Impact of a digital filter as a weak constraint in MM5 4DVAR: An observing system simulation experiment

In this study, a digital filter is introduced into the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5) four-dimensional variational data assimilation (4DVAR) system as a weak constraint to control high-frequency oscillations, which negatively affect assimilation performance. To assess the impact of the digital filter and to understand how the digital-filter 4DVAR functions, a series of observing system simulation experiments are conducted with the assimilation of global positioning system (GPS) refractivity soundings for a cyclogenesis case over the Antarctic region.

It is shown that the use of a digital filter, centered at the midpoint of the assimilation period, is effective in suppressing the high-frequency waves. The imbalance during the early period of assimilation is further reduced by utilizing an additional short-span filter, starting at the beginning of the assimilation period. The filtering of the wind field is found to be the most effective in suppressing high-frequency oscillations.