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

Reference:

Freitag, M. A., Nichols, N. K. 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.

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Official URL:

http://dx.doi.org/10.1002/qj.2002

Abstract

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.

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