Nonlinearity

Nonlinearity: Having more sophisticated models that can resolve processes at even higher resolutions introduces the need to address the nonlinearities of dynamical systems and observation operators. A closed form solution to deal with this problem does not yet exist in nonlinear data assimilation. The DA group at CIRA investigates approaches that can potentially lead to a solution to the nonlinearity problem in data assimilation. Some of the approaches we investigate include the following:

 

  • The use of iterative minimization, which can be divided into constrained (e.g. Gauss-Newton, Levenberg-Marquardt) and unconstrained (e.g. Conjugate-gradient, Quasi-Newton) methods
  • Selecting customized minimization algorithms depending on the problem – Non-smooth algorithms in the presence of function or gradient discontinuities – Genetic/Simulated annealing algorithms for multi-modal probability distribution functions

 

Relevant Publications

2016

Kliewer, A. J., Fletcher, S. J., Jones, A. S. and J. M., Forsythe, 2016: Comparison of Gaussian, logarithmic transform and mixed Gaussian–log-normal distribution based 1DVAR microwave temperature–water-vapour mixing ratio retrievals. Q. J. Roy. Meteorol. Soc., 142: 274–286. doi: 10.1002/qj.2651

2015

Kliewer, A. J., S. J. Fletcher, A. S. Jones, and J. M. Forsythe, 2015: Identifying non-normal and lognormal characteristics of temperature, mixing ratio, surface pressure, and wind for data assimilation systems. Nonlin. Processes Geophys. Discuss., 2, 1363–1405

2014

Apodaca, K., M. Zupanski, M. DeMaria, J. A. Knaff, and L. D. Grasso, 2014: Development of a hybrid variational-ensemble data assimilation technique for observed lightning tested in a mesoscale model, Nonlin. Processes Geophys., 21, 1027-1041, doi:10.5194/npg-21-1027-2014, 2014.