Ensemble estimation of background-error variances in a three-dimensional variational data assimilation system for the global ocean

This paper studies the sensitivity of global ocean analyses to two flow-dependent formulations of the background-error standard deviations (sigma(b)) for temperature and salinity in a three-dimensional variational data assimilation (3D-Var) system. The first formulation is based on an empirical parameterization of sigma(b) in terms of the vertical gradients of the background temperature and salinity fields, while the second formulation involves a more sophisticated approach that derives sigma(b) from the spread of an ensemble of background states. The ensembles are created by explicitly perturbing both the surface fluxes (wind stress, fresh water and heat) used to force the model and the observations (temperature and salinity profiles) used in the assimilation process. The two formulations are compared in two cycled 3D-Var experiments for the period 1993-2000. In both experiments, the observation-error standard deviations (sigma(o)) are geographically dependent and estimated from a model-data comparison prior to assimilation. An additional 3D-Var experiment that employs the parametrized sigma(b) but a simpler sigma(o) formulation, and a control experiment involving no data assimilation, were also conducted and used for comparison. All 3D-Var experiments produce a significant reduction in the mean and standard deviation of the temperature and salinity innovations compared to those of the control experiment. The largest differences between the two sigma(b) formulations occur in the upper 150 m, where the parametrized sigma(b) are notably larger than the ensemble sigma(b). In this region, the innovation statistics are slightly better for the parametrized sigma(b). Statistical consistency checks indicate that both schemes underestimate sigma(b), the underestimation being stronger with the ensemble formulation. The error growth between cycles, however, is much reduced with the ensemble sigma(b), suggesting that the analyses produced with the ensemble sigma(b) are in better balance than those produced with the parametrized sigma(b). This claim is supported by independent data comparisons involving model fields not directly constrained by the assimilated temperature and salinity profiles. In particular, sea-surface height (SSH) anomalies in the northwest Atlantic and zonal velocities in the equatorial Pacific are clearly better with the ensemble sigma(b) than with the parametrized sigma(b). Results also show that while some aspects of those variables are improved with data assimilation (SSH anomalies and currents in the central and eastern Pacific), other aspects are degraded (SSH anomalies in the northwest Atlantic, currents in the western Pacific). Areas for improving the ensemble method and for making better use of the ensemble information are discussed. Copyright (C) 2009 Royal Meteorological Society