The Piecewise Parabolic Method (PPM), a numerical technique developed in astrophysics for modeling fluid flows with strong shocks and discontinuities is adapted for treating sharp gradients in small-scale meteorological flows. PPM differs substantially from conventional gridpoint techniques in three ways. First, PPM is a finite volume scheme, and thus represents physical variables as averages over a grid zone rather than single values at discrete points. Second, a unique, monotonic parabola is fit to the zone average of each dependent variable using information from neighboring zone averages. As shown in a series of one- and two-dimensional linear advection experiments, the use of parabolas provides for extremely accurate advection, particularly of sharp gradients. Furthermore, the monotonicity constraint renders PPM's solutions free from Gibbs oscillations. PPM's third attribute is that each zone boundary is treated as a discontinuity. Using the method of characteristic the nonlinear flux of qua... Abstract The Piecewise Parabolic Method (PPM), a numerical technique developed in astrophysics for modeling fluid flows with strong shocks and discontinuities is adapted for treating sharp gradients in small-scale meteorological flows. PPM differs substantially from conventional gridpoint techniques in three ways. First, PPM is a finite volume scheme, and thus represents physical variables as averages over a grid zone rather than single values at discrete points. Second, a unique, monotonic parabola is fit to the zone average of each dependent variable using information from neighboring zone averages. As shown in a series of one- and two-dimensional linear advection experiments, the use of parabolas provides for extremely accurate advection, particularly of sharp gradients. Furthermore, the monotonicity constraint renders PPM's solutions free from Gibbs oscillations. PPM's third attribute is that each zone boundary is treated as a discontinuity. Using the method of characteristic the nonlinear flux of qua...