1. 1 Numerical Weather Prediction Parameterization of diabatic processes Convection III The ECMWF convection scheme Christian Jakob and Peter Bechtold

2. 2 A bulk mass flux scheme: What needs to be considered Entrainment/Detrainment Downdraughts Link to cloud parameterization Cloud base mass flux - Closure Type of convection shallow/deep Where does convection occur Generation and fallout of precipitation

3. 3 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

4. 4 Large-scale budget equations: M=ρw; M u >0; M d <0 Mass-flux transport in up- and downdraughts condensation in updraughts Heat (dry static energy): Prec. evaporation in downdraughts Prec. evaporation below cloud base Melting of precipitation Freezing of condensate in updraughts Humidity:

5. 5 Large-scale budget equations Cloud condensate: Momentum: Cloud fraction: (supposing fraction 1-a of environment is cloud free)

6. 6 Large-scale budget equations Nota: These tendency equations have been written in flux form which by definition is conservative. It can be solved either explicitly (just apply vertical discretisation) or implicitly (see later). Other forms of this equation can be obtained by explicitly using the derivatives (given on Page 10), so that entrainment/detrainment terms appear. The following form is particular suitable if one wants to solve the mass flux equations with a Semi-Lagrangien scheme; note that this equation is valid for all variables T, q, u, v, and that all source terms (apart from melting term) have cancelled out

7. 7 Occurrence of convection: make a first-guess parcel ascent Updraft Source Layer LCL ETL CTL 1)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 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 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%.

8. 8 Cloud model equations – updraughts E and D are positive by definition Kinetic Energy (vertical velocity) – use height coordinates Momentum Liquid Water/Ice HeatHumidity Mass (Continuity)

9. 9 Downdraughts 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)

10. 10 Cloud model equations – downdraughts E and D are defined positive Mass Heat Humidity Momentum

11. 11 Entrainment/Detrainment (1) Updraught “Turbulent” entrainment/detrainment Organized entrainment is linked to moisture convergence, but only applied in lower part of the cloud (this part of scheme is questionable) However, for shallow convection detrainment should exceed entrainment (mass flux decreases with height – this possibility is still experimental ε and δ are generally given in units (1/m) since (Simpson 1971) defined entrainment in plume with radius R as ε =0.2/R ; for convective clouds R is of order 1500 m for deep and R=100 or 50 m for shallow

12. 12 Entrainment/Detrainment (2) Organized detrainment: Only when negative buoyancy (K decreases with height), compute mass flux at level z+Δz with following relation: with and

13. 13 Precipitation Generation of precipitation in updraughts Simple representation of Bergeron process included in c 0 and l crit Liquid+solid precipitation fluxes: Where P rain and P snow are the fluxes of precip in form of rain and snow at pressure level p. G rain and G snow are the conversion rates from cloud water into rain and cloud ice into snow. The evaporation of precip in the downdraughts e down, and below cloud base e subcld, has been split further into water and ice components. Melt denotes melting of snow.

14. 14 Precipitation Fallout of precipitation from updraughts Evaporation of precipitation 1. Precipitation evaporates to keep downdraughts saturated 2. Precipitation evaporates below cloud base

15. 15 Closure - Deep convection 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) The quantity required by the parametrization is the cloud base mass-flux. How can the above assumption converted into this quantity ?

16. 16 Closure - Deep convection Assume:

17. 17 Closure - Deep convection i.e., ignore detrainment where M n-1 are the mass fluxes from a previous first guess updraft/downdraft computation

18. 18 Closure - Shallow convection Based on PBL equilibrium : what goes in must go out - no downdraughts Withand

19. 19 Closure - Midlevel convection 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:

20. 20 Vertical Discretisation k k+1/2 k-1/2 (M u l u ) k+1/2 (M u l u ) k-1/2 EulEulEulEul DuluDulu DuluDulu cucu G P,u (M u l) k-1/2 (M u l) k+1/2 Fluxes on half-levels, state variable and tendencies on full levels

21. 21 Numerics: solving Tendency = advection equation explicit solution if ψ = T,q In order to obtain a better and more stable “upstream” solution (“compensating subsidence”, use shifted half-level values to obtain: Use vertical discretisation with fluxes on half levels (k+1/2), and tendencies on full levels k, so that

22. 22 Numerics: implicit advection if ψ = T,q => Only bi-diagonal linear system, and tendency is obtained as For “upstream” discretisation as before one obtains: Use temporal discretisation with on RHS taken at future time and not at current time

23. 23 Numerics: Semi Lagrangien advection if ψ = T,q Advection velocity

24. 24 Convective source terms - Cloud fraction Define GCM gridbox if cloud fills box in the vertical Now derive**

25. 25 Convective source terms - Cloud fraction Mass-flux concept for transport of cloud mass Updraughts are always cloudy Environment air: a parts are cloudy Is there any cloud mass produced in the grid box ? M u - only transport in the vertical D u - only transport of cloud mass from updraught to environment

26. 26 Convective source terms - Cloud fraction E u - transports environment air into updraughts (1-a) parts of this air are not cloudy, but will be converted into cloudy air inside the updraught, hence Introduce source and transport term into **, use convection scheme, do a little algebra.

27. 27 Tracer transport experiments (1) Single-column simulations: Stability Surface precipitation; continental convection during ARM

28. 28 Tracer transport experiments (1) Stability in implicit and explicit advection instabilities Implicit solution is stable. If mass fluxes increases, mass flux scheme behaves like a diffusion scheme: well- mixed tracer in short time

29. 29 Tracer transport experiments (2) Single-column against CRM Surface precipitation; tropical oceanic convection during TOGA-COARE

30. 30 Tracer transport experiments (2) IFS Single-column and global model against CRM Boundary-layer Tracer Boundary-layer tracer is quickly transported up to tropopause Forced SCM and CRM simulations compare reasonably well In GCM tropopause higher, normal, as forcing in other runs had errors in upper troposphere

31. 31 Tracer transport experiments (2) IFS Single-column and global model against CRM Mid-tropospheric Tracer Mid-tropospheric tracer is transported upward by convective draughts, but also slowly subsides due to cumulus induced environmental subsidence IFS SCM (convection parameterization) diffuses tracer somewhat more than CRM