TROPICAL CYCLONE PREDICTION USING A BAROTROPIC MODEL INITIALIZED BY AGENERALIZED INVERSE METHOD

A nested, nondivergent barotropic numerical weather prediction model f or forecasting tropical cyclone motion out to 48 h is initialized at t ime t = 0 by assimilating data from the preceding 24 h. The assimilati on scheme finds the generalized inverse of the model and data for -24 less-than-or-equal-to t less-than-or-equal-to 0. That is, the inverse estimate of the streamfunction is a weighted least-squares best fit to the initial conditions at t = -24, to the data at t = -12 and t = 0, and to the dynamics and the boundary conditions in the interval -24 le ss-than-or-equal-to t less-than-or-equal-to 0. In particular, the dyna mics are imposed only as a weak constraint. The inverse estimate satis fies the Euler-Lagrange equations for a least-squares penalty function al; these nonlinear equations are solved using an iterative technique that yields a sequence of linear Euler-Lagrange equations. A represent er expansion produces explicit expressions for the reduced penalty fun ctional, which may be shown to be a chi2 variable with as many degrees of freedom as there are data. The representer expansion also yields e xpressions for the posterior covariance of the various residuals. The inverse method was tested on ten cases from four different tropical cy clones observed in the South China Sea during the 1990 Tropical Cyclon e Motion Program (TCM-90). Predictions of cyclone tracks out to 48 h w ere compared with the Australian Weather Bureau's operational barotrop ic model which has no data assimilation procedure, and with a simple n udging scheme. In the latter, a model integration from t = -24 to t = 0 is nudged toward target analyses at t = -12 and at t = 0. Compared w ith the no-data assimilation and nudging forecasts, the inverse method yielded reductions in mean track forecast error of about 14% and 10%, respectively, at 24 h, reducing to 10% and 7% at 48 h. The results we re quite consistent, with the inverse method providing the smallest me an position error in all ten cases. In addition, all the numerical pre dictions were compared with a CLIPER (climatology and persistence) sch eme. The inverse scheme yielded the lowest mean errors at all times t = 12, 24, 36, and 48 h, with improvements over CLIPER being 26% at 24 h and 29% at 48 h.