GFDL - Geophysical Fluid Dynamics Laboratory

Tag 1: Introduction

Sub-tag 1: Evolution of FV3 development

Para title 1: Finite-Volume schemes

The FV core started its life at NASA/Goddard Space Flight Center (GSFC) during early and mid-90s as an offline transport model with emphasis on the conservation, accuracy, consistency (tracer to tracer correlation), and efficiency of the transport process. The development and applications of monotonicity-preserving Finite-­Volume schemes at GSFC were motivated in part by the need to have a ?fix? for the noisy and unphysical negative water vapor and chemical species (Lin et al. 1994, and Lin and Rood 1996). It subsequently has been used by several high-­profile Chemistry Transport Models (CTMs), including the NASA community GMI model (Rotman et al., 2001), GOCART (Chin et al., 2000), and the Harvard University­developed GEOS­CHEM model. This transport module has also been used by several climate models, including the ECHAM5 AGCM.

Para title 2: Shallow-water model

Motivated by the success of monotonicity-­preserving FV schemes in CTM applications, a consistently formulated shallow ­water model was developed. This solver was first presented at the 1994 PDE on the Sphere Workshop, and years later published by Lin and Rood (1997). The Lin-­Rood algorithm for shallow ­water equations maintains mass conservation and a key Mimetic property of ?no false vorticity generation?, and for the first time in computational geophysical fluid dynamics, uses high ­order monotonic advection consistently for momentum and all other prognostic variables, instead of the inconsistent hybrid finite ­difference and finite volume approach used by practically all other ?finite ­volume? models today.

Para title 3: FV hydrostatic dynamical core

The full 3D hydrostatic dynamical core, the FV core, was constructed based on the Lin-­Rood (1996) transport algorithm and the Lin-­Rood shallow ­water algorithm (1997). The pressure gradient force is evaluated by the Lin (1997) finite-­volume integration method, derived from Green?s integral theorem based directly on first principles, and demonstrated errors an order of magnitude smaller than other well ­known pressure ­gradient schemes. Finally, the vertical discretization is the ?vertically Lagrangian? scheme described by Lin (2004).

Para title 4: From FV to FV3

A non-­hydrostatic extension was documented in an unpublished manuscript. The most unique aspect of the FV3 is its Lagrangian vertical coordinate, which is computationally efficient as well as more accurate given the same vertical resolution. Recently, a more computationally efficient non-­hydrostatic solver is implemented using a traditional semi-implicit approach for treating the vertically propagating sound waves. This faster solver is the default. The Riemann solver option is more efficient for grid spacings smaller than 1­ km, and also more accurate, because sound waves are treated nearly exactly.