The smoother extension of the nonlinear ensemble transform filter

AbstractThe recently-proposed nonlinear ensemble transform filter (NETF) is extended to a fixed-lag smoother. The NETF approximates Bayes’ theorem by applying a square root update. The smoother (NETS) is derived and formulated in a joint framework with the filter. The new smoother method is evaluated using the low-dimensional, highly nonlinear Lorenz-96 model and a square-box configuration of the NEMO ocean model, which is nonlinear and has a higher dimensionality. The new smoother is evaluated within the same assimilation framework against the local error subspace transform Kalman filter (LESTKF) and its smoother extension (LESTKS), which are state-of-the-art ensemble square-root Kalman techniques. In the case of the Lorenz-96 model, both the filter NETF and its smoother extension NETS provide lower errors than the LESTKF and LESTKS for sufficiently large ensembles. In addition, the NETS shows a distinct dependence on the smoother lag, which results in a stronger error increase beyond the optimal lag of ...