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Lp‐norm regularization approaches in variational data assimilation

Abstract : This article presents a formulation of the 4DVar objective function using as a penalty term a Lp‐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 L2‐norm that tends to oversmooth the solution, and the L1‐norm that tends to ”oversparsify” it, in addition to making the problem non‐smooth. We show the benefits of using this strategy on different setups through numerical experiments where the background and measurements noise covariance are known and a sharp solution is expected.
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https://hal.archives-ouvertes.fr/hal-03160275
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Submitted on : Friday, March 5, 2021 - 9:47:24 AM
Last modification on : Tuesday, October 19, 2021 - 2:24:23 PM

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Antoine Bernigaud, Serge Gratton, Flavia Lenti, Ehouarn Simon, Oumaima Sohab. Lp‐norm regularization approaches in variational data assimilation. Quarterly Journal of the Royal Meteorological Society, Wiley, 2021, 147, pp.2067 - 2081. ⟨10.1002/qj.4010⟩. ⟨hal-03160275⟩

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