Title: Resolution of sharp fronts in the presence of model error using L1-regularized variational assimilation

Authors: M.A. Freitag (Department of Mathematical Sciences, University of Bath)
N.K. Nichols (Department of Mathematics and Statistics, University of Reading)
C.J. Budd (Department of Mathematical Sciences, University of Bath)

Strong-constraint 4D-variational (4DVar) data assimilation methods do not perform well where there are sharp gradients, such as fronts or shocks, in the dynamics - particularly in cases where the background state contains a displacement error in the position of the front. Where model errors are present, the strong-constraint variational method also produces inaccurate analyses. In both cases the analysis is chosen to compensate on average for the background and model errors over the time window. The analysis therefore may smear the shock front and may include over/undershoots, leading to oscillations and phase errors in the forecast.

Here we introduce an alternative form of the variational problem. We show first that the 4DVar scheme can be interpreted as a form of Tikhonov, or L2 - regularization, commonly used to treat ill-posed inverse problems. The regularization term constrains the analysis to remain close to the background in the L2-norm {least-squares sense). An alternative process that has proved valuable in image processing for recovering sharp edges is L1-norm regularization. We apply this approach to the variational assimilation problem in cases where shocks are present and give examples where the L1-norm technique performs more effectively in the presence of model error than the standard L2-norm regularization.

GMAO Head: Michele Rienecker Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: May 27 2011