A Perspective on the Role of the Dynamical Core in the Development of Weather and Climate Models
 Richard B. Rood
 … show all 1 hide
Purchase on Springer.com
$29.95 / €24.95 / £19.95*
* Final gross prices may vary according to local VAT.
Abstract
This chapter aims to place the dynamical core of weather and climate models into the context of the model as a system of components. Building from basic definitions that describe models and their applications, the chapter details the component structure of a presentday atmospheric model. This facilitates the categorization of model components into types and the basic description of the dynamical core. An important point in this categorization is that the separation between ‘dynamics’ and ‘physics’ is not always clear; there is overlap. This overlap becomes more important as the spatial resolution of models increases, with resolved scales and parameterized processes becoming more conflated. From this categorization an oversimple, intuitive list of the parts of a dynamical core is made. Following this, the equations of motion are analyzed, and the designbased evolution of the dynamical core described in Lin (2004, Monthly Weather Review) is discussed. This leads to a more complete description of the dynamical core, which explicitly includes the specification of topography and grids on which the equations of motion are solved. Finally, a set of important problems for future consideration is provided. This set emphasizes the modeling system as a whole and the need to focus on physical consistency, on the scientific investigation of coupling, on the representation of physical and numerical dissipation (subscale mixing and filtering), and on the robust representation of divergent flows. This systembased approach of model building stands in contrast to a componentbased approach and influences the details of component algorithms.
 Adcroft A, Hallberg R (2006) On methods for solving the oceanic equations of motion in generalized vertical coordinates. Ocean Modeling 11:224–233 CrossRef
 Adcroft A, Campin JM, Hill C, Marshall J (2004) Implementation of an atmosphericocean general circulation model on the expanded spherical cube. Mon Wea Rev 132:2845–2863 CrossRef
 Adcroft A, Hallberg R, Harrison M (2008) A finite volume discretization of the pressure gradient force using analytic integration. Ocean Modeling 22:106–113 CrossRef
 Allen DJ, Douglass AR, Rood RB, Guthrie PD (1991) Application of a monotonic upstreambiased transport scheme to threedimensional constituent transport calculations. Mon Wea Rev 119:2456–2464 CrossRef
 Andrews DG, Mcintyre ME (1978) An exact theory of nonlinear waves on a Lagrangianmean flow. J Fluid Mech 89(4):609–646 CrossRef
 Bala G, Rood RB, Bader D, Mirin A, Ivanova D, Drui C (2008) Simulated climate near steep topography: sensitivity to dynamical methods for atmospheric transport. Geophys Res Lett 35, l14807, doi:10.1029/2008GL033204 CrossRef
 Bates JR, Moorthi S, Higgins RW (1993) Global multilevel atmospheric model using a vector semiLagrangian finitedifference scheme. Part I: Adiabatic formulation. Mon Wea Rev 121(1): 244–263
 Beres JH, Garcia RR, Boville BA, Sassi F (2005) Implementation of a gravity wave source spectrum parameterization dependent on the properties of convection in the Whole Atmosphere Community Climate model (WACCM). J Geophys Res 110, d10108,doi:10,1029/2004JD005504 CrossRef
 Bey I, Jacob DJ, Yantosca RM, Logan JA, Field B, Fiore AM, Li Q, Liu H, Mickley LJ, Schultz M (2001) Global modeling of tropospheric chemistry with assimilated meteorology: Model description and evaluation. J Geophys Res 106:23,073–23,096
 Boris JP, Book DL (1973) Flux corrected transport. I. SHASTA, a fluid transport algorithm that works. J Comput Phys 11:38–69 CrossRef
 Collins WD, Rasch PJ, Boville BA, Hack JJ, McCaa JR, Williamson DL, Kiehl JT, Briegleb BP, Bitz CM, Lin SJ, Zhang M, Dai Y (2004) Description of the NCAR Community Atmosphere Model (CAM3.0). NCAR Technical Note NCAR/TN464+STR, National Center for Atmospheric Research, Boulder, Colorado, 214 pp., available from http://www.ucar.edu/library/collections/technotes/technotes.jsp
 Dickinson RE, Ridley EC, Roble RG (1981) A 3dimensional generalcirculation model of the thermosphere. J Geophys ResSpace Physics 86:1499–1512 CrossRef
 Douglass AR, Rood RB, Kawa SR, Allen DJ (1997) A threedimensional simulation of the evolution of the middle latitude winter ozone in the middle stratosphere. J Geophys Res 102:19,217–19,232
 Dudhia J (1993) A nonhydrostatic version of the Penn StateNCAR mesoscale model: Validation tests and simulation of an atlantic cyclone and cold front. Mon Wea Rev 121:1493–1513 CrossRef
 Fahey DW, Solomon S, Kawa SR, Loewenstein M, Podolske JR, Strahan SE, Chan KR (1990) A diagnostic for denitrification in the winter polar stratospheres. Nature 345:698–702 CrossRef
 Farge M, Sadourny R (1989) Wavevortex dynamics in rotating shallow water. J Fluid Mech 206:433–462 CrossRef
 Fomichev VI, Ward WE, Beagley SR, McLandress C, McConnell JC, McFarlane NA, Shepherd TG (2002) Extended Canadian Middle Atmosphere Model: Zonalmean climatology and physical parameterizations. J Geophys Res  Atmospheres 107(D10):4087 CrossRef
 Gassmann A, Herzog HJ (2007) A consistent timesplit numerical scheme applied to the nonhydrostatic compressible equations. Mon Wea Rev 135:20–36 CrossRef
 Godunov SK (1959) A difference scheme for numerical computation of discontinuous solutions of equations in fluid dynamics. Math Sb 47:271, also: Cornell Aero. Lab. translation
 Holton JR (2004) An introduction to dynamic meteorology, Fourth edn. Academic Press, Inc., ISBN 0123540151, 535 pp.
 Jacobson MZ (2005) Fundamentals of atmospheric modeling, 2nd edn. Cambridge University Press, 813 pp.
 Jöckel P, von Kuhlmann R, Lawrence MG, Steil B, Brenninkmelter CAM, Crutzen PJ, Rasch PJ, Eaton B (2001) On a fundamental problem in implementing fluxform advection schemes for tracer transport in 3dimensional general circulation and chemistry transport models. Quart J Roy Meteor Soc 127:1035–1052
 Johnson SD, Battisti DS, Sarachik ES (2000) Empirically derived Markov models and prediction of tropical Pacific sea surface temperature anomalies. J Climate 13:3–17 CrossRef
 van Leer B (1979) Towards the ultimate conservative difference scheme. V. A secondorder sequel to Godunov’s method. J Comput Phys 32:101–136
 Lin SJ (1997) A finite volume integration method for computing pressure gradient forces in general vertical coordinates. Quart J Roy Meteor Soc 123:1749–1762
 Lin SJ (2004) A “vertically Lagrangian” finitevolume dynamical core for global models. Mon Wea Rev 132:2293–2307 CrossRef
 Lin SJ, Rood RB (1996) Multidimensional fluxform semiLagrangian transport scheme. Mon Wea Rev 124:2046–2070 CrossRef
 Lin SJ, Rood RB (1997) An explicit fluxform semiLagrangian shallow water model on the sphere. Quart J Roy Meteor Soc 123:2477–2498 CrossRef
 Machenhauer B, Kaas E, Lauritzen PH (2008) Finite volume techniques in atmospheric models. In: Ciarlet P, Temam R, Tribbia J (eds) Handbook of numerical analysis: Special volume on computational methods for the atmosphere and oceans, vol 14, Elsevier, pp 3–120, 784 pp.
 McCrea GJ, Gooden WR, Seinfield JH (1982) Numerical solution of the atmospheric diffusion equation for chemically reacting flows. J Comput Phys 14:1–42 CrossRef
 Mechoso CR, Yamazaki K, Kitoh A, Arakawa A (1985) Numerical forecasts of stratospheric warming events during the winter of 1979. Mon Wea Rev 113:1015–1029 CrossRef
 Mote P, O’Neill A (eds) (2000) Numerical Modeling of the Global Atmosphere in the Climate System. Kluwer Academic Publishers, NATO Science Series C: Mathematical and Physical Sciences Vol. 550, ISBN 0792363019, 517 pp.
 Plumb RA, Ko MKW (1992) Interrelationships between mixing ratios of long lived stratospheric constituents. J Geophys Res 97:10,145–10,156
 Prather MJ (1986) Numerical advection by conservation of secondorder moments. J Geophys Res 91:6671–6681 CrossRef
 Putman WM, Lin SJ (2009) A finitevolume dynamical core on the cubedsphere grid. In: Numerical Modeling of Space Plasma Flows: Astronum2008, Astronomical Society of the Pacific Conference Series, vol 406, pp 268–276
 Rančić M, Zhang H, SavicJovcic V (2008) Nonlinear advection schemes on the octagonal grid. Mon Wea Rev 136:4668–4686 CrossRef
 Randall DA (2000) General Circulation Model Development: Past, Present, and Future. Academic Press, 807 pp.
 Rasch PJ, Williamson DL (1991) The sensitivity of a general circulation model climate to the moisture transport formulation. J Geophy Res 96:13,123–13,137
 Rasch PJ, Coleman DB, Mahowald N, Williamson DL, Lin SJ, Boville BA, Hess P (2006) Characteristics of atmospheric transport using three numerical formulations for atmospheric dynamics in a single gcm framework. J Climate 19:2243–2266 CrossRef
 Rienecker MM, Suarez MJ, Todling R, Bacmeister J, Takacs L, Liu HC, Gu W, Sienkiewicz M, Koster RD, Gelaro R, Stajner I, Nielsen E (2008) The GEOS5 data assimilation system – Documentation of versions 5.0.1 and 5.1.0. Technical Report Series on Global Modeling and Data Assimilation NASA/TM2007104606, Vol. 27, NASA Goddard Space Flight Center, 92 pp.
 Ringler TD, Heikes RP, Randall DA (2000) Modeling the atmospheric general circulation using a spherical geodesic grid: A new class of dynamical cores. Mon Wea Rev 128:2471’–2489
 Rood RB (1987) Numerical advection algorithms and their role in atmospheric transport and chemistry models. Rev Geophys 25:71–100 CrossRef
 Rotman D, Tannahill JR, Kinnison DE, Connell PS, Bergmann D, Proctor D, Rodriguez JM, Lin SJ, Rood RB, Prather MJ, Rasch PJ, Considine DB, Ramaroson R, Kawa SR (2001) Global modeling initiative assessment model: Model description, integration, and testing of the transport shell. J Geophys Res 106(D2)(10.1029/2000JD900463):1669–1692 CrossRef
 Sadourny R (1972) Conservative finitedifference approximations of the primitive equations on quasiuniform spherical grids. Mon Wea Rev 100:136–144 CrossRef
 Sadourny R, Arakawa A, Mintz Y (1968) Integration of the nondivergent barotropic vorticity equation with an icosahedralhexagonal grid for the sphere. Mon Wea Rev 96:351–356 CrossRef
 Santer BD, Wigley TML, Gaffen DJ, Bengtsson L, Doutriaux C, Boyle JS, Esch M, Hnilo JJ, Jones PD, Meehl GA, Roeckner E, Taylor KE, Wehner MF (2000) Interpreting differential temperature trends at the surface and in the lower troposphere. Science 287:1227–1232 CrossRef
 Satoh M (2004) Atmospheric circulation dynamics and general circulation models. Springer (Praxis), 643 pp.
 Schoeberl MR, Strobel DF (1980) Numericalsimulation of sudden stratospheric warmings. J Atmos Sci 37:214–236 CrossRef
 Schoeberl MR, Douglass AR, Zhu Z, Pawson S (2003) A comparison of the lower stratospheric agespectra derived from a general circulation model and two data assimilation systems. J Geophys Res 108, no. 4113 CrossRef
 Skamarock WC, Klemp JB (1992) The stability of timesplit numerical methods for the hydrostatic and the nonhydrostatic elastic equations. Mon Wea Rev 120:2109–2127 CrossRef
 Staniforth A, Wood N, Cole J (2002) Analysis of the numerics of physicsdynamics coupling. Quart J R Meteor Soc 128(586):2779–2799 CrossRef
 Strang G (1968) On the construction and comparison of difference schemes. SIAM J Numer Anal 5:506–517 CrossRef
 Thuburn J (2008a) Numerical wave propagation on the hexagonal Cgrid. J Comput Phys 227: 5836–5858 CrossRef
 Thuburn J (2008b) Some conservation issues for dynamical cores of NWP and climate models. J Comput Phys 227(7):3715–3730 CrossRef
 Trenberth KE (ed) (1992) Climate System Modeling. Cambridge University Press, 788 pp.
 Vallis GK (1992) Mechanism and parameterizations of geostrophic adjustment and a variational approach to balanced flow. J Atmos Sci 49:1144–1160 CrossRef
 Walko RL, Avissar R (2008) The OceanLandAtmosphere Model (OLAM). Part I: Shallowwater tests. Mon Wea Rev 136:4033–4044
 Washington WM, Parkinson CL (l2005) An introduction to threedimensional climate modeling, 2nd edn. University Science Books, iSBN: 1891389351, 353 pp.
 White AA, B J Hoskins IR, Staniforth A (2005) Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasihydrostatic and nonhydrostatic. Quart J Roy Meteor Soc 131:2081Ð2107 CrossRef
 White L, Adcroft A (2008) A highorder finite volume remapping scheme for nonuniform grids: The piecewise quartic method (PQM). J Comput Phys 227:7394–7422 CrossRef
 Wicker LJ, Skamarock WC (1998) A timesplitting scheme for the elastic equations incorporating secondorder RungeKutta time differencing. Mon Wea Rev 126:1992–1999 CrossRef
 Williamson DL (1968) Integration of the barotropic vorticity equations on a spherical geodesic grid. Tellus 20:642–653 CrossRef
 Williamson DL (2002) Timesplit versus processsplit coupling of parameterizations and dynamical core. Mon Wea Rev 130:2779–2799 CrossRef
 Williamson DL (2007) The evolution of dynamical cores for global atmospheric models. J Meteorol Soc Japan 85B:241–269 CrossRef
 Yanenko NN (1971) The method of fractional steps. SpringerVerlag
 Zalesak ST (1981) Very high order and pseudospectral fluxcorrected transport (FCT) algorithms for conservation laws. In: Vichnevetsky R, Steplman RS (eds) Advances in Computer Methods for Partial Differential Equations IV, International Association for Mathematics and Computers in Simulation, Rutgers University, New Brunswick, N.J.
 Title
 A Perspective on the Role of the Dynamical Core in the Development of Weather and Climate Models
 Book Title
 Numerical Techniques for Global Atmospheric Models
 Pages
 pp 513537
 Copyright
 2011
 DOI
 10.1007/9783642116407_15
 Print ISBN
 9783642116391
 Online ISBN
 9783642116407
 Series Title
 Lecture Notes in Computational Science and Engineering
 Series Volume
 80
 Series ISSN
 14397358
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 Editors

 Peter Lauritzen ^{(ID1)}
 Christiane Jablonowski ^{(ID2)}
 Mark Taylor ^{(ID3)}
 Ramachandran Nair ^{(ID4)}
 Editor Affiliations

 ID1. Atmospheric Research, Dept. Climate/Global Dyn., National Center for
 ID2. Dept. Atmospheric, Oceanic &, Space Sciences, University of Michigan
 ID3. Organization 1433, MS0370, Sandia National Laboratories
 ID4. (NCAR), Inst. for Mathematics Applied to, National Center for Atmospheric Research
 Authors

 Richard B. Rood ^{(1)}
 Author Affiliations

 1. Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, 2455 Hayward Street, Ann Arbor, MI, 48109, USA
Continue reading...
To view the rest of this content please follow the download PDF link above.