An Isentropic and Sigma Coordinate hybrid Numerical Model: Model Development and Some Initial Tests

Abstract

Several recent efforts in the development of isentropic numerical models for atmospheric simulation have used sigma coordinates for prediction within the lower troposphere. Sigma coordinates are used in this region to provide a grid structure with uniform resolution for predicting planetary boundary layer processes and to avoid the problem of the intersection of information surfaces with the earth's surface. While successful simulations have been completed, none of the hybrid models provided for the conservation of mass and other properties with respect to transport through the common interface between the sigma and isentropic model domains. The primary problem is to match boundary conditions across the interface while providing for full interaction between the two model domains in the presence of diabatic beating and viscous forces without introducing spurious sources of mass, momentum or energy. In this paper, a solution is presented which matches transport boundary conditions at the interface and conserves atmospheric properties without parameterization. The development of an isentropic and sigma coordinate hybrid model, based on the flux form of the primitive equations, is discussed. In this development phase, primary emphasis is on the unique modeling aspects related to the intersection of isentropic surfaces with the common boundary and the conservation of physical properties during exchange between the two model domains. Initial model simulations of a jet streak propagating in a zonal channel are presented that were designed to test the feasibility of the hybrid model approach. The results show that: 1) With respect to transport processes, mass, momentum and energy are conserved for the entire model domain. Vertical transport of properties through the interface between the two model domains is matched exactly. 2) The flux formulation of the hybrid model with a vertically staggered grid maintains a smooth transition at the interface level without need for artificial adjustments. 3) The time rates of change of total momentum and energy are associated primarily with physical forcing. The effects of truncation errors resulting from initialization of emerging grid points in the truncated isentropic region, based on a redistribution of mass and momentum consistent with conservation of these properties, yields minor pressure and wind perturbations in the truncated and sigma grid volumes. Although the perturbations are stable and quickly damp, the need to initialize grid points in the sensitive model region above the boundary layer is a problem with hybrid models which merits further attention.