Conservation laws and ensemble Kalman filter algorithms
Final Report Abstract
The principal objective of this project was to develop an ensemble-based data assimilation algorithm that replicates properties of nonlinear dynamical systems such as conservation of mass, angular momentum, energy and enstrophy. To this end, first, it was examined how data assimilation algorithms such as the ensemble Kalman filter affect the conservation properties in idealized nonlinear 2d shallow water model experiments. Second, an ensemble-based algorithm was developed to obtain solutions that conserve energy and enstrophy. The conservation of energy and enstrophy was expected to improve the nonlinear energy cascade in the system. It was found that the kinetic energy and enstrophy spectra in experiments with the enstrophy constraint are considerably closer to the true spectra, in particular at the smallest resolvable scales. Therefore, imposing conservation of enstrophy within the data assimilation algorithm effectively avoids the spurious energy cascade of rotational part and thereby successfully suppresses the noise generated by the data assimilation algorithm. The possible impact on the accuracy of prediction was examined as well. It was found that the 14-day deterministic free forecast, starting from the initial condition enforced by both total energy and enstrophy constraints, produces the best prediction. The same holds for the ensemble free forecasts.
Publications
- 2016: An efficient modular volume-‐‑scanning radar forward operator for NWP models: description and coupling to the COSMO model, Q. J. R. Meteorol. Soc., 142, 3234-3256
Zeng, Y., U. Blahak, D. Jerger
(See online at https://doi.org/10.1002/qj.2904) - 2016: Study of Conservation Laws with the Local Ensemble Transform Kalman Filter, Q. J. R. Meteorol. Soc., 142:699, 2359–2372
Zeng Y., T. Janjic
(See online at https://doi.org/10.1002/qj.2829) - Approaches to convective scale data assimilation, Proceedings of CAWCR Annual Workshop 2016, Melbourne, December 5th-9th, 2016
Janjic, T., H. Lange, Y. Ruckstuhl and Y. Zeng
- 2017: Ensemble-type Kalman filter algorithm conserving mass, total energy and enstrophy, Q. J. R. Meteorol. Soc., 143:708, 2902–2914
Zeng, Y., T. Janjic, Y. Ruckstuhl and M. Verlaan
(See online at https://doi.org/10.1002/qj.3142) - 2018: Editorial for Advances in data assimilation methods, Q. J. R. Meteorol. Soc., 144:713, 1189-1190
Janjic, T., R. Potthast, P. J. Van Leeuwen
(See online at https://doi.org/10.1002/qj.3382)
