The atmospheric general circulation model ECHAM6 Model description M.A. Giorgetta, E. Roeckner, T. Mauritsen, J. Bader, T. Crueger, M. Esch, S. Rast, L. Kornblueh, H. Schmidt, S. Kinne, C. Hohenegger, B. Möbis, T. Krismer, K.–H. Wieners, B. Stevens 135 Berichte zur Erdsystemforschung 2013 Reports on Earth System Science 135 Berichte zur Erdsystemforschung 2013 The atmospheric general circulation model ECHAM6 Model description M.A. Giorgetta, E. Roeckner, T. Mauritsen, J. Bader, T. Crueger, M. Esch, S. Rast, L. Kornblueh, H. Schmidt, S. Kinne, C. Hohenegger, B. Möbis, T. Krismer, K.–H. Wieners, B. Stevens 135 Reports on Earth System Science 2013 ISSN 1614-1199 M.A. Giorgetta, E. Roeckner, T. Mauritsen, J. Bader, T. Crueger, M. Esch, S. Rast1, L. Kornblueh, H. Schmidt, S. Kinne, C. Hohenegger, B. Möbis, T. Krismer, K.–H. Wieners, B. Stevens Max-Planck-Institut für Meteorologie Bundesstrasse 53 20146 Hamburg [email protected] ISSN 1614-1199 The atmospheric general circulation model ECHAM6 Model description M.A. Giorgetta, E. Roeckner, T. Mauritsen, J. Bader, T. Crueger, M. Esch, S. Rast, L. Kornblueh, H. Schmidt, S. Kinne, C. Hohenegger, B. Möbis, T. Krismer, K.–H. Wieners, B. Stevens Hamburg, June 21, 2013 Contents 1. Introduction 9 2. Atmosphere 11 2.1. Dynamical Core.................................... 12 2.1.1. The continuous equations.......................... 12 2.1.2. Horizontal discretization........................... 15 2.1.3. Vertical discretization............................ 20 2.1.4. Time integration scheme........................... 28 2.1.5. Nudging of dynamical variables....................... 33 2.2. Transport....................................... 36 2.3. Radiative Transfer.................................. 39 2.3.1. Correlated k method............................. 39 2.3.2. Shortwave................................... 41 2.3.3. Longwave radiation............................. 44 2.3.4. Radiative Properties............................. 45 2.3.5. Implementation and Numerical Aspects.................. 45 2.4. Turbulent transport and surface fluxes....................... 46 2.4.1. Conservative variables and definitions................... 46 2.4.2. TKE closure model.............................. 47 2.4.3. Interaction with the surface......................... 51 2.4.4. Numerical solution.............................. 53 2.4.5. Solving the TKE-equation.......................... 55 2.5. Cumulus convection................................. 57 2.5.1. Organized entrainment............................ 57 2.5.2. Organized detrainment............................ 58 2.5.3. Adjustment closure.............................. 59 2.5.4. Trigger of cumulus convection........................ 61 2.6. Large-scale cloud scheme............................... 62 2.6.1. Governing equations............................. 62 2.6.2. Cloud cover.................................. 63 2.6.3. Sedimentation and cloud microphysics................... 64 2.7. Parameterization of the momentum flux deposition due to a gravity wave spectrum 73 2.7.1. Hines Doppler spread theory........................ 73 2.7.2. The Hines Doppler Spread Parameterization (HDSP)........... 74 2.7.3. Summary................................... 79 2.7.4. Implementation Details........................... 80 2.8. Parameterized gravity wave drag from subgrid scale orography......... 82 2.8.1. Representation of the subgrid scale orography............... 82 2.8.2. Gravity wave drag from subgrid-scale orography............. 82 2.8.3. Gravity wave drag.............................. 84 2.9. Water Vapor in the Middle Atmosphere...................... 86 3 3. Land 87 4. Slab Ocean and Sea Ice 88 4.1. Slab ocean....................................... 89 4.2. Sea Ice......................................... 91 4.2.1. Calculation of sea ice melting separately for bare/snow covered ice and meltponds................................... 91 4.2.2. Snow on ice.................................. 93 4.2.3. New sea ice albedo scheme......................... 95 5. Atmosphere surface coupling 102 6. Model resolutions and resolution dependent parameters 103 6.1. Model resolutions and resolution-dependent parameters............. 104 6.1.1. Available model resolutions......................... 104 6.1.2. Resolution-dependent parameters...................... 104 6.1.3. Code implementation............................ 105 7. External data 106 7.1. Solar irradiation................................... 107 7.1.1. Historic.................................... 107 7.1.2. Scenarios................................... 108 7.1.3. Climatologies................................. 108 7.2. CO2, CH4, N2O, CFCs............................... 110 7.2.1. 1850-present, present to 2100 and beyond................. 110 7.3. Ozone......................................... 111 7.3.1. Historic.................................... 111 7.3.2. Scenarios................................... 112 7.3.3. Climatologies................................. 113 7.4. Aerosols........................................ 114 7.4.1. Tropospheric aerosols............................ 114 7.4.2. Stratospheric aerosols............................ 122 7.5. Sea surface temperature and ice cover....................... 127 7.5.1. Historic.................................... 127 7.5.2. Climatologies................................. 127 7.5.3. Aqua planet.................................. 127 7.6. Land data....................................... 128 7.6.1. Land sea maps................................ 128 7.6.2. Orography.................................. 128 7.6.3. Vegetation maps............................... 128 8. Errata 129 8.1. Albedo of melt–ponds................................ 130 8.2. Bug in anthropogenic aerosol data set....................... 130 8.3. Energy conservation violation............................ 130 8.4. Bug in gravity wave drag parameterization – Asymmetry............ 131 8.5. Horizontal diffusion in MR resolution........................ 131 A. The unparameterized equations 132 A.1. Introduction...................................... 133 4 A.2. The advective form of the unparameterized equations.............. 134 A.2.1. The material derivative........................... 134 A.2.2. The equation of state............................ 134 A.2.3. Mass conservation.............................. 135 A.2.4. The velocity equation............................ 135 A.2.5. The thermodynamic equation........................ 135 A.3. The flux forms of the equations........................... 136 A.4. The introduction of diffusive fluxes......................... 137 A.5. Approximations and definitions........................... 139 A.6. Return to the advective form............................ 139 A.7. The model equations................................. 140 B. Orbital Variations 142 B.1. Introduction...................................... 142 B.1.1. Obliquity................................... 142 B.1.2. Eccentricity.................................. 143 B.1.3. Precession................................... 144 B.2. Precise orbit determination based on VSOP87................... 144 B.2.1. VSOP — Variations Séculaires des Orbites Planétaires.......... 144 B.2.2. Nutation................................... 147 B.3. Kepler based orbit for paleoclimate applications.................. 148 B.4. Differences in the daily insolation due to the two given orbits.......... 149 B.5. Orbit tables...................................... 152 References 164 5 List of Tables 2.1. Truncation and associated number of Gaussian latitudes............. 20 2.2. Vertical-coordinate parameters........................... 24 2.3. Band structure for longwave radiative transfer................... 40 2.4. Band structure for shortwave radiative transfer.................. 41 2.5. Parameters, symbols and control parameters of namelist GWSCTL....... 81 4.1. Sea ice albedo parameterization scheme...................... 96 4.2. Constants for bare sea ice albedo.......................... 97 4.3. Constants for melt pond fraction as a function of melt pond depth for multiyear ice........................................... 99 4.4. Constants for melt pond albedo........................... 101 7.1. Solar irradiation as defined for the original SRTM radiation scheme....... 109 7.2. Pressure levels in Pa of ozone climatology..................... 111 7.3. Refractive indices of sulfate, dust, and sea salt.................. 116 7.4. File names of files containing tropospheric aerosol optical properties...... 122 7.5. Pressure coordinate for optical properties of aerosols............... 123 7.6. Wavelength bands for optical properties of volcanic aerosols........... 124 7.7. Available land sea masks dependent on ECHAM6 and MPI-OM resolution... 128 B.1. First summand of heliocentric latitude (VSOP87D)................ 153 B.2. Second summand of heliocentric latitude (VSOP87D).............. 154 B.3. Third summand of heliocentric latitude (VSOP87D)............... 155 B.4. Fourth summand of heliocentric latitude (VSOP87D)............... 155 B.5. Fifth summand of heliocentric latitude (VSOP87D)................ 156 B.6. Sixth summand of heliocentric latitude (VSOP87D)............... 156 B.7. First summand of heliocentric longitude (VSOP87D)............... 156 B.8. Second summand of heliocentric longitude (VSOP87D).............. 156 B.9. First summand of distance (VSOP87D)...................... 158 B.10.Second summand of distance (VSOP87D)..................... 158 B.11.Third summand of distance (VSOP87D).....................