A Study of 4D-Var and EnKF Coupling

34 35 Coupling parameter-estimation (CPE) that uses observations in a medium to 36 estimate the parameters in other media may increase the coherence and consistence of 37 estimated parameters in a coupled system, through the uses of co-varying relationship 38 between variables residing in different media. However, accurately evaluating the 39 strength of co-varying of different media is usually difficult due to the different 40 characteristic time scales at which flows vary in different media and thereby many 41 challenges exist for CPE. With a simple coupled system that characterize the interaction 42 of multiple time scale media, this study explores the feasibility of four dimensional 43 variational analysis (4D-Var) and ensemble Kalman filter (EnKF) for CPE. It is found 44 that while the 4D-Var CPE strongly depends on the length of the minimization time 45 window in general, an appropriate inflation scheme is a key for the success of the EnKF 46 CPE. Also, while both algorithms perform well to estimate the parameters of slow47 varying media using the observations in the medium characterized with high-frequency 48 flows, the 4D-Var CPE has more capability than the EnKF CPE to estimate the 49 parameters of quickly-varying media using the observations in slow-varying media due to 50 the use of pure linear regression in filtering. These simple model results provide some 51 insights for improving climate estimation and prediction by combining a coupled general 52 circulation model with the modern climate observing system. 53 54