1 numerical weather prediction parametrization of diabatic processes convection ii the...
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Numerical Weather Prediction Parametrization of diabatic processes
Convection II
The parametrization of convection
Peter Bechtold, Christian Jakob, David Gregory
(with contributions from J. Kain (NOAA/NSLL)
2
Outline
• Aims of convection parametrization
• Overview over approaches to convection parametrization
• The mass-flux approach
3
Caniaux, Redelsperger, Lafore, JAS 1994
Q1c is dominated by condensation term
10
10
5z (
km
)
(K/h)-1 2
c-e
Q1-Qrtrans c-e
Q2
10
5z (
km
)
(K/h)
trans
-1-2 0 21
a b
but for Q2 the transport and condensation terms are equally important
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 parametrisation total Q1 and Q2
p
secLQQQ RC
)(11
4
Task of convection parametrisation:in practice this means:
Determine vertical distribution of heating, moistening and momentum changes
Cloud model
Determine the overall amount of the energy conversion, convective precipitation=heat release
Closure
Determine occurrence/localisation of convection
Trigger
5
Constraints for convection parametrisation
• 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 (T511, EPS,
seasonal prediction)
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Types of convection schemes
• Schemes based on moisture budgets– 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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The “Kuo” scheme
Closure: Convective activity is linked to large-scale moisture convergence
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
8
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
2) Draw a moist adiabat for this air
3) Compute a first-guess temperature-adjustment profile (Tref)
4) Compute a first-guess dewpoint-adjustment profile (qref)
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Adjustment schemes:The Next Step is an Enthalpy Adjustment
First Law of Thermodynamics: vvp dqLdTCdH
With Parameterized Convection, each grid-point column is treated in isolation. Total column latent heating must be directly proportional to total column drying, or dH = 0.
dpqqLdpTTC vvref
P
P v
P
P refp
t
b
t
b
)(
Enthalpy is not conserved for first-guess profiles for this sounding!
Must shift Tref and qvref to the left…
a
b
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Imposing Enthalpy Adjustment:
a
Shift profiles to the left in order to conserve enthalpy
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Adjustment scheme:Adjusted Enthalpy Profiles:
b
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The mass-flux approach
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 approach
Reminder:
with 0
Hence
'
)(
= =0 0
and therefore
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The mass-flux approach:Cloud – 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 approach:Cloud-Environment decomposition
ecec 1 1
With the above:
and
ec 1
Average over cumulus elements Average over environment
Use Reynolds averaging again for cumulus elements and environment separately:
cccc and
eeee
=
0
=
0
Neglect subplume correlations
(see also Siebesma and Cuijpers, JAS 1995 for a discussion of the validity of the top-hat assumption)
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The mass-flux approach
Then after some algebra (for your exercise) :
ecec
1
Further simplifications :
The small area approximation
ec ;1)1(1
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The mass-flux approach
Then :
c c e
Define convective mass-flux:
cc
cM wg
Then
ccgM
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The 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, as usual, a cloud model and a closure to determine the absolute (scaled) value of the massflux.
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Mass-flux entraining plume cloud models
Cumulus element i
Continuity:
0
p
Mg
ti
iii
Heat:
i
iiiii
ii Lcp
sMgss
t
s
Specific humidity:
i
iiiii
ii cp
qMgqq
t
q
Entraining plume model
i
i
ic
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Mass-flux entraining plume cloud 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, e.g.
p
Mg c
with i i i
iiic MM , ,
e.g., Tiedtke (1989), Gregory and Rowntree (1990), Kain and Fritsch (1990)
3. Spectral method
D
dpmpM Bc
0
),()()(
e.g., Arakawa and Schubert (1974) and derivatives
Important: No matter which simplification - we always describe a cloud ensemble, not individual clouds (even in bulk models)
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Large-scale cumulus effects deduced using mass-flux models
p
ssMgecLQ
cc
C
)(
)(1
Assume for simplicity: Bulk model, ccci
i
cMg
p
Lcss
p
sMg c
cc
Combine:
Lessp
sgMQ c
cC
)(1
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Large-scale cumulus effects deduced using mass-flux models
Lessp
sgMQ c
cC
)(1
Physical interpretation (can be dangerous after a lot of maths):
Convection affects the large scales by
Heating through compensating subsidence between cumulus elements (term 1)
The detrainment of cloud air into the environment (term 2)
Evaporation of cloud and precipitation (term 3)
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.
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Alternatives to the entraining plume model - Episodic mixing
Observations show that the entraining plume model might be a poor representation of individual cumulus clouds.
Therefore alternative mixing models have been proposed - most prominently the episodic (or stochastic) mixing model (Raymond and Blyth, 1986, JAS; Emanuel, 1991, JAS)
Conceptual idea: Mixing is episodic and different parts of an updraught mix differently
Basic implementation:
assume a stochastic distribution of mixing fractions for part of the updraught air - create N mixtures
Version 1: find level of neutral buoyancy of each mixture
Version 2: move mixture to next level above or below and mix again - repeat until level of neutral buoyancy is reached
Although physically appealing the model is very complex and practically difficult to use
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Closure in mass-flux parametrizations
The cloud 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: time scale ~ 1h
Equilibrium in CAPE or similar quantity (e.g., cloud work function)
Boundary-layer equilibrium
Shallow convection: time scale ? ~ 3h
idem deep convection, but also turbulent closure (Fs=surface heat flux, ZPBL=boundary-layer height)
1/3
* *; ,cb PBL
p
g HSM a w w z
c
Grant (2001)
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CAPE closure - the basic idea
large-scale processes generate CAPE
Convection consumes
CAPE
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CAPE closure - the basic idea
Downdraughts
Convection consumes
CAPE
Surface processes
also generate CAPE
b
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Boundary Layer Equilibrium closure (1) as used for shallow convection in the IFS
1[ ] 0;
( ) [ ] ;
[ ( ) ( )]
LCL LCL LCL
s
s
s s s
LCL
s
P P Phs
p v h s
P P Prad dyn
P
S LCL S conv p v
Prad dyn
u u uconv c p v l
Fh T qdp C L dp dp F h
t t t p g
T qF F P F F C L dp with
t t
F M C T T L q q q
1) Assuming boundary-layer equilibrium of moist static energy hs
2) What goes in goes out
Therefore, by integrating from the surface (s) to cloud base (LCL) including all processes that contribute to the moist static energy, one obtains the flux on top of the boundary-layer that is assumed to be the convective flux Mc (neglect downdraft contributions)
Fs is surface moist static energy flux
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Boundary Layer Equilibrium closure (2) – as suggested for deep convection
Postulate: tropical balanced temperature anomalies associated with wave activity are small (<1 K) compared to buoyant ascending parcels ….. gravity wave induced motions are short lived
Convection is controlled through boundary layer entropy balance - sub-cloud layer entropy is in quasi-equilibrium – flux out of boundary-layer must equal surface flux ….boundary-layer recovers through surface fluxes from convective drying/cooling
Raymond, 1995, JAS; Raymond, 1997, in Smith Textbook
Fs is surface heat flux
)(
);()(
0,
,
,,
,
PBLedes
uc
uc
dcPBLe
de
dcPBLe
ue
ucS
convSPBLe
FM
MMMMF
FFconst
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Summary (1)
• Convection parametrisations need to provide a physically realistic forcing/response on the resolved model scales and need to be practical
• a number of approaches to convection parametrisation exist
• basic ingredients to present convection parametrisations 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 parametrisation …….
33
Summary (2)
• The mass-flux approach can also be used for the parametrization of shallow convection.
It can also be directly applied to the transport of chemical species
• The parametrized effects of convection on humidity and clouds strongly depend on the assumptions about microphysics and mixing in the cloud model --> uncertain and active research area
• …………. Future we already have alternative approaches based on explicit representation (Multi-model approach) or might have approaches based on Wavelets or Neural Networks
34
Trigger Functions
CAPECloudDepth
CIN Moist.Conv.
Sub-cloudMass conv.
Cloud-layerMoisture ∂(CAPE)/∂t
BMJ(Eta)
Grell(RUC, AVN)
KF
(Research)
Bougeault(Meteo FR)
Tiedtke(ECMWF)
Bechtold(Research)
Emanuel(NOGAPS,research)
Gregory/Rown(UKMO)
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Closure Assumptions (Intensity)
CAPE Cloud-layermoisture
MoistureConverg.
∂(CAPE)/∂t SubcloudQuasi-equil.
BMJ(Eta)
Grell(RUC, AVN)
KF(Research)
Bougeault(Meteo FR)
Tiedtke(ECMWF)
shallow
Bechtold(Research)
Emanuel(Research)
Gregory/Rown
(UKMO)
36
Vertical Distribution of Heat, Moisture Entraining/Detraining
Plume
Convective Adjustment
Buoyancy SortingCloud Model
BMJ(Eta)
Grell(RUC, AVN)
KF(Research)
Bougeault(Meteo FR)
Tiedtke(ECMWF)
Bechtold(Research)
Emanuel(Research)
Gregory/Rowntree
(UKMO)