|Title||A multivariate treatment of bias for sequential data assimilation: application to the tropical oceans.|
|Publication Type||Technical memorandum|
|Secondary Title||ECMWF Technical Memoranda|
|Authors||Alonso-Balmaseda, M, Dee, DP, Vidard, A, Anderson, DLT|
|Place Published||Shinfield Park, Reading|
This paper discusses the problems arising from the presence of system bias in ocean data assimilation, taking examples from the ocean analysis systems used at ECMWF for seasonal forecasting. It is shown that the presence of system bias can be damaging for the representation of interannual variability due to the non stationary nature of the observing system. It is also shown that some of the bias in the eastern Paci?c is caused by the data assimilation process, and it seems to be linked to the existence of a spurious vertical circulation. An explicit multivariate algorithm for treatment of bias in sequential data assimilation has been formulated using the framework developed by Dee and DaSilva. The generalised scheme allows the multivariate constraints for the bias to be different from those for the state vector error covariance matrices, and in particular it encompasses the pressure gradient correction scheme of Bell et al. as a special case. A simple model for the time evolution of the bias is also provided. The algorithm has been implemented in the ECMWF ocean data assimilation system. Several ocean reanalysis experiments have been conducted to evaluate the sensitivity of the results to the choice of multivariate formulations and to the choice of time parameters. Confirming previous studies, results show that the pressure correction scheme is successful in reducing the bias in temperature while also reducing the error in the velocity field. Direct bias correction of only the temperature field can consistently reduce the mean assimilation increment, but at the expense of increasing the error in the velocity field. Results also show a large sensitivity to the choice of the parameters controlling the time evolution of the bias.