1 Numerical Weather Prediction Parameterization of diabatic processes Convection III The ECMWF convection scheme Christian Jakob and Peter Bechtold
Mar 27, 2015
1
Numerical Weather Prediction Parameterization of diabatic processes
Convection IIIThe ECMWF convection scheme
Christian Jakob and Peter Bechtold
2
A bulk mass flux scheme:What needs to be considered
Entrainment/Detrainment
Downdraughts
Link to cloud parameterization
Cloud base mass flux - Closure
Type of convection shallow/deep
Where does convection occur
Generation and fallout of precipitation
3
Basic Features
• Bulk mass-flux scheme• Entraining/detraining plume cloud model• 3 types of convection: deep, shallow and mid-level - mutually
exclusive• saturated downdraughts• simple microphysics scheme• closure dependent on type of convection
– deep: CAPE adjustment– shallow: PBL equilibrium
• strong link to cloud parameterization - convection provides source for cloud condensate
4
Large-scale budget equations: M=ρw; Mu>0; Md<0
)()()( FMLeecLsMMsMsMp
gt
sfsubclddududduu
cu
Mass-flux transport in up- and downdraughts
condensation in updraughts
Heat (dry static energy): Prec. evaporation in downdraughts
Prec. evaporation below cloud base
Melting of precipitation
Freezing of condensate in updraughts
Humidity:
subclddududduucu
eecqMMqMqMp
gt
q
)(
5
Large-scale budget equations
Cloud condensate:
uucu
lDt
l
uMMuMuMp
gt
ududduu
cu
)(
Momentum:
vMMvMvMp
gt
vdudduu
cu
)(
uucu
lDat
a)1(
Cloud fraction:
(supposing fraction 1-a of environment is cloud free)
6
Large-scale budget equations
Nota: These tendency equations have been written in flux form which by definition is conservative. It can be solved either explicitly (just apply vertical discretisation) or implicitly (see later).
Other forms of this equation can be obtained by explicitly using the derivatives (given on Page 10), so that entrainment/detrainment terms appear. The following form is particular suitable if one wants to solve the mass flux equations with a Semi-Lagrangien scheme;
note that this equation is valid for all variables T, q, u, v, and that all source terms (apart from melting term) have cancelled out
)()()(
dduuducu
DDp
MMgt
7
Numerics: implicit advection
;)( SMp
gt
uu
Pr
pS
1n1kψ
uk
uk
uk
uk
uk
uk
nk MMMM
p
tgψ-ψ 2/12/12/12/12/12/1
1nk
1nk ψ
2/12/1 kk PPp
if ψ = T,q
=> Only bi-diagonal linear systemtS
For u,v, and tracer initialise: 1-ku
1/2-k ψψ
Use temporal discretisation with on RHS taken at future time and not at current time
Use vertical discretisation with fluxes on half levels (k+1/2), and tendencies on full levels k, so that
n1n
8
Numerics: Semi Lagrangien advection
;)( SMp
gt
uu
Pr
pS
if ψ = T,q
;)(
uuu D
p
g
pgM
tdt
d
Advection velocity
;)(
uudep Dp
g
tt
)( tgMPdep u
9
Occurrence of convection:make a first-guess parcel ascent
Updraft Source Layer
LCL
ETL
CTL
1) Test for shallow convection: add T and q perturbation based on turbulence theory to surface parcel. Do ascent with w-equation and strong entrainment, check for LCL, continue ascent until w<0. If w(LCL)>0 and P(CTL)-P(LCL)<200 hPa : shallow convection
2) Now test for deep convection with similar procedure. Start close to surface, form a 30hPa mixed-layer, lift to LCL, do cloud ascent with small entrainment+water fallout. Deep convection when P(CTL)-P(LCL)>200 hPa. If not …. test subsequent mixed-layer, lift to LCL etc. … and so on until 700 hPa
3) If neither shallow nor deep convection is found a third type of convection – “midlevel” – is activated, originating from any model level above 500 m if large-scale ascent and RH>80%.
10
Cloud model equations – updraughtsE and D are positive by definition
uuu DE
p
Mg
uuuuuu LcsDsE
p
sMg
uuuuuu cqDqE
p
qMg
uPuuuuuu GclDlE
p
lMg ,
uuuuu uDuE
p
uMg
uuuuu vDvE
p
vMg
2 ,
)1(
12)1(
2, u
uv
vuvud
u
uu wK
T
TTg
fKC
M
E
z
K
Kinetic Energy (vertical velocity) – use height coordinates
Momentum
Liquid Water/Ice
Heat Humidity
Mass (Continuity)
11
Cloud model equations – downdraughtsE and D are defined positive
ddd DE
p
Mg
dddddd LesDsE
p
sMg
dddddd eqDqE
p
qMg
ddddd uDuE
p
uMg
ddddd vDvE
p
vMg
Mass
Heat
Humidity
Momentum
12
Entrainment/Detrainment (1)
Updraught2,1, uuu EEE 2,1, uuu DDD
//
//
1,
1,
uuuuu
uuuuu
MpzgMD
MpzgME
“Turbulent” entrainment/detrainment
convection shallowfor 103
convection midlevel and deepfor 102.114
14
m
muu
Organized entrainment is linked to moisture convergence, but only applied in lower part of the cloud (this part of scheme is questionable)
z
qwqv
qE hu
12,
However, for shallow convection detrainment should exceed entrainment (mass flux decreases with height – this possibility is still experimental
ε and δ are generally given in units (1/m) since (Simpson 1971) defined entrainment in plume with radius R as ε=0.2/R ; for convective clouds R is of order 1500 m for deep and R=100 or 50 m for shallow
13
Entrainment/Detrainment (2)
Organized detrainment:
zzK
zK
zzM
zM
u
u
u
u
)(
Only when negative buoyancy (K decreases with height), compute mass flux at level z+Δz with following relation:
with
2
2u
u
wK
and
uuDu
uu Bf
KCM
E
z
K
)1(
12)1(
14
Precipitation
2
10,
crit
u
l
l
uu
uuP elw
cMG
Generation of precipitation in updraughts
Simple representation of Bergeron process included in c0 and lcrit
Liquid+solid precipitation fluxes:
gdpMelteeGpP
gdpMelteeGpP
P
Ptop
snowsubcld
snowdown
snowsnow
P
Ptop
rainsubcld
raindown
rainrain
/)()(
/)()(
Where Prain and Psnow are the fluxes of precip in form of rain and snow at pressure level p. Grain and Gsnow are the conversion rates from cloud water into rain and cloud ice into snow. The evaporation of precip in the downdraughts edown, and below cloud base esubcld, has been split
further into water and ice components. Melt denotes melting of snow.
15
Precipitation
uu
precufallout r
zw
VMS
Fallout of precipitation from updraughts
2.0, 32.5 urainprec rV 2.0
, 66.2 uiceprec rV
Evaporation of precipitation
1. Precipitation evaporates to keep downdraughts saturated
2. Precipitation evaporates below cloud base
05.0fraction cloud a assume ,
3
21
Pppqqe
surf
ssubcld
16
Closure - Deep convection
Convection counteracts destabilization of the atmosphere by large-scale processes and radiation - Stability measure used: CAPE
assume that convection reduces CAPE to 0 over a given timescale, i.e.,
CAPECAPE
t
CAPE
cu
0
Originally proposed by Fritsch and Chappel, 1980, JAS
implemented at ECMWF in December 1997 by Gregory (Gregory et al., 2000, QJRMS)
The quantity required by the parametrization is the cloud base mass-flux.
How can the above assumption converted into this quantity ?
17
Closure - Deep convection
dzgCAPE
cloudv
vcv
dzttgt
CAPE
cloudv
vcv
cv
v
cu
2
Assume:
1 and cloud, statesteady i.e., ,0
v
cv
cv
t
dzt
gt
CAPE
cu
v
cloudvcu
1
18
Closure - Deep convection
z
M
tvc
cu
v
i.e., ignore detrainment
CAPE
dzz
Mg
t
CAPE v
cloudv
c
cu
dtdubuduc MMMMM ,, utd MM ,
cloud
v
vn
bu
n
cloud
v
vdu
bu
dzzM
Mg
CAPE
dzz
g
CAPE
M
11
1,
1,
where Mn-1 are the mass fluxes from a previous first guess updraft/downdraft computation
19
Closure - Shallow convection
Based on PBL equilibrium - no downdraughts
0
1
0
dz
t
h
t
h
t
h
z
hwcbase
raddynturb
conv
cbase
dzt
h
0
0
With cbaseubucbaseconv hhMhw ,, and 00, convhw
cbaseu
cbase
raddynturb
bu hh
dzth
th
th
M
0
,
20
Closure - Midlevel convection
Roots of clouds originate outside PBL
assume midlevel convection exists if there is large-scale ascent, RH>80% and there is a convectively unstable layer
Closure:bbu wM ,
21
Downdraughts
1. Find level of free sinking (LFS)
highest model level for which an equal saturated mixture of cloud and environmental air becomes negatively buoyant
2. Closure 3.0 ,, buLFSd MM
3. Entrainment/Detrainment
turbulent and organized part similar to updraughts (but simpler)