Add diagnostic for zonal and meridional transports

[navidcy]

Zonal or meridional averages of mass/volume transports are common diagnostics (eg for meridional overturning circulation).

At the moment, when a grid cell's local x and y directions don't align with the constant latitude/longitude we don't have a straightforward way of outputting the transport along the constant latitude or longitude. To compute zonal or meridional averages of vector quantities we need to know the local angle of the grid cell (angle the forms with the grid cell's line of constant x compared to the North-South) and then form the linear combination of the x- and y-components of the quantity in question. This is relevant in the Arctic region on a tripolar grid.

(A documentation of this very same issue together with some diagrams to explain at COSIMA/cosima-recipes#510.)

It would be nice to implement a diagnostic for that.

[stajouri]

Yes I agree. I came across this issue recently for computing the AMOC in the North Atlantic Ocean in NEMO. It is not straightforward to compute the truly meridional AMOC because the local angle of the grid cell is not saved as an output.
I found this function rotate_vector for the NEMO model: https://github.com/knaughten/nemo_python/blob/22e1d3e4ca7d4ad2cc066e4aa1cadf889c9b13d3/utils.py#L582
Then it is possible to use the rotated vector to compute the AMOC.

This is specific to NEMO but can maybe be of some inspiration to generalize/extent to other curvilinear grids.

[glwagner]

That's probably the analogue of the intrinsic_vector / extrinsic_vector abstraction we have in Oceananigans

[glwagner]

The only thing that is a bit confusing to me is that the result still must be approximate. If we want to compute the exact transport across planes that pierce the grid (eg do not correspond with grid lines), we may need to do a bit more than rotate vectors right?

[glwagner]

Maybe all we need is to conservatively regrid the transport on to a LatitudeLongitudeGrid, and then rotated the regridded components?

[taimoorsohail]

FYI - conservative regridding has been implemented for tracers (not transports yet) in CliMA/Oceananigans.jl#4782