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Joshua P. Hacker and Lili Lei

, product that reduces the elements of in Eq. (7) and is denoted . When solving the statistical analysis equation with scalar regressions as in Anderson (2003) , the localization is applied as a factor to each regression coefficient. Because the ensemble statistics are derived from an ensemble filter including some form of localization, the analysis increment from a hypothetical observation would be subject to the same localization. Thus, in Eqs. (6) and (7) the same approach would be used

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