gfs deep and shallow cumulus convection schemes

GFS Deep and Shallow Cumulus Convection

Schemes

Jongil Han

Introduction

2

Fz

wt

(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

Deep cumulus convection (sascnv): simplified Arakawa-Schubert (SAS) convection scheme

3

uMw

• Use a bulk mass-flux scheme, which works well for a situation with well-organized updraft and complementary environment such as cumulus convection.

• Updraft fraction over a grid size is assumed to be negligibly small.• To determine the cloud base mass flux, a quasi-equilibrium closure of

Arakawa and Shubert (1974) is used, where the destabilization of an air column by the large-scale atmosphere is nearly balanced by the stabilization due to the cumulus.

• For the cloud model, a entraining and detraining plume model is used.


4

z

1 )()( hh

zh

])([)]([ lrqqqz

qqlvv

lv

Cloud model (updraft)

LqgzTch p Moist static energy

100 002.0, mcMqcr l

111 002.0, mcMqcl l

Rain

Detrainment into grid scale liquid water

η: normalized mass flux, ql: moist excess in updraftε: entrainment rate, δ: detrainment rate


Entrainment and detrainment rates

1100 )1()( FRHcFz

zz 1.0)(0

)()( 00 bzzz 4

1 100.1 c

)(0 bzz

3

1

2

0 ,

sb

s

sb

s

qqF

qqF

in sub-cloud layers

above cloud base

5NEMS/GFS Modeling Summer School

6

))(()( 0 zhMINzhd

2

10 I

MIM b

Downdraft

32 00496.00953.0639.0591.11 SSS 1-β: precipitation efficiency S: averaged vertical wind shear

z0: downdraft initiating level

I1: normalized condensationI2: normalized evaporation

Downdraft is assumed to be saturated.

3.02

1 II


7

Quasi-equilibrium closure

0

cub

ls dtdAM

dtdA

)()( 0

wAwaA

dtdA

ls

tMAA

dtdA

bcu

dzzhzhzTc

gAT

B

z

z p

)()(1)(

p

s

p Tq

cL

A: cloud work function, Mb: cloud base mass flux A0: reference cloud work function, : adjustment time scale (20-60 min) : cloud work function after modification of the thermodynamic fields by an arbitrary amount of mass flux, over a small time interval, .A

,bM t

AAtM

wAwaAM b

b

)()( 0


h*h

Convection trigger

LFC

ks

k2

k1

P(ks)-P(k1) < 120~180mb (proportional to w)

P(k1)-P(k2) < 25mb

h: moist static energy h*: saturation moist static energy


A

hs

hc

0.1A

Overshoot of the cloud top

T

B

T

B

z

zp

z

zdz

Tchhgdz

TTTgA


Convective momentum transport with convection-induced pressure gradient force effect

VVzVMc

tV

uu

1)1(

C=0.55: effect of convection-induced pressure gradient force


Shallow cumulus convection scheme (shalcnv)

• Use a bulk mass-flux parameterization same as deep convection scheme.

• Separation of deep and shallow convection is determined by cloud depth (currently 150 mb).

• Entrainment rate is given to be inversely proportional to height (which is based on the LES studies) and much larger than that in the deep convection scheme.

• Mass flux at cloud base is given as a function of the surface buoyancy flux (Grant, 2001). This differs from the deep convection scheme, which uses a quasi-equilibrium closure of Arakawa and Shubert (1974).


Shallow convection scheme

• It is assumed there exists only updraft (no downdraft).• Entrainment rate:

Siebesma et al.2003:

• Detrainment rate = Entrainment rate at cloud base

zce

1

ce =0.3


Shallow convection scheme

Mass flux at cloud base:

Mb=0.03 w* (Grant, 2001)

3/1

00* ))(/( hwTgw v

(Convective boundary layer velocity scale)


• Most of mass flux cumulus convection schemes have been developed under assumption that the updraft area is negligibly small over the grid box.

• This assumption of small updraft area breaks down more and more often as the grid sizes get smaller and smaller (say less than 5 km).

• Develop a scale-aware cumulus convection scheme that is applicable to any horizontal resolution.

Future development: a scale-aware cumulus convection scheme


uuuuuu wMwM ~)1(~,

uuuu www ~)1( uuuu hhh ~)1(

)~

(~)( hhMhhMhw uuuu

For the cumulus updraft, σu: updraft area fraction (0~1.0) hu: moist static energy

Scale-aware cumulus convection scheme (initial theoretical derivation by Hua-Lu Pan at EMC)


hhwhMz

hDhEth

uuuuuuuconv

~~1~1

uu ww /

0~

uuuu DhhEhMzCloud model:

Scale-aware cumulus convection scheme

• Mass flux can be directly derived from an updraft velocity equation rather than using the quasi-equilibrium assumption which may not be valid any longer as grid size becomes much smaller.

v

vvu

u

TTTgbwb

zw

22

1

2


ALBERTO

18

Revised package24 h accumulated precipitation ending at 12 UTC, July 24, 2008 from (a) observation and 12-36 h forecasts with (b) control GFS and (c) revised model

Total precipitation (grid scale+convective)

19

Siebesma & Cuijpers (1995, JAS)

Siebesma et al. (2003, JAS)

LES studies

20

gfs deep and shallow cumulus convection schemes

Documents