A multivariate treatment of bias for sequential data assimilation: Application to the tropical oceans

This paper discusses the problems arising from the presence of system bias in ocean data assimilation taking examples from the ECMWF ocean reanalysis used for seasonal forecasting. The examples illustrate how in a biased system, the non-stationary nature of the observing system is a handicap for the reliable representation of climate variability. It is also shown how the bias can be aggravated by the assimilation process, as is the case for the temperature bias in the eastern equatorial Pacific, linked to a spurious vertical circulation generated by the data assimilation. A generalized algorithm for treatment of bias in sequential data assimilation has been implemented. The scheme allows the control variables of the bias to be different from those for the state vector. Experiments were conducted to evaluate the sensitivity of the results to the choice of bias variables. Results highlight the importance of the correct choice of variables for the bias: while correcting the bias in the pressure field reduces the bias in temperature and in the velocity field, the direct correction of the bias in the temperature field reduces the temperature bias, but significantly increases the error in the velocity field. Analysis of the error statistics reveals that the bias term is not constant in time, but exhibits large interannual fluctuations. The bias alaorithm has been encralized further to include temporal variations of the bias term. A memory factor is included to allow for the slow variations of the bias, and a prescribed bias term is added to represent errors known a priori. Several experiments have been conducted to illustrate the sensitivity of the results to the time evolution of the bias. Copyright (c) 2007 Royal Meteorological Society.