Transcript Numerical Weather Prediction Parametrization of diabatic

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)
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Outline
• Aims of convection parametrization
• Overview over approaches to convection parametrization
• The mass-flux approach
2
Task of convection parametrisation
total Q1 and Q2
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
Q1C
 s
 Q1  QR  L(c  e ) 
p
a
b
10
trans
5
z (km)
z (km)
10
Q1-Qr
trans
c-e
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Q2
Q1c is dominated by
condensation term
c-e
-1
0(K/h)
1
2
-2
-1
(K/h)0
but for Q2 the transport and condensation terms are equally important
1
2
3
Caniaux, Redelsperger, Lafore, JAS 1994
Task of convection parametrisation:
in practice this means:
Determine occurrence/localisation of convection
Trigger
Determine vertical distribution of heating, moistening and
momentum changes
Cloud model
Determine the overall amount of the energy conversion,
convective precipitation=heat release
Closure
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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

  q 
P  (1  b) 
 dz
t ls
0
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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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.,
Tref  T
 T 
  

 t conv.
qref  q
 q 
  

 t 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.
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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 temperatureadjustment profile (Tref)
4) Compute a first-guess dewpointadjustment profile (qref)
Adjustment schemes:
The Next Step is an Enthalpy Adjustment
First Law of
Thermodynamics:
dH  C p dT  Lv dqv
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.

Pt
Pb
C p Tref  T dp   Lv (qvref  qv )dp
Pt
Pb
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b
a
Enthalpy is not conserved for
first-guess profiles for this
sounding!
Must shift Tref and qvref to the
left…
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
Q1C
 s
 L(c  e ) 
p
Condensation term
Eddy transport term
Aim: Look for a simple expression of the eddy transport term
   ?
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The mass-flux approach
Reminder:
    
Hence
  0
with
     (   )
     '      
0
and therefore
0
      
    
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The mass-flux approach:
Cloud – Environment decomposition
Cumulus area: a
Fractional coverage with
cumulus elements:
a

A
Define area average:
    1   
c
Total Area: A
c
e
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e
The mass-flux approach:
Cloud-Environment decomposition
(see also Siebesma and Cuijpers, JAS 1995 for a discussion
of the validity of the top-hat assumption)
With the above:
     1   
c
Average over cumulus elements
and
e
Average over environment
    c  1    e  c  1    e 
Use Reynolds averaging again for cumulus elements and environment separately:
c
c
     
e
and
e
     
e
e
=
c
=
c
0
0
Neglect subplume correlations
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The mass-flux approach
Then after some algebra (for your exercise) :
      


  1     c   e  c   e

Further simplifications :
The small area approximation
  1  (1   )  1;
  
c
e
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The mass-flux approach
Then :
    c   c   e 
Define convective mass-flux:
 c
Mc 
  wc
g
Then

c


    gMc   

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The mass-flux approach
With the above we can rewrite:
Q1C




 M c (s c  s )
 L (c  e )  g
p
 M c (q c  q )
Q2  L(c  e )  Lg
p
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
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absolute (scaled) value of the massflux.
Mass-flux entraining plume cloud models
Entraining plume model
Continuity:
 i
M i
 i  i  g
0
t
p
Heat:
Cumulus element i
 i si 
M i si 
  i si   i s  g
 Lci
t
p
i
Specific humidity:
ci
i
 i qi 
M i qi 
  i qi   i q  g
 ci
t
p
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Mass-flux entraining plume cloud models
Simplifying assumptions:
X
0
1. Steady state plumes, i.e.,
t
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.
g
M c
    with
p
M c   M i ,     i ,    i
i
i
i
e.g., Tiedtke (1989), Gregory and Rowntree (1990), Kain and Fritsch (1990)
3. Spectral method
D
M c ( p )   mB ( ) ( p,  )d
0
e.g., Arakawa and Schubert (1974) and derivatives
Important: No matter which simplification - we always describe a cloud ensemble, 22
not
individual clouds (even in bulk models)
Large-scale cumulus effects deduced using
mass-flux models
Assume for simplicity: Bulk model, c 
c
i
c
i
Q1C

 M c (s c  s )
 L(c  e)  g
p
M c
g
  
p



 Mcs c
g
 s  s c  Lc
p
Combine:
Q1C   gMc
s
  ( s c  s )  Le
p
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Large-scale cumulus effects deduced using
mass-flux models
Q1C   gMc
s
  ( s c  s )  Le
p
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


g
HS
Grant (2001)
M bc  a  w* ; w*   zPBL
,


c p 

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CAPE closure - the basic idea
Convection
consumes
CAPE
large-scale processes
generate CAPE
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CAPE closure - the basic idea
b
Convection
consumes
CAPE
Surface processes
also generate CAPE
Downdraughts
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Boundary Layer Equilibrium closure (1)
as used for shallow convection in the IFS
1)
2)
Assuming boundary-layer equilibrium of moist static energy hs
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 boundarylayer that is assumed to be the convective flux Mc (neglect downdraft contributions)
PLCL

Ps
hs
T
q
dp   [C p  Lv ] dp 
t
t
t
Ps
PLCL
rad  dyn
 FS  F ( PLCL )  FS  Fconv 
PLCL

Ps
PLCL

Ps
Fhs
1
dp 0; Fhs   hs
p
g
T
q
[C p  Lv ] dp; with
t
t
rad  dyn
Fconv  M c [C p (T u  T )  Lv (q u  qlu  q )]
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
e, PBL  const , FS  Fconv  0
FS  M cu ( eu   e, PBL )  M cd ( ed   e, PBL );
 M cu 
F
s
M cd  M cu
 ( ed   e, PBL )
Fs is surface heat flux
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Raymond, 1995, JAS; Raymond, 1997, in Smith Textbook
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 …….
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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
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Trigger Functions
CAPE
BMJ
(Eta)
Grell
(RUC, AVN)
KF
(Research)
Bougeault
(Meteo FR)
Tiedtke
(ECMWF)
Bechtold
(Research)
Emanuel
(UKMO)
CIN
Moist.
Conv.
Sub-cloud
Mass conv.
 
  

Cloud-layer
Moisture
∂(CAPE)/∂t


  


  
  

Gregory/Rown

(NOGAPS
,research)
Cloud
Depth



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Closure Assumptions (Intensity)
CAPE
BMJ
(Eta)
Grell
(RUC, AVN)
KF
(Research)


Bechtold
(Research)



shallow

(Research)
(UKMO)
Subcloud
Quasi-equil.

Emanuel
Gregory/Rown
∂(CAPE)/∂t

(Meteo FR)
(ECMWF)
Moisture
Converg.

Bougeault
Tiedtke
Cloud-layer
moisture

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Vertical Distribution of Heat, Moisture
Entraining/Detraining Convective Buoyancy
Adjustment Sorting
Plume
Cloud Model
BMJ

(Eta)
Grell
(RUC, AVN)
KF
(Research)
Bougeault
(Meteo FR)
Tiedtke
(ECMWF)
Bechtold
(Research)





Emanuel

(Research)
Gregory/Rowntree
(UKMO)

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