GFDL - Geophysical Fluid Dynamics Laboratory

FV3: Finite-Volume Cubed-Sphere Dynamical Core

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The GFDL Finite­ Volume Cubed-Sphere Dynamical Core (FV3) is a scalable and flexible dynamical core capable of both hydrostatic and non-hydrostatic atmospheric simulations. The design of FV3 was guided by these tenets:

  1. Discretization should be guided by physical principles as much as possible.
  2. A fast model is a good model! Computational efficiency is crucial.

FV3 was “reverse engineered” to incorporate properties which have been used in engineering for decades, but only first adopted in atmospheric science by FV3.

FV3 has been chosen as one of the candidates for the Next Generation Global Prediction System project (NGGPS), designed to upgrade the current operational Global Forecast System to run as a unified, fully-coupled system in NOAA’s Environmental Modeling System infrastructure.

This website describes FV3, including the evolution of its development, basic algorithm, and its global variable resolution capabilities, in both nested and stretched grid configurations. The Performance page explains how efficient FV3 can be.

Dynamics isn’t the whole story. Coupling to physics and the ocean is necessary! Please see the Applications page for the family of models using FV3 and examples of how FV3 has been successfully implemented.

Development History

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 University-­developed GEOS­CHEM model. This transport module has also been used by several climate models, including the ECHAM5 AGCM.

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.

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).

From FV to FV3

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 non­hydrostatic 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 resolution finer than 1­km, and also more accurate, because sound waves are treated nearly exactly. A description of the non-hydrostatic extension can be found on the Key Components page.