No abstract

Ensemble-based Kalman smoother algorithms extend ensemble Kalman filters to reduce the estimation error of past model states utilizing observational information from the future. Like the filters they extend, current smoothing algorithms are optimal only for linear models. However, the ensemble methods are typically applied with high-dimensional nonlinear models, which also require the application of localization in the data assimilation. In this paper, the influence of the model nonlinearity and of the application of localization on the smoother performance is studied. Numerical experiments show that the observational information can be successfully utilized over smoothing lags several times the error doubling time of the model. Localization limits the smoother lag by spatial decorrelation. However, if the localization is well tuned, the usable lag of the smoother, and hence the usable amount of observational information, is maximized. The localization reduces the estimation errors of the smoother even more than those of the filter. As the smoother reuses the transformation matrix of the filter, it profits stronger from increases of the ensemble size than the filter. With respect to inflation and localization, the experiments also show that the same configuration that yields the smallest estimation errors for the filter without smoothing also results in the smallest errors of the smoothed states. Thus, smoothing only adds the lag as a further tunable parameter.