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 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 set‐ups through numerical experiments where the background and measurement noise covariances are known and a sharp solution is expected.

中文翻译：

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变数数据同化中的Lp-norm正则化方法

本文介绍了使用1 <  p  <2的L _p-范数作为惩罚项的4D-Var目标函数的表述。这种方法是由数据同化中遇到的问题的性质所激发的，为此，这种规范可能更适合于解决变量的广义高斯分布。它还旨在在倾向于使解决方案过于平滑的L ₂范数与L ₁之间做出折衷。-除了使问题变得不平滑之外，还倾向于“夸大其词”的规范。我们通过数值实验展示了在不同的设置上使用该策略的好处，其中背景噪声和测量噪声的协方差是已知的，并且有望得到更精确的解决方案。