Multivariate Error Covariance Estimates by Monte Carlo Simulation for Assimilation Studies in the Pacific Ocean

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–observation differences. In most practical applications, simple covariances are usually prescribed. Rarely are cross covariances between different model variables used. Here a comparison is made between a univariate optimal interpolation (UOI) scheme and a multivariate OI algorithm (MvOI) in the assimilation of ocean temperature profiles. In the UOI case only temperature is updated using a Gaussian covariance function. In the MvOI, salinity, zonal, and meridional velocities as well as temperature are updated using an empirically estimated multivariate covariance matrix. Earlier studies have shown that a univariate OI has a detrimental effect on the salinity and velocity fields of the model. Apparently, in a sequential framework it is important to analyze temperature and salinity together. For the MvOI an estimate of the forecast error statistics is made by Monte Carlo techniques from an ensemble of model forecasts. An important advantage of using an ensemble of ocean states is that it provides a natural way to estimate cross covariances between the fields of different physical variables constituting the model-state vector, at the same time incorporating the model’s dynamical and thermodynamical constraints as well as the effects of physical boundaries. Only temperature observations from the Tropical Atmosphere–Ocean array have been assimilated in this study. To investigate the efficacy of the multivariate scheme, two data assimilation experiments are validated with a large independent set of recently published subsurface observations of salinity, zonal velocity, and temperature. For reference, a control run with no data assimilation is used to check how the data assimilation affects systematic model errors. While the performance of the UOI and MvOI is similar with respect to the temperature field, the salinity and velocity fields are greatly improved when the multivariate correction is used, as is evident from the analyses of the rms differences between these fields and independent observations. The MvOI assimilation is found to improve upon the control run in generating water masses with properties close to the observed, while the UOI fails to maintain the temperature and salinity structure.