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
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