A Study of 4 D-Var and EnKF Coupling 1 Parameter-Estimation with a Simple Coupled 2 System

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

34 35耦合参数估计（CPE）利用一种介质中的观测来估计其他介质中的参数，通过利用不同介质中变量之间的协变关系，可能会提高耦合系统中估计参数的一致性和连贯性。然而，由于不同介质中流动变化的特征时间尺度不同，准确评估不同介质的协变强度通常很困难，因此CPE面临许多挑战。本研究通过一个表征多时间尺度介质相互作用的简单耦合系统，探讨了四维变分分析（4D - Var）和集合卡尔曼滤波（EnKF）用于CPE的可行性。研究发现，虽然一般来说4D - Var CPE在很大程度上取决于最小化时间窗口的长度，但适当的膨胀方案是EnKF CPE成功的关键。此外，虽然两种算法在利用高频流动特征介质中的观测来估计慢变介质的参数时都表现良好，但由于在滤波中使用了纯线性回归，4D - Var CPE比EnKF CPE更有能力利用慢变介质中的观测来估计快变介质的参数。这些简单的模型结果为通过将耦合的大气环流模式与现代气候观测系统相结合来改进气候估计和预测提供了一些见解。