Lp-norm regularization approaches in variational data assimilation

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.