Monotonic Digit Filter for Limited-Area Model

Numerical diffusion or filter are used in most numerical models in order to eliminate small-scale (near two-grid intervals in wavelength) waves. However, conventional diffusion or filter schemes introduce the noise, and indeed few people realized, by filters themselves. For instance, most filters are troubled when they are put to use on meteorological fields with sharp gradient or with steep slope and consequently, the recurrence of undesirable numerical high-frequent oscillations (overshooting and undershooting) seems to be inevitable. Particularly when diffusion or filter is implemented in limited-area models, serious side effects on the limited-area boundaries often contaminate the modeling results. The merits and demerits are surveyed for commonly used diffusion or filter operations. A new type of monotonic digit filter is suggested to prevent overshooting and undershooting (due to the computational shock and Gibbs oscillation) nearby the discontinuous or nearly discontinuous locations when the filtering process was carried out, meanwhile the high selective property of damping is retained. Moreover, the new filter is designed on the implicit framework so that it can easily handle the problem of boundary diminishing in limited-area modeling.