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. It is also revealed that the imposed weak constraint significantly reduces the wave-reflection problem caused by imperfect upper boundary conditions. It is concluded that the weakly constrained 4DVAR with digital filters not only reduces dynamic imbalance, but also significantly improves the qualities of analysis and forecast. Without projecting its solution onto the high-frequency waves, which diminish rapidly with forecast time, the constrained 4DVAR is able to yield additional improvement in the model initial condition in the larger-scale range and hence utilizes the available observations more effectively when compared with the unconstrained 4DVAR.