State-of-the-art stochastic data assimilation methods for high-dimensional non-Gaussian problems

Figures & data

Table 1. Overview of the sizes of matrices that are used in different filter methods.

Variable	EnKF	SEIK	ESSE	ETKF	EAKF	EnSRF	SEnKF	ESTKF
$\mathsf{T}$	$N_e\times N_e$	$N_e-1\times N_e-1$	${\tilde{N}}_e\times {\tilde{N}}_e$	$N_e\times N_e$	$N_e\times N_e$	$N_e\times N_e$	$N_e\times N_e$	$N_e-1\times N_e-1$
$\mathsf{U}$	–	–	$N_x\times N_e$	$N_e\times N_e$	$N_e\times N_e$	$N_e\times N_e$	$N_e\times N_e$	$N_e-1\times N_e-1$
$\mathrm{\Sigma }$	–	–	$N_e\times N_e$	$N_e\times N_e$	$N_e\times N_y$	$N_e\times min(N_e,N_y)$	$N_e\times N_y$	$N_e-1\times N_e-1$
$\mathsf{V}$	$N_y\times N_y$	–	$N_e\times N_e$	–	$N_y\times N_y$	$min(N_e,N_y)\times N_y$	–	–
$\mathsf{L}$	–	$N_x\times N_e-1$	–	–	–	–	–	$N_x\times N_e-1$
$\mathsf{A}$	–	$N_e\times N_e-1$	–	–	–	–	–	$N_e\times N_e-1$

Table 2. Overview of filter methods available from Sangoma project website.

Filter	Section	Comment
EnKF	5.1	includes covariance localisation
EnsRF	5.6	includes covariance localisation
ETKF/LETKF	5.4	ETKF is without localisation; LETKF includes domain/observation localisation
ESTKF/LESTKF	5.9	ESTKF is without localisation; LESTKF includes domain/observation localisation
NETF	7.1	without localisation