an ensemble adjustment kalman filter for data assimilation集合卡尔曼滤波数据同化的调整.pdfVIP

2884 M O N T H L Y W E A T H E R R E V I E W VOLUME 129 An Ensemble Adjustment Kalman Filter for Data Assimilation JEFFREY L. ANDERSON Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey (Manuscript received 29 September 2000, in final form 11 June 2001) ABSTRACT A theory for estimating the probability distribution of the state of a model given a set of observations exists. This nonlinear filtering theory unifies the data assimilation and ensemble generation problem that have been key foci of prediction and predictability research for numerical weather and ocean prediction applications. A new algorithm, referred to as an ensemble adjustment Kalman filter, and the more traditional implementation of the ensemble Kalman filter in which ‘‘perturbed observations’’ are used, are derived as Monte Carlo ap- proximations to the nonlinear filter. Both ensemble Kalman filter methods produce assimilations with small ensemble mean errors while providing reasonable measures of uncertainty in the assimilated variables. The ensemble methods can assimilate observations with a nonlinear relation to model state variables and can also use observations to estimate the value of imprecisely known model parameters. These ensemble filter methods are shown to have significant advantages over four-dimensional variational assimilation in low-order models and scale easily to