diffZG

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

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Declaration

 wz = diffZG(w)

Parameters

• w variable with dimensions \((x,y,z)\)

Returns

• wz 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,

\[\partial_z w = \mathcal{F}^{-1} \left[ \frac{1}{h_j} \mathcal{G}\left[ w \right] \right]\]

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