The parameterization of moist convection

1. 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

2. 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

3. 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

4. Cloud model Closure Task of convection parameterizationin practice this means: Determine occurrence/localisation of convection Trigger Determine vertical distribution of heating, moistening and momentum changes Determine the overall amount / intensity of the energy conversion, convective precipitation=heat release

5. 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) )

6. 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.

7. 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

8. 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.

9. 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) 3 4 2 4) Compute a first-guess dewpoint-adjustment profile (qref) 1 Procedure followed by BMJ scheme… T Tdew

10. Type III: Mass-flux schemes Condensation term Eddy transport term Aim: Look for a simple expression of the eddy transport term

11. with = = 0 0 The mass-flux approach Reminder: Reynolds averaging (boundary layer lecture) Hence and therefore

12. Cumulus area: a Total Area: A The mass-flux approach:Cloud – Environment decomposition Fractional coverage with cumulus elements: Define area average:

13. 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

14. The mass-flux approach Plume model 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 a plume model and a closure.

15. Heat: Cumulus element i Specific humidity: The entraining plume model Entraining plume model Mass: Detrainment rate Entrainment rate Interaction (mixing) with the plume environment Area

16. 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:

17. Substitution of bulk mass flux model into Q1 and Q2 Combine:

18. 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.

19. 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)

20. Convection consumes CAPE large-scale processes generate CAPE CAPE closure - the basic idea 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

21. 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

22. 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 …….

23. 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

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. 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 IFS Documentation, Part IV: Physical processes Chapter V: Convection cucall satur cuini cumastrn 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 Prec. evaporation in downdraughts Freezing of condensate in updraughts Prec. evaporation below cloud base Melting of precipitation Mass-flux transport in up- and downdraughts condensation in updraughts cudtdqn Heat (dry static energy): 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 CTL ETL Updraft Source Layer cubasen cubasemcn • 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 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 – updraftsE 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 – downdraftsE 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 500-1000 m for deep and R=50-100 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 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. 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? 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 PBL advection mixed layer Advantages: * computational efficiency & model transparency * good for studying interactions between fast parameterized physics

43. Behavior Single column model (SCM) experiments Surface precipitation; continental convection during ARM 43

44. Behavior Single column model (SCM) experiments SCM simulation at Cabauw, 12-15 May 2008 Deep convective plume, depositing cloud water at ~ 8km 44

45. Behavior Single column model (SCM) experiments SCM simulation at Cabauw, 31 May – 3 June 2008 Deep convective plumes 45