gfs vertical turbulent mixing scheme

GFS Vertical Turbulent Mixing Scheme

Jongil Han

Introduction

2

F

zw

t

(1) (2)

Φ: θ, q, u, v, ….

(1) Tendency due to subgrid cumulus convection, turbulent mixing, and gravity wave drag.

(2) All tendency terms due to advection and diabatic processes.

NEMS/GFS Modeling Summer School

GFS vertical mixing scheme (moninq)

3

• It is a first order K-theory-based scheme under down-gradient diffusion assumption, where K is eddy-diffusivity.

• For the daytime planetary boundary layer (PBL), an eddy-diffusivity (profile) counter-gradient (EDCG) mixing approach is adopted to take into account nonlocal transport by strong updraft.

• For the vertical diffusion in nighttime stable boundary layer and layers above PBL, a local K is used (which is a function of local gradient Richardson number, local wind shear, and a mixing length).

• Include stratocumulus-top driven turbulence mixing based on Lock et al.’s (2000) study.

• Enhance stratocumulus top driven diffusion when the condition for cloud top entrainment instability is met.

NEMS/GFS Modeling Summer School

hsurfh z

Kw 2

1

hzzwK s

surfm

surfm

surfh KK 1Pr

hww

sh

0)(5.6

EDCG approach for unstable PBL

3/13*

3* 7 wuws

NEMS/GFS Modeling Summer School 4

bm

h

Pr

Stratocumulus-top driven turbulence mixing (Lock et al., 2000)


(Buoyancy reversal term is neglected)

Stratocumulus-top driven turbulence mixing

hsurfh

Sch

surfh K

zKKw

)/()(0

3pbbSc cRzhgV

2/12

185.0

bb

b

bb

bSc

Sch zh

zzzh

zzVK

phv c

Rcwb

)(

,7.0 tep qLcif c=1.0

c=0.2

(CTEI condition; MacVean and Mason, 1990)

(Moeng et al., 1999)


PBL height (h) in unstable BL

))(()( 2

sv

vacr hg

hURbh

Rbcr=0.25

ss w

wz 0

1)(

5.6)(

h = height of zero heat flux, not that of minimum heat flux

• Daytime PBL grows by surface heating and entrainment flux at the PBL top.

• h is intentionally enhanced with a thermal excess to have an implicit entrainment flux at the PBL top


Diffusion in the stable boundary layer and the layers above the PBL

zURiflK hmhm

)(,

2,

2

zU

zTgRi v

0

111lkzl

l0 = 150 m for unstable condition

30 m for stable condition

• Use a local diffusion scheme (Louis, 1979)

zKw h

2511)(Ri

Rif h

Ri1.21Pr

2/1286.11

81)(

Ri

RiRif h

2/1746.11

81)(

Ri

RiRifm

Stable condition

Unstable condition


• The GFS EDCG scheme under-predicts the PBL growth for the convection-dominated (strongly unstable) PBL (Noh et al., 2003; Siebesma et al., 2007) .

• Siebesma et al. (2007) show that the underestimation of the daytime PBL growth EDCG is due to too weak entrainment flux at the PBL top which is caused by positive constant CG term over the entire.

• With the EDMF scheme, the CG term in the EDCG scheme is replaced by a mass-flux scheme.

Near future development: Eddy-Diffusion Mass-Flux (EDMF) PBL scheme (Siebesma et al., 2007)


293.0 293.5 294.0 294.5 295.0 295.5 296.0 296.5 297.0 297.5 298.00

500

1000

1500

2000

2500

3000

3500

4000 θ at hour 8

LESEDEDCG

θ (k)

Hei

ght (

m)

SCM (single column model) test with EDCG scheme


-0.2 0.0 0.2 0.4 0.6 0.8 1.00

500

1000

1500

2000

2500

3000

3500

4000

Normalized heat flux (EDCG)

TotalEDCG

Normalized heat flux

Hei

ght (

m)

SCM test with EDCG scheme


-0.2 0 0.2 0.4 0.6 0.8 10

500

1000

1500

2000

2500

3000

3500

4000Normalized heat flux at hour 8

LES (resolved)EDCG


Hei

ght (

m)

SCM test with EDCG scheme


EDMF PBL scheme

z

Kwhw

w

s

0)(5.6

GFS PBL scheme (EDCG scheme)

EDMF scheme

)(

uMz

Kw


Fig. 1. Sketch of a convective updraft embedded in a turbulent eddy structure. (from Siebesma et al., 2007)

EDMF PBL scheme


u

uu gbwb

zw

22

1

2

Updraft velocity equation:

uwM 1.0 Soares et al. (2004)

zM

M1

,...,,],[

)()(

vuqgzTcswhere

Mz

M

p

uu

zzhzz

ce )(11

b1=2.0, b2=4.0(Soares et al., 2004)

ce=0.37, h: height of wu=0

EDMF PBL scheme


))(()( 2

sv

vacr hg

hURbh

Rbcr=0.25

EDCG:

EDMF:

ss w

wz 0

1)(

5.6)(

h = height of zero heat flux

)( 1zs for ED part

h=height of wu=0 for MF part

EDMF PBL scheme


-0.2 0.0 0.2 0.4 0.6 0.8 1.00

500

1000

1500

2000

2500

3000

3500

4000

Normalized heat flux (EDMF)

TotalEDMF


Hei

ght (

m)

SCM test with EDMF scheme


-0.2 0 0.2 0.4 0.6 0.8 10

500

1000

1500

2000

2500

3000

3500

4000Normalized heat flux at hour 8

LES (resolved)EDCG


Hei

ght (

m)



293.0 293.5 294.0 294.5 295.0 295.5 296.0 296.5 297.0 297.5 298.00

500

1000

1500

2000

2500

3000

3500

4000 θ at hour 8

LESEDEDCGEDMF-ce37b240w7

θ (k)

Hei

ght (

m)



21NEMS/GFS Modeling Summer School

gfs vertical turbulent mixing scheme

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