1. The parameterization of moist convection
ECMWF Training Course
02 May 2000
The parameterization of moist convection
Peter Bechtold, Christian Jakob, David Gregory
With contributions from J. Kain (NOAA/NSLL)
Original ECMWF lecture has been adjusted to fit into today’s schedule
Roel Neggers, KNMI
Moist Processes

2. Outline of second hour Parameterizing moist convection
ECMWF Training Course
02 May 2000
Outline 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
Moist Processes

3. Task of convection parameterization total Q1 and Q2
ECMWF Training Course
02 May 2000
Task of convection parameterization 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
Apparent heat source
Radiation
Condensation/
Evaporation
Transport
Apparent moisture sink
Moist Processes

4. Task of convection parameterization in practice this means:
ECMWF Training Course
02 May 2000
Task of convection parameterization 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 / intensity of the energy conversion, convective precipitation=heat release
Closure
Moist Processes

5. Constraints for convection parameterization
ECMWF Training Course
02 May 2000
Constraints 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) )
Moist Processes

6. Types of convection schemes
ECMWF Training Course
02 May 2000
Types 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.
Moist Processes

7. ECMWF Training Course
02 May 2000
Type I: “Kuo” schemes
Closure: Convective activity is linked to large-scale moisture convergence: “what comes in must rain out”
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
Moist Processes

8. Type II: Adjustment schemes
ECMWF Training Course
02 May 2000
Type 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.,
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.
Moist Processes

9. Procedure followed by BMJ scheme…T
Tdew
4) Compute a first-guess dewpoint-adjustment profile (qref) 4
3) Compute a first-guess temperature-adjustment profile (Tref) 3
1) Find the most unstable air in lowest ~ 200 mb 1
2) Draw a moist adiabat for this air 2

10. Type III: Mass-flux schemes
ECMWF Training Course
02 May 2000
Type III: Mass-flux schemes
Condensation term
Eddy transport term
Aim: Look for a simple expression of the eddy transport term
Moist Processes

11. The mass-flux approach
ECMWF Training Course
02 May 2000
The mass-flux approach
Reminder: Reynolds averaging (boundary layer lecture)
with
Hence =
and therefore
Moist Processes

12. The mass-flux approach: Cloud – Environment decomposition
ECMWF Training Course
02 May 2000
The mass-flux approach: Cloud – Environment decomposition
Cumulus area: a
Fractional coverage with cumulus elements:
Define area average:
Total Area: A
Moist Processes

13. The mass-flux approach
ECMWF Training Course
02 May 2000
The mass-flux approach
Make some assumptions:
Neglect subplume correlations
Small area approximation:
Then :
Define convective mass-flux:
Then
Mass flux
Excess of plume over enviroment
Moist Processes

14. The mass-flux approach
ECMWF Training Course
02 May 2000
The mass-flux approach
With the above we can rewrite:
Plume model
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.
Moist Processes

15. The entraining plume model
ECMWF Training Course
02 May 2000
The entraining plume model
Entraining plume model
Mass:
Cumulus element i
Heat:
Detrainment rate
Specific humidity:
Entrainment rate
Interaction (mixing) with the plume environment
Area
Moist Processes

16. Bulk entraining plume models
ECMWF Training Course
02 May 2000
Bulk entraining plume models
Simplifying assumptions:
1. Steady state plumes, i.e.,
Most mass-flux convection parametrizations today still make that assumption, some however are prognostic
2. Bulk mass-flux approach
A single bulk plume describes the effect of a whole ensemble of clouds:
Sum over all cumulus elements:
Moist Processes

17. Substitution of bulk mass flux model into Q1 and Q2
ECMWF Training Course
02 May 2000
Substitution of bulk mass flux model into Q1 and Q2
Combine:
Moist Processes

18. Evaporation of cloud and precipitation (term III)
ECMWF Training Course
02 May 2000
Interpretation I II
III
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.
Moist Processes

19. Closures in mass-flux parameterizations
ECMWF Training Course
02 May 2000
Closures 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)
Moist Processes

20. CAPE closure - the basic idea
ECMWF Training Course
02 May 2000
CAPE closure - the basic idea
large-scale processes generate CAPE
Convection consumes CAPE
Find the magnitude of Mbc so that profile is adjusted to reference profile
Principle can also be applied to boundary-layer humidity / moist static energy
Moist Processes

21. Turbulence closures - the basic idea
ECMWF Training Course
02 May 2000
Turbulence 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
Grant (2001):
w’B’=surface buoyancy flux
h=subcloud mixed-layer height
a~0.05 is updraft fraction 21
Moist Processes

22. ECMWF Training Course
02 May 2000
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 …….
Moist Processes

23. The ECMWF convection scheme “Let’s get technical”
ECMWF Training Course
02 May 2000
The ECMWF convection scheme “Let’s get technical”
Peter Bechtold and Christian Jakob
Original ECMWF lecture has been adjusted to fit into today’s schedule
Roel Neggers, KNMI 23
Moist Processes

24. A bulk mass flux scheme: What needs to be considered
Link to cloud parameterization
Entrainment/Detrainment
Type of convection: shallow/deep/midlevel
Cloud base mass flux - Closure
Downdraughts
Generation and fallout of precipitation
Where does convection occur 24

25. Entraining/detraining plume cloud model
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 25

26. Main flow chart callpar cucall
IFS Documentation, Part IV: Physical processes Chapter V: Convection
cucall
satur
cumastrn
cuini
cubasen
cuascn
cubasemcn
cuentr
cudlfsn
cuddrafn
cuascn
cubasemcn
cuentr
cuflxn
cudtdqn
cuccdia
cududv
custrat

27. Convective terms in LS budget equations: M=ρw; Mu>0; Md<0
cudtdqn
Heat (dry static energy):
Prec. evaporation in downdraughts
Freezing of condensate in updraughts
condensation in updraughts
Melting of precipitation
Mass-flux transport in up- and downdraughts
Prec. evaporation below cloud base
Humidity: 27

28. Convective terms in LS budget equations
cududv
Momentum:
Cloud condensate:
Source terms in cloud-scheme
Cloud fraction: (supposing fraction 1-a of environment is cloud free) 28

29. Occurrence of convection (triggering) make a first-guess parcel ascent
cubasen
cubasemcn
Updraft Source Layer
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
ETL
CTL
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 T
Tdew
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%.
LCL 29

30. Plume model equations – updrafts E and D are positive by definition
cuascn
Mass (Continuity)
Heat
Humidity
Liquid Water/Ice
Momentum
Kinetic Energy (vertical velocity) – use height coordinates 30

31. Downdrafts
cudlfsn
cuddrafn
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. Entrainment/Detrainment
turbulent and organized part similar to updraughts (but simpler) 31

32. Cloud model equations – downdrafts E and D are defined positive
cuddrafn
Mass
Heat
Humidity
Momentum 32

33. Entrainment/Detrainment (1)
cuentr
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 m for deep and R= m for shallow  
Scaling function to mimick a cloud ensemble
Constants 33

34. Entrainment/Detrainment (2)
cuentr
Organized detrainment:
Only when negative buoyancy (K decreases with height), compute mass flux at level z+Δz with following relation:
org
org Mu
with
Updraft mass flux
and 34

35. Precipitation fluxes
cuflxn
Two interacting shafts: Liquid (rain) and solid (snow)
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.
Generation of precipitation in updraughts (Sundqvist)
Simple representation of Bergeron process included in c0 and lcrit 35

36. Precipitation Fallout of precipitation from updraughts
cuflxn
Fallout of precipitation from updraughts
Evaporation of precipitation (Kessler)
1. Precipitation evaporates to keep downdraughts saturated
2. Precipitation evaporates below cloud base 36

37. Closure - Deep convection
cumastrn
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.,
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 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? 37

38. Closure - Deep convection
cumastrn
Assume:
Now use this equation to back out the cloud base mass flux Mu,b 38

39. Closure - Deep convection
cumastrn
The idea: assume stabilization is mainly caused by compensating subsidence: v
i.e., ignore detrainment Me Mc
where Mt-1 are the mass fluxes from a previous first guess updraft/downdraft computation 39

40. Closure - Shallow convection
cumastrn
Based on PBL equilibrium for moist static energy h: what goes in must go out - including downdraughts
Mu,b
cbase 40

41. Closure - Midlevel convection
cumastrn
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: 41

42. Studying model behavior at process level:
Single column model (SCM) simulation
Time-integration of a single column of sub-grid parameterizations in isolated mode,
using prescribed large-scale forcings sw lw
free troposphere
subsidence
cloud layer
LS forcings: slow processes
PBL
advection
mixed layer
Advantages:
* computational efficiency & model transparency
* good for studying interactions between fast parameterized physics

43. Behavior Single column model (SCM) experiments
ECMWF Training Course
02 May 2000
Behavior Single column model (SCM) experiments
Surface precipitation; continental convection during ARM 43
Moist Processes

44. Behavior Single column model (SCM) experiments
ECMWF Training Course
02 May 2000
Behavior Single column model (SCM) experiments
SCM simulation at Cabauw, May 2008
Deep convective plume, depositing cloud water at ~ 8km 44
Moist Processes

45. Behavior Single column model (SCM) experiments
ECMWF Training Course
02 May 2000
Behavior Single column model (SCM) experiments
SCM simulation at Cabauw, 31 May – 3 June 2008
Deep convective plumes 45
Moist Processes