Mathematical Geosciences

, Volume 51, Issue 2, pp 187–207 | Cite as

Quantification of Optimal Choices of Parameters in Lognormal Variational Data Assimilation and Their Chaotic Behavior

  • Steven J. FletcherEmail author
  • Anton J. Kliewer
  • Andrew S. Jones


An important property of variational-based data assimilation is the ability to define a functional formulation such that the minimum of that functional can be any state that is desired. Thus, it is possible to define cost functions such that the minimum of the background error component is the mean, median or the mode of a multivariate lognormal distribution, where, unlike the multivariate Gaussian distributions, these statistics are not equivalent. Therefore, for lognormal distributions it is shown here that there are regions where each one of these three statistics are optimal at minimizing the errors, given estimates of an a priori state. Also, as part of this work, a chaotic signal was detected with respect to the first guess to the Newton–Raphson solver that affect the accuracy of the solution to several decimal places.


Lognormal variational data assimilation Mode Median Mean Newton–Raphson Newton fractals 



This work was supported by the National Science Foundation award numbers #AGS-1038790 and #AGS-1738206.


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Copyright information

© International Association for Mathematical Geosciences 2018

Authors and Affiliations

  • Steven J. Fletcher
    • 1
    Email author
  • Anton J. Kliewer
    • 1
  • Andrew S. Jones
    • 1
  1. 1.Cooperative Institute for Research in the AtmosphereColorado State UniversityFort CollinsUSA

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