Assimilation of oceanographic observations with estimates of vertical background‐error covariances by a Bayesian hierarchical model

A new method to estimate the vertical part of the background-error covariance matrix for an ocean variational data assimilation system is presented and tested in the Mediterranean operational daily analysis system. The operational, seasonally varying error covariances are compared with high-frequency estimates from a Bayesian Hierarchical Model (BHM) which estimates distributions for the vertical error covariances from two data-stage inputs: model anomalies and differences between model background and observations, i.e. so-called misfits. It is found that the posterior mean BHM-error covariance estimates that vary on 5-day time-scales reduce the misfits root mean square of the analysis vertical profiles of temperature and salinity by 10-20% versus analyses arising from covariances that vary on seasonal time-scales or those from the BHM given only model anomalies as data stage inputs.