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.
|Pages (from-to)||665 -668|
|Number of pages||4|
|Journal||PAMM - Proceedings in Applied Mathematics and Mechanics|
|Publication status||Published - Dec 2010|
Freitag, M. A., Nichols, N. K., & Budd, C. J. (2010). L1-regularisation for ill-posed problems in variational data assimilation. PAMM - Proceedings in Applied Mathematics and Mechanics, 10(1), 665 -668. https://doi.org/10.1002/pamm.201010324