Partial Analysis Increments as Diagnostic for LETKF Data Assimilation Systems

Theresa Diefenbach, George Craig, Christian Keil, Leonhard Scheck, Martin Weissmann

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed


Local Ensemble Transform Kalman Filters (LETKF) allow to explicitly calculate the Kalman gain and by this the contribution of individual observations to the analysis field. While this is a known feature, the information on the analysis contribution of individual observations (partial analysis increment) has not been used as systematic diagnostic up to now despite providing valuable information. In this study, we demonstrate three potential applications based on partial analysis increments in the regional modelling system of Deutscher Wetterdienst and propose their use for optimising LETKF data assimilation systems, in particular with respect to satellite data assimilation and localisation.

While the exact calculation of partial analysis increments would require saving the large, five-dimensional ensemble weight matrix in the analysis step, it is possible to compute an approximation from standard LETKF output.

We calculate the Kalman gain based on ensemble analysis perturbations, which is an approximation in case of localisation. However, this only introduces minor errors as the localisation function changes very gradually among nearby grid points. On the other hand, the influence of observations always depends on the presence of other observations and settings for the observation error and for localisation. However, the influence of observations behaves approximately linearly, meaning that the assimilation of other observations primarily decreases the magnitude of the influence, but does not change the overall structure of the partial analysis increments.

This means that the calculation of partial analysis increments can be used as an efficient diagnostic to investigate the three-dimensional influence of observations in the assimilation system. Furthermore, the diagnostic can be used to detect if the influence of additional experimental observations is in accordance with other observations without conducting computationally expensive single-observation experiments. Last but not least, the calculation can be used to approximate the influence an observation would have when applying different assimilation settings.
Seiten (von - bis)740-756
FachzeitschriftQuarterly Journal of the Royal Meteorological Society
PublikationsstatusVeröffentlicht - 1 Apr. 2023

ÖFOS 2012

  • 105206 Meteorologie