The Implementation of Potential Vorticity as a Leading Control Variable in Var.

Ross Bannister, Ian Roulstone, Mike Cullen, Nancy Nichols



Why not use model variables as control parameters?

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  • (in -space) contains elements and cannot be represented explicitly.
  • (in -space) is badly conditioned .



Solution: for variational data assimilation vary weights of the eigenvectors of (instead of components of ).

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diagonal matrix of e.values, columns of are e.functions.

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This problem is much better conditioned.



But, this can't be done directly

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What parameters?

Existing scheme (pragmatic/engineering approach)

Subspace Parameter .
Captures most of the flow
Captures most of the rest of the flow
Captures most of the rest of the flow

These are orthogonal but not uncorrelated

Proposed scheme (physics approach)

Subspace Parameter .
"Balanced" / "slow manifold" ()
Captures most of the rest of the flow
Captures most of the rest of the flow
  • These are orthogonal, but are expected to be only weakly correlated.
  • The new parameters are thought to evolve independently, each occupying a separate region in normal mode space.


Why not assimilate using only the leading parameter?



What grid staggering for new parameters?

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