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Masaki Satoh and Tomoe Nasuno Frontier System Research for Global Change/ Saitama Inst. Tech.

Radiative-convective equilibrium calculations with cloud resolving models: A standard experiment and parameter study. Masaki Satoh and Tomoe Nasuno Frontier System Research for Global Change/ Saitama Inst. Tech. Fifth International SRNWP-workshop on nonhydrostatic modelling

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Masaki Satoh and Tomoe Nasuno Frontier System Research for Global Change/ Saitama Inst. Tech.

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  1. Radiative-convective equilibrium calculations with cloud resolving models: A standard experiment and parameter study Masaki Satoh and Tomoe Nasuno Frontier System Research for Global Change/ Saitama Inst. Tech. Fifth International SRNWP-workshop on nonhydrostatic modelling 27-29 Oct. 2003, Bad Orb, Germany

  2. Outline • Motivation • A global cloud resolving model • Investigation of physics • Model formulation • Nonhydrostatic core • Radiative-convective equilibrium experiments • Setup • Parameter study • Summary

  3. Motivation • Development of a global cloud resolving model • Nonhydrostatic ICosahedral Atmospheric Model (NICAM) ⇒ Δx = 3.5km on the Earth Simulator 2hours for one day simulation if 320 nodes are used (half of ES) • Climate study 　　⇒ direct calculation of cloud-radiation interaction ⇒ Radiative-convective equilibrium NICAM By H.Tomita

  4. RegionalNonhydrostatic model • Regional Nonhydrostatic model (Satoh, 2002,2003,MWR) • A subset of the global cloud resolving model (NICAM) • Cartesian coordinates • The same dynamical framework as NICAM except for the metrics • Model hierarchy: can be used as 1D-vertical, 2D-slice, and 3D-regional models • Development of new dynamical schemes: Dynamical framework and advection scheme • Study of physics: cloud-radiation interaction

  5. Characteristicｓ of the nonhydrostatic model • Fully compressible non-hydrostatic equations • Horizontally explicit and vertically implicit time integration with time splitting • The Helmholtz equation is formulated for vertical velocity not for pressure: • a switch for a hydrostatic/non-hydrostatic option can be introduced. • Conservation of the domain integrals (Satoh 2002, 2003,MWR) • The finite volume method using flux form equations • Density, momentum, and total energy are conserved. • Conservation of total energy including TKE budget • Tracer advecion • Third order upwind, or UTOPIA • Consistency with Continuity • Exact treatment of moist thermodynamics (Ooyama 1990, 2001). • Dependency of latent heat on temperature and specific heats of water substance • Transports of water, momentum, and energy due to rain. • An accurate transport scheme for rain (Xiao et al 2003,MWR) • Conservative Semi-Lagrangian scheme with 3rd order

  6. Dry formulation • Conservative flux form equations for density R, momentum V, and total energy E+K+G: where

  7. Governing equations (Ooyama, 1990,2000） Transports due to rain Release of potential energy of rain

  8. Characteristicｓ of the nonhydrostatic model (2) • Physics • Cloud physics: Choice of ice process for the global model is an issue. Warm rain (bulk method) Ice process: Grabowski(1998; simple 3 categories) (courtesy of W.G.) planned: Lin et al.(1983); Grabowski (1999: 5 categories) Bin or Spectral expansion method (K.Suzuki) • Turbulence: 1.5TKE (Deardorff) or Mellor and Yamada Level 2, 2.5 • Surface flux: Louis (1982) • Radiation: MSTRN-X (Nakajima et al, 2000, courtesy of CCSR)

  9. Radiative-convective equilibrium studies • Small domain experiments • Investigation of many parameters: physics and external parameters • Comparison between different models • Feasible on many computers: • 100km x 100km，Δx=2km (Tompkins and Craig 1998) • Can be used as a standard test • Large domain experiments • 1000km x 100km (Tompkins 2001) • 3D domain： 1000 km x 1000 km，Δx=2km • Equatorial belt2Dor 3D：　40000km x 100km • Global experiments on ES • Aqua planet with uniform SST (Sumi; Grabowsky 2003) • Aqua planet with prescribed SST distribution (Hayashi and Sumi; APE) • AMIP，…: Realizable climate condition is an equilibrium state of fully interactive radiative and convective processes.

  10. Large domain experiments • 3D large domain experiment: following Tompkins (2001) • 1000 km x 100 km x 21 km • Δx= 2 km • Uniform radiative cooling (-2K/day) • Tropical SST (302K) • Long-time simulation (56 days) • No large scale forcing: pure RCE exp. • Use of MRI/NPD-NHM (Courtesy of Dr. T.Kato)

  11. Rainwater (z=35m) y-averaged (100 km) Large-scale organization Loosely organized (small scale) 10 days 1000 km

  12. Issues of radiative-convective equilibrium experiments • Strong dependency on artificial parameters • Surface flux with bulk formula: Depends on minimum surface velocity: Umin • Control of the shear: Mean winds develop internally. • Strong interaction with radiation • Domain size, resolution, numerical diffusion… • Model dependency ⇒Requires a suitable standard setup • To understand parameter dependency • To know model characteristics Shie et al. (2003)

  13. Small domain experiments • Basically follows Tompkins & Craig (1998) • Dimension: 3D or 2D • 100km × 100km × 25km200km×200km(3D); 1000km, 5000km(2D) • Δx=Δy=2km4, 10km • Lowest level: 20m, 54 layersdepend on number of vertical layers? • Periodic boundary condition • Fixed sea surface temperature with 300Kor 302K • Radiation: interactive with clouds and humidity prescribed radiative cooling: 2K/day (z<9km) decreases to zero at z=12km or 1K/day, or interactive radiation (require solar flux and ozone profile) • Surface flux: minimum velocity for the bulk coefficient: Umin=4m/s or 1, 7m/s • No large-scale forcing: no momentum source or nudging to prescribed zonal wind (0m/s) • No Coriolis forcing: f=0 • Total integration time: 60(spin up)+40days • Initial condition: uniform temperature(250K) or TOGA-COARE, Marshall islands

  14. Control experiment • 100km × 100km, Δx＝2km • Warm rain • Prescribed cooling: -2K/day • TKE • Bulk method Umin=4m/s • Uniform initial cond. T=250K temperature Relative humidity Precipitation

  15. Mass weighted mean temperature & precipitable water CTL Courtesy of W.K. Tao

  16. Problems and further experiments Bulk coefficient and minimum velocity Ice phase Statistic of maximum of the vertical velocity • Problems of the control experiment • Too cold and too dry • Too moist in the upper troposphere • Domain size & grid intervals: Are they sufficiently large and fine? If not, in what sense?

  17. Bulk coefficient and minimum velocity • CTL：control case : bulk formula, Umin=4m/s • Umin=1, 7 m/s: minimum wind for bulk coeff.=1, 7m/s • CD=0.001, 0.01: constant bulk coefficient

  18. Surface temperature jump 56 175 Radiative cooling Ts: surface temperautre, T0: atmospheric bottom temperature qs: surface humidity, q0: atmospheric bottom humidity q*: saturation humidity, r: relative humidity CDV: bulk coefficient x surface velocity F: Total radiative cooling Sh: sensible heat flux, Evap: evaporation flux

  19. Bulk Coefficient Possible range of Bulk coefficient

  20. Saturation in the upper troposphere • CTL：control case with Kessler: Autoconversion rate: Cloud water [kg/kg] Relative humidity

  21. Relative humidity Berry G98 G03 RE9

  22. Autoconversion rate Grabowsky(2003): Robe and Emanuel(1996): Grabowsky(1998): simple ice (3categories) temperature dependent snow/rain • CTL：control case with Kessler • Berry

  23. Domain size, grid interval, and 3D vs 2D • 3D 100km CTL 100km x 100km Δx=Δy=2km • 3D 200km 200km x 200km Δx=Δy=2km • 3D 200km,dx=4km 200km x 200km Δx=Δy=4km • 3D 500km,dx=10km 500km x 500km Δx=Δy=10km • 2D 1000km 1000km Δx=2km • 2D 5000km 5000km Δx=2km

  24. PDF of maximum vertical velocity 100km x 100km, ⊿x=2km 200km x 200km, ⊿x=2km 200km x 200km, ⊿x=4km

  25. Summary(1) • A new regional non-hydrostatic model using a conservative scheme. • Conservation of mass and total energy. • Accurate formulation of moist process. • A subset of a global nonhydrostatic model with icosahedral grid (NICAM) • Radiative-convective equilibrium experiments • Proposal of a standard experiment • To be used for investigation of physics and parameters

  26. Summary(2) • Parameter dependency • Large dependency on surface flux • Cloud physics: conventional warm rain scheme is inappropriate; require ice physics • Domain size and resolution • As the grid interval becomes coarser • Colder mean temperature and less precipitable water • Larger CAPE • At the same resolution (Δx=2km), • Mean temperature and precipitable water take closer values. • Statistics (PDF) of Wmax depend on domain size. • 200km x 200km is preferable rather than 100km x 100km.

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