Data assimilation algorithms combine a numerical model with observations in a quantitative way. For an optimal combination either variational minimization algorithms or ensemble-based estimation methods are applied.The computations of a data assimilation application are usually far more costly than a pure model integration. To cope with the large computational costs, a good scalability of the assimilation program is required. The ensemble-based methods have been shown to exhibit a particularly good scalability due to the natural parallelism inherent in the integration of an ensemble of model states. However, also the scalability of the estimation method -commonly based on the Kalman filter -is important. This study discusses implementation strategies for ensemble-based filter algorithms. Particularly efficient is a strong coupling between the model and the assimilation algorithm into a single executable program. The coupling can be performed with minimal changes to the numerical model itself and leads to a model with data assimilation extension. The scalability of the data assimilation system * Corresponding author.Email address: lars.nerger@awi.de (Lars Nerger)Manuscript accepted for publication in Computers & Geosciences March 30, 2012 is examined using the example of an implementation of an ocean circulation model with the Parallel Data Assimilation Framework (PDAF) into which synthetic sea surface height data are assimilated.

Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, including the geosciences, but their application to high‐dimensional geoscience systems has been limited due to their inefficiency in high‐dimensional systems in standard settings. However, huge progress has been made, and this limitation is disappearing fast due to recent developments in proposal densities, the use of ideas from (optimal) transportation, the use of localization and intelligent adaptive resampling strategies. Furthermore, powerful hybrids between particle filters and ensemble Kalman filters and variational methods have been developed. We present a state‐of‐the‐art discussion of present efforts of developing particle filters for high‐dimensional nonlinear geoscience state‐estimation problems, with an emphasis on atmospheric and oceanic applications, including many new ideas, derivations and unifications, highlighting hidden connections, including pseudo‐code, and generating a valuable tool and guide for the community. Initial experiments show that particle filters can be competitive with present‐day methods for numerical weather prediction, suggesting that they will become mainstream soon.

In recent years, several ensemble-based Kalman filter algorithms have been developed that have been classified as ensemble square root Kalman filters. Parallel to this development, the singular ''evolutive'' interpolated Kalman (SEIK) filter has been introduced and applied in several studies. Some publications note that the SEIK filter is an ensemble Kalman filter or even an ensemble square root Kalman filter. This study examines the relation of the SEIK filter to ensemble square root filters in detail. It shows that the SEIK filter is indeed an ensemble square root Kalman filter. Furthermore, a variant of the SEIK filter, the error subspace transform Kalman filter (ESTKF), is presented that results in identical ensemble transformations to those of the ensemble transform Kalman filter (ETKF), while having a slightly lower computational cost. Numerical experiments are conducted to compare the performance of three filters (SEIK, ETKF, and ESTKF) using deterministic and random ensemble transformations. The results show better performance for the ETKF and ESTKF methods over the SEIK filter as long as this filter is not applied with a symmetric square root. The findings unify the separate developments that have been performed for the SEIK filter and the other ensemble square root Kalman filters.

The impact of assimilating sea ice thickness data derived from ESA's Soil Moisture and Ocean Salinity (SMOS) satellite together with Special Sensor Microwave Imager/Sounder (SSMIS) sea ice concentration data of the National Snow and Ice Data Center (NSIDC) in a coupled sea ice-ocean model is examined. A period of 3 months from 1 November 2011 to 31 January 2012 is selected to assess the forecast skill of the assimilation system. The 24 h forecasts and longer forecasts are based on the Massachusetts Institute of Technology general circulation model (MITgcm), and the assimilation is performed by a localized Singular Evolutive Interpolated Kalman (LSEIK) filter. For comparison, the assimilation is repeated only with the SSMIS sea ice concentrations. By running two different assimilation experiments, and comparing with the unassimilated model, independent satellite-derived data, and in situ observation, it is shown that the SMOS ice thickness assimilation leads to improved thickness forecasts. With SMOS thickness data, the sea ice concentration forecasts also agree better with observations, although this improvement is smaller.

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