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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 [Link]

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 [Link]

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. [Link]