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Re: [ferret_users] Ocean vertical velocity calculation in z-coordinate



Hi Yangxing,
Sorry for not responding sooner to your previous e-mail. Unless one has an instrument to physically measure vertical velocity, it has to be inferred through a kinematic method (using the mass continuity constraint). For the atmosphere (my study) we use boundary conditions at the lids (surface and tropopause), however there are errors introduced from using the tropopause as the upper lid since it is not truly rigid. You are doing the same thing for the ocean. You should read "Alternative Solutions to the Classical Vertical Velocity Problem" by J.J. O'Brien that I have attached. One can get fancy with a variational technique to minimize the error, but the basic method is the same (using mass continuity constraint). If you are dealing with situations that have appreciable buoyancy you should be using the anelastic form of the mass continuity equation. I use this for deep clouds in the atmosphere and I believe there is a similar type of convection in the ocean, but that is up to your discretion.

Steve



Quoting "william s. kessler" <william.s.kessler@xxxxxxxx>:

When I come on a situation like this I would list some actual numbers in a small region to see what is happening. In this case list u,u [i=@shf:1],u[i=@shf:-1], and v(similar), for your location and time. Do the calculation by hand and see if Ferret is doing what you think it should.

One possibility to check is the z=@iin definition. Try defining wlayer=zbox*conv, then list wlayer[z=@rsum]. Is it the same?

I wonder about your SET REGION command. Is that preventing Ferret from properly computing x=@ddc? In general, SET REGION is a bad thing to do, and almost always unnecessary. You have to remember to CAN REG after, or else this persists in the session, giving unexpected results later. Why not just put the specification x=85w in the plot statement as you have with y=30s? And it is confusing the way you have defined ww with the y-value specified in the definition, but not w. I think if you organize these things better, the problems might become clear.

I.e. omit y in the definition of ww, can reg/all, then

plot/y=30s/x=85w/l=1/z=0:300 ww,w

And find out how SODA calculates w. See if there are subtleties in their estimate, and why they do it that way. There could be a good reason.

Billy K

On 18Dec 2007, at 4:39 PM, yangxing zheng wrote:

Hi,

    Last time, I asked for help in calculating w in
the ocean assuming we have u, v at each level. I
remember some suggest use continuity equation.
However, I try this way, but error is large.

   I just simply do this way (assume rho's effect is
small)

   let conv = (u[x=@ddc] + v[y=@ddc])*(-1.0)
   let w = conv[z=@iin]

  Steve suggests impose boundary condition w = 0 at
the surface(z=0?).

  I test the soda data which provides w data.

set data soda_20x_mon.mc

let div = (-1)*(u[x=@ddc] + v[y=@ddc])
let ww = div[y=30s,z=@iin]

set region/x=85w/l=1
plot ww[z=0:300],w[y=30s,z=0:300]

The figure is attached. w is provided by SODA that is
calculated within the model. ww is of course the
vertical value using ferret.

 Does anyone have idea between the two? Any better
calculation is welcome.


Yangxing


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=======================================================
Stephen R. Guimond
Graduate Research Assistant
Center for Ocean-Atmospheric Prediction Studies (COAPS)
Tallahassee, FL 32304
=======================================================

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