1. ECMWF Training Course Peter Bechtold and Christian Jakob
02 May 2000
Numerical Weather Prediction Parametrization of diabatic processes Convection I An overview
Peter Bechtold and Christian Jakob
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2. Lectures: Exercises Convection
ECMWF Training Course
02 May 2000
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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3. Offline convection Code:
ECMWF Training Course
02 May 2000
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
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4. Convection Parametrisation and Dynamics - Text Books
ECMWF Training Course
02 May 2000
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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5. How does it look like ?
Pre-frontal deep convection July 2010 near Baden-Baden Germany
Rayleigh-Benard cellular convection
Cumulus under Stratocumulus, South UK, July 2008
Classic plume experiment

6. Moist convection : Global
Deep and shallow convection
Intense deep
ITCZ at 10ºN
Sc convection
African Squall lines
SPCZ
IR GOES METEOSAT 7/04/2003

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)
Mc is the convective mass flux (see later)

9. Outline General: Convection and tropical circulations
ECMWF Training Course
02 May 2000
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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10. 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
about 3 mm/day is falling globally, but most i.e. 5-7 mm/day in the Tropics

11. Model Tendencies – Tropical Equilibria
ECMWF Training Course
Model Tendencies – Tropical Equilibria
02 May 2000
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
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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
ECMWF Training Course
02 May 2000
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17. Convection and tropical circulations (4) The Walker zonal Circulation
ECMWF Training Course
02 May 2000
Convection and tropical circulations (4) The Walker zonal Circulation
From Salby (1996)
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18. Convection and tropical circulations (5) Tropical waves: Rossby, Kelvin, Gravity, African easterly waves
a Squall line
Analytical: solve shallow water equations

19. Convection and tropical circulations (7)
The KELVIN wave
V=0
50/50 rotational/divergent
50/50 KE/PE
Strong zonal wind along the Equator
Symmetric around the Equator
Eastward moving ~18 m/s

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

21. 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

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

23. African easterly waves
ECMWF Training Course
02 May 2000
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.
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)
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24. West-African meteorology – easterly waves
Mid-level dry “Harmattan”
Low-levelMonsoon flow
Upper-level easterlies
Monsoon flow ,Easterly waves, and midlatitude-tropical mixing
Hovmoeller plots as an easy way to plot wave (propagation)

25. Reminder : useful relations for the Streamfunction expressing the rotational (non divergent part) of the horizontal wind field
Streamfunction like vorticity is a scalar function that allows to describe the flow (i.e. both u and v)
Streamfunction and vorticity:
Geostrophic Streamfunction and Geopotential:
Nota: Streamfunction ≠ Streamline which is defined by

26. Hovmoeller plots as an easy way to plot wave (propagation)
Analysis
Comparison Analysis – Forecast for African 850 hPa winds (“easterly waves”). No filtering required
from a series of 2-day Forecasts

27. MJO 11 Nov. 2011 Sat+ECMWF analysis
ECMWF Training Course
02 May 2000
MJO 11 Nov Sat+ECMWF analysis
U850
U200
@ECMWF
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28. Wavenumber frequency Diagrams of OLR

29. Wavenumber frequency Diagrams of OLR same as previous but latest cycle and background spectrum substracted
Cy38r1 (2012)
NOAA Satellite

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 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

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 m

32. 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

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 m

36. Midlatitude Convection (6) Forcing of ageostrophic circulations/convection in the right entrance and left exit side of upper-level Jet
Acceleration/deceleration of Jet
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

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:
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/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

40. Summary: What is convection doing, where does it occur
ECMWF Training Course
02 May 2000
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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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)
ECMWF Training Course
02 May 2000
Buoyancy - physics of Archimedes (1)
Body in a fluid
Assume fluid to be in hydrostatic equlibrium
Forces:
Top
Bottom
Gravity
Net Force:
Acceleration:
Emanuel, 1994
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43. Buoyancy (2) Vertical momentum equation: Neglect second order terms
ECMWF Training Course
02 May 2000
Buoyancy (2)
Vertical momentum equation:
Neglect second order terms
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44. B - buoyancy acceleration
ECMWF Training Course
02 May 2000
Buoyancy (3) = = =
B - buoyancy acceleration
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45. Buoyancy (4) Contributions
ECMWF Training Course
02 May 2000
Buoyancy (4) Contributions
Buoyancy acceleration:
Dry air:
Often (but not always):
Then
Hence
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46. Buoyancy (5) Contributions
ECMWF Training Course
02 May 2000
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
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47. Non-hydrostat. Pressure gradient effects
ECMWF Training Course
02 May 2000
Non-hydrostat. Pressure gradient effects 15 10 5
-0.02
0.02
0.04
-0.04 P
Z (km)
(ms-2) B
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)
CRM analysis of the terms
Guichard and Gregory
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48. Convective Available Potential Energy (CAPE)
ECMWF Training Course
02 May 2000
Definition:
Example:
Much larger than observed - what’s going on ?
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.
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49. Convection in thermodynamic diagrams (1) using Tephigram/Emagram
ECMWF Training Course
02 May 2000
LNB
CAPE
Idealised Profile
CIN
LFC
LCL
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50. Θe is conserved during moist adiabatic ascent
ECMWF Training Course
02 May 2000
Convection in thermodynamic diagrams (2) using equivalent Potential Temperature and saturated equivalent Potential Temperature
GATE Sounding θ
Θe is conserved during moist adiabatic ascent
CAPE
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 minimum level of θe in the mid-troposphere.
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51. Importance of choice of moist adiabat in CAPE calculations
ECMWF Training Course
02 May 2000
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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52. Importance of choice of moist adiabat in CAPE calculations
ECMWF Training Course
02 May 2000
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
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53. Non-dimensional dynamical equations
no distinction has been made between a horizontal and vertical length scale L
If we now express the geopotential as a hydrostatic Φ0 and non-hydrostatic contribution, then the non-hydrostatic vertical acceleration can be expressed through a perturbation term
where

54. Non-dimensional dynamical equations
Dividing by UU/L one obtains the final non-dimensional form
where the Richardson number, the Rossby number and the Reynolds number become apparent.
In atmospheric motions the Reynolds number is very large, so the molecular diffusion term is neglected. Also, for large scales the Rossby number is of O(1) or smaller, only for small scales it becomes large and the Coriolis term can be neglected.

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 entraining plume cloud top entrainment
ECMWF Training Course
02 May 2000
Mixing models
undiluted
entraining plume
cloud top entrainment
stochastic mixing
after Raymond,1993
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57. Effect of mixing on parcel ascent
ECMWF Training Course
02 May 2000
Effect of mixing on parcel ascent
No dilution
Moderate dilution
Heavy dilution
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58. Large-scale effects of convection (1) Q1 and Q2
ECMWF Training Course
02 May 2000
Large-scale effects of convection (1) Q1 and Q2
Thermodynamic equation (dry static energy) :
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
Define averaging operator over area A such that:
and
Apply to thermodynamic equation, neglect horizontal second order terms, use averaged continuity equation:
In convective regions these terms will be dominated by convection
“sub-grid” terms
“large-scale observable” terms
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59. Large-scale effects of convection (2) Q1 and Q2
ECMWF Training Course
02 May 2000
Large-scale effects of convection (2) Q1 and Q2
Apparent heat source
Define:
Apparent moisture sink
Analogous:
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:
with
Moist static energy
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60. Large-scale effects of convection (3) vertical integrals of Q1 and Q2
ECMWF Training Course
02 May 2000
Large-scale effects of convection (3) vertical integrals of Q1 and Q2
Surface Precipitation flux
Surface sensible Heat flux
Surface Precipitation
Surface latent Heat flux
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61. Large-scale effects of convection (3) Deep convection
ECMWF Training Course
02 May 2000
Large-scale effects of convection (3) Deep convection
Tropical Atlantic
Yanai and Johnson, 1993
Tropical Pacific
Yanai et al., 1973, JAS
Note the typical tropical maximum of Q1 at 500 hPa, Q2 maximum is lower and typically at 800 hPa
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62. Large-scale effects of convection (5) Shallow convection
ECMWF Training Course
02 May 2000
Large-scale effects of convection (5) Shallow convection
500
600
700
800
900
1000 -2 2
-10 -6
-14 Q2 Q1 QR
(K/day)
P(hPa)
q-difference of simulation without and with shallow convection. Without shallow boundary-layer is too moist and upper-troposphere too dry ! -2
Nitta and Esbensen, 1974, MWR
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63. Effects of mesoscale organization The two modes of convective heating
ECMWF Training Course
02 May 2000
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
P(hPa)
300
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64. Zonal average convective Q1 in IFS
P (hPa)
Latitude

65. Convective quasi-equilibrium (1)
ECMWF Training Course
02 May 2000
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.
v (700 hPa)
-w (700 hPa)
Precipitation
Observational evidence:
GARP Atlantic Tropical Experiment (1974)
Thompson et al., JAS, 1979
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66. ECMWF Training Course
02 May 2000
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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