Data Assimilation for a Coupled Ocean–Atmosphere Model. Part I: Sequential State Estimation

Abstract

The assimilation problem for the coupled ocean?atmosphere system in the tropical Pacific is investigated using an advanced sequential estimator, the extended Kalman filter (EKF). The intermediate coupled model used in this study consists of an upper-ocean model and a steady-state atmospheric response to it. Model errors arise from the uncertainty in atmospheric wind stress. Data assimilation is applied in this idealized context to produce a time-continuous, dynamically consistent description of the model's El Niño?Southern Oscillation, based on incomplete and inaccurate observations. This study has two parts: Part I (the present paper) deals with state estimation for the coupled system, assuming that model parameters are correct, while Part II will deal with simultaneous state and parameter estimation. The dynamical structure of forecast errors is estimated sequentially using a linearized Kalman filter and compared with that of an uncoupled ocean model. The coupling produces large changes in the structure of the error-correlation field. For example, error correlations with opposite signs in the western and eastern part of the model basin are caused by wind stress feedbacks. The full EKF method is used to assimilate various model-generated synthetic oceanic datasets into the coupled model in an identical-twin framework. The assimilated datasets include the sea surface temperature and a combination of wave velocities and thermocline depth anomaly. With the EKF, the model's forecast-assimilation cycle is able to estimate correctly the phase and amplitude of the basic ENSO oscillation while using very few observations. This includes a set of observations that only cover a single meridional section of the ocean, preferably in the eastern basin.