21.4.4 Robert time filter

The Robert time filter (enabled by option robert_time_filter) is applied every time step in conjunction with using a leapfrog scheme. Schematically, this amounts to:

$$\overline{h^\tau} = h^\tau + smooth\cdot((h^{\tau+1} + h^{\tau-1})/2 - h^\tau )$$ (21.62)

where $\overline{h^\tau}$ is the filtered value of the prognostic variable h at time level $\tau$ and smooth is an adjustable parameter which may be set via namelist. The default value is smooth=0.01 which is a reasonably small value. The largest value possible is smooth=0.2 which is a very heavy smoothing. The Robert time filter will give smoother solutions than periodic application of either forward or Euler backward mixing steps. The disadvantage of the Robert time filter is that it requires an extra read through of data on disk. However, if option ramdrive is enabled and disk data is actually held in memory, the extra overhead for reading is small. However, for other I/O options where disk data is stored on rotating disk, the overhead may result in a substantial increase in wall clock time.

Caveat: As implemented, the Robert time filter will not work correctly when applied to surface currents for the purpose of Doppler shilting windspeeds when restart files are involved for anything other than option simple_sbc. The reason is that on non-restart time steps, unfiltered values of $u^\tau$ are used. However, filtered values of $u^\tau$ are written to the restart file. Therefore, when re-starting from a restart file, filtered values of $u^\tau$ are loaded from disk and used on the first time step of a restart. This is difficult to remedy since the barotropic portion of $u^{\tau+1}$ is unknown at the time the filter is applied. Filtering the tracer fields will preserve answers across restart points. The difference in answers due to this error in velocity is very tiny judging from the observation that if the error is not accounted for in the tracer fields, the differences in surface tracer boundary conditions is the the 6th decimal place.

  

Figure 21.1: Time discretization used in MOM when memory window is partially opened and fully opened. components