The generalized inverse of a nonlinear quasigeostrophic ocean circulation model

Abstract The generalized inverse is constructed for a nonlinear, single-layer quasigeostrophic model, together with initial conditions and a finite number of interior data. With the exception of doubly Periodic boundary condition all constraints are weak. The inverse minimizes a penalty functional that is quadratic in the errors in prior estimates of the model forcing, the initial conditions, and the measurements. The quadratic form consists of the inverses of the prior error covariances. The nonlinear Euler-Lagrange equations are solved iteratively. Each iterate is a linear Euler-Lagrange problem, which in turn is solved in terms of a prior streamfunction estimate, plus a finite-linear combination of representers (one for each linear measurement functional). The sequence of inverse streamfunction estimates is bounded and so has at least one limit Point. The sequence of representer matrices is uniformly positive definite and so the limiting inverse is a minimum, rather than simply an extremum of the penal...