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 !!!

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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

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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

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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)

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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

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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

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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

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Distribution of convective clouds

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Global: Convective cloud types (2)proxy distribution of deep and shallow convective clouds as obtained from IFS Cy33r1 (spring 2008)

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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

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Comparison Cloudsat precip (left) from low, middle and high clouds (space radar) and IFS Cy31r1 (right)

Angela Benedetti, Graeme Stephens

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Convection and tropical circulations (3) ITCZ and the Hadley meridional circulation: the role of trade-wind cumuli and deep tropical towers

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Convection and tropical circulations (4)The Walker zonal Circulation

From Salby (1996)

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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

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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

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Convection and tropical circulations (8)The Kelvin wave, OLR composite

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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

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Convection and tropical circulations (10)The Equatorial Rossby wave, OLR composite

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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)

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Wavenumber frequency Diagrams of OLR

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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

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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

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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

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Midlatitude Convection (3) European MCSs (Morel and Sénési, 2001)Density Map of Triggering ….. over Orography

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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)

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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

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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

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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.

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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

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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

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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”

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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 !

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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

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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

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Buoyancy (3)

z

p

z

pg

z

p

z

p

dt

dw

1111

=

g

=

g

=

B - buoyancy acceleration

1dw pg

dt dz

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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

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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

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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

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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 ?

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Convection in thermodynamic diagrams (1)using Tephigram/Emagram

Idealised Profile

LCL

LFC

LNB

CIN

CA

PE

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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

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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

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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

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Mixing and 3D flowsubcloud and cloud-layer Circulations

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

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Mixing models

undiluted

after Raymond,1993

entraining plume cloud top entrainment stochastic mixing

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Effect of mixing on parcel ascent

No dilution

Heavy dilution

Moderate dilution

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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

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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

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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

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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

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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

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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

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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