Least squares algorithms for data assimilation require estimates of both background error covariances and observational error covariances. The specification of these errors is an essential part of designing an assimilation system; the relative sizes of these uncertainties determine the extent to which the state variables are drawn toward the observational information. Observational error covariances are typically computed as the sum of measurement/instrumental errors and "representativeness error." In a coarse-resolution ocean general circulation model the errors of representation are the dominant contribution to observational error covariance over large portions of the globe, and the size of these errors will vary by the type of observation and the geographic region. They may also vary from model to model. A straightforward approach for estimating model-dependent, spatially varying observational error variances that are suitable for least squares ocean data assimilating systems is presented here. The author proposes an ensemble-based estimator of the true observational error variance and outlines the assumptions necessary for the estimator to be unbiased. The author also presents the variance (or uncertainty) associated with the estimator under certain conditions. The analytic expressions for the expected value and variance of the estimator are validated with a simple autoregressive model and illustrated for the nominal 1° resolution POP2 global ocean general circulation model.
