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Native wind transport for LAM domains #594

Description

@thomasmelvin

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Brief description

Transport the wind components in their native W2 space for regional & Cartesian domains

Further details of the issue.

The current transport scheme for wind fields in gungho averages the fields from W2 (face centres) to W3 (cell centres) and then transports them using the existing scalar transport scheme. Additionally, as part of the projection from W2 to W3 the wind components are computed in the geocentric (X,Y,Z) coordinate system which may not (and generally isn't) aligned with the model mesh. An upshot of this is that the "vertical" and "horizontal" wind components are combined before the transport and then backed out again after the transport.

During testing of RAL and idealised LAM domains (RCE & CBL experiments) it was found that lfric showed a distinctive uptick in the energy spectra of the vertical wind at the grid scale. This was theorised to be caused by the averaging of the winds to W3 points as part of the transport scheme. This means that any grid scale noise in the wind will not be seen by the transport scheme and so it will not damp the noise.

The solution is to transport the wind components on their native W2 points. This is done by using the existing Semi-Lagrangian scheme transport scheme. Two additional points to the implementation are that:

  1. The "vertical" W2 component is modified before and after transport so that the transported component is parallel to gravity (instead of normal to cell faces). This means there is no change in direction of this component in a model column over orography as the model levels flatten out.
  2. In spherical domains a rotation matrix is applied to the transported wind increments to account for the change in direction of basis vectors over the region of transport.

Implementing this scheme greatly reduces the grid scale noise seen in the energy spectra and was done at https://code.metoffice.gov.uk/trac/lfric_apps/log/main/branches/dev/thomasmelvin/git_migration_native_w2_sl for testing in ral configurations and will be targeted for lfric_apps v3.3

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