L1-regularisation for ill-posed problems in variational data assimilation |
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| Authors: | Melina A. Freitag Nancy K. Nichols Chris J. Budd |
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| Affiliation: | 1. Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK;2. Department of Mathematics, University of Reading, PO Box 220 Whiteknights, Reading, RG6 6AX, UK |
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| Abstract: | We consider four-dimensional variational data assimilation (4DVar) and show that it can be interpreted as Tikhonov or L2-regularisation, a widely used method for solving ill-posed inverse problems. It is known from image restoration and geophysical problems that an alternative regularisation, namely L1-norm regularisation, recovers sharp edges better than L2-norm regularisation. We apply this idea to 4DVar for problems where shocks and model error are present and give two examples which show that L1-norm regularisation performs much better than the standard L2-norm regularisation in 4DVar. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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