Articles | Volume 25, issue 3
Nonlin. Processes Geophys., 25, 713–729, 2018

Special issue: Numerical modeling, predictability and data assimilation in...

Nonlin. Processes Geophys., 25, 713–729, 2018

Research article 19 Sep 2018

Research article | 19 Sep 2018

Nonlinear effects in 4D-Var

Massimo Bonavita et al.

Related subject area

Subject: Predictability, probabilistic forecasts, data assimilation, inverse problems | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
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Revised manuscript accepted for NPG
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Cited articles

Andersson, E., Fisher, M., Holm, E., Isaksen, L., Radnòti, G., and Trémolet, Y.: Will the 4D-Var approach be defeated by nonlinearity? ECMWF Tech. Memo. 479, available at: (last access: 1 September 2018), 2005. 
Bauer, P., Geer, A. J., Lopez, P., and Salmond, D.: Direct 4D-Var assimilation of all-sky radiances. Part I: Implementation, Q. J. Roy. Meteor. Soc., 136, 1868–1885., 2010. 
Björck, A.: Numerical methods for least squares problems, SIAM, Philadelphia, ISBN 0-89871-360-9, 1996. 
Bonavita, M., Trémolet, Y., Holm, E., Lang, S. T. K., Chrust, M., Janisková, M., Lopez, P., Laloyaux, P., De Rosnay, P., Fisher, M., Hamrud, M., and English, S.: A Strategy for Data Assimilation, ECMWF Technical Memorandum n. 800, available at: (last access: 1 September 2018), 2017a. 
Bonavita, M., Dahoui, M., Lopez, P., Prates, F., Hólm, E., De Chiara, G., Geer, A., Isaksen, L., and Ingleby, B.: On the initialization of Tropical Cyclones. ECMWF Technical Memorandum n. 810, available at (last access: 1 September 2018), 2017b. 
Short summary
This paper deals with the effects of nonlinearity in a state-of-the-art atmospheric global data assimilation system. It is shown that these effects have become increasingly important over the years due to increased model resolution and use of nonlinear observations. The ability to deal with nonlinearities has thus become a crucial asset of data assimilation algorithms. At ECMWF this is done in a perturbative fashion. Advantages and limitations of this technique are discussed.