SRNWP Oct., 2003, Bad Orb 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 Fifth International SRNWP-workshop on nonhydrostatic modelling Oct. 2003, Bad Orb, Germany

SRNWP Oct., 2003, Bad OrbOutline Motivation A global cloud resolving model Investigation of physics Model formulation Nonhydrostatic core Radiative-convective equilibrium experiments Setup Parameter study Summary

SRNWP Oct., 2003, Bad OrbMotivation 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

SRNWP Oct., 2003, Bad Orb Regional Nonhydrostatic 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

SRNWP Oct., 2003, Bad Orb Characteristic ｓ 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 3 rd order

SRNWP Oct., 2003, Bad Orb Dry formulation Conservative flux form equations for density R, momentum V, and total energy E+K+G: where

SRNWP Oct., 2003, Bad Orb Governing equations ( Ooyama, 1990,2000 ） Transports due to rain Release of potential energy of rain

SRNWP Oct., 2003, Bad Orb Characteristic ｓ 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 )

SRNWP Oct., 2003, Bad Orb 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 belt 2D or 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.

SRNWP Oct., 2003, Bad Orb 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)

SRNWP Oct., 2003, Bad Orb Large-scale organization Loosely organized (small scale) 10 days 1000 km Rainwater (z=35m) y-averaged (100 km)

SRNWP Oct., 2003, Bad Orb Issues of radiative-convective equilibrium experiments Strong dependency on artificial parameters Surface flux with bulk formula: Depends on minimum surface velocity: U min 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)

SRNWP Oct., 2003, Bad Orb Small domain experiments Basically follows Tompkins & Craig (1998) Dimension: 3D or 2D 100km × 100km × 25km 200km×200km(3D); 1000km, 5000km(2D) Δx=Δy=2km 4, 10km Lowest level: 20m, 54 layers depend on number of vertical layers? Periodic boundary condition Fixed sea surface temperature with 300K or 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: U min =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

SRNWP Oct., 2003, Bad Orb Control experiment 100km × 100km, Δx ＝ 2km Warm rain Prescribed cooling: -2K/day TKE Bulk method Umin=4m/s Uniform initial cond. T=250K Precipitation Relative humidity temperature

SRNWP Oct., 2003, Bad Orb Mass weighted mean temperature & precipitable water CTL Courtesy of W.K. Tao

SRNWP Oct., 2003, Bad Orb Problems and further experiments 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? Bulk coefficient and minimum velocity Statistic of maximum of the vertical velocity Ice phase

SRNWP Oct., 2003, Bad Orb 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 C D =0.001, 0.01: constant bulk coefficient

SRNWP Oct., 2003, Bad Orb Surface temperature jump Radiative cooling T s : surface temperautre, T 0 : atmospheric bottom temperature q s : surface humidity, q 0 : atmospheric bottom humidity q*: saturation humidity, r: relative humidity C D V: bulk coefficient x surface velocity F: Total radiative cooling Sh: sensible heat flux, Evap: evaporation flux

SRNWP Oct., 2003, Bad Orb Possible range of Bulk coefficient Bulk Coefficient

SRNWP Oct., 2003, Bad Orb Saturation in the upper troposphere CTL ： control case with Kessler: Autoconversion rate: Cloud water [kg/kg] Relative humidity

SRNWP Oct., 2003, Bad Orb Relative humidity G98 Berry G03RE9

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

SRNWP Oct., 2003, Bad Orb 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

SRNWP Oct., 2003, Bad Orb PDF of maximum vertical velocity 100km x 100km, ⊿ x=2km 200km x 200km, ⊿ x=2km 200km x 200km, ⊿ x=4km

SRNWP Oct., 2003, Bad OrbSummary(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

SRNWP Oct., 2003, Bad OrbSummary(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 W max depend on domain size. 200km x 200km is preferable rather than 100km x 100km.