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Data assimilation means to find an (approximate) trajectory of a dynamical model that (approximately) matches a given set of observations. A direct evaluation of the trajectory against the available observations is likely to yield a too optimistic view of performance, since the observations were already used to find the solution. A possible remedy is presented which simply consists of estimating that optimism, thereby giving a more realistic picture of the "out of sample" performance. Our approach is inspired by methods from statistical learning employed for model selection and assessment purposes in statistics. Applying similar ideas to data assimilation algorithms yields an operationally viable means of assessment. The approach can be used to improve the performance of models or the data assimilation itself. This is illustrated by optimising the feedback gain for data assimilation employing linear feedback.

Assessing the performance of data assimilation algorithms which employ linear error feedback