The aim of this contribution is to provide a description of the difference between Kalman filter and particle filter when the state space is of high dimension. In the Gaussian framework, KF and PF give the same theoretical result. However, in high dimension and using finite sampling for the Gaussian distribution, the PF is not able to reproduce the solution produced by the KF. This discrepancy is highlighted from the convergence property of the Gaussian law toward a hypersphere: in high dimension, any finite sample of a Gaussian law lies within a hypersphere centered in the mean of the Gaussian law and of radius square-root of the trace of the covariance matrix. This concentration of probability suggests the use of norm as a criterium that discriminates whether a forecast sample can be compatible or not with a given analysis state. The contribution illustrates important characteristics that have to be considered for the high dimension but does not introduce a new approach to face the curse of dimensionality.

The purpose of adaptive observation strategies is to design optimal observation networks in a prognostic way. The implementation of such strategies is based on adaptive observation numerical techniques that provide guidance on where to deploy future additional observations. Most advanced techniques account for the dynamical aspects of the atmosphere and the data assimilation system (DAS). This study aims to assess the influence of the model trajectory on the Kalman Filter Sensitivity (KFS) method used at Météo-France. KFS is an adjoint-based method identifying sensitive areas by means of a forecast score variance. Targeted observations are designed to reduce this score variance. In its first version, KFS was not able to deal with trajectory uncertainties. An ensemble-based approach is undertaken to investigate if it is possible to account for these uncertainties. We assess the robustness of the method regarding trajectory errors and propose a practical solution. To avoid high computational costs, a simplified framework is used. We perform experiments with a two-layer quasi-