A fully-compressible nonhydrostatic cell-integrated semi-Lagrangian atmospheric solver with conservative and consistent transport

Traditional semi-Lagrangian dynamical solvers are widely used in current global numerical weather prediction (NWP) and climate models, but are known to lack inherent mass-conserving properties. Some newer approaches utilize a cell-integrated (conservative) semi-Lagrangian (CISL) semi-implicit solver, which is inherently mass-conserving. However, existing CISL semi-implicit solvers lack consistent formulation among the discrete continuity equation and other discrete conservation equations for scalar tracers such as water vapour and air pollutants. Such inconsistency can lead to spurious generation or removal of scalar mass. In this dissertation, a new cell-integrated semi-Lagrangian (CISL) semi-implicit nonhydrostatic solver is presented with consistent discrete mass conservation equations for air and all tracers, and which preserves the shape of tracer-mass distribution. The discretization does not depend on a mean reference state, but maintains the same framework as typical semi-implicit CISL solvers, where a linear Helmholtz equation is constructed and a single application of the cell-integrated transport scheme is needed for scalar transport. Tests of this new solver are made for a series of increasingly complex flow scenarios. The initial testbed utilizes the hydrostatic, incompressible, shallow-water equations, for which the new solver is shown to be numerically stable. It maintains accuracy comparable to other existing solvers even for a highly nonlinear unstable jet. The second suite of tests are for nonhydrostatic two-dimensional (x-z) fully compressible flows in the atmosphere as governed by the moist Euler equations, which compare well to several idealized benchmark test cases from the literature. The third flow scenario is complex orography, where the nonhydrostatic equations are transformed to use a terrain-following height coordinate. Results from test cases of dry and moist flows over idealized mountain shapes are presented. In summary, the prototype development work presented in this dissertation shows that the proposed CISL nonhydrostatic solver with conservative and consistent transport may be a desirable candidate for a dynamical core in comprehensive global NWP and climate models.Science, Faculty ofEarth, Ocean and Atmospheric Sciences, Department ofGraduat