Multiple-truncation incremental approach for four-dimensional variational data assimilation

The incremental approach provides an approximate solution to four-dimensional variational data assimilation (4D-Var) at a reasonable CPU cost. An extension of this approach is studied, namely the multiple-truncation incremental technique, and is compared to the standard and single-truncation incremental implementations of 4D-Var, using a two-dimensional barotropic vorticity-equation model. The quasi-continuous approach deals with the cut-off problem and spreads the computer requirements over time. Quasi-continuous incremental and quasi-continuous multiple-truncation incremental techniques are assessed. The same number of iterations is specified in all the experiments. The multiple-truncation incremental technique is found to produce a good approximate analysis sit a lower CPU cost. Applying the quasi-continuous approach to the incremental methods adds some benefit in terms of computer time.