1. ECMWF Training Course
02 May 2000
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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2. Outline Aims of convection parametrization
ECMWF Training Course
02 May 2000
Outline
Aims of convection parametrization
Overview over approaches to convection parametrization
The mass-flux approach
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3. Task of convection parametrisation(1) total Q1 and Q2
ECMWF Training Course
02 May 2000
Task of convection parametrisation(1) 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
Recall: these effects are represented by Q1-QR, Q2 and Q3
Hence: parametrization needs to describe CONVECTIVE CONTRIBUTIONS to Q1/Q2: condensation/evaporation and transport terms and their vertical distribution.
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4. ECMWF Training Course
02 May 2000
Task of convection parametrization (2) Convective contributions to Q1 and Q2
Conservation: Vertical integral of Q1 convective = surface convective precipitation
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5. Task of convection parametrisation: in practice this means:
ECMWF Training Course
02 May 2000
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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6. Constraints for convection parametrisation
ECMWF Training Course
02 May 2000
Constraints for convection parametrisation
Physical
remove convective instability and produce subgrid-scale convective precipitation (heating/drying) in unsaturated model grids
maintain a realistic vertical thermodynamic and wind structure
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, midlatitudinal and front/post-frontal convection)
Computational
be simple and efficient for different model/forecast configurations (T511, EPS, seasonal prediction)
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7. Types of convection schemes
ECMWF Training Course
02 May 2000
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, 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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8. ECMWF Training Course
02 May 2000
The “Kuo” scheme
Closure: Convective activity is linked to large-scale moisture convergence
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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9. Adjustment schemes e.g. Betts and Miller, 1986, QJRMS:
ECMWF Training Course
02 May 2000
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.
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10. 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)

11. Adjustment schemes: The Next Step is an Enthalpy Adjustment
First Law of Thermodynamics:
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.

12. Enthalpy is not conserved for first-guess profiles for this sounding!
Must shift Tref and qvref to the left…

13. Imposing Enthalpy Adjustment:

14. Adjustment scheme: Adjusted Enthalpy Profiles:

15. The mass-flux approach
ECMWF Training Course
02 May 2000
The mass-flux approach
Condensation term
Eddy transport term
Aim: Look for a simple expression of the eddy transport term
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16. The mass-flux approach
ECMWF Training Course
02 May 2000
The mass-flux approach
Reminder:
with
Hence =
and therefore
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17. 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
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18. ECMWF Training Course
02 May 2000
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:
Average over cumulus elements
Average over environment
and
Use Reynolds averaging again for cumulus elements and environment separately:
and =
Neglect subplume correlations
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19. The mass-flux approach
ECMWF Training Course
02 May 2000
The mass-flux approach
Then after some algebra (for your exercise) :
Further simplifications :
The small are approximation
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20. The mass-flux approach
ECMWF Training Course
02 May 2000
The mass-flux approach
Then :
Define convective mass-flux:
Then
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21. The mass-flux approach
ECMWF Training Course
02 May 2000
The mass-flux approach
With the above we can rewrite:
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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22. Mass-flux entraining plume cloud models
ECMWF Training Course
02 May 2000
Mass-flux entraining plume cloud models
Continuity:
Heat:
Specific humidity:
Entraining plume model
Cumulus element i
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23. Mass-flux entraining plume cloud models
ECMWF Training Course
02 May 2000
Mass-flux entraining plume cloud 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
Sum over all cumulus elements, e.g.
with
e.g., Tiedtke (1989), Gregory and Rowntree (1990), Kain and Fritsch (1990)
3. Spectral method
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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24. Large-scale cumulus effects deduced using mass-flux models
ECMWF Training Course
02 May 2000
Large-scale cumulus effects deduced using mass-flux models
Assume for simplicity: Bulk model,
Combine:
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25. Large-scale cumulus effects deduced using mass-flux models
ECMWF Training Course
02 May 2000
Large-scale cumulus effects deduced using mass-flux models
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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26. Deducing mass-flux model parameters from observations (1)
ECMWF Training Course
02 May 2000
Deducing mass-flux model parameters from observations (1)
The mass-flux entraining plume models (both bulk and spectral) have been used to interpret observations of Q1 and Q2. (in all following figures M is defined in units of omega!)
Yanai and Johnson, 1993, Meteor. Monogr.
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27. ECMWF Training Course
02 May 2000
Deducing mass-flux model parameters from observations (2) - use cloud model
Yanai and Johnson, 1993
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28. Deducing mass-flux model parameters from observations (3)
ECMWF Training Course
02 May 2000
Deducing mass-flux model parameters from observations (3)
Mass flux models can also be applied to convective downdraughts
Yanai and Johnson, 1993
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29. Caniaux, Redelsperger, Lafore, JAS 1994
ECMWF Training Course
02 May 2000
Deducing convective and stratiform heating profiles from Cloud Res. Model (1) Heat Budget of Squall Line
important:
Q1c is dominated by condensation term
The convective and stratiform parts are computed by partitioning the whole domain as function of rainfall and/or updraft intensity
Caniaux, Redelsperger, Lafore, JAS 1994
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30. ECMWF Training Course
02 May 2000
Deducing convective and stratiform heating profiles from Cloud Res. Model (2) Heat Budget of Squall Line
but for Q2 the transport and condensation terms are equally important
Note again that the stratiform (mesoscale) heating maximum occurs above the convective maximum
Caniaux, Redelsperger, Lafore, JAS 1994, Guichard et al. 1997
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31. Alternatives to the entraining plume model - Episodic mixing
ECMWF Training Course
02 May 2000
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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32. Closure in mass-flux parametrizations
ECMWF Training Course
02 May 2000
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)
Grant (2001)
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33. CAPE closure - the basic idea
ECMWF Training Course
02 May 2000
CAPE closure - the basic idea
large-scale processes generate CAPE
Convection consumes CAPE
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34. CAPE closure - the basic idea
ECMWF Training Course
02 May 2000
CAPE closure - the basic idea
Surface processes also generate CAPE (difficult to include in closure)
Convection consumes CAPE
Downdraughts
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35. Fs is surface moist static energy flux
ECMWF Training Course
02 May 2000
Boundary Layer Equilibrium closure (1) as used for shallow convection in the IFS
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 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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36. Raymond, 1995, JAS; Raymond, 1997, in Smith Textbook
ECMWF Training Course
02 May 2000
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
Fs is surface heat flux
Raymond, 1995, JAS; Raymond, 1997, in Smith Textbook
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37. ECMWF Training Course
02 May 2000
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 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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38. ECMWF Training Course
02 May 2000
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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39.   Trigger Functions Moist. Conv. Sub-cloud Mass conv. Cloud-layer
CAPE
Cloud
Depth
CIN
Moist.
Conv.
Sub-cloud
Mass conv.
Cloud-layer
Moisture
∂(CAPE)/∂t
BMJ
(Eta) 
Grell
(RUC, AVN) KF
(Research)
Bougeault
(Meteo FR)
Tiedtke
(ECMWF)
Bechtold
Emanuel
(NOGAPS
,research)
Gregory/Rown
(UKMO) 

40. Closure Assumptions (Intensity)
CAPE
Cloud-layer
moisture
Moisture
Converg.
∂(CAPE)/∂t
Subcloud
Quasi-equil.
BMJ
(Eta) 
Grell
(RUC, AVN) KF
(Research)
Bougeault
(Meteo FR)
Tiedtke
(ECMWF)
shallow
Bechtold
Emanuel
Gregory/Rown
(UKMO) 

41. Vertical Distribution of Heat, Moisture Entraining/Detraining
Entraining/Detraining
Plume
Convective
Adjustment
Buoyancy Sorting
Cloud Model
BMJ
(Eta) 
Grell
(RUC, AVN) KF
(Research)
Bougeault
(Meteo FR)
Tiedtke
(ECMWF)
Bechtold
Emanuel
Gregory/Rowntree
(UKMO) 