STATISTICAL DYNAMICAL METHODS OF ENSEMBLE PREDICTION AND DATA ASSIMILATION DURING BLOCKING

In this chapter we discuss the application of inhomogeneous statistical closure models to ensemble prediction and data assimilation. The quasi-diagonal direct; interaction approximation (QDIA) represents a tractable closure for investigating general turbulent geophysical fluids. The QDIA may also he used to examine ensemble prediction methods and to develop novel statistical dynamical data assimilation methods. Using the QDIA and the method of bred perturbations we first examine the role of non-Gaussian terms in ensemble prediction. We demonstrate both the importance of the cumulative contribution of non-Gaussian correlations to the evolved error tendency as well as the role of the covariances in the small scale instantaneous errors, thereby extending the work of Epstein(13) and Fleming(19,20) to models without any explicit cumulant discard hypothesis. Further, the QDIA closure is shown to be valid for both strongly non-Gaussian and strongly inhomogeneous flows. The formal similarities between statistical turbulence theory and ensemble averaged data assimilation techniques leads naturally to the development of closure based spectral data assimilation techniques. In the second part, of this chapter we compare ensemble averaged Kalman (stochastic), square root (deterministic) and statistical dynamical data assimilation methodologies, examining the use of random and flow correlated observational error perturbations and issues related to sampling error. Forecast error covariances, typically under-predicted in the ensemble Kalman filter (EnKF) are shown to occur largely due to sampling error resulting from the traditional use of random observational error perturbations. Flow correlated observational errors are shown to be demonstrably preferable For generating forecast; error perturbations in order to correctly capture error evolution. Atmospheric regime transitions are often associated with the formation of large scale coherent structures, commonly known as blocks. These blocking events are typically associated with rapidly growing flow instabilities; that lead to a loss of predictability and enhanced error growth. Results from the QDIA statistical closure and ensemble averaged direct numerical simulations are presented specifically for Northern Hemisphere flow during the formation of it series of large and persistent blocking events between mid-October and mid-November 1979.