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Expanding the validity of the ensemble Kalman filter without the intrinsic need for inflation

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Figure

Figure 1. Schematic of the traditional standpoint on the analysis ofthe EnKF (top row), what it actually does using a Gaussian priorsampled from three particles (middle row), and using a predictiveprior accounting for the uncertainty due to sampling (botto
Figure 2. Analysis error variance when applying sequential dataassimilation to xk+1 = αxk with (ζ = 0.75, dashed line) or without(ζ = 1, full line) multiplicative inflation on the prior, as a functionof the model growth α
Figure 3. Average analysis RMSE for the primal EnKF-N, the dualEnKF-N, the approximate EnKF-N, and the EnKF with uniform op-timally tuned inflation, applied to the Lorenz-95 model, as a func-tion of the time step between updates
Figure 4. Average analysis RMSE for the EnKF-N with Jeffreys’hyperprior, with the EnKF-N based on the Dirac–Jeffreys hyper-prior, with the EnKF-N based on the Jeffreys hyperprior but enforc-ing schemes R1 or R2, and the EnKF with uniform optimally tunedinfl
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