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

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Numerical Weather Prediction Parameterization of diabatic processes

Convection IIIThe ECMWF convection scheme

Peter Bechtold and Christian Jakob

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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

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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

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

)()()( FMLeecLsMMsMsMp

gt

sfsubclddududduu

cu

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:

subclddududduucu

eecqMMqMqMp

gt

q

)(

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Large-scale budget equations

Cloud condensate:

u ucu

lD l

t

uMMuMuMp

gt

ududduu

cu

)(

Momentum:

vMMvMvMp

gt

vdudduu

cu

)(

uucu

lDat

a)1(

Cloud fraction:

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

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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 )()()(

dduuducu

DDp

MMgt

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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. 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%.

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Cloud model equations – updraughtsE and D are positive by definition

uuu DEp

Mg

uuuuuu LcsDsE

p

sMg

uuuuuu cqDqE

p

qMg

uPuuuuuu GclDlE

p

lMg ,

uuuuu uDuE

p

uMg

uuuuu vDvE

p

vMg

2,1

(1 )2 , (1 ) 2

v u vu u ud u u

u v

T TK E wC K g K

z M f T

Kinetic Energy (vertical velocity) – use height coordinates

Momentum

Liquid Water/Ice

Heat Humidity

Mass (Continuity)

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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, , 0.3d LFS u bM M

3. Entrainment/Detrainment

turbulent and organized part similar to updraughts (but simpler)

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Cloud model equations – downdraughtsE and D are defined positive

ddd DEp

Mg

dddddd LesDsE

p

sMg

dddddd eqDqE

p

qMg

ddddd uDuE

p

uMg

ddddd vDvE

p

vMg

Mass

Heat

Humidity

Momentum

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Entrainment/Detrainment (1)

u u uu u org turb org

M M Mg E D

p

1 1 2

00

3

3 1 4 11 2

1.3 1.3 ;

1.75 10 ; 0.75 10 ;

turbs

buoybuoy

s

sbase

qc F c RH F c

q

qc m c m F

q

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

NB: This is a simple 1-RH or saturation deficit formulation for the organised entrainment, but any other formulation using buoyancy or also works

,e es

turb

org

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Entrainment/Detrainment (2)

Organized detrainment:

zzK

zK

zzM

zM

u

u

u

u

)(

Only when negative buoyancy (K decreases with height), compute mass flux at level z+Δz with following relation:

with

2

2u

u

wK

anduuD

u

uu Bf

KCM

E

z

K

)1(

12)1(

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Precipitation

2

10,

crit

u

l

l

uu

uuP elw

cMG

Generation of precipitation in updraughts

Simple representation of Bergeron process included in c0 and lcrit

Liquid+solid precipitation fluxes:

gdpMelteeGpP

gdpMelteeGpP

P

Ptop

snowsubcld

snowdown

snowsnow

P

Ptop

rainsubcld

raindown

rainrain

/)()(

/)()(

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.

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Precipitation

uu

precufallout r

zw

VMS

Fallout of precipitation from updraughts

2.0, 32.5 urainprec rV 2.0

, 66.2 uiceprec rV

Evaporation of precipitation

1. Precipitation evaporates to keep downdraughts saturated

2. Precipitation evaporates below cloud base

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, assume a cloud fraction 0.05surf

subcld s

p p Pe RHq q

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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.,

CAPECAPE

t

CAPE

cu

0

• 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)

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

H

u nH W

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Closure - Deep convection

cv v

vcloud

CAPE g dz

dzttgt

CAPE

cloudv

vcv

cv

v

cu

2

Assume:

1 and cloud, statesteady i.e., ,0

v

cv

cv

t

dzt

gt

CAPE

cu

v

cloudvcu

1

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Closure - Deep convection

z

M

tvc

cu

v

i.e., ignore detrainment

CAPE

dzz

Mg

t

CAPE v

cloudv

c

cu

dtdubuduc MMMMM ,, utd MM ,

1

, ,11 1

nu b u b

nv vu d

v vcloud cloud

CAPE CAPE

M Mg dz g M dz

z z

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

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Closure - Shallow convection

Based on PBL equilibrium : what goes in must go out - including downdraughts

0

0cbase

conv

turb dyn rad

w h h h hdz

z t t t

0

0cbase h

dzt

With

,,

(1 ) ; / ;u b u d u dcbaseconv cbasew h M h h h M M and

00, convhw

0

,(1 )

cbase

turb dyn rad

u b

u d cbase

h h hdz

t t tM

h h h

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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:bbu wM ,

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Vertical Discretisation

k

k+1/2

k-1/2

(Mulu)k+1/2

(Mulu)k-1/2

Eul Eul

Dulu Dulu

cu

GP,u

(Mul)k-1/2(Mul)k-1/2

(Mul)k+1/2 (Mul)k+1/2

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

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Numerics: solving Tendency = advection equation explicit solution

( ) ;u u

conv

g M St p

Pr

pS

1/ 2 1/ 2 1/ 2 1/ 2 1/ 2 1/ 2u u u u u ukk k k k k k

conv

gM M M M S

t p

k k -1ψ ψ

2/12/1 kk PPp

if ψ = T,q

In order to obtain a better and more stable “upstream” solution (“compensating subsidence”, use shifted half-level values to obtain:

k -1/2 k -1ψ ψ

Use vertical discretisation with fluxes on half levels (k+1/2), and tendencies on full levels k, so that

1/ 2 1/ 2 1/ 2 1/ 2 1/ 2 1/ 2u u u u u ukk k k k k k k

conv

gM M M M S

t p

k+1/2 k -1/2ψ ψ

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Numerics: implicit advection

( ) ;u u

conv

g M St p

Prp

S

1/2 1/2 1/2 1/2 1/2 1/2

1/2 1/2 1/2 1/2 1/2 1/2

n u u u u u u nk k k k k k k k

u u n+1 u u u u nk k k -1 k k k k k

tψ -ψ g M M M M tS

p

t(1+M )ψ -M ψ g M M tS

p

n 1 n 1 n 1k k k -1

n 1k

ψ ψ

2/12/1 kk PPp

if ψ = T,q

=> Only bi-diagonal linear system, and tendency is obtained

as

For “upstream” discretisation as before one obtains:

k -1/2 k -1ψ ψ

Use temporal discretisation with on RHS taken at future time and not at current time

n1n

1n nk k k

convt t

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Numerics: Semi Lagrangien advection

;)( SMp

gt

uu

Pr

pS

if ψ = T,q

;)(

uuu D

p

g

pgM

tdt

d

Advection velocity

( ) ;dep u u

conv

gD

t t p

)( tgMPdep u

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

Surface precipitation; continental convection during ARM

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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

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Tracer transport experiments(2) Single-column against CRM

Surface precipitation; tropical oceanic convection during TOGA-COARE

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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

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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

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