Hmmm. I read your message too quickly.There IS a problem, but it is not with d/dy. MFC showed me the discussion of this point in a "really nice book" (Synoptic-dynamic meteorology in mid-latitudes. Bluestein, 1992). Bluestein notes that (in the northern hemisphere) a uniform west wind (or eastward current) is parallel to latitude circles, and therefore rotating (in this case dv/dx.gt.0). A uniform south wind (northward current) is converging and has du/dx.lt.0. However "since latitude circles are truly parallel to each other, there is no correction necessary for du/dy or dv/dy". He therefore finds the relative vorticity:
zeta = dv/dx - du/dy + (u/a)tan(phi) , where a is the radius of the earth and phi the latitude.
The divergence is: Div(u) = du/dx + dv/dy - (v/a)tan(phi)And note that the correction terms will be very small except near the poles.
Am I still missing something? Billy On Jun 25, 2008, at 3:05 PM, Ryo Furue wrote:
Hi Billy, Thanks for your highest praise! | Amazingly, I think Ryo is wrong about the sphere/cosine business. If | (u,v) is given on a lat/lon grid, then Ferret will do this | automatically. But, I don't think Ferret distinguishes vectors from scalars when it takes derivatives. Derivatives of vectors are different from those of scalars. Look at my formula again: d(u cos(phi))/dy u[y=@DDC] would give you du/dy, which isn't what we want, right? Or would Ferret somehow figure out that u is an x-component of a vector and multiply the cosine factor before taking the derivative? Cheers, Ryo