Tropical Cyclone Prediction Using a Barotropic Model Initialized by a Generalized Inverse Method

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Abstract
A nested, nondivergent barotropic numerical weather prediction model for forecasting tropical cyclone motion out to 48 h is initialized at time t = 0 by assimilating data from the preceding 24 h. The assimilation scheme finds the generalized inverse of the model and data for −24 ≤ t ≤ 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 ≤ t ≤ 0. In particular, the dynamics are imposed only as a weak constraint. The inverse estimate satisfies the Euler-Lagrange equations for a least-squares penalty functional; these nonlinear equations are solved using an iterative technique that yields a sequence of linear Euler-Lagrange equations. A representer expansion produces explicit expressions for the reduced penalty functional, which may be shown to be a χ2 variable with as many degrees of freedom as them are data. The represent... Abstract A nested, nondivergent barotropic numerical weather prediction model for forecasting tropical cyclone motion out to 48 h is initialized at time t = 0 by assimilating data from the preceding 24 h. The assimilation scheme finds the generalized inverse of the model and data for −24 ≤ t ≤ 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 ≤ t ≤ 0. In particular, the dynamics are imposed only as a weak constraint. The inverse estimate satisfies the Euler-Lagrange equations for a least-squares penalty functional; these nonlinear equations are solved using an iterative technique that yields a sequence of linear Euler-Lagrange equations. A representer expansion produces explicit expressions for the reduced penalty functional, which may be shown to be a χ2 variable with as many degrees of freedom as them are data. The represent...

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