# Derivatives

```Hello,

I am having a hard time understanding how Ferret calculates the center
difference (@ddc) derivatives for data with lat/lon grids.  For example,
as a test I created a solid body wind field cdf file for ferret to
ingest (solid body w.r.t a spherical earth).  I then hand caluclated
vertical vorticity at 20s to ensure the field was truly solid body  by
using the centered diff formula for spherical coordinates:

-1/[r*cos(v)*[U(v-1)*cos(v-1)-U(v+1)*cos(v+1)]/[(v-1)-(v+1)]

where r is the radius of the earth

v is the latitude of angle, in this case 20s (except converted to

U(v-1) is the zonal velocity at the v-1, or 19s latitude etc.

This matched the answer given by theory: f=2*omega*sin(v)

When I ingest the data into ferret, I get constant vorticity at each
latitude line which is expected.  However, it appears Ferret leaves off
the cos factors on the zonal velocity.  Why does ferret do this?  Does
it depend on how you display the fields onto a background map, ie if use
a curvi-linear display of data it will add the cosines in but if in a
"map flat" display" it won't??  Would greatly appreciate any comments on
this problem (hopefully, you understand what I am even talking about).

Scocks
Texas A&M University

```