Alison Fowler, University of Reading

The impact of observations with correlated errors: a one dimensional study

Sarah Dance, Joanne Waller


Operational centres are putting effort into estimating correlated observational errors and accounting for them within their data assimilation systems. This advance towards a more optimal assimilation system is expected to improve the accuracy of the analysis and the forecast skill. For a simple one dimensional system, we study how the correlation length scales of the observational error statistics affects the impact the observations can have on the analysis in the theoretical case when the structure of the observation error correlations are known and accounted for perfectly. It is found that observations with increasingly larger error correlation lengthscales provide increasingly more information about smaller scale features and increasingly less information about larger scale features. The total information content of the observations across all scales, as measured by degrees of freedom for signal and mutual information, depends not only on the observation error correlation length but also on the a-priori (background) error correlation length. In general, we see an increase in information content as the observation error correlation length increases, however for large background error correlation length this increase is not monotonic and hence it is possible for observations with correlated errors to provide less information than those with uncorrelated errors. These results can be used to inform the debate as to when using observations with correlated observation errors is beneficial and when it is better to thin the data.

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