A Unification of Ensemble Square Root Kalman Filters

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 SEIK (Singular ``Evolutive'' Interpolated Kalman) 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

Assimilation of dynamic topography in a global model

Absolute dynamic topography, i.e. the difference between time dependent multi-mission altimetric sea surface height and one of the most recent GOCE and GRACE based geoids, is assimilated in a global ocean general circulation model. To this end we apply an ensemble based Kalman technique, the "Error Subspace Transform Kalman Filter" (ESTKF). Here we present an update of our work. First of all the geoid is improved over previous versions. The ocean model now includes better dynamics and full sea-ice ocean interactions and more realistic surface forcing. Finally the assimilation method is augmented by a fixed lag smoother technique. This smoother allows to significantly improve the model performance, most strikingly in the first adjustment phase

A regulated localization method for ensemble-based Kalman filters

Data assimilation applications with large-scale numerical models exhibit extreme requirements on computational resources. Good scalability of the assimilation system is necessary to make these applications feasible. Sequential data assimilation methods based on ensemble forecasts, like ensemble-based Kalman filters, provide such good scalability, because the forecast of each ensemble member can be performed independently. However, this parallelism has to be combined with the parallelization of both the numerical model and the data assimilation algorithm. In order to simplify the implementation of scalable data assimilation systems based on existing numerical models, the Parallel Data Assimilation Framework PDAF (http://pdaf.awi.de) has been developed. PDAF provides support for implementing a data assimilation system with parallel ensemble forecasts and parallel numerical models. Further, it includes several optimized parallel filter algorithms, like the Ensemble Transform Kalman Filter. We will discuss the philosophy behind PDAF as well as features and scalability of data assimilation systems based on PDAF on the example of data assimilation with the finite element ocean model FEOM

SEIK - the unknown ensemble Kalman filter

The SEIK filter (Singular "Evolutive" Interpolated Kalman filter) hasbeen introduced in 1998 by D.T. Pham as a variant of the SEEK filter,which is a reduced-rank approximation of the Extended KalmanFilter. In recent years, it has been shown that the SEIK filter isan ensemble-based Kalman filter that uses a factorization rather thansquare-root of the state error covariance matrix. Unfortunately, theexistence of the SEIK filter as an ensemble-based Kalman filter withsimilar efficiency as the later introduced ensemble square-root Kalmanfilters, appears to be widely unknown and the SEIK filter is omittedin reviews about ensemble-based Kalman filters. To raise the attentionabout the SEIK filter as a very efficient ensemble-based Kalmanfilter, we review the filter algorithm and compare it with ensemblesquare-root Kalman filter algorithms. For a practical comparison theSEIK filter and the Ensemble Transformation Kalman filter (ETKF) areapplied in twin experiments assimilating sea level anomaly data intothe finite-element ocean model FEOM

The impact of the new gravity field models on the Mean Dynamic Ocean Topography and the derived geostrophic velocities

The absolute Mean Dynamic ocean Topography (MDT) can be determined from an accurate geoid model and a Mean Sea Surface (MSS). The MSS is derived using long-term time series of sea surface heights from multi-mission satellite altimetry. Recently, data from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite has become available. Now, GOCE and GRACE satellite data can be combined to obtain a geoid with higher accuracy and spatial resolution than before. The improvement in the geoid accuracy and resolution implies improvements in the resolution of MDT. From only 6 months of GOCE data, oceanographic fields like mean dynamic topography and geostrophic velocities are given in a fine spatial scale that has been poorly resolved previously. This is especially true in the areas of strong currents like Agulhas, Gulf, Kuroshio and Antarctic Circumpolar Current. Geostrophic velocities derived from only satellite data show very good agreement with geostrophic velocities measured by drifters. In addition the assimilation of this data set allows us to obtain all surface and subsurface ocean variables consistent with new MDT, giving promising results in comparison to the free model