## A ‘‘vertically Lagrangian’’ finite-volume dynamical core for global models (2004)

Venue: | Weather Rev |

Citations: | 74 - 9 self |

### BibTeX

@ARTICLE{Lin04a‘‘vertically,

author = {Shian-jiann Lin},

title = {A ‘‘vertically Lagrangian’’ finite-volume dynamical core for global models},

journal = {Weather Rev},

year = {2004},

pages = {2293--2307}

}

### Years of Citing Articles

### OpenURL

### Abstract

A finite-volume dynamical core with a terrain-following Lagrangian control-volume discretization is described. The vertically Lagrangian discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water system. The 2D horizontalto-Lagrangian-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-Lagrangian algorithm. Time marching is split-explicit, with large time steps for scalar transport, and small fractional steps for the Lagrangian dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for remapping the state variables periodically from the floating Lagrangian control-volume to an Eulerian terrain-following coordinate for dealing with ‘‘physical parameterizations’ ’ and to prevent severe distortion of the Lagrangian surfaces. Deterministic baroclinic wave-growth tests and long-term integrations using the Held–Suarez forcing are presented. Impact of the monotonicity constraint is discussed. 1.

### Citations

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Citation Context ...sed algorithms suitable for global modeling of both weather and climate systems. There exists a rich body of literature on high-performance finite-volume schemes designed for other disciplines (e.g., =-=Roe 1981-=-; Colella and Woodward 1984; Woodward and Colella 1984; Shu and Osher 1988; Harten 1989; Huynh 1996; Leveque 2002). However, the Corresponding author address: Shian-Jiann Lin, NOAA/Geophysical Fluid D... |

485 |
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Citation Context ...climate systems. There exists a rich body of literature on high-performance finite-volume schemes designed for other disciplines (e.g., Roe 1981; Colella and Woodward 1984; Woodward and Colella 1984; =-=Shu and Osher 1988-=-; Harten 1989; Huynh 1996; Leveque 2002). However, the Corresponding author address: Shian-Jiann Lin, NOAA/Geophysical Fluid Dynamics Laboratory, Forrestal Campus, Princeton University, Princeton, NJ ... |

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Citation Context ...thms suitable for global modeling of both weather and climate systems. There exists a rich body of literature on high-performance finite-volume schemes designed for other disciplines (e.g., Roe 1981; =-=Colella and Woodward 1984-=-; Woodward and Colella 1984; Shu and Osher 1988; Harten 1989; Huynh 1996; Leveque 2002). However, the Corresponding author address: Shian-Jiann Lin, NOAA/Geophysical Fluid Dynamics Laboratory, Forrest... |

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Citation Context ...or applying the previously mentioned 1D algorithms would produce unacceptably large errors near the poles where the splitting errors are greatly amplified by the convergence of the meridians (Lin and =-=Rood 1996-=-). A milestone toward the goal of developing a finitevolume dynamical core was achieved in early 1994 1 with the development of the multidimensional Flux-Form Semi-Lagrangian Transport scheme (FFSL; L... |

61 |
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Citation Context ...tal energy conserving remapping algorithm is described in section 4. We present in section 5, the deterministic baroclinic wave growth tests and long-term integrations using the Held– Suarez forcing (=-=Held and Suarez 1994-=-). Concluding remarks are given in section 6. 2. Discretization of the horizontal transport process We shall follow the equations and notations in appendix A. Since the vertical transport terms vanish... |

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Citation Context ...re exists a rich body of literature on high-performance finite-volume schemes designed for other disciplines (e.g., Roe 1981; Colella and Woodward 1984; Woodward and Colella 1984; Shu and Osher 1988; =-=Harten 1989-=-; Huynh 1996; Leveque 2002). However, the Corresponding author address: Shian-Jiann Lin, NOAA/Geophysical Fluid Dynamics Laboratory, Forrestal Campus, Princeton University, Princeton, NJ 08544-0308. E... |

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Citation Context ...it Eulerian spectral model. This not-so-small time step made the fully explicit shallow water algorithm computationally competitive with the spectral and finite-difference methods (e.g., Bourke 1974; =-=Arakawa and Lamb 1981-=-; Ringler et al. 2000). The final piece needed for the completion of the finitevolume dynamical core was developed after the discovery of a simple finite-volume integration method for computing the pr... |

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Citation Context ...l time step is about 2 to 3 times larger than a model based on Arakawa and Lamb’s scheme on the C grid. It is possible to avoid the use of the zonal filter if, for example, the ‘‘Cubed Sphere grid’’ (=-=Sadourny 1972-=-; Ronchi et al. 1996) is chosen. However, this would require a significant rewrite of the model codes including physics parameterizations, the land model, and most of the postprocessing packages. The ... |

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Citation Context ...about 2 to 3 times larger than a model based on Arakawa and Lamb’s scheme on the C grid. It is possible to avoid the use of the zonal filter if, for example, the ‘‘Cubed Sphere grid’’ (Sadourny 1972; =-=Ronchi et al. 1996-=-) is chosen. However, this would require a significant rewrite of the model codes including physics parameterizations, the land model, and most of the postprocessing packages. The size of the small ti... |

20 |
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Citation Context ...pletion of the finitevolume dynamical core was developed after the discovery of a simple finite-volume integration method for computing the pressure gradient in general terrain-following coordinates (=-=Lin 1997-=-, 1998; referred to as L97 and L98 hereafter). It is well known that the standard mathematical transformation of the pressure gradient term in terrain-following coordinates results in two large-in-mag... |

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Citation Context ...e finite-volume algorithms for global modeling at NASA Goddard Space Flight Center (GSFC) started in the late 1980s and early 1990s with focus on the transport process of chemical constituents (e.g., =-=Rood 1987-=-; Allen et al. 1996) and water vapor (Lin et al. 1994). These algorithms were derived and evolved from the modern 1D finite-volume algorithms pioneered by Van Leer (1977) and Colella and Woodward (198... |

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Citation Context ... cos�) , � � (u � � ), A cos� �� �� 2 ��2� sin� � � � (u cos�) . Note that the last term in Eqs. (A6) and (A7) vanishes if � is a conservative quantity [e.g., entropy under adiabatic condition (e.g., =-=Hsu and Arakawa 1990-=-) or an imaginary conservative tracer (see section 3)], and the 3D divergence operator becomes 2D along constant � surfaces. APPENDIX B Relaxed Monotonicity Constraints for PPM The original PPM as des... |

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Citation Context ...DIX A The Governing Equations for the Hydrostatic Atmosphere For reference, we present the governing equations for the hydrostatic atmosphere on the sphere with a general vertical coordinate � (e.g., =-=Kasahara 1974-=-). Using standard notations, the hydrostatic balance equation is 1 �p � g � 0, (A1) � �z FIG. 9. Temperature differences (K) due to the application of the monotonicity constraint. where � is the densi... |

11 |
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Citation Context ...ons. In addition to the effort at NASA GSFC, finite-volume schemes have also been developed or applied elsewhere for modeling geophysical flows (e.g., Carpenter et al. 1990, Machenhauer and Olk 1995; =-=Thuburn 1996-=-). The challenge to us was to develop computationally competitive and physically based algorithms suitable for global modeling of both weather and climate systems. There exists a rich body of literatu... |

10 | Thompson (2000), Atmospheric sulfur cycle simulated in the global model GOCART: Model description and global properties - Chin, Rood, et al. |

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Citation Context ... consistent transport of the mass, the absolute vorticity, and hence, the potential vorticity, a two-grid two-step ‘‘reversed engineering approach’’ was developed. It has the advantage of the Z grid (=-=Randall 1994-=-) without its computational expense of solving an elliptic equation. The time discretization for treating the gravity waves on both grids is the explicit ‘‘forward–backward’’ scheme, which is conditio... |

8 | Modeling the atmospheric general circulation using a spherical geodesic grid: A new class of dynamical cores - Ringler, Heikes |

6 | Transport-induced interannual variability of carbon monoxide determined using a chemistry and transport - Doddridge, Hudson, et al. - 1996 |

5 | A class of the van Leer-type transport schemes and its applications to the moisture transport in a General Circulation - Lin, Chao, et al. - 1994 |

5 | R.: Global Modeling Initiative assessment model: Model description, integration, and testing of the transport - Rotman, Tannahill, et al. |

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Citation Context ...ich body of literature on high-performance finite-volume schemes designed for other disciplines (e.g., Roe 1981; Colella and Woodward 1984; Woodward and Colella 1984; Shu and Osher 1988; Harten 1989; =-=Huynh 1996-=-; Leveque 2002). However, the Corresponding author address: Shian-Jiann Lin, NOAA/Geophysical Fluid Dynamics Laboratory, Forrestal Campus, Princeton University, Princeton, NJ 08544-0308. E-mail: Shian... |

3 |
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Citation Context ...trigger the growth of the baroclinic instability, a localized initial temperature perturbation centered at 45�N and 90�E is superimposed to the mean field. Previous theoretical studies (e.g., Lin and =-=Pierrehumbert 1993-=-)2302 MONTHLY WEATHER REVIEW VOLUME 132 indicated that the localized disturbance will propagate eastward while growing exponentially. Due to nonlinearity and periodicity of the spherical geometry, th... |

2 | On the development of a cellintegrated semi-Lagrangian shallow water model on the sphere - Machenhauer, Olk - 1996 |

1 |
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Citation Context ... astrophysics and aerospace engineering applications. In addition to the effort at NASA GSFC, finite-volume schemes have also been developed or applied elsewhere for modeling geophysical flows (e.g., =-=Carpenter et al. 1990-=-, Machenhauer and Olk 1995; Thuburn 1996). The challenge to us was to develop computationally competitive and physically based algorithms suitable for global modeling of both weather and climate syste... |