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Matthias Sommer and Sebastian Reich

Abstract

Applying concepts of analytical mechanics to numerical discretization techniques for geophysical flows has recently been proposed. So far, mostly the role of the conservation laws for energy- and vorticity-based quantities has been discussed, but recently the conservation of phase space volume has also been addressed. This topic relates directly to questions in statistical fluid mechanics and in ensemble weather and climate forecasting. Here, phase space volume behavior of different spatial and temporal discretization schemes for the shallow-water equations on the sphere are investigated. Combinations of spatially symmetric and common temporal discretizations are compared. Furthermore, the relation between time reversibility and long-time volume averages is addressed.

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Georg A. Gottwald, Lewis Mitchell, and Sebastian Reich

Abstract

The problem of an ensemble Kalman filter when only partial observations are available is considered. In particular, the situation is investigated where the observational space consists of variables that are directly observable with known observational error, and of variables of which only their climatic variance and mean are given. To limit the variance of the latter poorly resolved variables a variance-limiting Kalman filter (VLKF) is derived in a variational setting. The VLKF for a simple linear toy model is analyzed and its range of optimal performance is determined. The VLKF is explored in an ensemble transform setting for the Lorenz-96 system, and it is shown that incorporating the information of the variance of some unobservable variables can improve the skill and also increase the stability of the data assimilation procedure.

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