1 peter bechtold and christian jakob numerical weather prediction parametrization of diabatic...
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1Peter 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’Atmosphère, 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 ?
6African Squall lines
Moist convection : Global
IR GOES METEOSAT 7/04/2003
SPCZ
ITCZ at 10ºN
Deep and shallow convectionIntense 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
At
m
VolAdU
VolUDiv c
tAVol
111
limlim00
Mc 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 very 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( ) /20
( )
( ) ; ( )
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/divergent50/50 KE/PEStrong zonal wind along the
EquatorSymmetric around the EquatorEastward 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)
SymmetricKE>PEKE max at Equator,PE max off
the EquatorWestward 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-levelMonsoon flow
Mid-level dry “Harmattan”
Upper-level easterlies
Hovmoeller plots as an easy way to plot wave (propagation)
27
Wavenumber frequency Diagrams of OLR
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
Thermally direct circulation
Thermally indirect circulation
ag fvvvfdt
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
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:
wz
VP zL
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 number R=CAPE/S2,
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 and last lecture)
Follow some Tools and Concepts !
40
Buoyancy - physics of Archimedes (1)
Body in a fluid Assume fluid to be in hydrostatic equlibrium
gdz
dp2
2
.2 const ghp 22
Forces:
Top yxghFtop 12
Bottom yxghFbot 22
Gravity zyxgFgrav 1
Net Force: zyxgzyxgyxhhgFFFF gravbottop )()( 121122
Acceleration:1
12
1
)(
gzyxF
MFA
body
Emanuel, 1994
41
Buoyancy (2)
Vertical momentum equation:
gz
p
dt
dw
1
ppp gz
p
gz
pp
dt
dw
)(1
2
11
1
111
Neglect second order terms
42
Buoyancy (3)
z
p
z
pg
z
p
z
p
dt
dw
1111
=
g
=
g
=
B - buoyancy acceleration
1dw pg
dt dz
43
Buoyancy (4)Contributions
gB
Buoyancy acceleration:
Dry air:
Often (but not always):T
TgB
T
T
p
p
and
z
p
T
Tg
dt
dw
1
Then
Hence on)decelerati (downwardon accelarati upward0 parcel) (warm 0 dt
dwT
on)accelerati (downwardon decelerati upward0 parcel) (cold 0 dt
dwT
2
p p pT p T
RT RT RT p T
44
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
TB g g q q
T
45
Non-hydrostat. Pressure gradient effects
gz
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
46
Convective Available Potential Energy (CAPE)
Definition:
dzT
TTgCAPE
top
base env
envcld
top
base
BdzldFCAPE
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
Tg
dz
dw
dz
dww
dt
dw
2
2
1
CAPEdzT
Tgzw
z
22)(0
2
CAPEw 2
160 msw
10kmdepth Cloud ,250 ,5 KTKT
Example:
Much larger than observed - what’s going on ?
47
Convection in thermodynamic diagrams (1)using Tephigram/Emagram
Idealised Profile
LCL
LFC
LNB
CIN
CA
PE
48
Convection in thermodynamic diagrams (2)using equivalent Potential Temperature and saturated equivalent Potential Temperature
θ
Θe(T,q)Θesat(T)
Θe is conserved during
moist adiabatic ascentCAPE
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 minimum level of θe in the mid-troposphere.
GATE Sounding
49
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
50
Importance of choice of moist adiabat in CAPE calculations
CAPE - reversible adiabat without freezing vs. irreversible adiabat
Emanuel, 1994Reversible CAPE much smaller, typically by a factor of 2 with respect to irreversible
53
Mixing and 3D flowsubcloud and cloud-layer Circulations
From high-resolution LES simulation (dx=dy=50 m) Vaillancourt, You, Grabowski, JAS 1997
54
Mixing models
undiluted
after Raymond,1993
entraining plume cloud top entrainment stochastic mixing
55
Effect of mixing on parcel ascent
No dilution
Heavy dilution
Moderate dilution
56
In convective regions these terms will be dominated by convection
Large-scale effects of convection (1) Q1 and Q2
Thermodynamic equation (dry static energy) :
)( ecLQp
ssv
t
sRh
Define averaging operator over area A such that:
A
dAA
1 and
Apply to thermodynamic equation, neglect horizontal second order terms, use averaged continuity equation:
p
secLQ
p
ssv
t
sRh
)(
“large-scale observable” terms “sub-grid” terms
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
57
Large-scale effects of convection (2)Q1 and Q2
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
secLQQ R
)(1Apparent heat source
Analogous:p
qLecLQ
)(2Apparent moisture sink
p
vQ h
3Apparent momentum source
Note that:
p
hQQQ R
21 with Lqsh Moist static energy
58
Large-scale effects of convection (3)vertical integrals of Q1 and Q2
HSLg
dpQTwCL
g
dpQ
g
dpQ
Ps
Pt
RPsPp
Ps
Pt
R
Ps
Pt
Pr)(Pr1
HLLqwLLg
dpQ PsP
Ps
Pt
Pr)(Pr2
Surface Precipitation flux
Surface Precipitation
Surface sensible Heat flux
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
61
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 60P(
hPa)
300
62
Zonal average convective Q1 in IFSP
(hP
a)
Latitude
63
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)
hPa
Precipitation
GARP Atlantic Tropical Experiment (1974)
Thompson et al., JAS, 1979
64
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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