Climate Audit

Ian S

#2 It seems to me that most of the state variables of climate exhibit fractal self similarity. For example, if I were to show you a graph of temperatures over time, but not show you the timescale, could you tell me what the approximate timescale was? I don’t think so. Chaos that results in this type of scale independent fractal behavior is equally chaotic and unpredictable at all scales.

It’s like the stock market. Can one predict population characteristics of the stock market? No. [well they can go ahead and predict if they like, but don’t put your money on them 😉 ]. Similarly with climate, it seems quite likely that long-term behavior is no more predictable than short-term behavior going by the fractal self similarity nature of the measured state variables.

cheers,

Ian

Margo

Re 3: Ian,
Molecular diffusivity tends to provide a cutoff frequency at small scales. So, if you ‘climate’ behavior will tend to be self-similar to all scales, that’s probably not true. In climate flows, these small scales are truly small.

Re 2: People do a lot of work trying to predict the average behavior of non-linear systems. Predicting the average long term behavior is often no easier than predicting instantaneous behavior over a long time period. ( Depending on the problem doing one may be more difficult than the other– it just depends.)

Fluid mechanicians doing research have run DNS (direct numerical simulation) codes that fully resolve the flow behavior at all scales and then take averages to find out what happens on average. (These DNS computations are limited to relatively simple flows and take a lot of computational power.)

Researchers have developed codes to predict the average behavior of some systems involving fluid flow, heat transfer and mass transfer fairly well without resorting to tuning; other flows can’t be predicted well.

Ian S

#5 unpredictable at all scales was far too strong a word for me to use (the weather this second will probably be extremely similar to the weather in the next second, so obviously self-similarity does not apply at this short a time scale). How about “unpredictable at most scales of interest with regard to predicting the effects of global warming?” One has to be so extremely careful with their choice of words on this site!! All these hypervigilant auditors 😉

Gerald Browning

John A (#1):

The large, nonphysical dissipation (compared to the real atmosphere) used in the atmospheric portion of the coupled climate models together with the mesh not yet resolving the smaller scales of motion under 10 km prevents the unbounded exponential growth from being seen at this stage. However, Willis has indicated that the CCSM3 is doing worse than the CCSM2 and this could be the beginning of the problem. I am waiting to hear from Willis in this regard.

If one peruses the CCSM documentation, one sees that only a few resolutions are guaranteed to work. If the equations are well posed and no tuning of physics or dissipation is required, the convergence to the true solution of the continuous system should occur automatically for an accurate and stable numerical method, at least for short time periods. This is not the case for the unforced, hydrostatic system.

Also note that the non-hydrostatic models are closer to the full inviscid (viscous) NS equations and once the solution is properly resolved by a stable numerical method, the solution should be closer to the correct continuous solution. These solutions have indicated severe problems with fast, bounded exponential growth and cascade to scales not resolvable by a model.

Gerald Browning

Margo (#5):

I agree with all of your statements. The problem with the hydrostatic system is that it is ill posed. Instead of running complicated coupled climate models for hours on end, this can be resolved by running the inviscid, unforced CAM model in the presence of a simple jet at higher and higher resolutions for less than one day of simulated time. A fairly cheap method to determine if there is a problem with the continuous system?

TAC

#12 Ian, thanks for the reply. I find the self-similarity issue fascinating (btw, Demetris Koutsoyiannis, an occasional visitor to CA, has written a lot on this topic), even though I don’t have a good physical explanation for it. In any case, it continues to amaze me that so many studies in climate science (not to mention climate modeling) fail to recognize this seemingly ubiquitous property of natural systems.

Francois Ouellette

Willis et al.

I agree. Personnally, I’m not at all convinced that GCM’s are useful at all if all you want to know is the response to increased GHG’s. I mean, you’re trying to simulate a hugely complex system that is notoriously nonlinear, just to figure out what’s going to happen if you only change ONE parameter?

On the one hand, GCM’s should be useful to understand the characteristics of a STABLE climate: if, starting from first principles, plus a limited number of parameters, you can reproduce some emergent properties of the Earth’s climate, then that helps you decipher why and how those properties come about. But we all understand that what you get there is a qualitative picture, with only modest numerical accuracy w/r to observations. Still, a useful tool. IMO, if you ever get to the point where you can reproduce the climate’s natural variability on a global as well as a regional scale, then you know you’re in business. Are we there yet? I don’t know, not being a specialist. But that’s only for a STABLE climate, ie. forcings do not change, or they change within their known range of variability and known dynamics.

Now you really want to know what’s going to happen if you change ONE forcing, say GHG. Two things can happen. One, if the perturbation is small enough, the response is linear. Fine, but then you don’t really need a complex GCM. All you need is a simple physical model, which will give you the actual reponse (say forcing + feedback), and whether you plug this into the GCM or not, you get roughly the same answer. And it has been shown here that this is exactly what happens: GCM simulations do no better than a simple linear response! IOW what you get out of the GCM is exactly what you put in there in the first place.

But it MAY be the case that the system does NOT respond linearly. In fact, the Earth’s climate is known not to respond linearly to small changes in forcings: just look at the glacial cycle, where the minuscule changes in solar insolation result in huge global and regional responses. So we know that the climate response is full of nonlinearities and thresholds, in which case a tiny change in the parameters leads to a very different response. The paper by Didier Paillard on glacial cycles is a nice example: he shows a model that accurately reproduces the sea level for the past million year, using threshold values. But if he wants to forecast the future, he has to chose within a range of values for one threshold that give indistinguishable responses for the past, but hugely different responses for the future! So, are the GCMs useful in that case? Not at all, because if you try to capture this nonlinear behavior, you will always be limited by the resolution, but if you increase the resolution, you get right into the scale of the turbulent behavior and you’re screwed again because now you have the resolution, but not the boundary conditions! So you still have to resort to parametrization, knowing that slightly different values of your parameters will give you very different responses.

That’s why I don’t believe that GCM’s are the right approach if all you want to know is the response to GHG’s. A better physical understanding should at least give you an approximate answer that you can roughly trust. If I were in control of the climate research budgets, I would put less money into GCM’s and more into simpler, physical models. At least in a simple model, you can figure out what’s going on. GCM’s are so complex that at some point nobody really knows what they’re doing.

Bob Weber

Is the climate deterministic? If so then a GCM can be written if we know all of the parameters and their behavior.
Or is the climate chaotic? If so then no computer program can make reliable predictions beyond a relatively short time.

Bob

bender

Re #18
Bob, chaos is deterministic (= extreme sensitivity to initial conditions + an inability to know past conditions with abosolute precision). Read Lorenz’s “Deterministic non-periodic flow”.

Willis Eschenbach

I’d been wondering why the climate models don’t show any negative feedback, because it always seemed to me that increasing cloud albedo (from increasing evaporation in a warming world) would lead to less sunlight hitting the earth, and that the models should show that.

Upon closer examination, I find that despite large errors in cloud cover (~15% in the GISS E model) the albedo is quite close to the measured value. This is because the albedo is parameterized, rather than calculated. To quote from the Schmidt description of the GISS E model,

The net albedo and TOA radiation balance are to some extent tuned for, and so it should be no surprise that they are similar across models and to observations.

Near as I can tell, “to some extent” means they calculate the surface albedo, and “parameterize” the cloud albedo, but they’re not real clear about that.

In any case, this means that the models are incapable of modeling albedo feedbacks, because the albedo is not tied to the physical conditions, but is just a best guess.

Given assumptions of that size … there’s nothing the models can’t “prove”. Exponential growth damped out by ultra-high viscosity? Hey, no problem …

w.

Steve McIntyre

The net albedo and TOA radiation balance are to some extent tuned for, and so it should be no surprise that they are similar across models and to observations.

Whether the methodology is any good or not, what a ridiculous description of the methodology? “to some extent tuned for” – I wonder what the operational tuning procedure was.

gb

GB,

I do not understand some of the things you are saying. Why do you say that the dissipation is unphysical? If one simulates a turbulent flow but does not fully resolve all scales it should crash because the system cannot get rid of its energy (at least if there is a forward cascade of energy). In that case a subgrid model that acts as a sink of energy must be implemented, quite physical indeed. The rapid cascade in high resolution models can also be physically correct and there is in principal also nothing wrong with the idea that the parameterization must be changed as the resolution is changed. To develop a subgrid model or a parameterization one has to invoke assumptions/approximations at some point. In other, there does not exist a parameterization but there are several possibilities and one can tell only after testing which one is better but fundamentally there is nothing wrong with that. At the moment, observations are lacking and the knowledge about the dynamics of smaller/mesoscale motions in the atmosphere and oceans is rather limited and this hinders the development of more physical correct and accurate parameterizations.

Gerald Browning

Lubos (#16):

Addendum. You might want to peruse the Math. Comp. manuscript I cited earlier. There solutions of the incompressible NS equations are computed deterministically for long periods of time. There are mathematical estimates for the smallest scale that will appear for a given kinematic viscosity (see Henshaw, Kreiss, and Reyna cite in that manuscript). The reason that turbulence has not been computed correctly before is because the solution was not properly resolved or the boundaries handled incorrectly.

Jerry

Gary Strand

Re: 29

Please substitute “rapid error growth” for “rapid growth”.

(It sure would be nice to go back and make minor changes in one’s posts!)

Ian S

#29 Gary,

What is meant by unphysical? I assume that you mean that the models match past temperatures (sort-of)? But isn’t this basically circular logic. Models are fine-tuned until they match past temperatures are they not? On the other hand, when it comes to predicting future temperatures and properties they fail spectacularly in a very short time period ( as has been mentioned in several other posts). It is my understanding that the models do not match reality ( Antarctica temperatures, troposphere temperatures, recent Ocean cooling, so on and so forth) and ( I may be wrong about this one) are not even capable of predicting El Nià±o etc? So, in this sense they become un-physical very quickly. Use your model to predict temperatures 5/10 whatever years from now. When the time comes we will see how ‘physical’ the model really is 😉

By the way, one can create models to match past stock market histories very nicely and general stock behavior even more easily, just don’t kid yourself that this means they can predict the future. I believe this is what is occurring.

Ian

Gary Strand

Re: 32

By “unphysical” I mean that the model ends up with the climate of Venus, not Earth.

If, as Gerry asserts, error growth very rapidly makes a system completely unstable, then how do climate models manage to run for decades of model time without rapidly creating planets that are not Earth? In the old days, climate models did “flux corrections”, but many models have moved away from them and don’t rely on them at all.

Dave Dardinger

re: #34,

I think what needs to be done is to examine exactly what is being done in a model, in a mathematical sense. Obviously we can’t look at every equation and all grid cells, but something could still be done by looking at likely critical paths.

Let’s say a worry is that CCSM3 doesn’t allow a reasonable amount of convective heat flow to the upper atmoshere as surface temperatures increase. What equations / methods are used for this process and what is a link to the code where the equations / methods are implemented? Also is there any point elsewhere in the code which examines the results of this process and adjusts something else to keep the results “physical”?

What I think would ease everyone’s minds here is to work through a few such examples with someone who can ease the search (such as yourself) and people who can throw pointed questions out which can be batted back and forth without letting people get upset and political. There are actually a lot of people here who’d be willing to dig in and find things if there were a specific question trying to be answered and there was a committment to actually come to a final conclusion on the situation. More long-range, if say 5-6 such “problems” were worked through and the majority agreed that the methodology use in CCSM3 was reasonable and physical, then there’d be a greatly enhanced tendency to accept results produced by the model.

Pending getting a buy-in by yourself or others to do this sort of thing, it might be useful for people to suggest such limited audit problems which might be solved.

Dan Hughes

I have some comments on numerical solution methods that I think are applicable to AOLGCM calculations here.

All corrections and comments appreciated.

Margo

Re 18: Jerry, you said:

I am very familiar with the so called microphysics packages (reference on request). They have their own set of mathematical and physical issues.

I’m requesting!

Re 23:

Assuming instability of the Navier-Stokes equations when applied to the climate problem, is it necessarily the case that one cannot predict a meaningful “average effect” (where the average is computed over multiple realizations) of a change to the coefficients of the differential equation?

One can often predict a mathematical meaningful “average effect” and it has been done. You can look up “Direct Numerical Simulation” (DNS) and find papers where people have done this in a variety of cases. The solve the NS equations with no parameterizations. To get average behavior, they calculate averages directly from many instances. (Note: You’re search will not produce papers describing solutions in flows anywhere near as complicated as climate models because no computer is large to permit such runs. GCM’s contain parameterizations for a number of things. Also, once you introduce a parameterization, you’ve introduced the same approxiation into every run. So, averaging will just tell you the average effect of a model containing that approximation. )

Re 26:

Why do you say that the dissipation is unphysical?

I can’t answer for Jerry, but I’d call the dissipation in a model “unphysical” if it’s in there for one of any three reasons:
1) the sub-grid models do not correctly describe the average effect of small scales (which can happen because it’s not easy to capture the average effect in a manner that is correct in all possible conditions.)
2) the dissipation is introduced not to reflect any physical instability, but only to avoid a numerical stability. (This appears to be done in some GISS models near the poles where a false, and very large, viscosity, in introduced to avoid problems when the courant number for the grid cell approaches 1.)
3) the discretization process itself introduces a false diffusivity that is in some way proportional to the grid size (or some power of the grid size.)

These ‘unphysical’ viscosities may or may not cause noticable inaccuracies– but I’d say the term “unphysical” would apply.

Jerry Re 27:
Lubos is using the term instability the way I find it meaningful.

People in continuum mechanics traditionally call certain types of analyses “stability analyses”. One finds a steady state (or sometimes just stable time dependent ) solution– which may apply in some condition. Then, you study that solution to determine if that solution is stable to small deviations from the steady state solution. If you introduce a small disturbance to the solution, and find it decays, the solution is called “stable”. If the small deviation grows exponentially, it is “unstable”.

Gerald Browning

Gary Strand (#29):

I find it amusing that you are unable to answer basic questions about the coupled climate model that you supposedly code for IPCC, but claim to know so much about ill posedness. Large dissipation can overcome many model flaws. Please run the same set of experiments on the CAM model that Lu et al. did on the WRF. Hand waving doesn’t cut it with me.

Jerry

Gerald Browning

Margo (#40):

Here is a reference that describes typical microphysics using scaling as is normally done in fluid dynamics:

Lu C., P. Schultz, and G.L. Browning (2002):
Scaling the microphysics equations and analyzing the variability of hydrometeor production rates in a controlled parameter space.

Advances in Atmospheric Sciences

Gerald Browning

Margo (#40):

Well stated. Only a few questions. In number 2, I assume you (also) mean numerical instability like nonlinear instability? If a model uses a parameterization that is in error by 100%, then the forecast or error bars do not have much meaning?

Jerry

Gerald Browning

Bill F. (#37):

Very well stated. See corresponding mathematical explanation
in #43.

Jerry

jae

A lot of the mathematics discussed here is over my head, but IMHO, the climate models are nothing more than a classical example of overfitting by careful selection of parameters.

Margo

Pat,
Unfortunately, I couldn’t turn it out in a month for two reasons:
1) I have a real job that I need to attend to and
2) I don’t know enough specifically about what’s in the models to know how close or far off they should be.

My major difficulty with the stuff that I have found is that the few papers that I do find in peer reviewed journals give what I would call ridiculously cursory explanation of the mathematical models in the codes. That would be ok if I also saw references to the “theory manuals” describing the mathematical models, but I don’t see those references. (In honesty, it’s the lack of citations to the theory manual that surprises me most. The full theory is generally so long you expect it in a theory manual or ph.d thesis. Still, You usually see such citatons in papers in Journal of Fluid Mechanics, Physics of Fluids etc. People are usually thrilled to cite their own theory manuals, Ph. D. theses etc. So, I’m not understanding why things are this opaque in Journals like J. Climate.)

Now, mind you, I assume if I spent enough time, I’d find these theory manuals, but, unfortunately, I do have other things to do.

But, when people here do discuss things I happen to know about, I can pipe in.

Pat Frank

#52 — Margo, that’s why you’d pair up with Jerry. He apparently does know what’s in the models. Between the two of you, you’ve got everything well covered. You two would write a killer paper.

And in that paper, you could note among all the other things, the peculiar lack of reference to theory manuals that seems unique to climate science modeling.

Paul Penrose

A very interesting converstation. My question is simple: how can I even evalutate the meaning of the model outputs if there are no error bars reported with them? Reporting a temp increase of 3 degrees C +/? is, frankly, meaningless. So until an analysis of the internal errors and how they propagate through the simulation is performed, the models simply can’t be used to predict, or project if you wish, future temperature trends. Maybe Gary has a different perspective on this, but I’ve yet to see him address this issue.

Gerald Browning

Pat Frank (#54):

Thank you for the complement to Margo and me. Obviously she is a very skilled writer
and quite knowledgable about the scientific issues. This blog has been an inspiration
to me because I can discuss the issues openly and not have to battle reviewers
with vested interests.Thanks to Steve M. for this opportunity and to all of the other posters that have discussed the issues in an open and frank manner.

Jerry

Paul Penrose

Re: #59
Jerry,
I’m glad you are looking into these issues, but this type of analysis should have already been performed by the modelers, if, and this is an important condition, if they wish to have their results used to bolster the AGW hypothesis and/or support advocacy for change of government policy with regard to climate and the environment. Now I’ve heard some modelers claim that their models are just research tools and that they can’t help how others use them, but htis is BS. If the modelers feel that the results of their research has been used inappropriately by AGW advocates and policy makers (ie. in the public sphere), then it’s their duty to stand up and make a public stink about it, otherwise it’s easy to take their silence as tacit approval.

Dan Hughes

Instability in Code Calculations

The continuous equations might model physical instabilities, and the numerical solution method might reflect its instabilities, but there are much more mundane things that will effect stability of a calculation.

Discontinuities in any and all dependent variables will cause instability. Many of these are the physical instabilities modeled by the continuous equations. Discontinuities in density, temperature, and velocity, for examples, give the Kelvin, Helmholtz, Rayleigh, and Taylor (and combinations thereof) kinds of physical instabilities in fluids. Such discontinuities occur at the interfaces between subsystems modeled; atmosphere-ocean, for example. Some physical instabilities are governed by the critical gradient for some dependent variables; the Richardson number, for example, or gradients that are inverse to a natural stable state. Some flows might be surface-tension dominated and discontinuities in surface tension, or even an adverse gradient in surface tension could caused instabilities in these flows. All the physical instabilities will be bounded; mother nature just will not allow truly exponential un-bounded growth of these instabilities. Linear analyses of the continuous equations applied to the onset of the motions following the instabilities might indicate exponential growth, but the analyses typically omit the nonlinear effects that will lead to bounded growth.

The numerical solution method is required to correctly reflect the physical situation for each physical instability. Often, it is usually the case that accurate spatial and temporal numerical resolution of the physical instability is not important for a particular application calculation.

Discontinuities in the discrete geometric grid used to represent the solution domain for the problem will also cause instabilities and non-physical calculated results.

Improper, or incorrect, boundary condition specification, in either the continuous or discrete numerical domain, can cause instabilities.

The list is very long and each must be investigated in detail to ensure that the numerical method correctly reflects the physical situations.

An important source of numerically-introduced instabilities are in the many algebraic correlations and models that are very important parts of many models and codes developed for real-world applications of inherently complex physical phenomena and processes. The resistance to motion at an interface in such models is usually represented by correlations for the drag between the fluid and another material. I suspect that the ever-present (omnipresent?) parameterizations in the AOLGCM models are generally algebraic. All the algebraic equations must be carefully constructed so as not to introduce discontinuities. Again, generally it is a good idea to ensure that the algebraic equations are continuous functions of its independent variables plus the first derivatives should also be continuous. Spline fits will do this job, but frequently the process is not applied to the algebraic equations until it is discovered that one of them is causing problems.

Finally, certain intrinsic-functions in the language used to construct the code frequently in discontinuities. In the FORTRAN language, as an example, the MAX and MIN statements have the potential to introduce discontinuities into the numerical solution methods. MAX and MIN constructs are frequently used to bound the range of dependent variables. Variables that should always be positive, for example, can be bounded by use of these. Another application frequently seen is to limit the change in a dependent variable between time steps, or iterations. These are very bad ideas, however, because such statements present pure step-function like changes to the numerical methods. The variable and its derivative are both discontinuous. The discontinuities present perturbations to the discrete equations and associated numerical solution methods. Such perturbations will generally introduce non-physical instabilities into the numerical solutions.

One thing that makes careful consideration of all possible discontinuities very important relative to the AOLGCM models/codes is the presence of sensitivity to initial conditions. The perturbations act exactly like changes in initial conditions that then initiate the chaotic response that is said to be a part of these models/codes. So far as I know the dynamical-system properties and characteristics of equation systems that contain discontinuities and exhibit chaotic response has yet to be determined.

Armand MacMurray

Re:#63
It seems that experimentalists looking for “new physics” should be studying the climate system… 🙂

Margo

Well, they do know negative mass doesn’t happen. . .

I looked for the reference. It’s Schmidt et al J. Climate jan 2006. p. 158
Discussing tracers (like water vapor) they say:

“Occasionally, divergence along a certain direction might lead to temporarily negative gridbox masses. These exotic circumstances happen rather infrequently in the troposphere but are common in stratospheric polar regions experiencing strong accelerations from parameterized gravity waves and/or Rayley friction. Therefore, we limit the advenction globally to prevent more than half the mass of any box being depleted in any one advection time step.”

So, it appears these negative water vapor masses have appeared, but they do try to fix it up somehow. (I’m not sure what they mean by saying they limit advection globally. It doesn’t sound like they mean they reduce the time step which is stated as 30 minutes. Do they mean they fudge the transport velocity of the fluid when calculating the water vapor budget? And they do this globally? That would seem very weird. Oh well. . .)

Gerald Browning

Steve M.,

I will try to find a link or make my own plots and send them to you for posting so people can actually see the seriousness of these mathematical issues. Then I think the discussions will be more to the point and not drift off onto side issues.

Jerry

TAC

#67 FORTRAN differentiates between INTEGER and FLOATING POINT (REAL and DOUBLE PRECISION) arithmetic. This makes a big difference when it comes to division. Thus, for REAL x, x=54/10 yields x=5.0 while x=54./10. yields x=5.4. For operators requiring two arguments (i.e. +,-,*,/), if one of the arguments is INTEGER and the other FLOATING POINT, the INTEGER will be promoted to FLOATING POINT before the operator is applied. So x=54/10. yields x=5.4.

This is all nonsense except to people of a certain age.

Paul Penrose

This is a well known problem with representing fractional values using binary storage. Even when the mantissa can be expressed with a single base-10 digit, like .4, it may not be the case in base 2. In this particular example .4 in base-10 is .0110011011… in base-2 and is in fact indeterminate. This can lead to subtle representational errors that normally are not a problem if you have 32 or 64 bits to store the value in and are not performing an interative calculation. However in areas like modeling you are likely to be iterating many times, so this has to be accounted for. Do you just allow things to truncate or do you perform rounding of some sort? How does this affect the calculation? Sometimes through the use of clever scaling and rearranging the order of intermediate calculations you can reduce (and sometimes eliminate) these effects. Who knows how the modelers have handled this; they aren’t saying, at least not as far as I know.

Earle Williams

Bob K.’s example in #67 is a real problem because of the way floating point numbers are represented, as Paul describes in #72. It is also something that should be taught to every scientist in their first programming class. It certainly was taught to me in CompSci 201 some 25 years ago. The solution to the “is equal” test isn’t actually to test if they are equal but to test if they are within an arbitrarily small value of each other. That value might be determined by the compiler or it might be hard-coded by the programmer.

There shouldn’t be any comparison like Bob K describes in these models. It is just so rudimentally wrong that I cannot accept that any vetted model would have such inherent issues. That said, the comparison certainly could be in there. It would be like sending your comuter off for repair and getting it back with duct tape holding the side panel on.

The comparison I was taught to test for equality of floating numbers is:
if( absolute_value(x – y)

Earle Williams

Re #74
Curses! Foiled by the less than symbol!

Anyways, I shan’t bother with reconstructing my closing paragraphs. The test though is to see if the absolute value of the difference is less than the arbitrarily small number. If it is less, then the two values are considered equal.

(Apologies if this gets posted twice)

Bob K

Mea culpa I said 32 bit floats in my above comment. They were actually 64 bit.

I just tried comparing 64 bit x and y to a 64 bit constant value of 5.4.

The y calculation 54/10 turns out to be equal to the constant. Not so with x = 5.1 + .3

y > x by 8.88178419700125E-16

It seems the compiler handles the constant the same as the division.

Also tried 32 bit floats all around and they were all equal.

The problem is the shear number of people working on the coding over the past couple decades. Along with the cross-pollination of code fragments between models. Pick a couple hundred people out of any profession and you’re bound to find examples of the Peter Principle in action. Some V&V would definitely be appropriate.

TAC

#72, #77 Paul, your point is well taken. In fact, just this past week I have learned a bit more about this topic than I’d have liked. I am not a FORTRAN programmer (aside from graduate school; we all were back then), but nonetheless had to spend the past two weeks tightening up numerical algorithms in a FORTRAN code so that, in double precision, it now reliably produces 3 digits of precision in the final result.

IMHO, if you have any concern for civilization, FORTRAN constitutes a considerably greater threat than AGW.

Jaye

I also was unsure whether BobK’s issue had to do with FORTRAN’s quirky arithmetic rules or because of limited machine precision. However, the test example he provided would fail for the former reason and not the latter (modern versions of FORTRAN are somewhat tolerant wrt tests), and BobK admitted he was unfamiliar with FORTRAN.

The “error” is an implicit type conversion, that is either happening or not happening based on what the compiler sees. Has nothing to do with precision…and I would really call it “quirky arithmetic rules” but type conversion. Most languages do this sort of thing.

fFreddy

Re #82, Jaye

…but type conversion. Most languages do this sort of thing.

All the more reason to be disciplined, and to switch on strong type checking. Dunno if Fortran can do this, but C sure can.

Jaye Bass

Dunno if Fortran can do this, but C sure can.

Fortran has a keyword “implicit none” which forces one to declare types. I occasionally have to hold my nose and deal with legacy fortran. In the course of doing that there are a few old fogeys I’d like to have cursed into oblivion for not using “implicit none”.

Most academic code is pretty sloppy, buggy and unmaintainable. I wouldn’t be surprised if there are tons of unknown bugs in code like ModelE.

Margo

“If it is undisputed that N-S equations exhibit chaotic behavior , does the temporal mean of a parameter exhibit also a chaotic behavior ?”

The answer depends a bit on what you call “temporal mean”.
However, using a definition like “Reynolds Averaged”, which can actually be a bit vague, often the mean behavior is not chaotic.

Long before we could model behavior, we knew the mean flow behavior is many systems of engineering interest is quite predictable and not chaotic. That’s why we can size pumps for water systems, predict heat transfer inside double pane windows etc. We didn’t need to run models to figure out the average behavior in these cases is not chaotic, we can tell from experiments.

There are cases where what one might call “averaged” flow could conceivably be “chaotic”. I’m trying to think of a confirmed case that’s been observed in a lab but I can’t off hand.

But you know what? Modeling even single phase flows with non-chaotic mean behavior is itself difficult. Modeling coupled heat transfer and flow is even more difficult.

gb

Re # 89:

‘A new book argues that nature is too complex and depends on too many processes that are poorly understood or little monitored to be modeled using computer programs’

What a nonsense. Should we stop all science? Natural sciences are about modelling processes in nature, what else? And yes, that can be difficult. But does that imply we shouldn’t try to?

Re # 87:

Simulating chaotic or turbulent flows is perfectly meaningful. People do it already for more than 30 years. It is because turbulent flows, which are governed by the N-S equations have a well defined mean, variance of the fluctuations and other statistical properties. For the atmosphere and the ocean it is less clear how large and what the time scales of these fluctuations are.

Tom Vonk

The answer depends a bit on what you call “temporal mean”.
However, using a definition like “Reynolds Averaged”, which can actually be a bit vague, often the mean behavior is not chaotic.

Thanks , yes , that’s what I have been thinking about .
I can broadly understand the maths involved with this treatement in the case of a compressible fluid and I played a bit with it .
Of course as I am doing that in my spare time , I have not the time (and probably the knowledge) to read a century of papers concerning what actually the Reynolds stresses are and how they behave .
However as long as one only stays at that stage there is no problem – after all the only thing I did was a variable change which gives me just another expression of N-S where I transferred the original problem in another problem where the Reynolds stresses appear but the equations are still as chaotic as they originally were .
Now where I do have a problem is when one goes a step farther and assumes that the “perturbation” element is random and eventually adds further conditions – like normal distribution and/or mean = 0 .
That makes then the calculations a bit simpler and from what I understood looking at a couple of ENSO models , that is precisely what they do .

Now what I’d like to know is what kind of validity has in GENERAL such an assumption – I mean what influence has such an assumption on the behavior of the numerically calculated solution vs real behavior of the flow over a long period of time .
I can’t get rid of the impression that there is something circular in the argument – if I assume that the “fluctuation” is random then I cannot say that the mean became more predictible because … the “fluctuations” are random

Of course being engineer , I perfectly know that we can calculate pressure drops in turbulent flows .
Well at least in suitable conditions 🙂
But that is not the question , the question is the one of the relevance of stochastics in the general case of a compressible N-S flow .
And I wouldn’t even go in the questions concerning the smoothness and continuity of the functions that are conditions to have well defined means .

Steve Sadlov

RE: #89 – Indeed, from time to time, there is discussion of earthquake prediction. Interestingly, the issues are, if not similar to climate systems, not entirely dissimilar. The mantle is a highly viscous semi liquid, believed to be slowly flowing in large convection cells. The crust is plastic material of lighter and cooler phases floating on top of the mantle. The crust has become a series of plates due to the underlying convection. While the overall sense of plate motion is reasonably well understood, the minutae of behavior at plate boundaries are only know after the fact. Chaos prevents anything better, at present.

Dan Hughes

We frequently see appeals to the Navier-Stokes equations and turbulence as an analogy to the chaotic response seen in weather/AOLGCM models and calculations. The analogy is not correct for the reason Jerry gives in #95. The ‘chaotic’ response of turbulence is only seen when sufficient temporal and spatial resolution is used in numerical solution methods (DNS) applied to the Navier-Stokes equations. Additionally, I think the case is that calculated data is time-averaged and spatially-correlated in order to recover the mean-flow state. In other words the decomposition of the flow into mean and fluctuating parts as mentioned in #87 above is recovered from the very-high resolution calculations.

The AOLGCM model equations do not apply at the scales of resolutions needed to model the trubulent flow. And certainly AOLGCM calculations are not done at these levels of resolution with the discrete equations. Additionally, the decomposition, which has been very successfully applied, assumes a random model for the turbulent fluctuations, so that the time average is zero. Chaotic responses are not random and the time-averages are not zero.

I think that it is also the case that the only two known properties of turbulent flows derived from theory by Kolmogorov (Kolmogoroff) are based on random motions, not chaotic. Finally, I think numerical solutions to the Navier-Stokes equations can be shown to converge as the sizes of the discrete spatial and temporal are refined sufficiently to resolve the smallest scales in the flow. These scales are in turn related to the two known theoretical results mention previously. These Kolmogorov scales are tiny and computing power to carry out actually useful and practical calculations is not yet available.

All corrections appreciated.

Dan Hughes

Google, using ‘with all these words’, turbulence banerjee ucsb.

The microscopic details of the fluid motions at and near the interface between the atmosphere and bodies of water determine the uptake of gases, CO2 for example, by the liquid. The problem has been studied for decades. Turbulence is of first-order importance.

Margo

I think that it is also the case that the only two known properties of turbulent flows derived from theory by Kolmogorov (Kolmogoroff) are based on random motions, not chaotic.

The Kolmogorov time and length scale are derived by assuming that the scales of the smallest eddies are affected by only two factors: kinematic viscosity and the viscous dissipation rate. That’s pretty much all the physics in the derivation.

Once you make that assumption, the length and time scales are obtained by purely dimensional consideration. (Actually, there is also a Kolomogorov velocity scale, but you get that by dividing the length by the time. It’s not independent.)

Experiments show the turbulent energy spectrum it does drop off very rapidly near these scales. (The shape of the drop off is understood and discussed in Tennekes and Lumley.)

These Kolmogorov scales are tiny and computing power to carry out actually useful and practical calculations is not yet available.

Direct Numerical Simulation (DNS) models flows down to the Kolomogorov scales. These computations are done by turbulence modelers; use of these codes is restricted to research projects. Results of DNS compuations are often presented at engineering conferences.

Sanjoy Bannerjee wrote this book:
Direct Numerical Simulation of Turbulence and Scalar Exchange at Gas-Liquid Interfaces.

Engineers developing products don’t use DNS; it’s much too computationally intensive. Needless to say, climate models are not “DNS-like”.

Gerald Browning

Dan (#96):

DNS computations for the 2D, viscous, incompressible NS equations in a doubly periodic domain have been carried out for kinematic viscosities down to sizes typically considered reasonable for real fluids. Although not mentioned in the Math. Comp. article, Heinz and I tried without success to find a suitable closure for resolutions that are not sufficient to resolve the minimal scale for a particular kinematic viscosity. This is one of the advantages of having a convergent numerical solution, i.e., these closures can be tested to determine their impact on the real solution.

There have been similar computations performed in 3D by Ystrom and Kreiss (without and with forcing), but the kinematic viscosity is limited by the computing power that is available. Nonetheless, there are indications that the smallest scale estimate also holds in 3D (assuming the velocities are bounded).

Dan Hughes

re: #96 et al. I missed a word in this sentence: “Finally, I think numerical solutions to the Navier-Stokes equations can be shown to converge as the sizes of the discrete spatial and temporal are refined sufficiently to resolve the smallest scales in the flow.” I should have included, “… discrete spatial and temporal increments are refined…” And I wanted to say after that,”Unlike the much simpler equation systems in which chaotic dynamical responses are studied.”

The computing power needed to accurately resolve the smallest motions in turbulent flows generally goes as the Reynolds number cubed.

I think that the dimension of turbulence as a chaotic dynamical-system, again measured by the Kolmogorov scales, is much too large to be a candidate for interpretation as a low-dimensional chaotic system. The degrees of freedom for turbulent flows is measured by the macroscopic, or integral-scale, Reynolds number raised to the (9/4) power. The integral-scale Reynolds number can be calculated in terms of the Kolmogorov scales, too. The integral-scale Reynolds is the one usually encountered in engineering analysis of turbulent flows. I think there are few, if any, methods developed to determine dynamical-system dimensions above about 10 to 11.

Corrections and clarifications appreciated.

Gerald Browning

One of the problems with both climate and weather models is that they use switches (if tests) in their parameterizations. These lead to discontinuous forcing terms that cause considerable difficulties for the numerics.
(reference available). These problems are in addition to the inaccuracies
of the forcing terms.

Jerry

Tom Vonk

Reading in the last IPCC report that they have put a number on the “confidence” that the
author of a model has in the ability of his model to rightly predict the relevant parameters ,
I would like to know how EXACTLY is this number calculated .
For instance high confidence means 80 % and very high confidence 90 % .
What is the process that enables to say “My model represents the reality at at least 80 %” ?
I mean that is a very different thing to say “Given the accuracy of the data X , the accuracy of the output is Y” and to say “My model doesn’t take everything in account but with what it does take in account we can trust its predictions to 80 %” .
I mean no author of a model would come and say “My model is a heap of steaming HS
and I don’t trust it at all ”
I can think of no rational process that could quantify something that I don’t know and obviously things that I don’t know and don’t use in a model have an unknown impact .
Unless they organise a kind of vote where they compare outputs of different models and if they
predict similar things then they say that they are confident .
But confident how ?
What is the difference between being confident at 80% and being confident at 90% ?

Tom Vonk

Jerry that was actually not a comment but a true question 🙂
Do you know how they REALLY do it ?
Is there a written procedure or a kind of QC or what ?
And if yes , where could I find it ?

Gerald Browning

Tom (#110):

The hydrostatic climate models are ill posed, so there is no way to have confidence in the models because as the mesh is reduced (assuming the dissipation is also reduced to more realistic values), the numerical solution will grow larger and larger in a smaller and smaller period of time as it approaches the inviscid continuous solution which is unbounded in any small amount of time.

And a nonhydrostatic model grows exponentially fast (100 times faster time scale than the large scale solution) in time near any jet so that no confidence intervals can be placed on them if the mesh size is reduced.

IMHO, only by keeping the mesh size and the dissipation too large can either of these models continue to run for long periods of time.

Jerry

Paul Penrose

Please don’t go to email. Some of us lurkers are enjoying your conversation.

Paul Penrose

Jerry,
I look forward to seeing more information on your experiments. Often I learn more in one thread on this blog than I did in an entire quarter of college. Thanks for taking the time to educate us here.

John Reid

Please don’t go to email. Some of us lurkers are enjoying your conversation.

I agree. What a great thread!

JR

Dan Hughes

re: #112. Jerry, I have calculated the eigenvalues of the characteristic equation for the PDEs for a hydrostatic model. I find them to be real and distinct and so the equations are strictly hyperbolic. I think that this means that initial-value, boundary-value problems based on the equations, given that the boundary condition specifications are consistent with the eigenvectors, is well-posed. As far as I can tell, the momentum and energy equations do not account for diffusion of momentum and energy, respectively. Otherwise the equations would not be hyperbolic.

Will you provide additional information relative to the basis of the ill-posedness of hydrostatic models?

All these years when I have read that the AOLGCM models are based on the fundamental continuous equations of conservation of mass, momentum, and energy, I took it at face value. So far I have not found an AOLGCM model that is based on these equations. All, as I have always suspected, apply assumptions that greatly simplify the basic fundamental continuous equations. Additionally, none of the public mentions of the models and codes have ever noted that some numerical methods, applied to the conservation forms, do not in fact conserve mass and energy.

Finally, can you tell me if I correctly understand that there is no resistance to the fluid motion in the vertical direction. I’m thinking that is potentially a source for problems. Additionally, the hydrostatic modeling, I think, means that pressure changes are instantaneously transmitted throughout the flow thus allowing for extremely easy introduction of lots o’ kinks and flow oscillations. Fluid motions in the vertical direction have no inertia.

Thanks

Gerald Browning

As I am working on displaying the contour plots mentioned above, I would like to add a bit of simple mathematics to discuss ill posed and well (properly) posed behavior. One of the simplest examples that can be used to show both types of behavior is the heat equation (see my original post on Numerical Climate Models)

where

is a function of space and time. The subscripts denote partial differentiation. For simplicity assume a separable solution of the form

Substituting into the original equation one obtains

where k is the horizontal wave number. The solution of this simple ODE in time for each fixed value of k is

Now if is positive (normal heat equation), then the solution decays exponentially for each k and is bounded above by the initial condition.

But if is negative (heat equation backwards in time), then the solution is not bounded in any small interval of time because the horizontal wave number can be arbitrarily large for a general function.

Gerald Browning

Paul Penrose, John Reid, and others,

If you have any questions about the example or brief explanation, please ask. I will be happy to explain in as much detail as required until everyone feels they are comfortable with the example. Then when the contour plots are discussed, hopefully everyone will have a better feeling for the significance of the plots.

Don’t be shy! I am here to help. 🙂

Jerry

Gerald Browning

Dan (#123):

The mesoscale models used to be based on the hydrostatic system. Only when pressure was applied because of the ill posedness of the IBVP for that system did the mesoscale models switch to the nonhydrostatic system. There are hundreds of references that support this. Give me a break.

Jerry

Gerald Browning

Jim (#127):

Sorry I used the wrong name in #126. The atmospheric equations have a term that is not present in the NS equations (but it becomes less important at the smaller scales where the system starts to behave more as the NS equations), namely the gravity term. This has a very important impact (see Tellus reference by Browning and Kreiss that discusses the various scales for the atmospheric equations) and is the cause of many of the problems with the hydrostatic system.

Jerry

Gerald Browning

Jim (# 127):

Read the Lu et al. reference at the top of this thread. Their results are sufficient to show the problem with the nonhydrostatic equations near a jet
(no need to wait for my plots).

Jerry

Jim D

Jerry,
Going back to #1 and the Lu et al. reference, I see that paper as not presenting any problem
with the nonhydrostatic equations, but just presenting results that look like a successful
simulation of a mechanism for clear-air turbulence, in some way validating the nonhydrostatic
equations and model.
I am not sure when you say that the nonhydrostatic solution may depart from reality,
whether you are suggesting that these modes won’t exist in reality, or whether they
do exist but can’t be forecast accurately. I agree with the latter statement only.

Gerald Browning

The second x in the above message should also have been a subscript.
One of the problems of not having a previewer for tex 😦

Dave Dardinger

re #135 re #133 etc.

I think you do a pretty good job of making the equations understandable but I expect how people react would be all over the board. Some people will say, “Ho, hum. Why doesn’t he get to something I don’t know already. Others throw up their hands and wish you’d speak a language they understand and still others are in my boat and recognize a lot this tongue but get lost at a few places and wish we had a dictionary handy. Part of the trouble is that even if you clearly define terms as you go along, the definitions won’t carry along from post to post and that makes it hard to remember what a given equation means. For instance, I’m assuming u sub t or u sub x are general functions of some sort, but I don’t know if they’re supposed to be differentials or linear functions or higher order functions, etc. I’m assuming the sub t means a function of time rather than temperature since we’re dealing in general terms.

Perhaps specific examples and maybe even problems would help those interested in learning the details to get a better feel for things.

gb

Sorry Jerry, I don’t get what you are trying to say. My point is that if you use a (coarse) grid you are not solving the N-S equations or nonhydrostatic equations or whatever but in fact the filtered governing equations. In any book on turbulence one can find these equations. There one can see that these fitered equations contain a so-called subgrid-scale stress/dissipation term. This term has to be taken into account, otherwise you solve a set equations that is incomplete. In particular at places with intense shear (near jets) this subgrid-term can be quite large I suspect. Using some kind of eddy viscosity is just not unphysical or can you tell us what is missing in the equations?

Gerald Browning

Dave (#136),

I did not expect everyone to understand the mathematical examples. But those that have any basic knowledge of calculus should be able to understand a scalar function of space and time and partial differentiation. And I offered to explain any details to those that are truly interested in understanding the simple mathematical examples, but whose calculus is a bit rusty. Paul Penrose has indicated that his calculus skills are a bit rusty and that is the kind of response I would expect from an inquisitive person seeking to understand the equations and I will answer any technical questions that he might have. On the other hand, gb (hides behind initials) clearly claims to understand calculus (he cites turbulence texts) and I find his response is probably one from a person that has a political agenda.

It is easy to move back to a previous comment on a thread. What terms would you like me to define for you to save you having to look them up?

Jerry

Margo

Gerry B said:
[blockquote]The atmospheric equations have a term that is not present in the NS equations (but it becomes less important at the smaller scales where the system starts to behave more as the NS equations), namely the gravity term.[/blockquote]

I haven’t read your paper, but I would think the gravity terms would be important in some instances.

If someone does take a Reynolds averaging method approach or filtered approach (which is presumably what gb is thinking about), then, if we account for gravity, we’ll see the scalar product of (the covariance of the density and velocity) and (gravity). (Sorry, I don’t know Latex or I’d write that in mathematical terms. Anyway it’s sort of [ro’u’]* g . ) The term may create or destroy turbulence ( and should have a pretty strong tendency to create it, since low density packets of fluid will tend to rise).

Given the way hydrodynamic instabilities work, the effect likely happens at quite large scales and produce turbulence at larger scales.

If someone just replaced the effect of gravity with the average hydrostatic effect, the modeled system would totally lose the physical effect of the gravity terms on the turbulence. If they kept the gravity terms but modeled them badly, they’d get a poor representation of the physical effect. And, if they are using a turbulence model for (ro’ u’) based on the assumption that turbulence production is dominated by the interaction between the Reynolds stresses and the mean shear, when, it’s in fact, dominated — or at least significantly influenced– by bouyancy driven events, their model for the production term will be qualitatively incorrect. (And you could go so far as to call such a parameterization “unphysical”.)

Is it the effect of this term you are discussing?

If gb wants to get a feel for what these would do, he can grab Tennekes and Lumley, add the gravity term, and repeat the derivation of the TKE equations for variable density fluid. The terms will pop right out.

Gerald Browning

Juan (#143),

One of the major problems with the hydrostatic approximation is that it changed the mathematical properties of the original unmodified, inviscid system (the principal part of the original system is essentially a hyperbolic system, but not symmetric for large scale motions). Oliger and Sundstrom showed that the initial boundary value problem for the hydrostatic system with any point wise lateral boundary conditions is always ill posed. This led Heinz and me to look at ways to treat the original system in an alternate manner. If you look at our 1986 Tellus manuscript, you will find a complete analysis for all scales of motion for the original system and the introduction of a hyperbolic system that has shown to accurately portray multiple scales of motion without a discontinuity in systems. If you look here on the ITCZ thread, there is a reference that shows the power of the multiscale system in handling multiple scales of motion in a continuous manner. It is well posed for both the IVP and the IBVP for all scales of motion. The reference shows how the system can recreate a mesoscale system very accurately with open boundary conditions. The second reference on the ITCZ thread shows similar results for a model with typical parameterizations.

Jerry

Gerald Browning

Juan (#142):

Thanks for the tip on the previewer for mimetex!!!!
I tried the example and that should be just what I need to help me debug my examples.

Jerry

Jean S

re #147: Yes, it is of some interest. However, when reading the article, remember to use your RealClimate -filter: the author is one of the leading alarmist-scientist in Finland. He was also an author of 4AR Chapter 11 (“Regional Climate Projections”). I’ve heard him to speak few times and read most of his publications, and I think he has problems of making a distinction between a computer model generated climate and the true one…

gb

Re # 142, Margo,

I am aware that a Coriolis and buoyancy term should be included. What I wanted to say was that atmospheric models don’t resolve the dissipation scales (Kolmogorov length scale). In other words, atmospheric don’t resolve the whole spectrum of scales present in the amtmosphere. As in large-eddy simulations a subgrid model should therefore be included. I have an article by Mahalov et al., GRL (2004), vol. 31, L23111. They report a successful DNS of jet-stream turbulence but with a vertical resolution of 1 to 10 m, much finer than what is possible with atmospheric models. A fair questions is if the subgrid models used in atmospheric models are accurate. Perhaps they are to dissipative. A constant viscosity as subgrid model is also not very physical. But not including some kind of subgrid model or eddy mixing parameter is not correct either.

To be honest, I am not an expert in geophysical flows so perhaps my interpretation is not completely correct. But I have quite some experience in simulations of turbulent flows and I do know what is required for a physical realistic simulation.

Margo

Re 150. (gb)

I am aware that a Coriolis and buoyancy term should be included. What I wanted to say was that atmospheric models don’t resolve the dissipation scales (Kolmogorov length scale).In other words, atmospheric don’t resolve the whole spectrum of scales present in the amtmosphere.

No, they don’t capture the Kolmogorov scale! 🙂

In fact, if you are thinking LES, the climate models probably don’t resolve any significant amount of turbulence. (Though I don’t know. Still, I think there is clearly a lot of turbulence at scales less than many kilometers.)

As far as I can determine, the GCM type climate climate models are more “Reynolds Average Navier Stokes” like; that is RANS models. That is to say, pre-LES type models. (The terminology used to describe the closures I recognize are o nly appropriate for RANS models, not LES models.)

The distinction is somewhat important because outside climate science, “sub-grid” is a term usually reserved to describe the sorts of closures required in LES, not Reynolds Average (RANS) type models. Reynolds Average models usually use the term “closure model” for the higher order moments that appear in averaged equations . (There is a something of a distinction, and strangely enough, the distinction matters when deriving the equations and the closures. That’s why you’ll also see LES modelers mention “Leonard Stresses” and “Reynolds Average” models refer to “Reynolds stresses”. The distinction between LES and RANS )

As in large-eddy simulations a subgrid model should therefore be included. I have an article by Mahalov et al., GRL (2004), vol. 31, L23111. They report a successful DNS of jet-stream turbulence but with a vertical resolution of 1 to 10 m, much finer than what is possible with atmospheric models.

Yep. DNS has been used for loads of things — at fairly low Reynolds numbers and fairly “uncomplicated” flow conditions.

Generally, people take the output and try to develop closure for RANS and/or LES models. This can be done with some success– provided the closure is only used in places where it applies.

That can be a trick in any complicated flow where many things might be happining. After all, you need to code to “recognize” enough about the solution to know what closure applies! Is the flow shear dominated? Bouyancy dominated? If you don’t know in advance, developing the proper closure is difficult– particularly in a RANS model.

There is a long history of people suggesting plausible closures that then didn’t work when you applied them just slightly outside the region where they were tested. That’s why RANS type models progressed from mixing length closures to k-epsilon (and similar) to full Reynolds stress modeling. It’s also why you find different closures in fluids with constant density, variable density due to thermal effect, compressible flows etc.

The hope for LES was to resolve some of the turbulence and assume the smaller scales all look alike. That tends to work better than RANS models– but as far as I can tell, climate models are RANS like! (Or LES at such a huge scale that they resolve none of the turbulence, which means, they will suffer from all the difficulties affecting a RANS code.)

A fair questions is if the subgrid models used in atmospheric models are accurate. Perhaps they are to dissipative.

“Are accurate or not” is often a difficult question. In RANS like models, the issue is general: Are they accurate in flow regimes where they are applied. (LES actually gets around some issues. That’s why people proposed it as a solution to the multitude of difficulties associated with RANS like models.)

It is clear that some GCM’s turn up viscosity for no other reason than to avoid numerical instabilities. This is not something that would give fluid dynamicists outside climate science the heebee jeebees. (Unless you can explain why it doesn’t matter in the situation under consideration.)

A constant viscosity as subgrid model is also not very physical. But not including some kind of subgrid model or eddy mixing parameter is not correct either.

I doubt any GCM uses a constant viscosity subgrid model.

The papers I’ve read suggest things like k-epsilon closures. (That is, 1980s-1990s era closures used in RANS models. ) I’ve read even older closures. But generally speaking, trying to find the precise descriptions of models in the published peer reviewed papers is… well… not easy. You can pull up reference after reference, and the level of description is sort of vague. (As I told my husband, “It’s turtles all the way down!” )

To be honest, I am not an expert in geophysical flows so perhaps my interpretation is not completely correct. But I have quite some experience in simulations of turbulent flows and I do know what is required for a physical realistic simulation.

I also don’t do geophysical flows.

Gerald Browning

Jim D (#123):

One of the most recent examples of a hydrostatic model used at fine scales is the NOAA Rapid Update Model (RUC). Also the NCAR MMM limited area model was hydrostatic for many years.

Jerry

Jim D

Jerry,
#154 Yes, hydrostatic models are being used close to 10 km grids where they still are valid,
but get much finer than that and you are in trouble, except in well-behaved cases like
non-breaking flow over topography, or highly stratified flow with little vertical motion
or resolved turbulence. Hydrostatic assumptions break down for any kind of resolved over-turning.

#153 Surely you are not expecting turbulent flow to be predicted deterministically.
It can only be simulated in a gross sense of having turbulence in the right places,
and that would be considered a success. It is somewhat like trying to predict every thunderstorm
or tornado in the right place, which is generally considered beyond determinism, given
the limitations of both the model and initial conditions. This is where ensembles come
in to give better probabilities, rather than trying to do things with a single deterministic
forecast. Fine-scale modling is definitely going in the probability/ensemble direction now.

Jim D

Jerry,
#157. On a 10 km grid, the shortest waves being resolved would be about 40 km.
These would still be very hydrostatic, and would not have growth rates
more than a few percent larger than the nonhydrostatic proper growth rates
in unstable stratification. These models have not had dissipation added to
control exponential growth, they mainly have dissipation to prevent
build-up of energy at poorly resolved scales less than 4 grid-lengths,
even in stable conditions, so it is a numerical rather than physical reason.
Also smooth models tend to perform better at root mean square error scores
than detailed models, as you might imagine, so operational centers have been
reluctant to reduce the dissipation for that reason too, because these scores
are the bottom line for them. Just my opinion here.

Gerald Browning

Jim D (#158} (continued),

A second order method on a 10 km mesh does not resolve a 40 km wave, especially when the large numerical dissipation is damping that wave. As has been stated earlier, if a numerical model does not resolve the real atmospheric spectrum, then it necessarily must use a large nonphysical dissipation, whether that be implicit (in the numerical method) or explicit (large dissipation coefficient). Then the forcing must be tuned to produce something that looks realistic, but the dynamics is not correct.

And doesn’t it seem contradictory to refine the mesh and leave the dissipation large in order to smooth the solution, in effect reducing the resolution of the solution. What has been gained?

Jerry

Jim D

Addressing #159-#161.

I meant that much below a 10 km grid the hydrostatic models become invalid, but
they are perfectly fine at 10 km or more, or in special cases at finer scales.
I am also of the opinion that some operational models have too much dissipation,
for reasons I mentioned in #158, but research models tend to try to minimize
dissipation to what is necessary for numerical reasons, or justifiable by
physical sub-grid mixing. I agree that if a hydrostatic model was used at
finer scales than its valid range, it may survive instability by using more dissipation
to suppress unrealistic growth rates, but I know of no one doing this, i.e. using
a hydrostatic model at, for instance, 1 km grid size.

Regarding fine-scale modeling, I was referring to cloud-resolving modeling, not DNS,
as DNS is not used in meteorology due to its limitation to neutral stratification.
Fine-scale modeling uses the nonhydrostatic equations. In a good model, there will
not be larger-than-natural dissipation at scales much larger than the grid scale,
and one could argue whether that is 4 grid-lengths, or 7, or more. That said,
these models represent realizations of the real atmosphere at some resolved scale,
and, because the eddies (or thunderstorms), won’t be forecast in the correct phase,
an ensemble at least can tell you something about the uncertainty in their location
or timing. Hope that helps.

Gerald Browning

Jim D. (#162),

You have not addressed the basic issue that a climate model (this is the climateaudit blog) uses very large unphysical dissipation because it is unable to handle all the atmospheric scales of motion and therefore must tune the forcings to make the spectrum appear realistic (but the dynamics is wrong). The climate models also use the hydrostatic approximation that has a number of problems, especially if the models are used at the finer resolutions that would be necessary to resolve real atmospheric features that are dynamically important.

The so called cloud resolving research models also have serious problems as can be seen in the rapid exponential growth near jets in the Lu et al. reference that uses the NCAR WRF model. The experiments in that reference do not involve any parameterizations (forcings) and those problems won’t magically disappear using ensembles. And when the microphysics is added, those parameterizations have their own set of problems.

The comment at the beginning of this thread summarizes these problems and IMHO so far no one has shown that the comment is incorrect.

Jerry

Gerald Browning

As promised, I am providing the links to four plots that I will discuss in great detail. These plots are the vertical velocity w at 12 hrs for the doubly periodic in x and y (w = 0 at bottom and top of 12 km atmosphere) for two resolutions for the inviscid multiscale model and for an inviscid hydrostatic model. Increasing the resolution for the multiscale model results in essentially the same solution:

Jerry

Gerald Browning

Margo (#165),

The article is in Mathematics of Computation. If you do a google scholar search on Browning Kreiss it is the second reference. (1989)

Jerry

Gerald Browning

I will discuss the above plots in more detail and add additional plots in the comments to follow.

Jerry

Gerald Browning

Margo (#165),

I forgot to mention that I had Sylvie make a minor correction to the
data assimilation program based on the Bounded Derivative Theory and it had
a major impact in the reduction of the error in the forecast. In fact the Canadian model started to outperform the US global model, even though
the formar uses a less accurate numerical method.

Jerry

Gerald Browning

Willis et al.,

It might be of interest to compare the vertical velocity in the low res versions of the two models. Both started from the same initial data,
but there are already differences in the low res runs at 12 hours.

Jerry

Gerald Browning

Jim D (#175),

1. Please cite a quantitative scale analysis that shows that it is appropriate to use the hydrostatic approximation down to 10 km. In this regard you might want to read the Tellus 1986 manuscript by Kreiss and me. And it will be shown that the cascade of enstropy down to the smaller scales where the hydrostatic balance is not applicable happens within hours, not days. The inappropriate damping of these scales has an impact on the spectrum, especially in longer runs (see Math. Comp. article). Your statement is pure semantics, not mathematical.

2. Please cite the type and size of dissipation in any hydrostatic model that is running at 10 km. I will be happy to add that operator to the hydrostatic model to determine its impact on the accuracy of the solution and the spectrum. Essentially this was done in the Browning, Hack, and Swarztrauber manuscript and the dissipation destroyed the spectral accuracy of the numerical method, i.e. all the cost of the extra computation of the pseudo-spectral method was wasted.

3. Clearly you do not want to understand that any numerical model that tries to simulate a physical problem with an exponential growth in time (let alone one that is very fast) will have problems. This is well known in the numerical analysis community.

4. I did not know that climate models (or for that matter NWP models) could accurately forecast the development and intensity of a hurricane. My argument was for the global Canadian weather model and the global US model. A cute gimmick to try to change the subject. If you look at the references on the ITCZ thread, I am fully aware of the importance of heating in smaller scales of motion. I just don’t trust the accuracy of the parameterizations, the interface conditions between the atmosphere and ocean, etc.

Jerry

gb

Jerry B.

Have you read post # 177? There Margo says that if you don’t resolve all scales of motion (like in an atmospheric model) you need a subgrid parameterization. That’s what I tried to explain a numner of times. Do you agree that some kind of parameterization of the subgrid scales is required in an atmospheric model or do you have another opinion?

I have read your Math. Comp. article (1989) and I don’t understand it. Do you claim that a numerical model of turbulence with and without a parameterization for the subgrid scales should converge to the same solution?

Another question. How do you know that the dissipation in atmospheric models is unphyscially large?

Gerald Browning

This is a test as suggested by Willis:

Multiscale Model (Lo Res)

Gerald Browning

Test3

Gerald Browning

Thumbnail

Gerald Browning

Lets try again.

These four plots are the vertical velocity w at 12 hrs and z = 3 km for the doubly periodic in x and y (2000 km by 2000 km domain) and rigid boundaries at z = 0 km and z = 12 km, i.e. w = 0 at the bottom and top boundaries, for two resolutions for the inviscid, multiscale (nonhydrostatic) model and for an inviscid, hydrostatic model (all runs start from the same large scale balanced state). Increasing the resolution for the multiscale model from 256 by 256 by 12 points (7 km by 7 km by 1 km) to 512 by 512 by 12 points (3.5 by 3.5 by 1 km) results in essentially the same solution.

Click on thumbnails to see full images.

But increasing the resolution in the hydrostatic model leads to a rapid cascade to smaller scales and the solution blows up.

The vertical velocity is shown because it is a very sensitive variable and crucial to determing storms in the presence of moisture. The vertical mesh is 1 km, but different verical mesh sizes, heights for the top boundary, and time integration schemes have also been tried with similar results.

The lateral domain was chosen to be doubly periodic so that there would be no boundary problems for the hydrostatic model. Of course then the Coriolis term must be shut off, but it is not crucial at these resolutions.

Jerry

gb

Re # 187

An atmospheric model does not solve the full governing equations but in fact the filtered governing equations whereby the small scales are removed. It is quite simple in mathematical terms to carry out a spatial filtering of the governing equations. If you do that you will find an additional term describing the flux of energy from the resolved scales to the unresolved scales. A subgrid model is meant to describe this process. You call it something artificial. However, a subgrid parameterization models in fact an existing physical process. If a subgrid parameterization does that correctly is another question but it is entirely reasonable and physically correct to add a subgrid model in an atmospheric model. Climate science is not unique in that respect. In very few practical applications turbulent flows can be fully resolved. If engineers at Boeing compute the flow around an airplane they use commercial fluid dynamics codes full with ‘artificial’ terms. I am working in engineering and there we develop many ‘artificial’ subgrid models. Numerical fluid dynamics codes with these subgrid models produce results that match experimental measurements quite well in general.

And it is not true that it is impossible evaluate how unphysical/physical these subgrid models are. There are observations: spectra, wind speed, ocean currents. In some cases there are quite large differences between model outputs and observations but in other cases the correspondence is quite good. For instance, computed spectra agree quite well with measurements. If subgrid models would be so bad that wouldn’t happen.

Margo

Re 187:

To make things worse , it is even impossible to evaluate how very unphysical this unphysical
something is because the physical part is ignored and unresolved .

Tome:
Strangely enough, sometimes rarely impossible to evaluate how unphysical an approximation is. However, someone has to try to evaluate how good or bad a closure model is.

The purpose of Browning and Kreiss 1989, (which I now read 🙂 ) is to examine how good or bad two very specific closures worked in a specific flow system. (If I understood correctly, the case examined was the evolution of decaying homogenous isotropic 2-D turbulence. This is a fairly “simple” flow, in the sense that the geometry is easy and the only “thing” going on is turbulence interacting with itself. So, it’s a good platform for testing whether or not a closure or subgrid parameterization has even the slightest hope of replacing the behavior of small scale turbulent fluctuations. )

Anyway, Browning and Kreiss began by calculation exact solutions, performing some grid independence tests to make sure the results of their exact comutation aren’t an artifact of failing to resolve scales. Because these sorts of exact solutions are now possible, that first result they present in their paper a sort of “numerical experiment”. These results are shown.

Now, as a practical matter, even though B&K ran this ‘exact’ computation, we know that this type of computation is limited to a small class of flows. (Because too much computing power is required in other flows. Using approximations would reduce the computational load. People want to know how well some approximations might work.

So, after running the numerical experiment, B&K changed the numerical model, introducing two specific parameterizations that had been proposed and used in the literature. One “parameterization” is called “chopping” (you just throw away energy from time to time). The other is called “hyperviscosity”. (I’d honestly never heard of anyone doing this–but then, my training is in experimental fluid mechanics. )

Browning and Kreiss showed that if the two parameterizations they tested quickly gave poor results for the evolution of two-dimensional turbulence. It’s a pretty nice test. (Though, it’s all written in a sort of “mathy” way. I would have also computed some measurements that mimic things one could measure in a lab, and compare those. But that’s because my training isn’t applied math. 🙂 )

Follows imho a “damned if you do , damned if you don’t” – if you go down you’ll be hit by Jerry’s exponential evolutions and if you stay up you’ll have just a pile of steaming HS .

The nice thing would be if I could find on the net somewhere a mathematical treatment for the case of statistical treatment .

You really need to take courses to understand statistical fluid mechanics for a number of reasons. First: There are different statistical approaches to modeling. (You’ll see I keep mentioning DNS, RANS, LES. Each is different.) The strengths and short comings are different in each type. Second: The “problems” are all in the closures (to use the correct term if you use RANS type averages) or “sub-grid” models (to use the correct term for LES models.) DNS works. It just can’t be used for flows of practical importance.

Jim D

Margo, thanks for the DNS explanation.
As I understand it, DNS assumes all eddies are resolved, so they have an
effective Reynolds number mostly defined by their grid resolution. So
since atmospheric Reynolds numbers are about 100000, DNS can’t be used for any
significant volume of atmosphere with current computers.
I am somewhat agreeing with gb in that what some people consider dynamics,
others consider physics or parameterzation. To me and most atmospheric people
turbulence has to be parameterized somehow.
When I say hydrostatic models are fine at resolved scales, I am only including
motions due to advection, pressure gradients, coriolis, and buoyancy, for which
analysis gives the well known dispersion relation ( I won’t risk TeX) that
omega squared equals (N squared times k squared) over (m squared plus k squared)
ignoring coriolis and an extra density variation term, where
omega is the frequency of gravity wave oscillation,
N is the Brunt-Vaisala frequency that depends on stratification,
k is the horizontal wavenumber (inversely proportional to wavelength)
m is the vertical wavenumber.
In hydrostatic models the denominator k squared is missing, severely distorting
behavior as k increases to m in size, but fine as long as m somehwat exceeds k.
This is what I base the validity of hydrostatic models on.
Obviously the atmosphere permits other waves, but acousic modes have no meteorological
significance, and larger scale waves due to rotation effects are handled better
by hydrostatic models, so it is gravity waves that are the limitation in resolved
dynamics. I mention this to clarify what I meant in previous e-mails when
referring to hydrostatic versus nonhydrostatic. If we are not talking about
gravity waves or unstably stratified resolved eddies, this may be besides the
point of this thread.

Gerald Browning

Jim D (#192),

It is not quite that simple. I will discuss this in more detail
when I return.

Please quantify the relationship between k and m in terms of length scales when the hydrostatic relationship fails for the general audience.

Jerry

Tom Vonk

To illustrate the problem , let’s take the ENSO .
It is not very complicated to understand the main causalities .
Btw by saying “main” is already an assumption because I admit without demonstration that poorly understood or “small” causalities are not “main” but anyway .
Now it is easy to see that this (simplified) system would behave like a delayed oscillator .
Starting from there I can build a model based on the delayed oscillator and begin to play with it .
And indeed the model will give results that look more or less like a real ENSO or at least like the idea I have of the real ENSO based on the very limited timeframe in which I have data that I consider reliable/sufficient .
From there I can begin to tinker with it making other assumptions , I can refine it and I can begin to make “predictions” .
I can even “prove” that I was right to neglect this and simplify that because when I change
this or that , the model shows a low sensibility for such changes .
But did I prove anything concerning the real ENSO ?
Of course not , I have proven that a delayed oscillator with N supplementary ad hoc assumptions has this and that property .
As the real ENSO is obviously no delayed oscillator , after all this work I am still left with the unanswered question about how relevant the prediction bit is and for how long .
I am not saying herewith that everything was useless , by using an analogy that has a
QUALITIATIVE justification I might get some QUALITATIVE insights in some short term
properties of the real ENSO .
But from there to quantitative predictions over a long period of time is a distance that might very well be infinite 🙂

Margo

Tom:
I think you and I are in general agreement. When I said you needed classes to understand statistical fluid dynamics, I meant you need it to understand the hows, whys, plusses and minuses of RANS (Reynolds Average Navier Stokes) type codes and LES (Large Eddy Simulations.) Any engineer or scientist can get a qualitative level understanding of what’s involved in DNS. “Research tool” doesn’t always mean “harder to understand”.

Strangely, I once characterized DNS as “the big hammer approach” to a coworker who’d just finished his Ph.D and was switching his projects as a result of change in employment. He thought I meant that “big hammer” as a bad thing. Six months later, after he’d started running doe DNS models for a particular project, we were talking about his results. And he said, “You know, there really is nothing like a ‘big hammer’!”. He’d finally realized that “the big hammer” is a good thing — provided you have one. He actually switched to useing “the big hammer” metaphor.

The problem is, we don’t usually have the big hammer.

I disagree with you one one minor point: LES type codes might help resolve the issues Jerry is identifying. However, I’m pretty sure those are also too computationaly intensive for GCM’s.
In an LES code, you’re filter must be set to resolve the large scales of motion that are anisotropic, and then only model small scale motions that are isotropic. There isn’t a distinct boundary separating “large” and “small scale”, but one can estimate these things and we absolutely know that GCM don’t resolve all scales of motion that are anisotropic!

At large Reynolds numbers, the subgrid models in LES should be more general than those used in RANS like codes because small scale turbulence does look similar in many, many flows. (However, these models are computationally intensive, and as far as I can tell, the GCMs are absolutely, positively not LES like. Or, if someone claims they are LES like, they think it’s ok to set the filter wider than anyone can justify based on known LES computations or theory. )

gb

Re # 198. There is no strict requirement that the subgrid scales should be isotropic in LES. However, if the subgrid scales are significantly affected by rotation or stratification one can’t use a subgrid model developed for Kolmogorov turbulence but has to develop a new model. Perhaps difficult but in principal possible.

I have seen articles where they present spectra computed with atmospheric models so they resolve a part of the ‘turbulent’ scales and I think we can consider them as some kind of LES. However, the turbulent motions are perhaps not resolved in the boundary layer but above only above it.

Tom Vonk

Margo

You are right .
It was actually my first motivation to come here because coming from DNS (yeah , right , the big hammer) I began to look at RANS and found that it didn’t make things simpler or more “operationnal” .
I also admit that my culture in the field of LES is at best approximative .
Problem being , of course , that having a job I have not much time to spend it on reading the
hundreds of publications that must have been written on that field .
Also coming from DNS , I have a very deep distrust in computers because since Turing and Goedel we know that everything is not calculable .
A computer is good to make very fast big amounts of additions but that is only useful when I
am perfectly sure that the additions it makes are only additions and nothing more .
That is very obviously not the case in climate modelling because here I ask from the computer that he replaces my understanding (or lack thereof) by telling me what will happen in a largely badly defined configuration .
Modelling can be useful in engineering for the reasons you already mentionned but it is poison and worse in theoretical science .
My goal would be to mathematically prove that systems like the climate are not calculable in
Turing sense but I am not sure that I have the time to reach it 🙂

Margo

Re 202

My goal would be to mathematically prove that systems like the climate are not calculable in

Oh, I suspect they are calculable given a big enough hammer. But who knows, it may turn out they aren’t. Still, even things that aren’t strictly speaking calculable may permit very good approximations.

Strangely enough, my “issues” are much more modest with regard to discussing models. I think there is something worthwhile in modeling. I also think there is a lot of overselling of many things going on; I think there are quite strong double standards for hypotheses testing seem to have materialized. (And surprisingly to some, I perceive these things even though I think there is more than likely some AGW going on right now. I just don’t see why thinking AGW is going on should lead to people overselling models and setting aside normal standards for hypothesis testing. )

Jim D

#205, Jerry, some responses, best I can.
1. From the dispersion relation when k approaches m, means when the horizontal scale
starts to get as small as the vertical scale. This depends on the depth of the
atmosphere which gives the smallest possible m. If k was 0.5*m (so the horizontal
scale is twice the vertical scale), and m was say 20 km, then k would correspond to 40 km.
Since this shows up as squares in the denominator, the error is 25% in the square of
omega, or maybe 12% in omega itself. So for resolved waves of 40 km and deep modes,
the 12% error is starting to look bad, but for 100 km, it becomes about 2%, much more
acceptable, and shallower modes are even more accurate. It’s a greay area, and depends
what error you are willing to accept to say which scale is poorly represented.
For unstable stratification N squared becomes negative and omega likewise becomes imaginary
and then represents a growth rate. So hydrostatic models overestimate the growth rate as
the approximation breaks down (due to the lack of a denominator term).

2. It is very easy to test hydrostatic along with nonhydrostatic models. Stable flow over
topography is a prime example of how to demonstrate the hydrostatic failure,
and has been done many times to test nonhydrostatic models
but that shows up well only around 2 km grid-lengths with mountain widths about 20 km.
This is not a viscous case, nor has anyone tried making the hydrostatic model viscous
to cure this problem. Maybe I am misunderstanding.

3. I was trying to make it clear you can’t run a weather or climate model with
all the parameterizations turned off, using an extreme example of a hurricane to
make the point. If you re-initialize the model every 12 hours with data assimilation,
maybe you can get away with it, but that is like cheating by giving the model the answer
every 12 hours. Good global models have value out to 7 days without data assimilation,
except at the beginning,
and I can assure you it would be much less than 7 days without parameterizations.
I am not sure of the point of #171 if it wasn’t a jab at the value of model physics.

Jim D

Jerry, on #207 points raised
1. This is a standard textbook formula based on the linear inviscid incompressible equations
with buoyancy and constant stratification, but ignoring the density scale height and coriolis,
which only slightly complicate the equation. I think the only thing it predicts that is ill-posed
is the hydrostatic approximation as the length scale decreases. Maximum growth rates occur
for infinitely small horizontal scales. This is a fundamental problem related to the
fact that the hydrostatic equations have no concept of “parcel theory” that limits
vertical kinetic energy based on available potential energy.

2. A 10 km hydrostatic climate model may still be OK, because it only resolves waves that
are much longer than the maximum vertical scale. Climate model tops usually are more like
30-50 km, however, so it starts to be questionable, based on the dispersion relation, and
climate and weather global models look to go nonhydrostatic in preparation for 10 km grids.
Heating is important. Radiation has a mean atmospheric cooling effect, plus surface
temperature effects that would lead to severe biases if ignored. Latent heat is a vital
energy source for the climate system. The dispersion relation can be modified for
idealized heating profiles, but the simplest thing is to take convectively unstable
cases as unstably stratified by using negative N squared.

3. Yes, I agree all the data available are used to provide the best possible initial
and, for non-global models, boundary conditions, but clearly
in forecast mode you don’t have data in the
future, so you are running the model for days without data assimilation.

4. Clearly more data helps, and it has to be used sensibly.

5. Yes, the results in #186 are in accord with the dispersion relation that
overpredicts hydrostatic growth rates at smaller scales, but limits them for
nonhydrostatic models. Not clear if you have just a numerical instability,
which you can check if reducing the timestep changes the solution.

6. The most common verification is 500 mb height anomaly correlations,
of the forecast with an analysis,
where skill is regarded as an 0.6 correlation. Skill extends beyond
7 days (after the last data assimilation) when averaging results over many forecasts.
Skill is shorter-lived for fine-scale things like precipitation forecasts, maybe 2-3 days at most.

gb

Jerry,

The dispersion relation can be found in for example ‘Elementary Fluid Dynamics’ by Acheson, ‘Physical fluid dynamics’ by Tritton and any book on geophysical fluid dynamics.

The come to a previous point. The smallest length scale in 3-D turbulence is the Kolmogorov length scale, see ‘A first course in turbulence’ by Tennekes and Lumley and in any other book on turbulence. No difficult mathematics is required. Simple and elegant dimensional reasoning will do.

I’m a bit amazed now. Before one starts to critise atmospheric models there is need to understand some of the basic physics of atmospheric flows?

gb

Margo,

Takahashi et al. (2006) GRL, vol. 33, L12812. There you can find a simulation of the mesoscale spectrum.

Re # 191. Reproducing observed spectra with a model is not trivial, it puts a quite severe restraint on it. Very few scientist have been able to reproduce the mesoscale spectrum with idealised models.

Jim D

Re #209

Jerry,

1. Yes, I am in mesoscale modeling, not climate modeling. I got onto this blog to
make sure the arguments don’t start reinforcing any misconceptions, as they
can tend to drift unless checked. I mainly wanted to respond to the first post,
and have not looked yet at Browning and Kreiss, so can’t comment on that.
The first post implied hydrostatic model’s have an error that is routinely
corrected by viscous terms (as I interpret it). I dispute that, and have shown
the reason that hydrostatic models have errors which depend on scale. If diffusion
helps, it only does so at some specific scales where you eliminate the wavelengths
that are causing problems.

2. I have not said that hydrostatic models are invalid at 10 km, just that
the approximation error starts to get significant for deep modes at that scale.
Specifically in #123 I referred to thunderstorms as an example of something
you can’t credibly model with a hydrostatic model. This would be less than 5 km grids
at most.
On the model top height issue, yes, mesoscale models usually put the top below
20 km, but at least above the tropopause. Climate models, and global models
such as ECMWF have tops nearer 1 mb ( 50 km), because there are some important
radiative things happening up there.

3. Did I not say that the anomaly correlation of the 500 mb height is the
standard measure of accuracy? This shows skill to beyond 7 days after the last data
assimilation. Do I need to explain what the 500 mb height is, or the term
anomaly correlation?

5. I’m just saying that hydrostatic models should have unrealistic growth rates
as the vertical and horizontal scales become comparable. If you carry on reducing
the grid down to 1 km, the hydrostatic model would get even worse, while the
nonhydrostatic solution would continue not to change, as is correct when there is
no small-scale forcing. Nonhydrostatic model growth is limited by N squared
as the scale goes to zero. This can be interpreted as having the kinetic energy
constrained by the available potential energy, as I mentioned before. The exponential
growth is limited realistically by energy conservation.

Jim D

Sorry for the repeats due to a technical error. Feel free to delete #213 and #214.

Gerald Browning

The Evolution of Limited Area Models

I have found a reference that I thought might lead to some insight as to the progression of limited area models at NCAR.

A Nonhydrostatic Version of the Penn State-NCAR Mesoscale Model: Validation Tests and Simulation of an Atlantic Cyclone and Cold Front

Monthly Weather Review, May 1993 , V 121, 1493-1513 by Jimy Dudia

I will quote a few lines from the introduction to the manuscript.

“The hydrostatic mesoscale model presented by Anthes and Warner (1978) has been employed to investigate meteorological phenomena on a wide range of scales ranging from continental-scale cyclone development to local valley flows.”

“With improvements in computer power it is becoming possible to use finer meshes. Higher resolutions reduce errors associated with finite differencing; thus it is clear the the future mesoscale model should not be constrained by the hydrostatic assumption, which effectively limits the resolution to around 10 km except in weak flow, nonconvective situations.”

“There are currently few nonhydrostatic models designed for use with ‘real data,’ that is, with data derived from three-dimensional , observed wind, temperature, and moisture soundings. ”

Does the second quote sound familiar?

Note that the Browning and Kreiss manuscript in Tellus appeared in
1986.

Jerry

Jim D

OK, yes, Jim Dudhia here, but not representing anyone but myself.
Not sure what you were implying with a quote from my Introduction,
but it was a well established fact, and just a statement of the obvious, as is
often found in Introductions. It served to justify the point of the paper which
was to introduce nonhydrostatic dynamics into what was previously the hydrostatic MM4.

1. Maybe I am missing the point, but atmospheric models are not normally dominated by
dissipation unless you are using them at scales where they barely resolve your
features of interest. The fact is that inviscid behavior is well handled
by models with adequate resolution if the dynamics is valid for the scale.
2. I can’t comment without reading the references, but the vertical velocity response
to heating is understandably proportional in a linear system.

Yes, I do know WRF too, and the upper sponge is to prevent upward propagating energy
from gravity waves from reflecting back down from the model top surface, so it simulates a deeper or infinite
atmosphere, which is more realistic since wave energy is not reflected from there in fact.
There is no important net vertical mass flux at such heights.
Lateral boundaries are specified from analyses when using a regional model and add some relaxation
zone to prevent noise. In the case of forecasts the “analyses” are actually usually
forecasts from a larger scale regional model or global model.
The top of the CCSM model is about 1 mb. I could find out, but I am guessing here.

3. I don’t work in global verification, so I can’t provide numbers any better than you can
research them. If, by L_2 norm, you mean rms error, there is skill if the forecast has less error
against the verifying analysis than a randomly chosen analysis does.
The 500 mb height is chosen because it is a smooth field representing positions of air
masses and jetstreams reasonably well in a single map. The first single-layer models
back in the 60’s only predicted this field, so it is traditional in some way.

As you have mentioned, the precipation is unreliable long before 7 days time. So basically when using large scale NWP models the parameterizations do not help in the first few days and are inaccurate shortly thereafter.
What impact does this have on climate models that run even coarser grids and do not use data assimilation to update the information?

It is not the parameterizations necessarily that are inaccurate, it is that smaller
scales have a shorter range of deterministic prediction than longer scales, and
precip is mostly tied to smaller scale features. Climate models do not deal with
deterministic prediction, only mean behavior over long periods. Climate is a very
different application that evaluates models using different metrics more
associated with this mean behavior. Their parameterizations have to pass tests based
on this type of evaluation before being used more extensively.

Willis Eschenbach

First, Jim D and Jerry B, thank you very much for a fascinating discussion of things computorial. I have learned much from your discussion, and I appreciate both the content and the tone of your posts.

Next, Jim D., I have a question that I have asked many times, but have never gotten a satisfactory answer. You say:

Climate models do not deal with deterministic prediction, only mean behavior over long periods.

My question is, if the deterministic predictions are incorrect or unreliable, what assurance do we have that the “mean behavior” will be reliable?

Now, I understand that if we throw a perfect die, we can predict that the number “4” will come up about one time out of six, despite the fact that we cannot predict any given throw. But this assumes that we understand the physics of the situation, that the die is perfect, that we know how many faces the die has … in other words, we not only have to have a perfect die, but a perfect understanding of the physical situation.

But we are nowhere near that level of understanding of climate. In fact, many of the models omit a variety of known forcings (e.g. dust, sea spray, etc.), all of them omit some known forcings (e.g. cosmic rays, methane from plants, DMS from plankton), and all of them omit the unknown forcings (e.g. … well, you know).

In addition, the models have huge known errors in various aspects of their “mean behavior”, errors which dwarf the signal we are interested in. The GISS model, for example, is off regarding DLR by ~ 15 W/m2, regarding cloud cover by ~ 15%, and has a host of other known erroneous results.

Given all of that, what assurance do we have that the models can get the “mean behavior” right? Since they are tuned to replicate the past, being able to replicate the past proves nothing, so what facts show that they can forecast the “mean behavior” of the most complex system we have ever tried to model?

All the best,

w.

Gerald Browning

Jim D.,

From your manuscript it is clear that Anthes made many runs at many different scales of motion using a hydrostatic model that is ill posed for the initial boundary value problem (now the initial value problem). How were the problems at the boundary and the propagation of the perturbations into the interior overcome?

In your manuscript, there are dissipative terms on every equation. But on a brief reading I have yet to find the size and type of these terms. Can you tell me on which page of your manuscript these can be found?

I would like to point out that the time split method used for many years in these models has been shown to be numerically unstable and that instability must be hidden by dissipation. In fact I believe that the WRF model no longer uses that method?

You stated the reason that modelers use a sponge layer at the top of the atmosphere. You did not explain its impact on the continuum solution when there is information coming from above the top of the model or on the accuracy of the approximation on the continuum solution.

The smoothing at the lateral sides of a limited area model have been employed by modelers for many years. Please run the test in the manuscript cited on the ITCZ thread to determine the impact on the continuum solution.

I find it interesting that you stated that you wanted to be on this thread
because you wanted to make sure things didn’t stray too far (or some such).
Did you mean that you didn’t want too much information about all of the fudge factors in the models to be revealed?

I do not agree with anything you said about climate models. As you go further in time in a model, things become harder, not easier. Clearly from the simple contour plots I have shown, the enstropy can cascade down from a balanced large scale motion to tiny scales not resolvable by
any model very quickly. At that point the only thing that can be done to stop the model from blowing up is to include an unphysically large dissipation that will have an impact on the spectrum.

Jerry

bender

Echoing fFreddy’s #211 support for this ongoing discussion. Fascinating.

Tom Vonk

I do not agree with anything you said about climate models. As you go further in time in a model, things become harder, not easier. Clearly from the simple contour plots I have shown, the enstropy can cascade down from a balanced large scale motion to tiny scales not resolvable by
any model very quickly. At that point the only thing that can be done to stop the model from blowing up is to include an unphysically large dissipation that will have an impact on the spectrum.

I fully agree with the above and it applies also to the Kolmogorov argument .
By staying “only” with Navier Stokes equations , it is well known that with the introduction of temporal means of the velocities , the equations don’t become easier , they become more complicated instead .
The equations cannot be solved for temporal means any better than for the instantaneous values .
Follows that tMean of U(x,t) is as fundamentally chaotic as U(x,t) .
After all it would be very astounding that the chaos (aka non predictability and exponential divergences) magically disappears only because somebody has chosen to make a mathematical change of variables in the relevant equations .

It is exactly for that reason that no climate model afaik is able to evaluate how legitimate it is to make predictions .
I don’t know by what process the IPCC modelers award themselves their “virtually certains” and “extremely unliklies” but I suspect that it is very similar to what I have seen in the evaluations of the ENSO model .
I mean one can’t stop laughing seeing phrases like : “The long term simulation with uncoupled atmospheric noise is considered to be the control run (“true” simulation or “observation”) and is used as initial condictions for the prediction runs and to verify the predictions .”
I am not joking , that’s what they really do – they analyse the model skills to predict by comparing it … to itself (Kirtman and Schopf , 1998)
More circular than that you can’t do !
Do these people still realise the difference between the reality and a numerical code ?
Before beginning to analyse irrelevancies like dispersion models (that are already approximations) , it is more than necessary to come back to fundamentals about predictability like Jerry does .

Tom Vonk

Think about it this way: none of the climate modelers have published confidence intervals for the outputs of their models; I don’t even know if it’s possible to compute them given the way the models are written.

Regardless how the models are written that is impossible .
By definition a confidence interval means that you can catch a real solution between 2 approximate solutions with a given confidence (>95%) .
Now if you take for variable “the spatial temperature average” which is what the models give you don’t even know if there is a unique solution to the (incomplete) set of equations you are trying to simulate numerically let alone what that temperature will really be .
Therefore there is no way you can tell what the confidence interval of your simulation is .
The only thing you can do is to run N models with M different sets of assumptions and analyse the sensitivity OF THE MODELS (not reality) to changes in assumptions .
Then you are in known field and get all possible results about ranges and standard deviations displayed by the models .
Needless to say that all this guarantees nothing whatsoever as for the behaviour of the real solution that is still as unknown as it was before .
Over shorter period of times you are “saved” by the inertia of the system that enables to prove that statistically the best weather prediction for tomorrow is to say that “It will be similar to the one observed today .” .
But as soon as the time gets longer you begin to be wrong and have no idea by how much .

Tom Vonk

I am certainly not a climate model expert .
But you could very seriously question the ability of the models to REALLY hindcast the climate .
On thing is sure – if you could initialise the model for , let us say 1850 (OK you have not the data but let’s suppose you have) and then make it run to 2000 , you would get no map for every year with the right temperatures , the right winds , the right cloudiness distribution and the right precipitations .
What you would get would be an artefact that looks like A climate yet is not THE climate .
Neither completely stupid , nor completely right .
However if what you saw was blatantly wrong , you could always play with the parametrisations to get a better fit .

That’s what R.Lindzen called “Crude data fitting based on a hopelessly naive assumption that somebody understands the natural variability .”

Jim D

Jerry,
Answering the questions in order.

From your manuscript it is clear that Anthes made many runs at many different scales of motion using a hydrostatic model that is ill posed for the initial boundary value problem (now the initial value problem). How were the problems at the boundary and the propagation of the perturbations into the interior overcome?

In your manuscript, there are dissipative terms on every equation. But on a brief reading I have yet to find the size and type of these terms. Can you tell me on which page of your manuscript these can be found?

I would like to point out that the time split method used for many years in these models has been shown to be numerically unstable and that instability must be hidden by dissipation. In fact I believe that the WRF model no longer uses that method?

You stated the reason that modelers use a sponge layer at the top of the atmosphere. You did not explain its impact on the continuum solution when there is information coming from above the top of the model or on the accuracy of the approximation on the continuum solution.

The smoothing at the lateral sides of a limited area model have been employed by modelers for many years. Please run the test in the manuscript cited on the ITCZ thread to determine the impact on the continuum solution.

I find it interesting that you stated that you wanted to be on this thread
because you wanted to make sure things didn’t stray too far (or some such).
Did you mean that you didn’t want too much information about all of the fudge factors in the models to be revealed?

I do not agree with anything you said about climate models. As you go further in time in a model, things become harder, not easier. Clearly from the simple contour plots I have shown, the enstropy can cascade down from a balanced large scale motion to tiny scales not resolvable by
any model very quickly. At that point the only thing that can be done to stop the model from blowing up is to include an unphysically large dissipation that will have an impact on the spectrum

First of all, there is nothing to hide about dissipation terms in models. It is known
how much these terms do in the solution, and the model predicts the weather verifiably anyway.

Boundaries are handled using the pragmatic approach of relaxing them towards analyses.
No math is needed to prove this works, just check the results.

The dissipation in MM5 is documented with other technical details in the Grell et al. NCAR Tech Note (1994)
with a title something like “Description of the Penn State/NCAR Mesoscale Model (MM5)”.
The paper only describes the difference between MM4 and MM5, so this was not in it.

Time split methods can be unstable when used with the wrong spatial scheme,
and the leapfrog scheme is also unstable without a time filter. Part of
the dissipation keeps numerical instabilities from growing, while part
represents Reynolds stresses, and in practice these are almost equal. There is also
a method for selectively damping sound waves to prevent their instability in the
split method. WRF also has such a sound-wave damper, but needs no additional
dissipation for numerical instability when odd-order advection schemes are
used because those have noise control built in.

Tests with the sponge layer show that it helps reduce reflection. This is
seen visually with comparisons of linear mountain waves against known
non-reflecting analytic solutions, but can also be quantified.

I am not sure I understand the test yet. Is it driven with complex real data,
because that is what we use?

I stated I wanted to monitor this thread to make sure the contributors
don’t go off track because I have seen threads on sites where it looks like
someone can say things that are known to be false by people in the field,
but go unanswered and therefore mislead. I’m sure you’ve seen that happen too.

I have said that large dissipation is only needed if you are doing something wrong
like using hydrostatic dynamics at fine scales. Nonhydrostatic models can be
run with little dissipation and give valid flows on all resolved scales. However
there are physics processes such as convection and boundary layer schemes to
handle some complex things occurring at unresolved scales, and that is a physics
issue, not dynamics.

Gerald Browning

Jim D. (#234):

Let us address one issue at a time.

Please state the type and size of dissipation you used in the experiments in your manuscript for every time dependent equation so the general reader will know how much Anthes and you used in the models for these equations.

Once those values are clearly stated, the discussion can proceed to the next step.

Jerry

MarkW

#235,

you state that confidence intervals are partially based on how “or how much models differ from each other”.

In other words, if two guesses are similar, it is assumed that both guesses are accurate?

I wasn’t aware that was how science was done.

Gerald Browning

Paul Linsay (#239),

This is a very valid point. I will discuss a well known example.

When the possibility of satellite observations was first introduced, a number of so called “twin experiments” were run with NWP models (e.g. see Roger Daley’s book for a discussion of these experiments). A control “forecast” was run with a particular NWP model. Then the initial data was perturbed and the new information that was to become available from a satellite was introduced from the first run into this second run of the model to determine if the “forecast” with the satellite data insertion over a period of time would improve (and it always did). However, when the satellite data became available, the results did not match those from the twin experiments. The reason (see Periodic Updating reference by Browning and Kreiss) was that the NWP models had excessive unphysically large dissipation so the error equation behaved as the heat equation in the above simple mathematical example, i.e. the models were not a true reflection of the real atmosphere and led to completely misleading results.

This example alone should give one pause about the use of information based on models with unphysically large dissipation, but it appears that this obvious lesson still has not been understood by a number of modelers.

Jerry

Gerald Browning

Community Atmospheric Model (CAM) Parameters

There is a table under the CAM documentation that shows the T31 model
uses a dissipation coefficient 20 times larger than the T85 model.
I am still searching for the height of the upper boundary, but have seen some indications in the code that the number of levels is 26 in all of the models. I will continue to search for this info, but if anyone knows the answer, please let me know. You would think that this info would not be that hard to find, but it seems to not be easy.

Jerry

Jim D

#236
Jerry,
The dissipation term is a fourth-order diffusion with two
parts to the coefficient. The constant part is 0.003 * dx^4 /dt
in units of m^4/s. The other part is proportional to deformation,
and is of comparable magnitude in practice.

Willis Eschenbach

Jim D., thank you kindly for your reply. You say:

Willis (sorry for truncating your name before). Feedbacks by their nature have to have something
to feed back on. If they completely mask the signal they remove their reason for existence.
I’m not an expert, and this is just an opinion. I believe there is a cloud feedback that is
negative too, but if it is missing in models, why is the cloud cover in the warmest part of the world,
the tropics, not higher than can be simulated by climate models? So if you imagine the world
just tending towards being more tropical, there is no reason to believe we don’t have the
important feedbacks already.

According to Gavin Schmidt et al., the albedo in the GISS models is not calculated from physical first principles, but is tuned for:

The net albedo and TOA radiation balance are to some extent tuned for, and so it should be no surprise that they are similar across models and to observations.

In addition, the cloud coverage in the GISS model is way different from reality, with the three GISS models reporting 57-59% global cloud cover and the ICCSP data showing 69%. According to the same report:

Total cloud cover is definitely too low.

So I’m not clear why you are claiming that the cloud cover “is … not higher than can be simulated by climate models”, since it is certainly higher than can be simulated by the GISS model, which is one of the best. And despite it being a world-class model, the report says:

The cloud radiative forcing is again very similar across the models and, in the global mean, similar to the ERBE analysis (Fig. 10). Looking more closely, the models have SW forcing in the Tropics that is too negative, but not negative enough in the midlatitudes. For the LW forcing, model values in the Tropics are too low (by up to 20 W m 2).

So we have a 20 W/m2 tropical error in the model (among many other errors of a similar size), but we should trust it to predict the effect of a 3.7 W/m2 increase from a CO2 doubling because it agrees with a simple model? …

In addition, since the albedo is not calculated but “tuned for”, the GISS model cannot show cloud feedback because of its design … I certainly hope that you don’t think that the lack of cloud feedback in the models means that there is no cloud feedback in the real world.

Finally, I think you misunderstand feedback. You say that “if [feedbacks] completely mask the signal they remove their reason for existence”. But consider the first use of feedback to control machinery, the flyball governor popularized by James Watt. It uses centrifugal feedback to limit a machine to a certain speed, thereby totally masking the signal … but it still continues to work.

Yes, simple models show why CO2 leads to warming, and the reassuring part about complex models
is that they agree with both simple models and data when run over the last 100 years.

Why is it reassuring that climate models agree with data when run over the last 100 years? Climate models are tuned and re-tuned until they agree with historical data, it would be very surprising if they did not agree with historical data … but that means nothing, because as they say in the stock broker’s ads, “Past success is no guarantee of future performance” …

Nor is it necessarily a good sign, when modeling a complex system, if a complex model agrees with a simple model … the issue is not whether the simple model and the complex model give the same result, it is whether the simple model (and thus the complex model) gives the correct result.

The other mechanisms you mention don’t seem to have timescales compatible with the observed warming, nor is there any evidence these things have changed recently, and people are watching them for sure.

Say what? The DMS/plankton connection has only recently been discovered, how can people have been watching that connection when we didn’t even know about it until last month? And Svensmark has recently provided more evidence that cosmic rays are a significant factor in the recent warming.

You seem to be in the Crichton/Inhofe school of a mass conspiracy driven by government funding. Why
would this administration want to fund global warming proofs? They have done everything to stifle
the evidence. We are lucky science has been funded at all in this environment.

I don’t follow this at all. If you can find one word I’ve written which suggests a “conspiracy”, I would be extremely surprised. And I think funding for climate change research is at an all-time high, so much so that people are claiming tenuous links between their research and climate change just to tap into some of that funding. Federal support for the R&D in the environmental sciences has tripled in the last 20 years, with over 2,000 separate grants related to climate change given in 2002, more than $2 billion in climate change grants in 2004, and $5.5 billion spent by the US Government in all areas of climate change in 2006.. In addition, much as I dislike Bush, the “Climate Change Research Initiative” was instituted under his Administration, not Clinton’s.

Also, you seem to be confusing the amount of funding with the direction of funding. While the amount of funding is controlled by the Administration, the direction of the funding is controlled by the bureaucrats who administer the grants … and as the example of James Hansen shows, many of them are staunch global warming supporters.

In short, I fear that my question about why we should trust climate models to give us accurate long-term forecasts when they cannot give us accurate short-term forecasts remains unanswered. To me, it is intimately connected to the problems which Jerry Browning is highlighting in this thread, which is that without artificial controls, climate models rapidly go way off the rails. These artificial controls, it seems to me, virtually guarantee that the long-term forecasts from these models will lack skill.

In closing, let me say that I appreciate your willingness to come here and discuss these matters, and I hope you will continue to do so.

All the best,

w.

MarkW

#223

The problem is the weasel word “credible”. When you define credible as showing high sensitivity to CO2, it’s hardly surprising
that all of the credible models show high sensitivity to CO2.

MarkW

While it is true that a feedback cannot mask 100% of the original signal, it’s also true that it can, and sometimes does mask more
than 99% of it.

In electronics it’s not hard to design feedback systems that mask all but a few parts per million of the original signal.

Gerald Browning

Jim Dudhia (#244),

Is the coefficient the same for every time dependent equation at every vertical level?

I assume that the hyperviscosity is written with a dx^4 in the denominator. Is that correct?

If the hyperviscosity is written as indicated above, isn’t it the case that the dx^4 terms cancel and the only crucial terms are the constant in front and dt?

What is the value of dt in your manuscript?

If the two dissipative terms are the same size, why add the second term, i.e. what role does it play?

What is the coefficient and formula for the second term?

How are the dissipation terms handled near a boundary with a model that provides the boundary data?

Is there dissipation associated with the second order finite difference scheme without any added explicit terms of the above form?

Jerry

Jim D

Is the coefficient the same for every time dependent equation at every vertical level?

I assume that the hyperviscosity is written with a dx^4 in the denominator. Is that correct?

If the hyperviscosity is written as indicated above, isn’t it the case that the dx^4 terms cancel and the only crucial terms are the constant in front and dt?

What is the value of dt in your manuscript?

If the two dissipative terms are the same size, why add the second term, i.e. what role does it play?

What is the coefficient and formula for the second term?

How are the dissipation terms handled near a boundary with a model that provides the boundary data?

Is there dissipation associated with the second order finite difference scheme without any added explicit terms of the above form?

Jerry,
Yes it is a constant for all variables everywhere.
dx^4 is in the denominator (1,-4,6,-4,1) stencil in each horizontal direction.
The number .003 becomes non-dimensional with it written as I have it.
With dx = 10 km, we would typically use dt = 30 seconds.
The first term is a background term needed for numerical stability, since low-order
schemes typically accumulate noise at small scales without such terms. The second
term is more of a Reynolds stress (i.e. physical sub-grid eddy) term. It goes
like .08 *dx^4 *D
where D is a 2d deformation term (like horizontal shear) in units of 1/seconds.
Near the boundary, this is reduced to 2nd-order diffusion with a stencil that
only needs one point on each side (1,-2,1) stencil. At the boundary itself, no
physics or diffusion is required because that point is specified from analyses.
The boundaries have separate relaxation terms in the 4 points in from the boundary.
The 2nd order space differencing used for advection is neutral (i.e. non-dissipative).
Hope that helps.

Paul Linsay

#255, JimD. To continue your analogy with the boiling pot: all the climate models give are average global temperature, average global pressure,…? If so, why does anyone care? Or for that matter, why does it take so much compute power?

Jim D

Willis (#246),
OK, I talk about climate models as a weather modeler, not an expert.
Climate models are tuned to get correct radiative balances, and they have tunable
parameters because they are at scales where sub-grid effects, like clouds,
have complex structures that are not easily represented in terms of grid-scale
variables (parameterized as it is called). Models rely heavily on physics
parameterizations, which why we are all still in the business of trying to improve them.
If GISS has those biases, I am sure they are figuring out how to solve them.
This is how science progresses. I don’t expect all models to have the same bias.
If they did, that would be very interesting, and someone could write a good paper
on solving it.

Conspiracy theory: I based that on this that you said

I don’t understand your claim that there is some incentive to discover a feedback mechanism which would show that global warming is not going to happen, since if a modeler does that, the funding for climate science and model development would dry up completely … what modeler wants that to happen?

I disagree strongly. Funding is done based on proposed research. No one knows what
results they will get at the proposal stage, so usually they get funded based on
whether they are asking interesting questions. An interesting question would be
something like how to avoid the albedo bias in GISS. If GISS solves this and it leads
to global warming being canceled by cloud feedback, that would be worth showing.
Such a paper would be acceptable if reasonable things are done to solve the problem.

Feedback: If cloud feedback was as strongly negative as would be needed to cancel
global warming, someone would be able to demonstrate that with warmer versus cooler
years’ data in the historical record. I believe Lindzen tried, but his data analysis seems not
to have been convincing.

DMS from plankton: Is DMS a long-lived greenhouse gas, or more likely, short-lived and
confined to ocean boundary layers, where it won’t have much effect. Or perhaps this is
a positive feedback mechanism if plankton increases with CO2 or warming? Questions to be asked.

Jim D

#256 Paul L,

To continue your analogy with the boiling pot: all the climate models give are average global temperature, average global pressure,…? If so, why does anyone care? Or for that matter, why does it take so much compute power?

Climate models add everything thought to be important in the mix. This includes weather turbulence.
They can give the time mean at any location, not just a global mean. Of course, this is just
a projection based on what they put in the model, but models are the only way to add so many
factors together.

Gerald Browning

Jim D (#257),

There have been several references given as replies to my first discussion on this site under Numerical Climate Models. In those references cited by others, the manuscripts stated that the climate models do not reproduce the climate even for a year. If those references are valid, then the climate models cannot be called a success.

And if as indicated in the mathematics cited at the beginning of this thread, demonstrated in several of NCAR’s own models, and in the above contour plots, the climate models are headed to a precipice and cannot be considered a success.

Also did you read the text about the disaster in twin experiments where the excessive dissipation led to completely erroneous results? I assume that cannot be considered a success?

Yes, it is possible to add dissipation mechanism after dissipation mechanism to a model and publish many manuscripts (and in some cases not even citing in the manuscript those mechanisms) and one can obtain something, but not necessarily even close to an accurate solution of the homogeneous (unforced) solution of the original continuum system or the real atmosphere.

Jerry

MarkW

If all climate models can do is create global averages (and the ones that I have seen aren’t very good at doing even that much).

Then why are so many people making predictions regarding how AGW is going to affect regional and even sub-regional climates?

Tom Vonk

Any time you analyze a stocastic process there is the possibility that the results are just random chance. The question is, what is the probability that the results are just random? A large part of statistics is in quantifying this probability, which is what confidance intervals are. Without them there is simply no way to know (or prove) that the results are likely to not be random. So I’m not assuming that the error bars are huge, I’m just saying that we don’t know they aren’t, and in fact we don’t even know what the probability is that they aren’t. This leaves you with no mathematical or statistical grounds to stand on when you say you believe the predictions of the climate models. All you have is your “gut feel”, or in other words, faith. Which I’m fine with, by the way, just don’t claim that these predictions are “scientific” or “prove” anything. Also claims that the climate model results support other work, like past temperature reconstructions, are dubious at best.

Yes . I am also exactly along this line . I can spend weeks staring at the N-S equations and manipulating them and I did , yet I can’t see a trace of randomness in it .
Even the weak hypothesis that one can solve the N-S in the general case when one assumes a certain dose of randomness would probably earn the Fields medal to the guy who would prove it .
Of course the strong hypothesis that the stochastical way is THE way to solve them is afaik completely out of reach .

So we re back again where we were .
We have a system with equations that we can’t solve , with known phenomenons where we don’t have equations and with phenomenons we don’t yet know about .
Hovering above everything we have the ill posedness of Jerry and the ominous interactions between resolved and unresolved dimensions that are arbitrary numerical artefacts anyway due to computer power considerations .
And the magical word should be “parametrisation” ?
Is that science anymore ?
Even the most basic test that defines science that is to compare predictions to experience doesn’t work because the modellers themselves say that their models give no measurable local predictions .
Local as in “when” will happen “what” , “where” .
At least meteorology makes sense because they know that they are forever limited by the fundamental chaos so don’t attempt to go too far and they make observable predictions like in “It will rain in Paris tomorrow .”

It is indeed matter of “faith” that making a computer run with some set of reasonable (but far from complete) assumptions , some sort of average result or “global” trend in an arbitrary time frame would not be too far (define too far) from the reality .
It will not be right in a smaller time frame and it will be unknown in a bigger time frame .
I simply can’t consider seriously something with such a massive demand for “faith” .

Jim D

I want to get it straight that I didn’t mean global climate models only give you global means
as output. They give you time-means, such as winter average max daily temp, for each position
depending on their resolution, and they give those means for the current and future climate.
So, in a sense they blur the stochastic randomness of weather. They also run climate models
several times to determine internal variability due to this randomness. You can also run
with different amounts of CO2, and see a signal of warming above the noise of this randomness,
and the warming is clearly related to the CO2 put in. It is incorrect to say you can’t predict
climate because of this randomness. The signal from CO2 is strong enough to see.
Tom, you say you can’t trust models because they use parameterizations. It would be
a long wait if you want to do climate with DNS and bin microphysics, so we use the models we have, and they
have shown some success with weather and climate that some people here choose to ignore.

Gerald Browning

Jim D (#267),

I have never heard of a numerical model having to use dissipation because of the low order of the numerical method.

Please run the cases you have been asked to run. Given that you have already run 10 km meshes, the inviscid runs above for less than a day should be trivial as you have both the hydrostatic and nonhydrostatic models available from your manuscript and a supercomputer (I only have my home PC).

There is always considerable verbage from you, but no mathematical proofs or convergence runs. Thus I have to believe that you are more interested in a smoke screen than science.

You are a modeler, provide the equivalent convergence runs for the inviscid runs discussed above or inviscid runs similar to Lu et al. that were run on NCAR’s WRF and Clark-Hall models. Enough gamemanship. Where are the results that support the accuracy and dynamical stability claims that you have made?

Jerry

Jim D

#268 Dave D,
The IR is always done with vertical integrations as you describe,
taking into account CO2, water vapor, ozone and clouds in each column.
CO2 and ozone are taken as a given profile, while the water vapor and clouds
vary as predicted variables. The theory for clear sky is well known,
and well simulated. It is the clouds that are trickier due to their complex
structures an compositions, and this is where the tuning goes into climate models.

MarkW

JimD,

So the idea is that it’s better to move forward with bad data, than risk waiting for accurate models?

Gerald Browning

Jim D (#273),

It appears that suddenly you have become an expert in climate models by describing how they handle cO2. Are you an expert in climate modeling?

And because you don’t want to run MM4 (hydrostatic and ill posed) even though Anthes ran it for years and published many manuscripts, or MM5, please feel free to run WRF. The numerics have no bearing on these continuum issues if they are accurate and stable and correctly approximate the continuum system.

I repeat, these are not numerical issues. they are much more serious than that.

I am still waiting for any evidence, mathematical or convergent numerical solutions.

I assume that you can run a model on your home computer just like I can.

Jerry

Dan Hughes

This paper Time-step Sensitivity of Nonlinear Atmospheric Models: Numerical Convergence, Truncation Error Growth and Ensemble Design addresses some of the important issues under discussion here. I have posted a couple of preliminary comments on the paper. Additional information will be added as I have time away from real life. There are other posts over there that address other important mathematical modeling and numerical solution issues.

At this time I can state that it is very likely that the small systems of nonlinear ODEs that exhibit chaotic response have never been numerically solved to convergence. All published numbers have been numerical noise that does not satisfy the continuous equations. The ramifications relative to NWPs and AOLGCMs very likely are great.

Tom Vonk

Dan .
Very enlightening – I particularly liked the remark about the Lyapounov coefficients .

How do you explain that despite all the peer reviewed papers showing that the numerical climate models do just that – produce numbers , there are still people believing that it shows a kind of “reality” ?
I mean if the numbers I get depend on the hardware , software , time and space steps not mentioning the parametrisation I choose AND if I know that I will never be able to demonstrate convergence then how can I get any scientific credibility by showing such numbers ?

Are such papers discussed in the frame of IPCC and if yes , why aren’t they mentionned ?

David

#32 >Use your model to predict temperatures 5/10 whatever years from now. When the time comes we will see how physical’ the model really is.

Ian, in case you missed it this has been done a number of times in the scientific literature lately. Probably the best example is the projections Hansen made to Congress in 1988. You can see this discussed in the PNAS (at http://www.pnas.org/cgi/content/full/103/39/14288#F2). The relevant figure is . Rahmstorf et al. 2007 (Science express, 1 Feb 2007) have done the same for the IPCC projections.

The predictions look pretty good to me. Does this convince you?

Jim D

Dave D, #274

Thanks for the reply and I’m glad that’s how CO2 is handled. Where would I go in the documentation to see just what figures were used? Am I right in assuming that X% of the available IR flux is assumed to be absorbed in each of a number of frequency bins taking into account that CO2 will share this flux with H20 and/or other substances?

The longwave schemes we have in MM5 and WRF are in a couple of papers. The RRTM scheme is
from Mlawer et al. (1997), I believe it is JGR. The CCSM scheme is in their Tech Note
downloadable from NCAR CGD’s pages. (to Jerry, weather modelers use radiation too,
but we keep our CO2 fixed). Only some of the frequency bins need to handle CO2 and ozone,
but I think they all handle water vapor (I also forgot methane is handled too). You seem
to know more about this than you are letting on, Dave. The schemes are mostly look-up
tables (thousands of elements) that are fit to the line-by-line (exact) model.

Jim D

Jerry,
Yes leapfrog plus second order schemes are neutral, but have poor behavior at
low resolution making damping these scales necessary.

And because you don’t want to run MM4 (hydrostatic and ill posed) even though Anthes ran it for years and published many manuscripts, or MM5, please feel free to run WRF. The numerics have no bearing on these continuum issues if they are accurate and stable and correctly approximate the continuum system.

I repeat, these are not numerical issues. they are much more serious than that.

I am still waiting for any evidence, mathematical or convergent numerical solutions.

I assume that you can run a model on your home computer just like I can.

I wish I understood your model problem better. I have mentioned why I think your hydrostatic
results don’t look good. Also, exponential growth only occurs while systems remain
linear, and are limited by nonlinear effects in any bounded model. Neither nature nor
models have exponential growth that is unbounded. Can you elucidate what this simulation
is exactly (initial and boundary conditions)?
I might consider it for WRF, but I don’t have a home computer with Fortran,
and would have to do that at work.

Jim D

(PS sorry for the double post above, I was getting an error message)

Tom Vonk,
It seems like where we disagree is the extent to which the atmosphere is
chaotic on time scales of a century. Recent history shows that there is
no reason to expect it has multiple attractors on this time scale, unlike the longer
scales of ice ages, Milankovitch cycles and
continental drift, where there are some very different “equilibrium” (attractor) states.
Changing ocean circulations certainly throw in a chaotic factor, but the experts
don’t seem to expect that to happen in the next century because of the slow ocean time scales.
The atmospheric state therefore moves around a single, but possibly slowly moving,
attractor (in Lorenz terms).
This is why it makes sense to regard the climate as the average of weather over time.
We can define climate in the same way for the next century as we have in the past
century, by averages because we have a slowly changing “equilibrium” state on the century scales.

Dave Dardinger

re: #285

Can anyone help me with links to any of Jim’s references? I don’t have direct access to journals.

Jim, I guess what I’d like to be able to do would be look at just how an absorbance figure gets used in the model program. It’s true that I have tried figuring things out in available models a time or two, but always get hung up trying to get my hands around it. I only really learn when I understand something. I can’t just memorize bare facts for very long. But once I understand the concept involved it’s mine forever. If there’s anyone here who could work up a baby program which would illustrate the concepts it would be grand; though I’m not holding my breath. I suspect it isn’t simply a case of running a few lines of R.

Tom Vonk

It seems like where we disagree is the extent to which the atmosphere is chaotic on time scales of a century. Recent history shows that there is no reason to expect it has multiple attractors on this time scale, unlike the longer scales of ice ages, Milankovitch cycles and continental drift, where there are some very different “equilibrium” (attractor) states. Changing ocean circulations certainly throw in a chaotic factor, but the experts don’t seem to expect that to happen in the next century because of the slow ocean time scales. The atmospheric state therefore moves around a single, but possibly slowly moving, attractor (in Lorenz terms).
This is why it makes sense to regard the climate as the average of weather over time. We can define climate in the same way for the next century as we have in the past century, by averages because we have a slowly changing “equilibrium” state on the century scales.

Jim I am afraid we disagree about more because I can’t make much sense of the above .

1) A strange attractor can NOT be determined by observation and specifically not for a thing like a climate .You’d already be hard pressed to say what is the dimension of the phase space in which you represent the “climate” . If you take a climate model then its associated phase space dimension would be PxN + K where N is the number of cells you use . That is a HUGE number and a strange attractor would be a subspace with a similar number of dimensions . You don’t even know if there is one , let alone what properties it has .

2) A chaotic system is not chaotic on a “time scale” . It is or it is not . And if it is , you will not make it to be less chaotic by making arbitrary mathematical assumptions concerning its dynamical parameters like f.ex taking a time average instead of an instantaneous value . It is like if you said that by taking a daily average of the air velocities you can predict weather in a week while you cannot if you use quasi instantaneous values .

3) I suspect that you confuse the speed of divergence of trajectories of the system in the phase space with the fact that they do diverge . The chaos has local causes due to the nonlinearities of the differential equations . But as soon as you pronounce the words “differential equations” you know that what matters is microscopic (dt , dx etc) and not global . You should read the paper that Dan linked – you’ll see that the trajectories depend on the time and space step you choose . That alone is enough reason to conclude that the models only produce numbers . The shadowing lemma (even if I am not really sure that it applies to a system that is not COMPLETELY described by a set of differential equations) would only insure that the numbers are not stupid or in other words that they look like a real climate . However the convergence proof is still completely out of reach and will probably always be because I am firmly convinced that you cannot establish a complete set of differential equations describing the evolution of the system . The only thing you can do is to neglect everything that is SUPPOSED constant , random , irrelevant and run computer programs with whatever is left .

4) Your reference to Milankovitch cycles seems to show that you consider the climate like a sum of random short term fluctuations that somehow “don’t matter” and “slow” chaotic long term evolutions . In other words everything that happens on a short time scale (define how short) is not deterministic chaos but random noise . So why should we bother with differential equations if they only produce random noise ?

5) Talking about “slowly changing “equilibrium” states at the scale of centuries” is stating the obvious . If I have a dynamic variable x(t) showing wildly chaotic yet bounded behavior and if I define X(T,t) the time average over T of x(t) then with increasing T , X(T,t) will change slower and slower . However the mathematical causality is x(t) -> X(T,t) and I can’t conclude anything about x(t) if I only observe X(T,t). More specifically the chaos and unpredictability didn’t disappear because X(T,t) changes “slowly” with a great enough T . The things get even worse because with a great enough T you will loose most of the relevant dynamics of x(t) because they will pass under the detection threshold .

Paul Linsay

#290, David,

I didn’t realize that the models had the resolution to compute temperatures only 2m off the ground. I thought their resolution was on the order of 100 km. Please reference the relevent models. The experts on this thread will be very interested in what you have to say.

Jim D

Jerry,

Your group (MMM) managed to run the WRF and Clark models for the Lu et al. cases. Try running them with the same two resolutions as above and only dynamics (no damping, physics, etc). That is called a convergence test and is a standard for all numerical methods for the homogeneous system to check that the numerical accuracy is as claimed. If the numerical methods are accurate and stable, then you should see a reduction in the error by the appropriate amount (4 for a 4th order in time and space numerical method)) for at least up to a day.

And frankly I don’t believe there isn’t a copy of a hydrostatic model lying around so that the same test can be run on it. You might ask Stan Benjamin for a copy of the RUC model that is hydrostatic and from the same source as the NCAR-Penn State model.

I restate that these are continuum issues and should appear in any clean numerical approximation of the hydrostatic and nonhydrostatic systems. The problems certainly appeared as expected in the Lu et al. manuscript (and evidently in the Mahalov manuscript although I have been unable to obtain a copy) and in the above simple tests.

And finally I point out that the new multiscale continuum system came from a rigorous mathematical proof of accuracy when compared with the original unmodified system based on the theory of hyperbolic systems.
No such proof ever existed for the hydrostatic system (and it cannot).

Also the reference above is a mathematical analysis of the problems with both systems. Clearly that analysis seems to be applicable to the Lu et al. manuscript and the cases shown above.

WRF has a hydrostatic option, so that is not an issue. I Lu et al. already used WRF, I am not
sure what I am supposed to do different. I think I just disagree with this methodology,
because how do you measure error or truth in these systems? They won’t converge to a solution
as the grid size reduces due to allowing finer eddies that may not have been permitted by
the coarser grid. The convergence tests we do with WRF involve using a fixed physical viscosity,
so that certain small scales really are not permitted, so I guess I am disagreeing with
you at a more fundamental level than just model results.

David

>I didn’t realize that the models had the resolution to compute temperatures only 2m off the ground. I thought their resolution was on the order of 100 km.

Paul you are mixing vertical with horizontal resolution. A “typical” climate model has around 30 levels (though weather models routinely have many more). The lowest level is typically 50-100m above the surface with an additional surface level (though there are marked variations from these rules).

A few minutes with google will turn up hundreds of papers which discuss climate models (or alternatively check out the massive bibliography attached to the IPCC reports). Groups like the Hadley Centre, CSIRO, NCAR are a good place to start. The model that Hansen used is referenced in the PNAS report.

Tom Vonk

The IPCC produce error estimates too, and this goes into the equation. If you don’t believe the error estimates either, you have to have a likely alternative scenario in mind, or a good reason to say why the error is higher than the consensus view.
I know this won’t go over well here, but that is my view.

Might that “http://www.maths.uwa.edu.au/~kevin/Papers/JAS07Teixeira.pdf” just be an excellent reason ?
And that “http://www.springerlink.com/content/g28u12g2617j5021/” might very well be an alternative likely scenario .
Not that I believe more in it than in any IPCC computer run but it is as likely as likely in climate guessing goes .
As for the “IPCC error estimates” … that horse has already been beaten to death , those are opinions and not error estimates .
It is not a matter of here or elsewhere so please stop talking “consensus view” – first there is none and second it has no scientific value anyway .

KevinUK

#302 PP

I agree with most of what you’ve said BUT I disagree with your assessment that the climate modellers deserve an “A for effort”. A think that like all good hired consultants they deserve an “A” for providing the answer to the policymakers which the policymakers have funded them to give. I think that perhaps with one or two exceptions the vast majority of climate modellers know that what they are doing is a complete waste of the hard earned taxes which the rest of us earn inorder to keep them in the style in which they have become accustomed to living. Most of them IMO are not in the least bit interested in applying the scientific method. On that basis I would rather not use the terms science and climate in the same sentence when referring to climate modelling. They have their ‘fifteen minutes of fame’ thanks to the politicians at the moment but I glad to say that they are now well into their fourteenth minute. Ultimate they need to understand that you can fool some of the people some of the time and maybe even some of the people most o fthe time but you cannot fool all the people all the time as eventually the scientific method will be applied by people like Steve and Ross and their claims will be refuted.

KevinUK

Gerald Browning

Jim Dudhia (#297),

Run the WRF model fourth order numerical approximation in space and time on both the hydrostatic and nonhydrostatic systems for the inviscid, unforced initial boundary value problem that Lu et al. did for the two resolutions above as I did. That will determine how rapidly the enstrophy can cascade down the spectrum for the Lu et al. example for convergent numerical approximations (at least in the first day or so) of the two different continuum systems and how much of a role the dissipation is playing in controlling that cascade.

Jerry

Willis Eschenbach

Jim D., you say:

In answer to other issues relating to climate scientists, I would say that scientists are motivated by the truth.

While this view is touching, it is also incredibly naive.

If you think that truth is what has driven Michael Mann to hide his data, tell us how. If you think that’s what impels James Hansen, the most widely quoted climate scientist on the planet, to not only get up on his soapbox during company time, but to claim that he is being “muzzled while doing so, please explain it to us.

Scientists are like everyone else, driven (in no particular order) by the usual mix of desire for recognition, fear of being proven wrong, wanting to get grants, looking for social approval, jealousy of other scientists, wish for security, aversion to going against the herd, and all the rest of the things that drive people. They fight over territory in the lab, and over honors in the public eye. And yes, somewhere in the mix, there is the truth … but unfortunately, it is elusive, doesn’t pay well, and may take decades to become evident.

And since in all likelihood, we won’t know “the truth” until some and perhaps all of today’s scientists are dead, the door is wide open for all of the other motives to come in. In particular, the desire for truth gets subsumed into the desire to have other scientists agree with you, which is what passes for “truth” in climate science these days … which is why AGW supporters are so dismissive and abusive towards those who dare to disagree with them. It also explains why they cling so hard to the fiction that climate models are data, and thus can be proxies for the unreachable truth.

w.

Tom Vonk

I was trying to convey that the atmosphere alone doesn’t jump to different climatic states, something else has to happen. Those “something else’s” involve the ocean, and CO2 content of the atmosphere, and possibly volcanoes, meteors, etc.
To the extent that those externals are known, there is no reason to believe in a fast chaotic transition. Climate models (given their number of points and variables) have a dimension of about a million. Of course, the accessible phase space is a small subset of this because of dynamical constraints and things like energy, mass and water conservation. Anyway, you asked for a dimension, so I gave it.

Jim so the dimension of the phase space is several millions assuming a spatial resolution around 200 km .
For every global spatial temperature average there is for all practical purposes an infinity of different dynamical states .
The notion itself of “transition” based on a single arbitrary parameter among millions (some global temperature average) doesn’t make much sense in the chaos theory .
The only thing external to this system is the Sun and possibly cosmic rays .
Now it would be very naive to believe that even for strictly constant Sun parameters the system goes in a steady state aka is represented by a single point in the phase space .
On the contrary it moves with chaotic pseudo periods related to the changes of Earth’s orbital parameters and Sun’s activity at all time scales from a day to millions of years .
So yes , the system does things “by itself” only by virtue of receiving and dissipating energy – the Lorenz system does everything “by itself” too .
You don’t need any external changes significant or otherwise to make it move – only linear systems need that .
You could make some educated statements about the neighbourhood where it moves (for a limited time) if and ONLY if you knew the topology of the strange attractor assuming there is one .
Yet nobody has a clue and I dare say nobody ever will for the simple reason that to establish this topology , you’d need a complete set of differential equations describing its dynamics and to solve them what seems to be out of reach .
Sorry but conservation of energy , momentum and mass doesn’t fit the bill again for the simple reason that there is an infinity of different dynamical states doing so . Lorenz’s system also conserves all that yet stays happily chaotic at all time scales .

A computer model hopes to have picked up one possible state among infinity at t ? Big deal , it will have to guess at t + dt again !
I understand that you work in meteorology – do you sincerely believe that you would be 24 times better at predicting at a given place daily temperature averages rather than hourly temperature averages (pick your time unit – day , week , month , year etc) ?

Gerald Browning

Jim Dudhia (#310),

That is exactly what I expected you to do in the end. Lots of verbiage and no mathematics or convergence tests.

If you were a scientist trying to understand what the continuum equations
are really doing, you would either derive the appropriate mathematical details or, at the very least, run the tests I have indicated to check the behavior of the systems with convergent numerical solutions. But given that you are a modeler that has fudged the numerics with all types of dissipation just in order to obtain a result, the outcome is no surprise.
You came to this thread mainly to hide what you have done to obtain such results. That is easily seen because every time I asked you a specific scientific question, you either changed the subject or did not provide a reasonable scientific answer. IMHO you should be ashamed of yourself.

I have included a mathematical reference at the top of this thread and contour plots to show convergent numerical solutions that agree with the mathematics. You have not touched either result and I think that any logical person can determine who is willing to back up their statements with hard facts.

Jerry

MarkW

JimD,

You write:
“CO2 leads to warming, but cloud albedo feedback will come along to rescue us, so don’t call it a crisis.
This looks like wishful thinking rather than science.”

How does this differ from the modelers declaring, a priori, that rising RHI will stay constant, throughout the atmosphere, as
temperatures rise? There is no evidence to support such a claim, and increasing evidence to doubt it. Yet it is the core around
which the catastrophic temperature rise predictions are built.

BTW, it is usually considered bad form to mischaracterize someone else’s argument.
Nobody said that the albedo of individual clouds would get greater. The claim is that there will be more clouds.
If you are going to try and ridicule someone else’s argument, it helps to get the other persons argument right. Otherwise it is you
who are being made to look the fool.

Jim D

MarkW,
I am actually not sure the cloud albedo fans all say the area will increase either.
I checked Lindzen’s “iris” paper, and part of his argument is that upper clouds will decrease
in area letting more IR out, but I confuse all those arguments, and would like to see a mechanism
for increased negative cloud feedback that can be tried out in a model. Lindzen proposed a GCM test of his
idea in 2001, but no results have been forthcoming.

MarkW and Tom,
This is where we disagree. You think of climate as an initial value problem, i.e. the final
state depends critically on the initial state (like the weather), while I believe the climate
state is somewhat independent of the initial state details after a few years of integration, being
determined mostly by the forcing terms.

Jerry,
I came to this thread to sort out hydrostatic versus nonhydrostatic dynamics, which I know
something about. I also was able to interpret your #186 plots as a failure of hydrostatic
dynamics. These seem to have nothing to do with dissipation because features are well resolved.
If you go the other direction and double your grid sizes, you should see dissipation effects.
Similarly, I don’t see a problem with the Lu et al. results as I said. They had an unstable
situation, probably due to low Richardson number, where finer scales led to resolving turbulence
that otherwise was not.

fFreddy

Re #315, Jim D

You think of climate as an initial value problem, i.e. the final state depends critically on the initial state (like the weather), while I believe the climate state is somewhat independent of the initial state details after a few years of integration, being determined mostly by the forcing terms.

So why waste time, money and super-computers on great big complicated models with lots of grid cells ? Why not make much simpler models that only focus on the forcings, and concentrate your efforts on getting them right ?

Gerald Browning

Jim Dudhia (#318),

I have already begun to read the WRF documentation and will make the necessary runs so that readers of this blog can see how the WRF model behaves relative to the contour plots above and the impact the multiple forms of dissipation in the numerical method, in the dissipation terms, at the top and lateral boundaries, etc. have on a continuum solution.

Then you can use all of the verbiage you would like to explain why the accuracy is what it is compared to a continuum solution.

Jerry

gb

Re # 319.

I do not really understand your ideas about dissipation, continuum solutions and why you look at contour plots. Consider the more general case of turbulence governed by the Navier-Stokes equations. What should the resolution be according to you in a fully resolved simulation? Then assume we do not resolve all scales but we have a model for the subgrid scales, i.e. we add an extra dissipation term. How do we validate that the dissipation model is correct? What kind of tests should we perform?

When we consider atmospheric models I do not understand how you can say that the models are wrong by comparing two model outputs. Since it is unknown what the dynamics is on mesoscales (does the kinetic energy go from large scales to small scales or from small to large scales? Are waves of importance or are there vortices?) the only way to validate a model is to compare model outputs with real observations.

Willis Eschenbach

Jim D, thanks for your response. You say:

Willis, it seems to be a sad impression you have of the scientific community. Everyone
esteems scientists that have been proven right by history, and forgets those who haven’t,
so why would anyone hide a truth to further their career? These things are found out,
and lead to disgrace and can be career-ending. The few cases making the news, like the
Korean cloning scandal, and cold fusion, are enough of a deterrent.
(rant mode on) People seem to think scientists are inventing a crisis based on flimsy facts, like the
recent record-breaking years, melting glaciers, ocean warming, etc. If they seem to
understand why these things are happening, they are criticized. If they can’t come up
with a reason this won’t continue into the future, they are criticized. Some say,
OK, CO2 leads to warming, but cloud albedo feedback will come along to rescue us, so don’t call it a crisis.
This looks like wishful thinking rather than science. There is not much that
increases cloud albedo, other than putting aerosols in them, which nature is not going to do on its own.
(rant mode off)

You said that scientists were “motivated by truth”. I said that the scientific community is motivated by all of the same emotions and drives as the rest of humanity … I hardly think this is a “sad impression” of the scientific community, but I do think this is an accurate one.

Next, I think you misrepresent people’s position regarding the observational data. There is general agreement these days that the world has been warming since the 1700s. Now, in a period of general warming, there are some things that we would expect to see, things that would be a surprise to us only if we didn’t see them. These include:

1) Record-breaking years, probably occurring in clumps.

2) Melting glaciers.

3) Warming oceans.

You seem to think that these things taken together constitute a “crisis”, that they are somehow unusual … but in fact, in a three century warming period, it would be unusual if we did not observe those things. There is no evidence that the recent end of this warming is any different than the earlier periods, either in the size of the trend, the total temperature change, or the length of the warming. Before you can say that there is a “crisis”, you need to show that the recent climate is unusual or anomalous in some way. What is your evidence for that?

This is science, not wistful thinking. What is wistful thinking is your claim that “there is not much that increases cloud albedo”, the simplest thing is increasing clouds. For example, a recent NASA study revealed that as the Arctic snow and ice have decreased, the total albedo hasn’t decreased (as is predicted in every one of the models), but has barely changed.

Why not? Because the cloud albedo has increased over the same period, due to the increased water content of the air. What is wistful thinking is the idea that the cloud albedo is constant. As a simple proof that it is not constant, it varies annually from summer to winter, and in addition there are a wide variety of studies showing longer-term changes in cloud albedo … how do you think that happens?

w.

Jim D

A few responses
#320 Dave D,
Generally it is considered that relative humidity is what is preserved as warming progresses.
This is why vapor increases, but clouds respond to and interact with the RH, and don’t increase.
Before people complain this is built into the models, it isn’t. This is what is found from
the models, and agrees with the scientific knowledge of cloud formation processes.

Jerry, I have many of the same questions as gb that I don’t think you have answered yet.
One way models like WRF have been tested against observations regarding energy is
by looking at the energy-wavelength spectrum, where the -3 exponent at large scales turns into
the -5/3 exponent at mesoscales as is observed by aircraft data.

Willis, the acceleration of the records is evident because prior to the 90’s we
haven’t had such a series of warmest-ever years. As I said, scientists understand
why this is happening, and it would be more surprising if it didn’t happen given what is known.
On the cloud/sea-ice issue, as we know, sea-ice melting is a positive feedback to global
warming, so if cloud cover is increasing, it leads to a negative feedback on that
positive feedback, but doesn’t help much with the underlying global warming. If you
want a negative cloud feedback for global warming itself, you need to look for something
that increases cloud cover in warmer regions.

Tom, the models do resolve this question, but you choose not to believe them. The purpose
of the ever increasing complexity in models, such as including vegetation prediction sub-models
and ocean and sea-ice coupling, is to look for responses that cannot be represented in simpler
models, but none have yet ben found that affect the conclusion that the forcing dtermines the
climate.

Gerald Browning

Jim Dudhia (#325),

A climate model or any time dependent continuum system can provide any spectrum or solution that you want by appropriately choosing (tuning) the forcing as shown by my earlier simple mathematical example.
That does not necessarily tell you anything about the accuracy of the numerical approximation of the continuum system or the accuracy of the parameterizations. In fact, because a climate model cannot resolve any of the main features (resolution is still not less than 100 km and they use the ill posed hydrostatic system), the forcings are necessarily unphysical if the model produces a spectrum similar to reality. I also noticed that the CCSM uses a sponge layer at its top and a number of other questionable dissipation mechanisms. What quantitative error checks have there been on these?

More of the same verbiage without any mathematical proof. You might buy a pair of waders.

The number of aircraft measurements is not sufficient to determine the spectrum of the global atmosphere because the routes are not dense over the entire globe and tend to be at certain elevations. You might want to read Roger Daley’s book.

BTW I have begun to read the WRF documentation and the number of different dissipation mechanisms is a riot (including one on the vertical velocity). From what I can tell there is not a single test showing the impact of these methods on the numerical accuracy of the approximation of the continuum system when all of the dissipative mechanisms and discontinuous forcings are active. The very fact that many different parameterizations of the same processes have been included tells us that these processes are not well understood as has been discussed many times before on this blog with references provided.

Ii I am able to compile the WRF model, many of these issues will become moot.

Jerry

Jim D

A variety of things to respond to in #326-#328
Dave D, the jump in your argument that I don’t follow is that a lower cloud base
leads to more negative feedback, because for low clouds the primary radiative
effect is cutting off surface shortwave due to their areal coverage, and I don’t think your
argument leads to any change in that respect.

Jerry, the w damping mechanism you mention is an option for operational forecasters who
don’t want to be limited by the time step and vertical motion. It is normally off for
scientific studies, and actually has very little effect on results.
I would ask how you explain that WRF has been used for LES studies and compares
as an equal to LES state-of-the-art models, if it is too dissipative. WRF’s numerical
methods minimize the dissipation.
I have also shown mathematically that you can’t call the hydrostatic option ill-posed
when it is used at the right scales (climate model scales), as it is then a very
good approximation to the full gravity wave frequency equation.

Tom, sorry only words from me again on this one. The question you asked

The day there would be a demonstration (computer calculations do not qualify) that :
a) either all dynamical paths converge to the SAME State(T)
b) or there is a statistical law governing the States(T) and independent of the dynamical paths
would be the day the problem would be solved .

I say that (b) is what is indicated by models. The future climate states (T) can be reached
by many paths, each starting from a different initial states (0). 2) As far as unicity goes,
that is reflected in the confidence of the warming due to a given CO2 scenario. If the
final states of their runs from different States(0) were wildly different, they would
have no confidence in any State(T). 3) Different resolutions affect the results, as does
using different models, but consensus is not affected. 4) There are standard times of
averaging, such as 3-month seasons. Obviously 3-month averages will differ from 6-month
averages, so I don’t understand this question. 5) there is no exact knowable solution,
except to measure current conditions, and no, not even weather models converge to the
exact measured state because that would require modeling every atom/butterfly, etc.
Models can converge to exact mathematical solutions using idealized test conditions
if that is what you mean. These mathematical solutions involve dry continuous inviscid
flows with small (linear) perturbations. Make it any more complicated, with physics
or nonlinearity, and the mathematical solution becomes impossible, making models the
only hope for the real atmosphere.

Dave Dardinger

re: #329 Jim,

for low clouds the primary radiative effect is cutting off surface shortwave due to their areal coverage

No, for low clouds the primary radiative effect is to reflect solar radiation away. The secondary effect is indeed to block IR but this is almost by definition less than the incoming radiation blocked.

High clouds are normally thinner and thus allow some to most solar radiation in and then can block IR from escaping (i.e. they’re more opaque in the IR). This makes them more a positive feedback. But the low clouds are a negative feedback because they’re denser and thus little solar radiation gets through. That’s why if you see “dark” clouds you know rain is possible.

Now, there are special circumstances to be considered, such as that if clouds don’t form during the day but form at night this could produce a positive feedback even with low clouds. It doesn’t sound to me like this is taken into consideration by models, but I could be wrong.

Jim D

Jerry, #332, LES is one area of modeling that tests model dissipation the most,
and I had he impression that this thread was about dissipation in models. At LES
scales we have a good idea what the sub-grid scale is supposed to do, and so
there are some ways of demonstrating these results without physics questions
coming into the dynamics. Now to your quiz.
1. I probably said it was unstable for the reason given in 2.
2. Leapfrog is neutral but very noisy and unusable unless time-filtered.
3. Probably no. Two different numerical methods can never give the same solution.
I actually don’t know what this question means. Semi-implicit methods are used for
sound wave sub-steps, and combined with leapfrog methods in MM5 for example.
4. WRF has 3 cumulus schemes and 7 microphysics schemes, but Grell-Devenyi
has up to 144 ensemble members.
5. No, I can’t imagine why this would be true.
6. Yes, cumulus schemes have on/off time discontinuities, and microphysics
deals with cloud edges.
7. Yes, they produce different latent heating profiles and results, otherwise why have
different schemes?
8. Currently LES is not driven by real-world boundaries, being idealized and periodic, so yes.
9. No, what mathematical example?

Jim D

#330, Tom, this is getting too philosophical for me.
I would say that you chose a good example with the stock market,
because that rises on the long term but is unpredictable on the short term.
Similarly for climate there are good reasons for future temperatures to be
warmer.
Of course we don’t know the exact solution of the climate system behavior,
but does that mean we give up? No, we look for approximate solutions, which
is what models are. They give an approximate solution to system behavior,
including the level of chaos (however you measure that). Yes, the models
could still be missing something pertinent to the climate in the next
hundred years, which is why no one attaches 100% certainty to climate
predictions, but the low level of uncertainty these days reflects the degree to which
the modelers believe they have all the major processes accounted for.

Gerald Browning

Jimy Dudhia (#333),

The heading for this thread is exponential growth in physical systems.
The specific points are that climate or weather models based on the hydrostatic system are ill posed for the IVP near a jet and that problem will start to show as the hydrostatic models reduce their resolution to around 10 km. And models based on the nonhydrostatic system have very fast exponential growth near a jet that will destroy the accuracy of any numerical approximation of the nonhydrostatic system in that neighborhood. I don’t think there is anything mentioned about LES in the lead in to this thread.

Now as to the specific points that you almost answered with one word as asked.

1. The leapfrog scheme is stable.

2. In test after test starting from balanced initial conditions, the unphysical component of the finite difference solution is not excited for long periods of time without any time filter. It can be excited by unbalanced initial conditions or discontinuous forcing. In the latter
instance I suggest you read the manuscript entitled “The impact of rough forcing on systems with multiple time scales” by Heinz Kreiss and me that appeared in JAS. In the cases I ran above, I also used the Runge-Kutta method with similar results just to ensure that the results were not dependent on the time integration method.

3. Read the manuscript by Steve Thomas and me that appeared in MWR.
I had Steve implement the semi-implicit numerical method the way that method was first introduced by Heinz Kreiss (a world reknown PDE expert
and numerical analyst). The contour plots from the two methods when using the same time step were indistinguishable as they should be if the numerical methods are converging to the solution of the continuum system.

I believe you switched the answers to 4 and 5.

4. The balanced conditions for midlatitude mesoscale storms is now well understood. Read the two manuscripts that appear on this blog under the ITCZ thread, one by Heinz and me in JAS and the other by Christian Page et al. in MWR. Christian implemented the balance in a mesoscale weather model with considerable success.

5. The number of different parameterizations is an indication of the uncertainty in the physics (forcings). As different ones lead to different
(latent) heating profiles, they also will lead to different solutions
for the same dynamics.

6. The discontinuities destroy the accuracy of the numerical method
and lead to considerable roughness in the numerical solution (see manuscript cited in 2.)

7. As stated above the physics is very poorly understood or else there would be no need for multiple schemes.

8. Periodic lateral boundaries for the idealized LES case is very different from all of the smoothing incorporated for a forecasting case. The very fact that you didn’t point this out tells me loads about your intentions.
But since you brought this up, why not run the cases in the Math. Comp. article by Heinz and me or in the SIAM journal on Multiscale Modeling and Simulation by Henshaw et al.

9. The simple mathematical argument appears in this thread (#43).

It appears to me that you are not reading the literature in your own area and the manuscripts cited repeatedly on this blog (e.g. at the beginning of this thread and the ITCZ thread ) or are choosing to ignore the manuscripts in the literature that point out the problems with
the incorrect application of numerical methods to PDE’s. It is time that you do so.

Jerry

Jim D

Jerry,
The area I agree with you is that there is uncertainty in the physics,
hence so many parameterizations, and why I am in a job. The problem is by no
means solved. It gets complex as soon as you go beyond the N-S equations to
deal with real atmospheric physics.
I also agree that the dynamics is well known, and pure dynamics solutions
can be found, and models with any reasonable numerical scheme will converge to the
same correct solution in those limited pure-dynamical cases (e.g. inviscid or
specified viscosity).
I disagree with the opening paragraph you had above. Being inaccurate in a highly
turbulent case does not mean the solution is completely invalid, or that the nonhydrostatic
equations have broken down. It just says the flow is less predictable in a deterministic
sense. To get turbulent flow completely accurately you need a model that can represent
all scales (like DNS), and completely accurate initial conditions. The dynamics equations are known,
but the computers aren’t there yet. Meanwhile we use sub-grid scale representations
of those eddies, and much of that science has been done in the LES field.

Jaye

It appears to me that you are not reading the literature in your own area and the manuscripts cited repeatedly on this blog (e.g. at the beginning of this thread and the ITCZ thread ) or are choosing to ignore the manuscripts in the literature that point out the problems with
the incorrect application of numerical methods to PDE’s. It is time that you do so.

Ouch…

Willis Eschenbach

Jim D., you say:

#336, Tom, if the climate stops warming in 10-30 years it will be a consequence of something unaccounted for in the IPCC scenarios (asteroids, nuclear wars, major volcanoes, come to mind). I couldn’t see the paper you suggested, but unless it has something on that scale, it is unlikely to counteract CO2, in my opinion. CO2 is not a subtle thing to do to the atmosphere, it is big, and it will not be a subtle thing that cancels it. You suggest climate scientists could have missed something, even barring a catastrophe, which is where I differ. Current climate is well understood in that there are no major mysteries as to why things are the way they are. Changing the climate changes regimes for sure, but not far beyond anything we know, in my opinion.

What evidence do you have that “CO2 is not a subtle thing to do to the atmosphere, it is big …”?

There is an interesting study, Is the Earth still recovering from the “Little Ice Age”? A possible cause of global warming by Dr. Syun-Ichi Akasofu, who is the director of the International Arctic Research Center at the University of Alaska Fairbanks. He points out that both long term termperature records (CET, Armagh, etc.), and a variety of proxies (ice cores, ice extent, etc.) indicate that the earth has been steadily warming (plus or minus natural variation) at about a half a degree per century for two centuries and likely as much as four centuries.

There is no reason to assume that this trend has suddenly stopped. Therefore, before we can assign any warming to CO2, we need to subtract out the long-term warming of about half a degree/century. The world warmed somewhere about 0.6°C in the 20th century … which would indicate that the CO2 contribution must be tiny.

The recent warming (1980 – present) is not statistically any faster, longer, or larger than the 1915-1945 warming. So where is the evidence that CO2 is “big” … please bear in mind that computer models are not evidence. Evidence is data and observations.

Where is the evidence?

w.

PS – if you don’t think that climate scientists have missed anything … time for a reality check. The climate is a chaotic, multistable, driven, optimally turbulent terawatt scale heat engine, with a host of both known and unknown forcings, natural oscillations, and feedbacks. It comprises five planet-wide subsystems (ocean, atmosphere, biosphere, lithosphere, and cryosphere), each of which has both natural and forced variability. Each of these subsystems has its own feedbacks and forcings, both individually and between the subsystems. The climate is the most complex system that we have ever tried to model, and we’ve only been working on the project for a few decades. We don’t have mathematics to calculate what’s happening even in simple turbulent systems, much less complex ones.

For example, in the 1970s, the effect of CO2 doubling was estimated at between 1.5° and 4.5°C, a very wide range. But now we’re in 2007, and because the scientists are not missing anything, our understanding of the climate has been greatly improved because of our wonderful climate models that aren’t missing anything either. Because of the greater understanding we’ve gained over the last 30 years, the effect of CO2 doubling is now estimated at … between 1.5° and 4.5°C.

Our understanding of the climate system is in its infancy. New, previously unknown forcings are discovered on a regular basis. For example, when plankton get too hot they emit DMS, which creates clouds above them and cools them down … care to guess how many climate models include that forcing?

Finally, most of the forcings we know about are poorly understood. The IPCC rates the Level of Scientific Understanding (LOSU) of the majority of the forcings used in GCMs as either Low or Very Low … and that doesn’t include such known forcings as cosmic rays or plankton DMS, which we know next to nothing about. Even such fundamental, basic questions as “do more clouds warm or cool the earth” are not resolved.

Major mysteries abound in climate science. Why did the earth cool from 1945-1970? (Please don’t insult our intelligence by saying “aerosols”, the data doesn’t support it.) Why has the earth warmed since the 1600s? Why was the early part of the Holocene warmer than it is today? Why has the earth not warmed since 2001? A recent NASA study showed that the reduced snow and ice in the Arctic haven’t reduced the total albedo, because as the ground albedo decreased, the cloud albedo increased … no one, not one climate scientist, predicted this hugely significant effect, and yet you think climate science is “well understood”, with no “major mysteries”?

Like I said, just a quick reality check …

Gerald Browning

Tom (#342),

You are not the problem and there is no need to apologize. 🙂

Jerry

Gerald Browning

John (#346),

Yes I will be happy to cite the references more specifically later this evening.

Jerry

Jim D

Tom,
The work you cited seems to be a frequency analysis that is then used to extrapolate
into the future based on cycles in the data that can’t be even proven given the length
of the historic record. It also doesn’t seem to offer any science beyond the statistics.
Good to have faith in something, but I wouldn’t put it in quasi-cyclic extrapolations.

Willis, ice cores are where the evidence is. CO2 hasn’t been at the current level for a
million years, and the global temperatures go with CO2. This isn’t just making it up.
OK, there are other mechanisms, methyl clathrates, hydrogen sulphide. You
only have to read Scientific American to find out about these. Some of them don’t happen
unless something else has already lowered sea-level or warmed the oceans to a tipping point,
but here we are only focussed on the next century. Anecdotes on regional warming and cooling
don’t prove global climate swings, while CO2 is a globally mixed gas. Regional changes may
result from changes in ocean circulations that do have very long time scales. Solar output
reduction may also account for the Little Ice Age, another slow change.
Why do you say the 1945-1970 cooling can’t be explained by aerosols or pollution when it can?
Are you invoking solar output as an alternative? I believe there is evidence to the contrary,
because the cooling was mainly in the areas downstream of industrial regions (e.g. Russia,
and not Australia), as I recall from the “Global Dimming” documentary.

John Baltutis

Re: #350

Better yet, I found the Chungu Lu document at: http://www.iap.ac.cn/html/qikan/aas/aas2002/200204/020404.pdf

Willis Eschenbach

Jim D, thank you for your reply to my question. I had asked where the evidence that adding CO2 to the atmosphere would result in large, significant changes that will be hard to “counteract”, as you put it. I’m sorry if I was not clear, I was not asking for evidence that CO2 levels are high, but for evidence that this will make a difference.

Regarding the aerosol theory, if it were correct then the Northern Hemisphere would have cooled much more than the Southern Hemisphere. But it did not do so. In addition, the drop was not slow as one would expect from increasing aerosols, but was quite rapid. Here’s the HadCRUT3 record for the period:

Note the plunge in the Southern Hemisphere was larger and steeper than that of the Northern Hemisphere … how do aerosols explain that?

But there is an even larger problem with the aerosol theory, which is that we don’t have measurements of aerosols for the period, so the theory is based on emissions data. However, there is no evidence that the emissions actually changed the amount of sunlight hitting the earth during that time. To the contrary, there is good evidence that there was no measurable change in atmospheric transmission during that time. Using pyrheliometer data, the authors of the paper

Hoyt, D. V. and C. Frohlich, 1983. Atmospheric transmission at Davos, Switzerland, 1909-1979. Climatic Change, 5, 61-72.

showed that in Switzerland there was no trend in atmospheric transmission. As you point out above, this is one of the areas where the IPCC claims the biggest trends in aerosols were occurring.

The pyrheliometric ratioing method is so accurate and stable, so much so that it even discovered one unknown eruption, as described in:

Hoyt, D. V., 1978. An explosive volcanic eruption in the Southern Hemisphere in 1928. Nature, 275, 630-632.

But despite that accuracy, it showed no drop in received sunlight post 1945. As far as I know, this paper has never been seriously challenged by any other studies of the question. I seem to recall that Doug Hoyt posts occasionally on this forum, and could probably tell us more.

Anyhow, that’s a couple of very strong reasons why the aerosol theory is an insult to our intelligence … because it doesn’t fit the observations.

I await your evidence for increased CO2 levels causing big, significant changes that will be hard to counteract, as well as evidence that aerosols caused the 1945-1975 cooling.

All the best,

w.

Gerald Browning

John (#351),

You are very resourceful! Let me know if you have any questions about any of the manuscripts. I will be happy to try to answer them.

Jerry

Jim D

(Sorry for the re-post, I got hit by that less-than sign again. Great that the back button works
to recover the message)
Willis,
Re: aerosols
Thanks for forcing me to read up a bit more on this.
I found a counterpoint paper below. So aerosols may not have an easily seen global impact
but they do have a noticeable local one.

*****
GEOPHYSICAL RESEARCH LETTERS, VOL. 32, L17802, doi:10.1029/2005GL023320, 2005
Alpert et al.
Abstract
From the 1950s to the 1980s, a significant decrease of surface solar radiation has been observed at different locations throughout the world. Here we show that this phenomenon, widely termed global dimming, is dominated by the large urban sites. The global-scale analysis of year-to-year variations of solar radiation fluxes shows a decline of 0.41 W/m2/yr for highly populated sites compared to only 0.16 W/m2/yr for sparsely populated sites ( less than 0.1 million). Since most of the globe has sparse population, this suggests that solar dimming is of local or regional nature. The dimming is sharpest for the sites at 10°N to 40°N with great industrial activity. In the equatorial regions even the opposite trend to dimming is observed for sparsely populated sites.

*****

I would also note that volcanic eruptions have a global impact on
aerosol amount from measurements, and there is some evidence of a global
temperature reduction after recent eruptions. It is just a matter of scale, but you can’t deny
that aerosols cause an effect on surface solar fluxes, and efforts to quantify it globally
(yes, using models), have succeeded in accounting for the non-warming period (1945-80).
How about the red sunsets due to aerosols? Isn’t that evidence enough of an impact?
Regarding the plots you show, I would interpret it as showing that there are global
and local aerosol effects, and what you see there are the global ones, due to the smaller
aerosols that stay in the atmosphere longer.
I will get to the CO2 issue in another post.

Willis Eschenbach

Grrr … I got bit by the dreaded “less than” symbol, it was in the quote so I didn’t notice it … I’ll try again, ignore #358.

Thanks for the link, Jim, it’s an interesting paper.

The paper uses data from GEBA, the Global Energy Balance Archive. However, instead of the much more accurate pyrheliometric ratioing method used by Hoyt et al., they used direct pyrheliometer readings. I have registered to obtain the GEBA data, to see what it says.

Taking a look at the paper you cited, I find the following curiosities:

1. They seem to never have heard of autocorrelation, or of the problems it causes. They divide the data into highly and sparsely populated sites. Then they say:

Moreover, the decline for highly populated sites during the
25-year period under investigation was approximately
2.6 times as large as the decline for sparsely populated
sites. In particular, the slope for large cities was estimated to
be 0.41 W/m2/yr compared to 0.16 W/m2/yr for sparsely
populated sites (Table 1). The goodness-of-fit measure (R2)
of 0.52 at the significance level p less than 0.001 indicates a good
fit of the linear trend for highly populated sites.

In fact, adjusted for autocorrelation, there is no significant difference between the trend of the sparsely and densely populated sites.

In addition, they’re playing fast and loose with the R^2 measure in a couple of ways. While the R^2 of the linear trend of the populated sites is 0.52, adjusted for autocorrelation it is not statistically significant (p = 0.06). Also, the R^2 of the linear trend of the less populated sites is 0.18, not statistically significant (p = 0.16), and for the entire dataset it is 0.43, also not statistically significant (p = 0.07).

2. They are assuming that the change in radiation is due to aerosols. However, this seems doubtful, because of the large year-to-year changes in radiative flux. The emission of aerosols doesn’t change a whole lot from year to year, but the radiative flux in the highly populated areas changed as much as 13 W/m2, and in the sparsely populated areas, by as much as 6 W/m2. Surely this can’t be due to aerosols alone, there would have to be other factors to make those large changes.

3. None of the sites that they reported on are south of 15° … curious … I would think they’d want to compare the NH and the SH.

4. They say:

The paradox, however,
is that the observed decline in broadband global solar
radiation concurred with the observed temperature increases
over land, by 0.09 K per decade, between 1951 and 1989
[Intergovernmental Panel on Climate Change, 2001]. This
puzzling evidence could, by all appearances, put in doubt
the dimming trend. Nevertheless, based on climate simulations
with the aid of a general circulation model, Liepert et
al. [2004] argued in favour of the real existence of
solar dimming, which they attributed to interactions of
greenhouse gas forcing combined with aerosol effects. They
found that reductions in surface solar radiation are only
partly compensated by enhanced down-welling longwave
radiation from the warmer and moister atmosphere.

While this all sounds good, it doesn’t work out mathematically. It is truly a paradox, since the land was warming from 1964 to 1989, while the “global dimming” was going on. From their paper, insolation decreased by 4 – 7 W/m2, and CO2 forcing increased by 0.6 W/m2 (using IPCC max figure of 4.5°C/doubling). Even if we assume a further doubling of the CO2 forcing from the mythical positive feedback (to 9°C/doubling), that’s still a net reduction of 3 – 6 W/m2 in forcing … meanwhile the land warmed in the NH. Doesn’t figure … one of the non-existent major mysteries of the climate, I guess.

5. Unfortunately, they do not give an area-averaged value for the global dimming. However, since urban areas are only about 0.2% of the land area, the area-averaged value over the Northern Hemisphere is likely much closer to the “sparsely populated” trend in global dimming than the “densely populated” trend. The fly in the ointment is that the “sparsely populated” trend is only -0.16 W/M2/yr, and is not statistically significant (p = 0.16!) …

In the meantime, while I wait for the GEBA data, here’s a post from Doug Hoyt on this question.

w.

Willis Eschenbach

Jim D., as always, good to hear from you. A couple of comments:

1. You say:

I will obviously not, based on just this, completely dismiss aerosols as having a cooling effect, especially since no alternative has been put forward.

I’ve never understood this line of reasoning. It’s the same reasoning that says “We don’t know what caused the recent warming, so it must be CO2”. If an argument is flawed, it is flawed whether it is the only explanation proposed, or whether it is one of fifty possible explanations. We should not hold on to it just because we don’t know the true answer.

2. In the ice ages, it is clear that initially CO2 has to be the effect, since it lags the temperature changes going into the ice ages. In addition, the cessation of the CO2 increase at the end of the transition out of the ice ages also lag the temperature change.

3. You can’t compare ppm of CO2 to temperature, the relationship is logarithmic. If CO2 were responsible for the ice ages, it would imply a climate sensitivity of 3.6°C per W/m2. The IPCC estimate is 0.4° – 1.2°C per W/m2. If that were actually the sensitivity, we should have seen about a 5.5°C temperature rise since 1900 …

w.

Tom Vonk

Tom,
The work you cited seems to be a frequency analysis that is then used to extrapolate into the future based on cycles in the data that can’t be even proven given the length of the historic record. It also doesn’t seem to offer any science beyond the statistics. Good to have faith in something, but I wouldn’t put it in quasi-cyclic extrapolations.

Ah … “faith” again !
I have neither “faith” in the numerical models based on stochastical assumptions nor in frequency analysis using the same assumptions .
What I am saying is that one can’t have it both ways .
IF the climate can be adequately modelled by neglecting the differential equations describing its dynamics and assuming the “long terme averages + noise” hypothesis THEN very obviously the evolution of the “long term averages” will show in any serious stochastical frequency analysis .
That is exactly what is happening in the work I quoted – the only way to dismiss this paper would be to say that the statistics are not relevant to the problem but then the “long term trends + noise” hypothesis would not be relevant either .
It should be clear by now , given the evidence quoted in this thread , that neither the convergence nor the unicity of computer models is adequately documented and that’s an understatement – it can’t actually be proven .

MarkW

#360, Jim D:

I’d be interested in knowing why you are so conviced that something is cooling down the planet.
Is it not more reasonable to assume that the models are broken?

Jim D

Willis,

I’ve never understood this line of reasoning. It’s the same reasoning that says “We don’t know what caused the recent warming, so it must be CO2’€³. If an argument is flawed, it is flawed whether it is the only explanation proposed, or whether it is one of fifty possible explanations. We should not hold on
to it just because we don’t know the true answer.

This one will answer MarkW too.
I know I didn’t say this well, but I am more convinced by the arguments for aerosol-induced cooling than the
ones against it, but I also think this is a side issue that came up because I claimed everything was explainable.
I would say that wiggles of the magnitude of this period have shown up in the past records, and the underlying
temperature rise that started in 1900 hasn’t, so the aerosol cooling mechanism isn’t critical to the warming issue.,
and wiggles of this size, even if somehow natural, won’t do much to stop warming.

2. In the ice ages, it is clear that initially CO2 has to be the effect, since it lags the temperature changes going into the ice ages. In addition, the cessation of the CO2 increase at the end of the transition out of the ice ages also lag the temperature change.

I didn’t think it was clear which one lagged because of the time resolution of the data, but that fits
the normal ice age mechanism that it comes from orbital and precession effects which force temperature,
not CO2 directly. So when the temperature rises CO2 is released from the ocean.
However, this is not an argument against the possibility of CO2 leading temperature, especially
with the radiative effect of CO2.

3. You can’t compare ppm of CO2 to temperature, the relationship is logarithmic. If CO2 were responsible for the ice ages, it would imply a climate sensitivity of 3.6°C per W/m2. The IPCC estimate is 0.4° – 1.2°C per W/m2. If that were actually the sensitivity, we should have seen about a 5.5°C temperature rise since 1900 …

If you prefer, I could have said that a 50% increase in CO2 went with a 10 C increase, which is even more impressive.
Indeed, this argument I used is not a “standard” one. I was trying to emphasize a correlation
that is clearly not accidental, and it follows from this correlation alone that more CO2 leads to higher temp.
I suspect the effect is not as big now as in the ice ages because we have lost most of the positive
feedback from ice albedo, but the effect is unlikely to shut off completely while polar ice is still around.

Jim D

Tom, #364 on LES,
I agree with this. There never will be a perfect sub-grid scheme. Luckily in
weather there is a scale separation that permits us to model thunderstorms, for example
on 1 km grids because the dominant motions are resolved. I am not saying the sub-grid scheme choice
has no effect, but we can understand a lot about thunderstorms with even a very simple
sub-grid scheme. [However there are now scientists who say you need more like a 200 m grid
(basically LES) to do thunderstorms properly.]
On the other hand, in areas like boundary-layer growth, sub-grid
schemes are front and center, and we are still working on getting PBL schemes better.

Gerald Browning

Jimy Dudhia (#369),

There is no rigorous mathematical proof that there is a distinct scale separation, only that there have been two distinct types of numerical models (hydrostatic for the large scale motions and nonhydrostatic for the mesoscale with the latter change only taking place fairly recently) with very different assumptions in each. You continue to assert things that are not proved or are folklore. If the enstrophy can cascade down from balanced large scale flow in a matter of hours because of large exponential growth near a jet, locally the scales are not separated , i.e. smaller scales can form very quickly even from a balanced large scale state.

Jerry

MarkW

The only argument I have ever seen in favor of aerosol cooling, is that it makes the models work.
Comparison with the real world shows that aerosols don’t work. That is, we don’t have a good number for how many aerosols were released during the time in question. We know very little about the distribution of types of aerosols that were released. We know very little about aerosols actually affect climate.

Beyond the uncertainty is the absolute fact that while most of the aerosols were being released in the NH, most of the cooling that is being blamed on aerosols occurred in the SH. Maybe it’s more of the teleconnections that magically make trees respond to temperature changes hundreds of miles away?

Beyond that is the fact that India and China are releasing huge quantities of aerosols over the last few decades, so the claim that aerosols only cooled the climate during the 70’s still fails the real world test.

I suspect that the reason you cling to belief that aerosols fix the problems with the models, has more to do with your attachment to the models.

Jim D

#371, Jerry,
In a lot of atmospheric systems, the smallest scales act just like diffusion, which
is simply represented in models. That is, the small scales are just a sink of energy or enstrophy,
and contribute nothing else in those cases. Thunderstorm models and large-scale circulation
models represent those processes fine with just diffusion representing the small scales.
In three-dimensional turbulence energy cascades to smaller scales, unless it is an unstable
situation, when growth from small scales does occur. Idealized models of thunderstorms are often
initiated with a resolved bubble so that they don’t have to develop the growth from small scales
themselves, or in forecasting with storm-scale models we rely on convergence lines to release
the convective instability in the right place, and this works quite well. So, yes, small scales
matter in development, but after the storm has developed they just contribute diffusion.

MarkW

JimD,

Some aerosols reflect, some absorb, some have different characteristics based on altitudes and conditions.

Nobody has ever said that aerosols have no affect. The point is, we don’t know enough about the amount, distribution and makeup of the aerosols that have been released over the years to have a solid feel for what contribution they made at any given year.

The modelers declare that X amount of aerosols “fixes” their models, and since X is a reasonable guess, (in their opinions) then X must have been the amount released.

You still haven’t tried to explain why the aerosols had more affect in the southern hemisphere, even though most of them were released in the northern hemisphere. Nor have you tried to explain away the assumption that aerosol production has gone down in recent decades, despite the fact that it hasn’t.

MarkW

JimD,

Only one explanation is needed. We have nothing that “shows” that CO2 is causing the warming. There is an assumption that it must be, since no other “acceptable” explanation has been put forward.

The problem is, several explanations have been put forward. They are just dismissed because the “the models show us that CO2 is all the explanation we need”.

Jim D

(I am going to be on travel, so this is it for about a week).

MarkW.
OK, various isses raised.
Aerosols; yes, they reflect and absorb. I agree,
it is complex, and modelers have to put some numbers in, and justify those numbers for peer review.
I hope the review system works for issues like this.

Warming: OK, interesting about the UHI (urban heat island effect), and maybe you answered your
own question about early-century warming with that one.
However, more recent warming has been confirmed by satellite (after some debate), and conforms
with the CO2 picture of warming near the surface and cooling higher up. Satellite data
is more global, so we can’t attribute that warming to sampling errors.

bender

Willis, yes, this is exactly how the peer review process works and what its purpose is. The idea is to make sure the interpretation given to the data is coherent, that the experimentation was done correctly, and that the methods are repeatable. The correctness of the result is for posterity, not peers, to judge – and this through repeated experimentation. Peer review can not achieve that.

Tom Vonk

As far as convergence goes, it is easy to show models converge to certain mathematical inviscid linear solutions, like flow over a hill. And anything, you can get mathematics to do with the NS system, you can get a model to do. Regarding chaos, climate models consist of many interacting systems (atmosphere, ocean, ice, land, vegetation, etc.), and therefore have the complexity to produce chaos if such existed. However, as I began this part of the argument with,
the century time scale is short for chaotic transitions in something as highly inertial as the climate system, and it is quite non-chaotic, and in a sense boring and predictable, when you only run these models 100 years. CO2 traps
heat in the system, and the atmosphere warms. No surprise, and what grounds are there for expecting a surprise?
How else do you solve this question, other than with models?

So some models converge to certain and linear solutions ?
As the climate is neither certain nor linear that says ?
I have tons of examples where models converge to certain solutions in certain circumstances yet such examples don’t even begin to hint at to what the general N-S modelling would converge to .
As for the chaotic behavior it would be nice if you stopped repeating the same mantra and brought some mathematically supported argument if any .
So the climate is non chaotic and predictable ?
What would actually be the parameters that are so absolutely predictable with 99,9 % certainty ?
The average temperature ? The average humidity ? The average cloudiness ? The average precipitation ?
Where is that magical time scale threshold that transforms a chaotic system in a non chaotic one ?
Where is the proof (not that is likely that one will ever exist) that global space averages are totally independent of the distribution of local space averages and their dynamics ?
You should really look a bit more in depth how behaves the Lorenz’s system to understand what chaotic means .
Approximate the climate to a steady state system in equilibrium is really the degree zero of physics .

What should we do with computers in climate modelling ?
Mothball them and spend the wasted billions in fundamental physics of non-linear chaotic systems .
Once we understand them better and especially understand what the computers can and can not do , then we can do some educated choices .

Gerald Browning

Tom (#385),

Jim Dudhia stated:

And anything, you can get mathematics to do with the NS system, you can get a model to do.

What Jim Dudhia obviously did not say is that you can get a numerical model to do anything you want it to do by adding large, unphysical dissipation, fudging (smoothing) all of the boundary conditions, and tuning the myriad parameters (forcing). IMHO this is not science and a kind description might be that it is trial and error.

Jerry

Steve Thomas

Just wanted to provide further evidence that discontinuous forcing, such as in the Grell moist convective scheme used
in MM5 (and also WRF?) destroys numerical accuracy
(of leap-frog and other schemes):

Sensitivity Analysis of the MM5 Mesoscale Weather Model to
Initial Teperature Data using Automatic Differentiation
by C. H. Bischof, G. D Pusch and R. Knoesel
Argonne National Labs

They show how discontinuous forcing triggers so-called
convective bombs or grid point storms that exhibit +/-
oscillations. The order of accuracy is reduced to zero.

esceptico

Bischof, automatic differentiation and other MM5 papers

http://www.sc.rwth-aachen.de/bischof/

http://www.autodiff.org/?module=Applications&application=SAoaMWM

http://www-fp.mcs.anl.gov/autodiff/tech_reports.html

ftp://info.mcs.anl.gov/pub/tech_reports/reports/P532.ps.Z

Dan Hughes

Re: # 389 and following

It should not be necessary to use a ‘big hammer’ tool such as automatic differentiation to re-discover the obvious. All discontinuities in all aspects of both the continuous and discrete equations have the potential to reduce the order of the truncation error to zero. A simple convergence study will reveal the actual order of the discrete approximations. All functions, and at least the first derivatives, must be continuous. See # 62 above.

For how much longer will the basic fundamentals of analysis of numerical methods continue to be ignored and simple true facts be re-discovered while at the same time ‘predictions’ using fundamentally flawed models and methods are presented?

The ‘chaotic response’ seen in NWP and GCM codes is all numerical error. Until all the potential sources of such numerical errors have been eliminated the calculated numbers do not represent solutions to even the discrete approximations. Additional discussions are given here. All comments and corrections for the material presented there are appreciated.

The lack of more nearly accurate calculation of observed data is due firstly to numerical errors and additionally to model errors. Chaos has nothing to do with it.

Gerald Browning

Dan Hughes (#393),

We are in agreement. The obvious question is which agencies are continuing
to fund such nonsense at the expense of quality scientific research.

Jerry

MarkW

YOu put cosmic rays in, the same way you put aerosols in.
You guess.

Jim D

Jerry,
Thanks for your constructive comments.
I agree rough forcing leads to poor-looking numerical solutions.
It would be amazing if it didn’t, and a sure sign of over-smoothing.
The time-splitting method is unstable if not used carefully. A little
experimentation shows that simple and selective acoustic-mode filters stabilize it, as is
clear in the papers describing the use of sound-wave time-splitting.
About 1000 published papers have used MM5 and WRF successfully. How can those be ignored
when talking about the literature? I think one of those might have noticed an instability
by now if it existed. Not only WRF and MM5, but RAMS too. Are you going to
criticize Cotton, Tripoli, Pielke and other RAMS developers and users too? How about
NCEP’s NMM model using time-splitting for the US national weather forecasts,
as also do German, French and Japanese weather models? Unstable methods don’t become so popular.

MarkW

JimD,

I’ve asked you this before. Why is it that you are willing to wait until everything is known about one phenomena (cosmic rays) before putting it into your models, but other phenomena (aerosol) you are eager to rush them into your models before much is known about them?

Is it because the aerosols protect the conclusion that you want to support, while cosmic rays undercut it?

Jim D

#401 MarkW,
If there is an equation for cosmic ray nuclei helping condensation of cloud droplets (I am guessing that is
the proposed mechanism), it would need to be demonstrated that this of similar magnitude to all the other
nucleation mechanisms before it is worth including. Aerosols, on the other hand have observable
effects on cloud nucleation in dirty air. Is cosmic ray nucleation observable or just part of the background noise?

Gerald Browning

Jimy Dudhia (#404),

As usual you did not answer my questions. How many MM4 (ill posed hydrostatic) model manuscripts were published. Please answer that question as then I think the general reader will have a pretty good idea of the quality of the “science” to expect from your modeling group.

And now we design numerical methods around the type of computer and ignore their stability? There’s a new concept.

Is Durran a numerical analyst of Kreiss’ caliper? Not even close. I suggest you read the Oliger, Sundstrom, and Kreiss book on numerical methods for PDE’s. These are famous and reputable applied mathematicians and numerical analysts. And there are even proofs included for all of the methods. In particular, how to properly do the semi-implicit method that will produce the correct solution.

As I recall, the Klemp wilhelmson splitting method artificially damps the divergence (and requires a time filter that is not second order accurate). Wrong thing to do for mesoscale motions where the divergence becomes important. I had no problem seeing the instability of the method when I coded it for the MWR manuscript. And you forgot to mention what happens at open lateral boundaries where you have arbitrarily added dissipation. You are not interested in accurate numerics, just in producing some output.

I am still waiting for you to run the well documented development of a mesoscale storm shown in our multiscale manuscript when all of your boundary games and dissipation mechanisms are active. You don’t seem too excited to do so. Is it possible that it might show exactly what I have been saying?

I still have not heard from Roger Pielke Sr. Maybe you should call him. Or does he have a higher standard of ethics than the editor that Joe and Bill managed to influence at MWR. BTW that same editor later wanted to work with me and confided that he was in a bad position when Joe and Bill played their little game.

Were you able to read any of the manuscripts I cited. Evidently not.
Page’s manuscript will appear shortly. Enjoy.

From what I can tell, the local forecasters are looking at Doppler radar and satellite imagery to obtain a pretty good idea of how to forecast the weather in the near short term and coming day or so. Why do we need numerical models for this. Evidently mainly to support archaic groups such as yours.

Jerry

Jim D

MarkW,
Have you observed the cosmic ray effect on cloud formation? I’m intrigued by what
that looks like. Usually things that are not observable are also not modelable.
How many cosmic ray particles are there per aerosol particle? Do many even make it into the
troposphere? These are the questions.
Aerosol effects on the other hand are seen in aircraft contrails, and even steamship plumes
affecing low cumulus droplet densities, and obviously downstream of industrial areas,
and in maritime versus continental cloud formation. What, if anything, about clouds is noticeable from
cosmic ray effects, or can’t be explained by other means?

Gerald Browning

Jimy Dudhia (#408),

Answer the question. How many publications were based on Anthes MM4 ill posed hydrostatic model?

This gives the general reader a good understanding how multiple modeling publications don’t mean a thing without mathematical analysis.

Jerry

Dave Dardinger

re” #410 Bender

In essence I agree, but as someone who doesn’t have the math a the tip of my fingers, I wish there was a less time consuming way of deciding who is right. I’m a skeptic by nature, not just because of training or political inclination. So when I see someone like Dr. Browning pounding Dr. Dudhia rather mercylessly I eventually start having thoughts like, “What if Dudhia is actually right, but just not as articulate in the Blog atmosphere?” I know I should read a bunch of the important papers, but as I say, that’s time consuming.

But it is useful for people like yourself who have read the papers to weigh in on your conclusions. It doesn’t obviate my responsibility to be informed myself, but I don’t have to feel as much doubt as to what I’d decide if I did do the reading. Thanks!

Gerald Browning

Dave (#410),

I have given Jimy Dudhia an obvious way in which to show who is right, i.e.
by running the same example in our multiscale manuscript to determine the impact on the numerical accuracy of all of the ad hoc treatments
of the lateral and vertical boundaries, the questionable numerical method,
and the large, unphysical dissipation using their latest model.
No response.

We have analyzed the time split numerical method and found it to be unstable. Jimy’s response is that, yes it is unstable, but it runs fast.
No mention of the impact at lateral boundaries or the necessary damping mechanisms. A properly implemented semi-implicit method provided the same solution as the leapfrog system for the multiscale model.

I have asked Jimy to run the same convergence tests that I did. No response. Others that have run similar unforced tests near a jet
using two different NCAR models have seen the problem indicated by the mathematical theory.

Jimy Dudhia raised the issue of quality versus quantity. So I asked how many manuscripts were published using Anthes ill posed hydrostatic MM4 model to show that quality and quantity are two different things. (Of course this also reflects on the peer review process in the corresponding journals.) No response.

I had Sylvie Gravel (RPN) run a number of cases with the Canadian global weather model (manuscript rejected for obvious reasons but copy available). The same results could be obtained without any forcing except a simple lower order drag as the mathematics shows if the forcings have relative errors O(1). The only thing that keeps the model on track is the periodic updating (assimilation) of wind data near the jet level exactly as expected from the mathematical theory in our updating manuscript. When a simple change in the data updating (assimilation) was made according to mathematical theory, the improvement was dramatic. And now Christian Page (Canadian) has shown that our mathematical theory about the slowly evolving solution in time can be used in a practical model to provide a balanced solution. Jimy’s response?

I have cited manuscripts that contain mathematical proofs and numerical examples to better understand the theory for every one of my points.
Jimy’s response – change the subject or twist my words.

Are we beyond a reasonable doubt at this point? If so, ask Jimy how the accuracy of the WRF model is measured when it is used in forecast mode.
His response is that they now deal in probabilities. This is no surprise given that there are large uncertainties in the continuum system near a jet, large uncertainties and discontinuities in the forcings, an unstable
numerical method with questionable damping mechanisms and ad hoc dissipation procedures near the lateral and vertical boundaries. And you ask why the local forecasters are relying on Doppler radar and satellite imagery for the near term?

And to top this all off, intimidation of an Editor and rejection of multiple manuscripts based on politics even when the manuscripts contained mathematical proofs. IMHO I find all of this quite pathetic.

Jerry

MarkW

JimD,

You know as well as I do, that given the disperse nature of cosmic rays, it is impossible to compare an individual spot to another, the way you can with aerosols. Your objection is highly disengenuous.

Likewise, you know as well as I do, that cosmic rays have been shown to have an affect on cloud formation in cloud tank experiments.

Jim D

To clarify, my 1993 paper introduced MM5, a nonhydrostatic successor to MM4.
I have no reason to suppose MM4 was any better or worse than other models of its
generation. Likewise, in the 90’s MM5 was of a similar generation to COAMPS,
hydrostatic Eta, NMM, RAMS, RSM, hydrostatic RUC, ARPS, and that’s just in the US.
Was it better or worse than all those? I don’t know. They all had their advantages and disadvantages.
I don’t know if you are complaining about the specific models NCAR has been involved in,
or this long list. If you had a specific complaint, I could give a specific answer.

What model has ever predicted a tornado? That capability is beyond data assimilation.
Models have simulated tornadoes, which is different, but not predicted them. It is not
a model limitation, because we know the equations, and we now finally have the computers.
It is a data limitation, because we don’t know the initial state well enough in 3d.

Regarding model accuracy, the best objective evaluation is given by the forecasters
who use the products, and whose decisions are influenced by them. They are not modelers,
and aren’t afraid to criticize. Their evaluation is useful, being unbiased. I am taking
part in an annual program in Norman, Oklahoma this Spring where modelers sit with forecasters at the
Storm Prediction Center, and these forecasters experiment with the guidance given by new model products.
This keeps our feet on the ground regarding how models fit in the forecasting process, and
the problems that remain to be solved, but is also encouraging because it represents a direct
application of our work in a meaningful area.

Dissipation: All models have dissipation, except perhaps DNS which is not yet practical for
the atmosphere over large areas. The aim is to dissipate things that are not resolved,
and leave things alone that are. The success of this is measured by looking at energy-wavelength spectra for
which the correct slope is known. Dissipation is not to hide anything. Overly dissipative models are
not respected, because they inefficiently use computer memory to resolve a grid that is much smaller than the
effective resolution.

Dave Dardinger

re:418,

I probably shouldn’t get into an argument I don’t have expertise in, but I have a couple of questions. 1. If supersaturated conditions don’t occur very often, then what are Jet contrails all about? And 2. It’d seem to me that every rising air column, except perhaps over desert areas, will eventually reach a point of saturation and then the question is just how many droplet forming particles are available. If there aren’t enough to produce all the droplets possible, then some degree of supersaturation will occur. Are there studies about just how likely a paucity of droplet forming centers are to occur; at the margins I mean. Obviously a lot of the time there are plenty. But if say 5% of the time droplets aren’t forming then this has an affect.

Gerald Browning

Jimy Dudhia (#417),

IMHO, I must say that you are in the right group at NCAR and have been
trained well in deception by your mentors.

To start, I was not supporting the Canadian model. Sylvie’s was the only global modeling group that was willing to run the tests. Kudos to her group
for their honesty. What Sylvie’s results conclusively showed are that the forcing (parameterizations) in the Canadian global weather prediction model had O(1) relative errors in the forcing and those terms could be left out in the first 36 hours with no change in the forecast, exactly as expected from mathematical theory for forcing terms with errors of that size. Thus the parameterizations were unnecessary during that time period and constituted a misuse of computer resources that have continually been claimed to be the limiting factor in forecast accuracy (just like you do).

During and after that time period, the accuracy of the forecast deteriorated rapidly. The only thing that kept the Canadian global weather prediction model on track during that time period was the periodic updating (assimilation) of wind data in the jet stream. After the simple change that Sylvie made in the data assimilation program based on the Bounded Derivative mathematical theory, the Canadian global weather model outperformed the NOAA National Weather Service global weather model by an amount unheard of before that time (phrasing by others that saw the results) even though the NOAA global model used a higher order accurate (spectral) numerical method, again obviously a misuse of numerical methods and computer resources. I am more than happy to post the unpublished manuscript on this site so that all can judge for themselves what is going on in the global models.

Now these global models can be used to provide initial data and boundary conditions for limited area models such as WRF (for a clear picture of how this should be done in a mathematical manner according to theory, see the Multiscale Initialization manuscript by Kreiss and me). However, there are obviously a number of problems when doing so. The first is that the
initial data for the limited area model does not contain any of the smaller scale features possible in the limited area model (I will go into this in detail in a later comment) and the data is from a global model that is based on a different system of equations (hydrostatic system), parameterizations (forcings) and viscosity. Thus there are discontinuities in the dynamics (hydrostatic system for the global model that is ill posed for the IVP and IBVP versus nonhydrostatic system for the limited area model), the parameterizations (forcings), viscosity, and mesh size at any lateral boundary. This is one reason for all of the ad hoc smoothing near the lateral boundaries of the WRF model. A feature that is not resolved by the global model will not be portrayed accurately in incoming flow and a small scale feature that develops inside the limited area model that is not resolved by the global model will conflict with the global model boundary conditions on outflow. Both of these problems will destroy the accuracy of the numerical solution of the limited area model very quickly. In fact,
in many limited area manuscripts the contour plots were trimmed
before publication to hide the problems near the lateral boundaries.

Gravity waves are routinely surpressed in global weather prediction models
as they are considered to be unimportant for large scale motions. But they can and will be automatically generated by latent heating (smaller scale forcing) in a limited area model (see mathematical discussion and proofs in above Multiscale reference). These waves obviously
will also conflict with the boundary information from the global model
that does not contain those waves. We discuss very clearly in our manuscript how gravity waves are generated and the impact of not treating them properly if they are responsible for triggering storms.

I think it is very clear why you won’t run any of the “toy” problems as they will reveal all of the flaws in WRF as discussed above.

Because you have claimed such forecast accuracy from WRF, please show WRF forecasts for a number of consecutive days, the observational data for those days, the differences between the two contour plots and the mathematical norm of that difference at the mandatory levels.
I would surmise that I will be able to pick out the above problems with this info.

Have you called Roger Pielke Sr. yet to see if I have misinformed
the general reader?

Jerry

John Baltutis

Re: #422

Better would be a link to a copy that we could download. Maybe Steve M. or John A. could provide that convenience.

bender

#424 This IMHO is one of the most important points to be made that even smart people get wrong very frequently. If weather is chaotic at all scales then climate too is chaotic, such that structural features of the ocean-atmosphere circulation are not as invariant as modelers would have them be. It would be a useful thing to point out specific pieces of literature that get this wrong. Literature that assumes that because climatology = long-term weather, statistical averages and “confidence” intervals serve to put some bounds on the chaotic behavior of weather. If growth in physical systems is exponential, then features like jets and ocean currents are not immutable. Look at the multi-million year record of climate, which includes the PETM. It varies at all time scales. How then can one make use of the theory of large numbers (central limit thereom) that is the basis for statistics. You can not. Climatology as a statistical enterprise is an illusion resulting the very short time over which we have been measuring weather accurately on this planet.

I do not think RC posters understand this very basic thing about weather vs. climate. I was a reluctant convert to statistical climatology about a year ago. Now I’m recanting. I don’t think the experts have got it right. There is no central tendency in Earth’s climate.

Disclaimer: I am not a climatologist. I’m just like you: trying to learn what climatology is.

Mark T.

That’s a fundamental feature of chaos theory. A chaotic system exhibits the same amount of chaos at every level of observation.

Mark

Spence_UK

This has been a fascinating and informative thread, and I’d like to say thanks to those participating. It has been a very interesting read. Thanks in particular to Dr Browning for kicking the discussion off, and to Dr Dudhia for taking time to present what I assume is the “consensus” view. It would be great if you guys could agree and complete an experiment to help to resolve differences in views, as Dr. Browning suggests.

The issues around chaos and long-term weather have been a particular bone of contention with me. Tom Vonk’s post earlier probably captures most of my view on the subject; bender and Steve also. I really wish a climate scientist would explain to me why climate isn’t chaotic; so far the explanations are usually very weak, going to great efforts to define climate, but at no point do they define chaos, nor do they attempt to define a test for chaos. The test then applied is usually to eyeball a graph and determine whether it looks “random” or not. Of course, chaos can produce patterns as well as random looking output, so this test is atrociously weak.

The issue of self-similarity / scale invariance is an important one though, and in some ways separable from the issue of chaos. If amplitude fluctuations are greater at longer timescales, as noted above, by long-term averaging, all you do is move to a different scale. Again, this is not necessarily evidence of chaos (both chaotic and non-chaotic systems can exhibit this behaviour), but either way it renders averaging of no use for determining some underlying state.

Cartoon examples have limited value, but can be useful. Looking at the Mandelbrot set (a simple chaotic system, albeit a discrete system, rather than continuous like the weather/climate system), it is easy to observe self-similarity at different scales, patterns in the output, and unpredictable behaviour. I would note that whilst the chaotic behaviour exists over an infinite range of reducing scales, as you move up in scale there is a finite limit at which point chaotic behaviour stops. I suspect this may well be true of climate as well; as you expand in scale, eventually some other boundary condition steps in, and averaging will begin to work. Looking at long-term proxies, my guess is this probably kicks in at around the 100-million year scale, at which point the temperature varies over its maximum likely range.

Anything shorter than that, is anybody’s guess. Of course, I could be wrong on longer scales; it might be an illusion due to inadequate data!

bender

Oh, and on “central tendency”.

In a spatially extensive turbulent terawatt heat engine such as earth you can expect many many equilibrium states and substates. Although there may exist central tendencies, the problem is the states to which the system is tending toward are not fixed. It would be a mistake to try to think in terms of a single central limit to which a system tends. The attractor is not a point. It’s far more complex than that. Far more complex even than Lorenz’s simple 3-equation “butterfly” attractor. New states would be created and destroyed as the solar-earth-climate system goes though its machinations. On top of that you have planetary perturbations (such as mid-Atlantic CO2 expulsion) capable of shocking the system between super states. Good luck with your gaussian ideal.

Gerald Browning

I will post Sylvie’s unpublished (rejected) manuscript. I might not have the final version, but one that is sufficient to illustrate all of the main points and one that can be discussed in detail.

Jerry

jae

According to this treatise, there can be some predictability of climate, despite its chaotic and non-linear characteristics (or am I reading this wrong?):

However, if, contrary to the IPCC’s attitude, the sun is taken seriously as a dominant factor in climate change, this opens up a possibility to predict climate features correctly without any support by supercomputers. A string of examples will be presented. The chaotic character of weather and climate does not stand in the way of such predictions. Sensitive dependance on initial conditions is only valid with regard to processes within the climate system. E. N. Lorenz has stressed that only non-periodic systems are plagued by limited predictability. External periodic or quasiperiodic systems can positively force their rhythm on the climate system. This is not only the case with the periodic change of day and night and the Milankovitch cycle, but also with variations in solar energy output as far as they are periodic or quasiperiodic. The 11-year sunspot cycle meets these conditions, but plays no predominant role in the practice of predictions. Most important are solar cycles which are without exception related to the sun’s fundamental oscillation about the center of mass of the solar system and form a fractal into which cycles of different length, but similar function are integrated. The solar dynamo theory developed by H. Babcock, the first still rudimental theory of sunspot activity, starts from the premise that the dynamics of the magnetic sunspot cycle is driven by the sun’s rotation. Yet this theory only takes into account the sun’s spin momentum, related to its rotation on its axis, but not its orbital angular momentum linked to its very irregular oscillation about the center of mass of the solar system (CM).

bender

If climate is mostly periodically forced, then yes, predictability at all time scales is achievable – if you work out all the periodic forcings. The time-scales over which climate is not predictable is then the time-scales over which the terawatt heat engine produces deterministic non-periodic flow, in the language of Lorenz. The question is to what extent are things periodically forced and to what extent internally chaotic. It’s not a qualitative question, it’s a matter of degree.

I know you love your periodicities, jae. I too am optimistic that we haven’t heard the last of Milankovitch, etc. But you know the problems with solar theory as it stands now, I don’t need to tell you.

Jim D

I have never said climate is not chaotic, because the ice ages clearly show
other equilibrium states that are fairly stable. I am saying that on the Century
time scale there isn’t yet a known mechanism by which we will enter an ice age
or a runaway global warming feedback leading to more than a 10 C increase,
and the simple reason is thermal inertia. The oceans, in particular store a
lot of the earth’s heat energy as they have well over 100 times the heat content of the
atmosphere (by my reckoning, someone should check). They maintain a background temperature
which is a major counter-agent to anything that might try to pull the atmosphere
away from its near-equilibrium with it. Warming the ocean by a few degrees will
take centuries when forcings are the size of CO2 forcing.
Even if you believe the temperature record is fractal, that indicates that on smaller
timescales the wiggles also get smaller in amplitude.

bender

Not sure if #439 is in reply to bender, but my #436-438 were in response to jae, not anything Jim D has said.
Jim D, would you care to have the first crack at spinning the Gravel story?

Steve McIntyre

This thread has stayed on topic for a remarkably long time. So here’s a continuation.