Successful climate prediction at seasonal-to-interannual time scales depends on the optimal initialization of the land surface states, in particular soil moisture. Such optimal initialization can be achieved by assimilating soil moisture observations into the land model prior to the forecast. We assess the performance of the Extended Kalman filter (EKF) and the Ensemble Kalman filter (EnKF) for soil moisture estimation when used with the Catchment Land Surface Model (CLSM) of the NASA Seasonal-to-Interannual Prediction Project (NSIPP).

In a twin experiment set up in the south-eastern United States, we assimilate synthetic observations of surface soil moisture once every three days into the CLSM. The EKF is limited for computational reasons to an effectively one-dimensional (vertical) implementation, which is assessed against a like implementation of the EnKF. While the EKF approximates the error covariance propagation by linearizing the model, the EnKF nonlinearly propagates an ensemble of model trajectories to derive sample forecast error covariances at the update time. Its main approximation is the size of the ensemble.

We find that both methods are able to derive satisfactory estimates of soil moisture. In the case of the EnKF, just 10 ensemble members prove sufficient. Differences in the forecast error variances appear when the EKF forecast error variances diverge in a few cases as a result of the linearization of the propagation step. For both the EKF and the EnKF we find that the actual estimation errors are consistently larger than filter-derived forecast and analysis error variances. The forecast error correlations between the state variables of the CLSM and the (observed) surface soil moisture differ significantly as a result of the linearizations inherent in the EKF. While the EKF produces unrealistic error correlations, the EnKF is able to estimate such local error correlations satisfactorily with 30 ensemble members. Furthermore, the ensemble distribution of the CLSM state variables (soil moisture excesses and deficits) is typically symmetric even under relatively dry or wet conditions which lessens the negative impact of nonlinearities on the quality of the soil moisture estimates.

In the current implementation, the computational cost of the EKF corresponds roughly to an ensemble with four members. Although the EnKF is computationally more expensive, it does not require a tangent-linear model and allows to `plug-and-play' different models with relative ease. It is straightforward to extend the EnKF to account for horizontal error correlations. For the EKF, this is not possible without significant additional approximations. In summary, the EnKF is a very promising candidate for the large-scale soil moisture initialization that is required for seasonal-to-interannual forecasts.