1. ECMWF Training Course Peter Bechtold and Christian Jakob
02 May 2000
Numerical Weather Prediction Parameterization of diabatic processes Convection III The ECMWF convection scheme
Peter Bechtold and Christian Jakob
Moist Processes

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. Large-scale budget equations: M=ρw; Mu>0; Md<0
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:

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-Lagrangian scheme;
note that this equation is valid for all variables T, q, u, v, and that all source terms (apart from melting of precipitation term) have cancelled out

7. Occurrence of convection: make a first-guess parcel ascent
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
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 – updraughts E 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 – downdraughts E and D are defined positive
Mass
Heat
Humidity
Momentum

11. Entrainment/Detrainment (1)
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
Constants
Scaling function to mimick a cloud ensemble
NB: This is a simple 1-RH or saturation deficit formulation for the organised entrainment, but any other formulation using buoyancy or also works

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), 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)
The quantity required by the parameterization is the cloud base mass-flux. How can we get this?

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 - including 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. Vertical Discretisation
ECMWF Training Course
02 May 2000
Vertical Discretisation
Fluxes on half-levels, state variable and tendencies on full levels
(Mul)k-1/2
(Mulu)k-1/2 k
k+1/2
k-1/2
Dulu cu
Eul
(Mul)k+1/2
(Mulu)k+1/2
GP,u
Moist Processes

21. Numerics: solving Tendency = advection equation explicit solution
ECMWF Training Course
02 May 2000
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:
Moist Processes

22. Numerics: implicit advection
ECMWF Training Course
02 May 2000
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
Moist Processes

23. Numerics: Semi Lagrangien advection
ECMWF Training Course
02 May 2000
Numerics: Semi Lagrangien advection
if ψ = T,q
Advection velocity
Moist Processes

24. Convective source terms - Cloud fraction
ECMWF Training Course
02 May 2000
Convective source terms - Cloud fraction
Define
GCM gridbox
if cloud fills box in the vertical
Now derive **
Moist Processes

25. Convective source terms - Cloud fraction
ECMWF Training Course
02 May 2000
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 ?
Mu - only transport in the vertical
Du - only transport of cloud mass from updraught to environment
Moist Processes

26. Convective source terms - Cloud fraction
ECMWF Training Course
02 May 2000
Convective source terms - Cloud fraction
Eu - 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.
Moist Processes

27. Tracer transport experiments (1) Single-column simulations: Stability
ECMWF Training Course
Tracer transport experiments (1) Single-column simulations: Stability
02 May 2000
Surface precipitation; continental convection during ARM
Moist Processes

28. ECMWF Training Course
02 May 2000
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
Moist Processes

29. Tracer transport experiments (2) Single-column against CRM
ECMWF Training Course
Tracer transport experiments (2) Single-column against CRM
02 May 2000
Surface precipitation; tropical oceanic convection during TOGA-COARE
Moist Processes

30. ECMWF Training Course
Tracer transport experiments (2) IFS Single-column and global model against CRM
02 May 2000
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
Moist Processes

31. ECMWF Training Course
Tracer transport experiments (2) IFS Single-column and global model against CRM
02 May 2000
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
Moist Processes

32. IFS small aqua planet configuration: to see how far we can go with parametrised vs explicit global convection
Example Vis5D: explicit simulation of deep convective system at T159 (with R/40 ~ Δx<3 km)
Without parametrised convection the IFS results are quite sensitive to the numerics and to the tuning of the microphysics.
Want to exploit convection globally in the 1-16 km resolution range using T159 (125 km) and T1279 (16 km) truncation with R/10-> dx=125 – 1.5 km range
We are currently testing the non-hydrostatic version on a small aqua planet, here is an example of a thunderstorm
using truncation T159 with 1/40 of the earth radius, so an effective resolution of 3 km. And we will use this technique to study the behavior and transition of our convection (scheme) in the grey zone, ie between 10 and 1 km resolution