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A data assimilation method for log‐normally distributed observational errors
Author(s) -
Fletcher S. J.,
Zupanski M.
Publication year - 2006
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1256/qj.05.222
Subject(s) - univariate , preconditioner , hessian matrix , jacobian matrix and determinant , mathematics , statistic , data assimilation , function (biology) , observational study , bayesian probability , minification , computer science , mathematical optimization , statistics , econometrics , multivariate statistics , geography , iterative method , evolutionary biology , meteorology , biology
In this paper we change the standard assumption made in the Bayesian framework of variational data assimilation to allow for observational errors that are log‐normally distributed. We address the question of which statistic best describes the distribution for the univariate and multivariate cases to justify our choice of the mode. From this choice we derive the associated cost function, Jacobian and Hessian with a normal background. We also find the solution to the Jacobian equal to zero in both model and observational space. Given the Hessian that we derive, we define a preconditioner to aid in the minimization of the cost function. We extend this to define a general form for the preconditioner, given a certain type of cost function. Copyright © 2006 Royal Meteorological Society