Design of a nonhydrostatic atmospheric model based on a generalized vertical coordinate

Abstract

The isentropic system of equations has particular advantages in the numerical modeling of weather and climate. These include the elimination of the vertical velocity in adiabatic flow, which simplifies the motion to a two-dimensional problem and greatly reduces the numerical errors associated with vertical advection. Vertical resolution is enhanced in regions of high static stability which leads to better resolving of features such as the tropopause boundary. Also, sharp horizontal gradients of atmospheric properties found along frontal boundaries in traditional Eulerian coordinate systems are nonexistent in the isentropic coordinate framework. The extreme isentropic overturning that can occur in fine-scale atmospheric motion presents a challenge to nonhydrostatic modeling with the isentropic vertical coordinate. This dissertation presents a new nonhydrostatic atmospheric model based on a generalized vertical coordinate. The coordinate is specified in a similar manner as Konor and Arakawa, but elements of arbitrary Eulerian-Lagrangian methods are added to provide the flexibility to maintain coordinate monotonicity in regions of negative static stability and return the coordinate levels to their isentropic targets in statically stable regions. The model is mass-conserving and implements a vertical differencing scheme that satisfies two additional integral constraints for the limiting case of z-coordinates. The hybrid vertical coordinate model is tested with mountain wave experiments which include a downslope windstorm with breaking gravity waves. The results show that the advantages of the isentropic coordinate are realized in the model with regards to vertical tracer and momentum transport. Also, the isentropic overturning associated with the wave breaking is successfully handled by the coordinate formulation.