9. Physical Constants¶
Following the American Meteorological Society convention, the model uses the International System of Units (SI) (see August 1974 Bulletin of the American Meteorological Society, Vol. 55, No. 8, pp. 926-930).
![\begin{aligned}
\begin{array}{lcll}
a & = & 6.37122 \times 10^{6} \quad\mathrm{m} & \mathrm{ Radius \: of \: earth} \\
g & = & 9.80616 \quad\mathrm{m \: s^{-2}} & \mathrm{ Acceleration \: due \: to \: gravity}\\
\pi & = & 3.14159265358979323846 & \mathrm{Pi} \\
t_s & = & 86164.0 \quad\mathrm{s} & \mathrm{ Earth's \: sidereal \: day}\\
\Omega & = & 2*\pi/t_s \quad\mathrm{[s^{-1}]} & \mathrm{ Earth's \: angular \: velocity}\\
\sigma_{B} & = & 5.67 \times 10^{-8} \quad\mathrm{W \: m^{-2} \: K^{-4}} & \mathrm{ Stefan-Boltzmann \: constant}\\
k & = & 1.38065 \times 10^{-23} \quad\mathrm{J K^{-1}} & \mathrm{ Boltzmann \: constant}\\
N & = & 6.02214 \times 10^{26} & \mathrm{Avogadro's \: number}\\
R^* & = & k\,N \quad\mathrm{[J K^{-1}]} & \mathrm{ Universal \: gas \: constant}\\
m_{air} & = & 28.966 \quad\mathrm{kg} & \mathrm{ Molecular \: weight \: of \: dry \: air}\\
R & = & R^*/m_{air} \quad\mathrm{[J \: kg^{-1} \: K^{-1}]} & \mathrm{ Gas \: constant \: for \: dry \: air}\\
m_{v} & = & 18.016 \quad\mathrm{kg} & \mathrm{ Molecular \: weight \: of \: water \: vapor}\\
R_{v} & = & R^*/m_{v} \quad\mathrm{[J \: kg^{-1} \: K^{-1}]} & \mathrm{ Gas \: constant \: for \: water \: vapor}\\
c_{p} & = & 1.00464 \times 10^{3} \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Specific \: heat \: of \: dry \: air \: at \: constant \: pressure}\\
\kappa & = & 2/5 & \mathrm{Von \: Karman \: constant} \\
z_{vir} & = & R_{v}/R-1 & \mathrm{Ratio \:of \:gas \:constants \:for \:water \:vapor \:and \:dry \:air} \\
L_{v} & = & 2.501 \times 10^{6} \quad\mathrm{J \: kg^{-1}} & \mathrm{ Latent \: heat \: of \: vaporization}\\
L_{i} & = & 3.337 \times 10^{5} \quad\mathrm{J \: kg^{-1}} & \mathrm{ Latent \: heat \: of \: fusion}\\
\rho_{H_{2}O} & = & 1.0 \times 10^{3} \quad\mathrm{kg \: m^{-3}} & \mathrm{ Density \: of \: liquid \: water}\\
c_{pv} & = & 1.81 \times 10^{3} \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Specific \:heat \: of \: water \: vapor \: at \: constant \: pressure}\\
T_{melt} & = & 273.16 \quad\mathrm{^{\circ}K} & \mathrm{ Melting \: point \: of \: ice}\\
p_{std} & = & 1.01325 \times 10^{5} \quad\mathrm{Pa} & \mathrm{ Standard \: pressure}\\
\rho_{air} & = & p_{std}/(R\,T_{melt}) \quad\mathrm{[kg m^{-3}]} & \mathrm{ Density \: of \: dry \: air \: at \: standard \: pressure/temperature}
\end{array}\end{aligned}](../_images/math/d3974138e009ffd22c6c8ab5f884a73f647c4117.png)
The model code defines these constants to the stated accuracy. We do not mean to imply that these constants are known to this accuracy nor that the low-order digits are significant to the physical approximations employed.
10. Bibliography¶
| [Ant86] | R. A. Anthes. Summary of workshop on the NCAR Community Climate/forecast Models 14–26 July 1985, Boulder, Colorado. Bull. Am. Meteorol. Soc., 67:94–198, 1986. |
| [AL81] | A. Arakawa and V. R. Lamb. A potential enstrophy and energy conserving scheme for the shallow-water equations. Mon. Wea. Rev., 109:18–36, 1981. |
| [Ass72] | R. Asselin. Frequency filter for time integrations. Mon. Wea. Rev., 100:487–490, 1972. |
| [BJC79] | A. P. M. Baede, M. Jarraud, and U. Cubasch. Adiabatic formulation and organization of ECMWF’s model. Technical Report 15, ECMWF, Reading, U.K., 1979. |
| [BK73] | P. M. Banks and G. Kockarts. Aeronomy, Part B. Academic Press, San Diego, Calif., 1973. 355 pp. |
| [BSHB90] | J. R. Bates, F. H M. Semazzi, R. W. Higgins, and S. R. Barros. 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, 1990. |
| [BRO92] | L. Bath, J. Rosinski, and J. Olson. User’s Guide to NCAR CCM2. Technical Report NCAR/TN-379+IA, National Center for Atmospheric Research, Boulder, CO, 1992. 156~pp. |
| [BDW+87] | L. M. Bath, M. A. Dias, D. L. Williamson, G. S. Williamson, and R. J. Wolski. User’s Guide to NCAR CCM1. Technical Report NCAR/TN-286+IA, National Center for Atmospheric Research, Boulder, CO, 1987. 173~pp. |
| [Bon96] | G. B. Bonan. A land surface model (LSM version 1.0) for ecological, hydrological, and atmospheric studies: Technical description and user’s guide. Technical Report NCAR/TN-417+STR, National Center for Atmospheric Research, Boulder, CO, 1996. 150~pp. |
| [BMPT77] | W. Bourke, B. McAvaney, K. Puri, and R. Thurling. Global modeling of atmospheric flow by spectral methods. In Methods in Computational Physics, volume 17, pages 267–324. Academic Press, New York, 1977. |
| [BB03] | B. A. Boville and C. S. Bretherton. Heating and dissipation in the NCAR community atmosphere model. J.~Climate, 16:3877–3887, 2003. |
| [BOT99] | G. P. Brasseur, J. J. Orlando, and G. S. Tyndall. Atmospheric Chemistry and Global Change. Topics in Environmental Chemistry. Oxford University Press, Oxford University Press, 1999. |
| [Bri92] | B. P. Briegleb. Delta-Eddington approximation for solar radiation in the NCAR Community Climate Model. J.~Geophys. Res., 97:7603–7612, 1992. |
| [BBH+02] | B. P. Briegleb, C. M. Bitz, E. C. Hunke, W. H. Lipscomb, and J. L. Schramm. Description of the community climate system model version 2 sea ice model. Technical Report, National Center for Atmospheric Research, 2002. http://www.ccsm.ucar.edu/models/ice-csim4. |
| [CoteS88] | J. Côté and A. Staniforth. A two-time-level semi-Lagrangian semi-implicit scheme for spectral models. Mon. Wea. Rev., 116:2003–2012, 1988. |
| [CLBRG90] | D. Cariolle, A. Lasserre-Bigorry, J.-F. Royer, and J.-F. Geleyn. A general circulation model simulation of the springtime antarctic ozone decrease and its impact on mid-latitudes. J. Geophys. Res., 95:1883–1898, 1990. |
| [Che86] | R. M. Chervin. Interannual variability and seasonal climate predictability. J.~Atmos. Sci., 43:233–251, 1986. |
| [CW84] | P. Colella and P. R. Woodward. The piecewise parabolic method (ppm) for gas-dynamical simulations. J.~Comp.~Phys., 54:174–201, 1984. |
| [DGHS76] | R. Daley, C. Girard, J. Henderson, and I. Simmonds. Short-term forecasting with a multi-level spectral primitive equation model. Part I—model formulation. Atmosphere, 14:98–116, 1976. |
| [DFS+05] | John Dennis, Aimé Fournier, William F. Spotz, Amik St.-Cyr, Mark A. Taylor, Stephen J. Thomas, and Henry Tufo. High resolution mesh convergence properties and parallel efficiency of a spectral element atmospheric dynamical core. Int. J. High Perf. Comput. Appl., 19:225–235, 2005. |
| [DFM02] | M. O. Deville, P. F. Fischer, and E. H. Mund. High Order Methods for Incompressible Fluid Flow. Cambridge University Press, 1 edition, 8 2002. ISBN 9780521453097. |
| [DHSKW87] | R. E. Dickinson, A. Henderson-Sellers, P. J. Kennedy, and M. F. Wilson. Biosphere-atmosphere transfer scheme (BATS) for the NCAR Community Climate Model. Technical Report NCAR/TN-275+STR, National Center for Atmospheric Research, Boulder, Colorado, 1987. 69~pp. |
| [Dutsch86] | H. U. Dütsch. Vertical ozone distribution on a global scale. Pure Appl. Geophys., 116:511–529, 1986. |
| [EWH+10] | L. K. Emmons, S. Walters, P. G. Hess, J.-F. Lamarque, G. G. Pfister, D. Fillmore, C. Granier, A. Guenther, D. Kinnison, T. Laepple, J. Orlando, X. Tie, G. Tyndall, C. Wiedinmyer, S. L. Baughcum, and S. Kloster. Description and evaluation of the Model for Ozone and Related chemical Tracers, version 4 (MOZART-4). Geosci. Model Dev., 3:43–67, 2010. doi:10.5194/gmd-3-43-2010. |
| [FD85] | D. C. Fritts and T. J. Dunkerton. Fluxes of heat and constituents due to convectively unstable gravity waves. jas, 42:549–556, 1985. |
| [Gar01] | R. R. Garcia. Parameterization of planetary wave breaking in the middle atmosphere. jas, 2001. |
| [GMK+07] | R. R. Garcia, D. R. Marsh, D. E. Kinnison, B. A. Boville, and F. Sassi. Simulation of secular trends in the middle atmosphere, 1950-2003. J. Geophys. Res., 112:doi:10.1029/2006JD007485, 2007. |
| [GS85] | R. R. Garcia and S. Solomon. The effect of breaking gravity waves on the dynamical and chemical composition of the mesosphere and lower thermosphere. J. Geophys. Res., 90:3850–3868, 1985. |
| [GMG08] | A. Gettelman, H. Morrison, and S. J. Ghan. A new two-moment bulk stratiform cloud microphysics scheme in the NCAR Community Atmosphere Model (CAM3), Part II: single-column and global results. J. Clim., 21(15):3660–3679, 2008. |
| [G+10] | A. Gettelman and others. Multi-model assessment of the upper troposphere and lower stratosphere: tropics and trends. in press J. Geophys. Res., 2010. |
| [GZ07] | S. J. Ghan and R. A. Zaveri. Parameterization of optical properties for hydrated internally-mixed aerosol. J.~Geophys. Res., 112:DOI~10.1029/2006JD007927, 2007. |
| [Gir99] | F. X. Giraldo. Trajectory calculations for spherical geodesic grids in cartesian space. Mon. Wea. Rev., 127:1651–1662, 1999. |
| [GKI97] | D. Gregory, R. Kershaw, and P. M. Inness. Parametrization of momentum transport by convection. II: Tests in single-column and general circulation models. Q.~J.~R.~Meteorol. Soc., 123:1153–1183, 1997. |
| [GCFS99] | R. J. Griffin, D. R. Cocker, R. C. Flagan, and J. H. Seinfeld. Organic aerosol formation from the oxidation of biogenic hydrocarbons. J. Geophys. Res., 104:3555 – 3567, 1999. |
| [Hac94] | J. J. Hack. Parameterization of moist convection in the National Center for Atmospheric Research Community Climate Model (CCM2). J.~Geophys. Res., 99:5551–5568, 1994. |
| [HBWB89] | J. J. Hack, L. M. Bath, G. W. Williamson, and B. A. Boville. Modifications and enhancements to the NCAR Community Climate Model (CCM1). Technical Report NCAR/TN-336+STR, National Center for Atmospheric Research, Boulder, Colorado, 1989. 97~pp. |
| [HBB+93] | J. J. Hack, B. A. Boville, B. P. Briegleb, J. T. Kiehl, P. J. Rasch, and D. L. Williamson. Description of the NCAR Community Climate Model (CCM2). Technical Report NCAR/TN-382+STR, National Center for Atmospheric Research, 1993. 120~pp. |
| [HHH+08] | C. L. Heald, D. K. Henze, L. W. Horowitz, J. Feddema, J.-F. Lamarque, A. Guenther, P. G. Hess, F. Vitt, J. H. Seinfeld, A. H. Goldstein, and I. Fung. Predicted change in global secondary organic aerosol concentrations in response to future climate, emissions, and land-use change. J. Geophys. Res., 2008. doi:10.1029/2007JD009092. |
| [Hei01] | J. H. Heinbockel. Introduction to Tensor Calculus and Continuum Mechanics. Trafford Publishing, Victoria, B.C., 12 2001. ISBN 9781553691334. |
| [HS94] | I. M. Held and M. J. Suarez. A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bull. Am. Meteorol. Soc., 75:1825–1830, 1994. |
| [HSN+08] | D. K. Henze, J. H. Seinfeld, N. L. Ng, J. H. Kroll, T.-M. Fu, D. J. Jacob, and C. L. Heald. Global modeling of secondary organic aerosol formation from aromatic hydrocarbons: high- vs. low-yield pathways. Atmospheric Chemistry and Physics, 8(9):2405–2420, 2008. URL: http://www.atmos-chem-phys.net/8/2405/2008/, doi:10.5194/acp-8-2405-2008. |
| [Hil56] | F. B. Hildebrand. Introduction to Numerical Analysis. McGraw-Hill, New York, New York, 1956. 511~pp. |
| [Hol82] | J. R. Holton. The role of gravity wave induced drag and diffusion in the momentum budget of the mesosphere. J. Atmos. Sci., 39:791–799, 1982. |
| [HB93] | A. A. M. Holtslag and B. A. Boville. Local versus nonlocal boundary-layer diffusion in a global climate model. J.~Climate, 6:1825–1842, 1993. |
| [Hor99] | M. Hortal. Aspects of the numerics of the ECMWF model. In Proceedings of ECMWF Seminar: Recent developments in numerical methods for atmospheric modelling, 7–11 September 1998, 127–143. 1999. |
| [HA90] | Y.-J. G. Hsu and A. Arakawa. Numerical modeling of the atmosphere with an isentropic vertical coordinate. Mon. Wea. Rev., 118:1933–1959, 1990. |
| [IDM+08] | M.J. Iacono, J.S. Delamere, E.J. Mlawer, M.W. Shephard, S.A. Clough, and W.D. Collins. Radiative forcing by long-lived greenhouse gases: calculations with the aer radiative transfer models. J.~Geophys. Res., 2008. |
| [JW06] | Christiane Jablonowski and David L. Williamson. A baroclinic instability test case for atmospheric model dynamical cores. Q.~J.~R.~Meteorol. Soc., 132:2943–2975, 2006. doi:10.1256/qj.06.n. |
| [KS05] | George Em Karniadakis and Spencer J. Sherwin. Spectral/$hp$ Element Methods for Computational Fluid Dynamics (Numerical Mathematics and Scientific Computation). Oxford University Press, USA, 2 edition, 8 2005. ISBN 9780198528692. |
| [Kas74] | A. Kasahara. Various vertical coordinate systems used for numerical weather prediction. Mon. Wea. Rev., 102:509–522, 1974. |
| [KHB+96] | J. T. Kiehl, J. Hack, G. Bonan, B. Boville, B. Briegleb, D. Williamson, and P. Rasch. Description of the NCAR Community Climate Model (CCM3). Technical Report NCAR/TN-420+STR, National Center for Atmospheric Research, Boulder, Colorado, 1996. 152~pp. |
| [KHB94] | J. T. Kiehl, J. J. Hack, and B. P. Briegleb. The simulated Earth radiation budget of the National Center for Atmospheric Research Community Climate Model CCM2 and comparisons with the Earth Radiation Budget Experiment (ERBE). J.~Geophys. Res., 99:20815–20827, 1994. |
| [LTB+04] | D. A. Lack, X. X. Tie, N. D. Bofinger, A. N. Wiegand, and S. Madronich. Seasonal variability of secondary organic aerosol: A global modeling study. J. Geophys. Res., 2004. doi:10.1029/2003JD003418. |
| [LEH+12] | J.-F. Lamarque, L. K. Emmons, P. G. Hess, D. E. Kinnison, S. Tilmes, F. Vitt, C. L. Heald, E. A. Holland, P. H. Lauritzen, J. Neu, J. J. Orlando, P. J. Rasch, and G. K. Tyndall. CAM-chem: Description and evaluation of interactive atmospheric chemistry in the Community Earth System Model. Geoscientific Model Development, 5(2):369–411, 2012. URL: http://www.geosci-model-dev.net/5/369/2012/, doi:10.5194/gmd-5-369-2012. |
| [LHE+05] | J.-F. Lamarque, P. Hess, L. Emmons, L. Buja, W. Washington, and C. Granier. Tropospheric ozone evolution between 1890 and 1990. J. Geophys. Res., 110:D08304, 2005. doi:10.1029/2004JD005537. |
| [LJTN09] | Peter Lauritzen, Christiane Jablonowski, Mark Taylor, and Ramachandran Nair. Rotated versions of the jablonowski steady-state and baroclinic wave test cases: a dynamical core intercomparison. Journal of Advances in Modeling Earth Systems, 2009. URL: http://adv-model-earth-syst.org/index.php/JAMES/article/view/26. |
| [LAC+03] | H. Liao, P. J. Adams, S. H. Chung, J. H. Seinfeld, L. J. Mickley, and D. J. Jacob. Interactions between tropospheric chemistry and aerosols in a unified general circulation model. J. Geophys. Res., 108:4001, 2003. |
| [LCSW94] | S.-J. Lin, W. C. Chao, Y. C. Sud, and G. K. Walker. A class of the van leer-type transport schemes and its applications to the moisture transport in a general circulation model. Mon. Wea. Rev., 122:1575–1593, 1994. |
| [LR96] | S.-J. Lin and R. B. Rood. Multidimensional flux form semi-lagrangian transport schemes. Mon. Wea. Rev., 124:2046–2070, 1996. |
| [LR97] | S.-J. Lin and R. B. Rood. An explicit flux-form semi-lagrangian shallow water model on the sphere. Q.~J.~R.~Meteorol. Soc., 123:2531–2533, 1997. |
| [Lin04] | Shian-Jiann Lin. A vertically lagrangian finite-volume dynamical core for global models. Mon. Wea. Rev., 132:2293–2397, 2004. |
| [Lin81] | R. S. Lindzen. Turbulence and stress due to gravity wave and tidal breakdown. J. Geophys. Res., 86:9701–9714, 1981. |
| [LEG+12] | X. Liu, R. C. Easter, S. J. Ghan, R. Zaveri, P. Rasch, X. Shi, J.-F. Lamarque, A. Gettelman, H. Morrison, F. Vitt, A. Conley, S. Park, R. Neale, C. Hannay, A. M. L. Ekman, P. Hess, N. Mahowald, W. Collins, M. J. Iacono, C. S. Bretherton, M. G. Flanner, and D. Mitchell. Toward a minimal representation of aerosols in climate models: description and evaluation in the community atmosphere model cam5. Geoscientific Model Development, 5(3):709–739, 2012. URL: http://www.geosci-model-dev.net/5/709/2012/, doi:10.5194/gmd-5-709-2012. |
| [LG10] | X. Liu and S. Ghan. A modal aerosol model implementation in the Community Atmosphere Model, version 5 (CAM5). J.~Atmos. Sci., ():, 2010. |
| [LPGW07] | X. Liu, J. E. Penner, S. J. Ghan, and M. Wang. Inclusion of ice microphysics in the NCAR Community Atmosphere Model version 3 (CAM3). J. Clim., 20:4526–4547, 2007. |
| [Mac79] | B. Machenhauer. The spectral method. In Numerical Methods Used in Atmospheric Models, GARP Publication Series No. 17, 121–275. World Meteorological Organization, Geneva, Switzerland, 1979. |
| [Mac98] | B. Machenhauer. MPI workshop on conservative transport schemes. In Report No. 265. Max-planck-Institute for Meteorology, 1998. |
| [MP87] | Yvon Maday and A. T. Patera. Spectral element methods for the incompressible Navier Stokes equations. In A. K. Noor and J. Tinsley Oden, editors, State of the Art Surveys on Computational Mechanics, number in, chapter, pages 71–143. ASME, New York, edition, 1987. |
| [MLTW06] | N. Mahowald, J.-F. Lamarque, X. X. Tie, and E Wolff. Seasalt aerosol response to climate change: last glacial maximum, preindustrial, and doubled carbon dioxide climates. J. Geophys. Res., 2006. doi:10.1029/2005JD006459. |
| [MML+06] | N. M. Mahowald, D. R. Muhs, S. Levis, P. J. Rasch, M. Yoshioka, C. S. Zender, and C. Luo. Change in atmospheric mineral aerosols in response to climate: last glacial period, preindustrial, modern, and doubled carbon dioxide climates. J. Geophys. Res., 2006. doi:10210.11029/12005JD006653. |
| [Man69] | S. Manabe. Climate and the ocean circulation: 1. The atmospheric circulation and the hydrology of the earth’s surface. Mon. Wea. Rev., 97:739–774, 1969. |
| [MBP78] | B. J. McAvaney, W. Bourke, and K. Puri. A global spectral model for simulation of the general circulation. J.~Atmos. Sci., 35:1557–1583, 1978. |
| [McF87] | N. A. McFarlane. The effect of orographically excited gravity wave drag on the general circulation of the lower stratosphere and troposphere. J. Atmos. Sci., 44:1775–1800, 1987. |
| [McI89] | M. E. McIntyre. On dynamics and transport near the polar mesopause in summer. J. Geophys. Res., 94:14,617–14,628, 1989. |
| [MOH+00] | C.A. McLinden, S.C. Olsen, B. Hannegan, O. Wild, and M.J. Prather. Stratospheric ozone in 3-d models: a simple chemistry and the cross-tropopause flux. J. Geophys. Res., 105:14,653–14,665, 2000. |
| [MDPL02] | S. Metzger, F. Dentener, S. Pandis, and J. Lelieveld. Gas/aerosol partitioning: 1. A computationally efficient model. J. Geophys. Res., 107:4323, 2002. doi:doi:10.1029/2001JD001102. |
| [Mit02] | D. L. Mitchell. Effective diameter in radiation transfer: general definition, applications and limitations. J.~Atmos. Sci., 59:2330–2346, 2002. |
| [MG08] | H. Morrison and A. Gettelman. A new two-moment bulk stratiform cloud microphysics scheme in the NCAR Community Atmosphere Model (CAM3), Part I: description and numerical tests. J. Clim., 21(15):3642–3659, 2008. |
| [NH01a] | R. B. Neale and B. J. Hoskins. A standard test case for AGCMs including their physical parametrizations: II: Results for the Met Office Model. Atmos. Sci. Lett., 1:108–114, 2001. doi:10.1006/asle.2000.0024. |
| [NH01b] | R. B. Neale and B. J. Hoskins. A standard test case for AGCMs including their physical parametrizations: I: The proposal. Atmos. Sci. Lett., 1:101–107, 2001. doi:10.1006/asle.2000.0022. |
| [NRJ08] | R. B. Neale, J. H. Richter, and M. Jochum. The impact of convection on ENSO: from a delayed oscillator to a series of events. J.~Climate, 21:5904–5924, 2008. |
| [NDWN07] | P. A. Newman, J. S. Daniel, D. W. Waugh, and E. R. Nash. A new formulation of equivalent effective stratospheric chlorine (EESC). Atmos. Chem. Phys., 7(17):4537–4552, 2007. |
| [NKC+07] | N. L. Ng, J. H. Kroll, A. W. H. Chan, P. S. Chhabra, R. C. Flagan, and J. H. Seinfeld. Secondary organic aerosol formation from m-xylene, toluene, and benzene. Atmospheric Chemistry and Physics, 7(14):3909–3922, 2007. URL: http://www.atmos-chem-phys.net/7/3909/2007/, doi:10.5194/acp-7-3909-2007. |
| [OJG+97] | J. R. Odum, T. P. W. Jungkamp, R. J. Griffin, H. J. L. Forstner, R. C. Flagan, and J. H. Seinfeld. Aromatics, reformulated gasoline, and atmospheric organic aerosol formation. Environ. Sci. Technol., 31:1890–1897, 1997. |
| [Ors74] | S. A. Orszag. Fourier series on spheres. Mon. Wea. Rev., 102:56–75, 1974. |
| [Pan94] | J. F. Pankow. An absorption model of the gas aerosol partitioning involved in the formation of secondary organic aerosol. Atmos. Environ., 28:189 – 193, 1994. |
| [PM03] | R.and H. W. Barker Pincus and J.-J. Morcrette. A fast, flexible, approximation technique for computing radiative transfer in inhomogeneous cloud fields. J.~Geophys. Res., 108(D13):4376, 2003. doi:10.1029/2002JD003322. |
| [Pra92] | M.J. Prather. Catastrophic loss of stratospheric ozone in dense volcanic clouds. J. Geophys. Res., 97:187–10,191, 1992. |
| [RBB95] | P. J. Rasch, B. A. Boville, and G. P. Brasseur. A three-dimensional general circulation model with coupled chemistry for the middle atmosphere. J.~Geophys. Res., 100:9041–9071, 1995. |
| [RKristjansson98] | P. J. Rasch and J. E. Kristjánsson. A comparison of the CCM3 model climate using diagnosed and predicted condensate parameterizations. J.~Climate, 11:1587–1614, 1998. |
| [RW90] | P. J. Rasch and D. L. Williamson. On shape-preserving interpolation and semi-Lagrangian transport. SIAM J.~Sci. Stat. Comput., 11:656–687, 1990. |
| [RB86] | D. J. Raymond and A. M. Blyth. A stochastic mixing model for non-precipitating cumulus clouds. J.~Atmos. Sci., 43:2708–2718, 1986. |
| [RB92] | D. J. Raymond and A. M. Blyth. Extension of the stochastic mixing model to cumulonimbus clouds. J.~Atmos. Sci., 49:1968–1983, 1992. |
| [RR08] | J. H. Richter and P. J. Rasch. Effects of convective momentum transport on the atmospheric circulation in the community atmosphere model, version 3. J.~Climate, 21:1487–1499, 2008. |
| [RHaDAR00] | T. D. Ringler, R. P. Heikes, and and D. A. Randall. Modeling the atmospheric general circulation using a spherical geodesic grid: a new class of dynamical cores. Mon. Wea. Rev., 128:2471–2490, 2000. |
| [RT96] | H. Ritchie and M. Tanguay. A comparison of spatially averaged Eulerian and semi-Lagrangian treatments of mountains. Mon. Wea. Rev., 124:167–181, 1996. |
| [Rob66] | A. J. Robert. The integration of a low order spectral form of the primitive meteorological equations. J.~Meteorol. Soc. Japan, 44:237–245, 1966. |
| [RBB+03] | L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino. The HITRAN molecular spectroscopic database: Edition of 2000 including updates of 2001. J.~Quant. Spectrosc. Radiat. Transfer, 2003. |
| [Sad72] | R. Sadourny. Conservative finite-difference approximations of the primitive equations on quasi-uniform spherical grids. Mon. Wea. Rev., 100(2):136–144, 1972. |
| [SPDIC96] | A. Sandu, F. A. Potra, V. Damian-Iordache, and G. R. Carmichael. Efficient implementation of fully implicit methods for atmospheric chemistry. J. Comp. Phys., 129:101–110, 1996. |
| [SVvL+97] | A. Sandu, J.G. Verwer, M. van Loon, G.R. Carmichael, F.A. Potra, D. Dabdub, and J.H. Seinfeld. Benchmarking stiff ODE solvers for atmospheric chemistry problems I: implicit versus explicit. Atmospheric Environment, 31:3151–3166, 1997. |
| [San60] | W. E. Sangster. A meteorological coordinate system in which the Earth’s surface is a coordinate surface. PhD thesis, University of Chicago, Department of Geophysical Sciences, 1960. |
| [SBWW83] | R. K. Sato, L. M. Bath, D. L. Williamson, and G. S. Williamson. User’s guide to NCAR CCMOB. Technical Report NCAR/TN-211+IA, National Center for Atmospheric Research, Boulder, Colorado, 1983. 133~pp. |
| [Sat04] | Masaki Satoh. Atmospheric Circulation Dynamics and Circulation Models (Springer Praxis Books / Environmental Sciences). Springer, 1 edition, 6 2004. ISBN 9783540426387. |
| [SB81] | A. J. Simmons and D. M. Burridge. An energy and angular momentum conserving vertical finite-difference scheme and hybrid vertical coordinates. Mon. Wea. Rev., 109:758–766, 1981. |
| [SStrufing81] | A. J. Simmons and R. Strüfing. An energy and angular-momentum conserving finite-difference scheme, hybrid coordinates and medium-range weather prediction. Technical Report ECMWF Report No. 28, European Centre for Medium–Range Weather Forecasts, Reading, U.K., 1981. 68~pp. |
| [SStrufing83] | A. J. Simmons and R. Strüfing. Numerical forecasts of stratospheric warming events using a model with hybrid vertical coordinate. Q.~J.~R.~Meteorol. Soc., 109:81–111, 1983. |
| [SPW01] | S. J. Smith, H. Pitcher, and T. M. L. Wigley. Global and regional anthropogenic sulfur dioxide emissions. Glob. Biogeochem. Cycles, 29:99–119, 2001. |
| [SR02] | Raymond J. Spiteri and Steven J. Ruuth. A new class of optimal high-order strong-stability-preserving time discretization methods. SIAM J. Numer. Anal., 40(2):469–491, 2002. doi:http://dx.doi.org/10.1137/S0036142901389025. |
| [SWG03] | Andrew Staniforth, Nigel Wood, and Claude Girard. Energy and energy-like invariants for deep non-hydrostatic atmospheres. Q.~J.~R.~Meteorol. Soc., 129:3495–3499, 2003. |
| [Sta45] | V. P. Starr. A quasi-lagrangian system of hydrodynamical equations. J.~Meteor., 2:227–237, 1945. |
| [ST95] | M. J. Suarez and L. L. Takacs. Documentation of the aries/geos dynamical core: version 2. Technical Report Technical Memorandum 104 606 Vol. 5, NASA, 1995. |
| [Sun88] | H. Sundqvist. Parameterization of condensation and associated clouds in models for weather prediction and general circulation simulation. In M. E. Schlesinger, editor, Physically-based Modeling and Simulation of Climate and Climate Change, volume 1, pages 433–461. Kluwer Academic, 1988. |
| [TEStCyr08] | M. A. Taylor, J. Edwards, and A. St.Cyr. Petascale atmospheric models for the community climate system model: new developments and evaluation of scalable dynamical cores. J. Phys. Conf. Ser., 2008. doi:10.1088/1742-6596/125/1/012023. |
| [Tay10] | M.A. Taylor. Conservation of mass and energy for the moist atmospheric primitive equations on unstructured grids. In M. A. Taylor P. H. Lauritzen, C. Jablonowski and R. D. Nair., editors, Numerical Techniques for Global Atmospheric Models, Springer Lecture Notes in Computational Science and Engineering, volume. Springer, 2010. |
| [TTI97] | Mark Taylor, J. Tribbia, and M. Iskandarani. The spectral element method for the shallow water equations on the sphere. J.~Comp.~Phys., 130():92–108, 1997. |
| [TF10] | Mark A. Taylor and Aimé Fournier. A compatible and conservative spectral element method on unstructured grids. J.~Comp.~Phys., In Press:–, 2010. doi:10.1016/j.jcp.2010.04.008. |
| [TStCyrF09] | Mark A. Taylor, A. St.Cyr, and Aimé Fournier. A non-oscillatory advection operator for the compatible spectral element method. In Computational Science ICCS 2009 Part II, Lecture Notes in Computer Science 5545, volume, 273–282. Berlin / Heidelberg, 2009. Springer. |
| [Tem97] | C. Temperton. Treatment of the Coriolis terms in semi-Lagrangian spectral models. In C. Lin, R. Laprise, and H. Ritchie, editors, Atmospheric and Ocean Modelling. The André J.~Robert Memorial Volume, pages 293–302. Canadian Meteorological and Oceanographic Society, Ottawa, Canada, 1997. |
| [TL00] | S.J. Thomas and R.D. Loft. Parallel semi-implicit spectral element methods for atmospheric general circulation models. J.~Sci. Comput., 15:499–518, 2000. |
| [TMW+05a] | X. Tie, S. Madronich, S. Walters, D. P. Edwards, P. Ginoux, N. Mahowald, R. Zhang, C. Lou, and G. Brasseur. Assessment of the global impact of aerosols on tropospheric oxidants. J. Geophys. Res., 110:D03204, 2005. doi:10.1029/2004JD005359. |
| [TMW+05b] | X. X. Tie, S. Madronich, S. Walters, D. P. Edwards, P. Ginoux, N. Mahowald, R. Y. Zhang, C. Lou, and G. Brasseur. Assessment of the global impact of aerosols on tropopshic ozidants. J.~Geophys. Res., 2005. doi:10.1029/2004JD005359. |
| [VW08] | S. Vavrus and D. Waliser. An improved parameterization for simulating arctic cloud amount in the CCSM3 climate model. J.~Climate, 21:5673–5687, 2008. |
| [WLS05] | Y.-M. Wang, J.L. Lean, and N.R. Sheeley. Modeling the sun’s magnetic field and irradiance since 1713. The Astrophysical Journal, 2005. URL: http://stacks.iop.org/0004-637X/625/i=1/a=522. |
| [Was82] | W. M. Washington. Documentation for the Community Climate Model (CCM), Version $\emptyset $. Technical Report NTIS No. PB82 194192, National Center for Atmospheric Research, Boulder, Colorado, 1982. |
| [Wil83] | D. L. Williamson. Description of NCAR Community Climate Model (CCM0B). Technical Report NCAR/TN-210+STR, National Center for Atmospheric Research, Boulder, Colorado, 1983. NTIS No. PB83 23106888, 88~pp. |
| [Wil02] | D. L. Williamson. Time-split versus process-split coupling of parameterizations and dynamical core. Mon. Wea. Rev., 130:2024–2041, 2002. |
| [WBS+83] | D. L. Williamson, L. M. Bath, R. K. Sato, T. A. Mayer, and M. L. Kuhn. Documentation of NCAR CCM0B program modules. Technical Report NCAR/TN-212+IA, National Center for Atmospheric Research, Boulder, Colorado, 1983. NTIS No. PB83 263996, 198~pp. |
| [WKR+87] | D. L. Williamson, J. T. Kiehl, V. Ramanathan, R. E. Dickinson, and J. J. Hack. Description of NCAR Community Climate Model (CCM1). Technical Report NCAR/TN-285+STR, National Center for Atmospheric Research, Boulder, Colorado, 1987. 112~pp. |
| [WO94a] | D. L. Williamson and J. G. Olson. Climate simulations with a semi-Lagrangian version of the NCAR Community Climate Model. Mon. Wea. Rev., 122:1594–1610, 1994. |
| [WO94b] | D. L. Williamson and J. G. Olson. Climate simulations with a semi-lagrangian version of the NCAR community climate model. Mon. Wea. Rev., 122:1594–1610, 1994. |
| [WR89] | D. L. Williamson and P. J. Rasch. Two-dimensional semi-Lagrangian transport with shape-preserving interpolation. Mon. Wea. Rev., 117:102–129, 1989. |
| [WR00] | D. L. Williamson and J. M. Rosinski. Accuracy of reduced grid calculations. Q.~J.~R.~Meteorol. Soc., 126:1619–1640, 2000. |
| [WW84] | D. L. Williamson and G. S. Williamson. Circulation statistics from January and July simulations with the NCAR Community Climate Model (CCM0B). Technical Report NCAR/TN-224+STR,, National Center for Atmospheric Research, Boulder, Colorado, 1984. NTIS No. PB85 165637/AS, 112~pp. |
| [Wil93] | G. S. Williamson. CCM2 datasets and circulation statistics. Technical Report NCAR/TN-391+STR, National Center for Atmospheric Research, Boulder, Colorado, 1993. 85~pp. |
| [WW87] | G. S. Williamson and D. L. Williamson. Circulation statistics from seasonal and perpetual January and July simulations with the NCAR Community Climate Model (CCM1): R15. Technical Report NCAR/TN-302+STR, National Center for Atmospheric Research, Boulder, Colorado, 1987. 199~pp. |
| [Wis96] | W. J. Wiscombe. Mie scattering calculations: advances in technique and fast, vector-speed computer codes. Technical Report Tech. Note. NCAR/TN-140+STR, NCAR, 1996. |
| [ZWS05] | Mohamed Zerroukat, Nigel Wood, and Andrew Staniforth. 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, 2005. doi:10.1256/qj.04.97. |
| [ZM95] | G. J. Zhang and N. A. McFarlane. Sensitivity of climate simulations to the parameterization of cumulus convection in the Canadian Climate Centre general circulation model. Atmosphere-Ocean, 33:407–446, 1995. |
| [ZLB+03] | M. Zhang, W. Lin, C. S. Bretherton, J. J. Hack, and P. J. Rasch. A modified formulation of fractional stratiform condensation rate in the NCAR community atmospheric model CAM2. J.~Geophys. Res., 2003. |
| [LamarqueBondEyring+10] | J.-F. Lamarque, T. C. Bond, V. Eyring, C. Granier, A. Heil, Z. Klimont, D. Lee, C. Liousse, A. Mieville, B. Owen, M. G. Schultz, D. Shindell, S. J. Smith, E. Stehfest, J. van Aardenne, O. R. Cooper, M. Kainuma, N. Mahowald, J. R. McConnell, V. Naik, K. Riahi, and D. P. van Vuuren. Historical (1850-2000) gridded anthropogenic and biomass burning emissions of reactive gases and aerosols: methodology and application. Atmospheric Chemistry & Physics Discussions, 10:4963–5019, February 2010. |
| [RanvcicPM96] | M. Rančić, R.J. Purser, and F. Mesinger. A global shallow-water model using an expanded spherical cube: gnomonic versus conformal coordinates. Q.~J.~R.~Meteorol. Soc., 122:959–982, 1996. |
| [SanderSPeal06] | Sander, S. P., et al. Chemical kinetics and photochemical data for use in atmospheric studies. Evaluation number 15. Technical Report Publication 06-02, Jet Propulsion Laboratory, Pasadena, CA, Jet Propulsion Laboratory, Pasadena, CA, 2006. |