FIM: A vertically flow-following, finite-volume icosahedral model

Global Spectral models have gained almost universal acceptance in the last several decades. However, drawbacks of high-resolution spectral models in terms of operation counts and communication overheads on massive parallel processors have led, in recent years, to the development of new types of grid-point global models discretized on geodesic grids [see, e.g., Tomita et al. (2001)]. Among those, the icosahedral grid is attractive because it achieves quasi-uniform coverage of the globe with minimal regional variations in the shape of grid cells. If configured as a grid consisting of a large number of hexagonal cells (with 12 embedded pentagons), the icosahedral grid is particularly suitable for finite-volume numerics in which conventional finitedifference operators are replaced by numerically approximated line integrals along cell boundaries. Williamson (1968) and Sadourny et al. (1968) were the first to solve shallow-water equations on icosahedral grids using finite-difference formulations. More recently, Colorado State University modelers (Heikes and Randall 1995; Ringler et al. 2000) developed an icosahedral-hexagonal shallow-water model (SWM) based on finite-volume numerics. The German Weather Service is currently using an icosahedralhexagonal model for operational global weather prediction (Majewski et al. 2002). A Japanese group (Tomita et al. 2004) has developed a nonhydrostatic general circulation model (GCM) formulated on an icosahedralhexagonal grid. A flow-following finite-volume icosahedral model (FIM) is currently under development in the Global Systems Division of NOAA’s Earth System Research Laboratory, with assistance from the Environmental Modeling Center (EMC) at the National Centers for Environmental Prediction (NCEP). The model combines a finite-volume icosahedral SWM solver with a “flowfollowing” vertical coordinate whose surfaces may deform freely according to air flow. Aloft, the flowfollowing coordinate is isentropic, which reduces spurious nonphysical entropy sources in adiabatic flow (Johnson (1997)), while near the surface the coordinate surfaces are terrain-following. The coordinate is an improved version of the hybrid σ-θ coordinate successfully used in atmospheric and ocean models such as RUC (Rapid Update Cycle) and HYCOM (HYbrid Coordinate Ocean Model).