Generalized inversion of a global numerical weather prediction model

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We construct the generalized inverse of a global numerical weather prediction (NWP) model, in order to prepare initial conditions for the model at time “t=0 hrs”. The inverse finds a weighted, least-squares best-fit to the dynamics for −24<t<0, to the previous initial condition att=−24, and to data att=−24,t=−18,t=−12 andt=0. That is, the inverse is a weak-constraint, four-dimensional variational assimilation scheme. The best-fit is found by solving the nonlinear Euler-Lagrange (EL) equations which determine the local extrema of a penalty functional. The latter is quadratic in the dynamical, initial and data residuals. The EL equations are solved using iterated representer expansions. The technique yields optimal conditioning of the very large minimization problem, which has ∼109 hydrodynamical and thermodynamical variables defined on a 4-dimensional, space-time grid.