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Numerical Techniques for Global Atmospheric Models pp 185–250Cite as

Atmospheric Transport Schemes: Desirable Properties and a Semi-Lagrangian View on Finite-Volume Discretizations

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 80))

Abstract

This chapter has twofold purpose. After a short introduction to the mass continuity equations in atmospheric models, desirable properties for mass transport schemes intended for meteorological applications are discussed in some detail. This includes a discussion on the complications caused by the non-linearity of most problems of interest that makes it hard to define accuracy and convergence as the ‘truth’ is not known. Thereafter, some finite-volume schemes from the atmospheric literature are reviewed and discussed. To complement the large existing literature on finite-volume schemes, a less frequently discussed semi-Lagrangian derivation of the finite-volume method is given that focuses on ‘remap-type’ schemes where the space and time discretizations are combined rather than separated. A discussion on the challenges in deriving accurate schemes intended for global models and non-traditional spherical grids is given as well.

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References

  • van Albada GD, van Leer B, Roberts WW (1982) A comparative study of computational methods in cosmic gas dynamics. Astronomy and Astrophysics 108:76–84

    MATH  Google Scholar 

  • Artebrant R, Torrilhon M (2008) Increasing the accuracy in locally divergence-preserving finite volume schemes for MHD. J Comput Phys 227(6):3405–3427

    Article  MATH  MathSciNet  Google Scholar 

  • Barth T, Frederickson P (1990) Higher-order solution of the Euler equations on unstructured grids using quadratic reconstruction. In: AIAA Paper 90-0013

    Google Scholar 

  • Barth T, Jespersen D (1989) The design and application of upwind schemes on unstructured meshes. Proc AIAA 27th Aerospace Sciences Meeting, Reno

    Google Scholar 

  • Bates JR, McDonald A (1982) Multiply-upstream, semi-Lagrangian advective schemes: Analysis and application to a multi-level primitive equation model. Mon Wea Rev 110(12):1831–1842

    Article  Google Scholar 

  • Blossey PN, Durran DR (2008) Selective monotonicity preservation in scalar advection. J Comput Phys 227(10):5160–5183

    Article  MATH  MathSciNet  Google Scholar 

  • Bockman SF (1989) Generalizing the formula for areas of polygons to moments. The American Mathematical Monthly 96:131–132

    Article  MATH  MathSciNet  Google Scholar 

  • Brasseur GP, Hauglustaine DA, Walters S, Rasch PJ, Muller JF, Granier C, Tie XX (1998)

    Google Scholar 

  • MOZART, a global chemical transport model for ozone and related chemical tracers: 1. model description. J Geophys Res 103:28,265–28,289

    Google Scholar 

  • Colella P, Sekora MD (2008) A limiter for ppm that preserves accuracy at smooth extrema. J Comput Phys 227:7069–7076 1686

    MathSciNet  Google Scholar 

  • Colella P, Woodward PR (1984) The piecewise parabolic method (PPM) for gas-dynamical simulations. J Comput Phys 54:174–201

    Article  MATH  MathSciNet  Google Scholar 

  • Collins WD, Rasch PJ, Boville BA, Hack JJ, McCaa JR, Williamson DL, Kiehl JT, Briegleb B (2004) Description of the NCAR Community Atmosphere Model (CAM 3.0). NCAR Tech. Note, NCAR/TN-464CSTR

    Google Scholar 

  • van Dop H, Addis R, Fraser G, Girardi F, Graziani G, Inoue Y, Kelly N, KlugW,Kulmala A, Nodop K, Pretel J (1998) Etex: A European tracer experiment; observations, dispersion modelling and emergency response. Atmospheric Environment 32:4089–4094

    Article  Google Scholar 

  • Doswell CAI (1984) A kinematic analysis of frontogenesis associated with a nondivergent vortex. J Atmos Sci pp 1242–1248

    Google Scholar 

  • Dukowicz JK (1984) Conservative rezoning (remapping) for general quadrilateral meshes. J Com-put Phys 54:411–424 1698

    Google Scholar 

  • Dukowicz JK, Baumgardner JR (2000) Incremental remapping as a transport/advection algorithm. J Comput Phys 160:318–335

    Article  MATH  Google Scholar 

  • Dukowicz JK, Kodis JW (1987) Accurate conservative remapping (rezoning) for arbitrary Lagrangian-Eulerian computations. SIAM Journal on Scientific and Statistical Computing 8(3):305–321

    Article  MATH  MathSciNet  Google Scholar 

  • Durran DD (1999) Numerical Methods for Wave Equations in Geophysical Fluid Dynamics, Springer-Verlag

    Google Scholar 

  • Eluszkiewicz J, Hemler RS, Mahlman JD, Bruhwiler L, Takacs LL (2000) Sensitivity of age-of-air calculations to the choice of advection scheme. J Atmos Sci 57:3185–3201

    Article  Google Scholar 

  • Galmarini S, Bianconi R, Addis R, Andronopoulos S, Astrup P, Bartzis JC, Bellasio R, Buck-ley R, Champion H, Chino M, D’Amours R, Davakis E, Eleveld H, Glaab H, Manning A, Mikkelsen T, Pechinger U, Polreich E, Prodanova M, Slaper H, Syrakov D, Terada H, der Auwera LV (2004) Ensemble dispersion forecasting–part II: Application and evaluation.Atmospheric Environment 38:4619–4632

    Google Scholar 

  • Garimella R, Kucharik M, Shashkov M (2007) An efficient linearity and bound preserving conservative interpolation (remapping) on polyhedral meshes. Computers & Fluids 36:224–237

    Article  MATH  MathSciNet  Google Scholar 

  • Girardi F, Graziani G, van Veltzen D, Galmarini S, Mosca S, Bianconi R, Bellasio R, Klug W (1998) The ETEX project. EUR report 181-43 en., Office for official publication of the European Communities, Luxembourg, 108 pp

    Google Scholar 

  • 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 Haltiner GJ, Williams RT (1980) Numerical Prediction and Dynamic Meteorology. John Wiley & Sons, 477 pp.

    Google Scholar 

  • Harris LM, Lauritzen PH,Mittal R (2010) A flux-form version of the conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed sphere grid. J Comput Phys In press Harten A (1983) On the symmetric form of systems of conservation laws with entropy. J Comput Phys 49:151–164

    Google Scholar 

  • Harten A, Engquist B, Osher S, Chakravarthy SR (1987) Uniformly high order accurate essentially non-oscillatory schemes iii. J Comput Phys 71:231–303

    Article  MATH  MathSciNet  Google Scholar 

  • Hirt CW, Amsden AA, Cook JL (1974) An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J Comput Phys 14(3):227–253

    Article  MATH  Google Scholar 

  • Hortal M (2002) The development and testing of a new two-time-level semi-Lagrangian scheme (SETTLS) in the ecmwf forecast model. Q J R Meteorol Soc 128(583):1671–1687

    Article  Google Scholar 

  • Jablonowski C, Lauritzen PH, Taylor MA, Nair RD (2010) Idealized test cases for the dynamical cores of atmospheric general circulation models. Geoscientific Model Development In prep.

    Google Scholar 

  • http://esse.engin.umich.edu/admg/publications.phpJöckel P, von Kuhlmann R, Lawrence MG, Steil B, Brenninkmeijer C, Crutzen PJ, Rasch PJ

  • Eaton B (2001) On a fundamental problem in implementing flux-form advection schemes for tracer transport in 3-dimensional general circulation and chemistry transport models. QJR

    Google Scholar 

  • Meteorol Soc 127(573):1035–1052 Jones PW (1999) First- and second-order conservative remapping schemes for grids in spherical coordinates. Mon Wea Rev 127:2204–2210

    Google Scholar 

  • Lamarque JF, Kinnison DE, Hess PG, Vitt F (2008) Simulated lower stratospheric trends between 1970 and 2005: Identifying the role of climate and composition changes. J Geophys Res 113(D12301)

    Google Scholar 

  • Laprise JP, Plante A (1995) A class of semi-Lagrangian integrated-mass (SLIM) numerical transport algorithms. Mon Wea Rev 123:553–565

    Article  Google Scholar 

  • Lauritzen PH (2007) A stability analysis of finite-volume advection schemes permitting long time steps. Mon Wea Rev 135:2658–2673

    Article  Google Scholar 

  • Lauritzen PH, Nair RD (2008) Monotone and conservative cascade remapping between spher- ical grids (CaRS): Regular latitude-longitude and cubed-sphere grids. Mon Wea Rev 136: 1416–1432

    Article  Google Scholar 

  • Lauritzen PH, Thuburn J (2010) Evaluating advection/transport schemes using scatter plots and numerical mixing diagnostics. Quart J Roy Met Soc In prep

    Google Scholar 

  • Lauritzen PH, Kaas E,Machenhauer B (2006) A mass-conservative semi-implicit semi-Lagrangian limited area shallow water model on the sphere. Mon Wea Rev 134:1205–1221

    Article  Google Scholar 

  • Lauritzen PH, Kaas E, Machenhauer B, Lindberg K (2008) A mass-conservative version of the semi-implicit semi-Lagrangian HIRLAM. QJR Meteorol Soc 134

    Google Scholar 

  • Lauritzen PH, Nair RD, Ullrich PA (2010) A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid. J Comput Phys 229:1401–1424

    Article  MATH  MathSciNet  Google Scholar 

  • Lee SM, Yoon SC, Byun DW (2004) The effect of mass inconsistency of the meteorological field generated by a common meteorological model on air quality modeling. Atmospheric

    Google Scholar 

  • Environment 38(18):2917–2926 van Leer B (1977) Towards the ultimate conservative difference scheme. IV: A new approach to numerical convection. J Comput Phys 23:276–299

    Google Scholar 

  • Leonard BP (1991) The ULTIMATE conservative difference scheme applied to unsteady one- dimensional advection. Comput Methods Appl Mech Eng 88:17–74

    Article  MATH  Google Scholar 

  • Leonard BP, Lock A,MacVean M(1996) Conservative explicit unrestricted-time-step multidimen- sional constancy-preserving advection schemes. Mon Wea Rev 124:2588–2606

    Article  Google Scholar 

  • Leslie LM, Dietachmayer GS (1997) Comparing schemes for integrating the Euler equations. Mon Wea Rev 125(7):1687–1691

    Article  Google Scholar 

  • LeVeque RJ (1996) High-resolution conservative algorithms for advection in incompressible flow. SIAM Journal on Numerical Analysis 33:627–665

    Article  MATH  MathSciNet  Google Scholar 

  • Levy MN, Nair RD, Tufo HM (2007) High-order Galerkin method for scalable global atmospheric models. Comput Geosci 33:1022–1035

    Article  Google Scholar 

  • Lin SJ (2004) A ’vertically Lagrangian’ finite-volume dynamical core for global models. MonWea Rev 132:2293–2307

    Google Scholar 

  • Lin SJ, Rood RB (1996) Multidimensional flux-form semi-Lagrangian transport schemes. Mon Wea Rev 124:2046–2070

    Article  Google Scholar 

  • Lipscomb WH, Ringler TD (2005) An incremental remapping transport scheme on a spherical geodesic grid. Mon Wea Rev 133:2335–2350

    Article  Google Scholar 

  • Liu Y, wang Shu C, Tadmor E, Zhang M (2007) Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction. SIAM J Numer Anal pp 45–2442

    Google Scholar 

  • Lorenz EN (1982) Atmospheric predictability experiments with a large numerical model. Tellus pp 505–513

    Google Scholar 

  • Machenhauer B, Kaas E, Lauritzen PH (2009) Finite volume methods in meteorology, in: R. Temam, J. Tribbia, P. Ciarlet (Eds.), Computational methods for the atmosphere and the oceans. Handbook of Numerical Analysis 14, Elsevier, 2009, pp.3-120

    Google Scholar 

  • McGregor JL (2005) Geostrophic adjustment for reversibly staggered grids. Mon Wea Rev 133:1119–1128

    Article  Google Scholar 

  • Miura H (2007) An upwind-biased conservative advection scheme for spherical hexagonal- pentagonal grids. Mon Wea Rev 135:4038–4044

    Article  Google Scholar 

  • Moorthi S, Higgins RW, Bates JR (1995) A global multilevel atmospheric model using a vec- tor semi-Lagrangian finite-difference scheme. Part II: Version with physics. Mon Wea Rev 123(5):1523–1541 1794

    Google Scholar 

  • Morrison H, Gettelman A (2008) A new two-moment bulk stratiform cloud microphysics scheme in the community atmosphere model, version 3 (CAM3). Part I: Description and numerical tests. J Climate 21:3642–3659 1797

    Google Scholar 

  • Nair RD, Jablonowski C (2008)Moving vortices on the sphere: A test case for horizontal advection problems. Mon Wea Rev 136:699–711

    Google Scholar 

  • Nair RD, Lauritzen PH (2010) A class of deformational flow test cases for linear transport problems on the sphere. J Comput Phys 229:8868–8887

    Article  MATH  MathSciNet  Google Scholar 

  • Nair RD, Machenhauer B (2002) The mass-conservative cell-integrated semi-Lagrangian advec- tion scheme on the sphere. Mon Wea Rev 130(3):649–667

    Article  Google Scholar 

  • Nair RD, Scroggs JS, Semazzi FHM (2002) Efficient conservative global transport schemes for climate and atmospheric chemistry models. Mon Wea Rev 130(8):2059–2073

    Article  Google Scholar 

  • Nair RD, Choi HW, Tufo HM(2009) Computational aspects of a scalable high-order discontinuous

    Google Scholar 

  • Galerkin atmospheric dynamical core. Computers & Fluids 38:309–319Norman MR, Nair RD (2008) Inherently conservative nonpolynomial-based remapping schemes: Application to semi-Lagrangian transport. Mon Wea Rev 126:5044–5061

    Google Scholar 

  • Norman MR, Semazzi FHM, Nair RD (2009) Conservative cascade interpolation on the sphere: An intercomparison of various non-oscillatory reconstructions. Quart J Roy Met Soc 135:795–805

    Article  Google Scholar 

  • Ovtchinnikov M, Easter RC (2009) Nonlinear advection algorithms applied to interrelated tracers: Errors and implications for modeling aerosol-cloud interactions. Mon Wea Rev 137:632–644

    Article  Google Scholar 

  • Pietrzak J (1998) The use of TVD limiters for forward-in-time upstream-biased advection schemes in ocean modeling. Mon Wea Rev 126:812–830

    Article  Google Scholar 

  • Plumb RA (2007) Tracer interrelationships in the stratosphere. Rev Geophys 45(RG4005)

    Google Scholar 

  • Plumb RA, Ko M (1992) Interrelationships between mixing ratios of long-lived stratospheric constituents. J Geophys Res 97:10,145–10,156

    Google Scholar 

  • Prather MJ, Zhu X, Strahan SE, Steenrod SD, Rodriguez JM (2008) Quantifying errors in trace species transport modeling. Proceedings of the National Academy of Science pp 19,617–19,621

    Google Scholar 

  • Purser RJ, Leslie LM (1991) An efficient interpolation procedure for high-order three-dimensional semi-Lagrangian models. Mon Wea Rev 119:2492–2498

    Article  Google Scholar 

  • PutmanWM, Lin SJ (2007) Finite-volume transport on various cubed-sphere grids. J Comput Phys 227(1):55–78

    Article  MathSciNet  Google Scholar 

  • Ranˇci´c M (1992) Semi-Lagrangian piecewise biparabolic scheme for two-dimensional horizontal advection of a passive scalar. Mon Wea Rev 120:1394–1405

    Google Scholar 

  • Rasch PJ, Coleman DB, Mahowald N,Williamson DL, Lin SJ, Boville BA, Hess P (2006) Charac- teristics of atmospheric transport using three numerical formulations for atmospheric dynamics in a single GCM framework. J Climate 19:2243–2266

    Article  Google Scholar 

  • Roe PL (1985) Lecture Notes in Applied Mathematics, vol 22, New York: Springer-Verlag, chap

    Google Scholar 

  • Some contributions to modeling of discontinuous flows, pp 163–193

    Google Scholar 

  • Rood RB (1987) Numerical advection algorithms and their role in atmospheric transport and chemistry models. Rev Geophys 25:71–100

    Article  Google Scholar 

  • Schär C, Smolarkiewicz PK (1996) A synchronous and iterative flux-correction formalism for coupled transport equations. J Comput Phys 128:101–120

    Article  MATH  MathSciNet  Google Scholar 

  • Smolarkiewicz PK (2006) Multidimensional positive definite advection transport algorithm: An overview. Int J Numer Methods Fluids 50:1123–1144

    Article  MATH  MathSciNet  Google Scholar 

  • Smolarkiewicz PK, Grabowski WW (1990) The multidimensional positive definite advection transport algorithm: Nonoscillatory option. J Comput Phys 86:355–375

    Article  MATH  Google Scholar 

  • Staniforth A, Côté J (1991) Semi-Lagrangian integration schemes for atmospheric models-a review. Mon Wea Rev 119:2206–2223

    Article  Google Scholar 

  • Staniforth A, White A, Wood N (2003) Analysis of semi-Lagrangian trajectory computations. Q J R Meteorol Soc 129(591):2065–2085

    Article  Google Scholar 

  • Starr VP (1945) A quasi-Lagrangian system of hydrodynamical equations. J Atmos Sci 2:227–237

    MathSciNet  Google Scholar 

  • Strang G (1968) On the construction and comparison of difference schemes. SIAM J Numer Anal 5:506–517

    Article  MATH  MathSciNet  Google Scholar 

  • Thuburn J (2008) Some conservation issues for the dynamical cores of NWP and climate models. J Comput Phys 227:3715–3730 1848

    Article  MathSciNet  Google Scholar 

  • Thuburn J, Mclntyre M (1997) Numerical advection schemes, cross-isentropic random walks, and correlations between chemical species. J Geophys Res 102(D6):6775–6797

    Google Scholar 

  • Thuburn J, Zerroukat M, Wood N, Staniforth A (2010) Coupling a mass conserving semi- Lagrangian scheme (SLICE) to a semi-implicit discretization of the shallow-water equations: Minimizing the dependence on a reference atmosphere. Q J R Meteorol Soc 136:146–154

    Article  Google Scholar 

  • Toro EF (1999) Riemann Solvers and Numerical Methods for Fluid Dynamics, Second edn. Springer, ISBN-10: 3540659668, 624 pp.

    Google Scholar 

  • Trenberth KE, Smith L (2005) The mass of the atmosphere: A constraint on global analyses. J Climate 18:864–875

    Article  Google Scholar 

  • Ullrich PA, Lauritzen PH, Jablonowski C (2009) Geometrically exact conservative remap- ping (GECoRe): Regular latitude-longitude and cubed-sphere grids. Mon Wea Rev 137(6): 1721–1741

    Article  Google Scholar 

  • Ullrich PA, Jablonowski C, van Leer BL (2010) Riemann-solver-based high-order finite-volume models for the shallow-water equations on the sphere. J Comput Phys 229:6104–6134

    Article  MATH  MathSciNet  Google Scholar 

  • Waugh DW, Hall TM (2002) Age of stratospheric air: Theory, observations, and models. Rev Geophys 40

    Google Scholar 

  • Waugh DW, Plumb RA, Elkins JW, Fahey DW, Boering KA, Dutton GS, Volk CM, Keim E, Gao RS, Daube BC, Wofsy SC, Loewenstein M, Podolske JR, Chan KR, Proffitt MH, Kelly KK

    Google Scholar 

  • Newman PA, Lait LR (1997) Mixing of polar vortex air into middle latitudes as revealed by tracer-tracer scatterplots. J Geophys Res 120(D11):119–134

    Google Scholar 

  • White L, Adcroft A (2008) A high-order finite volume remapping scheme for nonuniform grids: The piecewise quartic method (PQM). J Comput Phys 227:7394–7422

    Article  MATH  MathSciNet  Google Scholar 

  • Wild O, Prather MJ (2006) Global tropospheric ozone modeling: Quantifying errors due to grid resolution. J Geophys Res 111(D11305)

    Google Scholar 

  • Williamson DL, Olson J (1994) Climate simulations with a semi-Lagrangian version of the NCAR Community Climate Model. Mon Wea Rev 122(7):1594–1610

    Article  Google Scholar 

  • Williamson DL, Drake JB, Hack JJ, Jakob R, Swarztrauber PN (1992) A standard test set for numerical approximations to the shallow water equations in spherical geometry. J Comput Phys 102:211–224

    Article  MATH  MathSciNet  Google Scholar 

  • Xiao F, Yabe T, Peng X, Kobayashi H (2002) Conservative and oscillation-less atmospheric transport schemes based on rational functions. J Geophys Res 107(D22):4609

    Google Scholar 

  • Yabe T, Tanaka R, Nakamura T, Xiao F (2001) An exactly conservative semi-Lagrangian scheme (cip csl) in one dimension. Mon Wea Rev 129(2):332–334

    Article  Google Scholar 

  • Yeh KS (2007) The streamline subgrid integration method: I. quasi-monotonic second-order transport schemes. J Comput Phys 225:1632–1652

    Article  MATH  MathSciNet  Google Scholar 

  • Zalesak ST (1979) Fully multidimensional flux-corrected transport algorithms for fluids. J Comput Phys 31:335–362

    Article  MATH  MathSciNet  Google Scholar 

  • Zerroukat M, Wood N, Staniforth A (2002) SLICE: A semi-Lagrangian inherently conserving and efficient scheme for transport problems. Q J R Meteorol Soc 128:2801–2820

    Article  Google Scholar 

  • Zerroukat M, Wood N, Staniforth A (2004) SLICE-S: A semi-Lagrangian inherently conserving and efficient scheme for transport problems on the sphere. Q J R Meteorol Soc 130:2649–2664

    Article  Google Scholar 

  • Zerroukat M, Wood N, Staniforth A (2005) A monotonic and positive-definite filter for a semi-Lagrangian inherently conserving and efficient (SLICE) scheme. Q J R Meteorol Soc 131(611):2923–2936

    Article  Google Scholar 

  • Zerroukat M, Wood N, Staniforth A (2006) The parabolic spline method (PSM) for conservative transport problems. Int J Numer Meth Fluids 51:1297–1318

    Article  MATH  MathSciNet  Google Scholar 

  • Zerroukat M, Wood N, Staniforth A (2007) Application of the parabolic spline method (PSM) to a multi-dimensional conservative semi-Lagrangian transport scheme (SLICE). J Comput Phys 225:935–948

    Article  MATH  MathSciNet  Google Scholar 

  • Zerroukat M, Staniforth A, Wood N (2010) The monotonic quartic spline method (QSM) for conservative transport problems. J Comput Phys 229:1150–1166

    Article  MATH  MathSciNet  Google Scholar 

  • Zhang K, Wan H, Wang B, Zhang M (2008) Consistency problem with tracer advection in the atmospheric model GAMIL. Adv Atmos Sci 25(2)

    Google Scholar 

  • Zubov VA, Rozanov EV, Schlesinger ME (1999) Hybrid scheme for three-dimensional advective transport. Mon Wea Rev 127(6):1335–1346

    Article  Google Scholar 

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Acknowledgements

Thanks to Dr. S. Galmarini (Institute for Environment and Sustainability, European Commission, Joint Research Center) and Dr. A. Baklanov (Danish Meteorological Institute) for details on the ETEX experiment. Many fruitful discussions with Dr. D.L. Williamson (NCAR), Dr. P. Rasch (PNNL), Dr. A.Gettelman (NCAR), Dr. W. Skamarock (NCAR), Dr. M. Taylor (Sandia National Laboratories) and Dr. R. Mittal (NCAR) are acknowledged as well as the internal review performed by Dr. D.L. Williamson and Dr. C. Erath, and the anonymous and Editor (Dr. C. Jablonowski and Dr. M.A. Taylor) reviews. The authors gratefully acknowledge Prof. J.Thuburn’s suggestions on numerical mixing tests. The first and third authors were partially supported by the DOE BER Program under award DE-SC0001658. The National Center for Atmospheric Research is sponsored by the National Science Foundation.

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  1. National Center for Atmospheric Research, 1850 Table Mesa Drive, Boulder, CO, 80305, USA

    Peter H. Lauritzen & Ramachandran D. Nair

  2. University of Michigan, 2455 Hayward St., Ann Arbor, MI, 48109, USA

    Paul A. Ullrich

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  1. Peter H. Lauritzen
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Correspondence to Peter H. Lauritzen .

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Editors and Affiliations

  1. Atmospheric Research, Dept. Climate/Global Dyn., National Center for, Boulder, Colorado, USA

    Peter Lauritzen

  2. Dept. Atmospheric, Oceanic &, Space Sciences, University of Michigan, Hayward St. 2455, Ann Arbor, 48109, Michigan, USA

    Christiane Jablonowski

  3. Organization 1433, MS-0370, Sandia National Laboratories, Albuquerque, New Mexico, USA

    Mark Taylor

  4. (NCAR), Inst. for Mathematics Applied to, National Center for Atmospheric Research, Boulder, Colorado, USA

    Ramachandran Nair

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Lauritzen, P.H., Ullrich, P.A., Nair, R.D. (2011). Atmospheric Transport Schemes: Desirable Properties and a Semi-Lagrangian View on Finite-Volume Discretizations. In: Lauritzen, P., Jablonowski, C., Taylor, M., Nair, R. (eds) Numerical Techniques for Global Atmospheric Models. Lecture Notes in Computational Science and Engineering, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11640-7_8

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