humans is another one of those processes that is constantly occurring and adding energy into the climate system

Worldwide energy consumption by the human race is over 446 Quadrillion BTUs at the present time. This is equivalent to 131,400 TWhr or 471,000 PJ (= 10^15 J) per year. If we take an average efficiency to be 33%, the total energy conversion is about 3 times the consumption, or 1,413,000 PJ per year = 1.413 x 10^21 J/year. This is within a factor of 10 of the value used by Dwyer. (While we consumed about one-third of the total conversion, all the energy converted will always reside in the climate system until it is lost to space.) Can this be another source of internal energy conversion that cannot be ignored over long time scales as an equilibrium state is approached.

The thermal state of the planet, as measured by the temperature, is a strong function of the thermodynamic processes occurring within the climate system. The temperature distribution near the surface is determined by the transport and storage of the energy additions to the system; not by the energy additions alone.

Chaos and Butterflies

Dissipative systems (physical or mathematical)will have several attractors (assuming they exist). The typical Lorenz-like ODE systems are dissipative, and conserve energy in the dissipationless limit. Thus these systems, the original 1963 and the later 1984/1990 systems are examples, have more than a single attractor. The dissipative and energy-conserving-in-the-dissipationless-limit properties are generally considered necessary in order for systems of ODEs to be Lorenz-like.

The oscillatory/periodic-like/aperiodic response seen in calculational results from these systems remains bounded due primarily to the linear terms on the right-hand sides of the equations. The plots of the dependent variables from Lorenz-like ODEs ‘look’ like bounded numerical instabilities. These are damping terms in the equations; the resistance offered to fluid motions, for example. If the coefficients on these terms are increased slightly from the usual default values of unity, the system can be shown to become a little under-damped to massive over-damping with the trajectories smoothly approaching equilibrium states. The effect is very dramatic on graphical plots.

It is possible to find values of the coefficients that produce periodic responses having almost no change in frequency or amplitude. And some values will bring the initial trajectory motion away from the initial point to a screeching halt at a new equilibrium point. In general, the chaotic response properties are lost and deterministic predictability returns.

I suspect, but haven’t yet done any calculations, that coefficient values less than unity might lead to unbounded responses. The non-linear terms in the equations might also provide contributions that assist in maintaining bounded-ness. It would also be of interest to investigate the effects of modeling the momentum-equation resistance as a non-linear function such as in turbulent flows.

The numerical solution methods used in NWP and AOLGCM models/codes have both implicit and explicit numerical damping in addition to the physical damping contained in the basic-equation models for mass, momentum, and energy for the fluid motions. These systems are dissipative and might be energy-conserving in the dissipationless limit. I do not know that if the ‘momentum dissipation’ terms are not present the codes can even maintain bounded responses. The effects of the numerical damping relative to the ‘chaotic response’ properties of the continuous equations are not known, of course.

When performing an initial-value sensitivity analysis, specified initial conditions are varied and the response of the calculations are observed. It is not possible a priori to know to which attractor for a dissipative system a given trajectory will approach. It seems that this property means that even long-range calculations of responses cannot be assumed/hypothesized to be reliable. Again, all this assumes that attractor(s) exist.

All corrections appreciated.

John A

Dan, your link is a trackback. When you link to another blog, it submits a trackback comment on the target blog that links back to your own.

Tom Vonk

#194

Well literally you are right – noone is expert in chaotic systems .
However on the mathematical side those systems call for specific treatments and exhibit specific behavior – propagation of errors , convergence , metrics of trajectories in the phase space , non linear PDE equations etc .
Experts in those fields are by extension (kind of) experts in chaotic systems .
However numerical analysts (LED , RANS) and people dealing with stochastical methods mostly understand nothing about chaos because they precisely look for specific physical cases where chaos can be “eliminated” by considering that small scale phenomenons (small scale is to be understood here both as spatial and temporal) are random .
As chaos is NOT equal to (stationary state + random fluctuations) this family of methods is wrong in the general case and the domain of validity of the approximation is constrained to certain spatio-temporal intervals that are in most cases poorly defined – some simple cases of turbulence which is a particular case of chaos can be treated that way .
The deterministic chaos has most probably its origin in the non linear interaction between feed back loops that produce a mixture of amplifications and dampings whose relative strength is changing all the time .
It is when those relative strengths unpredictibly change (f.ex a prevailing amplification trend gives way to a prevailing damping trend) that the system goes to a fast chaotic transition that is one of the signatures of deterministic chaos
If the interactions are weak the system is quasi separable and the chaos is weak if the interactions are strong it is not separable and the chaos is strong .
The climate is a system that has an astronomically large number of interacting feed back loops most of them interacting strongly on different typical time scales .
As such it is probably beyond any attempt to be adequately simulated over a long period of time like centuries .

Dan Hughes

re: #196

That is a very important point Jerry. I understand that valid DNS results are independent of the discrete spatial and temporal increments for each realization. If this is not the case, of what use are the continuous equations?

This situation is in stark contrast to the GCM, and maybe NWP, case(s) in that it is known that the calculated numbers are functions of the discrete increments. What do the continuous equations provide under this conditions?

Gerald Browning

Dan Hughes (#197),

The numerical solutions are not independent of the space and time increments, but as the space and time increments are refined,
the solution converges to the continuum solution of the unforced, incompressible NS equations if the spatial resolution is sufficient to resolve the minimal scale indicated by Henshaw, Kreiss, and Reyna
for a given kinematic viscosity coefficient and the numerical method is accurate (consistent) and stable (satisfies the CFL criterion).

Convergent numerical runs have been made in 2D for kinematic coefficients that are essentially the ones that exist in real applications. The
turbulence is not chaotic, but converges to the same solution for a fixed period of time. There have also been 3D resolution runs made with no surprises for as high as resolutions as currently possible.

Thus the turbulence is not chaotic, just very fine scale that must be resolved.
If the turbulence is not properly resolved, the model will blow up
because of an accumulation of energy at the highest waves due to the unresolved cascade of enstrophy. Then the only way around that problem is to add either an explicit (eddy viscosity)
or implicit (numerical scheme) unphysically large dissipation. Of course the latter alters the numerical solution and it will not converge to the
continuum solution with the correct kinematic viscosity.

Jerry

Gerald Browning

Tom (#198),

You might want to peruse the manuscript by Henshaw, Kreiss, and Reyna
and the associated manuscripts by Kreiss and his students. The results are quite illuminating. Let me know if you have any problem finding those
references and I can be more specific.

Jerry

Gerald Browning

Tom,

Look at the reference in the SIAM journal of Multiscale Modeling
and Simulation (volume 2) by Henshaw and Kreiss. There are numerical runs that support the minimal scale estimates for very high Reynolds numbers for the unforced, incompressible NS equations in 2D. The runs are made for the doubly periodic domain so that boundary conditions do not become an issue
(many numerical runs use unstable boundary conditions). And there are 3D runs by Kreiss and Enstrom. Let me know if you are not able to find the references and I will provide more specific info.

Jerry

Gerald Browning

Tom,

I know there was a manuscript that preceded the 2D publication available at Los Alamos. Also there were some manuscripts that preceded the 3D publications from UCLA. Look under Bill Henshaws site at LLNL for the references.

Jerry

Gerald Browning

Tom (Addendum),

Both the 2D and 3D manuscripts are available from Bill’s website.
The estimates have been published in various journals and I think
may also be available on an open site. Ask Bill for info.

Jerry

Gerald Browning

John (#208),

Hats off to you for tracking down the manuscripts and posting the links.
If anyone has any questions about any of the manuscripts I will be happy
to try to answer them and I know Bill would also be happy to respond.
I can pick out the exact manuscripts from the lists if desired.

Jerry

Steve Thomas

Jerry

I no longer have your contact info but would
very much like to get together to chat.
I’m no longer at NCAR.

Steve

MarkR

The IPCC says “Climate change refers to a statistically significant variation in either the mean state of the climate or in its variability, persisting for an extended period (typically decades or longer).” Clearly from this definition IPCC scientists never anticipated the possibility that the variation and/or its mean state should be undefined in the sense of mathematical convergence, which will be true for most fractal distributions. As the outcome of a chaotic process, most, perhaps all, weather related variables will have high fractal dimension, and many will have non-convergent moments. This happens in chaotic systems because the mean state is forever changing (like the DJ Industrials) and is not static with stable fluctuations (like your checking account). In turn, all subsequent data samples beyond a training period will likely be “statistically significant”, for which the only solution is a heroic effort at averaging (think PCA) and or “outlier rejection” (think dropping parts of data sets). Once upon a time it was thought that if we could just get enough data points and subtract enough cycles, all data would be smooth and regular. We now know that the universe is not fundamentally smooth, and our little planet embedded in it is not either.

Allan Ames

Perhaps Allan could join this discussion as well?

ALLAN AMES

Re: 213 MarkR, 212 Steve

Has there been discussion of what sort of statistics we might expect from exponential, or any other type of system?

A related question is, how could we get switched over to thinking about the type of variability, rather than summary parameters of an arbitrarily assumed distribution?

The Vostok O18 data is a beautiful bi (or more) modal, just what you would expect from a system with exponential growth followed by collapse. (How do I include a graph without a web site?)

Steve McIntyre

#215. A simple way is to set up an account at esnips.com or something like that, upload there and link.

Gerald Browning

How did we get into fractals? This is all supposition and not based on any theory that I know.

For smaller scales of motion in the atmosphere and ocean, the slowly evolving solutions in time approach solutions of the incompressible, NS equations. Once the minimal scales for the incompressible, NS equations are properly resolved, the manuscripts cited above show that errors in the forcing of the incompressible NS equations lead to differences in the solutions of the size of the errors in the forcing. And they also show that it is possible to recreate the small scales by continually assimilating the large scales. These results have useful applications to many flows.

The problem with atmospheric models is that the kinematic viscosity
is unphysically large (not even close to resolving the minimal scale for the atmosphere if one exists) and the forcing terms have O(1) errors at all scales, i.e. the errors in the forcing terms are not small.
Thus atmospheric models do not satisfy the above conditions and never will. In addition, the hydrostatic system is ill posed and the nonhydrostatic system is sensitive (displays fast exponential growth) near a jet.

Jerry

ALLAN AMES

re: 219 Gerald Browning– Why fractals?
Tom Vonk gave a lovely explanation. Mine would be simpler. How do you know you are describing the proper system if you cannot match the variability? If the empirical data says something is bimodal, and you produce a gaussian, hasn’t something been left out? Then, don’t you know, the thing you left out will turn around and bite you.

Tom Vonk

Jerry
In order to avoid misunderstandings – I have never said that there was a strange attractor for the climate .
I have indeed said that it is not proven that there is one and I even think that it is impossible to prove it because the system is so complex that we will never have a complete set of equations describing it .
However there are many phenomenons be it the glacial/interglacial transition , multidecadal events like the ENSO or gaz absorption at the liquid/gaz interface or indeed the weather that are definitely chaotic .
What I said was IF there was a strange attractor THEN its structure was fractal (see f.ex “On chaos, fractals and turbulence” Peinke &al Physica Scripta, Vol. T49, p.672 or “Fractal Dimension as a Measure of the Chaotic Behavior of Taylor-Couette Flow” Olsen &al) .
Regarding the particular case of N-S that represent a subset of the climate problem I will come to it later when I have read the papers you linked to .
I have always seen 2 different problems with N-S .
First is the existence , unicity and properties of a solution of the general N-S equations and this problem is not yet solved .
Second is numerical simulations of particular cases of N-S with particular assumptions (like boundary conditions , form of forcings etc) and there is the problem already mentioned by Dan Hughes that IF the numerical methods in those particular cases converge , to WHAT they converge .

Gerald Browning

Tom (#223),

How are fluid experiments run for Taylor-Couette flow with infinitely long cylinders?

If the flow is simulated by a computer model, what are the continuum
and discrete boundary conditions at the top and bottom of the cylinders and at the lateral boundaries?

How physical is the Taylor-Couette problem?

Jerry

Steve Sadlov

Update …. so here is the reality of the heat of today. To recap, NWS proged a heat event based on a progressive ridge. They proged a sea breeze only close to the immediate coast, and northerlies everywhere else. They proged a rapid heat up to “summer like levels of high heat.” If I were to take it at face value, I would have expected us to be cracking 90 in many locations, for there to be 80s in places along SF Bay and in the LA basin to very near the shore and for there to be many, many temps well into the 90s elsewhere. In reality? A few 90s, with a strong on shore push, especially in SoCal. Let’s see how long this “heat wave” lasts and how intense it actually gets.

NoCal actuals for 1500 PDT

SoCal actuals for 1500 PDT

Wind map for SF Bay, Delta and near coastal waters

Gerald Browning

Steve (#227),

I see that the winds are in knots at 10 m. But I was unable to switch to the site that discusses the interpolation scheme. What are the winds aloft,
i.e. near the jet?

Jerry

Steve Sadlov

Jerry, I still have not found anything on winds aloft, other than the one off daily radiosonde run at OAK.

[In terms of the actual vs forecast of the heat event:

A STRONG RIDGE STRETCHING FROM THE PACIFIC INTO CENTRAL CALIFORNIA
WILL CONTINUE THE HOT INLAND TEMPS THROUGH THE END OF THE WEEK…
EVEN THOUGH THERE SHOULD BE SEVERAL DEGREES COOLING EACH DAY. AS
HEIGHTS LOWER AND A SEA BREEZE DEVELOPS…THE COAST SHOULD BE
SIGNIFICANTLY COOLER BY FRIDAY. A TROUGH MOVING ACROSS THE PACIFIC NW
WILL BRING A RETURN OF STRATUS TO THE COAST WITH AN INCREASING
ONSHORE FLOW FRIDAY MORNING.

So stick a fork in this one, it’s getting cut short, lowering heights under way. Gave us a day and a 1/2, pretty wimpy as these things go. NWS got it half right but as usual overplayed the warming / increasing hts card]

PaulM

# 224
The Lorenz eqns are viscous. They describe a simplified single overturning convection cell. Equivalently, think of the motion of air in a tyre that is heated from below. The three variables in the equations are the up-down and left-right temperature difference and the speed of the overturning. The system is dissipative (ie energy is lost) due to viscosity and thermal diffusion, but it is driven by the heating from below.
The Lorenz equations have chaotic solutions. Although they are not an accurate model of the atmosphere, or even a single convection cell, more accurate simulations of convection also show chaos, so convection cells in the Earths atmosphere are probably chaotic. Of course it is not possible to ‘prove’ this in the precise mathematical sense.
As for ‘the climate equations’, as Tom says, the whole system is too complex even to write down or agree on, so the question is meaningless. But it would be simple to check whether GCMs are chaotic. I expect someone has done that. My guess would be yes.

Steve Sadlov

RE: #234 – Here is a template for the sort of characterization methology I would want to see NCAR use to certify their models. This is, mind you, only an inkling, only a snap shot of a subset of the tools and metrics (in Sigma parlance, the X and x measures). The actual, realized methodology that NCAR would have to use would clearly be much more intricate and complicated. This is simply to set the tone of my expecatations:

http://www.du.edu/~jcalvert/tech/fluids/vortex.htm

Gerald Browning

Paul M (#2330,

If the Lorenz equations are viscous, what was the size and type of viscostiy used in the original derivation and what was the scale of motion?
A reference will suffice. Thank you.

Jerry

Tom Vonk

Jerry #224
There is a number of necessary conditions to have a chaotic behavior – high dependence on initial/boundary conditions , non linearity , existence of energy dissipation , existence of thresholds and fast transitions between states , growing error/unstabilities .
The phenomenons I have mentioned and many others present all the necessary conditions and stay indeed unpredictible over the long term .
That is not a formal proof but as there is no proof of the contrary either , the balance of evidence points to chaos .
To the Lorenz system see : http://www.maths.uwa.edu.au/~kevin/Papers/JAS07Teixeira.pdf
That was at the core of my discussion with J.Dudia that he has probably not understood .
The numerical simulation of a chaotic system presents a high dependence on the time and space steps .
As the time step you use is not freely chosen but depends on the hardware available and as
the exact solution is not known , there is no way to say that a numerical simulation of a
chaotic system converges to anything meaningful and indeed in the Lorenz case it does not .

Jerry #225
See http://www.citebase.org/fulltext?format=application%2Fpdf&identifier=oai%3AarXiv.org%3Aphysics%2F0210009 .
The infinite cylinder is only a limit case with mathematical interest .
It is obviously unphysical as the solution must be invariant by a Z translation while the physical solution is not .
The staggering complexity of the chaos transition in the Taylor Couette flow has been illustrated by D.J.Tritton in “Physical Fluids Dynamics” where he shows a chart giving the different states of the system in a plane defined by the rotations of the 2 cylinders .
There are 2 dozen of states going from Couette flow to a fully developped turbulence through different pseudo stationnary structures . Parts of the plane are labelled “unknown” as there is no knowledge about the behavior in those regions . .
That translates mathematically that the N-S have multiple solutions for a given Reynolds and geometry .

PaulM #233
Nobody has ever checked that for the good reason that the GCM are not chaotic by construction .
They don’t solve N-S , they are not sensible to initial/boundary conditions , they consider that unresolved dimensions are either (gaussian) noise or parametrised , they use systematically time averages to smooth fluctuations , they impose tunings to insure that runs converge for the particular space and time steps they choose , they neglect hundreds of interactions and feedbacks , they never analyse sensibility on time and space steps etc .
I would bet that in the preliminary runs they have found some more or less intense chaotic behavior .
But as they can’t afford that – indeed it would mean that for different 100 year runs they get different final states – any trace of chaos is probably “tuned” out .
That way the runs converge but to what , only God knows .

Gerald Browning

Tom Vonk (#239),

See my response to Paul M. I have yet to see anything that is a rigorous proof that the atmosphere is or is not chaotic. Until that is shown (and I would surmise that is not possible for the exact reasons mentioned above), this is all a moot point.

Jerry

Gerald Browning

Tom Vonk (#239),

I see in the above reference that there is a reference to Kreiss’ theorem. It appears that Heinz (or Gunilla if plane flow) has already looked into this problem analytically? Also the equations are the viscous, incompressible NS equations to which the Henshaw, Kreiss, Reyna estimates apply for the unforced, periodic case. This case is being forced by the rotation of the cylinders and again the question arises as to the physical reality of the experiment.

Jerry

Gerald Browning

Tom Vonk (#244)

If each experimental apparatus provides the same flow for the same fluid and Reynolds
number, why have there been so many publications? Does each publication just use a different fluid
or radius? It seems to me this provides an infinite number of possibilities (publications), but not much physical insight if the experiment cannot be related to a real world fluid and Reynolds number?
And what about the Kreiss analysis, i.e. how does that fit in?

I also believe that the fluid is not incompressible, but rather slightly compressible.
This will have an impact on any theory that is based on the apparatus. In addition, there are particles injected into the flow that have some impact on the fluid, i.e. it is not a pure
fluid. I see a number of scientific issues that to me are not fully resolved even for the manuscript you cited.

A forced (nonchaotic) PDE system does not have to converge to a fixed point or a periodic trajectory?
As shown it can produce any solution that one wants.

The modifier “probable” is not a mathematical proof and neither is an experimental apparatus
that has a number of issues related to its design?

Jerry

PaulM

Jerry
You really are missing the main points. Lorenz is just a simple model to illustrate chaos. It is not true the ‘all the chaos commotion is based on this model’. There are numerous other simple models that also show chaos. In more complicated systems (as I said before) it is impossible to ‘prove’ chaos in the rigorous mathematical sense, so it is a waste of time talking about this. Taylor Couette flow is just another model to illustrate instability and transition to chaos and turbulence in fluids (it has a close analogy with convection, centrifugal force replaces buoyancy).
You say ‘each experimental apparatus provides the same flow for the same fluid and Reynolds number’ – again, this is confused. For small Re there are transitions to the same regular (for example periodic) flow but for larger Re there is chaos so the exact flow is quite different in each realisation. There are thousands of experiments and numerical simulations that show chaos (exponential divergence) at large Reynolds / Rayleigh number (regardless of how the boundary conditions are discretised). So it’s bucketloads of evidence but no real proof – a bit like evolution!
As for the climate, we dont even know what the key physics is, but I am now repeating my earlier post and Tom’s. But in general if you make the system more complicated, it stays chaotic or gets more chaotic.

Gerald Browning

Paul M (#247),

I am not missing the point. There are many differential systems that show
chaotic behavior. That is not a proof that the atmosphere is chaotic nor
the NS equations. In fact, for the periodic cases we see convergence and stability to perturbations of the numerical approximations. Thus these cases do not display chaotic behavior if the minimal scale is properly resolved. This case is just as valid as the Taylor-Couette problem.

Let us stay with a single fluid (say water) for the Taylor-Couette flow between rotating cylinders. What is the physical reality that this
apparatus is suppose to describe? Is it just a problem to demonstrate
that the fluid behaves very differently when forced using different
cylinder heights, radii, and rotation rates. Is this a surprise?
Clearly different forcing will provide different solutions for the same
fluid.

And in the corresponding numerical simulations is the flow properly resolved for the given fluid and viscosity?

Jerry

Tom Vonk

Jerry # 250

I think that we lost the track and can’t see your point anymore .
You focus on a word (suggests) within an argumentation that goes much farther than this one word .
What’s the matter with “physical” ?
Water is physical , Reynolds are physical , boundary conditions are physical – everything in the Taylor Couette experiment is physical .
If for some reason you don’t like the idea of cylinders , take Rayleigh Benard – it’s as physical as physical goes and there are no cylinders .
Yet the results are the same .
PaulM is right that you probably missed the point – there is no surprise that even a simple physical system described by N-S equations presents chaotic behavior .
Deterministic chaos is the rule in fluids and steady states an exception .
Do you think that the weather can be predicted over an infinite time with accuracy provided that it is “properly resolved” ?
If so , where is the proof and what is the “proper resolution” ?

Actually the understanding of chaos dynamics in natural systems is completely beyond simple finite-difference numerical runs on N-S equations .
The only relevant methods explore the metrics of the attractors , exponential separations of trajectories of solutions , fractal dimensions , Lyapounov coefficients etc .
One has to stop to look after deterministic predictability which is impossible but look instead at patterns and topology .
A specifically challenging problem is the one of systems with attractors having an extremely large number of dimensions like typically the weather or climate .
What happens when a Lorenz like physical chaotic system with a low number of dimensions sees this number increased ?
That is still an open question even if everything we know today suggests (suggests as in “nothing known suggests the opposite”) that the chaos intensifies .
For a good summary see f.ex : http://www.nls.physics.ucsb.edu/papers/Ah_Benard_03.pdf
As the research on this field is rather young , there is still much work to be done but the chaotic behavior (=aperiodic time dynamics) of fluid systems is established both theoretically and experimentally beyond any doubt .

Gerald Browning

All,

I thought you might be interested in the abstract for the following seminar
at NCAR.

Advances in Explicit Convective Forecasting with WRF-ARF
Morris Weismann (MMM)
Wednesday Sept 19 at 11:00 A.M.

The abstract is available in the seminar announcement and roughly states that there has not been any improvement in the quality of forecasting with
the fine mesh (1 km) WRf model and that the large scale is not generating the smaller scales properly.

Note that this is the exact problem that this thread has discussed in consideable detail, i.e. that fast exponential growth in the continuum solution will lead to large errors in any fine scale numerical model
and the problem will become more apparent as a model starts to resolve features on the order of 10 km.

Jerry

Larry

So if I may clarify what should be obvious, the problem is inherent in the equations, and until we have computers with many orders of magnitude more RAM and FLOPS (or vast arrays), these models are never going to produce accurate results?

Gerald Browning

Larry (#255),

The problem has little to do with computer FLOPS or RAM. The problem is inherent in the sensitivity of the large scale continuous equations in the presence of vertical shear. If there is any error in the large scale observations, the sensitivity will display itself as incorrect locations of smaller scale storms even if the physical
parameterizations were perfect (which by now we know is not the case). That is why ensemble forecasts have been tried, but that does not solve the inherent sensitivity.

Using initial and boundary data from a weather prediction model with less resolution will lead to incorrect initial and boundary data and this will also lead to incorrect smaller scale storms.

We were able to recreate an analytic mesoscale storm under ideal circumstances, i.e. knowing the initial small scale vertical component of the vorticity, the exact heating, and the correct large scale boundary conditions. None of these are known in real cases and the presence of typical vertical shear leads to fast exponential growth in the neighborhood of the shear.

Jerry

bender

[bump]
Chaotic (complex, multistable) systems may appear ergodic for a while, but then their lack of ergodicity is revealed by an unexpected change in state, such as the emergence of a novel flow. What I want to know is whether the climate system is thought (by GCMers in particular) to behave in this way, and if so, how one can possibly justify tuning to a superficially stable substate (such as a subset of 20th weather/climate scenarios).

If I understand what Gerald Browning has been saying for the last year, then the GCMs are damned. If that is the case, then the role of misplaced faith in propping up the IPCC/AGW conspiracy is critical. Expose that and the house of cards will come down very quickly, of its own accord.

Gavin Schmidt, please reply.

Gunnar

Gerald, you might be right, if you are saying that the GCMs are useless. However, climate should not be approached as a really long weather forecast.

Larry, that’s a recurring point you make that I agree with. I too recoil when folks seem to actually expect AGW people to be intellectually honest. Like they will say, “Oh, I see, you’re right, Never mind then…”

lucia

@Gerry in 249:
In response to: “Let us stay with a single fluid (say water) for the Taylor-Couette flow between rotating cylinders. What is the physical reality that this apparatus is suppose to describe? ”
Taylor Couette flow describes…. Taylor Couette flow! This apparatus is used in viscometry, where use is restricted to low Reynolds number. So, this has always been a physical of interest– if for no other reason than to study itself. (It gets used for other things too.)

Still, I’m not entirely sure what larger point Tom is trying to make by pointing us to the Ohio State Reference. Yes. People have observed loads of complex, pretty phenomenon during transition to full blown turbulence. Various forms of stability analyses have been applied to describe what is seen.

Meaning… what in terms of Global Climate Change? Or for full blown turbulence? Or for GCMs? Maybe it means something; unless Tom can explicitly connect these pretty pictures to computations of full blow turbulent flows, I’m throwing my vote in with you and say, I’m not seeing how the pretty flow viz pictures relate to GCM’s.

Gerald Browning

Gunnar (#261):

Why shouldn’t climate be approached as a long term weather forecast?
That is exactly what it is. And currently NCAR is moving the WRF fine resolution limited area model to a global version, i.e. a long term fine scale weather forecast. Unless someone can prove that the smaller scales of motion in the atmosphere do not have an impact on the climate over a long period of time, then those scales must be accurately computed to obtain that feedback.(The current HKR smallest scale estimates for the incompressible NS equations indicate that only when the smallest scales are resolved by a numerical model is the solution accurately computed.) And that is certainly not the case with any global climate model
and it will never be with fast exponential growth near shear in the basic dynamical system. The latter result for numerical approximations of exponentially growing solutions is is well known in numerical analysis.

The comment that preceded this one describes what it would take in order to have any confidence in the results from a numerical model. And as stated there, none of the conditions have been satisfied for any climate model.

Jerry

MrPete

bender, could the assumption of ergodicity be related to the assumptions inherent in the Uniformitarian Principle?

physical and biological processes that link current environmental processes with current patterns of tree growth must have been in operation in the past (after Fritts 1976). In other words, “the present is the key to the past,” originally stated by James Hutton in 1785. However, dendrochronology adds a new “twist” to this principle: “the past is the key to the future.” In other words, by knowing environmental conditions that operated in the past (by analyzing such conditions in tree rings), we can better predict and/or manage such environmental conditions in the future.

The discussion in this thread gives me great pause when considering dendroclimatology’s assumptions.

MrPete

(Obviously) I’m not an expert in any of this… I get pretty far with general education and common sense…

Am I making bad assumptions, perhaps applying UP at the wrong level/scale? I’m thinking that perturbations such as:

* Major continental airflow shifts
* External damage (nearby tree falls, destroying half the bark; fallen tree rots and is gone.)
* Root growth into new nutrient pockets

…cause havoc with these assumptions. Some might claim these are rare outliers. But standing in the middle of a BCP forest, surrounded by trees that almost all have been beaten to a pulp for centuries, it is hard to see such events as “rare” 😉

lucia

@Bender (in italics).

I’m not a climatologist.
Nor am I. I”m a mechanical engineer by training.

Honestly, I’m a bit puzzled by any focus on ergodicity.

But it seems to me that there are some basic agents like heat and heat exchange, water and fluid flow, etc. that you can assume do not change their behavior over time. This is tending to satisfy the uniformitarian principle. But because the agents behave nonlinearly, they do not satisfy the ergodicity assumption.

From a mathematical point of view, flows in general are not proven to ergodic.

That said, wide classes of flows have been observed in nature, studied in labs and treated analytically. They appear to be ergodic.

There are a very few situations in which solutions are not ergodic, but as an empirical matter, it takes some doing to find them. Yes– there are those who look for them. If you examine carefully, the Reynolds numbers will tend to be relatively low. Moreover, when the statistical properties of these types of flows are observed over sufficiently long periods of time, they appear to be ergodic. (Experiments that don’t collect statistical properties, or which are not examined for long times can’t be used to ‘prove’ some flows are ergodic.)

As an engineer doing casual thinking about climatology, I would not look to the NS, energy equations etc. to find ergodicity. If the climate is ergodic, I’d be surprised if that arose out of the non-linear nature of the Navier Stokes equations themselves. It arises out of something else. (Possibly ice forming in northern climes, then melting. Possibly other things.)

Emergent features (such as the walker circulation, THC, ENSO, etc.) may or may not be structurally stable. (Some may be, others not.)
Is there any really any disagreement that, at least, in some sense, these ENSO and Walker circulation aren’t entirely, totally, rock solid, stable structures? There are analogs in transition to turbulence. In certain experiments at controlled, moderate Re numbers you see patches of turbulence within laminar flows. The patches may have short lifetimes, vanish, re-appear and do all sort of interesting things.

But does this invalidate, or cast in doubt, any assumption of ergodicity?

I may be mistaken, but I’m pretty sure that — as an empirical matter– when flows of this type are observed over sufficiently long periods of time, they appear to be ergodic. They may “flip” back and forth between a few states– but many, many flips, between states, it appears you end up with a system where you can interchange time and ensemble averaging. (At least as far as one can tell empirically. Lucky for graduate students, “a long time” in a laboratory experiment is rarely longer than 1 hour, and more commonly, no longer than 1 second. Lucky for engineers, good design generally means avoiding flows that slowly flip back and forth between various states. It would be really bad if the lift on an airplane wing varied between two values, with each lasting, on, 1 minute or more.)

So, the upshot is, knowing what I know about flow, ergodicity, and applying ensemble averages, I’m not to concerned about absolute lack of ergodicity in climate arising out of the navier stokes equations, though I would defer judgment on the possibility of non-ergodicity arising out of other factors. (Ice sheets forming and melting? Continents moving? External radiative forcing functions? )

In this sense, these higher-order “agents”, if they are intermittent, do not conform to the uniformitarian principle. Such a system is certainly not ergodic.
I’d be cautious saying “certainly not ergodic”. At best, you can say “have not been proven to be ergodic either using mathematics or empirically”.

And if they are not ergodic then you can not assemble “ensemble runs” and assume they are representative of the true ensemble expectation; the mean and the expectation are never equal.
True… but if they are ergodic, you can interchange them.

This explains why I am so interested in the weather/climate scenarios that climatologists use to generate “ensemble” runs. An ensemble has a very precise meaning in statistics. Not so in climatology.

On the one hand, I defer judgement on whether climatologist application of statistics and ensemble averaging to climate is done correctly. I’d need to know more. I am certain that at a minimum, assumptions are involved.

After all, assumptions are used when applying ensemble averaging to every transport model I’ve ever seen. Certainly, ergodicity is assumed . In engineering problems (where we can often isolate factors leaving only dominant ones) assumptions are often either empirically based or semi-empirically based.

I’d be surprised if climatology is an exception in this regard. (The open question is always: does a very common place — almost routine — assumption apply to a new physical system? The answer might be “no”. The other open question: Assuming the system is ergodic, is the time scale for the computations sufficiently large to approach the ensemble average. )

Still, I’d be very surprised if “ensemble” doesn’t mean the same thing in climatology as in statistics. Those working in mechanics use the term the same way statisticians do, so why wouldn’t climatalogists?

(As for having a clue how those in mechanics or climatology might use “ensemble average”, Google Liljegren “ensemble average”; you’ll find me. Don’t confuse me with my husband though. 🙂 )

bender

Lucia #271,
Thanks for parsing my contribution. I will consider it. For folks who want to understand what ergodicity is and why it’s important, lucia’s got the nub of it: it’s about the interchangeability of time series and series ensembles. If the two have the same statistical properties, they are interchangeable, and the process is ergodic. Then statistical inference (in terms of extrapolating to the uncertain future) is greatly simplified.

My question is about how many ensembles you need and how long the series need to be before you get that interchangeability. The higher this requirement, the more likely the GCM tunings are to be in error as a result of misrepresenting the internal variability. My complaint is that the folks at RC don’t seem to understand the question. Yet, clearly, lucia does. Watt’s up with that?

Steve Sadlov

RE: #270 – RE: “Meterology assumes that the sun and earth are constant.”

Here’s a grey area. Look at the NWS 72 hour – 365 day outlooks. Superimposed on them is an overt “AGW” signal. The NWS assumes AGW as a “meteo factor” in models out past about 72 hours.

Mark T.

For folks who want to understand what ergodicity is and why it’s important, lucia’s got the nub of it: it’s about the interchangeability of time series and series ensembles.

This is an important point that seems to have been lost in the definition someone found in one of the other threads (from ask.com). Ergodicity allows swapping of the statistics, which is beneficial particularly when you have only a limited amount of time series data available, but for all of the ensemble. As I recall, Mann makes this assumption in his modified RegEM method, without any explanation that I know of, which Jean S. first pointed out (his nanmean function). I have not had time to dig into this… soon.

Interestingly, the only text I have that actually provides a lucid definition of this (whith most of a chapter dedicated to ergodicity) is the Papoulis book “Probability, Random Variables and Stochastic Processes” (I have the 2nd edition, the more recent edition has an additional author). Ziemer and Tranter mention the concept briefly in “Principles of Communications.” None of my other signal processing texts even list it in the index.

Mark

lucia

Bender: My question is about how many ensembles you need and how long the series need to be before you get that interchangeability.

I think this is the correct question. I have no idea what the correct answer is — because I have no idea what the time scales associated with the full range of relevant phenomena might be. I also have no idea how many ensembles of “weather 2007” those running a particular GCM run, as I’m not at all familiar with that literature.

Why would I know:I’m a mechanical engineer. Based on my background, the most I’d say with confidence is that I see a long time scale in the ice cores. So, the absolute upper bound for interchanging time and ensemble averages appears to be several ice ages.

But don’t get too excited and think I’m suggesting the correct answer is anywhere near the length of an ice age. If predicting climate is framed a bit differently, the correct answer may well be 1 year.

One might also be able to learn a lot by framing the problem differently. I’ll explain by way of analogy:

My husband graduate thesis involved modeling the diffusion of passive scalars (smoke) in the boundary layer. ( Think military smoke screens.) On the one hand, if you at the problem of predicting where smoke travels on average over the course of a full day, you would realize there is an imposed length scale of at least 1 day. The “forcing” function for smoke is atmospheric conditions, and even on average, atmospheric conditions change dramatically over the course of a day. (Worse, the weather could change, and things all look different on the next day.)

Fortunately, for both modeling and, more importantly, data collection and processing– which were done in the field, there is a separation of scales. So, it was possible to separate the turbulent diffusion problem from the weather prediction problem.

Analyzing the data was more difficult than formulating a model because even if you can formulate the two issue separately, the sun still rose during the experiments, and so, trying to decide whether the turbulence had changed “too much” to test a hypothesis describing the instantaneous response of smoke particles to turbulence was difficult.

In the end, Jim had to formulate a method of partitioning the data to minimize uncertainty intervals due to both a) sample size and b) change in the statistical properties of the forcing function during the measurement period.

It turned out to be possible to make something of the data because there was a large separation of scales. The time scale of the turbulence (seconds) was very short compared to 1 day.

So, it turns out, even though the first estimate of a time scale for interchanging time and ensemble averaging sounded like “you will never graduate”, the problem could be framed in a different way. It turns out that if you know some initial conditions, and information of forcing functions etc. You can predict the behavior of a smoke plume. ( The ultimate method was monte carlo simulation, which, of course, involves tracking individual smoke molecules.)

@Gunnar: With regard to your sediment example…sometimes you can’t predict where individual leaves go and you can’t predict the average behavior either. Some of the factors that complicate the small scale problem are retained. If you don’t deal with them, they screw up your macroscale prediction. That is to say, if your sub-grid parameterization fails to capture phenomena that affect particle transport on average, your macroscale model will also be wrong on average. Macroscale models that contain micro-or- meso scale closures often contain tuning parameters. The tunings can be flow dependent; they often are.

“Can’t get the small scale right” => “Can’t develop a reliable general macroscale model that relies on sub-grid parameterizations” is the rule.
“Can’t get the small scale right” => “Can develop a reliable general macroscale model that relies on sub-grid parameterizations” is, unfortunately, the exception.

Back to Bender: Yet, clearly, lucia does. Watt’s up with that?
My training is as an experimentalist?

Gunnar

>> @Gunnar: With regard to your sediment example…sometimes you can’t predict where individual leaves go and you can’t predict the average behavior either

lucia, don’t forget that I also said “and different focus”. I agree with what you say about micro vs macro scale, but it may not be relevant. In the example, the sediment study is not a true macro version of the leaf study. They are also differently focused, ie different equations, different inputs, different outputs. They only thing they have in common may be the river.

Similarly, a correctly approached climatology and the meteorology needed to predict whether one should bring an umbrella tomorrow, may only have in common that they involve the mythical planet of origin, which some say is called Earth.

Sam Urbinto

Weather is rather a simple thing, basically wind speed, barometric pressure, relative humidity and temperature.

What’s the weather like tomorrow? Well, I might be able to guess cold and dry and windy if it was that day yesterday and I don’t see any atmospheric conditions likely to change it. But then again, something could change in the pattern, and a low or high pressure system shift and make the weather different. So wearther is basicially current conditions.

Climate is rather simple also, it’s

the composite or generally prevailing weather conditions of a region, as temperature, air pressure, humidity, precipitation, sunshine, cloudiness, and winds, throughout the year, averaged over a series of years.

Or perhaps a bit more complicated:

A region’s usual weather patterns. The climate at any point on Earth is determined by things such as the general movement of the atmosphere, the proximity of the oceans, and the altitude of the location.

Note: The climate also is affected by the sun, by changes in the orbit of the Earth, by plate tectonics…

… and by human activities, primarily changing the properties of the surface of the Earth, and by the release of particulates and greenhouse gasses that influence the greenhouse effect and carbon cycle in various random overlapping interlocked ways.

MrPete

Note to new visitors: what you are seeing here is the benefit of a multidisciplinary team getting involved in significant scientific issues.

If you ever start wondering whether CA brings any value, look around in the archives for more of this kind of discussion. There may be few if any real climate scientists here, but that doesn’t seem to harm the level of discussion too much.

😀

Gunnar

>> My naive assumption was that climate models are based on an energy balance

Your assumption was not naive, it was rational. Now, I don’t speak from personal experience (life is too short to start looking at GCM code), but my understanding is that GCMs are derived from the weather models, hence, the name, General Circulation Model. To simplify, the took a meteorology GCM, cut out parts that were making the simulation run too long, added Arrhenius, and fiddled till they got it to predict doom and gloom.

My understanding is that there is NO thermodynamics (despite the fact that the name seems to match what we’re trying to do, must be some denialist plot), no Henry’s law (Henry? has that been peer reviewed by the team?), etc. How else do you think that they could come up with a model that predicts that changing C02 from .000171% to .00034% of the mass of the oceans would cause the oceans to warm up by 4 deg C?

Whatever is in that model, it sure isn’t 1st law.

Gerald Browning

Larry (#282),

The numerical climate models damp energy thru unphysical large dissipation and create new energy thru unphysical forcing. They are then run for long periods of time until the total model energy ceases to oscillate as rapidly as in the beginning. It is no small effort to achieve this model energy balance as it is not real and the forcing must be retuned for different resolutions as the dissipation is (hopefully) reduced at finer resolutions. This should come as no surprise as the models are nowhere close to using the correct size or type of dissipation and this serious problem (along with many others) must be artificially overcome. The error in the numerical solution as compared to reality is completely in question.

Tonight I will provide a basic error analysis for numerical approximations
of a differential equation with an exponentially growing solution to show that there is a serious problem with any finite difference approximation
of such a system. The analysis will be simple and easy to understand
for anyone that has had basic calculus. Then the only question is do such solutions appear in the basic dynamical system used in global circulation
(or weather forecast) models. The answer is yes as indicated above and therefore no numerical model based on the equations of motion
for the atmosphere will ever compute perturbations near jets correctly.
These perturbations are thought to initiate mesoscale storms (according to the scientists at NCAR as the source generator for these exponentially growning solutions supposedly has been retained for that reason). Whether this is true or not, the perturbations will never be computed correctly so the models will never converge to a continuum solution as required in the comment above.

I hope this analysis will be beneficial.

Jerry

Gunnar

>> micro-scale modeling and the details are relevant to getting the macro-scale transport models correct.

This is a straw man, since this is changing the point.

>> I could write more, but it’s difficult to organize the appropriate type of discussion without knowing whether your background is physics, chemistry, statistics, engineering &etc.

Since you don’t appear to be asking in order to make a fallacious argument by authority argument, I’ll answer. I have a BSEE, as does my wife & older brother, while my father had a PhD in EE. My mother has a masters in history, my uncle a PhD in Physics.

bender

Mr Pete #285:
I agree. And I want to thank Gerry, lucia, Nasif and others for helping to bring my question (and my formerly muddled understanding) to a fine point. See what distributed communication can accomplish?

I conclude that the questions I was asking at RC on this topic were indeed sensible, if maybe a little ill-phrased. To prove my point I want to call attention to the John Christy interview being cited in “unthreaded #24”. A must-read. John Christy would understand the ergodicity problem with time-series lengths and ensemble sizes. Why? Because he is a real scientist, interested in the truth, and devoted to self-criticism as a way of preventing self-deception. Like lucia, he understands the value of experimentalism.

Larry

Gunnar, if I were you, I wouldn’t be trying to explain chaos to a fluid mechanics specialist. I can guarantee you that Lucia understands chaos theory perfectly. What you’re doing is like a chemist trying to explain spread spectrum to you. Quit while you’re behind.

Larry

If I understand this, Lucia and Gerry are arguing that weather and climate are for practical purposes not different, and Gunner is saying that they are. Did I get that right? Scientist/engineer cultural divide notwithstanding, I’m finding the scientists’ position more persuasive on this one, if I understood it correctly.

Sam Urbinto

I’m not sure Larry, but if that’s what the discussion is, nobody’s making it clear.
And if so, they’re probably both correct but not communicating. You can’t have climate without weather, the definition of climate in the dictionary is weather over time in “an area”. On the other hand, climate involves things that are not normally thought of as weather. Heat content of the oceans, GHG behaviors, albedo, cloud feedback, cosmic rays….

I’d say weather is created by things that are focused in on with climate, but nobody really thinks about them as weather, although many create or impact the weather.

Same but different.

Are we having this discussion, or is it something else?

Sam Urbinto

Reading that post, it sounds like that’s what you’re saying Gunnar.

It’s more a matter of determining the terminology first before starting to discuss the specifics.

Is it fair to say we have two different ways to describe the two, and two different ways to think about the two? That they are in some ways the same and in some ways different?

Weather causes climate. The things focused on in both are different, but they’re all interlocked. What they are is how they’re thought of and which aspect is highlighted.

Gerald Browning

Larry (#290),

My training is in differential equations and numerical analysis. In the case of time dependent partial differential equations, we split the initial value problem into the initial conditions and forcing (the latter includes all forms of forcing whether it be from the sun, latent heating, etc.). The solution can be written as a sum of the homogeneous system (no forcing) plus a forced component. If there are problems with the solution operator of the homogeneous problem, then the forcing will not make things better. And in the case of climate models, there are problems with the solution operator that impact numerical methods and with the unphysical forcings (parameterizations).

Jerry

Larry

303, but what most people here want to know is the differential equations describing what? The radiation, or the fluid mechanics? Based on my understanding, fluid mechanics is a much more difficult diff eq problem because of nonlinearity. Am I correct that the problem is with the fluid mechanical solutions?

Gerald Browning

Exponential Growing Solutions (tutorial)

Consider the simple scalar ordinary differential equation (ODE)

du/dt = a u

where u(t) is only a function of time t, a is real and positive,
and u(0) is given. The solution of this ODE is

u(t) = u(0) exp (at)

as can be verified by substitution.
Clearly the solution grows exponentially in time and such solutions are physically possible and allowed for in mathematical and numerical analysis theories (more about this in the following tutorial). Now let us approximate the ODE by the finite difference equation

L v = a v

where v is a difference function defined on a grid of size h and L v represents the finite difference approximation of du/dt, e.g. L v could be [v ((j+1)h)- v(j h)]/h.

To determine the error of the finite difference approximation we can write
L v = du/dt + tau where tau is the truncation error determined by Taylor series expansion. For accuracy tau must approach 0 as the grid size h approaches 0. Here we shall assume that the finite difference mesh size is 0 so that we can write the above truncation error equation in the form Lv= du/dt, i.e. the truncation error is 0. Subtracting the equation for v from the equation for u, the error E = u-v satisfies the equation

dE/dt = a E

and the error E satisfies the same equation as u. Thus any nonzero initial error will grow exponentially in time. (An initial error can come from a number of sources including observational error, forcing error, numerical error, etc.) The point is that the numerical solution will then deviate from the true solution exponentially fast in time.

Jerry

Gerald Browning

Ill posedness (tutorial)

Exponential solutions that are bounded in a finite time interval such as in the previous tutorial are allowed in mathematical theory and fluid dynamics, but as can be seen are a serious problem for numerical approximations. Now let us look at a more serious type of problem.

Consider the ODE (obtained from a Fourier series representation of a PDE)

du/dt = k u

where the integer k can take on any positive value. Now the growth is unbounded in any finite time interval (by choosing k sufficiently large). This type of behavior (unbounded exponential growth in any finite time interval) is called ill posedness of the differential equation and means that the solution is not physically reasonable nor computable.

To see how this problem affects numerical approximations of the
ill posed hydrostatic system used in the majority of global climate models, see the numerical runs on this thread. The numerical solution not only does not converge, it blows up as the mesh size is reduced exactly as expected in this tutorial.

Jerry

Gerald Browning

welikerocks (#304),

Exactly. The weather can be changed by many factors, but it is the long term behavior of weather that will show if there is climate change.
Ask a climatologist to precisely define climate. Don’t be surprised if the answers vary all over the place. 🙂

Jerry

Larry

309, reaching way back through the cobwebs, I seem to remember that there are “marching” solutions, and “relaxation” solutions to numerical diff eq problems, and the marching ones, as you describe, have the problems associated with extrapolation, because in essence that’s what they’re doing, where the relaxation solutions are interpolations, and thus better behaved. I’m assuming that the kinds of problems faced in the models are only suitable for marching solutions? In that case, I understand full the intractability of the problem.

lucia

@Larry:
I think Gerry is concerned with the illposedness of the continuum formulation. That is to say, he is discussing a problem that happens before you code the problem up, and which can’t be fixed up by any method of marching forward in time. I think you are thinking of problems that may occur when even well-posed systems get discretized.

I’m not familiar with the specific physical problem Jerrry is discussing, but “ill-posedness” is considered a very bad thing in a model for a real physical system.

MrPete

forest & trees:

I must understand that removing fuel (slash) from the bottom three meters of each individual tree (micro level understanding) will radically change the fire characteristics of the whole forest (macro level)…

I must understand how a tree responds to strip barking (micro level) to properly interpret the ensemble composite ‘response’ of a regional stripbark chronology (macro) over time.

A lesson learned long ago from developing GIS and thematic mapping… get the micro picture wrong and the macro picture will be garbage. It is rare that they are so disconnected that one can study macro without any concern for micro.

Gerald Browning

lucia (#315),

That is exactly correct. The cause of the ill posedness in the continuum
equations is the hydrostatic assumption in the neighborhood of
vertical shear (jet stream), i.e. the gravity waves have unbounded exponential growth as in the tutorial above. The gravity waves are also the source of the fast exponential growth in the nonhydrostatic system.
See the reference cited in the earlier thread.

Jerry

Gerald Browning

Signing off for the night. If anyone has additional questions relative to the tutorials or plots, I will try to answer them tomorrow.

Jerry

Gerald Browning

Steve (#322),

I would like to address your comment tomorrow.

Jerry

Gunnar

>> “leaves aren’t sediment”. Are we next going to move on to rabbits aren’t kangaroos. I’m now mystified by the what analogy you are trying to draw between weather and climate. Given your little remark about dilatation effects and your later explanations, I begin to suspect my mistake was to attempt to infuse some sensible meaning into your analogy

I went back over my posts to see if I insulted you in some way. I couldn’t find anything to explain this ridicule. I’m tempted to explain it again, but I think I explained it quite clearly in 298. Maybe, you’re in a place where you cannot adjust your level of abstraction?

Maybe the disconnect is not just scientist vs engineer, it’s abstract conceptual thinking vs concrete detailed math thinking.

I gave an analogy which you misunderstood as an example of micro vs macro, when it clearly wasn’t. I think the analogy is valid, since no one has pointed out where it’s wrong.

To illustrate the concept, imagine if you earned the post of Chief Climatologist of Earth, and you use the science of meteorology to study and predict the climate. Then, one day, the sun strengthened by 10%. The climate changed. The emperor comes to you and says “Why didn’t you predict this change?” And you respond, “I’m sorry your highness, my detailed weather model (micro) should have predicted this change, but they failed me, and I failed you”. The emperor says, one more failure, and it will be your head. Then, the planet’s orbit changes, and the climate changes again. The ending is not good.

Summary: It’s not a micro vs macro problem, no matter how much you want it to be. The problems are completely different, thus, so must the sciences of climatology and Meteorology be different. Climate can change the Weather, but Weather can’t change the Climate. Sorry, if this upsets you.

Conclusion: the argument against AGW “if you can’t predict the weather, how can you predict the climate” is invalid.

Gunnar

>> You may not think your question to me about taking account of time dilation is amounts to a rhetorical slap or eyeroll but I certainly do.

No, it was a serious comment, and meant to counter the argument made by you that micro effects are always important for macro analysis. It was certainly not meant to offend you, and if you took it that way, I apologize. The point still stands. Your principle:

The two problems are always related because forests are collections of many trees. More importantly, if we want to figure out how to correctly treat the forest as some sort of “average”, we do that by studying the “micro” problem

All I have to do is think of one contradictory example, and your assertion is invalidated. You say that one ALWAYS has to study the micro effects before studying macro effects. So, I ask you, do I need to consider time dilation effects prior to my road trip or not?

>> How is the person asked, or others, supposed to take that sort of question?

As a critical thinking counter argument. I speculate that you don’t like to be contradicted.

>> In 298, you say a number of things that make no sense what-so-ever. I could responded like this

Yet, you don’t explain why they don’t make sense to you.

>> If you thought I was, then you missed my point: fluid dynamics, no matter how chaotic, is irrelevant to climate, Wrong.

As Larry pointed out, I did overstate that, but the corrected statement would be: weather, no matter how chaotic, is irrelevant to climate. More specifically, the fact that the math to predict whether a storm will hit San Fran one month from now is impossible (or ill-posed as Jerry says) is irrelevant to a proper study of the climate.

>> which at the essence, is a thermodynamics problem. Wrong.

Care to support your assertion? I’m really curious as to how you would calculate temperature without involving thermodynamics.

>> Your arguments are founded on false ‘facts.’ Period.

Me thinks thou dost protest too much.

Larry

Ok, I think I just answered my own question about why the fluid mechanical modeling is so critical. It’s the feedback mechanisms that are so dicey.

Sam Urbinto

Gunnar; I totally agree, that is an invalid argument. Weather doesn’t have trends like climate does, comparing the predicting of them is not a valid concept. But we’re all in a circular argument, let me try and clarify everything.

Let me see if I can distill your #298
1) Weather – storm, not predictable in any meaningful sense.
2) The output of the sun is less chaotic, fairly stable, and therefore more predictable.

A meteorologist deals with the first, a climatologist the second. But then:

Concept 1: The sun doesn’t do anything to climate, it does something to the weather. The weather over time creates the climate. But you don’t really study the sun when you’re looking into weather. You might mention it’ll be out today though. 🙂

Concept 2: One of the things done when trying to predict climate change is to take how the sun is acting into account. Not anywhere in the way you look at it when thinking weather.

Don’t mix the concepts up, the first is cause/effect, the second is investigating the mechanisms.

“climatology is completely different than meteorology.” I don’t think anyone was arguing that they are the same thing (I think “completely different” is a overstated so I phrase it as they are not the same thing. )They are different fields of study, and discussing how they are similar or different is one topic. How weather over time is climate is another topic. I would say there’s some overlap between climatology and meteorology, but the mechanisms that overlap are looked at in a different way for different things. So in that way, they are completely different, but the differences are at times not so complete.

But trying to discuss both subjects (-ology and weather/climate) at once is just confusing things.

As I said, before discussing something, you have to get the terminology being used decided upon. For example, there’s a lot of stuff in statistics I don’t understand, and one of the reasons is a great deal of the math is beyond me, and another is the words and descriptions differ from the way I would describe them from a computer science standpoint where there is overlap/similarity.

I thought I made a good analogy of you can’t see the forest for the pesky trees. 🙂 But this is one of the things that makes me question the idea that there is such a thing as a “global temperature” or at least that the concept is meaningful. Taking the micro (local temp 35 C at airport thermometer location at measurement time) and making it a macro (departure from average global temp of 14 C (or whatever) over the course of a year). Be that as it may, certain other discussions require that it be taken as a given that it does exist and is meaningful; discussing the anomaly trend and its causes for example.

Now, would a weatherman discuss CO2 outgassing from the oceans in a forecast? Probably not. Does that have an impact on climate? I would say yes, because it does affect the portions of weather that result in climate. So in that way “weather” is not “climate”. But let’s just talk about one thing.

Weather and climate are not the same in the sense that weather is local short term (current) behavior, and climate is “some area” and how the patterns of weather act over time. In the sense that one creates the other, they are the same in the sense of a worm is not a butterfly and a tadpole is not a frog; weather is climate at a different stage of development. 🙂

Which is not exactly a micro-macro issue. What is one however, is turning the measured temperature (one aspect of weather) into a global temperature anomaly (one aspect of climate).

Returning to the forest fire analogy, if I don’t know at the start of a fire that the bulk of trees are ones that burn quickly and are in a fairly dry brushy area, I won’t know that fire will behave differently than the last one I saw that involved trees that burn slowly that are in a fairly moist grassy area. Or it could be some area that involves a mix of both.

But I don’t need to know the exact characteristics of every single tree for that purpose. I don’t think it makes it any easier to discuss this to try and generalize everything, especially not in absolutes. You have to know the purpose of what you’re doing to put things into perspective.

lucia

@Gunnar:

1) To answer your direct question:
No, I am not going to support my assertion that your unsupported bald claims are simply wrong. Several others have also told you they are wrong, and even provided the required support.

2) As to your notion that you have falsified my statement that macro and micro problems are always related: You are wrong. Accounting for time dilation effects has nothing to do with the “micro” / “macro” ways of looking at how long it takes for people to get from point A to B.

Estimating how long it takes one family (possibly your family) is the micro problem. You should account for whatever matters. I suggest accounting for potty breaks, and delays for explosive pointless arguments that result in the driver pulling off the side of the road and stewing. Unless you have rocket thrusters on your care, I’d suggest neglecting time dilatation effects.

Estimating how long it might take huge number of families similar to yours all traveling between the two cities for some popular event (like vacation, skiing season, christmas break) etc. would be the macro problem. “Sub-models” from the micro problem are necessary for this problem. (In this problem, one might also be able to account for the traffic jams that will ensue when all these argumentative people get behind the wheels of their cars and end up on the same problem.)

Note: The problems are related.
Note: time dilation is irrelevant to both problems.

3) Based on 327: you don’t understand what “ill posed” means.

4) The difficulties in predicting weather may or may not preclude predicting climate. That is an open question. I don’t know the answer, but it on why the difficulties exist and whether or not these go away when the “average” (climate) problem is addressed. Your bald claim otherwise does not resolve the question.

5) Trying to prove yourself right using obscure questions, mysterious incomprehensible analogies and telling other people you are the concrete thinker is futile. I’d suggest just stating your claims and trying to provide support.

Failing that, state your claim, tell people aren’t going to spend time supporting them and admit it’s fair enough if others don’t wish to be convinced.

Like this: When you say “weather, no matter how chaotic, is irrelevant to climate”, you are wrong. In fact, that’s bunk. But I’m not going to try to convince you by giving evidence. Feel free to continue believing that if you like.

@Larry–
328 and 329 look about right.

Will you share your popcorn? 🙂

MarkW

I’m probably going to regret jumping in here, but …

I don’t believe Larry declared that you have to be able to predict weather in order to predict climate.

He stated that in order to predict weather, you have to be able to model such things as individual storms. He went on to say that until we have an understanding of how storms work, we can’t model climate.

I believe he is claiming that we can’t predict either weather, or climate, because we don’t have a basic understanding of how the atmosphere works yet.

To put it another way, it’s not that one, climate, depends on the other, weather. It’s that they both depend on an understanding of the atmosphere that we just don’t have yet.

Larry

That’s about right. To correctly model feedback, we need to have circulation models that generate storms and other dynamics that result in the aggregate statistics being about right. This is not the same as predicting the weather, but it’s made out of the same things. More importantly, the problems that Gerry was talking about will prevent these from giving good aggregate statistics. Or at least that’s the issue raised here.

It should be easy to confirm or falsify this with a number of different model runs. If you tweak the resolution of the model, and the feedback changes, you got problems.

Gerald Browning

The reason that these discussions have become so heated is that no one has produced a mathematical definition of climate. Assume that there was a perfect model (analytical or numerical) that described the weather on the earth from moment to moment. Then define weather prediction and climate in terms of a mathematical formula that involves the output variables from that model. My guess is that there will not be any single answer by
a climatologist or anyone else. If that is the case, then arguing about the difference or similarities is pointless. And if there is a single answer, then a discussion of the flaws in any model can be discussed separately.

Jerry

Larry

339, I don’t think we need a mathematical definition of climate; we just need a mathematical definition of climate sensitivity. That’s what we need to condense from the behavior of the GCMs.

phil

Gunnar, forgive me for jumping in here, but in very broad terms climate is the integral of weather. While it may be very difficult to predict ONE storm accurately and it is not necessary to predict every single storm accurately, in order to take the integral of all the storms to come up with climate, you DO have to be able to accurately model weather in the aggregate to predict climate. The difficulty I have with the climate predictors is that their claims of accuracy far exceed the very measurable inaccuracy of weather predictions. They say they have many different measurements and they are all iid. But, when you look at them in detail, not only are the measurements not all measuring the same variable (i.e. many are proxies), but even the direct temperature measurements turn out not to be so iid.

You are correct in that it is possible to do top-down modeling (and I studied and did a little bit of that kind of modeling in school), but as I understand it, the predictors are not claiming that their models are top-down models, so the criticism of a disconnect with the micro elements of their models I think has validity.

If there are some top-down models I am unaware of, I would be very interested in seeing how they are constructed.

Gunnar

>> climate is the integral of weather

again, while true, that is a statement about the object being studied. Just like the puck doesn’t go into the back of the net without it’s atoms.

Gerald Browning

Larry (#342),

This is not a factual statement. Might I suggest that you peruse the minimal scale estimate manuscript by Henshaw, Kreiss, and Reyna
cited here many times.

Jerry

Sam Urbinto

We’re all trying to discuss something abstract that has no answer, perhaps. Like the blind guys and the elephant, or two people on opposite sides of a curved wall arguing if it’s convex or concave with the guy looking at the top of the wall North and seeing a half left circle and a guy at the underneath looking South who sees a half right circle.

comment-160933 MarkW, I think you put that well. I was merely disagreeing that ‘no weather prediction’ doesn’t have to equal ‘no tools for modeling feedback’.

But I tend to think of climate in terms of how the dictionary defines it, weather over time. Modeling either of them is a different thing (and are different things) but they depend on each other (or as you said, both depend on the same types of things, like clouds). And notice, I did say that how accurate and meaningful the models are is another issue. So once again, multiple topics that need to be discussed in separate ways.

I don’t think it’s needed to be able to model individual storms, rather to model the patterns so they are similar. Which is why I said, all we can get is an idea of how things basically work.

comment-160942 Gunnar, it depends on how you define climate. You define it as changes to temperature (which is not really the overall energy level, but close enough). I don’t. I define it as weather patterns over time. And weather is created by, among other things, the sun. I think we’re arguing over concepts and minutia we don’t need to argue about. I think they key here is that if we don’t understand how clouds work well, how clouds interact with water vapor, CO2, oceans and everything else in the cycle (including the clouds) we can’t model all the interactions well if at all.

And it’s not brain power to conceptualize the difference that’s the point, it’s not discussing multiple subjects at once as if they’re all the same thing, using terminology that’s not agreed upon, and that’s from different aspects of the issue and different viewpoints. That’s why I said circular, perhaps not the best choice of words.

comment-160943 Larry As soon as we get a model that when run takes what it was like 10 20 30 40 and 50 years ago and spits out results of what like 10 20 30 40 and 50 years(the now) later, and what it will be like in 10 years from now, I’ll let you know in 10 years I’m convinced the models are anything but guesses using poorly understood aspects. But we can’t say we can’t model them, just that the models are vague indications of poorly understood systems.

I wasn’t even trying to discuss models per se, just that there’s a difference between not understanding something and not being able to model it at all (no matter how badly!).

comment-160956 Gunnar, If you define climate as the entirety of the system, every aspect of the cause of weather and everything that affects it in any way, directly or indirectly…. I suppose I am a bit perplexed at you stating that man changing the attributes of the Earth is climate. Man chaning attributes of the Earth affects weather.

And this too. So is plate tectonics part of the climate or of climatology?

gb

Re # 345:

I wouldn’t formualte it like that. Chaos or turbulence in the atmosphere and ocean is important. It has a large influence in fact on the cicrculations in both the ocean and the atmosphere and consequently on climate. So, in any GCM the effect of turbulence (which is not resolved or only partly) has to be taken into account with parameterizations. But the aim of the parameterizations is not to mimic every single eddy but more the average effect of the turbulent eddies on the larger resolved scales and processes. This approach is probably sufficient for climate modelling. The same is done in all engineering models of turbulent models. The average effect of the turbulent eddies is modelled as good as possible. The resulting model does not predict exactly where and when an eddy will exist and how strong it is (this would be perhaps similar as weather prediction) but tries to capture the mean effect of the eddies which can still be good enough the compute the mean flow/drag (climate?). People can look this up in textbooks on turbulence or perhaps try a google and type in something like “large-eddy simulation”. There they use this approach.

Larry

As soon as we get a model that when run takes what it was like 10 20 30 40 and 50 years ago and spits out results of what like 10 20 30 40 and 50 years(the now) later, and what it will be like in 10 years from now, I’ll let you know in 10 years I’m convinced the models are anything but guesses using poorly understood aspects. But we can’t say we can’t model them, just that the models are vague indications of poorly understood systems.

Nonsense. If they’re really any good, we can go back in time, and see how well they predict the recent past. We don’t have to wait to see if they have predictive power. But, we can’t let our knowlege of the recent past influence our parameter selection.

Gunnar

>> I suppose I am a bit perplexed at you stating that man changing the attributes of the Earth is climate. So is plate tectonics part of the climate or of climatology?

To study the climate, one needs to study all the things that can affect it. This includes man’s actions, plate tectonics, etc. That means that these are part of climatology. It does not mean that they are part of the climate.

Sorry for the broken record folks, but… “object of study” vs “our study of”. Our study of something depends on why we are studying it. The purpose of meteorology is to predict the weather, an inherently difficult problem, because the weather is chaotic (even though Spence isn’t convinced it is [giggle]). The purpose of climatology is to study all the things that could affect the average temperature of earth. See conclusion in #325.

Gerald Browning

gb (#351),

Pure nonsense. The only mathematical proof that exists shows that if you do not properly resolve the minimal scales in a solution of the compressible NS equations, the numerical result is not accurate. LES is just another parameterization. You need to read the mathematical literature cited on this site.

Jerry

Gerald Browning

Gunnar (#356),

So where is your mathematical formula? Are you saying it is the mean temperature of the earth? For how long a time period is the spatial average of temperature suppose to be taken and at what vertical level?

Stop the verbiage and produce something rational.

Jerry

Gunnar

#350 >> But the only way to model chemistry from first principles is to model the sum of all of the chaotic behavior.

Only way? Are you saying that there was no science of chemistry before they modelled chaotic behaviour? Which came first, Ohm’s law or quantum electrodynamics? And even now, to design a power grid or a generator, I don’t need the quantum stuff.

#350 >> So yes, chaotic behavior does cause Gretzky to score. It also causes your car engine to run smoothly

A ridiculous statement. Again, you are confusing the object and the study of. Science is not reality, it’s the study of it. Conceptualize the abstraction. The atoms are necessary, in order for the puck to exist, otherwise, Gretzky can’t score. However, we don’t need to study chaotic atomic “vibration” in order to figure how anything about hockey.

#351 >> atmosphere and consequently on climate. So, in any GCM the effect of turbulence

It may be a factor, but there are other causes to climate change. Climatology must study those causes. A GCM may not be the primary tool needed for climatology.

Larry

Gunnar, whatever. You’re not even reading the words on the monitor. What part of “model from first principles” don’t you understand?

gb

Re # 357:

Jerry, perhaps you need to open a textbook or look in the literature. You just keep on refering to articles where you are one of the co-authors, but this is just a very, very small subset of the vast material on numerical simulations (direct numerical simulations, large-eddy simulation, just use google, don’t be afraid) of turbulent flows. Yes, you are right. If your goal is to reproduce one particular realisation precisely you need to resolve all scales and need to have to completely the same initial conditions. However, if your goal is to reproduce the averaged statistics (mean velocity, momentum transfer, drag. The averaged stats are the only thing that you want to know in engineering) you can use larg-eddy simulation for example, which doesn’ resolve all scales but uses a subgrid model. If you have a good subgrid then a large-eddy simulation can closely reproduce (not precisely) the averaged statistics obtained from a fully resolved simulation or experiments. There are scores of papers that prove this. I don’t think Jerry is so openminded to ever accept this, but at least I hope that other people look a bit further than just the papers mentioned by Jerry if they want to know more about the subject. Something similar should be possible with an ocean/atmospheric model.

Spence_UK

However, we don’t need to study chaotic atomic “vibration” in order to figure how anything about hockey.

Of course not. Molecular (not atomic) vibrations describe the IR spectra of molecules, not their motion. Why would the IR spectra of molecules influence a game of hockey?

Gunnar

>> you still haven’t yet got it. I’ll have another try because I’m a sucker for punishment (!)

Thanks for the ignorant straw man, Spence.

>> I didn’t say it was or it wasn’t

which confirms what I said: “even though Spence isn’t convinced it is”

That said, there is no proof or disproof that weather (or climate) is chaotic

I don’t need mathematical proof to confirm observation during the thousands of days I’ve been alive.

>> you’ve got against a peer-reviewed paper is “giggle” then you have a lot to learn

If the best comeback you have to logical arguments is a “peer reviewed” paper that questions whether weather is chaotic or not, then I have a right to giggle.

>> So where is your mathematical formula?

Who says you need a mathematical formula to define a concept?

>> Are you saying it is the mean temperature of the earth?

It’s not me saying it, that’s how the term is used, by both AGWers and anti-AGWers alike. The ideal would be to measure the Joules of energy.

>> Stop the verbiage and produce something rational.

[giggling] I think giggling is a more polite and mature response to ad-hominem.

>> Molecular (not atomic) vibrations describe the IR spectra of molecules, not their motion.

cause the IR radiation, not describe.

>> Why would the IR spectra of molecules influence a game of hockey?

Exactly. Why would the ability or non ability to predict a storm 20 days hence affect our ability to study how the sun, moon, stars, earth orbit, man etc, affect the climate? Using logic, I worked you into completely agreeing with my point.

Larry

Why would the IR spectra of molecules influence a game of hockey?

It’s not just the IR spectra, or all of the spectra, it’s all of chemistry that’s determined by those vibrations. And biology is determined by chemistry, and the hockey game is determined by biology. If those molecules don’t move, the game doesn’t happen.

D. Patterson

355 Gunnar says:

November 14th, 2007 at 12:47 pm

The purpose of meteorology is to predict the weather, an inherently difficult problem, because the weather is chaotic (even though Spence isn’t convinced it is [giggle]). The purpose of climatology is to study all the things that could affect the average temperature of earth.

No. Meteorology is a part of atmospheric science. Climatology is a branch of meteorology which concerns itself with the long-term statistical trends in the meteorological conditions in areas of the planet which exhibit persistent differences in such meteorological trends. The study of temperatures in the different climatogical areas is just one of many climatological conditions which compise the subject areas studied in climate science. The study of temperature is and never has been the sole subject of climate science, and the fact that different areas exhibit different climates with different meteorological conditions, including temperatures, is direct proof there is no such thing as an “average temperature of the Earth in the study of climatology. Whatever the average kinetic-heat content of the plantary atmosphere may be at any given period of time, that condition is the composite result of far more than just the sum of meteorological conditions that are the subject of study in climatology. That is why climatology is a sub-part of the broader disciplines of atmospheric science and physical science. Any approach to the study of climates which focuses on the study of temperatures while neglecting all of the other meteorological conditions and non-atmospheric conditions is utterly invalid and whimsical.

MarkW

There are several aspects to predicting weather.
1) whether a particular storm will hit Chicago or South Bend.
2) whether a particular storm will start at 1pm or 5pm.
3) how big will the storm(s) be
4) how long will the storm last

factors 1 & 2 are irrelevant when it comes to predicting climate.
factors 3 & 4 are relevant when it comes to predicting climate.

Gunnar is concentrating on factors 1 & 2. Hence his leaf in a stream example.
He is however ignoring factors 3 & 4.

Larry

376, the real issue here is, is it possible to know 3 and 4 without knowing 1 and 2? The important climate statistics depend on the details, and I don’t think anybody’s come up with a good way to arrive at the statistics without developing the details first. That’s what we’re all arguing about; is a detailed simulation of the atmosphere’s flows necessary in order to calculate climate sensitivity, or is there a short cut? If you think there’s a short cut, show me.

Larry

The motion of the molecules is quite separate to the molecular vibrations.

Oh? Enlighten me.

Gunnar

#374, I agree! My tweaks:

Whatever the average kinetic-heat content of the plantary atmosphere may be at any given period of time, that condition is the composite result of far more than just the sum of meteorological conditions that are the subject of [current] study in climatology, which is in it’s infancy. That is why climatology is a sub-part of the broader disciplines of atmospheric science and physical science [and many other sciences]. Any approach to the study of climates which focuses on the study of temperatures [(like current AGW papers) while neglecting all of the other meteorological conditions and non-atmospheric conditions [like solar, orbit, stars, man] is utterly invalid and whimsical.

Corrected statement of climatology purpose: The purpose of climatology is to study all the things that could affect the average kinetic-heat content of the planetary atmosphere.

Steve McIntyre

Mandelbrot (of fractals fame) pondered (See http://www.climateaudit.org/?p=396 http://www.climateaudit.org/?p=382

After this preliminary, let us return to the distinction between macrometeorology and climatology. It can be shown that to make these fields distinct, the spectral density of the fluctuations much have a clear-cut “dip” in the region of wavelengths near λ with large amounts of energy located on both sides of λ. But in fact no clear-cut dip is ever observed.

When one wishes to determine whether or not such distinct regimes are in fact observed, short hydrological records of 50 or 100 years are of little use. Much longer records are needed; thus we followed Hurst in looking for very long records among the fossil weather data exemplified by varve thickness and tree ring indices. However even when the R/s diagrams are so extended, they still do not exhibit the kinds of breaks that identifies two distinct fields.

In summary the distinctions between macrometeorology and climatology or between climatology and Paleoclimatology are unquestionably useful in ordinary discourse. But they are not intrinsic to the underlying phenomena.

Spence_UK

Re #379

The motion of molecules can be quite predictable, even under complex situations.

Lets take a simple system. Let’s put two hockey pucks in the middle of space, with no other matter nearby. The pucks will, quite predictably, move towards each other under gravity. They will bounce of each other, causing a loss of energy (primarily into heat). The will bounce away, until gravity brings them together again, again with a loss of energy, until eventually they will stop still, in the middle of space, resting against each other.

Lets expand that now, to billions of pucks in space, all moving randomly, colliding with one another. The pucks will exhibit Brownian motion, just like molecules in a gas. But Brownian motion behaves predictably on a large scale. Why? Because the error growth with respect to the initial conditions grows with the square root of time (simple mathematical demonstration of this). It is the evolution of errors of a random walk. Because of this, long term averaging – which reduces error linearly with time – eventually cancels out the random fluctuations.

This is why, when a force is exerted on the puck, it flies in a predictable direction.

The key is the evolution of errors. If errors evolve in a linear manner, averaging can cancel them. If errors evolve with an order lower than linear, averaging yields good results. If errors evolve with a higher order than linear, then averaging yields nothing – the error growth, even with averaging, accelerates away from you.

That is why the difference between a system exhibiting exponential error growth, or linear error growth, are critical to understanding whether it is easier or more difficult to solve problems on a larger scale.

Incidentally, my view on the game of hockey, is not on the larger scale issues of how the game progresses, but on the small scale issue that Gunnar was eluding to – when a puck is hit correctly in a certain direction, it goes in that direction, irrespective of the complexities of molecular behaviour.

Spence_UK

Re #380

Nice explanation, very neat! 🙂

Thanks.

lucia

@Gerry– 339.
“The reason that these discussions have become so heated is that no one has produced a mathematical definition of climate.”

Possibly, but the dictionary, national labs, the usda, GISS, and a variety of science departments at universities seem to share some the idea that climate is some sort of average of weather. Definitions of climate.

Definitions that separate weather from climate appear to be rather.idiosyncratic.

@Larry on 341– I think an accurate definition of climate sensitivity pre-supposes an accurate definition of climate. If climate is an ensemble average of weather,then climate sensitivity is a change in the any statistical property as a function of a forcing. (Example: Change in global average temperature as a function of increased CO2.)

@Larry– 368. Are you commenting on the difference in opinion about LES vs. DNS between gb and Gerry? That’s a very real issue and the argument actually is about whether or not one can get summary statistics like climate sensitivity by running GCM.

As to Gerry and gb’s specific claims: Both are saying some correct things. But, if you boil it down to “So, can we get climate sensitivity.” I don’t know! 🙂

Why not” I don’t know if LES resolves things well enough to provide decent answers on the AGW problem. I just not familiar with the literature on GCM’s, how LES may be implemented in the models or what runs have been done to demonstrate accuracy.

Generally speaking, the current state of LES is that it’s a decent tool when used properly — but it doesn’t always work straight out of the box for absolutely everything.

DNS is the only tool that is know to give correct answer in every problem all the time. However, DNS is too computationally intensive to use in most engineering flows. We certainly can’t apply that to the whole planet.

To get back to the question you asked long ago:

When assessing whether or not a parameterization (like LES) works, scientists and engineers do ask questions like:

“We can’t predict individual storms. So, how can be sure we predict their aggregate effect in an LES model?”

These questions are ordinarily considered good questions, and quite a bit of work is done to try to determine whether or not the models (like LES) capture the aggregate effect of storms (or any feature) sufficiently well to predict average behavior . (By the way, is the “micro scale” vs “macro scale” question. )

Sam Urbinto

Dr. Liljegren: This is a definition issue (although to be truthful, I don’t always feel as if everyone is having the same conversation at all; such is common in matters that are by nature abstract e. g. global climate)

As far as the discussion, all, I simply point everyone to my comment at http://www.climateaudit.org/?p=1516#comment-161068

The fact is they are both atmospheric sciences. They simply focus they studies on different things, and while both do not cover the same exact areas, they both cover the same thing at their core. That’s why they’re both atmposheric sciences.

You don’t need to know how a certain individual storm is going to act (weather), but you have to know how they act in general (climate). As long as we agree on that, can we “move on”? 😀

This boils down to, and I’ll paraphrase Gunnar, kinda:

You can talk about weather.
You can talk about climate.
You can study weather.
You can study climate.
You don’t have to study weather to study climate, but you have to understand them both, on different levels of abstraction.

So unless somebody wants to argue that both aren’t atmospheric sciences, there is nothing to discuss but the specifics of a specific topic. And I think that’s what Dr. Browning was alluding to in asking for a mathematical formula.

Larry

Lucia, if I understand you correctly, a corollary of that would be that if we can’t define climate, we can’t define climate sensitivity. CS is a rather core concept. Are you saying that it doesn’t exist? Are you saying that if you remove all dynamics and noise, we can’t know how much the GMT changes with a doubling of CO2? I don’t think that’s right.

I suppose that example implies that climate is the limit of weather as time approaches infinity.

Gunnar

Sam, thanks, you got me right. We should be able to move on, without any anti-AGW straw men about not being able to predict climate change, because we can’t predict the weather.

Larry

Umm….hydrogen don’t have no neutrons.

welikerocks

Sidebar: This web page gives a history of climatology
It was all about statistics and weather Gunner; in the beginning at least. And its current form (the climatology you describe or see) is a pretty new form.
link

It’s still all about statistics! (networking, groups and meetings too) Its a fun club! 😉

lucia

@Larry– Yes. At least in some sense, we need some definition of “climate” to define “climate sensitivity”. I’m not suggesting climate sensitivity doesn’t exist — I’m just saying that for two people to agree on the definition of “climate sensitivity”, those two people need to agree on a definition of climate. Later, if they wish to quantify “climate sensitivity”, they need to agree on metric.

So, you could have a set of three compatible definitions like this.

1) Climate is the average characteristics of weather. (This would mean the average of any quantity that can be averaged. It might even include standard deviations etc. Also, we can argue about what sort of average is applied to any measurable characteristic. )

2) “Climate sensitivity to X” would then be any change in the average climate as a result of a change in an external variable X. This would be a generic idea.

3) By official decree, we could decide the metric used to measure climate sensitivity will be the global average temperature based on measurements at stations “A, B, C…. Z”.

If you don’t agree on (1) it’s very difficult to agree on (2) and nearly impossible to come up with a metric (3).

Later on, even if you agree on 1,2 & 3, there will be difficulties that have to do with usage. Notice, I slot “climate sensitivity to X” under #2?

It appears the IPPC uses the term “climate sensitivity” to describe this specific metric : ” the equilibrium change in global mean surface temperature following a doubling of the atmospheric (equivalent) CO2 concentration.”

Meanwhile, you’ll see the state of California and the AMS use “climate sensitivity” this way:

“the equilibrium response of the climate to a change in radiative forcing; for example, a doubling of the carbon dioxide concentration. (EPA)”.
http://www.climatechange.ca.gov/glossary/letter_c.html

“climate sensitivity—1. The magnitude of a climatic response to a perturbing influence. 2. In mathematical modeling of the climate, the difference between simulations when the magnitude of a given parameter is changed. 3. In the context of global climate change, the equilibrium change in global mean surface temperature following a unit change in radiative forcing.”

The AMS usage fits my (2) above.

Are you saying that if you remove all dynamics and noise, we can’t know how much the GMT changes with a doubling of CO2? I don’t think that’s right.
I’m afraid I’m not sure I understand what you are asking me,… If we remove all dynamics and noise from what? STill, I suspect you are asking me about my comments on the Gerry/gb argument. So, I’ll try to answer..

1) If we retain all dynamics in a “DNS-like” computational model, and remove all “noise” do to round-off etc, we should absolutely positively be able to predict h ow much GMT changes with a doubling of CO2. Arguments between GB and Gerry would evaporate because we’ve captured everything in the computation. (These models aren’t used.)

2) If we remove all dynamics from a computational model to predict climate, I doubt we could predict anything at all about what happens if we double CO2.

3) If we include dynamics but mess them up a little (or even a lot), we may be able to get “good enough” predictions. Or, the predictions may be horrible. It depends on how messed up the dynamics are, and whether or not those matter. Also, we can’t know in advance, and there is nothing in the results that lets us know the answers are wrong. (This is where arguments about LES ensue. I don’t know the answer.)

“LES” which gb favors, falls in category ‘3’. It messes up the dynamics a least a little.

If I understand Gerry, he thinks LES models don’t capture the aggregate effect of the relevant dynamics well enough. He advances some valid arguments to support his view..

“gb”, thinks LES models do capture the aggregate effect of all relevant dynamics well enough. He advances some valid arguments to support his view.

I can’t chose between the two views, but that’s because I simply don’t know enough about GCM’s.

Does that answer the question you intended to ask?

Larry

Lucia, but the metric is well defined (sort of). There’s a version of climate sensitivity in W/m^3, and one in terms of degrees C. Both are in response to a doubling of CO2 (because the logarithmic form of concentration dependence is uncontroversial). So now that we’ve nailed that down, is climate defined?

Spence_UK

You mean, I don’t understand the math behind chaos. I do understand what the chaos concept is.

From what you’ve said so far, I’m not sure you do. You certainly do not understand the scaling structure associated with chaotic systems. That is a pivotal aspect that would prevent you from thinking errors can always be averaged away. Exponential error propagation cannot be averaged away by moving to larger scales. It gets worse. This is a critical, and very simple to understand concept, that entirely refutes your arguments. The only reason the examples you give work is because none of them involve exponential propagation of errors from initial conditions, i.e. none exhibit chaotic behaviour.

which would be an argument about whether weather is chaotic or not. That’s a straw man that I don’t need to answer, since my point is not that weather is chaotic, although I’m quite certain it is. (see #270, 281, 294, 298, 306 and the conclusion in #325)

The document I linked to described chaos in the context of scale behaviour. Climate is merely rescaled weather (in the context of an IPCC like definition). But you still don’t understand the fundamental relationship between scale, chaos, exponential error propagation etc.

If you are quite certain that weather is chaotic, you should publish. It has yet to be demonstrated convincingly, as far as I am aware. Your arguments do not adequately test for chaos. The document I linked describes many of the simple errors people make when inferring chaotic behaviour, and some of the accepted methods of test.

I’m talking about the study of things, not the object itself. Hello? Can you possibly switch abstraction levels? You misunderstood my logic completely, I’ll clarify:

premise: Molecular vibration is chaotic
premise: Some people may choose to STUDY those molecular vibrations
premise: Some people may choose to STUDY how to win a hockey game
premise: Studying molecular vibrations does not help win hockey games
Conclusion: Studying the chaos of puck molecular vibrations is not necesary to winning

Then your argument is irrelevant. Winning a hockey game cannot be inferred from molecular vibrations because they are an irrelevant, separable system. I can set up a double pendulum at home, it will exhibit chaotic behaviour – and lo and behold – it will not influence any hockey matches. Weather is not separable from climate – the two are closely linked. If there is a scaling relationship between the two, and long term persistence, then weather influences climate. If exponential error propagation exists, then moving to longer scales makes prediction more difficult, not easier.

But Dr. Browning is right. Chaos is irrelevant. Non-chaotic systems can exhibit these problems as much as chaotic systems, so the point is moot anyway.

Spence_UK

A valuable excerpt from a paper by Prof Koutsoyiannis here which includes valuable insights on scale:

Dominant doctrines behind paleoclimatic methodologies, which may influence the validity of results, are the (manichean) dichotomy of natural time series into deterministic and random components (“signal” and “noise”), and the (procrustean) suppression of low frequency fluctuations of time series so that they comply with an ab initio postulate of a Markovian behavior [see also Wegman et al., 2006] The dichotomy “signal” vs. “noise” has been borrowed from electronics, where indeed is meaningful, but lacks meaning in geophysics (unless noise is used to describe errors, either in measurements or in models).

All natural processes are Nature’s signals – not noises even when they “look like” noise. To describe these signals one may use either a deterministic or a stochastic approach but this is totally different from admitting that natural processes consist of two types of components. Obviously, a stochastic approach can incorporate any known deterministic dynamics (cf. the modeling of periodicity by cyclostationary stochastic models) but again this should not be confused as separation of components [Koutsoyiannis, 2003, 2006]. Such a separation, unfortunately very commonly performed, entails risk of misrepresentation of low frequency natural fluctuations as “deterministic trends”.

It must be a good paper, because it cites ClimateAudit 😉

Pat Keating

392 Gunnar

Only something external can affect the average weather, and that’s what climatology is about.

There are many kinds of ‘average’. If you are referring to an average over say 100 million years, that is quite different from say an average over a 100-year period. The former is not too meaningful or useful in the context of ‘climate’ as far as mortal humans are concerned.

The latter is more meaningful, but your statement is wrong for that kind of average. The average weather for each century can and will vary from one century to the next without the need to invoke “external somethings”.

What are you using as YOUR averaging period?

Sam Urbinto

I meant the definitions of climate and weather.

In case nobody noticed, I switched between using chaotic and not using it. It doesn’t matter if it is or isn’t.

This is my last word on the subject, they are clearly defined. You could always go argue with the editors of wikipedia on the subject too! 🙂

http://www.answers.com/topic/weather

http://www.answers.com/topic/climate

http://www.answers.com/meteorology

http://www.answers.com/topic/climatology

Climatology
The scientific study of climate. Climate is the expected mean and variability of the weather conditions for a particular location, season, and time of day. The climate is often described in terms of the mean values of meteorological variables such as temperature, precipitation, wind, humidity, and cloud cover. A complete description also includes the variability of these quantities, and their extreme values. The climate of a region often has regular seasonal and diurnal variations, with the climate for January being very different from that for July at most locations. Climate also exhibits significant year-to-year variability and longer-term changes on both a regional and global basis.

The goals of climatology are to provide a comprehensive description of the Earth’s climate over the range of geographic scales, to understand its features in terms of fundamental physical principles, and to develop models of the Earth’s climate for sensitivity studies and for the prediction of future changes that may result from natural and human causes. See also Climate history; Climate modeling; Climate modification; Weather.

——————————————————————————–

Larry

Lucia,

IPCC members must have agreed absent addition of CO2, equilibrium exists.

Or that there’s an equilibrium, if all forcings are held constant, that forms a baseline on which the chaos of weather is superimposed. I believe that’s the assumption. Then, they try to determine how doubling CO2 perturbs that.

Spence_UK

@Spence_uk: I think Gunnar is the only one discussing or describing weather or climate in terms of chaos.

Lucia, indeed, that is why I’m not really arguing with anyone else 😉

The interesting thing (to me) is the IPCC members must have agreed absent addition of CO2, equilibrium exists. This means we should all be arguing about whether or not “equlilbrium” is possible and not about “ensemble averaging” vs “time averaging”.

Indeed, and there is a really nice discussion here (click on preprint) on the consequences of long-term persistence / scaling behaviour on averages, and what they mean (note: no need to invoke chaos!); particularly the intro (pp1-3) and doesn’t the “long-range dependence” plot on pg 8 just look so much like a global mean temperature plot? It has the correct scaling behaviour too, which stochastic / markovian models lack.

Steve Sadlov

RE: #278 – Scorecard, Day 1, PM. NWS now slightly backpeddling regarding occluded front slated to move in from the Pacific tomorrow and Friday, now saying POPS in the northern part of the CWA. But still sticking to their guns about dramatic AGW signal superimposed on normal seasonal cooling and dampening, resulting in killer, unprecedented late season offshore event after Friday. We’ll see.

Larry

Oh, don’t tell me that it depends on what “is” is…

Pat Keating

418 lucia
Ontology is too rich and abstract for me — I’m just a simple physicist. But the ice-core record looks a lot like a noisy bistable oscillator output to me. It spends a lot more time transitioning from one limit to the other than sitting in equilibrium.

BTW, there was an interesting oscillator-period shortening to 10^5 yr about half a million years ago. Nobody seems to care, but I wonder why?

Pat Keating

420 Gunnar

In fact, I’m talking about a geographic average. Time averages are not very interesting.

You are talking about spatial averaging, not time-averaging? What on earth would be a sensible use of taking an average of the weather in India, Spain, Iceland, and Russia?

Sam Urbinto

larry, all I’m saying is that the chaos stuff I’ve read uses weather as an example at times. I’m not trying to discuss the merits if “Sensitive Dependence on Initial Conditions” applies to weather or not. I don’t know and it’s not really relevant to the conversation if it’s chaotic or not.

gunnar, sometimes (*ahem*) you frustrate me. I’m not using a straw-man argument. I’m not even really arguing at all. I’m telling you that the idea of a global mean average temperature is helpful for thinking about some things, but isn’t real. It isn’t a thing. It’s just some derived number. Just because it’s “valid” to average averages of averaged huge areas for an anomaly doesn’t mean the number is meaningful, even if it’s accurate. Get over it.

I fear I’ve made it so Dr. Liljegren thinks I’m either pro- or anti- AGW theory (idea, hypothesis, whatever). I just don’t know. I have made it clear many times that I don’t care what the truth is, I just want to know it. Arguing about minutia is rather counter productive (what is is)

Pat Keating, if you look at the absolute values of the anomaly for GHCN-ERSST, it also tends to bounce up and down from around .7 or so (as a global mean anomaly) So I agree whole-heartedly!

I’m not really trying to figure anything out, Spence_UK. I’m just saying in chaos theory the case is made that weather is chaotic, so it’s not like it’s anything new.

Lastly, let me state this one more time, if I could.

YOU CAN’T HAVE CLIMATE UNLESS YOU HAVE WEATHER.

And that they’re both sub-disciplines of the atmospheric sciences.

lucia

@ Sam Urbinto 425
Don’t worry. I can’t begin to guess if you are pro-or anti AGW based on I’ve read. I’m fine with either point of view and like you don’t know what the truth is. Over time, I’m likely to get every one angry.

This is probably not important, but if you feel the need to use “dr” it’s probably wise to use “dr. lucia”. There is another “Dr. Liljegren”. Probably no-one on this thread has heard of Jim, but he used to actually work on projects in the area of climate change. (Not GCM’s!)

So, in the off chance a random reader might get confused, “Lucia” is better!

Spence_UK

If you believe that everyone is barking up the wrong tree, you should publish.

No need. Prof. Koutsoyiannis has already published this viewpoint. From the peer-reviewed articles I linked to above, one of which you giggled at. Worth noting one of the articles I linked to above was rejected by GRL, but accepted by a hydrological journal. Shows the reluctance to accept these concepts in climate science circles. I suspect the story they tell ties in well, from a stats viewpoint, to Dr Browning’s work. I can’t tell for sure, but there seem to be certain similarities; and both viewpoints appear to be under censorship from the climate science peer review process. Someone doesn’t seem to want this viewpoint in climate science.

Except that I agree with the quoted text in 407. I have said the exact same thing in this blog.

Then read the papers. The direct consequence of this is that the fine scale structure has large scale structure consequences. The postulate is that the causal mechanism of the event (e.g. storm, rainfall) exhibits self-similarity. If you want to argue that an additional, anthropogenic influence is dominating behaviour above this self-similarity, you need to test the natural clustering behaviour of events, which is a direct consequence of the fine detail of weather, not from the broad brush of climate.

bender

Those philosophizing on the nature of the difference between weather and climate should re-read Neil Haven’s #3. The question is not whether global averages are meaningful, but how meaningful. If climate (measured by whatever set of parameters you like) has central tendency, then a mean is very meaningful. The more complex the equilibrium state, the less meaningful a single parameter is. If weather is governed by a strange atrractor, not a single point attractor, then so is climate to some degree. Some have remarked on a tendency toward long-term global bistability. i.e. There is no central tendency; there are two tendencies. That is in the time-domain. i.e. A long-time average may do a poor job of describing the climate system’s state at any given time.

How about in the spatial domain, since we are talking about the meaningfulness of global spatial averages? Well, the same multi-stable behavior observed in the time-domain appears in the spatial domain as well, whether you are talking short-term weather or long-term climate. How comfortable are you with a single scalar parameter as a descriptor when there is persistent regionality? Of course, the global circulation records do not go back that far, but there is evidence emerging that ocean currents, for example, may be intermittent, or reversible, that atmospheric ciculation may snap in and out of certain configurations, and persist that way for quite some time. What is “stable” over secular scales may not be stable over millenial scales. I don’t see how one can argue that chaos exists at weather scales, but not climatic scales. Chaos is not temporal, it is spatiotemporal. And it is not necessarily featureless – not if the attractors are strange.

Here is where the artifical distinction between weather and climate really breaks down. Is ENSO/PDO/NAO/THC “stable”? Is jet stream “weather” or “climate”? Given that these emergent features are post-hoc classifications of meso-scale phenomena, maybe other characterizations would be possible at other times. We don’t know. We haven’t been observing the system in enough detail long enough to know. Some features are convincingly stable like polar jets and ITCZ, others less so.

I don’t like the dichotomy of weather vs. climate, but of course there are good practical reasons why we are taught to think that way. I just think that statistical meteoclimatology is in its infancy and we should keep open minds. Remember that an average is not always meaningful, even if it is calculable. Fluid systems are more complex than that.

My intent here is not to correct anyone (especially not lucia or Gerry), but merely to highlight that there is some truth in all these comments. Let’s try to be civil and keep a high SNR ratio on this thread. Save the trolling self-indlugence for “unthreaded”.

Steve Sadlov

By the way, alluding to some of the BCP related threads, this is a classicscenario for formation of a Tonapah Low!

Gerald Browning

Gunnar.

Lucia and I have both discussed our scientific background. Can you describe yours. Thank you.

Jerry

Larry

434, I was able to get that from other comments, but what the (largely engineering) crowd here I think is having trouble with is translating that into terms that have something to do with the calculation of the climate sensitivity (which is the goal here). If you don’t make that connection, this is all a lot of abstract gobbledygook. So to bridge that gap, please confirm that the problems in the numerical models that you’re describing make the calculation of climate feedback (and thus climate sensitivity) inaccurate. Is that a fair statement?

Larry T

One of the things I like about C is the number of well qualified contributors that post here both for AGW and against. I wish that SM would add to the website a way to go to the credentials of these well qualified individuals and see their backgrounds and expertise. I am not as well qualfied as others to comment on various issues but I have B.S. Mathematics and did graduate work both in Applied Mathematics and Computer Science. My early career was Space related and have continued interests in the effects of solar activity on our weather and computer modeling of physical systems. My speciality over later years was data base administration and data integrity. After I finish upgrading my personal computer with some compilers, I hope to be able to contribute and no longer just be an avid reader of the site. So please continue to identify your backgrounds bacause it adds to the credability of the site.

steven mosher

RE 438. Dr. Browning

Your threads are like being back in school. And with Lucia, gb, bender, dan hughes and others the SNR
is very high. So my head hurts and thats a good thing.

Once in while we need a break. Which is why I love Sadlovian interludes about the forecast.

Gerald Browning

Larry T (#439),

I think you will find that the honest contributors on this site will have no problem citing their backgrounds or credentials or even their true identities. It is the ones that cite none of these that I think have typically been problems. 🙂

Jerry

Gerald Browning

steven mosher (#441),

Well being back in school could be a good thing or a bad thing. 🙂

I prefer not to be too technical because then one loses some of the audience. On the other hand, when you use simple mathematical examples and numerical demonstrations, the SNR drops considerably. My hope is that between the two approaches, there will be a better understanding
of the care that must be taken when using numerical models to predict
physical reality and the problems with weather and climate models.

I will try to answer any reasonable question by those seeking knowledge, and will defend any of my statements with rigorous mathematics if necessary.

Jerry

Larry

I’m not trying to hide anything, I just didn’t think it was important. I have a MSChE, and PEs in ChE, CsE, and EE. I’m familiar with the nature of the Navier-Stokes problem, but used to talking about it in different terms. But I don’t think this has anything to do with my issue; I’m just trying to understand the ramifications of this for the climate issue.

With this level of discussion, I’m not sure that I could articulate that this makes the climate sensitivity estimates close, way off, or garbage. Sorry if I seem fixated on that, but as far as I can see, that’s the connection to CA. Or is there a connection to another climate issue? I’m not trying to be negative, I’m just trying to make sure I understand the downstream consequences of this.

Gerald Browning

Larry (#447),

You have been asking reasonable questions and I have been trying to answer them in the best way I can. You have not been one of the problems and so I find it no surprise that you have been so open.

Keep asking questions if I do not make sense.

Jerry

Gerald Browning

Larry (#447),

I think most climate models use a mesh size ~ 100 km. They are not able to resolve any mesoscale (100 km length scale) features (hurricane details, squall lines, fronts, thunderstorms, etc.) with a finite difference mesh
of that size even if the model forcings were perfect (which they are not).
In order to resolve features on the next to the largest scale (1000 km),
the model would have to use a mesh size of 10 km or less. At that point the numerical problems cited above occur, i.e. the numerical solution will become nonsense. So climate models do not resolve the very basic features of the atmosphere and use parameterizations (artificial forcings)
in an attempt to account for those features. It has been shown in both a global weather prediction model (Sylvie Gravel’s manuscript) and in NCAR’s own climate model (David Williamson manuscript) that these forcings lead to a solution that deviates from reality in a matter of hours. You can tune these forcings to stay closer to reality over a few days (see discussion of boundary layer approximation in Sylvie’s manuscript), but that does not mean the numerical solution is any closer to reality, especially over longer time periods. In Sylvie manuscript the errors in the boundary layer
parameterization propagated vertically and caused O(1) errors in the solution within 36 hours. The only reason that the model continued to stay on track was the assimilation of new wind obs every every 6-12 hours
(reference by BK). If a model is not even close to reality, there is no scientific case that it is useful for anything.

Jerry

Gerald Browning

lucia (#450),

Just a few technical comments. Stability analysis for numerical analysts
investigating time dependent ODE’s and PDE’s usually refers to the stability of numerical approximations of the systems. The analysis
of posedness is of the continuum PDE system itself. The continuum system
must be well posed before any attempts are made at numerical approximations. Then the finite difference approximation must be checked for accuracy and stability to ensure convergence (Lax’s equivalence theorem). If open boundaries are present, a more complicated posedness and stability analysis are required (Kreiss).

The ill posedness of the hydrostatic system and the rapid growth of the
nonhydrostatic system is caused by the gravitational term, not the Coriolis term.

For those that want to see demonstrations of both problems in the corresponding systems, they can look at the plots mentioned above. Both use multiple decreasing resolutions to display the problems, i.e. convergence tests that should be run on all numerical models.

Jerry

Pat Keating

453 Jerry
I ran the GISS Model II with our infamous carboniferous GHG at 1 ppm instead of 280 (or 300). It ran for about 30 years, going to a ‘new’ ice age (12C lower, 40% of the water vapor, rel to initial/present-day), before going unstable.

Any ideas on why would it go unstable after running OK for 30 years?

Larry

Gunnar, the enthalpy of the atmosphere is zip compared to the enthalpy of the oceans. I presume that was what you were driving at with the “energy level”?

lucia

Stability analysis for numerical analysts investigating time dependent ODE’s and PDE’s usually refers to the stability of numerical approximations of the systems. The analysis of posedness is of the continuum PDE system itself.
Yes– I was under the impression the ill posed issue related to the continuum model. Similar erupt arguments over developing parameterizations for multiphase flow equation. Ill-possed-ness in the continuum equations is a big no-no. Big.

I suspect your comment is prompted by the fact that I I brought up gb’s discussions and claims about LES. I brought this up because LES has the particular feature that the “eddy viscosity” (if you wish to call model for the Leonard stresses that) should automatically vanish as the grid size drops. That’s the way that method works.

So, if the eddy viscosity acts as a patch to cover ill-posedness, then LES may work at large grid sizes and then stop working as the grid sizes drop because, to use a metaphor, the bandaid gets taken off. Worse results at smaller grid sides is the opposite of what LES is supposed to do.

But basically: If you are correct about ill-posedness and gb is correct the GCM’s use LES, then the modelers will soon be scratching their heads when they reduce the grid size and things get worse not better.

But, I don’t know if GCM’s use LES. They may use a RANS type (Reynolds averaged Navier Stokes) formulation. Under this concept, “eddy viscosity” describes momentum transport due to turbulent fluctuations and the mean flow. The amount of energy in the small scales has nothing to do with the grid size. Consequently, the eddy viscosity parameterization is grid independent. It won’t vanish as the grid size gets smaller.

So, in that case, the response to the idea that eddy viscosity is unphysical would be: “it’s physical. It’s just not a molecular property. ” Arguments could ensue as to whether their closure for eddy viscosity provides the correct magnitude in any particular case, but the patch for the ill-posedness would remain intact as grid sizes dropped. Modelers also won’t see things blow up as the grid size vanishes.

That said: gb says the GCM’s are LES. The idea of LES is newer RANS, and is introduced to resolves problems with getting RANS to work in general cases. (There is also a progression of creating more and more and more complicated RANS formulations to fix up lack of generality of the earliest formulations. RANS and LES coexist, and I don’t know which is used in GCM’s. Likely both are.)

bender

Consider that the only purpose of averaging for time is to remove the “noise” of weather. A global spatial average does this.

Perhaps. But what do you do to remove the “noise” of climate, recalling that exponential growth may lead to strange attractors and feature-laden “noise” structures at ALL time scales? Over what time-scale do you integrate weather to get climate? Or is this not possible, as Spence_UK seems to suggest (in #429 and elsewhere)?

(lucia, love your use of brackets.)

lucia

@bender — You’re an honest to goodness statistician right? I have a few honest to goodness stats questions and also some “how to do that with R” questions. Would you be someone I can ask? (Sorry to go off topic.)

Gunnar

Re: A global spatial average does this.

>> But what do you do to remove the “noise” of climate,

As I have independently concluded and stated in this blog, which is also stated in #407, there is no noise in climate, by definition.

>> recalling that exponential growth may lead to strange attractors and feature-laden “noise” structures at ALL time scales?

That is someone’s unverified hypothesis, especially when it comes to long term weather. It’s also completely dependent on the time averaged definition of climate. In fact, with this improved definition, the whole problem goes away, since this “strange attractors” hypothesis could be true at all time scales, and not effect globally averaged temperature, ie climate.

>> Over what time-scale do you integrate weather to get climate?

Who says we have to? A global spatial average does this. Climate is a word that denotes a concept. Concepts are valid or invalid, based on a comparison to reality. There is a reality to a global, spatially averaged, temperature. There is no reality associated with a time averaged temperature, since it is only a contrivance of the analyst. Physical reality is affected in real time. The reality described by the time averaged view looks like this:

A Sun, with a constant solar strength averaged between night and day down to 341 W/m2 shines on earth, a flat plate in space. Summer is averaged with winter, solar minumum averaged with maximum. In this make believe world, people don’t put sun screen on, since when averaged over night and day, the sun isn’t strong enough to burn skin. If a house starts to burn, firemen don’t come, because when averaged over a long enough period, there is no danger.

Reality doesn’t work that way. And btw, did you hear? The Mississipi just swung wildly all over the place. It was a real mess. One minute, a nice town in Iowa was 40 miles from the river, the next, the river came right through the town. The smart folks from the University took time off from torturing grad students to point out that “the chaos in the river flow works on the macro scale as well”.

bender

#463
I know what I know: just enough to get by. Ask away in unthreaded. I’ll help if I can. I know R.

Gunnar

You >> “What is the climate in northwest Alaska?” does make sense.

Me: >> Right, and it’s spatially averaged. All too easy.

I need to clarify this. Because you gave an area, it’s clear that the information is spatially averaged. When someone looks up information about the climate of a certain area, they are NOT interested in the average over a whole year. They want to know how hot it gets in the summer, and how cold it gets in the winter.

I don’t the know the annual average where I live, nor do I care. I’m just pointing out the defacto definition is different than what you very highly educated people are using, and the defacto definition makes sense. If that takes the fun out of your very exciting discussion of strange attractors, I apologize.

Gerald Browning

bender (#470),

I think that we have established that Gunnar only uses nonsensical verbiage.
I wouldn’t waste any more time on him. Also note that he won’t mention any of his credentials
or background. Sound familiar.

Jerry

Pat Keating

468, 469
I will eschew further argument/discussion with you — it is too frustrating. Perhaps you and I are from different planets…….

Gerald Browning

lucia (#455),

I have a few additional comments and will get back to you.
Your arguments are eminently reasonable and I was just describing the mathematical lingo for comparison with the fluid dynamical lingo.

Jerry

Pat Keating

472
Seriously, as a neophyte in climate modeling, I was somewhat (but not totally) surprised. I think of a mere 1-300ppm of the carboniferous gas embedded in a lot of N2, O2, and H2O as a perturbation, so that a decent model should be able to handle that range. It is obvious, from the ice-age result obtained, that to the modelers it is much more than a perturbation.
Of course, to be fair, the model was developed before the lag in CO2 level was discovered……..

MrPete

Another page on Conway’s Life with a great “applet” that lets you see how it works. Zoom to level 0 to see a lot of detail.

lucia

MrPete in 478
You have my view right. And with the qualifications as stated, you can add, I also agree with Bender. That’s why I was discussing the micro/marco scale point of view issue.
You’re example is great. Sounds like a very educational game.

@Gerry–
In 291, Gunnar gave his credentials this way:
“I have a BSEE, as does my wife & older brother, while my father had a PhD in EE. My mother has a masters in history, my uncle a PhD in Physics.”

Gunnar

>> In 291, Gunnar gave his credentials this way

Ahh, you shouldn’t have told him, since he is clearly pursuing a logic fallacy.

steven mosher

MrPete,

You must get Wolframs book.
http://www.wolframscience.com/

bender

-dismissive
-presumptive
-ad hom
-redundant

yep, it’s a troll.

Ok, Gunnar, I’m not going to engage you point-by-point on your ridiculous rebuttal becauae it’s an infinite regress with you. But I’m listening. Just tell us, in a snappy paragraph that is on-topic, what is this amazingly insightful argument of yours that we’re so incapable of seeing? We’ll try hard to keep up with your brilliance. Make it fast, my carbonic soup is bubbling.

Gunnar

#487, >> it’s a troll

careful, you just defined many posters here as trolls.

>> in a snappy paragraph

read #480

Larry

It’s all a big conspiracy, ain’t it?

Mosh – that Utube is perfect.

bender

Gunnar,
Your attitude is ironic given I (and Mr Pete) are the only ones here trying to salvage something from your train wreck of an argument. You should be nice to us. #480 – which I already read – is incoherent, which is why I asked for something coherent.

To be generous, your fundamental argument seems to be that:
(1) there are certain features (i.e. oceanic & atmospheric flows) of the climate system that are persistent, either indefinitely, or over incredibly long time scales, and
(2) that this persistence justifies a division of time-scale between that which is “meteorological” vs “climatological”, and
(3) therefore arguments about “exponential growth in physical systems” do not apply at those longer time-scales.

Forgive if I misrepresent anything, it is not intentional. Regardless, my sense is this is the RC perspective. So I will continue.

Now, being a soup cook, I do not have a professional opinion. I merely want to understand:
(1) the empirical basis for the assertion that certain features of the climate are immutable (or persistent)
(2) the empirical basis behind the assertion that the internal variability of the terawatt heat engine is miniscule compared to the external forcing
(3) the logical basis behind the assertion that the GCMs have been tuned to a “representative” set of weather/climate scenarios

I don’t have an argument. Only questions. Can you answer any of them? (My prediction is you’ll try to unask all of them.)

MrPete

Gunnar, your pool analogy states your perspective very well. Unfortunately, neither you nor the modelers have provided any evidence to support this assumption.

Jerry and Lucia are providing a detailed education, for those who have ears to hear, about exactly why your assumption is incorrect.

You won’t be able to counter their argument with ever more strident exclamations. They hear you. You need to hear what they are saying. They have evidence to *prove* that the measurement/analysis systems/methods are connected, not independent.

Larry

494, if you read Gerry and Lucia’s comments carefully, you’ll see that a flow field around a (relatively small) object and a flow field in open space (subject to hydrostatics) are two entirely different problems. And that’s not even bringing the Coriolis effect, and temperature gradients, and humidity gradients, and a number of other factors into the picture.

steven mosher

RE 490.

I am not a teacher.

I wrote ” sometimes I HAD a kid in class” If I were currently a teacher I would have written
“sometimes I HAVE a kid in class”

I fail to see how you have clarified anything or can clarify anything when you
cannot begin to understand the implications of a simple sentence.

Larry

Don’t. Rattle. Cage.

bender

climate is the spatial average of weather, not time averaged

Ok, thanks a lot for that. [Backs carefully away from cage.]

Larry

504, but over what scale? Enough so that these variations (pressure temperature, etc.) enter the picture? There’s a lot more to this than just fluid mechanics.

Here’s a challenge: Simulate a cloud. Produce a 3D data set of a) albedo effect, and b) IR absorption. Include in the IR calculation effect of heat bypassing the absorption by vertical convection. Think you can do all that? Good luck.

gb

Bender, I have never worked with climate models. I have an engineering backgroud and do research into turbulent flows. However, I have read quite a lot about climate, atmospheric dynamics etc. and now a bit about the parameterizations they use. These are somtimes not that different from the ones used in engineering models. Circulations are not parameterized directly so far I know, rather they are the output of a good ocean/atmospheric model with correct parameterizations. How many parameters? Depends on the complexity of the model. How are the parameters determined? There is no single answer to that question I think. The ocean circulation is quite a lot determined by the vertical mixing parameter. So this one is chosen so that about the correct circulation is obtained. Direct observations of vertical mixing are rather poor and cannot be used yet to constrain the parameters, unfortunately.

bender

the point about timescales is moot if climate is the spatial average of weather, not time averaged

[From a safe distance from the cage:] And that’s why the point isn’t moot: climate is the time-average of weather.

e.g. The Californian climate is warmer than the Norwegian climate. We know that because we’ve been observing them for decades and when you integrate over that time-scale, you can make an inference about the past difference. Future difference is another keetle of fish. [Whoops, troll bait.] And this is where ergodicity (i.e. statistical interchangeability of time-series and series ensembles) starts to matter.

The science of global climate change makes uses of spatial averages of (instantaneous) weather and (time-averaged) climate simply because it’s easier to track one variable in a vector than one hundred in a matrix. Convenience is not correctness, however, and this parsimony comes at a cost. The question being asked is: what is that cost?

I am critical of the GCMs, but my criticism has a logical and empirical foundation. Let’s constrain ourselves to reality and reason, shall we?

bender

#507
Appreciate the reply. Every nugget I can gather helps me to formulate a more precise question. Your last sentence is very interesting. Gives me some sense that my questions are not that irrelevant [whereas at RC I was either dismissed or parsed to death].

Sam Urbinto

I just ran the Life sim, lightweight spaceship like 5 nexts. It stabilized at a square of 4 against the wall up top near the right, about 20 squares in. Then I filled in a random space with cells with a mouse drag and it’s gotten to a point alternating between a cross and a circle of 12 cells total, the cross’ 3 x 4 centered around a box of 9 cells. Pretty cool.

Okay, Gunnar, which is it:

“only a few really desparate anti-AGW types are resorting to the straw man argument that the earth does not have an average temperature, ie the ‘average kinetic-heat content of the planetary atmosphere’.” or “Thus, the time averaged metric does not describe any actual reality. It is simply a contrivance.”

Of course the Earth has an “average temperature”. Care to tell us what it is? But don’t forget to include all levels of the atmosphere, the soil, the water and the core.

Or did you mean the average temperature of “rural” samples of air in the boundry layer, and samples of the surface of the seas (excluding the top 180 squares) by satellite over x amount of time?

Given that you’re ignoring everything about climate except temperature, I’ll question the meaning of tracking the anomaly of the averaged between tmax/tmin land samplings averaged over 5×5 grids of randomly placed (and somewhat questionable at times) ground stations, and the averaged 2×2 water top-layer sampling that are then combined, adjusted, averaged and re-averaged over time. Oh, wait. Hmmmm. There’s that pesky time thing.

I don’t deny that the number has been bistable between about +/-.8 for the last 125 years, and that the trend of it is +.7 over the last 125 years. Gee…. Wow, that’s time again.

I don’t agree that you can yank one component out of the system, regardless if it seems to correlate to that rise or not. Even if you could do that, nobody’s shown that the known OCO rise correlates in a cause/effect relationship to that number. But I can’t rule it out.

But in order to figure out what the system is doing, you have to understand how the system functions, and in order to understand how the system functions, you need to get to that point. So while climatologists may not be doing meterology, they have to understand it to model it . Which is why the models can’t get to more than the level we’re at if we don’t understand clouds etc. Which is why weather patterns over time have to be studied – boundry layer, mesoscale, synoptic scale and global scale. Are you really claiming that climatology doesn’t deal with dynamic meteorology over time?

But I do agree that not being able to forecast weather does not have to equal being unable to predict the climate. The question is how well. I agree with you somewhat there about the models; I don’t agree the models should be abandoned, but they certainly need to be taken with a grain of salt.

“the pool water is shaken, rotated and disturbed into complete turbulence. However chaotic or non-chaotic,”

It meets the definition of chaos, being that it has a sensitive dependence on initial conditions, it seems to me. Doesn’t matter. Now, given what you wrote there, climate is leaks in the pool, then I need to understand how turbulent the water is and in what ways it will act so I can figure out how much will leak and if the cracks are going to get bigger and in what ways. The leaking water and the ways it acts is certainly not irrelevant to the fact it’s leaking. How do I figure out when and how I need to increase or reduce the water flow if I don’t know how that’s operating? How do I stop the pool from totally breaking if I don’t know how the water is affecting the pool? I find your argument that there’s no time scales involved a strange one, I have to look at the cracks long-term. Yes, I know, that’s probably a bad analogy, since you can’t control the weather.

Not having to take weather into account and understand it and use tools and data about the weather to figure out climate is equally so incorrect. Like saying you can take apart a car and put it back together without understanding any of the systems, at least to the degree you need to know what tools to pick and how to use them.

That’s probably a bad analogy also. Hopefully you get my points though.

You say “the turbulence can never change the amount of water in the pool”. Sure it can. It becomes turbulent enough to exit the pool. It evaporates faster if it’s going up in the air and increasing its surface area by being in the air and some of it is breaking into drops. And for that, guess what. I need to know how it’s behaving, not at some instant, but over time, to know how much is getting out.

How can you possibly argue with “Climate is the average and variations of weather in a region over long periods of time”(wiki) “the statistical description in terms of the mean and variability of relevant quantities over a period of time ranging from months to thousands or millions of years”(ipcc) “The composite or generally prevailing weather conditions of a region, throughout the year, averaged over a series of years.”(nws)

bender

you spatially averaged as the first step.

[Sigh] Substitute ‘Fresno’ for ‘California’ and ‘Oslo’ for ‘Norway’ and re-run the analysis.

an alien … could properly conclude that the climate in CA is warmer than Norway. With your definition, he could not, without sticking around for 30 years.

Yes, he could make on inference based on a single second or hour or day’s observation, but there’s a chance he’d be wrong. Integrating over time reduces the variance in your estimate and thus shields you somewhat from making an incorrect inference. There are times when Oslo’s daily temperature exceedsd that of Fresno. The question is: are there are entire centuries where that might be the case!?

Larry

It occurs to me that the weather/climate dichotomy is a topic which deserves its own thread. It’s a distraction here.

steven mosher

“If an alien landed on earth, first in Norway, then in California, spoke to no one, read nothing,
he could properly conclude that the climate in CA is warmer than Norway. ”

Well today if he flew from Bergen Norway ( 46F) and landed at Mount Shasta later on today ( 39F)
he would conclude the opposite.

Maybe this alien who speaks to no one and reads nothing is you. That is what I would properly conclude.

Gerald Browning

Larry (#517),

We are in agreement again. I have comments on the difference, but they do not belong on this thread.

Jerry

Gerald Browning

Pat Keating (#477),

Do you work for GISS or are you just running their model for interest?

What type of graphical output do you have available to determine the
cause of the bloup?

Jerry

steven mosher

RE 524. Hi Pat, Have you taken a look at the MIT GCM? I was going to download and play with it
( ModelE made me ill) and the code looks to be more competantly constructed.

Gerald Browning

Pat Keating (#524),

Did you save the entire model data every so often, every 10 years, so the model could be restarted?

What continuum dynamical system of equations is approximated in the model, e.g. is it the hydrostatic system?

Is it a pseudo spectral or finite difference numerical approximation?

What are the grid sizes in the three spatial directions?

Does the model run stably for more than 30 years using the unmodifed version?

Somewhere on this site I proved that if one is allowed to tune the forcing (parameterizations), one can compute any solution (or spectrum) that one wants even with the wrong system of equations. The proof is easier than me searching for where I made the comment. 🙂

Jerry

Gerald Browning

The LES Question (tutorial)

I assume that LES will work in both 2D and 3D. Convergent numerical solutions of the incompressible 2D Navier-Stokes equations can be (and have been) computed with kinematic viscosties (Reynolds numbers) of real fluids
(references previously cited and available). Given these convergent solutions, it would be trivial to test the LES methods against the converged solutions for accuracy.

It is my guess that the solutions will be different, especially over longer time periods.

Jerry

lucia

Jerry– Sure. It could be worth while to stuff in an LES subgrid model, run it and show what happens and compare. I’m not very familiar with 2D turbulence, but simple googling reveals all sorts of people publishing papers on 2D turbulence and apparently doing exact computations. Sounds like LES of 2D turbulence could be a a good project for a graduate student. 🙂

You’d probably want to demonstrate some problems that worked well, and then apply it to the case where you expect LES to blow up.

Pat Keating

525
Steve
No, I didn’t want to get too much into very complex models (I don’t have that much time). The edgcm model is easy to use, but the trade-off is that you can’t make internal changes, just change some of the parameters.

D. Patterson

534 bender says:
November 17th, 2007 at 8:45 am

Cage? I was under the impression it was the pit for blood sports!

D. Patterson

Oh, that. He who lives in barn and throws out many strawmen burns brightly in the winds of geostrophic chaos with each passing of the Sun, Moon, and stars.

Weather is to climate what a fart is to a biography.

How are you with Haiku?

kim

Skeptics chirp in the Catbird Seat.
Alarmists all up the tree.
===========

kim

Rocket Man beats gorille
With holy hockey stick.
Goreblimey.
==============

Gerald Browning

Lucia (#531),

Check the manuscript by Heinz and me in Math. Comp. for convergent solutions in 2D. There are similar manuscripts by Henshaw et al.
available (see Henshaw’s website).

Jerry

Gerald Browning

Pat (#532),

As discussed above, a model with very crude resolution cannot describe
physical reality and the parameterizations therefore try to describe the impact of these small scale features over very large grid boxes (in your case 800 km by 1000 km in the horizontal). I believe that is one reason that orgs like NCAR are willing to provide model code to anyone. They know darn well that they cannot be run at the resolutions they do without the use of a supercomputer and also many times without the assistance of people in the organization (results in collaborative pubs and citations).
That is a pathetic given the poor quality of the science.

Jerry

Gunnar

>> one that sleeps, over in his cage

He that chooses to design and build something, rather than waste time with insulting people who are either unable or unwilling to formulate precise concepts, continuously confusing each other with meaningless details in a dead end line of thought, totally devoid of integrating abstract concepts.

People can operate either

by a conscious, rational, disciplined process of thought and scrupulously logical deliberation — or let your subconscious accumulate a junk heap of unwarranted conclusions, false generalizations, undefined contradictions, undigested slogans, unidentified wishes, doubts and fears, thrown together by chance, but integrated by your subconscious into a kind of mongrel philosophy and fused into a single, solid weight: self-doubt, like a ball and chain in the place where your mind’s wings should have grown. -Ayn Rand

Gerald Browning

Larry (#544),

Exactly. The amount of computer power to solve for convergent numerical solutions in 2D for high (realistic) Reynolds numbers is staggering.
There 2D Fourier transforms were used for the doubly periodic case using the pseudo spectral numerical method. The satisfying thing is that the solutions actually converged when the model resolved the number of spatial waves indicated in the smallest scale estimates. The use of additional resolution produced the same solution, i.e. the solutions were not chaotic!
Quite a surprise to a number of people.

Jerry

lucia

i.e. the solutions were not chaotic! Quite a surprise to a number of people.
Though not others. After all, it’s not as though engineers who work in areas where transport phenomena are important have embraced chaos as a way to truly understand or quantify phenomena of interest.

Though you will find it mentioned by a few who work in some highly specialize areas, we prefer to let those who insist on repeating “chaos, chaos, chaos” occupy remote corners at cocktail parties where they wonder why no one takes their intonations seriously.

MrPete

There’s a new thread for this discussion.