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

The incremental approach provides an approximate solution of 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 at a lower CPU cost. Applying the quasi-continuous approach to
the incremental methods adds some benefit in terms of computer time.