1 the parameterization of moist convection peter bechtold, christian jakob, david gregory with...
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The parameterization of moist convectionThe parameterization of moist convection
Peter Bechtold, Christian Jakob, David GregoryWith contributions from J. Kain (NOAA/NSLL)
Original ECMWF lecture has been adjusted to fit into today’s schedule
Roel Neggers, KNMI
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Outline of second hourOutline of second hour
Parameterizing moist convection
• Aspects: triggering, vertical distribution, closure• Types of convection schemes• The mass-flux approach
The ECMWF convection scheme
• Flow chart• Main equations• Behavior
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To calculate the collective effects of an ensemble of convective clouds in a model column as a function of grid-scale variables. Hence parameterization needs to describe Condensation/Evaporation and Transport
Task of convection parameterization Task of convection parameterization total Q1 and Q2total Q1 and Q2
RC QQQ 11p
secLQQ R
)(1
p
qLecLQ
)(2
Apparent heat source
Apparent moisture sink
TransportCondensation/Evaporation
Radiation
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Task of convection parameterizationTask of convection parameterizationin practice this meansin practice this means::
Determine vertical distribution of heating, moistening and momentum changes
Cloud model
Determine the overall amount / intensity of the energy conversion, convective precipitation=heat release
Closure
Determine occurrence/localisation of convection
Trigger
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Constraints for convection parameterizationConstraints for convection parameterization
• Physical– remove convective instability and produce subgrid-scale convective
precipitation (heating/drying) in unsaturated model grids– produce a realistic mean tropical climate– maintain a realistic variability on a wide range of time-scales– produce a realistic response to changes in boundary conditions
(e.g., El Nino)– be applicable to a wide range of scales (typical 10 – 200 km) and
types of convection (deep tropical, shallow, midlatitude and front/post-frontal convection)
• Computational– be simple and efficient for different model/forecast configurations
(T799 (25 km), EPS, seasonal prediction T159 (125 km) )
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Types of convection schemesTypes of convection schemes
• Moisture budget schemes– Kuo, 1965, 1974, J. Atmos. Sci.
• Adjustment schemes– moist convective adjustement, Manabe, 1965, Mon. Wea. Rev.– penetrative adjustment scheme, Betts and Miller, 1986, Quart. J. Roy.
Met. Soc., Betts-Miller-Janic• Mass-flux schemes (bulk+spectral)
– Entraining plume - spectral model, Arakawa and Schubert, 1974, Fraedrich (1973,1976), Neggers et al (2002), Cheinet (2004), all J. Atmos. Sci. ,
– Entraining/detraining plume - bulk model, e.g., Bougeault, 1985, Mon. Wea. Rev., Tiedtke, 1989, Mon. Wea. Rev., Gregory and Rowntree, 1990, Mon. Wea . Rev., Kain and Fritsch, 1990, J. Atmos. Sci., Donner , 1993, J. Atmos. Sci., Bechtold et al 2001, Quart. J. Roy. Met. Soc.
– Episodic mixing, Emanuel, 1991, J. Atmos. Sci.
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Type I: “Kuo” schemesType I: “Kuo” schemes
Closure: Convective activity is linked to large-scale moisture convergence: “what comes in must rain out”
0
(1 )ls
qP b dz
t
Vertical distribution of heating and moistening: adjust grid-mean to moist adiabat
Main problem: here convection is assumed to consume water and not energy -> …. Positive feedback loop of moisture convergence
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Type II: Adjustment schemesType II: Adjustment schemes
e.g. Betts and Miller, 1986, QJRMS:
When atmosphere is unstable to parcel lifted from PBL and there is a deep moist layer - adjust state back to reference profile over some time-scale, i.e.,
t
q ref
conv
.TT
t
T ref
conv
.
Tref is constructed from moist adiabat from cloud base but no
universal reference profiles for q exist. However, scheme is robust and produces “smooth” fields.
Procedure followed by BMJ scheme…
1) Find the most unstable air in lowest ~ 200 mb
1
2) Draw a moist adiabat for this air
2
3) Compute a first-guess temperature-adjustment profile (Tref)3
4) Compute a first-guess dewpoint-adjustment profile (qref)
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TTdew
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Type III: Mass-flux schemesType III: Mass-flux schemes
p
secLQ C
)(1
Aim: Look for a simple expression of the eddy transport term
Condensation term Eddy transport term
?
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The mass-flux approachThe mass-flux approach
Reminder: Reynolds averaging (boundary layer lecture)
with 0
Hence
'
)(
= =0 0
and therefore
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The mass-flux approach:The mass-flux approach:Cloud – Environment decompositionCloud – Environment decomposition
Total Area: A
Cumulus area: a
Fractional coverage with cumulus elements:
A
a
Define area average:
ec 1
ec
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The mass-flux approachThe mass-flux approach
Then : c c e
Define convective mass-flux: cc
cM wg
Then ccgM
• Neglect subplume correlations
• Small area approximation:
•
Make some assumptions:
1)1(1 ec
Mass flux Excess of plume over enviroment
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The mass-flux approachThe mass-flux approach
With the above we can rewrite:
p
ssMgecLQ
cc
C
)(
)(1
p
qqMLgecLQ
cc
)(
)(2
To predict the influence of convection on the large-scale with this approach we now need to describe the convective mass-flux, the values of the thermodynamic (and momentum) variables inside the convective elements and the condensation/evaporation term.
This requires a plume model and a closure.
Plume model
The entraining plume modelThe entraining plume model
Cumulus element i
Mass:
0i ii i
MD E g
t p
Heat:
i i i ii i i i
s M sD s E s g Lc
t p
Specific humidity:
i i i ii i i i
q M qD q E q g c
t p
Entraining plume model
iD
iEEntrainment rate
Detrainment rate
iciM
ii qs ,
iArea
Interaction (mixing) with the plume environment
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Bulk entraining plume modelsBulk entraining plume models
Simplifying assumptions:
1. Steady state plumes, i.e.,
0
t
X
Most mass-flux convection parametrizations today still make that assumption, some however are prognostic
2. Bulk mass-flux approach
Sum over all cumulus elements: A single bulk plume describes the effect of a whole ensemble of clouds:
i
ic MM
i
iicc s
As 1
iiic
c qA
q 1
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Substitution of bulk mass flux model into QSubstitution of bulk mass flux model into Q11 and Q and Q22
p
ssMgecLQ
cc
C
)(
)(1
cMg E D
p
cc c
M sg Es Ds Lc
p
Combine:
1 ( )cC c
sQ gM D s s Le
p
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InterpretationInterpretation
1 ( )cC c
sQ gM D s s Le
p
Convection affects the large scales by
Heating through compensating subsidence between cumulus elements (term I)
The detrainment of cloud air into the environment (term II)
Evaporation of cloud and precipitation (term III)
Note: The condensation heating does not appear directly in Q1. It is however a crucial part of the cloud model, where this heat is transformed in kinetic energy of the updrafts.
Similar derivations are possible for Q2.
I II III
Closures in mass-flux parameterizationsClosures in mass-flux parameterizations
The plume model determines the vertical structure of convective heating and moistening (microphysics, variation of mass flux with height, entrainment/detrainment assumptions).
The determination of the overall magnitude of the heating (i.e., surface precipitation in deep convection) requires the determination of the mass-flux at cloud base. - Closure problem
Types of closures:
Deep convection:
Equilibrium in CAPE or similar quantity (e.g., cloud work function)
Shallow convection:
Boundary-layer equilibrium
Mixed-layer turbulence closures (e.g. Grant 2001; Neggers 2008,2009)
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CAPE closure - the basic ideaCAPE closure - the basic idea
large-scale processes generate CAPE
Convection consumes
CAPE Find the magnitude of Mb
c so that profile is adjusted to reference profile
Principle can also be applied to boundary-layer humidity / moist static energy
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Turbulence closures - the basic ideaTurbulence closures - the basic idea
Tie the magnitude of Mbc to sub-cloud layer turbulence
Motivation: cumulus thermals are observed to be deeply rooted in the sub-cloud layer
w’B’=surface buoyancy flux h=subcloud mixed-layer heighta~0.05 is updraft fraction 3
1
** '' sc
b BwhwwaM
Grant (2001):
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Summary (1)Summary (1)
• Convection parameterizations need to provide a physically realistic forcing/response on the resolved model scales and need to be practical
• a number of approaches to convection parameterization exist
• basic ingredients to present convection parameterizations are a method to trigger convection, a cloud model and a closure assumption
• the mass-flux approach has been successfully applied to both interpretation of data and convection parameterization …….
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The ECMWF convection schemeThe ECMWF convection scheme
“Let’s get technical”“Let’s get technical”
Peter Bechtold and Christian JakobOriginal ECMWF lecture has been adjusted to fit into today’s schedule Roel Neggers, KNMI
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A bulk mass flux scheme:A bulk mass flux scheme:What needs to be considered What needs to be considered
Entrainment/Detrainment
Downdraughts
Link to cloud parameterization
Cloud base mass flux - Closure
Type of convection: shallow/deep/midlevel
Where does convection occur
Generation and fallout of precipitation
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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
callpar
Main flow chartMain flow chart
cucallsatur
cumastrn cuini
cubasen
cuascn
cudlfsn
cuddrafn
cuflxn
cudtdqn
cududvcuccdia
custrat
cubasemcn
cuentr
cuascncubasemcn
cuentr
IFS Documentation, Part IV: Physical processes Chapter V: Convection
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Convective terms in LS budget equations: Convective terms in LS budget equations: M=M=ρw; Mρw; Muu>0; M>0; Mdd<0 <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
)(
cudtdqn
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Convective terms in LS budget equationsConvective terms in LS budget equations
Cloud condensate:
u ucu
lD l
t
uMMuMuMp
gt
ududduu
cu
)(
Momentum:
vMMvMvMp
gt
vdudduu
cu
)(
u
cu
Da
t
a)1(
Cloud fraction: (supposing fraction 1-a of environment is cloud free)
Source terms in cloud-scheme
cududv
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Occurrence of convection (triggering)Occurrence of convection (triggering)make a first-guess parcel ascentmake 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(LCL)-P(CTL)>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%.
cubasen cubasemcn
TTdew
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Plume model equations – updraftsPlume model equations – updraftsE and D are positive by definitionE 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
(1 )2 , (1 ) 2
v u vu u ud u u
u v
T TK E wC K g K
z M f T
Kinetic Energy (vertical velocity) – use height coordinates
Momentum
Liquid Water/Ice
Heat Humidity
Mass (Continuity)
cuascn
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DowndraftsDowndrafts
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, , 0.3d LFS u bM M
3. Entrainment/Detrainment
turbulent and organized part similar to updraughts (but simpler)
cudlfsn cuddrafn
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Cloud model equations – downdraftsCloud model equations – downdraftsE and D are defined positiveE 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
cuddrafn
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Entrainment/Detrainment (1)Entrainment/Detrainment (1)
u u uu u turb org turb org
M M Mg E D
p
0 1 2
, 0
3
4 3 10 1 2
;
; ; (10 10 );
sturb
sturb
org buoy
s
sbase
q qc F c F c
q
qc c c O m F
q
ε and δ are generally given in units (m-1) since (Simpson 1971) defined entrainment in plume with radius R as ε=0.2/R ; for convective clouds R is of order 500-1000 m for deep and R=50-100 m for shallow
Scaling function to mimick a cloud ensemble
Constants
cuentr
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Entrainment/Detrainment (2)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
anduuD
u
uu Bf
KCM
E
z
K
)1(
12)1(
cuentr
orgorgMu
Updraft mass flux
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Precipitation fluxesPrecipitation fluxes
2
10,
crit
u
l
l
uu
uuP elw
cMG
Generation of precipitation in updraughts (Sundqvist)
Simple representation of Bergeron process included in c0 and lcrit
Two interacting shafts: Liquid (rain) and solid (snow)
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.
cuflxn
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PrecipitationPrecipitation
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 (Kessler)
1. Precipitation evaporates to keep downdraughts saturated
2. Precipitation evaporates below cloud base
3
12
, assume a cloud fraction 0.05surf
subcld s
p p Pe RH q q
cuflxn
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Closure - Deep convectionClosure - 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), using a constant time-scale that varies only as function of model resolution (720s T799, 1h T159)
• The time-scale is a very important quantity and has been changed in Nov. 2007 to be
equivalent to the convective turnover time-scale which is defined by the cloud thickness divided by the cloud average vertical velocity, and further scaled by a factor depending linearly on horizontal model resolution (it is typically of order 1.3 for T799 and 2.6 for T159)
Purpose: Estimate the cloud base mass-flux. How can we get this?
H
u nH W
cumastrn
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Closure - Deep convectionClosure - Deep convection
cv v
vcloud
CAPE g dz
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
Now use this equation to back out the cloud base mass flux Mu,b
cumastrn
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Closure - Deep convectionClosure - Deep convection
z
M
tvc
cu
v
i.e., ignore detrainment
CAPE
dzz
Mg
t
CAPE v
cloudv
c
cu
where Mt-1 are the mass fluxes from a previous first guess updraft/downdraft computation
The idea: assume stabilization is mainly caused by compensating subsidence:
McMe
v
cumastrn
top
b
z
z
v
vt
bu
tbu
dzzM
Mg
CAPE
M
1
1,
1,
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Closure - Shallow convectionClosure - Shallow convection
Based on PBL equilibrium for moist static energy h: what goes in must go out - including downdraughts
0
0cbase
conv
turb dyn rad
w h h h hdz
z t t t
0
0cbase h
dzt
,,
(1 ) ; / ;u b u d u dcbaseconv cbasew h M h h h M M 00, convhw
0
,(1 )
cbase
turb dyn rad
u b
u d cbase
h h hdz
t t tM
h h h
Mu,bcbase
cumastrn
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Closure - Midlevel convectionClosure - 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 ,
cumastrn
Studying model behavior at process level:Studying model behavior at process level:
Single column model (SCM) simulationSingle column model (SCM) simulation
Advantages:
* computational efficiency & model transparency
* good for studying interactions between fast parameterized physics
Time-integration of a single column of sub-grid parameterizations in isolated mode,
using prescribed large-scale forcings
cloud layer
mixed layer
free troposphere
PBL
sw lw
advection
subsidence
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BehaviorBehavior Single column model (SCM) experiments Single column model (SCM) experiments
Surface precipitation; continental convection during ARM
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BehaviorBehavior Single column model (SCM) experiments Single column model (SCM) experiments
SCM simulation at Cabauw, 12-15 May 2008
Deep convective plume, depositing cloud water at ~ 8km
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BehaviorBehavior Single column model (SCM) experiments Single column model (SCM) experiments
SCM simulation at Cabauw, 31 May – 3 June 2008
Deep convective plumes