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The Atmospheric General Circulation Model ECHAM5 Report No. 349 Model description by E. Roeckner • G. Bäuml • L. Bonaventura • R. Brokopf • M. Esch M. Giorgetta • S. Hagemann • I. Kirchner • L. Kornblueh E. Manzini • A. Rhodin • U. Schlese • U. Schulzweida • A. Tompkins Hamburg, November 2003 Authors E. Roeckner, G. Bäuml, Max-Planck-Institut für Meteorologie L. Bonaventura, R. Brokopf, Hamburg, Germany M. Esch, M. Giorgetta, S. Hagemann, L. Kornblueh, U. Schlese, U. Schulzweida I. Kirchner Freie Universität Berlin, Berlin, Germany E. Manzini Istituto Nazionale di Geofisica e Vulcanologia, Bologna, Italy A. Rhodin Deutscher Wetterdienst, Offenbach, Germany A. Tompkins European Centre for Medium Range Weather Forecasts, Reading, UK Max-Planck-Institut für Meteorologie Bundesstrasse 55 D - 20146 Hamburg Germany Tel.: +49-(0)40-4 11 73-0 Fax: +49-(0)40-4 11 73-298 e-mail: <name>@dkrz.de Web: www.mpimet.mpg.de Report No. 349 Model description by E. Roeckner • G. Bäuml • L. Bonaventura • R. Brokopf • M. Esch M. Giorgetta • S. Hagemann • I. Kirchner1 • L. Kornblueh E. Manzini2 • A. Rhodin3 • U. Schlese • U. Schulzweida • A. Tompkins4 Hamburg, November 2003 ISSN 0937 - 1060 1Freie Universität Berlin, Berlin, Germany 2Istituto Nazionale di Geofisica e Vulcanologia, Bologna, Italy 3Deutscher Wetterdienst, Offenbach, Germany 4European Centre for Medium Range Weather Forecasts, Reading, UK Abstract A detailed description of the fifth-generation ECHAM model is presented. Compared to the previous version, ECHAM4, a number of substantial changes have been introduced in both the numerics and physics of the model. These include a flux-form semi-Lagrangian transport scheme for positive definite variables like water components and chemical tracers, a new longwave ra- diation scheme, separate prognostic equations for cloud liquid water and cloud ice, a new cloud microphysical scheme and a prognostic-statistical cloud cover parameterization. The number of spectral intervals is increased in both the longwave and shortwave part of the spectrum. Changes have also been made in the representation of land surface processes, including an implicit cou- pling between the surface and the atmosphere, and in the representation of orographic drag forces. Also, a new dataset of land surface parameters has been compiled for the new model. On the other hand, horizontal and vertical diffusion, cumulus convection and also the spectral dynamics remain essentially unchanged. Acknowledgments The authors are grateful to Jean-Jacques Morcrette, ECMWF, for providing the ECMWF version of the RRTM code and to Francois Lott, LMD, who made the SSO scheme available to us. We gratefully acknowledge the help of David Dent, ECMWF, in improving the Legendre Transfor- mation code, and we thank Eckhard Tschirschnitz, NEC, for substantial support with respect to scalability and code optimization for vector and cache-based platforms. Contents 1. Introduction 5 2. Model dynamics 7 2.1. Introduction ........................................ 7 2.2. The continuous equations ................................ 8 2.3. Horizontal discretization ................................. 10 2.3.1. Spectral representation ............................. 10 2.3.2. Spectral/grid-point transforms, and the evaluation of spectral tendencies . 14 2.4. Vertical discretization .................................. 16 2.4.1. The hybrid vertical representation ....................... 16 2.4.2. The vertical finite-difference scheme ...................... 17 2.4.3. The surface-pressure tendency ......................... 17 2.4.4. The continuity equation ............................. 19 2.4.5. Vertical advection ................................ 19 2.4.6. The hydrostatic equation ............................ 19 2.4.7. The pressure gradient term ........................... 20 2.4.8. Energy-conversion term ............................. 21 2.5. Time integration scheme ................................. 21 2.5.1. The semi-implicit treatment of vorticity .................... 22 2.5.2. The semi-implicit treatment of divergence, temperature and surface pressure 24 3. Tracer advection 27 4. Horizontal diffusion 30 5. Surface fluxes and vertical diffusion 31 6. Surface processes 35 6.1. Heat budget of the soil .................................. 35 1 6.1.1. Land surface temperature ............................ 35 6.1.2. Soil temperatures ................................. 36 6.2. Water budget ....................................... 36 6.2.1. Interception of snow by the canopy ....................... 37 6.2.2. Snow at the surface ............................... 37 6.2.3. Interception of rain by the canopy ....................... 38 6.2.4. Soil water ..................................... 38 6.3. Lake model ........................................ 39 6.4. Sea-ice ........................................... 42 6.5. Coupling to mixed layer ocean ............................. 42 6.6. Surface albedo ...................................... 43 7. Subgrid scale orography parameterization 45 7.1. Introduction ........................................ 45 7.2. Representation of the subgrid scale orography ..................... 45 7.3. Low level drag and gravity wave stress ......................... 46 7.4. Gravity wave drag .................................... 47 8. Parameterization of the momentum flux deposition due to a gravity wave spectrum 49 8.1. Introduction ........................................ 49 8.2. Hines Doppler spread theory .............................. 49 8.3. The Hines Doppler Spread Parameterization (HDSP) ................. 50 8.3.1. Cutoff vertical wavenumber ........................... 52 8.3.2. Horizontal wind variance ............................ 53 8.3.3. Momentum flux deposition ........................... 54 8.4. Summary ......................................... 55 9. Cumulus convection 57 9.1. Organized entrainment .................................. 57 9.2. Organized detrainment .................................. 58 9.3. Adjustment closure .................................... 59 10.Stratiform cloud scheme 61 10.1. Governing equations ................................... 61 10.2. Cloud cover ........................................ 63 2 10.2.1. Cloud scheme framework ............................ 63 10.2.2. Distribution moments .............................. 64 10.3. Sedimentation and cloud microphysics ......................... 67 10.3.1. Sedimentation of cloud ice ............................ 67 10.3.2. Condensation/evaporation, deposition/sublimation and turbulence effects . 67 10.3.3. Freezing of cloud liquid water and melting of cloud ice ............ 69 10.3.4. Precipitation formation in warm clouds, cold clouds and in mixed-phase clouds ....................................... 70 10.3.5. Evaporation of rain and sublimation of snow and ice ............. 71 10.3.6. Precipitation ................................... 72 10.3.7. Mixing ratios of rain, falling ice and snow ................... 74 10.3.8. Solution method and parameter choice ..................... 75 11.Radiation 77 11.1. Atmospheric composition ................................ 78 11.1.1. Water vapour, cloud water, cloud ice, and cloud cover ............ 78 11.1.2. Carbon dioxide .................................. 78 11.1.3. Ozone ....................................... 78 11.1.4. Methane ...................................... 79 11.1.5. N2O ........................................ 79 11.1.6. CF Cs ....................................... 79 11.1.7. Aerosols ...................................... 79 11.2. Solar irradiation ..................................... 80 11.3. Shortwave radiation ................................... 81 11.3.1. Spectral resolution ................................ 84 11.3.2. Cloud optical properties ............................. 84 11.3.3. Cloud overlap assumption ............................ 87 11.4. Longwave radiation .................................... 87 11.4.1. Spectral resolution ................................ 88 11.4.2. Cloud optical properties ............................. 88 11.4.3. Cloud overlap assumption ............................ 90 11.4.4. Aerosol optical properties ............................ 90 11.4.5. Surface emissivity ................................ 91 3 12.Orbital Variations 92 12.1. Introduction ........................................ 92 12.1.1. Obliquity ..................................... 92 12.1.2. Eccentricity .................................... 93 12.1.3. Precession ..................................... 94 12.2. Precise orbit determination based on VSOP87 ..................... 94 12.2.1. VSOP | Variations S´eculairesdes Orbites Plan´etaires ............ 94 12.2.2. Nutation ..................................... 97 12.3. Kepler based orbit for paleoclimate applications .................... 98 12.4. Differences in the daily insolation due to the two given orbits ............ 99 A. The unparametrized equations 102 A.1. Introduction ........................................ 102 A.2. The advective form of the unparameterized equations ................ 103 A.2.1. The material derivative ............................. 103 A.2.2. The equation of state .............................. 103 A.2.3. Mass conservation ................................ 104 A.2.4. The velocity equation .............................. 104 A.2.5. The thermodynamic equation .......................... 104 A.3. The flux forms of the equations ............................. 105 A.4. The introduction of diffusive fluxes ........................... 106 A.5. Approximations and definitions ............................
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