| The Robert-Asselin time filter is widely used in numerical models of weather and climate. It
successfully suppresses the spurious computational mode associated with the leapfrog
time-stepping scheme. Unfortunately, it also weakly suppresses the physical mode and
severely degrades the numerical accuracy. These two concomitant problems are shown to
occur because the filter does not conserve the mean state, averaged over the three time slices
on which it operates.
The author proposes a simple modification to the Robert-Asselin filter, which does
conserve the three-time-level mean state. When used in conjunction with the leapfrog
scheme, the modification vastly reduces the impacts on the physical mode and increases the
numerical accuracy for amplitude errors by two orders, yielding third-order accuracy. The
modified filter could easily be incorporated into existing general circulation models of the
atmosphere and ocean. In principle, it should deliver more faithful simulations at almost no
additional computational expense. Alternatively, it may permit the use of longer time steps
with no loss of accuracy, reducing the computational expense of a given simulation. |