Numerical Weather Prediction
Parametrization of diabatic processes
Convection I
Peter Bechtold and Christian Jakob
1
Convection
• Lectures:
–
–
–
–
–
The nature of convection
Parametrisation of convection
The ECMWF mass-flux parametrisation and Tracer transport
Forecasting of Convection
Wavelets, Neural Networks and EOFs (in preparation)
• Exercises
– The big secret !!!
2
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
3
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’Atmosphère, 1975: Institut
Royal météorologique de Belgique
• Bohren and Albrecht, 1998: Atmospheric Thermodynamics.OUP
AP=Academic Press; OUP=Oxford University Press
4
How does it look like ?
5
Moist convection : Global
Deep and shallow convection
Intense deep
ITCZ at
10ºN
Sc convection
SPCZ
6
African Squall lines
IR GOES METEOSAT 7/04/2003
Convection and role of water vapor
Interaction of Tropics and
midlatitudes:
Dry air intrusions
modulate convection
(Rossby wave breaking)
7
Convection and upper-level Divergence
(determine divergence from variation of cold cloud top areas)

Div U 
1
lim
Vol  0 Vol
 
1 m
1 dA M c


A UdA  lim
A dt
z
t  0 Vol t
Mc is the convective mass
flux (see later)
8
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
9
Convection and tropical circulations (1)
It’s raining again… 2000/2001 rainfall rate as simulated by IFS CY30R2 and
compared to GPCP obs
about 3 mm/day is falling globally, but most i.e. 5-7 mm/day in the Tropics
10
Model Tendencies – Tropical Equilibria
Nevertheless, the
driving force for
atmospheric
dynamics and
convection is the
radiation
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 very similar
11
Convection and tropical circulations (2)
proxy distribution of deep and shallow convective clouds as obtained from IFS
12
Shallow Convection (1)
Field of tropical oceanic Cumuli
13
Shallow (Boundary-Layer) Convection (5)
Basic physics of
the trade-cumulus
boundary layer
Emanuel, 1994
15
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
17
Convection and tropical circulations (3)
ITCZ and the Hadley meridional circulation: the role of trade-wind cumuli
and deep tropical towers
18
Convection and tropical circulations (4)
The Walker zonal Circulation
From Salby (1996)
19
Convection and tropical circulations (5)
Tropical waves: Rossby, Kelvin, Gravity, African easterly waves
a Squall line20
Convection and tropical circulations (7)
The KELVIN wave
50/50 rotational/divergent
50/50 KE/PE
Strong zonal wind along the
Equator
Symmetric around the Equator
Eastward moving ~18 m/s
21
Convection and tropical circulations (8)
The Kelvin wave, OLR composite
22
Convection and tropical circulations (9)
The (n=1) Equatorial Rossby wave
Symmetric
KE>PE
KE max at Equator,PE max off
the Equator
Westward moving ~ 5 m/s
23
Convection and tropical circulations (10)
The Equatorial Rossby wave, OLR composite
24
African easterly waves
•
•
African easterly waves have periods of 2-6 days, typical wavelengths of about 2500 km
and propagation speeds around -8 m/s.
These waves are thought to originate from barotropic and baroclinic instability,
but the effects of diabatic (Cumulus) heating, the diurnal cycle and orography also
modulate the waves. For instability to exist, the quasi-potential vorticity gradient must
change sign in the domain, i.e for tropical North Africa it must become negative.
 g
 2U
1 
2   1 U 
   2  f0

; S  
y
y
p  S p 
 p
•
•
•
barotropic
baroclinic
Although the shear instability associated with the jet is present throughout the rainy
season, the waves appear to contribute to the development of rainfall systems only
during late summer as only then the can access the necessary moisture in the low-level
monsoon flow.
The exit region of the Tropcial easterly Jet – which is the consequence of the
outflow=divergence due to the Asian Monsoon - might also have an effect on convection
over tropical North Africa
The waves are generally confined to a latitudinal zone close and south of the Jet
Further reading: Diedhiou et al. (1998, GRL), Nicholson and Grist (2003,J. Clim), Hsieh and
Cook (2004, MWR), Grist (2002, MWR)
25
West-African meteorology – easterly waves
Mid-level dry
“Harmattan”
Low-levelMonsoon
flow
Upper-level
easterlies
Monsoon flow ,Easterly waves,
and midlatitude-tropical mixing
26
Hovmoeller plots as an easy way to plot wave
(propagation)
Analysis
10.8-9.9 2005
Comparison
Analysis –
Forecast for
African easterly
waves. No filtering
required
from a series
of 2-day
Forecasts
28
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 dθ/dz = dθ/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
29
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
30
Midlatitude Convection (2)
It’s raining again…
Europe climatology (Frei and Schär, 1998)
In Europe most intense precipitation is associated with orography, especially around the
Mediterranean, associated with strong large-scale forcing and mesoscale convective
systems
31
Midlatitude Convection (3)
European MCSs (Morel and Sénési, 2001)
Density Map of Triggering ….. over Orography
32
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)33
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
34
Midlatitude Convection (6)
Forcing of ageostrophic circulations/convection in the right entrance
and left exit side of upper-level Jet
Acceleration/deceleration of Jet
du
 f (v  v g )  fva
dt
Thermally indirect circulation
Total energy is conserved: e.g. at the exit region
where the Jet decelerates kinetic energy is
converted in potential energy
Thermally direct circulation 35
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.
36
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:
V
PL 
  z w
z
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
37
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
R=CAPE/S2,
number
where CAPE is the convective
available energy (see later) and S is the
difference between the mean wind
vector at 500 and 925 hPa
38
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”
39
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)
Follow some Tools and Concepts !
40
Buoyancy - physics of Archimedes (1)
Body in a fluid
dp2
  2 g
dz
Assume fluid to be in
hydrostatic equlibrium
2  const.
p2  2 gh
Forces:
Top
Ftop    2 gh1xy
Bottom
Fbot   2 gh2 xy
Gravity
Fgrav   1 gxyz
Net Force: F  Ftop  Fbot  Fgrav   2 g (h2  h1 )xy  1 gxyz  g (  2  1 )xyz
Acceleration:
A F
M body
F
1xyz
g
(  2  1 )
1
Emanuel, 1994
41
Buoyancy (2)
Vertical momentum equation:
dw
1 p

g
dt
 z
p  p  p
p
  g
z
    
dw
1  ( p  p)

g

dt

z
2

 1     
1
1
1
  1      
 
      1           

   
Neglect second order terms
42
Buoyancy (3)
dw
1 p 1 p
  1 p   1 p


g

dt
 z  z
  z   z
g
g
dw
1 p  

 g
dt
 dz 
B - buoyancy acceleration
43
Buoyancy (4)
Contributions
B
Buoyancy acceleration:
Dry air:
p
p
pT 
  p T 
  


 
RT
RT RT 2

p T
p
T
T

and B  g
p
T
T
Often (but not always):
Then
Hence


g

dw
T  1 p
g 
dt
T  z
dw
 0  upward accelarati on (downward decelerati on)
dt
dw
T   0 (cold parcel) 
 0  upward decelerati on (downward accelerati on)
dt
T   0 (warm parcel) 
44
Buoyancy (5)
Contributions
Cloudy air:
effects of humidity and condensate need to be taken into account

 T

B   g   g   0.608q  ql 

T

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
45
Non-hydrostat. Pressure gradient effects
dw
1 p  

 g
dt
 z 
15
P
B
Physics:
Z (km)
10
5
-0.04 -0.02
0 0.02 0.04
(ms-2)
CRM analysis of the terms
Guichard and Gregory
Vector field of the buoyancy pressuregradient force for a uniformly buoyant
parcel of finite dimensions in the x-z-plane.
(Houze, 1993, Textbook)
46
Convective Available Potential Energy (CAPE)
Definition:
 
CAPE   F  dl 
dw
dw 1 dw2
T
w

g
dt
dz 2 dz
T
top
 Bdz
z
w ( z )  2 g
2
base
0
top

CAPE 
base
g
Tcld  Tenv
dz
Tenv
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
dz  2  CAPE
T
w  2  CAPE
Example:
T   5K , T  250 K , Cloud depth  10km
w  60ms 1
Much larger than observed - what’s going
on ?
47
Thermodynamic diagrams
Constant
temperature
Moist
adiabat
Dry adiabat
Constant
mixing ratio
Tephigram
Constant
pressure
48
Convection in thermodynamic diagrams (1)
using Tephigram/Emagram
LNB
Idealised Profile
CIN
LFC
LCL
49
Convection in thermodynamic diagrams (2)
using equivalent Potential Temperature and
saturated equivalent Potential Temperature
GATE Sounding
θ
CAPE
Θe is conserved during
moist adiabatic ascent
Θesat(T)
Θe(T,q)
Note that no CAPE is available for parcels ascending above 900 hPa and that the tropical
atmosphere is stable above 600 hPa (θe increases) – downdrafts often originate at the 50
minimum level of θe in the mid-troposphere.
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
51
Importance of choice of moist adiabat in
CAPE calculations
CAPE - reversible
adiabat without
freezing vs.
irreversible
adiabat
Reversible CAPE much smaller, typically by a factor of 2 with
respect to irreversible
Emanuel, 1994
52
Mixing and 3D flow
subcloud and cloud-layer Circulations
From high-resolution LES simulation (dx=dy=50 m)
Vaillancourt, You, Grabowski, JAS 1997
54
Mixing models
undiluted
entraining plume
cloud top entrainment
stochastic mixing
55
after Raymond,1993
Effect of mixing on parcel ascent
No dilution
Moderate dilution
Heavy dilution
56
Large-scale effects of convection (1)
Q1 and Q2
Thermodynamic equation (dry static energy) :

s
s
 vh s 
 QR  L(c  e)
t
p
Define averaging operator over area A such that:

1
dA

AA
and
why use s and not T
s =CpT+gz
ds/dz= CpdT/dz+g
If dT/dz=-g/Cp (dry adiabatic
lapse rate), then ds=0
    
Apply to thermodynamic equation, neglect horizontal second order terms, use
averaged continuity equation:
In convective
regions these
s 
s
 s
 vhs  
 QR  L(c  e ) 
terms will be
t
p
p
dominated by
convection
“large-scale observable” terms “sub-grid” terms
57
Large-scale effects of convection (2)
Q1 and Q2
Define:
Analogous:
 s
Q1  QR  L(c  e ) 
p
 q
Q2  L(c  e )  L
p
  vh
Q3 
p
Apparent heat source
Apparent moisture sink
Apparent momentum source
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.
Note that:
 h
Q1  Q2  QR  
p
with
h  s  Lq
Moist static energy
58
Large-scale effects of convection (3)
vertical integrals of Q1 and Q2
Ps
dp
Q
Pt 1 g 
Ps
dp
Q
Pt R g  L Pr  C p (wT ) P  Ps 
Surface Precipitation
flux
Ps
 Q2
Pt
Ps
 QR
Pt
dp
 L Pr  HS
g
Surface sensible
Heat flux
dp
 L Pr  L( wq) P  Ps  L Pr  HL
g
Surface Precipitation
Surface latent
Heat flux
59
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
60
Large-scale effects of convection (5)
Shallow convection
500
600
P(hPa)
700
Q2
800
Q1
900
q-difference of simulation without and with
shallow convection. Without shallow
boundary-layer is too moist and uppertroposphere too dry !
QR
1000
-14
-10
-6
-2
0
2
(K/day)
-2
Nitta and Esbensen, 1974, MWR
61
Effects of mesoscale organization
The two modes of convective heating
Effects on heating
100
convective
200
P(hPa)
Structure
total
300
500
mesoscale
700
1000
-2
0
2
(K/day)
4
6
62
P (hPa)
Zonal average convective Q1 in IFS
63
Latitude
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)
GARP Atlantic Tropical Experiment (1974)
 (700 hPa)
Precipitation
64
Thompson et al., JAS, 1979
Summary (1)
• Convection is of crucial importance for the global energy and
water balance
• Convection generates and/or influences a number of phenomena
important to forecasting (thunderstorms, heavy precipitation,
hurricanes)
• On large horizontal scales convection is in quasi-equilibrium with
the large-scale forcing
• An important parameter for the strength of convection is CAPE
• Convection affects the atmosphere through condensation /
evaporation and eddy transports
65
Summary (2)
• The effect of convection on the large scale depends on type of
convection and synoptic situation
• 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
• Q1, Q2 and Q3 are quantities that reflect the time and space
average effect of convection (“unresolved scale”) and stratiform
heating/drying (“resolved scale”)
66