Tim writes,
Published 27th February 2016 Climate Audit published a small article in honour of Kreiss to do with atmospheric modelling, the hydrostatic balance… or not.
Comments follow from Names. I think the comments are worthy of a read and decode by Talkshop readers who have an interest in this kind of topic.
Gerry Browning: In Memory of Professor Heinz Kreiss
Gerry Browning writes:
The Correct System of Equations for Climate and Weather Models
The CA article is old, do not comment as though current.
https://climateaudit.org/2016/02/27/gerry-browning-in-memory-of-professor-heinz-kreiss/
Post by Tim
Tallbloke's Talkshop 
Hydrostatic equilibrium is a fact, and the tropopause lifted and descends depending on the pressure.
The large scale motions of the atmosphere are in approximate hydrostatic balance. However the primitive equations that assume exact hydrostatic balance are not the system that accurately describes the large scale motions of the atmosphere to first order. In fact they are mathematically ill posed for both the initial value and initial/boundary value problems. I recommend looking at the following link to see how bad the primitive equations are and how numerical trickery is being used to uncouple the noise caused by Richardson’s equation from the large scale geopotential.
https://drive.google.com/file/d/0B-WyFx7Wk5zLR0RHSG5velgtVkk/view?usp=sharing
IIRC this harks back to Essex’s seminal papers which are essentially about tending to something exact but never is exact, always an approximation. This kind of thing is unstable.
A long time ago I dabbled with real world modelling / prediction / etc. as part of doing things. When practical computers arrived I had a lot to learn. This very much included finding out the hard way on what is rational.
The upshot of this is not knowing the detail of or having experience of what these youngsters are doing with their climatic or weather toys but I don’t need to know, won’t work for rather obvious reasons they don’t get.
The correct system that describes the large scale atmospheric equations to first order of accuracy
is well posed for both the initial value and initial/boundary value problems as is the multiscale hyperbolic system introduced by Browning and Kreiss (2002). The multiscale system has also been proved to accurately describe the large scale and mesoscale atmospheric motions. This cannot be done for the hydrostatic system.
Jerry
Browning says;
hydrostatic balance, i.e., balance between the vertical pressure gradient and gravitational force,
There is no hydrostatic balance
The vertical pressure gradient of the atmosphere does not produce a force.
The horizontal pressure gradients produce wind. That is air moves to try to equalize pressure
Vertically the pressure gradient, the lapse rate, is stable.. There are not large vertical movements of air, wind, trying to to equalize vertical pressure differences.
There is no vertical pressure gradient force
Also the atmosphere does not cause downward gravitational force. This is proved by the zero reading on a force meter placed on a solid flat horizontal surface.
No vertical upward pressure gradient force
No downward gravitational force
Therefore no hydrostatic balance
ren says:
July 8, 2016 at 4:51 pm
Hydrostatic equilibrium is a fact, and the tropopause lifted and descends depending on the pressure
Please explain how “the tropopause lifted and descends depending on the pressure” is evidence for hydrostatic equilibrium