Christian Jakob and Peter Bechtold

1. Numerical Weather Prediction Parameterization of diabatic processesConvection IIIThe ECMWF convection scheme Christian Jakob and Peter Bechtold

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

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. 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 Large-scale budget equations: M=ρw; Mu>0; Md<0 Heat (dry static energy): Humidity:

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

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. CTL ETL Updraft Source Layer Occurrence of convection:make a first-guess parcel ascent • 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 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

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

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. Cloud model equations – downdraughtsE and D are defined positive Mass Heat Humidity Momentum

11. Entrainment/Detrainment (1) Updraught “Turbulent” entrainment/detrainment 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 However, for shallow convection detrainment should exceed entrainment (mass flux decreases with height – this possibility is still experimental Organized entrainment is linked to moisture convergence, but only applied in lower part of the cloud (this part of scheme is questionable)

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. Precipitation Liquid+solid precipitation fluxes: 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 Simple representation of Bergeron process included in c0 and lcrit

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

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. Closure - Deep convection Assume:

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

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

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. (Mul)k-1/2 (Mul)k-1/2 (Mulu)k-1/2 k-1/2 Dulu Dulu k Eul Eul k+1/2 (Mul)k+1/2 (Mul)k+1/2 (Mulu)k+1/2 Vertical Discretisation Fluxes on half-levels, state variable and tendencies on full levels cu GP,u

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

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

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

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

25. 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

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

27. 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

28. 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