The benefits of correlated observation errors for small scales

In operational data assimilation, observation errors are generally assumed to be uncorrelated, though some observations, such as satellite data, have correlated errors. We show that, if observation-error correlations are correctly accounted for, an observing instrument with spatially correlated errors is better able to resolve small scales than an instrument with the same error variance and uncorrelated errors. We explore the disadvantages of falsely assuming uncorrelated observation errors, investigating two methods of compensating for such mis-specification by either observation-error inflation or data thinning. We identify scenarios in which correctly specifying the covariance reduces small-scale error by over 99%.