diffZF

differentiates a variable of (x,y,z) by projecting onto the F-modes, differentiating, and transforming back to (x,y,z)

---

Declaration

 uz = diffZF(u)

Parameters

• u variable with dimensions $(x,y,z)$

Returns

• uz differentiated variable with dimensions $(x,y,z)$

Discussion

Each subclass implements this operation differently, depending on the vertical modes being used.

For hydrostatic vertical modes with a rigid-lid and zero buoyancy anomaly,

$${\partial }_{z}u=-\frac{1}{g}{N}^2(z){\mathcal{G}}^{-1}\left[\mathcal{F}\left[u\right]\right]$$

where we’ve used the same notation as defined for the discrete transformations.