Generalized inversion of a global numerical weather prediction model

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 at t = - 24, and to data at t = - 24, t = - 18, t = - 12 and t = 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 similar to 10(9) hydrodynamical and thermodynamical variables defined on a 4-dimensional, space-time grid. In addition to introducing the inverse NWP model, we demonstrate it on a medium-sized problem, namely, a study of the impact of reprocessed cloud track wind observations (RCTWO) from the 1990 Tropical Cyclone Motion Experiment (TCM-90). The impact is assessed in terms of the improvement of forecasts in the South China Sea at t = + 48 hours. The calculation shows that the computations are manageable, the iteration scheme converges, and that the RCTWO have a beneficial impact.