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?

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

What parameters?
Existing scheme (pragmatic/engineering approach)
These are orthogonal but not uncorrelated Proposed scheme (physics approach)

Why not assimilate using only the leading parameter?

What grid staggering for new parameters?
