# ECMWF-ConvScheme

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```					   Numerical Weather Prediction
Parameterization of diabatic processes

Convection III
The ECMWF convection scheme
Christian Jakob and Peter Bechtold

1
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                          2
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

3
Large-scale budget equations:
M=ρw; Mu>0; Md<0

Heat (dry static energy):                                      Prec. evaporation    Freezing of condensate in
in downdraughts             updraughts

Prec. evaporation      Melting of
Mass-flux transport in   condensation          below cloud base      precipitation
up- and downdraughts     in updraughts

Humidity:

4
Large-scale budget equations

Momentum:

Cloud condensate:

Cloud fraction:
(supposing fraction 1-a
of environment is cloud
free)                           5
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

6
Occurrence of convection:
make a first-guess parcel ascent

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. If
w(LCL)>0 and P(CTL)-P(LCL)<200 hPa : shallow convection
CTL
2) Now test for deep convection with similar procedure. Start
close to surface, form a 30hPa mixed-layer, lift to LCL, do
ETL          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
7
Updraft Source Layer
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

8
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)

9
Cloud model equations – downdraughts
E and D are defined positive

Mass

Heat

Humidity

Momentum

10
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)
11
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

12
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           13
Precipitation

Fallout of precipitation from updraughts

Evaporation of precipitation
1. Precipitation evaporates to keep downdraughts saturated
2. Precipitation evaporates below cloud base

14
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 ?

15
Closure - Deep convection

Assume:

16
Closure - Deep convection

i.e., ignore detrainment

where Mn-1 are the mass fluxes from a previous first guess updraft/downdraft computation
17
Closure - Shallow convection

Based on PBL equilibrium : what goes in must go out - no downdraughts

With                                          and

18
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:

19
Vertical Discretisation

Fluxes on half-levels, state variable and tendencies on full levels

(Mul)k-1/2
(Mul)k-1/2                            (Mulu)k-1/2
k-1/2
Dulu                                             Dulu
cu                                  k
Eul                                              Eul
k+1/2
(Mul)k+1/2            GP,u            (Mulu)k+1/2              (Mul)k+1/2
20
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:

21

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,
22
and tendency is obtained as
Numerics: Semi Lagrangien advection

if ψ = T,q

23
Tracer transport experiments
(1) Single-column simulations: Stability

Surface precipitation; continental convection during ARM

27
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
28
Tracer transport experiments
(2) Single-column against CRM

Surface precipitation; tropical oceanic convection during TOGA-COARE

29
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                       30
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
31

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