Nadeem Aamir , Institute of Numerical and Applied mathematics,University of Goettingen, Goettingen, Germany
Transformed and Generalized Localization for Ensemble Methods in Data Assimilation
Localization is an essential part of ensemble based assimilation schemes. The size of an ensemble is always much smaller than the dimension of the state space for the real numerical predictions. It is necessary to ensure a suffient number of degree's of freedom for the analysis ensemble and, thus, increase the rank of the system. Also, the small ensemble size gives an insufficent estimate of the background error correlations. Localization effectivly eliminates spurious correlations in the background ensemble between distant state variables.
As shown by Perianez et al (JMSJ 2014) the choice of the localization radius needs to depend on the number of ensemble members. However, a challenge arises when the observation operator under consideration is non-local (e.g. satellite radiance data), the localization which is applicable to the problem can be severly limited, with strong effects on the quality of the assimilation step.
In this work, see Aamir and Potthast (APAS 2015), we study a transformation approach to change non-local operators to local operators in transformed space, such that localization becomes applicable. We interpret this approach as a generalized localization and study its general algebraic formulation. Examples are provided for a compact integral operator and a non-local matrix observation operator to demonstrate the feasibility of the approach and study the quality of the assimilation by transformation.
In particular, we apply the approach to temperature profile reconstruction from infrared measurements given by the IASI Infrared Sounder and show that the approach is feasible for this important data type in atmospheric analysis and forecasting. Our work here is of conceptional and mathematical nature, but with its application in meteorology and operational numerical weather prediction (NWP) it touches very different
communities. We also believe that our derivations will work in a similar
way for particle filters.