Articles | Volume 28, issue 1
Nonlin. Processes Geophys., 28, 93–109, 2021
https://doi.org/10.5194/npg-28-93-2021
Nonlin. Processes Geophys., 28, 93–109, 2021
https://doi.org/10.5194/npg-28-93-2021

Research article 08 Feb 2021

Research article | 08 Feb 2021

Behavior of the iterative ensemble-based variational method in nonlinear problems

Shin'ya Nakano

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Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
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Cited articles

Bannister, R. N.: A review of operational methods of variational and ensemble-variational data assimilation, Q. J. Roy. Meteor. Soc., 143, 607–633, https://doi.org/10.1002/qj.2982, 2017. a
Bishop, C. H., Etherton, B. J., and Majumdar, S. J.: Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects, Mon. Weather Rev., 129, 420–436, 2001. a
Bocquet, M. and Sakov, P.: Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems, Nonlin. Processes Geophys., 19, 383–399, https://doi.org/10.5194/npg-19-383-2012, 2012. a
Bocquet, M. and Sakov, P.: Joint state and parameter estimation with an iterative ensemble Kalman smoother, Nonlin. Processes Geophys., 20, 803–818, https://doi.org/10.5194/npg-20-803-2013, 2013. a, b, c, d
Bocquet, M. and Sakov, P.: An iterative ensemble Kalman smoother, Q. J. Roy. Meteor. Soc., 140, 1521–1535, https://doi.org/10.1002/qj.2236, 2014. a, b, c, d
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Short summary
The ensemble-based variational method is a method for solving nonlinear data assimilation problems by using an ensemble of multiple simulation results. Although this method is derived based on a linear approximation, highly uncertain problems, in which system nonlinearity is significant, can also be solved by applying this method iteratively. This paper reformulated this iterative algorithm to analyze its behavior in high-dimensional nonlinear problems and discuss the convergence.