Optimization of a Hurricane Track Forecast Model with the Adjoint Model Equations

Abstract

The method of model fitting, or ?adjoint method,? is tested in a barotropic hurricane track forecast model. The model vorticity field at the beginning of an assimilation period is adjusted to minimize a cost function that is defined as the squared difference between the model vorticity and the vorticity from a sequence of analyses separated by 12 h. After the cost function is minimized, the model vortex clearly follows the observed storm track during the assimilation period, indicating that information about the past track of the storm is being included in the model solution. Track forecasts using the assimilation procedure are compared with control forecasts where the model is initialized with a single analysis at the end of the assimilation period. Results from a series of 18 forecasts for Hurricane Hugo (1989) show that with a 12-h assimilation period the average track forecast errors are smaller than those of the control forecasts out to about 48 h. The forecast errors using a 24-h assimilation period are larger than the errors with a 12-h assimilation period. The method described by Derber in which a forcing term that minimizes the cost function is added to the vorticity equation is applied to extend the length of the assimilation period. The forcing function has very localized extrema in the vicinity of the vortex because the scale of the vortex is comparable with the distance that the vortex moves during the assimilation period. This localized forcing interferes with the subsequent motion of the storm during the forecast period. The magnitude of the localized forcing is reduced if the vorticity at the beginning of the assimilation period is first adjusted, and then the forcing term is added to further reduce the cost function. When the combined procedure is used, the average track errors are smaller than the errors in the control simulations out to 72 h. Forecasts from tour additional storms from the 1989 Atlantic hurricane season are also presented. In two of these cases, the assimilation degrades the control forecasts. The degradation appears to be related to errors in the operational estimates of the storm positions and to poor first-guess fields used in the analyses.