1. ECMWF Training Course Peter Bechtold
02 May 2000
Numerical Weather Prediction Parametrization of diabatic processes Convection I: an overview
Peter Bechtold
Moist Processes

2. Convection Parametrisation and Dynamics - Text Books
ECMWF Training Course
02 May 2000
Convection Parametrisation and Dynamics - Text Books
Yano&Plant (Editors), 2015: Parameterization of atmospheric convection. World scientific, Imperial College Press
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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3. Convection=heat the bottom&cool the top
Pre-frontal deep convection July 2010 near Baden-Baden Germany
Rayleigh-Benard cellular convection
Classic plume experiment

4. Outline General: Convection and tropical circulations Tropical waves
ECMWF Training Course
02 May 2000
Outline
General:
Convection and tropical circulations
Tropical waves
Middle latitude 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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5. It’s raining again… 2000-2003 annual precipitation rate from IFS Cy42r1 (2016) GPCP2.2 dataset
about mm/day is falling globally, but most i.e. 5-7 mm/day in the Tropics

6. 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, for Temperature there is on average radiative-convective equilibrium; and convective-dynamic equilibrium over the large-scale disturbance, whereas for moisture there is roughly an equilibrium between dynamical transport (moistening) and convective drying Global Budgets are very similar
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7. Distribution of convective clouds
Johnson et al., 1999, JCL
Tri-modal: Shallow cumulus, Congestus attaining the melting level, Deep penetrating convection

8. Distribution of deep and shallow IFS Cy40r1 (2014)
Deep type including congestus

9. ECMWF Training Course
02 May 2000
Convection and tropical circulations (1) ITCZ and the Hadley meridional circulation: the role of trade-wind cumuli and deep tropical towers
Moist Processes

10. ECMWF Training Course
02 May 2000
Convection and tropical circulations (2) The Walker zonal Circulation and SST coupling
From Salby (1996)
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11. Rossby, Kelvin, MJO and African easterly Waves
Analytical: solve shallow water equations (see Lecture Note)

12. The Kelvin wave The n=1 Rossby wave
V=0, eastward moving ~18 m/s
sym. around equator
OLR anomaly shaded, winds max at equator
westward moving ~5 m/s
sym. around equator

13. Wavenumber frequency Diagrams of OLR
ECMWF Analysis
Cy40r1 6y (2014)
software courtesy Michael Herman (New Mexico Institute)
(all spectra have been divided by their own= smoothed background)

14. Rossby & MJO 5.3.2015-16.3 2015 Forecast base time 2015 03 09
ECMWF Training Course
02 May 2000
Forecast base time
How does it look, on top we have a satellite animation for March 2015, below the Rossby wave filtered OLR and lowest panel is the MJO filtered. What you see in the West Pacific is a strong MJO, spinning up two cyclones and a strong Rossby signal. Another interesting phenomenon is the enhanced convection over South America that is actually caused by a Rossby wave coming in.
Moist Processes

15. Kelvin Rossby & MJO 5.3.2015-16.3 2015 Forecast base time 2015 03 09
ECMWF Training Course
02 May 2000
Forecast base time
If we now also add the Kelvin filtered OLR on top, the we see for the MJO we have both a Kelvin and Rossby wave contribution. This product is new and is maintained in FD by Fernando Prates
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16. Normal mode projection and filtering
ECMWF Training Course
02 May 2000
Žagar et al. (Geosc. Mod. Dev. 2015)
850 hPa
The difference to what we did previously is that we apply the software to each 3D analysis field separately and then concatenate the fields to obtain a time series. Top is a time series of the full IFS analysis fields of wind and geopotential at 850 hPa for March 2015, below is Kelvin mode and below the first 5 rotational modes – so the circulation and also the MJO are mainly rotational. Linus has installed and maintains the software in FD and we are just starting to use it.
Moist Processes

17. Kelvin waves: vertical T-anomalies
ECMWF Training Course
Kelvin waves: vertical T-anomalies
02 May 2000
At z~10 km, warm anomaly and convective heating are in phase, leading to :
the conversion of potential in kinetic energy = αω
The generation of potential energy = N Q
The vertical structure of the wave anomalies is usually recovered by regression. Here it is done by taking a Kelvin wave filtered time series of the OLR and regress at each location where radiosondes are available in the West Pacific and at each vertical level the observed temperature time series to the Kelvin filtered OLR. So top is for the radiosonde observations and bottom are the results from a 10-year IFS run at T255 with Cy40r1 using the results at all the radiosonde locations.
So one finds the characteristic tilted structure, convection occurs at lag 0 which means that at 10 km warm anomaly and convective heating are in phase. The interaction of the convection with the wave occurs through the conversion of potential in kinetic energy and the generation of potential energy – the first to show this was Glen Shutts
see also G. Shutts ( 2006, Dyn. Atmos. Oc.)
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18. The MJO over Indian Ocean
ECMWF Training Course
02 May 2000
The MJO over Indian Ocean
U850
U200
27 November 2011: Meteosat 7 + ECMWF Analysis
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19. African Easterly waves
Hovmoeller diagrams as an easy way to plot waves (propagation + amplitude)
700 hPa wind, MSLP, and precip

20. Summary: the weather and thermal equilibria
ECMWF Training Course
02 May 2000
Summary: the weather and thermal equilibria
w ~ -0.5 cm/s
subsidence
~0.5 K/100 m
J/kg
Just two exercises to put the things further into numbers
100 mm/day precipitation heats the atmospheric column by 2867 W/m2 or by 25 K/day on average. This heating must be compensated by uplifting of
w ~ 10 cm/s  heavy precip/convection requires large-scale perturbation.
Moist Processes

21. Summary: effects and cause of convection
ECMWF Training Course
02 May 2000
Summary: effects and cause of convection
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 picture (not true for diurnal cycle convection!) is to consider it as reacting to the large-scale environment (e.g. tropical waves, mid-latitude frontal systems) =“quasi-equilibrium”; shallow convection redistributes moisture and heat
The effect of convection (local heat source) is fundamentally different in the middle latitudes 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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22. Buoyancy (1)- Archimedes said ‘Eureka!’
ECMWF Training Course
02 May 2000
Buoyancy (1)- Archimedes said ‘Eureka!’
Body in a fluid
Assume fluid to be in hydrostatic equlibrium
Forces:
Top
Bottom
Gravity
Net Force:
Acceleration:
Emanuel, 1994
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23. 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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24. B - buoyancy acceleration
ECMWF Training Course
02 May 2000
Buoyancy (3) = = =
B - buoyancy acceleration
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25. Buoyancy (4) T and P and Contributions
ECMWF Training Course
02 May 2000
Buoyancy (4) T and P and Contributions
Buoyancy acceleration:
Dry air:
Often (but not always):
Then
Hence
Moist Processes

26. Buoyancy (5) moist atmosphere
ECMWF Training Course
02 May 2000
Buoyancy (5) moist atmosphere
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
Moist Processes

27. 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
Moist Processes

28. 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.
Moist Processes

29. 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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30. 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.
Moist Processes

31. Mixing and 3D flow subcloud and cloud-layer Circulations
From high-resolution LES simulation (dx=dy=50 m) Vaillancourt, You, Grabowski, JAS 1997

32. 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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33. Effect of mixing on parcel ascent
ECMWF Training Course
02 May 2000
Effect of mixing on parcel ascent
No dilution
Heavy dilution
Moderate dilution
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34. 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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35. Large-scale effects of convection Q1 and Q2
ECMWF Training Course
02 May 2000
Large-scale effects of convection 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
Moist Processes

36. Large-scale effects of convection (2) vertical integrals of Q1 and Q2
ECMWF Training Course
02 May 2000
Large-scale effects of convection (2) vertical integrals of Q1 and Q2
Surface sensible Heat flux
Surface Precipitation flux
Surface latent Heat flux
Surface Precipitation
Moist Processes

37. Large-scale effects of convection (3)
ECMWF Training Course
02 May 2000
Large-scale effects of convection (3)
Budgets from Obs: Tropical Pacific
Yanai et al., 1973, JAS
courtesy Ji-Eun Kim and Chidong Zhang
Budgets Obs&IFS: Indian Ocean
Note the typical tropical maximum of Q1 at 500 hPa, Q2 maximum is lower and typically around hPa
Moist Processes

38. ECMWF Training Course
02 May 2000
Effects of mesoscale organization convective and stratiform heating modes
700 -2
(K/day)
convective
stratiform
total
1000
500
200
100 2 4 6
P(hPa)
300
Moist Processes

39. Zonal mean convective tendencies (deep & shallow) July 2013 and mass flux in IFS
Heating moistening
cloud layer drying subcloud layer

40. Convective quasi-equilibrium
ECMWF Training Course
02 May 2000
Convective quasi-equilibrium
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
Moist Processes

41. 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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