GENERALIZED INVERSION OF A GLOBAL NUMERICAL WEATHER PREDICTION MODEL

We construct the generalized inverse of a global numerical weather pre diction (NWP) model, in order to prepare initial conditions for the mo del 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 co ndition 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 vari ational assimilation scheme. The best-fit is found by solving the nonl inear Euler-Lagrange (EL) equations which determine the local extrema of a penalty functional. The latter is quadratic in the dynamical, ini tial and data residuals. The EL equations are solved using iterated re presenter expansions. The technique yields optimal conditioning of the very large minimization problem, which has similar to 10(9) hydrodyna mical and thermodynamical variables defined on a 4-dimensional, space- time grid. In addition to introducing the inverse NWP model, we demons trate it on a medium-sized problem, namely, a study of the impact of r eprocessed cloud track wind observations (RCTWO) from the 1990 Tropica l Cyclone Motion Experiment (TCM-90). The impact is assessed in terms of the improvement of forecasts in the South China Sea at t = + 48 hou rs. The calculation shows that the computations are manageable, the it eration scheme converges, and that the RCTWO have a beneficial impact.