On the impact of observation‐error correlations in data assimilation, with application to along‐track altimeter data

Abstract Data assimilation involves estimating the state of a system by combining observations from various sources with a background estimate of the state. The weights given to the observations and background state depend on their specified error covariance matrices. Observation errors are often assumed to be uncorrelated, even though this assumption is inaccurate for many modern datasets such as those from satellite observing systems. As methods allowing for a more realistic representation of observation‐error correlations are emerging, our aim in this article is to provide insight on their expected impact in data assimilation. First, we use a simple idealised system to analyse the effect of observation‐error correlations on the spectral characteristics of the solution. Next, we assess the relevance of these results in a more realistic setting, in which simulated along‐track (nadir) altimeter observations with correlated errors are assimilated in a global ocean model using a three‐dimensional variational assimilation (3D‐Var) method. Correlated observation errors are modelled in the 3D‐Var system using a diffusion operator. When the correlation length‐scale of the observation error is small compared with that of the background error, inflating the observation‐error variances can mitigate most of the negative effects from neglecting the observation‐error correlations. Accounting for observation‐error correlations in this situation still outperforms variance inflation, since it allows small‐scale information in the observations to be extracted more effectively while accelerating the convergence of the minimisation. Conversely, when the correlation length‐scale of the observation error is large compared with that of the background error, the effect of observation‐error correlations cannot be approximated properly with variance inflation. However, the correlation model needs to be constructed carefully to ensure the minimisation problem is adequately conditioned so that a robust solution can be obtained. Practical ways to achieve this are discussed.