The Pros and Cons of Diffusion, Filters and Fixers in Atmospheric General Circulation Models

Lecture Notes in Computational Science and Engineering

Volumn 80, Issue , 2011, Pages 381-493

  Jablonowski, Christiane ^a   Williamson, David L ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BANDPASS FILTERS; CLIMATE MODELS; CLOUDS; DAMPING; EARTH ATMOSPHERE; REYNOLDS NUMBER;

ATMOSPHERIC GENERAL CIRCULATION MODELS; COMPUTATIONAL STABILITY; CONSERVATION PROPERTIES; DIFFUSION MECHANISMS; DIFFUSION PROPERTIES; DISPERSION ERROR; DISSIPATIVE PROCESS; NUMERICAL SCHEME;

DIFFUSION;

EID: 85011309955     PISSN: 14397358     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-11640-7_13     Document Type: Chapter

References (243)

1. Andrews DG, Mahlman JD, Sinclair RW (1983) Eliassen-Palm diagnostics of wave-mean flow interaction in the GFDL “SKYHI” general circulation model. J Atmos Sci 40:2768-2784 Arakawa A (1966) Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow. Part I. J Comput Phys 1:119-143
2. Arakawa A., Hsu Y.J.G. (1990) Energy conserving and potential-enstrophy dissipating schemes for the shallow water equations. Mon Wea Rev 118:1960-1969
3. Arakawa A, Lamb VR (1981) A potential enstrophy and energy conserving scheme for the shallow water equations. Mon Wea Rev 109:18-36
4. Arakawa A, Suarez MJ (1983) Vertical differencing of the primitive equations in sigma coordinates. Mon WeaRev 111(1):34-45
5. Asselin R (1972) Frequency filter for time integrations. Mon Wea Rev 100(5):487-490
6. Baldauf M (2010) Linear stability analysis of Runge-Kutta based partial time-splitting schemes for the Euler equations. Mon Wea Rev 138:4475-4496
7. Bates JR, Semazzi FHM, Higgins RW, Barros SRM (1990) Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver. Mon Wea Rev 118:1615-1627
8. Bates JR, Moorthi S, Higgins RW (1993) A global multilevel atmospheric model using a vector semi-Lagrangian finite difference scheme. Part I: Adiabatic formulation. Mon Wea Rev 121:244-263
9. Becker E (2001) Symmetric stress tensor formulation of horizontal momentum diffusion in global models of atmospheric circulation. J Atmos Sci 58:269-282
10. Becker E (2003) Frictional heating in global climate models. Mon Wea Rev 131:508-520
11. Becker E, Burkhardt U (2007) Nonlinear horizontal diffusion for GCMs. Mon Wea Rev 135: 1439-1454
12. Bermejo R, Staniforth A (1992) The Conversion of Semi-Lagrangian Advection Schemes to QuasiMonotone Schemes. Mon Wea Rev 120:2622-2632
13. Black TL (1994) The new NMC mesoscale Eta model: Description and forecast examples. Weather and Forecasting 9:265-284
14. Boer GJ, Denis B (1997) Numerical covergence of the dynamics of a GCM. Climate Dynamics 13:359-374
15. Boer GJ, Shepherd TG (1983) Large-scale two-dimensional turbulence in the atmosphere. J Atmos Sci 40:164-184
16. Bonaventura L, Ringler T (2005) Analysis of discrete shallow-water models on geodesic Delaunay grids with C-type staggering. Mon Wea Rev 133:2351-2373
17. Bourke W, McAvaney B, Puri K, Thurling R (1977) Global modeling of atmospheric flow by spectral methods. In: Chang J (ed) Methods in Computational Physics, vol 17, Academic Press, pp 267-324
18. Boville BA (1986) Wave-mean flow interactions in a general circulation model of the troposphere and stratosphere. J Atmos Sci 43:1711-1725
19. Boviile BA (1991) Sensitivity of simulated climate to model resolution. J Climate 4:469-485
20. Boville BA (2000) Toward a complete model of the climate system. In: Mote P, O’Neill A (eds) Numerical modeling of the global atmosphere in the climate system, NATO Science Series C: Mathematical and Physical Sciences, vol 550, Kluwer Academic Publishers, pp 419-442
21. Boville BA, Baumhefner DP (1990) Simulated forecast error and climate drift resulting from the omission of the upper stratosphere in numerical models. Mon Wea Rev 118:1517-1530
22. Boville BA, Bretherton CS (2003) Heating and kinetic energy dissipation in the NCAR Community Atmosphere Model. J Climate 16:3877-3887
23. Boville BA, Gent PR (1998) The NCAR Climate System Model, version one. J Climate 11:1115-1130
24. Boville BA, Randel WJ (1986) Observations and simulation of the variability of the stratosphere and troposphere in January. J Atmos Sci 43:3015-3034
25. Bowler NE, Arribas A, Beare SE, Mylne KR, Shutts GJ (2009) The local ETKF and SKEB: Upgrades to the MOGREPS short-range ensemble prediction system. Quart J Roy Meteor Soc 135:767-776
26. Boyd J (1996) The Erfc-Log filter and the asymptotics of the Euler and Vandeven sum accelerations. In: Proc. of the Third International Conference on Spectral and High Order Methods, pp 267-276, ed. by A. V. Ilin and L. R. Scott, Houston J. Mathematics, Houston, Texas
27. Boyd J (1998) Two comments on filtering (artificial viscosity) for Chebyshev and Legendre spectral and spectral element methods: Preserving boundary conditions and interpretation of the filter as a diffusion. J Comput Phys 143:283-288
28. Burkhardt U, Becker E (2006) A consistent diffusion dissipation parameterization in the ECHAM climate model. Mon Wea Rev 134:1194-1204
29. Canuto C, Hussaini MY, Quarteroni A, Zang TA (1987) Spectral Methods in Fluid Dynamics. Springer, 600 pp.
30. Carpenter RL, Droegemeier KK, Woodward PR, Hane CE (1990) Application of the Piecewise Parabolic Method (PPM) to meteorological modeling. Mon Wea Rev 118:586-612
31. Chen TC, Wiin-Nielsen A (1978) Nonlinear cascades of atmospheric energy and enstrophy in a two-dimensional spectral index. Tellus 30:313-322
32. Colella P, Sekora MD (2008) A limiter for PPM that preserves accuracy at smooth extrema. J Comput Phys 227:7069-7076
33. Colella P, Woodward PR (1984) The Piecewise Parabolic Method (PPM) for gas-dynamical simulations. J Comput Phys 54:174-201
34. 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/TN-464+STR, National Center for Atmospheric Research, Boulder, Colorado, 214 pp., available from http://www.ucar.edu/library/ collections/technotes/technotes.jsp
35. Cordero E, Staniforth A (2004) A problem with the Robert-Asselin time filter for three-time-level semi-implicit semi-Lagrangian discretizations. Mon Wea Rev 132:600-610
36. Côté J, Gravel S, Staniforth A (1995) A generalized family of schemes that eliminate the spurious resonant response of semi-Lagrangian schemes to orographic forcing. Mon Wea Rev 123:3605-3613
37. Côté J, Gravel S, Méthot A, Patoine A, Roch M, Staniforth A (1998a) The operational CMC-MRB Global Environmental Multiscale (GEM) model. Part I: Design considerations and formulation. Mon Wea Rev 126(6):1373-1395
38. Côté J, Gravel S, Méthot A, Patoine A, Roch M, Staniforth A (1998b) The operational CMC-MRB Global Environmental Multiscale (GEM) model. Part I: Design considerations and formulation. Mon Wea Rev 126(6):1373-1395
39. Davies T, Cullen MJP, Malcolm AJ, Mawson MH, Staniforth A, White AA, Wood N (2005) A new dynamical core for the Met Office’s global and regional modelling of the atmosphere. Quart J Roy Meteor Soc 131(608):1759-1782
40. Deardorff JW (1970) A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J Fluid Mechanics 41:453-480
41. Déqué M, Cariolle D (1986) Some destabilizing properties of the Asselin time filter. Mon Wea Rev 114:880-884
42. Dey CH (1978) Noise suppression in a primitive equation prediction model. Mon Wea Rev 106:159-173
43. Doms G, Schâttler U (2002) A description of the nonhydrostatic regional model LM. Part I: Dynamics and numerics. Consortium for Small-Scale Modelling (COSMO) LM F90 2.18, German Weather Service, Offenbach, Germany, 134 pp., available from http://www.cosmo-model. org
44. Dubal M, Wood N, Staniforth A (2004) Analysis of parallel versus sequential splittings for timestepping physical parameterizations. Mon Wea Rev 132:121-132
45. Dubal M, Wood N, Staniforth A (2006) Some numerical properties of approaches to physics dynamics coupling for NWP. Quart J Roy Meteor Soc 132:27-42
46. Dudhia J (1993) A nonhydrostatic version of the Penn State-NCAR mesoscale model: Validation tests and simulation of an Atlantic cyclone and cold front. Mon Wea Rev 121:1493-1513
47. Durran DR (1999) Numerical methods for wave equations in geophysical fluid dynamics, First edn. Springer, 465 pp.
48. Durran DR (2010) Numerical methods for fluid dynamics: with applications in geophysics, Second edn. Springer, 516 pp.
49. Durran DR, Klemp JB (1983) A compressible model for the simulation of moist mountain waves. Mon Wea Rev 111:2341-2361
50. ECMWF (2010) Part III: Dynamics and numerical procedures. IFS Documentation - Cy36r1, Operational implementation 26 January 2010, European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading, England, 29 pp., available from http://www.ecmwf.int/ research/ifsdocs/CY36r1/index.html
51. Enomoto T, Kuwano-Yoshida A, Komori N, Ohfuchi W (2008) Description of AFES 2: Improvements for high-resolution and coupled simulations. In: Hamilton K, Ohfuchi W (eds) High resolution numerical modelling of the atmosphere and ocean, Springer, pp 77-97
52. Farge M, Sadourny R (1989) Wave-vortex dynamics in rotating shallow water. J Fluid Mech 206:433-462
53. Fiedler BH (2000) Dissipative heating in climate models. Quart J Roy Meteor Soc 126:925-939
54. Fox-Rabinovitz MS, Stenchikov GL, Suarez MJ, Takacs LL (1997) A finite-difference GCM dynamical core with a variable-resolution stretched grid. Mon Wea Rev 125:2943-2968
55. Fudeyasu H, Wang Y, Satoh M, Nasuno T, Miura H, Yanase W (2008) Global cloud-systemresolving model NICAM successfully simulated the lifecycles of two real tropical cyclones. Geophys Res Lett 35:L22,808
56. Gassmann A, Herzog HJ (2007) A consistent time-split numerical scheme applied to the nonhydrostatic compressible equations. Mon Wea Rev 135:20-36
57. Gelb A, Gleeson JP (2001) Spectral viscosity for shallow water equations in spherical geometry. Mon Wea Rev 129:2346-2360
58. GFS (2003) The GFS atmospheric model. NCEP Office Note 442, National Centers for Environmental Prediction (NCEP), Environmental Modeling Center, Camp Springs, Maryland, 14 pp., available from http://www.emc.ncep.noaa.gov/officenotes/index.shtml see also http://wwwt.emc.ncep.noaa.gov/?branch=GFS Gill AE (1982) Atmosphere-ocean dynamics. Academic Press, 768 pp.
59. Giraldo FX, Rosmond TE (2004) A scalable Spectral Element Eulerian Atmospheric Model (SEE-AM) for NWP: Dynamical core tests. Mon Wea Rev 132:133-153
60. Giraldo FX, Hesthaven JS, Wartburton T (2002) Nodal high-order discontinous Galerkin methods for the shallow water equations. J Comput Phys 181:499-525
61. Gordon CT, Stern WF (1982) A description of the GFDL global spectral model. Mon Wea Rev 110:625-644
62. Gravel S, Staniforth A, Côté J (1993) A stability analysis of a family of baroclinic semi-Lagrangian forecast models. Mon Wea Rev 121:815-824
63. Griffies SM, Hallberg RW (2000) Biharmonic friction with a Smagorinsky-like viscosity for use in large-scale Eddy-permitting ocean models. Mon Wea Rev 128:2935-2946
64. Gross ES, Bonaventura L, Rosatti G (2002) Consistency with continuity in conservative advection schemes for free-surface models. Int J Numer Meth Fluids 38:307-327
65. Haltiner GJ, Williams RT (1980) Numerical prediction and dynamic meteorology. John Wiley & Sons, 477 pp.
66. Hamilton K, Takahashi YO, Ohfuchi W (2008) Mesoscale spectrum of atmospheric motions investigated in a very fine resolution global general circulation model. J Geophys Res 113:D18,110
67. Hamming RW (1977) Digital filters. Prentice Hall, 226 pp.
68. Held IM, Suarez MJ (1994) A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bull Amer Meteor Soc 75(10):1825-1830
69. Hortal M (2002) The development and testing of a new two-time-level semi-Lagrangian scheme (SETTLS) in the ECMWF forecast model. Quart J Roy Meteor Soc 128(583):1671-1687
70. Hortal M, Simmons AJ (1991) Use of reduced grids in spectral models. Mon Wea Rev 119:1057-1074
71. Huang H, Stevens B, Margulis SA (2008) Application of dynamic subgrid-scale models for large-eddy simulation of the daytime convective boundary layer over heterogeneous surfaces. Boundary-Layer Meteorology 126:327-348
72. Huynh HY (1996) Schemes and constraints for advection. In: 15th International Conference on Numerical Methods in Fluid Dynamics, Monterey June 24-28, 1996, CA, USA
73. Jablonowski C (1998) Test der Dynamik zweier globaler Wettervorhersagemodelle des Deutschen Wetterdienstes: Der Held-Suarez Test. Master’s thesis, University of Bonn, Germany, Department of Meteorology, 140 pp.
74. Jablonowski C (2004) Adaptive grids in weather and climate modeling. PhD thesis, University of Michigan, Ann Arbor, MI, Department ofAtmospheric, Oceanic and Space Sciences, 292 pp.
75. Jablonowski C, Williamson DL (2006a) A baroclinic instabilitiy test case for atmospheric model dynamical cores. Quart J Roy Meteor Soc 132(621C):2943-2975
76. Jablonowski C, Williamson DL (2006b) A baroclinic wave test case for dynamical cores of General Circulation Models: Model intercomparisons. NCAR Tech. Note NCAR/TN-469CSTR, National Center for Atmospheric Research, Boulder, Colorado, 89 pp., available from http://www.ucar.edu/library/conections/technotes/technotes.jsp
77. Jablonowski C, Herzog M, Penner JE, Oehmke RC, Stout QF, van Leer B, Powell KG (2006) Block-structured adaptive grids on the sphere: Advection experiments. Mon Wea Rev 134:3691-3713
78. Jablonowski C, Oehmke RC, Stout QF (2009) Block-structured adaptive meshes and reduced grids for atmospheric general circulation models. Phil Trans R Soc A 367:4497-4522
79. Jakimow G, Yakimiw E, Robert A (1992) An implicit formulation for horizontal diffusion in gridpoint models. Mon Wea Rev 120:124-130
80. Jakob R, Hack JJ, Williamson DL (1993) Solutions to the shallow-water test set using the spectral transform method. NCAR Tech. Note NCAR/TN-388+STR, National Center for Atmospheric Research, Boulder, Colorado, 82 pp., available from http://www.ucar.edu/library/collections/ technotes/technotes.jsp
81. Janjic ZI (1990) The step-mountain coordinate: Physical package. Mon Wea Rev 118:1429-1443
82. Jöckel P, von Kuhlmann R, Lawrence MG, Steil B, Brenninkmelter CAM, 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. Quart J Roy Meteor Soc 127:1035-1052
83. Kalnay E (2003) Atmospheric modeling, data assimilation and predictability. Cambridge University Press, 341 pp.
84. Kalnay-Rivas E, Bayliss A, Storch J (1977) The 4th order GISS model of the global atmosphere. Beiträge zur Physik der Atmosphäre 50:299-311
85. Kasahara A (1974) Various vertical coordinate systems used for numerical weather prediction. Mon Wea Rev 102:509-522
86. Klemp JB, Durran DR (1983) An upper boundary condition permitting internal gravity wave radiation in numerical mesoscale models. Mon Wea Rev 111:430-444
87. Klemp JB, Lilly DK (1978) Numerical simulation of hydrostatic mountain waves. J Atmos Sci 35:78-107
88. Klemp JB, Skamarock WC, Dudhia J (2007) Conservative split-explicit time integration methods for the compressible nonhydrostatic equations. Mon Wea Rev 135:2897-2913
89. Klemp JB, Dudhia J, Hassiotis AD (2008) An upper gravity-wave absorbing layer for NWP applications. Mon Wea Rev 136:3987-4004
90. Knievel JC, Bryan GH, Hacker JP (2007) Explicit numerical diffusion in the WRF model. Mon Wea Rev 135:3808-3824
91. Koshyk JN, Boer GJ (1995) Parameterization of dynamical subgrid-scale processes in a spectral GCM. J Atmos Sci 52(7):965-976
92. Koshyk JN, Hamilton K (2001) The horizontal kinetic energy spectrum and spectral budget simulated by a high-resolution troposphere-stratosphere-mesosphere GCM. J Atmos Sci 58:329-348
93. Lander J, Hoskins BJ (1997) Believable scales and parameterizations in a spectral transform model. Mon Wea Rev 125:292-303
94. Laprise R, Girard C (1990) A spectral General Circulation Model using the piecewise-constant finite-element representation on a hybrid vertical coordinate system. J Climate 3:32-52
95. Lauritzen PH, Jablonowski C, Taylor MA, Nair RD (2010a) Rotated versions of the Jablonowski steady-state and baroclinic wave test cases: A dynamical core intercomparison. J Adv Model Earth Syst 2:Art. #15, 34 pp.
96. Lauritzen PH, Nair RD, Ullrich PA (2010b) A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid. J Comput Phys 229:1401-1424
97. Laursen L, Eliasen E (1989) On the effects of the damping mechanisms in an atmospheric general circulation model. Tellus Series A 41:385-400
98. van Leer B (1974) Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme. J Comput Phys 14:361-370
99. van Leer B (1977) Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection. J Comput Phys 23:276-299
100. Leith CE (1971) Atmospheric predictability and two-dimensional turbulence. J Atmos Sci 28: 145-161
101. LeVeque RJ (2002) Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, ISBN 0-521-00924-3, 558 pp.
102. Li Y, Moorthi S, Bates JR (1994) Direct solution of the implicit formulation of fourth order horizontal diffusion for gridpoint models on the sphere. NASA Technical Memorandum 104606, Vol. 2, NASA Goddard Space Flight Center, Greenbelt, Maryland, 42 pp.
103. Lin SJ (2004) A “vertically Lagrangian” finite-volume dynamical core for global models. Mon Wea Rev 132:2293-2307
104. Lin SJ, Rood RB (1996) Multidimensional flux-form semi-Lagrangian transport scheme. Mon Wea Rev 124:2046-2070
105. Lin SJ, Rood RB (1997) An explicit flux-form semi-Lagrangian shallow water model on the sphere.
106. Quart J Roy Meteor Soc 123:2477-2498
107. Lin YL (2007) Mesoscale dynamics. Cambridge University Press, 630 pp.
108. Lindberg K, Alexeev VA (2000) A study of the spurious orographic resonance in semi-implicit semi-Lagrangian models. Mon Wea Rev 128:1982-1989
109. Lynch P, Huang X (1992) Initialization of the HIRLAM model using a digital filter. Mon Wea Rev 120:1019-1034
110. Machenhauer B (1979) The spectral method. In: Kasahara A (ed) Numerical methods used in atmospheric models, vol 2, GARP Publications Series No 17, WMO and ICSU, Geneva, pp 121-275
111. MacVean MK (1983) The effects of horizontal diffusion on baroclinic development in a spectral model. Quart J Roy Meteor Soc 109:771-783
112. Mahlmann JD, Sinclair WW (1977) Tests of various numerical algorithms applied to a simple trace constituent air transport problem. In: Suffett IH (ed) Advances in Environmental Science and Technology, Part 1: The Fate of Pollutants in the Air and Water Environments, vol 8, Wiley, pp 223-252
113. Majewski D, Liermann D, Prohl P, Ritter B, Buchhold M, Hanisch T, Paul G, Wergen W, Baumgardner J (2002) The operational global icosahedral-hexagonal gridpoint model GME: Description and high-resolution tests. Mon Wea Rev 130:319-338
114. Majewski D, Frank H, Liermann D (2008) GME User’s Guide. Tech. Rep. corresponding to model version gmtri 2.17 and higher, German Weather Service DWD, Frankfurt, Germany, 70 pp.
115. McCorquodale P, Colella P (2010) A high-order finite-volume method for hyperbolic conservation laws on locally-refined grids. J. Comput. Phys., in review
116. McDonald A, Haugen J (1992) A two-time-level, three-dimensional semi-Lagrangian, semiimplicit, limited-area gridpoint model of the primitive equations. Mon Wea Rev 120(11):2603-2621
117. McDonald A, Haugen J (1993) A two time-level, three-dimensional, semi-Lagrangian, semiimplicit, limited-area gridpoint model of the primitive equations. Part II: Extension to hybrid vertical coordinates. Mon Wea Rev 121(7):2077-2087
118. McPherson RD, Stackpole JD (1973) Noise suppression in the eight-layer global model. Office Note 83, U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Service, National Meteorological Center, 36 pp., available from http://www. emc.ncep.noaa.gov/officenotes/index.shtml
119. Mellor GL (1985) Ensemble average, turbulence closure. In: Manabe S (ed) Advances in Geophysics, Issues in Atmos. And Ocean Modeling. Part B: Weather Dynamics, Academic Press, pp 345-357
120. Mesinger F, Arakawa A (1976) Numerical methods used in atmospheric models. In: GARP Publication Series No. 17, vol 1, World Meteorological Organization, p 64, Geneva, Switzerland
121. Mesinger F, Jovic D (2002) The Eta slope adjustment: Contender for an optimal steepening in a piecewise-linear advection scheme? Comparison tests. NCEP Office Note 439, National Centers for Environmental Prediction (NCEP), Environmental Modeling Center, Camp Springs, Maryland, 29 pp., available from http://www.emc.ncep.noaa.gov/officenotes/index.shtml
122. Nair RD (2009) Diffusion experiments with a global discontinuous Galerkin shallow-water model. MonWeaRev 137:3339-3350
123. Nastrom GD, Gage KS (1985) A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft. J Atmos Sci 42:950-960
124. Neale RB, Hoskins BJ (2000) A standard test for AGCMs including their physical parameteriza-tions: I: The proposal. Atmos Sci Lett 1:101-107
125. Neale RB, Chen CC, Gettelman A, Lauritzen PH, Park S, Williamson DL, Conley AJ, Garcia R, Kinnison D, Lamarque JF, Marsh D, Mills M, Smith AK, Tilmes S, Vitt F, Cameron-Smith P, Collins WD, Iacono MJ, Rasch PJ, Taylor M (2010) Description of the NCAR Community Atmosphere Model (CAM 5.0). NCAR Technical Note NCAR/TN-XXX+STR, National Center for Atmospheric Research, Boulder, Colorado, draft, available from http://www.cesm.ucar. edu/models/cesm 1.0/cam/
126. Nelson SP, Weible ML (1980) Three-dimensional Shuman filter. J Appl Meteor 19:464-469
127. Orr A, Wedi N (2009) The representation of non-orographic gravity waves in the IFS Part I: Assessment of the middle atmosphere climate with Rayleigh friction. ECMWF Technical Memorandum 592, European Centre for Medium-Range Weather Forecasts, Reading, U.K., 15 pp., available from http://www.ecmwf.int/publications/library/do/references/list/14
128. Orr A, Bechthold P, Scinocca J, Ern M, Janiskova M (2010) Improved middle atmosphere climate and forecasts in the ECMWF model through a non-orographic gravity wave drag parameterization. J Climate 23:5905-5926
129. Orszag SA (1971) On the elimination of aliasing in finite-difference schemes by filtering high-wavenumber components. J Atmos Sci 28:1074-1074
130. O’Sullivan D, Dunkerton TJ (1995) Generation of inertia-gravity waves in a simulated life cycle of baroclinic instability. J Atmos Sci 52:3695-3716
131. Phillips N (1959) An example of non-linear computational instability. In: Bolin B (ed) The Atmosphere and Sea in Motion, Oxford University Press, pp 501-504
132. Phillips NA (1957) A coordinate system having some special advantages for numerical forecasting. J Meteor 14:184-185
133. Polvani LM, Kushner PJ (2002) Tropospheric response to stratospheric perturbations in a relatively simple general circulation model. Geophys Res Lett 29(7):070,000-1
134. Polvani LM, Scott RK, Thomas SJ (2004) Numerically converged solutions of the global primitive equations for testing the dynamical core of atmospheric GCMs. Mon Wea Rev 132:2539-2552
135. Purser RJ (1987) The filtering of meteorological fields. J Climate and Appl Meteor 26:1764-1769
136. Purser RJ (1988) Degradation of numerical differencing caused by Fourier filtering at high latitudes. Mon Wea Rev 116:1057-1066
137. Purser RJ, Leslie LM (1994) An efficient semi-Lagrangian scheme using third-order semi-implicit time integration and forward trajectories. Mon Wea Rev 122(4):745-756
138. Putman WM, Lin SJ(2007) Finite-volume transport on various cubed-sphere grids. J Comput Phys 227:55-78
139. Putman WM, Lin SJ (2009) A finite-volume dynamical core on the cubed-sphere grid. In: Numerical Modeling of Space Plasma Flows: Astronum-2008, Astronomical Society of the Pacific Conference Series, vol 406, pp 268-276
140. Randall DA (1994) Geostrophic adjustment and the finite-difference shallow-water equations. Mon Wea Rev 122:1371-1377
141. Rasch PJ (1986) Toward atmospheres without tops: Absorbing upper boundary conditions for numerical models. Quart J Roy Meteor Soc 112:1195-1218
142. Rasch PJ, Williamson DL (1990a) Computational aspects of moisture transport in global models of the atmosphere. Quart J Roy Meteor Soc 116:1071-1090
143. Rasch PJ, Williamson DL (1990b) On shape-preserving interpolation and semi-Lagrangian transport. SIAM J Sci Stat Comput 11(4):656-687
144. Rasch PJ, Williamson DL (1991) The sensitivity of a general circulation model climate to the moisture transport formulation. J Geophy Res 96:13,123-137
145. Rasch PJ, Boville BA, Brasseur GP (1995) A three-dimensional general circulation model with coupled chemistry for the middle atmosphere. J Geophys Res 100:9041-9072
146. Raymond WH (1988) High-order low-pass implicit tangent filters for use in finite area calculations. MonWeaRev 116:2132-2141
147. Raymond WH, Garder A (1988) A spatial filter for use in finite area calculations. Mon Wea Rev 116:209-222
148. Raymond WH, Garder A (1991) A review of recursive and implicit filters. Mon Wea Rev 119: 477-495
149. Reames FM, Zapotocny TH (1999) Inert trace constituent transport in sigma and hybrid isentropic-sigma models. Part I: Nine advection algorithms. Mon Wea Rev 127:173-187
150. 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 GEOS-5 data assimilation system -Documentation of versions 5.0.1 and 5.1.0. Technical Report Series on Global Modeling and Data Assimilation NASA/TM-2007-104606, Vol. 27, NASA Goddard Space Flight Center, Greenbelt, Maryland, 92 pp.
151. Ripodas P, Gassmann A, Forstner J, Majewski D, Giorgetta M, Korn P, Kornblueh L, Wan H, Zângl G, Bonaventura L, Heinze T (2009) Icosahedral Shallow Water Model (ICOSWM): results of shallow water test cases and sensitivity to model parameters. Geosci Model Dev 2:231-251
152. Ritchie H, Temperton C, Simmons A, Hortal M, Davies T, Dent D, Hamrud M (1995) Implementation of the Semi-Lagrangian Method in a High-Resolution Version of the ECMWF Forecast Model. MonWeaRev 123:489-514
153. Rivest C, Staniforth A, Robert A (1994) Spurious resonant response of semi-Lagrangian discretizations to orographic forcing: Diagnosis and solution. Mon Wea Rev 122:366-376
154. Robert A, Lépine M (1997) Anomaly in the behaviour of the time filter used with the leapfrog scheme in atmospheric models. In: Lin CA, Laprise R, Ritchie H (eds) Numerical Methods in Atmospheric and Oceanic Modeling: The AndrJ. Robert Memorial Volume, Canadian Meteorological and Oceanographic Society/NRC Research Press, pp S3-S15
155. Robert AJ (1966) The Integration of a low order spectral form of the primitive meteorological equations. J Meteor Soc Japan 44(5):237-245
156. Roeckner E, Bâuml G, Bonaventura L, Brokopf R, Esch M, Hagemann MGS, Kirchner I, Kornblueh L, Manzini E, Rhodin A, Schlese U, Schulzweida U, Tompkins A (2003) The atmospheric general circulation model ECHAM5. Part I model description. Tech. Rep. 349, Max Planck Institute for Meteorology, 127 pp., available from http://www.mpimet.mpg.de/en/wissenschaft/modelle/echam/echam5.html
157. Rood RB (1987) Numerical advection algorithms and their role in atmospheric transport and chemistry models. Rev Geophys 25:71-100
158. Royer J (1986) Correction of negative mixing ratios in spectral models by global horizontal borrowing. MonWeaRev 114:1406-1410
159. Ruge JW, McCormick SF, Yee SYK (1995) Multilevel adaptive methods for semi-implicit solution of shallow-water equations on the sphere. Mon Wea Rev 123:2197-2205
160. Sadourny R (1975) The dynamics of finite-difference models of the shallow-water equations. J Atmos Sci 32:680-689
161. Sadourny R, Maynard K (1997) Formulations of lateral diffusion in geophysical fluid dynamics models. In: Lin CA, Laprise R, Ritchie H (eds) Numerical Methods in Atmospheric and Oceanic Modeling: The André J. Robert Memorial Volume, Canadian Meteorological and Oceanographic Society/NRC Research Press, pp 547-556
162. Sardeshmukh PD, Hoskins BI (1984) Spatial smoothing on the sphere. Mon Wea Rev 112:2524-2529
163. Satoh M (2002) Conservative scheme for the compressible nonhydrostatic models with the horizontally explicit and vertically implicit time integration scheme. Mon Wea Rev 130(5):1227-1245
164. Satoh M (2003) Conservative scheme for a compressible nonhydrostatic model with moist processes. Mon Wea Rev 131:1033-1050
165. Satoh M (2004) Atmospheric circulation dynamics and general circulation models. Springer (Praxis), 643 pp.
166. Satoh M, Matsuno T, Tomita H, Miura H, Nasuno T, Iga S (2008) Nonhydrostatic icosahe-dral atmospheric model (NICAM) for global cloud resolving simulations. J Comput Phys 227:3486-3514
167. Schlesinger RE, Uccellini LW, Johnson DR (1983) The effects of the Asselin time filter on numerical solutions to the linearized shallow-water wave equations. Mon, Wea, Rev, 111:455-467
168. Schmidt GA, Ruedy R, Hansen JE, Aleinov I, Bell N, Bauer M, Bauer S, Cairns B, Canuto V, Cheng Y, Del Genio A, Faluvegi G, Friend AD, Hall TM, Hu Y, Kelley M, Kiang NY, Koch D, Lacis AA, Lerner J, Lo KK, Miller RL, Nazarenko L, Oinas V, Perlwitz J, Perlwitz J, Rind D, Romanou A, Russell GL, Sato M, Shindell DT, Stone PH, Sun S, Tausnev N, Thresher D, Yao MS (2006) Present-day atmospheric simulations using GISS ModelE: Comparison to in situ, satellite, and reanalysis data. J Climate 19:153-192
169. Shapiro R (1970) Smoothing, filtering, and boundary effects. Rev Geophys and Space Phys 8(2):359-387
170. Shapiro R (1971) The use of linear filtering as a parameterization of atmospheric diffusion. J Atmos Sci 28:523-531
171. Shapiro R (1975) Linear filtering. Mathematics of Computation 29(132):1094-1097
172. Shepherd TG, Shaw TA (2004) The angular momentum constraint on climate sensitivity and downward Influence in the middle atmosphere. J Atmos Sci 61:2899-2908
173. Shepherd TG, Semeniuk K, Koshyk JN (1996) Sponge layer feedbacks in middle-atmosphere models. J Geophys Res 101:23,447-23,464
174. Shuman FG (1957) Numerical methods in weather prediction: II. Smoothing and filtering. Mon Wea Rev 85:357-361
175. Shuman FG (1969) On a special form for viscous terms. Office Note 32, U.S. Department of Commerce, Environmental Science Service Administration, Weather Bureau, 4 pp., available from http://www.emc.ncep.noaa.gov/officenotes/index.shtml
176. Shuman FG, Stackpole JD (1969) The currently operational NMC model, and results of a recent numerical experiment. In: Proc. WMO/IUGG Symp. Numerical Weather Prediction, Japan Meteorological Agency, Tokyo, Japan, pp II-85-98
177. Shutts G (2005) A kinetic energy backscatter algorithm for use in ensemble prediction systems. Quart J Roy Meteor Soc 131:3079-3102
178. Simmons AJ, Burridge DM (1981) An energy and angular-momentum conserving vertical finite-difference scheme and hybrid vertical coordinates. Mon Wea Rev 109:758-766
179. Skamarock WC (2004) Evaluating mesoscale NWP models using kinetic energy spectra. Mon Wea Rev 132:3019-3032
180. Skamarock WC, Klemp JB (1992) The stability of time-split numerical methods for the hydrostatic and the nonhydrostatic elastic equations. Mon Wea Rev 120:2109-2127
181. Skamarock WC, Klemp JB (2008) A time-split nonhydrostatic atmospheric model for weather research and forecasting applications. J Comput Phys 227:3465-3485
182. Skamarock WC, Klemp JB, Dudhia J, Gill DO, Barker DM, Duda MG, Huang XY, Wang W, Powers JG (2008) A description of the Advanced Research WRF Version 3. NCAR Tech. Note NCAR/TN-475+STR, National Center for Atmospheric Research, Boulder, Colorado, 113 pp., available from http://www.ucar.edu/library/collections/technotes/technotes.Jsp
183. Smagorinsky J (1963) General circulation experiments with the primitive equations. I. The basic experiment. Mon Wea Rev 91:99-164
184. Smagorinsky J (1993) Some historical remarks on the use of nonlinear viscosities. In: Galperin B, Orszag SA (eds) Large Eddy Simulation of Complex Engineering and Geophysical Flows, Cambridge University Press, pp 3-36
185. St-Cyr A, Jablonowski C, Dennis J, Thomas S, Tufo H (2008) A comparison of two shallow water models with non-conforming adaptive grids. Mon Wea Rev 136:1898-1922
186. Staniforth A, CôtJ (1991) Semi-Lagrangian integration schemes for atmospheric modeling - A review. MonWeaRev 119:2206-2223
187. Staniforth A, Wood N (2008) Aspects of the dynamical core of a nonhydrostatic, deep-atmosphere, unified weather and climate-prediction model. J Comput Phys 227(7):3445-3464
188. Staniforth A, White A, Wood N (2003) Analysis of semi-Lagrangian trajectory computations. Quart J Roy Meteor Soc 129(591):2065-2085
189. Staniforth A, White A, Wood N, Thuburn J, Zerroukat M, Cordero E, Davies T, Diamantakis M (2006) Joy of U.M. 6.3 - model formulation. Unified Model Documentation Paper No 15, UK Meteorological Service, Exeter, England, available from http://research.metoffice.gov.uk/ research/nwp/publications/papers/unified_model/
190. Stephenson DB (1994) The impact of changing the horizontal diffusion scheme on the northern winter climatology of a general circulation model. Quart J Roy Meteor Soc 120:211-226
191. Suarez MJ, Takacs LL (1995) Documentation of the ARIES/GEOS dynamical core: Version 2. NASA Technical Memorandum 104606, Vol. 5, NASA Goddard Space Flight Center, Greenbelt, Maryland, 45 pp.
192. Takacs L, SawyerW, Suarez MJ, Fox-Rabnovitz MS (1999) Filtering techniques on a stretched grid general circulation model. Tech. Rep. NASA/TM-1999-104606, Vol. 16, NASA Goddard Space Flight Center, Greenbelt, Maryland, 50 pp.
193. Takacs LL (1988) Effect of using a posteriori methods for the conservation of integral invariants. Mon Wea Rev 116:525-545
194. Takacs LL, Balgovind RC (1983) High-latitude filtering in global grid-point models. Mon Wea Rev 111:2005-015
195. Takahashi YO, Hamilton K, Ohfuchi W (2006) Explicit global simulation of the mesoscale spectrum of atmospheric motions. Geophys Res Lett 33:L12,812
196. Tandon MK (1987) Robert’s recursive frequency filter: A reexamination. Meteor Atmos Phys 37:48-59
197. Tanguay M, Yakimiw E, Ritchie H, Robert A (1992) Advantages of spatial averaging in semiimplicit semi-Lagrangian schemes. Mon Wea Rev 120:113-123
198. Tatsumi Y (1983) An economical explicit time integration scheme for a primitive model. J Meteorol Soc Japan 61:269-287
199. Taylor M, Tribbia J, Iskandarani M (1997) The spectral element method for the shallow water equations on the sphere. J Comput Phys 130:92-108
200. Taylor MA (2008) CAM/HOMME: Parallel scalability and aqua planet results for CAM on the cubed-sphere grid. Presentation at the Community Climate System Model (CCSM) Workshop in Breckenridge, CO, available online at http://www.ccsm.ucar.edu/events/ws.2008/ Presentations/Tarn/SEWG/Taylor_ccsm08.pdf
201. Taylor MA, Fournier A (2010) A compatible and conservative spectral element method on unstructured grids. J Comput Phys 229:5879-5895
202. Taylor MA, Edwards J, Thomas S, Nair RD (2007) A mass and energy conserving spectral element atmospheric dynamical core on the cubed-sphere grid. Journal of Physics: Conference Series 78:012,074, available online at http://www.iop.org/EJ/toc/1742-6596/78/!
203. Taylor MA, St-Cyr A, Fournier A (2009) A non-oscillatory advection operator for the compatible spectral element method. In: Allen G (ed) Computational Science DICCS 2009, Part II, Lecture Notes in Computer Science, vol 5545, Springer Berlin/Heidelberg, pp 273-282
204. Temperton C, Staniforth A (1987) An efficient two-time-level semi-Lagrangian semi-implicit integration scheme. Quart J Roy Meteor Soc 113:1025-1039
205. Terasaki K, Tanaka HL, Satoh M (2009) Characteristics of the kinetic energy spectrum of NICAM model atmosphere. SOLA 5:180-183
206. Thomas SJ, Loft RD (2005) The NCAR spectral element climate dynamical core: Semi-implicit Eulerian formulation. J Sci Comput 25:307-322
207. Thuburn J (1993) Use of a flux-limited scheme for vertical advection in a GCM. Quart J Roy Meteor Soc 119:469-487
208. Thuburn J (1997) TVD Schemes, Positive Schemes, and the Universal Limiter. Mon Wea Rev 125:1990-1993
209. Thuburn J (2008a) Numerical wave propagation on the hexagonal C-grid. J Comput Phys 227:5836-5858
210. Thuburn J (2008b) Some conservation issues for dynamical cores of NWP and climate models. J Comput Phys 227(7):3715-3730
211. Tomita H, Satoh M (2004) A new dynamical framework of nonhydrostatic global model using the icosahedral grid. Fluid Dyn Res 34:357-400
212. Tomita H, Miura H, Iga S, Nasuno T, Satoh M (2005) A global cloud-resolving simulation: Preliminary results from an aqua planet experiment. Geophys Res Lett 32:L08,805
213. Untch A, Hortal M (2004) A finite-element scheme for the vertical discretization of the semi-Lagrangian version of the ECMWF forecast model. Quart J Roy Meteor Soc 130:1505-1530
214. Vandeven H (1991) Family of spectral filters for discontinuous problems. J Sci Comput 6:159-192
215. Vâha F, Bénard P, Geleyn J, Simon A, Seity Y (2008) Semi-Lagrangian advection scheme with controlled damping: An alternative to nonlinear horizontal diffusion in a numerical weather prediction model. Quart J Roy Meteor Soc 134:523-537
216. Storch J (2004) On statistical dissipation in GCM-climate. Climate Dynamics 23:1-15
217. Wan H (2009) Developing and testing a hydrostatic atmospheric dynamical core on triangular grids. Reports on Earth System Science 65, Max Planck Institute for Meteorology, Hamburg, Germany, 153 pp., available from http://www.mpimet.mpg.de/en/wissenschaft/publikationen/berichte-erdsystemforschung.html
218. Wan H, Giorgetta MA, Bonaventura L (2008) Ensemble Held Suarez test with a spectral transform model: Variability, sensitivity, and convergence. Mon Wea Rev 136:1075-1092
219. Washington WM, Baumhefner DP (1975) A method of removing Lamb waves from initial data for primitive equation models. J Appl Meteor 14:114-119
220. White AA, B J Hoskins IR, Staniforth A (2005) Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic. Quart J Roy Meteor Soc 131:2081-2107
221. Whitehead J, Jablonowski C, Rood RB, Lauritzen PH (2011) A stability analysis of divergence damping on a latitude-longitude grid. Mon. Wea. Rev., accepted (pending revisions)
222. Williams PD (2009) A proposed modification to the Robert-Asselin time filter. Mon Wea Rev 137:2538-2546
223. Williamson DL (1976) Linear stability of finite-difference approximations on a uniform latitude-longitude grid with Fourier filtering. Mon Wea Rev 104:31-41
224. Williamson DL (1978) The Relative Importance of Resolution, Accuracy and Diffusion in Short-Range Forecasts with the NCAR Global Circulation Model. Mon Wea Rev 106:69-88
225. Williamson DL (1988) The effect of vertical finite difference approximations on simulations with the NCAR Community Climate Model. J Climate 1(1): 40-58
226. Williamson DL (1990) Semi-Lagrangian moisture transport in the NMC spectral model. Tellus 42A:413-428
227. Williamson DL (1997) Climate simulations with a spectral, semi-Lagrangian model with linear grids. In: Lin CA, Laprise R, Ritchie H (eds) Numerical Methods in Atmospheric and Oceanic Modeling: The AndrJ. Robert Memorial Volume, Canadian Meteorological and Oceanographic Society/NRC Research Press, pp 280-292
228. Williamson DL (2007) The evolution of dynamical cores for global atmospheric models. J Meteorol Soc Japan 85B:241-269
229. Williamson DL (2008a) Convergence of aqua-planet simulations with increasing resolution in the Community Atmospheric Model, Version3. Tellus 60A:848-862
230. Williamson DL (2008b) Equivalent finite volume and Eulerian spectral transform horizontal resolutions established from aqua-planet simulations. Tellus 60A:839-847
231. Williamson DL, Browning GL (1973) Comparison of grids and difference approximations for numerical weather prediction over the sphere. J Appl Meteor 12:264-274
232. Williamson DL, Laprise R (2000) Numerical approximations for global atmospheric general circulation models. In: Mote P, O’Neill A (eds) Numerical modeling of the global atmosphere in the climate system, NATO Science Series C: Mathematical and Physical Sciences, vol 550, Kluwer Academic Publishers, pp 127-219
233. Williamson DL, Olson JG (1994) Climate simulations with a semi-Lagiangian version of the NCAR Community Climate Model. Mon Wea Rev 122(7):1594-1610
234. Williamson DL, Rasch PJ (1989) Two-dimensional semi-Lagrangian transport with shapepreserving interpolation. Mon Wea Rev 117:102-129
235. Williamson DL, Rasch PJ (1994) Water vapor transport in the NCAR CCM2. Tellus A 46:34-51
236. 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
237. Williamson DL, Olson JG, Boville BA (1998) A comparison of semi-Lagrangian and Eulerian tropical climate simulations. Mon Wea Rev 126:1001-1012
238. Williamson DL, Olson J, Jablonowski C (2009) Two dynamical core formulation flaws exposed by a baroclinic instability test case. Mon Wea Rev 137:790-796
239. Wood N, Diamantakis M, Staniforth A (2007) A monotonically-damping second-order-accurate unconditionally-stable numerical scheme for diffusion. Quart J Roy Meteor Soc 133:1559-1573
240. Xue M (2000) High-order monotonic numerical diffusion and smoothing. Mon Wea Rev 128:2853-2864
241. Xue M, Droegemeier KK, Wong V (2000) The Advanced Regional Prediction System (ARPS) -A multi-scale nonhydrostatic atmospheric simulation and prediction model. Part I: Model dynamics and verification. Meteor Atmos Phys 75:161-193
242. Zalesak ST (1979) Fully multidimensional flux-corrected transport algorithms for fluids. J Comput Phys 31:335-362
243. Zubov VA, Rozanov EV, Schlesinger ME (1999) Hybrid scheme for three-dimensional advective transport. Mon Wea Rev 127:1335-1346