Comparison of hybrid four-dimensional data assimilation methods with and without the tangent linear and adjoint models for predicting the life cycle of Hurricane Karl (2010)

Two four-dimensional hybrid data assimilation systems based on the Weather Research and Forecasting (WRF) Model are applied over the life cycle of Hurricane Karl (2010). One method uses a mix of ensemble- and climate-based background error covariance in a four-dimensional variational data assimilation (4DVar) system that uses an adjoint model to assimilate observations over a time window (denoted E4DVar). The second method approximates the function of linearized models in 4DVar with perturbations generated from an ensemble forecast using the full nonlinear model (denoted 4DEnVar). Ensemble perturbations in 4DEnVar provide a four-dimensional covariance, which is combined with a static climate-based covariance for performing the data assimilation. In cycling data assimilation experiments, analyses produced by both methods provide more accurate intensity forecasts than E3DVar, owing mostly to a better representation of moisture near the developing storm. Despite providing a computationally efficient alternative to E4DVar, predictions made from 4DEnVar analyses are less accurate than E4DVar for the tested case study. Numerical experiments using identical background error statistics in both schemes reveal differences in the mesoscale structure of the developing storm, which are suspected to be responsible for this result. In particular, 4DEnVar analyses contain a less intense inner-core circulation and lower column relative humidity than E4DVar at analysis times closest to Karl's genesis, which lead to a persistent slow bias in intensifying the storm. These results suggest errors introduced in the linearization of the model for E4DVar may be less severe than errors introduced by the localization of time covariances. This study provides the first comparison of hybrid E4DVar and 4DEnVar for a tropical cyclone application.