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Zeng, Yuefei and Janjić, Tijana (2016): Study of conservation laws with the Local Ensemble Transform Kalman Filter. In: Quarterly Journal of the Royal Meteorological Society, Vol. 142, No. 699: pp. 2359-2372

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Numerical discretization schemes have a long history of incorporating the most important conservation properties of the continuous system in order to improve the prediction of the nonlinear flow. The question arises whether data assimilation algorithms should follow a similar approach. To address this issue, we explore the conservation properties during data assimilation using perfect model experiments with a 2D shallow-water model preserving important properties of the true nonlinear flow. The data assimilation scheme used here is the Local Ensemble Transform Kalman Filter with varying observed variables, inflation, localization radius and thinning interval. It is found that, during the assimilation, the total energy of the analysis ensemble mean converges with time towards the nature run value. However, enstrophy, divergence and the energy spectra are strongly affected by the data assimilation settings. Having in mind that the conservation of both the kinetic energy and enstrophy by the momentum advection schemes in the case of non-divergent flow prevents a systematic and unrealistic energy cascade towards the high wave numbers, we test the effects on the prediction depending on the type of error in the initial condition. During the assimilation, we assess the downward nonlinear energy cascade through a scalar, domain-averaged noise measure. We show that the accumulated noise during assimilation and the error of analysis are good indicators of the quality of the prediction.

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