A conserved topographical representation scheme using a thin-wall approximation in Z-coordinates

Abstract

As nonhydrostatic models have higher resolution, a topographical representation scheme is desirable as an alternative to the terrain-following approach, which is unstable for steep topography. We developed a conserved topographical representation scheme using a thin-wall approximation in z-coordinates (the CT scheme). This scheme is formulated by the flux-form finite-volume method with a flux limiter, so that the total integrals over the entire domain of prognostic variables are conserved: this is advantageous compared to the conventional thin-wall approximation method. The CT scheme is easily implemented for existing models that use the finite-volume method. We constructed the scheme to satisfy conservation of mass, horizontal momentum, and total energy. We compared the results of the CT scheme for an isolated mountain case with those of a step-mountain (SM) method. The CT scheme represents the propagation of gravity waves more accurately than the SM method. The upward flux of horizontal momentum becomes more vertically uniform for the CT scheme than for the SM method over time. In addition, the horizontal momentum budget shows that the total momentum is reduced by reaction force at the lower boundary with changes due to numerical damping in the upper layers and numerical filters in the free layers.