
Fig. 1
Observing network diagrams.

Fig. 2
Plots of vorticity for the true state and the resulting observations using the different networks at the 6th analysis time, for a particular random seed.
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Table 1. Parameter values used in the LETKF
Localisation length scale, l0.0050.020.007Inflation factor, ρ0.010.010.01
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Table 2. Parameter values used in the EWPF
Keep proportion, κ1.01.01.0Nudging factor, σ0.70.50.7

Fig. 3
Observing network 1, every other gridpoint. The total and unobserved RMSEs are almost exactly underneath the observed RMSE plots. This is due to the widespread information from the observations effectively constraining the whole system.

Fig. 4
Observing network 2, block of dense observations.

Fig. 5
Observing network 3, tracks of observations.

Fig. 6
Trajectories of two different points in the domain when using the different assimilation methods with observing network 3 for a single experiment.

Fig. A1
Performance of the EWPF under different parameters.

Fig. B1
Performance of the EWPF with the LETKS relaxation when κ=1.0.

Fig. B2
Performance of the EWPF with the LETKS relaxation when κ=0.75.

Fig. B3
Performance of the EWPF with the LETKS relaxation when κ=0.50.

Fig. B4
Performance of the EWPF with the LETKS relaxation when κ=0.25.
