PV of vertical normal modes

A modified formula for PV2 invlolves a partial orthogonalization between PV1 and PV2. The formulae for PV1 and modified PV2 are:

This modifcation did not orthogonalise sufficiently PV1 and PV2. We try also the following formulae (once more only PV2 has been modified):

This modification still does not give a large difference between the two modes (results below). The two quantities are expected to be orthogonal if:

the vorticity term dominates PV1 and PV2 (which it does), and
the vorticity increment is independent of height (which it is not - see below for global average profiles of vorticity increment).

.	PV missing mode 1	PV missing mode 2
Missing PV modes
.	ratio PV1/PV2	.
Ratio		.
.	Global mean vorticity profile	Global RMS vorticity profile
Vertical profiles

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