Journal cover Journal topic
Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

Journal metrics

  • IF value: 1.321 IF 1.321
  • IF 5-year<br/> value: 1.636 IF 5-year
  • SNIP value: 0.903 SNIP 0.903
  • SJR value: 0.709 SJR 0.709
  • IPP value: 1.455 IPP 1.455
  • h5-index value: 20 h5-index 20
© Author(s) 2014. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
31 Mar 2014
Review status
This discussion paper has been under review for the journal Nonlinear Processes in Geophysics (NPG). The revised manuscript was not accepted.
Data assimilation of two-dimensional geophysical flows with a Variational Ensemble Kalman Filter
Z. Mussa, I. Amour, A. Bibov, and T. Kauranne Lappeenranta University of Technology, Lappeenranta, Finland
Abstract. The Variational Ensemble Kalman Filter (VEnKF), a recent data assimilation method that combines a variational assimilation of the Bayesian estimation problem with an ensemble of forecasts, is demonstrated in two-dimensional geophysical flows using a Quasi-Geostrophic (QG) model and a shallow water model. Using a synthetic experiment, a two layer QG model with model bias is solved on a cylindrical 40 x 20 domain. The performance of VEnKF on the QG model with increasing ensemble size is compared with the classical Extended Kalman Filter (EKF). It is shown that although convergence can be achieved with just 20 ensemble members, increasing the number of members results in a better estimate that approaches the one produced by EKF.

In the second test case, a 2-D shallow water model is described using a real dam-break experiment. The VEnKF algorithm was used to assimilate observations obtained from a modified laboratory dam-break experiment with a two-dimensional setup of sensors at the downstream end. The wave meters are placed parallel to the direction of the flow alongside the flume walls to capture both cross flow and stream flow.

In both test cases, VEnKF was able to predict genuinely two-dimensional flow patterns when the sensors had a two-dimensional geometry and was stable against model bias in the first test case.

In the second test case, the experiments are complemented with an empirical study of the impact of observation interpolation on the stability of the VEnKF filter. In this study, a novel Courant–Friedrichs–Lewy type filter stability condition is observed that relates ensemble variance to the time interpolation distance between observations.

The results of the two experiments shows that VEnKF is a good candidate for data assimilation problems and can be implemented in higher dimensional nonlinear models.

Citation: Mussa, Z., Amour, I., Bibov, A., and Kauranne, T.: Data assimilation of two-dimensional geophysical flows with a Variational Ensemble Kalman Filter, Nonlin. Processes Geophys. Discuss., 1, 403-446, doi:10.5194/npgd-1-403-2014, 2014.
Z. Mussa et al.
Z. Mussa et al.


Total article views: 556 (including HTML, PDF, and XML)

HTML PDF XML Total BibTeX EndNote
306 199 51 556 20 18

Views and downloads (calculated since 31 Mar 2014)

Cumulative views and downloads (calculated since 31 Mar 2014)



Latest update: 23 Mar 2017
Publications Copernicus