In this chapter, we examine similarities and differences of the two information measures used in the current state-of-the-art data assimilation methods, the Degrees of Freedom (DOF) for signal and the E dimension. We evaluate these measures using simple arbitrary examples and a realistic ensemble data assimilation algorithm, including a complex atmospheric model and real observations.
The results indicate that the E dimension is more sensitive to the model dynamics and less sensitive to the amount and quality of the observations, while the opposite is true for the DOF for signal. These differences have to be taken into account when comparing the results of different data assimilation methods.
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Zupanski, D. (2009). Information Measures in Ensemble Data Assimilation. In: Park, S.K., Xu, L. (eds) Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71056-1_4
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