gfs deep and shallow cumulus convection schemes
DESCRIPTION
GFS Deep and Shallow Cumulus Convection Schemes. Jongil Han. Introduction. (1). (2). Φ : θ , q, u, v , …. Tendency due to subgrid cumulus convection, turbulent mixing, and gravity wave drag. (2) All tendency terms due to advection and diabatic processes. - PowerPoint PPT PresentationTRANSCRIPT
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.
NEMS/GFS Modeling Summer School
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
NEMS/GFS Modeling Summer School
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
NEMS/GFS Modeling Summer School
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
NEMS/GFS Modeling Summer School
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
8NEMS/GFS Modeling Summer School
A
hs
hc
0.1A
Overshoot of the cloud top
T
B
T
B
z
zp
z
zdz
Tchhgdz
TTTgA
9NEMS/GFS Modeling Summer School
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
10NEMS/GFS Modeling Summer School
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).
11NEMS/GFS Modeling Summer School
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
12NEMS/GFS Modeling Summer School
Shallow convection scheme
Mass flux at cloud base:
Mb=0.03 w* (Grant, 2001)
3/1
00* ))(/( hwTgw v
(Convective boundary layer velocity scale)
13NEMS/GFS Modeling Summer School
• 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
14NEMS/GFS Modeling Summer School
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)
15NEMS/GFS Modeling Summer School
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
16NEMS/GFS Modeling Summer School
17NEMS/GFS Modeling Summer School
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