One of the most difficult aspects of ocean state estimation is the prescription of the model forecast error covariances. The paucity of ocean observations limits our ability to estimate the covariance structures from model-data differences. In most practical applications, simple covariances are usually prescribed. Rarely are cross-covariances between different model variables used. Consistent with other groups that conduct seasonal forecasts with coupled models, the NASA Seasonal-to-Interannual (SI) Prediction Project (NSIPP) currently assumes that the model forecast error has a Gaussian spatial structure, and only the temperature field is analyzed in a univariate optimal interpolation (OI). However, it has been found that the univariate OI has a detrimental effect on the salinity and velocity fields of the model for assimilation cycles longer than 2 months.

A multivariate OI algorithm, which allows for salinity and current fields to be corrected as a result of the temperature assimilation has been implemented. The multivariate algorithm uses anisotropic, inhomogeneous model error covariances obtained by a Monte Carlo simulation. An ensemble of ocean states was generated by forcing the ocean model with an ensemble of air-sea fluxes reflecting the internal atmospheric variability. In all, en ensemble of 160 members was constructed. This matrix is naturally represented by a set of eofs, fewer in number than the ensemble size, allowing for an efficient analysis of its properties. The multivariate OI outperforms the univariate assimilation. The robustness of the empirical forecast error covariance estimate will be discussed. In particular, no significant seasonal dependence was found in the dominant covariance structures.