Hi Jonathan
... the beauty of physics ... and for once I have time to discuss ...
> The fact that the model is Eulerian doesn't mean you can't calculate
> Lagrangian derivatives.
Agreed, but they are only defined at grid points, that's Eulerian to me ...
> Omega is Dp/Dt, not partial dp/dt. I think you'd
> expect Dp/Dt calculated in an Eulerian model to be comparable with Dp/Dt
> following the parcels in a Lagrangian model.
The reality is that all velocities are bigD/Dt, and that's why we have so much
fun changing coordinate systems. The interesting thing about Lagrangian
thinking is that Eulerian models explicitly address the Lagrangian terms in
their equations ... but they're still Eulerian in formulation.
Compare with isentropic coordinates, where we can make statements about
Lagrangian behaviour on isentropic surfaces, we claim that the coordinates
are partly Lagrangian, but when we calculate them in a model using
differencing schemes that require us to evaluate the derivatives by using
Eulerian coordinates, they're Eulerian quantities.
> It's the same physical
> quantity, though differently computed, so should have the same standard
> name, I'd say. We shouldn't confuse the quantity itself with the method
> used to obtain it.
Fair comment, but see above.
> > velocity is simply rate of change of
> > displacement with time. In these coordinates, displacement is measured in
> > pressure, and so the words "vertical velocity in pressure coordinates"
> > would seem to cover it. The relationship of the coordinate system to the
> > horizontal is irrelevant isn't it?
>
> I agree that "vertical velocity in pressure coordinates" is a helpful way
> to introduce what the quantity is used for in a discussion of atmospheric
> dynamics, but I'm less happy with it as a choice of a standard name because
> (a) Pa s-1 is not the normal use of the word "velocity". Of course we may
> have other "kinds" of velocity such as "angular_velocity", but the phrase
> "vertical velocity" means m s-1 to me.
Velocity has a clear and unambiguous definition, it's
the rate of change of displacement with time. Displacement has inherent
coordinates. For some people velocity is mph ... and we get around this by
defining units ... so with this thing (whatever we call it), we have the
units to help us, putting the extra information in the standard name is
redundant.
> (b) It's not vertical, so this is an inaccurate name.
Hmmm ... if we take any elementary textbook, Holton, 3rd edition for example,
page 21 ... section 1.6.2 ... pressure as a vertical coordinate.
I don't think we should argue with textbooks unless they are fundamentally
wrong, and I think as physicists we all know what we mean by vertical
coordinates.
(see also Dtheta/Dt expressed as and called an "isentropic 'vertical
velocity'" where the inner quotes are David's, in AHL, Middle Atmosphere
Dynamics, p138).
Anyway, this argument could apply to u and v too .. they're not "true"
"horizontal" velocities in many coordinate systems ...
> (c) It doesn't say what its sign convention is.
It does. Dp/Dt has a sign convention ... and it's unambiguous.
> (d) It could be understood as meaning w(x,y,p) i.e. that "in pressure
> coordinates" distinguished w(x,y,p) from w(x,y,z). That would not be
> something we would include in a standard name, but I think it's a possible
> misinterpretation we should avoid.
I think this is a very fair point. However, there are plenty of aliases which
show what is meant (not least, omega).
> What if we just call it omega instead. :-) (joke - I think)
:-) :-)
I really think we are trying to put too much information in one box (the
standard name). I think standard bloat is a real issue to be careful of.
Don't we have a description field for the extended explanation?
Cheers,
Bryan
--
Bryan Lawrence, Head NCAS/British Atmospheric Data Centre
web: www.badc.nerc.ac.uk phone: +44 1235 445012
CLRC: Rutherford Appleton Laboratory, Chilton, Didcot, OX110QX, UK
Received on Wed Feb 11 2004 - 05:23:30 GMT
