Resolution of sharp fronts in the presence of model error in variational data assimilation

Freitag, M.A., Nichols, N.K. ORCID: https://orcid.org/0000-0003-1133-5220 and Budd, C.J. (2013) Resolution of sharp fronts in the presence of model error in variational data assimilation. Quarterly Journal of the Royal Meteorological Society, 139 (672). pp. 742-757. ISSN 1477-870X doi: 10.1002/qj.2002

Abstract/Summary

We show that the four-dimensional variational data assimilation method (4DVar) can be interpreted as a form of Tikhonov regularization, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularization recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularization. We apply this idea from stationary inverse problems to 4DVar, a dynamical inverse problem, and give examples for an L1-norm penalty approach and a mixed total variation (TV) L1–L2-norm penalty approach. For problems with model error where sharp fronts are present and the background and observation error covariances are known, the mixed TV L1–L2-norm penalty performs better than either the L1-norm method or the strong constraint 4DVar (L2-norm)method. A strength of the mixed TV L1–L2-norm regularization is that in the case where a simplified form of the background error covariance matrix is used it produces a much more accurate analysis than 4DVar. The method thus has the potential in numerical weather prediction to overcome operational problems with poorly tuned background error covariance matrices.