Parametrization of diabatic processes

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Dec 1, 2013 (3 years and 6 months ago)

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1

Peter Bechtold and Christian Jakob

Numerical Weather Prediction

Parametrization of diabatic processes

Convection I


An overview

2

Convection


Lectures:


An overview (only about 5 simple principles to remember)


Parametrisation of convection


The ECMWF mass
-
flux parametrisation and Tracer transport


Forecasting of Convection


Cellular automaton (in preparation)


Exercises


The big secret !!!

3

Convection


Aim of Lectures:


The

aim

of

the

lecture

is

only

to

give

a

rough

overview

of

convective

phenomena

and

parameterisation

concepts

in

numerical

models
.

The

student

is

not

expected

to

be

able

to

directly

write

a

new

convection

code
-

the

development

and

full

validation

of

a

new

convection

scheme

takes

time

(years)
.

There

are

many

details

in

a

parameterisation,

and

the

best

exercise

is

to

start

with

an

existing

code,

run

some

offline

examples

on

Soundings

and

dig

in

line

by

line


..

there

is

already

a

trend

toward

explicit

representation

of

convection

in

limited

area

NWP

(no

need

for

parameterization)

but

for

global

we

are

not

there

yet,

and

still

will

need

parameterizations

for

the

next

decade


Offline convection Code:


Can be obtained from
peter.bechtold@ecmwf.int



4

Convection Parametrisation and Dynamics
-

Text
Books



Emanuel, 1994: Atmospheric convection,
OUP


Houze R., 1993: Coud dynamics,

AP


Holton, 2004: An introduction to Dynamic Meteorology,
AP


Bluestein, 1993: Synoptic
-
Dynamic meteorology in midlatitudes, Vol II.
OUP


Peixoto and Ort, 1992: The physics of climate.
American Institute of Physics


Emanuel and Raymond, 1993: The representation of cumulus convection in
numerical models.
AMS Meteor. Monogr
.


Smith, 1997: The physics and parametrization of moist atmospheric
convection.
Kluwer


Dufour et v. Mieghem: Thermodynamique de l’Atmosph
è
re, 1975:
Institut
Royal météorologique de Belgique


Anbaum, 2010: Thermal Physics of the atmosphere. J
Wiley Publishers


AP=Academic Press; OUP=Oxford University Press

5

How does it look like ?

Pre
-
frontal deep convection July 2010 near Baden
-
Baden Germany

Cumulus under Stratocumulus, South UK, July
2008

Rayleigh
-
Benard cellular
convection

Classic plume experiment

6

African Squall lines

Moist convection : Global

IR GOES METEOSAT 7/04/2003

SPCZ

ITCZ at
10
ºN

Deep and shallow convection

Intense deep

Sc convection

7

Convection and role of water vapor

Interaction of Tropics and
midlatitudes:


Dry air intrusions
modulate convection
(Rossby wave breaking)

8

Convection and upper
-
level Divergence

(determine divergence from variation of cold cloud top areas)

z
M
dt
dA
A
t
m
Vol
A
d
U
Vol
U
Div
c
t
A
Vol












1
1
1
lim
lim
0
0






M
c

is the convective mass
flux (see later)

9

Outline

General:


Convection and tropical circulations


Midlatitude Convection


Shallow Convection

Useful concepts and tools:


Buoyancy


Convective Available Potential Energy


Soundings and thermodynamic diagrams


Convective quasi
-
equilibrium


Large
-
scale observational budgets

10

about 3 mm/day is falling globally, but most i.e. 5
-
7 mm/day in the Tropics

Convection and tropical circulations (1)

It’s raining again…
2000/2001 rainfall rate as simulated by IFS Cy36r4
(autumn 2010) and compared to GPCP version 2.1 dataset

11

Model Tendencies


Tropical Equilibria

Above the boundary layer, there is an equilibrium Radiation
-
Clouds
-
Dynamics
-
Convection for
Temperature, whereas for moisture there is roughly an equilibrium between dynamical
transport (moistening) and convective drying.
-

Global Budgets are ver
y similar

Nevertheless, the
driving force for
atmospheric
dynamics and
convection is the
radiation

12

Distribution of convective clouds

13

Global: Convective cloud types (2)

proxy distribution of deep and shallow convective clouds as obtained from IFS
Cy33r1 (spring 2008)

14

A third convective mode

Recent studies indicate, that
there is a
third important mode

of convection (besides deep and
shallow) in the tropics
consisting of mainly
cumulus
congestus

clouds terminating
near the
melting level

at around
5 km.

Johnson et al., 1999, JCL

15

Comparison Cloudsat precip
(left)

from low, middle and high
clouds (space radar) and IFS Cy31r1
(right)

Angela Benedetti, Graeme Stephens

16


Convection and tropical circulations (3)


ITCZ and the Hadley meridional circulation
:
the role of trade
-
wind cumuli
and deep tropical towers

17

Convection and tropical circulations (4)

The Walker zonal Circulation

From Salby (1996)

18

Convection and tropical circulations (5)

Tropical waves: Rossby, Kelvin, Gravity, African easterly waves

a Squall line

2
( )/2
0
( )
( );( )
ˆ ˆ
( ) ( );( )
i kx t y
i kx t
u u f y e f y e
v v y f y e v y Hermite Polynomials


 

 
 
Analytical: solve shallow water equations

19


Convection and tropical circulations (7)

50/50 rotational/divergent

50/50 KE/PE

Strong zonal wind along the
Equator

Symmetric around the Equator

Eastward moving ~18 m/s


The KELVIN wave

V=0

20

Convection and tropical circulations (8)

The Kelvin wave, OLR composite


21

Convection and tropical circulations (9)


Symmetric

KE>PE

KE max at Equator,PE max off
the Equator

Westward moving ~ 5 m/s


The (n=1) Equatorial Rossby wave

22

Convection and tropical circulations (10)

The Equatorial Rossby wave, OLR composite


24

West
-
African meteorology


easterly waves

Monsoon flow ,Easterly waves,
and midlatitude
-
tropical mixing

Low
-
level
Monsoon

flow

Mid
-
level dry
“Harmattan”

Upper
-
level
easterlies

Hovmoeller plots as an
easy way to plot wave
(propagation)

27

MJO 11 Nov. 2011 Sat+ECMWF analysis

@ECMWF

U850

U200

28


Wavenumber

frequency

Diagrams

of

OLR

29


Wavenumber

frequency

Diagrams

of

OLR

same

as

previous

but

latest

cycle

and

background

spectrum

substracted

NOAA Satellite

Cy38r1 (2012)

30

Convection and tropical circulations

Summary of tropical motions and scales



There are still uncertainties concerning our knowledge about the interaction between
convective and synoptic scales in the Tropics.



Horizontal temperature fluctuations in the Tropics are small
<1K/1000 km
; and in the
absence of precipitation the vertical motions(subsidence) tend to balance the cooling
through IR radiation loss:
w d
θ
/dz = d
θ
/dt_rad =
-
1
-
2 K/day => w ~
-
.5 cm/s



In the absence of condensation heating, tropical motions must be barotropic and cannot
convert PE in KE. Therefore they must be driven by precipitating disturbances or lateral
coupling with midlatitude systems.



When precipitation takes place, heating rates are strong;
e.g.
100 mm/day precip ~ energy flux of 2900 W/m2 or an average 30 K/day heating

of
the atmospheric column
=> w ~ 8.6 cm/s.

However, this positive mean motion is
composed of strong ascent of order
w ~ 1 m/s

in the Cumulus updrafts and slow
descending motion around (“compensating subsidence”)



when analysing the vorticity equation it appears that in precipitating disturbances the
vertical transport of vorticity (momentum) through Cumulus is important to balance the
divergence term

31

Midlatitude Convection (1)

Convection associated to synoptic forcing, orographic
uplift, and/or strong surface fluxes

A Supercell over Central US, Mai 1998, flight level 11800 m

32

Midlatitude Convection (2)

It’s raining again…

Europe climatology (
Frei and Sch
ä
r, 1998
)

In Europe most intense precipitation is associated with orography, especially around the
Mediterranean, associated with strong large
-
scale forcing and mesoscale convective
systems

33

Midlatitude Convection (3)


European MCSs (
Morel and Sénési, 2001
)

Density Map of Triggering ….. over Orography

34

Midlatitude Convection (4)


European MCSs (
Morel and Sénési, 2001
)

Time of Trigger and mean propagation

European (midlatitude) MCSs essentially form over orography (convective inhibition

see
later
-

offset by uplift) and then propagate with the midtropospheric flow (from SW to NE)

35

Midlatitude Convection (5)

along the main cold frontal band and in the cold core of the main
depression


17/02/97 during FASTEX

A Supercell over Central US, Mai 1998, flight level 11800 m

36

Midlatitude Convection (6)

Forcing of ageostrophic circulations/convection in the right entrance
and left exit side of upper
-
level Jet

Thermally direct circulation

Thermally indirect circulation

a
g
fv
v
v
f
dt
du



)
(
Acceleration/deceleration of Jet

Total energy is conserved: e.g. at the exit region
where the Jet decelerates kinetic energy is
converted in potential energy

37

Midlatitude Convection (7)

Conceptual model of a Squall line system with a trailing stratiform
area (from Houze et al. 1989)


Evaporation of precipitation

creates negatively buoyant air parcels. This can
lead to the generation of
convective
-
scale penetrative downdraughts.


In the
stratiform part

there is
heating/cooling couple

with an upper
-
level
mesoscale ascent, and a lower
-
level mesoscale downdraught, due to the
inflow of dry environmental air and the evaporation of stratiform rain.

38

Midlatitude Convection (8a)

Conceptual model of a rotating mesoscale convective system


tornadic thunderstorm
(from Lemon and Doswell, 1979)

Forward Flank downdraft
induced by evaporation of
precipitation

Rear Flank Downdraft induced by
dynamic pressure perturbation:
Interaction of updraft with shear
vector of environment:

w
z
V
P
z
L







The linear part of the dynamic pressure
perturbation is proportional to the
horizontal gradient of the vertical velocity
perturbation (updraft) times the
environmental shear vector

39

Midlatitude Convection (8b)

Origin and mechanism of generation of vertical vorticity

Conversion of horizontal vorticity at surface frontal boundary
in vertical vorticity by tilting in updraft

A

useful

quantity

in

estimating

the

storm

intensity

is

the


“bulk”

Richardson

number

R=CAPE/S
2
,


where

CAPE

is

the

convective

available

energy

(see

later)

and

S

is

the

difference

between

the

mean

wind

vector

at

500

and

925

hPa

40

Summary:

What is convection doing, where does it occur


Convection transports heat, water vapor, momentum … and chemical
constituents upwards …. Water vapor then condenses and falls out
-
> net
convective heating/drying


Deep Convection (precipitating convection) stabilizes the environment, an
approximate not necessarily complete picture is to consider it as reacting to the
large
-
scale environment (e.g. tropical waves, mid
-
latitude frontal systems)
=“quasi
-
equilibrium”; shallow convection redistributes the surface fluxes


The tropical atmosphere is in radiative(cooling) / convective(heating)
equilibrium

2K/day cooling in lowest 15 km corresponds to about 5 mm/day
precipitation.


The effect of convection (local heat source) is fundamentally different in the
midlatitudes and the Tropics. In the Tropics the Rossby radius of deformation
R=N H/f
(N=Brunt Vaisala Freq, f=Coriolis parameter, H=tropopause height)
is infinite, and
therefore the effects are not locally bounded, but spread globally via gravity
waves


“throwing a stone in a lake”



41

What we have not talked about


Organization of convection: Squall lines, Mesoscale convective
systems, tropical superclusters, and the influence of vertical wind
shear


The diurnal cycle of convection over land (see lecture Notes and
last lecture
)


Follow some Tools and Concepts !

42

Buoyancy
-

physics of Archimedes (1)

Body in a fluid

Assume fluid to be in
hydrostatic equlibrium

g
dz
dp
2
2



.
2
const


gh
p
2
2


Forces:

Top

y
x
gh
F
top




1
2

Bottom

y
x
gh
F
bot



2
2

Gravity

z
y
x
g
F
grav





1

Net Force:

z
y
x
g
z
y
x
g
y
x
h
h
g
F
F
F
F
grav
bot
top
















)
(
)
(
1
2
1
1
2
2




Acceleration:

1
1
2
1
)
(











g
z
y
x
F
M
F
A
body
Emanuel, 1994

43

Buoyancy (2)

Vertical momentum equation:

g
z
p
dt
dw






1
p
p
p









g
z
p





g
z
p
p
dt
dw









)
(
1






































2
1
1
1
1
1
1










Neglect second order terms





44

Buoyancy (3)

z
p
z
p
g
z
p
z
p
dt
dw


























1
1
1
1
g
g

B
-

buoyancy acceleration

1
dw p
g
dt dz

 
 

  
45

Buoyancy (4)

Contributions

g
B





Buoyancy acceleration:

Dry air:

Often

(
but not always
):

T
T
g
B
T
T
p
p






and

z
p
T
T
g
dt
dw







1
Then

Hence

on)
decelerati

(downward
on
accelarati

upward
0

parcel)

(warm

0





dt
dw
T
on)
accelerati

(downward
on
decelerati

upward
0

parcel)

(cold

0





dt
dw
T
2
p p pT p T
RT RT RT p T

 

    

      
46

Buoyancy (5)


Contributions

Cloudy air:

effects of humidity and condensate

need to be taken into account

In general
all 3 terms

are
important
. 1 K perturbation in T is equivalent to 5 g/kg
perturbation in water vapor or 3 g/kg in condensate

0.608
l
T
B g g q q
T


 
 

     
 
 
47

Non
-
hydrostat. Pressure gradient effects

g
z
p
dt
dw










1
CRM analysis of the terms

Physics:

Vector field of the buoyancy pressure
-
gradient force for a uniformly buoyant
parcel of finite dimensions in the x
-
z
-
plane.
(
Houze, 1993, Textbook
)

Guichard and Gregory

0

15

10

5

-
0.02

0.02

0.04

-
0.04

P

Z (km)

(ms
-
2
)

B

48

Convective Available Potential Energy (CAPE)

Definition:

dz
T
T
T
g
CAPE
top
base
env
env
cld








top
base
Bdz
l
d
F
CAPE


CAPE

represents
the amount of
potential energy of a parcel lifted
to its level of neutral buoyancy
.
This energy
can
potentially

be
released

as kinetic energy
in
convection.

T
T
g
dz
dw
dz
dw
w
dt
dw




2
2
1
CAPE
dz
T
T
g
z
w
z





2
2
)
(
0
2
CAPE
w


2
1
60


ms
w
10km
depth

Cloud

,
250

,
5




K
T
K
T
Example:

Much larger than observed
-

what’s going
on ?

49

Convection in thermodynamic diagrams (1)

using Tephigram/Emagram

Idealised Profile

LCL

LFC

LNB

CIN

50

Convection in thermodynamic diagrams (2)

using equivalent Potential Temperature and

saturated equivalent Potential Temperature

θ

Θ
e
(T,q)

Θ
esat
(T)

Θ
e

is conserved during
moist adiabatic ascent

CAPE

Note that no CAPE is available for parcels ascending above 900 hPa and that the tropical
atmosphere is stable above 600 hPa (
θ
e

increases)


downdrafts often originate at the
minimum level of
θ
e
in the mid
-
troposphere.

GATE Sounding

51

Importance of choice of moist adiabat in
CAPE calculations

Reversible moist adiabat:

Condensate remains in parcel at all
time.

Consequences:

Water loading (
gravity

acting on condensate)

Condensate needs to be heated
-

different
heat
capacity

than dry air

Phase transition

from water to ice leads to
extra heating

Irreversible moist adiabat (Pseudo
-
adiabat):

Condensate is removed
from parcel instantly

52

Importance of choice of moist adiabat in
CAPE calculations

CAPE
-

reversible

adiabat
without
freezing

vs.

irreversible

adiabat

Emanuel, 1994

Reversible CAPE much smaller, typically by a factor of 2 with
respect to irreversible

55

Mixing and 3D flow

subcloud and cloud
-
layer Circulations

From high
-
resolution LES simulation (dx=dy=50 m)
Vaillancourt, You, Grabowski, JAS 1997

56

Mixing models

undiluted

after Raymond,1993

entraining plume

cloud top entrainment

stochastic mixing

57

Effect of mixing on parcel ascent

No dilution

Heavy dilution

Moderate dilution

58

In convective
regions these
terms will be
dominated by
convection

Large
-
scale effects of convection (1)

Q
1

and Q
2

Thermodynamic equation (dry static energy) :

)
(
e
c
L
Q
p
s
s
v
t
s
R
h












Define averaging operator over area A such that:





A
dA
A
1
and







Apply to thermodynamic equation, neglect horizontal second order terms, use
averaged continuity equation:

p
s
e
c
L
Q
p
s
s
v
t
s
R
h

















)
(

“large
-
scale observable” terms

“sub
-
grid” terms

why use
s

and not
T

s =C
p
T+gz

ds/dz= C
p
dT/dz+g

If dT/dz=
-
g/C
p
(dry adiabatic
lapse rate), then ds=0

59

Large
-
scale effects of convection (2)

Q
1

and Q
2

This quantity
can be derived from observations

of the “large
-
scale” terms on the
l.h.s. of the area
-
averaged equations and
describe the influence of the “sub
-
grid”
processes on the atmosphere.


Define:

p
s
e
c
L
Q
Q
R









)
(
1
Apparent heat source

Analogous:

p
q
L
e
c
L
Q








)
(
2
Apparent moisture sink

p
v
Q
h








3
Apparent momentum source

Note that
:

p
h
Q
Q
Q
R









2
1
with

Lq
s
h


Moist static energy

60

Large
-
scale effects of convection (3)

vertical integrals of

Q
1

and Q
2

HS
L
g
dp
Q
T
w
C
L
g
dp
Q
g
dp
Q
Ps
Pt
R
Ps
P
p
Ps
Pt
R
Ps
Pt












Pr
)
(
Pr
1

HL
L
q
w
L
L
g
dp
Q
Ps
P
Ps
Pt








Pr
)
(
Pr
2

Surface Precipitation
flux

Surface Precipitation

Surface sensible
Heat flux

Surface latent
Heat flux

61

Large
-
scale effects of convection (3)

Deep convection

Tropical Pacific

Yanai et al., 1973, JAS

Tropical Atlantic

Yanai and Johnson, 1993

Note the typical tropical maximum of Q1 at 500 hPa, Q2 maximum is lower and
typically at 800 hPa

63

Effects of mesoscale organization

The two modes of convective heating

Structure

Effects on heating

700

-
2

(K/day)

convective

mesoscale

total

1000

500

200

100

2

4

6

0

P(hPa)

300

64

Zonal average convective Q1 in IFS

P (hPa)

Latitude

65

Convective quasi
-
equilibrium (1)

Arakawa and Schubert (1974)

postulated that the level of activity of
convection

is
such that their
stabilizing effect balances the destabilization by large
-
scale processes.

Observational evidence:

v (700 hPa)


 (700
hPa
)

Precipitation

G
ARP
A
tlantic
T
ropical
E
xperiment (1974)

Thompson et al., JAS, 1979


66

Summary


Convection affects the atmosphere through
condensation /
evaporation and eddy transports


On large horizontal scales convection is in
quasi
-
equilibrium

with
the large
-
scale forcing


Q1, Q2 and Q3

are quantities that reflect the time and space
average effect of convection (“unresolved scale”) and stratiform
heating/drying (“resolved scale”)


An
important parameter

for the strength of convection is
CAPE


Shallow convection

is present over very large (oceanic) areas, it
determines the redistribution of the surface fluxes and the
transport of vapor and momentum from the subtropics to the
ITCZ