srnwp 27-29 oct., 2003, bad orb masaki satoh and tomoe nasuno frontier system research for global...

SRNWP 27-29 Oct., 2003, Bad Orb

Masaki Satoh and Tomoe NasunoMasaki Satoh and Tomoe Nasuno

Frontier System Research for Global Change/Frontier System Research for Global Change/Saitama Inst. Tech.Saitama Inst. Tech.

Radiative-convective equilibrium calculations Radiative-convective equilibrium calculations with cloud resolving models:with cloud resolving models:

A standard experiment and parameter studyA standard experiment and parameter study

Fifth International SRNWP-workshop on nonhydrostatic modelling27-29 Oct. 2003, Bad Orb, Germany


OutlineOutline

MotivationA global cloud resolving model

Investigation of physics

Model formulationNonhydrostatic core

Radiative-convective equilibrium experimentsSetup

Parameter study

Summary


MotivationMotivation

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

NICAMNICAM

By H.Tomita


RegionalRegional 　　 Nonhydrostatic modelNonhydrostatic 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


CharacteristicCharacteristic ｓｓ of the nonhydrostatic modelof the nonhydrostatic model

Fully compressible non-hydrostatic equations Horizontally explicit and vertically implicit time integration with time splittin

g 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 equationsDensity, momentum, and total energy are conserved.Conservation of total energy including TKE budget

Tracer advecionThird order upwind, or UTOPIAConsistency with Continuity

Exact treatment of moist thermodynamics (Ooyama 1990, 2001).Dependency of latent heat on temperature and specific heats of water substanceTransports 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


Dry formulationDry formulation

Conservative flux form equations for density R, momentum V, and total energy E+K+G:

where

ETKE

Wj

zj

Vj

yj

Uj

xj

GChGKEt

Gx

wRgPz

Wt

Gx

vPy

Vt

Gx

uPx

Ut

Rt

vFv

V

V

V

V

V

2

0

2

gzGKpR

CTCeE

RpPwvuWVU

d

VV

in

,2

,

' ,' ,,,,,2v

V


Governing equations (Governing equations (Ooyama, 1990,2000Ooyama, 1990,2000 ））

Transports due to rain

Release of potential energy of rain


CharacteristicCharacteristic ｓｓ of the nonhydrostatic model (2)of the nonhydrostatic model (2)

PhysicsCloud 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)


Radiative-convective equilibrium studiesRadiative-convective equilibrium studies

Small domain experimentsInvestigation 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 experiments1000km x 100km (Tompkins 2001)

3D domain ： 1000 km x 1000 km ， Δx=2km

Equatorial belt 　 2D 　 or 　 3D ：　 40000km x 100km

Global experiments on ESAqua 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.


Large domain experimentsLarge domain experiments 3D large domain experiment: fo

llowing Tompkins (2001)1000 km x 100 km x 21 kmΔx= 2 kmUniform 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)


Large-scaleorganization

Looselyorganized(small scale)

10 days

1000 km

Rainwater (z=35m)

y-averaged(100 km)


Issues of radiative-convective equilibrium experimentsIssues 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)


Small domain experimentsSmall domain experiments

Basically follows Tompkins & Craig (1998)Dimension: 3D or 2D100km × 100km × 25km 200km×200km(3D); 1000km, 5000km(2D)Δx=Δy=2km 　　　　　　　　　 4, 10kmLowest level: 20m, 54 layers depend on number of vertical layers?Periodic boundary conditionFixed sea surface temperature with 300K or 302KRadiation: 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/sNo large-scale forcing: no momentum source

or nudging to prescribed zonal wind (0m/s)No Coriolis forcing: f=0Total integration time: 60(spin up)+40days Initial condition: uniform temperature(250K)

or TOGA-COARE, Marshall islands


Control experimentControl 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


Mass weighted mean temperature & precipitable waterMass weighted mean temperature & precipitable water

CTL

Courtesy of W.K. Tao


Problems and further experimentsProblems and further experiments

Problems of the control experimentToo 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


Bulk coefficient and minimum velocityBulk 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


)()1(

))]()(([

)]()([

*

**

00

spD

sspD

sspD

TqrLTCVC

TTrqTqLTCVC

qqLTTCVC

EvapShQdzF

56 175

Surface temperature jumpSurface temperature jump

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


pDVCCFT /max

)(8.0 *0 sTqq

TTTTqq s 00*

0 ),(8.0

pDs VCCqqLFT /)( 0

Possible range of

Bulk coefficient

Bulk CoefficientBulk Coefficient


Saturation in the upper troposphereSaturation in the upper troposphere

CTL ： control case with Kessler:Autoconversion rate:

g/kg 0.1

sec10

)(31

cr

auto

crcauto

q

K

qqKAUTO

Cloud water [kg/kg]

Relative humidity


Relative humidityRelative humidity

G98Berry

G03 RE9


Autoconversion rateAutoconversion rate

CTL ： control case with Kessler

Berry

g/kg 0.1

sec10

)(31

cr

auto

crcauto

q

K

qqKAUTO

Grabowsky(2003):

Robe and Emanuel(1996):

Grabowsky(1998): simple ice (3categories) temperature dependent snow/rain

g/kg 0.0

sec10 2

crq

C)02(T g/kg 0.0

C)0(T g/kg 0.1

sec10 3

cr

cr

q

q

1

2

c

c

q

qAUTO


Domain size, grid interval, and 3D vs 2DDomain 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


PDF of maximum vertical velocityPDF of maximum vertical velocity

100km x 100km, x=2km⊿

200km x 200km, x=2km⊿

200km x 200km, x=4km⊿


Summary(1)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 experimentsProposal of a standard experiment

To be used for investigation of physics and parameters


Summary(2)Summary(2)

Parameter dependency Large dependency on surface flux

Cloud physics: conventional warm rain scheme is inappropriate;

require ice physics

Domain size and resolutionAs 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.

srnwp 27-29 oct., 2003, bad orb masaki satoh and tomoe nasuno frontier system research for global...

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