Open-Ocean Modeling as an Inverse Problem: The Primitive Equations

The ill-posedness of regional primitive equation models is examined, using a regional shallow-water model. The ill-posedness is resolved by reformulation as a least-squares inverse problem, in the sense that the Euler-Lagrange or variational boundary conditions ensure unique solutions for the linearized problem. The inverses for nonlinear problems are calculated using variants of simulated annealing and massively parallel computing. Simple experiments compare the relative merits of pointwise measurements and path-integrated measurements in compensating for bad boundary data. Error statistics are calculated, despite the large dimension of the state space.