TY  - JOUR
A1  - Bergemann, Kay
A1  - Reich, Sebastian
T1  - A mollified ensemble Kalman filter
N2  - It is well recognized that discontinuous analysis increments of sequential data assimilation systems, such as ensemble Kalman filters, might lead to spurious high-frequency adjustment processes in the model dynamics. Various methods have been devised to spread out the analysis increments continuously over a fixed time interval centred about the analysis time. Among these techniques are nudging and incremental analysis updates (IAU). Here we propose another alternative, which may be viewed as a hybrid of nudging and IAU and which arises naturally from a recently proposed continuous formulation of the ensemble Kalman analysis step. A new slow-fast extension of the popular Lorenz-96 model is introduced to demonstrate the properties of the proposed mollified ensemble Kalman filter.
Y1  - 2010
UR  - http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1477-870X
U6  - https://doi.org/10.1002/Qj.672
SN  - 0035-9009
ER  - 
TY  - JOUR
A1  - Bergemann, Kay
A1  - Reich, Sebastian
T1  - A localization technique for ensemble Kalman filters
N2  - Ensemble Kalman filter techniques are widely used to assimilate observations into dynamical models. The phase- space dimension is typically much larger than the number of ensemble members, which leads to inaccurate results in the computed covariance matrices. These inaccuracies can lead, among other things, to spurious long-range correlations, which can be eliminated by Schur-product-based localization techniques. In this article, we propose a new technique for implementing such localization techniques within the class of ensemble transform/square-root Kalman filters. Our approach relies on a continuous embedding of the Kalman filter update for the ensemble members, i.e. we state an ordinary differential equation (ODE) with solutions that, over a unit time interval, are equivalent to the Kalman filter update. The ODE formulation forms a gradient system with the observations as a cost functional. Besides localization, the new ODE ensemble formulation should also find useful application in the context of nonlinear observation operators and observations that arrive continuously in time.
Y1  - 2010
UR  - http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1477-870X
U6  - https://doi.org/10.1002/Qj.591
SN  - 0035-9009
ER  -