A simple yet effective time-stepping improvement

Computational models of atmospheric and oceanic fluid dynamics mainly use leapfrog time stepping. The Robert–Asselin (RA) filter is usually applied after each leapfrog step, to suppress the computational mode. Unfortunately, the RA filter damps the physical mode and degrades the numerical accuracy. These two concomitant problems occur because the RA filter does not conserve the mean state, averaged over the three time slices on which it operates.

The presenter has recently proposed a simple modification to the RA filter, which does conserve the three-time-level mean state. The modified filter has become known as the Robert–Asselin–Williams (RAW) filter. When used in conjunction with the leapfrog scheme, the RAW filter eliminates the numerical damping of the physical mode and increases the amplitude accuracy by two orders, yielding third-order accuracy. The phase accuracy is unaffected and remains second-order.

The RAW filter can easily be incorporated into existing models of the atmosphere and ocean, typically via the insertion of just a single line of code. Better simulations are obtained, at almost no additional computational expense.

Results will be shown from two recent implementations of the RAW filter in atmospheric and oceanic models. First, in the SPEEDY atmosphere model, the skill of weather forecasts is found to be significantly improved. For example, in tropical surface pressure predictions, five-day forecasts made using the RAW filter have approximately the same skill as four-day forecasts made using the RA filter. Second, in a Hadley Centre ocean model, sea-surface temperature and sea-ice biases in the North Atlantic Ocean are found to be reduced. These improvements are encouraging for the use of the RAW filter in other models.