Summary
§ The online (adaptive) estimation of inflation parameter alone does not work without estimating the observational errors.

§ Estimating both of the observational errors and the inflation parameter simultaneously our approach works well on both the Lorenz-96 and the SPEEDY global model. It can also be applied to other ensemble based Kalman filters.

§ SPEEDY experiments show our approach can simultaneously estimate observational errors for different instruments.

§ Current work shows our method also works in the presence of random model errors.