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

Table 1.

VariableEnKFSEIKESSEETKFEAKFEnSRFSEnKFESTKF$\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.

FilterSectionCommentEnKF5.1includes covariance localisationEnsRF5.6includes covariance localisationETKF/LETKF5.4ETKF is without localisation; LETKF includes domain/observation localisationESTKF/LESTKF5.9ESTKF is without localisation; LESTKF includes domain/observation localisationNETF7.1without localisation