TY  - JOUR
A1  - Shin, Seoleun
A1  - Reich, Sebastian
A1  - Frank, Jason
T1  - Hydrostatic Hamiltonian particle-mesh (HPM) methods for atmospheric modelling
JF  - Quarterly journal of the Royal Meteorological Society
N2  - We develop a hydrostatic Hamiltonian particle-mesh (HPM) method for efficient long-term numerical integration of the atmosphere. In the HPM method, the hydrostatic approximation is interpreted as a holonomic constraint for the vertical position of particles. This can be viewed as defining a set of vertically buoyant horizontal meshes, with the altitude of each mesh point determined so as to satisfy the hydrostatic balance condition and with particles modelling horizontal advection between the moving meshes. We implement the method in a vertical-slice model and evaluate its performance for the simulation of idealized linear and nonlinear orographic flow in both dry and moist environments. The HPM method is able to capture the basic features of the gravity wave to a degree of accuracy comparable with that reported in the literature. The numerical solution in the moist experiment indicates that the influence of moisture on wave characteristics is represented reasonably well and the reduction of momentum flux is in good agreement with theoretical analysis.
KW  - conservative discretization
KW  - Lagrangian modeling
KW  - holonomic constraints
KW  - fluid mechanics
Y1  - 2012
U6  - https://doi.org/10.1002/qj.982
SN  - 0035-9009
VL  - 138
IS  - 666
SP  - 1388
EP  - 1399
PB  - Wiley-Blackwell
CY  - Hoboken
ER  - 
TY  - JOUR
A1  - Bergemann, Kay
A1  - Reich, Sebastian
T1  - An ensemble Kalman-Bucy filter for continuous data assimilation
JF  - Meteorologische Zeitschrift
N2  - The ensemble Kalman filter has emerged as a promising filter algorithm for nonlinear differential equations subject to intermittent observations. In this paper, we extend the well-known Kalman-Bucy filter for linear differential equations subject to continous observations to the ensemble setting and nonlinear differential equations. The proposed filter is called the ensemble Kalman-Bucy filter and its performance is demonstrated for a simple mechanical model (Langevin dynamics) subject to incremental observations of its velocity.
Y1  - 2012
U6  - https://doi.org/10.1127/0941-2948/2012/0307
SN  - 0941-2948
VL  - 21
IS  - 3
SP  - 213
EP  - 219
PB  - Schweizerbart
CY  - Stuttgart
ER  - 
TY  - JOUR
A1  - Reich, Sebastian
T1  - A Gaussian-mixture ensemble transform filter
JF  - Quarterly journal of the Royal Meteorological Society
N2  - We generalize the popular ensemble Kalman filter to an ensemble transform filter, in which the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian-mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions and the three-dimensional Lorenz-63 model). It is demonstrated that the EGMF is capable of tracking systems with non-Gaussian uni- and multimodal ensemble distributions.
KW  - data assimilation
KW  - ensemble Kalman filter
KW  - nonlinear filtering
KW  - Gaussian mixtures
KW  - Gaussian kernel estimators
Y1  - 2012
U6  - https://doi.org/10.1002/qj.898
SN  - 0035-9009
VL  - 138
IS  - 662
SP  - 222
EP  - 233
PB  - Wiley-Blackwell
CY  - Malden
ER  -