Re: Ferret: Vector plots of velocity on a C-grid

[Ryo Furue <furue@xxxxxxxxxx>]

Hi Billy,

| I have OGCM output on a C-grid. The temperature and velocity
| components are on a staggered grid structure. A single gridbox looks
| like:
| 
|   v  
| u T u 
|   v  
| 
| where the u-values are the currents in/out the east-west sides of the
| box, and the v-values out the north-south, and T is the temperature
| value defined in the center of the box. All these are on the same
| vertical level. 
[...]
| Anybody have a good idea how to do this as correctly as possible?

It depends on the definition of "correctly", but the following is
"correct" in terms of conservation of volume transport.

First, for a notational convenience, I redraw your grid as

            vm(j)
   um(i-1)  T        um(i)
            vm(j-1)

Index i is in the x-direction, and j in the y-direction.

Nest, let us regrid your velocity field onto the B-grid:

    uv(i-1,j)     uv(i,j)
                T
    uv(i-1,j-1)   uv(i,j-1)

uv's represent the corners of the T box, and the new u and v are
defined on these uv points.  Now, let us define the new velocity
components such that

    [u(i-1,j-1) + u(i-1,j)]/2 == um(i-1)
    [u(i,  j-1) + u(i,  j)]/2 == um(i)

    [v(i-1,j)   + v(i,j)  ]/2 == vm(j)
    [v(i-1,j-1) + v(i,j-1)]/2 == vm(j-1)

That is, um is the average of the u's to the south and north.
and vm is the average of the v's to the west and east.

In fact, the model I use employs the B-grid.  Although this model
uses the B-grid, the continuity equation is expressed on the C-grid,
as

    [um(i) - um(i-1)]/dx  + [vm(j) - vm(j-1)]/dy
  + [w(up) - w(down)]/dz = 0,

where um's and vm's are computed from u's and v's using the
relationship shown above.

I guess that your model uses a similar expression for
the continuity equation using um's and vm's.  Then, regridding
your um's and vm's onto the B-grid guarrantees the conservation
of volume transport.

One concern is land points.  If your land boxes coincide with T-boxes
(as they do in the model I use), then the new u and v should be
defined as zero on the vertices of the land boxes.

Hope this helps,
Ryo