Parametrization of Diabatic Processes

kayakjokeMécanique

22 févr. 2014 (il y a 3 années et 8 mois)

75 vue(s)

Numerical Weather Prediction
Parametrization of Diabatic Processes


Clouds (3)

The ECMWF Cloud Scheme

Richard Forbes

(with thanks to Adrian Tompkins)


forbes@ecmwf.int

2

The ECMWF Cloud Scheme

1.
Basic approach

2.
Sources and Sinks


Convective detrainment


Stratiform cloud formation and evaporation


Precipitation generation, melting and evaporation


Ice sedimentation numerics


Ice supersaturation

3.
Summary

Outline

3


Based on
Tiedtke

(1993)



Prognostic
moisture variables
:


Water vapour


Condensate (Liquid and Ice)


Cloud fraction



“Single moment” bulk
microphysics


Grid
-
box mean specific
humidities



Diagnostic precipitation


The ECMWF Cloud Scheme

WATER VAPOUR

CLOUD

Liquid/Ice

PRECIP
Rain/Snow

Evaporation

CLOUD
FRACTION

4

The ECMWF Cloud Scheme

Basic assumptions


Clouds fill the
whole model layer
in
the vertical (fraction=cover).


Clouds have the
same thermal state

as the environmental air
(homogeneous T).


Rain water/snow is diagnosed each
timestep (equilibrium assumption)

but is subject to evaporation /
sublimation and melting in the
column.


Cloud
ice

and
water

are
distinguished only as a function of
temperature
-

only one equation for
condensate is necessary.

1

0

-
23
°
C

0
°
C

Temperature

Liquid fraction

All
liquid

All
ice

Mixed
phase

5

x

y

Cloud

ECMWF cloud
parametrization

In the real world

Humidity variations in
cloud
-
free air

but,

No
in
-
cloud

variability

x

y

Cloud

Cloud free

Cloud free

The ECMWF Cloud Scheme

Representing sub
-
grid heterogeneity

6

A mixed ‘uniform
-
delta’ total
water distribution is assumed

q
t

G(q
t
)

q
s

Cloud cover is integral
under supersaturated
part of PDF

1
-
C

q
t

G(q
t
)

C

q
s

ECMWF cloud
parametrization

In the real world

The ECMWF Cloud Scheme

Representing sub
-
grid heterogeneity

7

Cloud condensate

Cloud fraction

1.

Convective Detrainment (deep and shallow)

1

2

2. (A)diabatic warming/cooling (radiation/dynamics)

3

3. Subgrid turbulent mixing (cloud top, horiz eddies)

4

4. Precipitation generation

5

5. Precipitation evaporation/melting

The ECMWF Cloud Scheme

Schematic of sources and sinks

6. Advection/sedimentation

Some (not all)
of these are
derived from a
pdf approach


8

)
(
)
(
)
(
)
(
l
P
l
BL
l
CV
l
l
q
G
e
c
q
S
q
S
q
A
t
q








)
(
)
(
)
(
)
(
C
G
e
c
C
S
C
S
C
A
t
C
P
BL
CV








Cloud liquid
water/ice
q
l

Cloud fraction C

A:

Transport of Cloud (Advection + Sedimentation)

S
CV

:

Detrainment from Convection

S
BL
:

Source/Sink Boundary Layer Processes

c:

Source due to Condensation

e:

Sink due to Evaporation

G
p
:

Precipitation Sink

The ECMWF Cloud Scheme

Sources and sinks

9

Convective Source Term

)
(
)
(
)
(
)
(
l
P
l
BL
l
CV
l
l
q
G
e
c
q
S
q
S
q
A
t
q








10

Convective source term

Linking clouds and convection

Basic idea:

Use
detrained condensate

as a
source for cloud water/ice


Examples:

Ose

(1993),
Tiedtke

(1993), Del
Genio

et
al.
(1996),
Fowler et al.
(1996)


Source terms

for cloud condensate
and fraction
can be derived

using
the
mass
-
flux

approach to
convection
parametrization
.

11

z
q
M
q
D
S
l
u
u
l
u
CV






k

k+1/2

k
-
1/2

(
M
u
q
lu
)
k+1/2

(
M
u
q
lu
)
k
-
1/2

(
-
M
u
q
l
)
k
-
1/2

(
-
M
u
q
l
)
k+1/2

D
u
q
lu

Standard equation for mass
flux convection scheme

ECHAM, ECMWF and many
others...

Convective source term

Source of water/ice condensate

Detrainment of mass from
cumulus updraughts

Updraught mass flux

12

k

k+1/2

k
-
1/2

(
M
u
C
)
k
-
1/2

(
M
u
C)
k+1/2

D
u

Similar
equation for the cloud fraction


z
C
M
D
C
S
u
u
CV






)
(
Convective source term

Source of cloud fraction

13

Microphysics
-

ECMWF Seminar on Parametrization 1
-
4 Sep 2008
13

Condensation and Evaporation

)
(
)
(
)
(
)
(
l
P
l
BL
l
CV
l
l
q
G
e
c
q
S
q
S
q
A
t
q








14

Local criterion

for cloud formation:
q

>
q
s
(
T,p
)

Two ways

to achieve this in an unsaturated parcel:

1.
Increase
q


2.
Decrease
q
s

Processes that can
increase
q

in a
gridbox


Convection

Cloud formation dealt with separately

Turbulent Mixing

Cloud formation dealt with separately

Advection

Stratiform cloud formation

Changes in water vapour,
q

15

Advection does not mix air !!!

It merely moves it around conserving
its properties, including clouds.

but………

there are
numerical problems

in models

u

t

)
(
1
1
T
q
q
s

2
1
T
T

)
(
2
2
T
q
q
s

t+
D
t



2
1
2
5
.
0
q
q
q




2
1
2
5
.
0
T
T
T


Because of the non
-
linearity of q
s
(T), q
2

> q
s
(T
2
) so cloud forms

This is a numerical problem and should not be used as cloud producing process!

Would be preferable to advect moist conserved quantities instead of T and q

q
s

T

q
t

T
1

T
2

q
1

q
2

Stratiform cloud formation

Numerical advection

16

Stratiform cloud formation

Changes in saturation, q
s

Postulate:


The
main (but not only) cloud production mechanisms

for
stratiform clouds are
due to changes in
q
s
. Hence we will
link
stratiform cloud formation to
dq
s
/dt
(i.e. changes in
p
,
T
).

diab
s
s
diab
s
adiab
s
s
dt
dT
dT
dq
dt
dp
dp
dq
dt
dq
dt
dq
dt
dq






























=

w

17

2
1
c
c
c


Existing
clouds

“New”

clouds

The cloud generation term is split into two components:

and assumes a mixed ‘uniform
-
delta’ total water distribution

s
q
1
-
C

q
t

G(q
t
)

C

)
(
)
(
)
(
)
(
l
l
P
l
BL
l
l
q
D
q
G
e
c
q
S
q
A
t
q








Stratiform cloud formation:


18

Stratiform cloud formation:

Increase of existing clouds,

c
1


Already
existing clouds

are assumed to be
at saturation

at the
grid
-
mean temperature. Any
change in q
s

will directly lead to
condensation
.

0

1



dt
dq
dt
dq
C
c
s
s
)
(
t
q
s
q
t

G(q
t
)

C

)
(
t
t
q
s
D

Note that this term would apply to a variety of PDFs for the
cloudy air (e.g. uniform distribution)

19

RH
crit

= 0.8 is used throughout most of the troposphere

Due to lack of knowledge concerning the variance of water
vapour in the clear sky regions we have to resort to the use
of a critical relative humidity,
RH
crit

s
q
q
t

G(q
t
)

)
(
e
v
q
q

crit
s
v
RH
q
q

Stratiform cloud formation:

Formation of new clouds, c
2


s
q
q
t

G(q
t
)

v
q
crit
s
v
RH
q
q

20

s
q
For the case of RH>RH
crit



)
(
2
1
2
v
s
s
q
q
q
C
C

D



D
s
l
q
C
q
D
D


D
2
1
1
-
C

q
t

G(q
t
)

C

s
q
D
e
q
)
(
2
e
s
q
q



)
(
2
1
e
s
s
q
q
q
C
C

D



D
e
s
v
q
C
Cq
q
)
1
(



We know
q
e

from

similarly

Stratiform cloud formation:

Formation of new clouds, c
2


21

s
q
1
-
C

q
t

G(q
t
)

C

Term inactive if
RH<RH
crit

Perhaps for large cooling this is inaccurate?

As s
tated
in the statistical scheme lecture:


1.
With prognostic cloud water and here cover we can write source and
sinks consistently with an underlying distribution function


2.
But in overcast or clear sky conditions we have a loss of information.
Hence the use of
Rh
crit

in clear sky conditions for cloud formation

Stratiform cloud formation:

Formation of new clouds, c
2


For the case of RH<RH
crit

22

Evaporation of clouds

Processes:
e=
e
1
+
e
2



Large
-
scale descent and
cumulus
-
induced subsidence


Diabatic heating


Turbulent mixing (
e
2
)

0

1


dt
dq
dt
dq
C
e
s
s
)
(
2
v
s
q
q
CK
e


)
(
t
q
s
q
t

G(q
t
)

C

)
(
t
t
q
s
D

Diffusion process proportional to the saturation deficit of the environmental air


No effect on cloud cover

where

K

= 5
.10
-
6

s
-
1

23

Problem: Reversible Scheme?

1
-
C

q
t

G(q
t
)

C

)
(
t
q
s
)
(
t
t
q
s
D

Cooling: Increases
cloud cover

1
-
C

q
t

G(q
t
)

C

)
(
t
q
s
)
(
t
t
q
s
D

Subsequent
warming
of
same magnitude: No
effect on cloud cover

Process not reversible

24

Precipitation Generation

+ Melting and Evaporation


)
(
)
(
)
(
)
(
l
P
l
BL
l
CV
l
l
q
G
e
c
q
S
q
S
q
A
t
q








25

Precipitation generation

Mixed phase and water clouds

Sundqvist

(1978
, 1989)






















2
2
1
1
2
1
0
F
F
ql
ql
l
P
crit
e
q
F
F
c
G
P
c
F
1
1
1


T
c
F



268
1
2
2
Accretion/aggregation

Bergeron Process

c
0
=10
-
4
s
-
1

c
1
=100

c
2
=0.5

q
l
crit
=0.3 g kg
-
1

q
l

q
l
crit

G
p

Representing
autoconversion

and
accretion

in the warm phase,
aggregation

and the
Bergeron process

in the mixed phase. (T >
-
23
°
C)

P
= precipitation rate

T

= temperature (K)

26

Precipitation generation

Ice clouds






















2
1
0
crit
qi
qi
i
P
e
q
c
G
c
0
=10
-
3
e
0.025(
T
-

273.15)
s
-
1

qi
crit
=3.10
-
5
kg kg
-
1

q
l

q
l
crit

G
p

Representing
aggregation

in the ice phase
(T <
-
23
°
C).

Rate decreases as the
temperature decreases.

27

Precipitation melting


The part of the grid box that contains precipitation is


assumed to cool to T
melt

over a timescale
tau







Occurs whenever wet bulb temperature T
w

> 0
°
C



Is limited such that cooling does not lead to T<0
°
C


melt
p
T
T
L
c
M


28

Precipitation evaporation



577
.
0
,
3
2
1
0
4
,
10
9
.
5
1
10
44
.
5























clr
P
clr
v
s
clr
P
P
C
P
p
p
q
q
C
E
Evaporation (Kessler 1969, Monogram)

29

Jakob and Klein (QJRMS, 2000)

Mimics radiation schemes by using a ‘2
-
column’ approach of
recording both cloud and clear precipitation fluxes

This allows a more accurate assessment of precipitation
evaporation

NUMERICS: Solved implicitly to
avoid numerical problems



t
t
v
t
t
s
t
v
t
t
v
q
q
t
q
q
D

D

D



D



















D


D


D

t
s
p
v
t
v
t
s
t
v
t
t
v
dT
dq
c
L
t
q
q
t
q
q
1
1


Precipitation Evaporation

30

Precipitation Evaporation


Numerical “Limiters” have to be applied to prevent grid
scale saturation


Clear sky region


t
D

t
D
Grid can not

saturate

Clear sky region


t
D

t
D
Grid slowly

saturates

31

Ice Particle Sedimentation

And Numerical Issues

)
(
)
(
)
(
)
(
l
P
l
BL
l
CV
l
l
q
G
e
c
q
S
q
S
q
A
t
q








32

Pure ice clouds (T<250 K)

Explicitly calculate ice settling flux:

IWC
v
i



16
.
0
100
29
.
3



IWC
v
i

Heymsfield and Donner (1990)

Ice falling
in cloud

below is
source for ice

in that layer, ice falling into
clear sky

is
converted into snow


Two size classes

of ice, boundary at
100
μ
m

















0
100
,
min
IWC
IWC
a
IWC
IWC
tot
tot
McFarquhar and Heymsfield (1997)

100
100




IWC
IWC
IWC
tot
For
IWC
<100

v
i

= 0.15m/s

For
IWC
>100

Illustration of sedimentation numerical issues with ice
sedimentation from

old

IFS Cycle 25r3 to Cycle 30r1

Ice Sedimentation
(before 30r2 in 2006)

Numerical problems

33

Real advection

Perfect advection

Problem
: we neglect
vertical subgrid
-
scales

w

Ice Sedimentation
(before 30r2 in 2006)

Numerical problems

34

Ice Sedimentation
(before 30r2 in 2006)

Further numerical problems

Since we only allow ice to fall one
layer in a timestep, and since the
cloud fills the layer in the vertical, the
cloud lower boundary is advected at
the CFL rate of
D
z /
D
t

Solution (not very satisfactory): Only
allow sedimentation of cloud mass
into existing cloudy regions, otherwise
convert to snow



Results in higher effective
sedimentation rates AND vertical
resolution sensitivity

Ice flux

Snow flux

35

100 vs 50

layer resolution

Ice flux

Snow flux



i
ice
i
q
v
dz
d
dt
dq


1

Sink at level
k

depends on dz

k

k+1

This is numerically correct, but if
then converted to snow and
“lost” will introduce a resolution
sensitivity

Ice Sedimentation
(before 30r2 in 2006)

Further numerical problems

36

v
i

= 0.15m/s modified by a function of temperature and
pressure

Modified Ice Representation
(from 31r1)

To tackle ice settling deficiency

Calculate ice settling flux

IWC
v
i

As seen earlier, an autoconversion term converts some
of the prognostic ice mass to the diagnostic "snow" flux,
which is then treated diagnostically.

Only one size class

of ice

with constant fall speed

Pure ice clouds (T<250 K)

(Heymsfield and Iaquinta, 2000)






















2
1
0
crit
qi
qi
i
P
e
q
c
G
37

Modified Numerics
(from 31r1)

To tackle ice settling deficiency



1
1
1
1
1
1

D
D
D










n
k
Z
V
Z
V
t
k
k
k
k
n
k
k
k
n
k
n
k
D
C








Options:

(1) Semi
-
Lagrangian

(2) Time splitting

(3) Implicit numerics


fall speed

Constant

Explicit Source/Sink

Advected quantity (e.g. ice)

Implicit Source/Sink

(not required for
short

timesteps)

Implicit
:

Upstream forward in time,

k=vertical level

n=time level



= cloud water (
q
X
)

Solution

what is short?








X
v
dz
d
D
C
dt
d
1



Z
t
k
V
n
k
Z
k
n
k
k
V
k
t
D
t
t
C
n
k
D
D
D





D


D

D


1
1
1
1
1
1





38

Improved Numerics
in SCM Cirrus Case

29r1 Scheme

30r2 Scheme

100 vs 50

layer resolution

time evolution of cloud cover and ice

time

cloud fraction

cloud fraction

cloud ice

cloud ice

39

Microphysics
-

ECMWF Seminar on Parametrization 1
-
4 Sep 2008
39

Cirrus Clouds and
Ice Supersaturation

)
(
)
(
)
(
)
(
l
P
l
BL
l
CV
l
l
q
G
e
c
q
S
q
S
q
A
t
q








40

Air that is supersaturated with
respect to ice is common


(Pictures courtesy of Klaus Gierens and Peter Spichtinger, DLR)

3000 km ice supersaturated segment
observed ahead of front

Aircraft flight data

Microwave limb sounders

41

Cirrus Clouds

Homogeneous nucleation


Want to represent super
-
saturation and homogeneous
nucleation


Include simple diagnostic parameterization in existing
ECMWF cloud scheme


Desires:


Supersaturated clear
-
sky states with respect to ice


Existence of ice crystals in locally subsaturated state


Only possible with extra prognostic equation ?

GCM gridbox

C

Clear sky

Cloudy region

42

q
v
cld

=?

q
v
env
=?

Cloud (q
i
cld
)

Clear

GCM gridbox

Three items of information: q
v
, q
i
, C (grid
-
box mean vapour, cloud ice and
cover)



We know q
i

occurs in the cloudy part of the gridbox



We know the mean in
-
cloud cloud ice (q
i
cld
=
q
i
/C)



What about the water vapour? In the days of
no ice supersaturation
:



Clouds: q
v
cld
=q
s



Clear sky: q
v
env
=(q
v
-
Cq
s
)/(1
-
C)

C

Unlike “parcel” models, or high resolution LES
models, we have to deal with subgrid variability

1
-
C

43

GCM gridbox

C

q
v
cld

q
v
env

q
v
+q
i

q
v
-
q
i
(1
-
C)/C

3.

Klaus Gierens
: Humidity in clear sky
part equal to the mean total water

4.

(q
v
-
Cq
s
)/(1
-
C)

q
s

Current assumption including
supersaturation
:

Hang on… Looks familiar???

q
v

q
v

2.

Lohmann and Karcher
:

Humidity uniform across gridcell

(q
v
-
Cq
s
)/(1
-
C)

q
s

1.

In the bad old days

No supersaturation

Different approaches to represent clear sky
and cloudy humidity

44

GCM gridbox

q
v

q
v

2.

Lohmann and Karcher
:

Humidity uniform across gridcell

q
v
cld

q
v
env

Ice is formed, q
i
increases, q
v
cld

reduces

Artificial flux of vapour from clear sky to cloudy regions!!!

Critical S
crit

reached

Assumption ignores fact that difference processes are occurring
on the subgrid
-
scale

q
v
env
=q
v
cld

uplifted box

From Mesoscale Model

1 timestep

1 timestep

45

GCM gridbox

q
v
cld

q
v
env

q
v
cld

reduces to q
s

Critical S
crit

reached

q
i

increases

q
v
env

unchanged

No artificial flux of vapour from clear sky from/to cloudy regions

Assumption seems reasonable: BUT!
Does not allow nucleation or
sublimation timescales

to be represented, due to hard adjustment

q
v
env

unchanged

q
i

decreases

uplifted box

4.

(q
v
-
Cq
s
)/(1
-
C)

q
s

Current assumption
: Hang
on… Looks familiar???

microphysics

Difference to
standard scheme
is that
environmental
humidity must
exceed S
crit

to
form new cloud

From GCM perspective

46

Region Lat:-60./60., Lon:0./360.
0.8
1.0
1.2
1.4
1.6
1.8
RH
0.001
0.010
0.100
1.000
10.000
Freq
default
clipping to Koop
new parameterization
Moziac
A

C

B

RH wrt ice
PDF

at 250hPa

one month
average

A: Numerics and interpolation for default model

B: The RH=1 microphysics mode

C: Drop due to GCM assumption of subgrid
fluctuations in total water

47

Summary of ECMWF Scheme


Scheme introduces two prognostic equations for cloud water/ice
and cloud mass.


Sources and sinks for each physical process


Some derived using assumptions concerning
subgrid
-
scale PDF for
vapour and clouds.

J
More
simple to implement than a prognostic statistical scheme
since “short cuts” are possible for some terms. Also nicer for
assimilation since prognostic quantities directly observable.

L
Loss
of information (no memory) in clear sky (a=0) or overcast
conditions (a=1) (critical relative
humidities

necessary etc).

L
Nothing to stop solution diverging for cloud cover and cloud water.
(
eg
.
q
l
>0, a=0). Unphysical “safety switches” necessary.

L
Diagnostic ice / water split and no ice
supersaturation

0<T<
-
23
°
C

L
Artificial split between prognostic ice and diagnostic snow variables

L
Many microphysical assumptions are empirically based

48

And in the future……..

49

ECMWF IFS Cloud Scheme Developments

WATER
VAPOUR

CLOUD

Liquid/Ice

PRECIP
Rain/Snow

Evaporation

CLOUD
FRACTION

CLOUD
FRACTION

Current Cloud Scheme

New Cloud Scheme



Prognostic condensate & cloud fraction



Diagnostic liquid/ice split as a function of
temperature between 0
°
C and
-
23
°
C



Diagnostic representation of precipitation



Prognostic liquid & ice & cloud fraction



Prognostic snow and rain (sediments/advects)



New additional sources and sinks



Existing sources and sink formulation retained
(cond/evap/autoconv)

New prognostic cloud microphysics

Representation of mixed phase


The most significant change in the new scheme is the
improved physical
representation of the mixed phase.


Current scheme:
diagnostic fn(T) split between ice and liquid cloud



(a crude approximation of the wide range of values observed in reality).


New scheme:
wide range of
supercooled

liquid water

for a given T.

PDF of liquid water
fraction of cloud for
the diagnostic mixed
phase scheme
(
dashed line
) and the
prognostic ice/liquid
scheme (
shading
)

51

Next time: Cloud Scheme Validation…..

Observations,

O
bservations
,




O
bservations

!

52

References

Jakob
, C., and S. A. Klein, 2000: A
parametrization

of the effects of cloud and precipitation overlap for
use in general
-
circulation models.
Quart. J. Roy.
Meteorol
. Soc.
,
126
, 2525
-
2544.


Sundqvist
, H. Berge, E.,
Kristjansson
, J. E., 1989: Condensation and cloud
parametrization

studies with
a
mesoscale

numerical weather prediction model.
Mon.
Wea
. Rev
.,
177
, 1641
-
1657.


Tiedtke
, M. 1993: Representation of clouds in large scale models.
Mon.
Wea
. Rev
.,
117
,

1779
-
1800.


Tompkins, A. M., K.
Gierens

and G.
Radel
, 2007: Ice
supersaturation

in the ECMWF integrated forecast
system.
Quart. J. Roy.
Meteorol
. Soc.
,
133
, 53
-
63.