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L p ‐norm regularization approaches in variational data assimilation
Author(s) -
Bernigaud Antoine,
Gratton Serge,
Lenti Flavia,
Simon Ehouarn,
Sohab Oumaima
Publication year - 2021
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 - 10.1002/qj.4010
Subject(s) - norm (philosophy) , gaussian , mathematics , regularization (linguistics) , data assimilation , mathematical optimization , computer science , physics , artificial intelligence , meteorology , quantum mechanics , political science , law
This article presents a formulation of the 4D‐Var objective function using as a penalty term a L p ‐norm with 1 < p < 2 . This approach is motivated by the nature of the problems encountered in data assimilation, for which such a norm may be more suited to tackle the generalized Gaussian distribution of the variables. It also aims at making a compromise between the L 2 ‐norm that tends to oversmooth the solution, and the L 1 ‐norm that tends to ‘oversparsify’ it, in addition to making the problem non‐smooth. We show the benefits of using this strategy on different set‐ups through numerical experiments where the background and measurement noise covariances are known and a sharp solution is expected.