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?

• (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 ).

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

This problem is much better conditioned.

But, this can't be done directly

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?