Data Assimilation for a Coupled Ocean-Atmosphere Model. Part II: Parameter Estimation

The parameter estimation 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 (ICM) used in this paper consists of a prognostic upper-ocean model and a diagnostic atmospheric model. Model errors arise from the uncertainty in atmospheric wind stress. First, the state and parameters are estimated simultaneously in an identical-twin framework, based on incomplete and inaccurate observations of the model state. Two parameters are estimated by including them into an augmented state vector. Modelgenerated oceanic data sets are assimilated to produce a time-continuous, dynamically consistent description of the model’s El Niño/Southern Oscillation. State estimation without correcting erroneous parameter values still permits recovering the true state to a certain extent, depending on the quality and accuracy of the observations, and the size of the discrepancy in the parameters. Estimating both state and parameter values simultaneously, though, produces much better results. Next, assimilating real sea surface temperatures observations from the Tropical Pacific for a 30-year period (1975–2004) to estimate both the state and parameters by the EKF method helps track the observations better, even when the ICM is not capable of simulating all the details of the observed state. Furthermore, unobserved ocean variables, such as zonal currents, are improved when model parameters are estimated. A key advantage of using this “augmented-state” approach is that the incremental cost of applying the EKF to joint state-and-parameter estimation is small compared to the cost of state estimation alone. This approach can be easily generalized to various reduced-state approximations of the EKF. 2