Jerry Browning writes the following about the balance between vertical velocity and total heating:
Browning and Kreiss (2002) have shown that as one moves from the large-scale features in the midlatitudes to the smaller scale features, a balance between the vertical velocity and the total heating must be maintained for the solution to evolve slowly in time.
The horizontal divergence of the balanced solution becomes important and the traditional balance equation of quasi-geostrophic dynamics must be extended. Recently this balance has been shown to provide a slowly evolving solution in time in a forecast model with physical parameterizations (Page et al. 2007).
The same balance between the vertical velocity and total heating applies near the equator for all scales of motion. Thus one might expect that if the solar variability has the most impact near the equator, e.g. in evaporation at the ocean surface, the variability is most likely to be seen in the vertical velocity near the equator.
References:
Browning, G. L. and H.-O. Kreiss: Multiscale bounded derivative initialization for an arbitrary domain, JAS, 59 ,1680 -1696
Page, C., L. Fillion and P. Zwack: Diagnosing summertime mesoscale vertical motion: implications for atmospheric data assimilation, MWR (Accepted, see PTA)
Climate Audit 
27 Comments
I’ve got a little bit of experience with monsoon climates in Asia. The way the Asian landmass is configured, with the exception of the Malay peninsula, we the most southerly monsoon affected areas intermingle with the ITCZ. What has long interested me has been the seemingly immense variability in the nature of the monsoonal systems from year to year. One year it’s almost all stratiform, showery, light precip, the next year the build ups predominate and it’s thunder and downpour city. Beneath the clouds, the former case tends to result in a coolish summer, and the latter muggy one with either full blast heat or momentary cool. Fascinating stuff ….
Has the double ITCZ bug been fixed in the models?
Here is an appaisal from Lawrence Livermore 16 august 2004 (196 pages)
Click to access model_appraisal.pdf
Quotes from the Appraisal Summary:
I asked that Steve add this post in order to make clear the importance of the balance of the vertical component of velocity and the total heating (sum of all effects added together) so that the balance could be discussed for its possible impact near the equator, especially on the ITCZ as Steve has surmised. A few additional points. Because of the importance of this balance to the slowly evolving solution, any errors in the parameterizations will have an immediate impact on the accuracy of a short term forecast and likely on longer term simulations as discussed on the other thread. Although the mathematics of this balance is now well established, this topic is not on as firm a foundation, but I think it is obvious that Steve’s hypothesis should be discussed with these balances in mind.
Jerry
From a paleoclimate point of view, I find ITCZ location very interesting. There’s very considerable evidence IMHO for a more northerly location of the ITCZ in the Medieval Warm Period (Newton et al GRL 2006 surveys some interesting proxies; also Richey et al 2007) and more southerly location in the LIA.
Steve M.,
Some of the arguments from the solar influence on the atmosphere (long wave, short wave, etc.) from the solar threads might be helpful to these discussions. It will be interesting to see where this leads.
Jerry
Steve M.,
As the season changes from winter to summer, doesn’t the jet move further north. What about the ITCZ? In the midlatitudes at the smaller scales, evaporative cooling and condensational heating play a major role in the vertical velocity of the mesoscale storms (see articles referenced above). The ITCZ supposedly forms, breaks up, and reforms, but the storms should be driven in the same manner?
Jerry
Is this topic apropos to the recent discussion of a major 19th century climate shift?
Climatic-Solar Connection!
What a hoot! After all the claims by AGW proponents that solar variability plays little or no role in climate variability, NCAR’s Gerald Meehl now states that he sees changes in the CCSM climate simulations impacting La Nina and El Nino due to the 11 year solar cycle (see NCAR’s main site for the announcement).
Do you think they finally read this thread or our scientific manuscripts on the importance of the total heating near the equator? LOL
Jerry
Heinz Kreiss always said that it would take 10 years before the field would catch up to the theory. Our manuscript on equatorial heating was published in 2000.
Jerry
Theoretical Explanation
I can now explain why the solar variability has an impact even though the variability is only 0.1%.
In the dynamical system the scaling coefficient that multiplies the two largest terms in the potential temperature equation (entropy equation) implies that there must be a balance between total heating and the vertical velocity for the solution to evolve slowly in time as mentioned above. That coefficient multiplies the perturbation heating (solar variability of the heating) in the perturbation equations. The product of the small change in solar heating and the large coefficient in the original scaled system can be very important over the periods of time of the solar cycle.
Jerry
Re: Gerald Browning (#10)
If you could put this explanation into a more conceptual format as opposed to the mathematical lingo, then maybe more of us morons might get an idea how such a small variation in the output of the sun could produce a significant forcing on our climate.
I know this is asking a lot, but what the heck. If I don’t ask, the possibility of getting an explanation a peon can understand is zero.
Molasses Ball
If a molasses ball (climate model with unrealistically large dissipation and inaccurate physical parameterizations) is able to show some connection between solar variability and the tropical ocean.
it seems reasonable to surmise that if the fluid was more like air instead of glue, the vertical velocities would be larger, there would be more rainfall, and there would be even more of a substantial impact. And if that is the case, then an external forcing that man does not control is the dominant
component of climate variability. Where does that leave the AGW arguments?
I might also note that the sun is at solar minimum with few or no sunspots (some even speculating it might be going into a Daltom minimum). Colorado has had a very rainy and cool summer after a previous 5 year drought. Any connection?
Jerry
COnsidering that viscosity increases the time or height of transfer unit required to transfer heat or mass in a boundary value conditioned problem such as the comparison of dropwise versus film condensation on a vertical surface Tanner et al, J Heat and Mass Transfer 8:419 (1965) and such staples as the 1916 Nusselt equation and discussion of Reynolds numbers and limitations of validity, does not a molasses ball fudge factor represent an admission that the model has exceeded its limitations of validity? A claim that the physics and math are nonetheless correct, is unbelievable. It is as though all the rules I had to learn have been invalidated. Such as “The Navier-Stokes equation (PDE) is the basis of the hydrodynamic analysis, which, as usual, PRECEDES the heat tranfer analysis” where even the simplified ODE had Re(L)to explain just laminar heat transfer. I wonder how you could write either the math or physics for this hyperviscous layer when it is stated that the physical properties of condensate vary with temperature, but the only property affected significantly is the viscosity (Bennet and Myers, 3rd ed, Momentum, Heat and Mass Transfer) and one is supposed to start with the N-S PDE!?!
John F. Pittman (#12),
The atmosphere (air) is suppose to behave like a hyperbolic system with small viscosity, not like molasses with large viscosity, i.e. a heat equation. It is standard practice in most fluid dynamical models (because of the limitations on computing power), to use unrealistically large viscosity so that a solution can be computed (even though it might be completely inaccurate). In the case of climate models,
the NS equations are modified by the assumption of hydrostatic equilibrium and the resulting IVP is ill posed. Look up convective adjustment to see how the climate modelers arbitrarily alter the flow to maintain hydrostatic equilibrium. Then note that when using unrealistically large viscosity, the model spectrum is quite different than in reality. So the parameterizations (physical forcings) are necessarily unrealistic in order to try to make the simulation appear realistic.
It is interesting to note that NCAR fired the first scientist to advocate a solar-climate interaction.
And now suddenly they state that they see an interaction in their molasses ball.
Also note that all of our manuscripts on the bounded derivative principle used the inviscid NS equations and have shown in theory and practice to lead to improvements in initialization and understanding of balanced flow for all scales of motion everywhere on the globe.
Jerry
http://www.gfdl.gov/bibliography/related_files/stg0701.pdf states “”The idea of directly changing the equation of motion was suggested by Browning and Kreiss (1986) as a way to improve numerical stability. The specific motivation was to make the grid-scale internal waves less hydrostatic. The computational opportunities and drawbacks of the idea were later investigated by Skamarock and Klemp (1994) and Macdonald et al. 2000).”” Have you reveiwed this and is thisa a good article to read? Thanks in advance.
John Pittman (#14),
A single statement in a manuscript does not make a rigorous mathematical argument.
The numerical method used by Skamarock and Klemp is numerically unstable and proven to be so in
the manuscript entitled “Splitting Methods for Problems With Different Timescales” (Browning and Kreiss, MWR, 1994).
The method we introduced in our 1986 article (cited by the manuscript you indicated) was introduced in order to find a well posed alternative to the ill posed primitive equations, i.e. the inviscid NS equations with the added assumption of hydrostatic equilibrium. In our 1986 manuscript we mathematically prove that the new system accurately describes the large scale motions of the atmosphere in the midlatitudes. The manuscript you cited did not cite any of our more recent work. This is very typical of
“atmospheric scientists”. In a number of our later manuscripts, we showed that the new system is a true multiscale system and can handle mesoscale (and smaller) flows in the midlatitudes and all scales of motion near the equator. I suggest you look at our manuscript entitled
“Multiscale Bounded Derivative Initialization for an Arbitrary Domain (JAS 2002).
That manuscript cites many of the mathematically rigorous articles leading up to it. The manuscript shows the power of the new system in handling multiple scales of motion in a domain with open boundaries, i.e. it shows the accuracy of the new well posed system and thatit can be numerically approximated by a stable numerical method even in the presence of open boundaries.
The mesoscale initialization method has been tested in practice (Fillion, Page, and Zwack, MWR).
There is a long history behind all of this work and the culmination indicated in the 2002 manuscript
shows the power of the new theory.
Jerry
Jerry: From a previous thread “” Therefore, any simplification of the original continuum equations should be checked to ensure that the simplified system accurately approximates the continuum solution of interest and is properly posed.”” and “” Numerical Modeling Considerations: Once the continuum system to be approximated has been determined to be properly posed, it can be approximated by a number of numerical methods, but all must be both accurate (consistent) and stable for the method to converge to the continuum solution of the initial-value problem (see Lax Equivalence Theorem in above reference). The accuracy of the numerical method determines how fast the numerical method will converge to the continuum solution, e.g. a fourth order method will take fewer mesh points than a second order method (assuming both are stable). However, the numerical accuracy can be reduced by a number of factors, e.g. errors in the approximations of the continuum equations or errors in the model. “”
I have a question. A hyperviscous unphysical layer would be contrary to a properly posed continuum system that CAN be approximated such that a simplified system would neither be stable nor accurate (consistent), my reasoning. The best of such an ill posed system would be either a consistent or a stable system, either in an indeterminate matrix or envelope of indeterminate magnitude. The order would be constrained to a realizable result if and only if the reduction of scale could be contained somehow correctly in the “forcing” of the illposed boundary of the non-physical, which could not by defintion be determined a priori, but with a nonphysical constraint must be post facto and will tend to suffer overfitting as one tries to determine the magnitude (assuming one has the order of magnitude correct). Is this correct?
John Pittman (#16),
Note that the proofs of the accuracy of the multiscale system are done in the continuum, i.e. they have nothing to do with numerical methods. Of course when using the multiscale system for modeling, it has the advantage of only resolving those features that can be resolved by the mesh. Any other features cannot be resolved (see discussion of gravity wave problems in Multiscale manuscript) so the use of this system is in some sense optimal for a given mesh (or multiple meshes).
If you look up the manuscript by S Thomas and me, you will see that a semi-implicit model for the
nonhydrostatic equation in the mesoscale case (theoreticaly shown to be both accurate and stable) produces the same solution as the multiscale system, but the latter works for all scales without the need to solve 3d elliptic equations at every step.
All numerical weather models, whether they be global climate or limited area forecast models,
add ad hoc boundary layers to the numerical approximations of the original system of equations.
The impact of these ad hoc approximations on a global weather model can be seen in Sylvie Gravel’s manuscript on this website. There it can easily be seen that the errors from these ad hoc parameterizations grow with time and destroy the accuracy of the model compared to obs in the matter of a few days. So you might be able to surmise what happens in a climate model.
You need to clarify your question so I can answer it more precisely, but hopefully these comments have addressed a number of issues that you have raised earlier.
Thanks Jerry. You said “”The impact of these ad hoc approximations on a global weather model can be seen in Sylvie Gravel’s manuscript on this website. There it can easily be seen that the errors from these ad hoc parameterizations grow with time and destroy the accuracy of the model compared to obs in the matter of a few days. So you might be able to surmise what happens in a climate model.”” answers the first question I had. I am also considering the claim that “weather is not climate” as indicated in my previous post about “”The best of such an ill posed system would be either a consistent or a stable system, either in an indeterminate matrix or envelope of indeterminate magnitude. The order would be constrained to a realizable result if and only if the reduction of scale could be contained somehow correctly in the “forcing” of the illposed boundary of the non-physical, which could not by defintion be determined a priori, but with a nonphysical constraint must be post facto and will tend to suffer overfitting as one tries to determine the magnitude (assuming one has the order of magnitude correct). Is this correct?””
Sorry for being unclear. But in the discussion that you had with Gavin on RC (That you posted on CA to make sure it was not edited, censored, ignored, your choice)it was my assumption that Gavin was claiming (perhaps retreating to a position of) weather is not climate and that the loss of specific information such as “resolving those features that can be resolved by the mesh” was made up by getting it “right”. IIRC, it was his claim of the models got the volcanoe sulfate input correct and therefore got all the rest correct. Note, I do not agree that getting the sulphate of a volcanoe even so much as gets the aerosol of a volcanoe correct, much less the rest of the global sulphate response correct. However, as an engineer I appreciate a simplification no matter how simplistic it is as long as that the simplification actually gives reproducible results (English has these moments, since my POV is that results ARE reproducible).
My question is “”CAN the ad hoc parameterizations that grow with time and destroy the accuracy of the model compared to obs in the matter of a few days BE ignored with the assumption that weather is not climate.””
Sorry for the simplistic wording but this was the essence of Gavin’s claim, IMO.
My position, not that I am “married to it” is that even claiming that weather is not climate results in (at best) an overfitted constraint that will show the symptoms of http://rankexploits.com/musings/wp-content/uploads/2009/07/changeincomputedtrends.jpg as I indicated with Comment #17010.
In explanation, the IPCC with their Bayesian inferencing do not concern themselves with either that “”the errors from these ad hoc parameterizations grow with time and destroy the accuracy of the model compared to obs in the matter of a few days”” nor that one or many parameterizations are incorrect. It is the constraint that matters most. Thus my question is, “can, say, a hyperviscous constraint meet the IPPC requirements or as in my opinion it is at best an overfitting due to replacing the a priori with an a posteriori as is implemented by the actual historical development of GCM’s?”
I also have other questions. LOL, tis true.
Re: John F. Pittman (#18), “CAN the ad hoc parameterizations that grow with time and destroy the accuracy of the model compared to obs in the matter of a few days BE ignored with the assumption that weather is not climate.”
Gavin’s view seems to be an implicit assumption that weather excursions are normally distributed along the time axis. In this view, one can ignore errors in weather because weather is a noise that tends to self-cancel, no matter what, across a climatological 30 years. When weather cancels, the remaining trend is climate, and whether the true weather or the wrongly calculated weather cancels, the climate trend is unaffected. Assuming the correct climate trend is modeled, of course (the big IPCC/AGW assumption).
One important point here is that climate is probably a chaotic walk among a set of meta-stable states, and the transition to a different state can likely be induced by an adventitious resonance with a weather fluctuation. That would mean, e.g., that inability to get the weather right would result in not getting the climate right. I’d guess the phase space of any local climate state would include a large number of shallow minima among which the climate wandered, kicked along at times by strong weather fluctuations.
Jerry:
Thanks for pointing to this new paper. This result is also being used to predict record-breaking warming in the coming 5-years as the sun reaches a new maximum:
link
It is hoped that a hot fall/winter will help push the Copenhagen agenda over the top.
I get the impression that the reason the slight increases has a significant heating effect is due to an associated strong positive feedback. In addition to your theoretical explanation, could you also give a conceptual explanation to the maths-challenged?
Thanks
Howard (#19)
I am not sure which paper you mean given that I have cited a number of them in response to John. Please
be more specific.
If you are referring to the NCAR (Meehl) manuscript, I point out that if the sun is the dominant component in climate variability and it goes into a Dalton (or Maunder) minimum, then we will have more to be concerned about than AGW.
I again point out that a numerical model is not a proof of anything unless it is close to a convergent numerical solution of the continuum dynamical (well posed) system with the correct type and and size of viscosity, the correct physics, and the correct boundary conditions. Current climate models do not meet any of these requirements and Sylvie’s manuscript shows what happens when a physical parameterization
is tuned to overcome problems in the model assumptions and is not the correct physics.
The WUWT website points out the problems with station data.
Where are the scientific facts and not just wild guesses ans scare mongering.
Jerry
John Pitmann (#18),
I wish that I could make a career claiming that I do not have the dynamical PDE system accurately approximated, that I do not have the correct spectrum (physical decay of enstrophy), and that I do not have the right forcing, but I have the right answer. Anyone for miracles? 🙂
Jerry
John F. Pittman (#14),
I have had a chance to peruse the manuscript you cited in #14. Here is my summary of our theory and the abuse of that theory by the authors of the manuscript.
Our original addition of a coefficient multiplying the vertical acceleration
term yielded a mathematical proof of the accuracy of the continuous modification of the inviscid NS equations (with Coriolis and gravity terms) for large scale motions in the midlatitudes. This modification was made in order to overcome the ill posedness of the hydrostatic system for open boundary problems (IBVP) in the midlatitudes so that the approximate system could be used to supply accurate, well posed boundary conditions for fine mesh limited area models. Note that the original proof was intended only for relatively short time periods, i.e. for forecasts. As our work progressed, the nature
of smaller scale motions in the midlatitudes (mesoscale and smaller) and all scales of motion nearer the equator became theoretically understood (the balance between vertical velocity and total heating). Under those circumstances, the original approximate system became a true multiscale model (Browning and Kreiss 2002). Here I also mention that the multiscale system is automatically well posed because it is a hyperbolic system that is mathematically well understood both for the initial and initial-boundary value problems.
The authors of the manuscript you cited have not provided any mathematical proof of their tweaking of our modification parameter, the shortening of the spectrum (moving convection closer to the large scale), or modifications of the physical parameterizations. Their trial and error approach is not science, but another tuning attempt. To me this is just a clear admission of the shortcomings of longer term integrations and of the serious parameterization (and other) flaws in current climate models.
Jerry
Re: Gerald Browning (#24), Thanks Jerry. It was their claim concerning convection that got my attention. I think I will still spend time on it wrt to your post in order to help expand my understanding.
Howard (#23),
First one must understand the reason for the balance between the vertical velocity
and the total heating. See our 1986 or 2002 manuscript or our manuscript on mesoscale motions for an explanation.
A simple scaling of the equations for midlatitude mesoscale motions is the simplest way to see that such a balance must exist for slowly evolving in time midlatitude mesoscale motions. That this balance must also hold for near equatorial motions is a simple extension of this argument. What is your background?
Jerry
John Pittman (#26),
Note that our 2002 manuscript shows how to accurately handle mesoscale (and even smaller scale) motions (with a practical illustration in the Fillion et al. manuscript). Maybe that is why they didn’t cite it. 🙂
If you have any further questions, let me know.
Jerry