Conservation laws and ensemble Kalman filter algorithms

• Applicant: Professorin Dr. Tijana Janjic Pfander
• Subject Area: Atmospheric Science
• Term: from 2014 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 261092378

Maintaining physical conservation laws numerically has long been recognized as being important in the development of numerical weather prediction (NWP) models independent of their resolution. In the broader context of data assimilation, however, concerted efforts to maintain conservation laws numerically and to understand the significance of doing so have begun only recently. The numerical models of the atmosphere that resolve highly nonlinear dynamics and physics are very sensitive to proper initial and boundary conditions. Consequently, data assimilation for NWP models that resolve many scales of motion and for observations of higher temporal/spatial density/resolution requires re-evaluating and improving methodology that is currently inherited from less nonlinear applications.The principal objective of this project is 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. Two problems will be addressed. First, conservation of mass and preservation of positivity have been shown in recent work by the principal investigator and colleagues to be important constraints for data assimilation algorithms. These two constraints have been incorporated into a new algorithm, the quadratic programming ensemble Kalman filter and tested for linear dynamics. In this project, the algorithm will be extended, implemented and tested with the non-hydrostatic, convection permitting COSMO-DE model in an idealized setup for the assimilation of radar reflectivity. As the second problem that will be addressed, it will be examined how data assimilation algorithms such as the ensemble Kalman filter and the quadratic programming ensemble Kalman filter affect the conservation properties in idealized nonlinear 2d shallow water model experiments and whether and how these ensemble based algorithms can be modified to obtain solutions that conserve angular momentum, energy and enstrophy. The conservation of energy and enstrophy is expected to improve the nonlinear energy cascade in the system. The possible impact on the accuracy of prediction will be examined as well.

• DFG Programme: Research Grants