Numerical Weather Prediction Parametrization of diabatic processes Convection I

1
Numerical Weather Prediction Parametrization of
diabatic processesConvection I

• Peter Bechtold and Christian Jakob

2
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 !!!

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_at_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
  lAtmosphère, 1975 Institut Royal météorologique
  de Belgique
• Bohren and Albrecht, 1998 Atmospheric
  Thermodynamics.OUP

APAcademic Press OUPOxford University Press
5
How does it look like ?
6
Moist convection Global
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
• 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
Convection and tropical circulations (1)Its
raining again 2000/2001 rainfall rate as
simulated by IFS Cy33r1 (spring 2008) and
compared to GPCP obs
about 3 mm/day is falling globally, but most i.e.
5-7 mm/day in the Tropics
11
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
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
Analytical solve shallow water equations
19
Convection and tropical circulations (7)
The KELVIN wave
V0

• 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 (n1) Equatorial Rossby wave

• Symmetric
• KEgtPE
• 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

• 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 they 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
  outflowdivergence 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 to 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)
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
Hovmoeller plots as an easy way to plot wave
(propagation)
Analysis 10.8-9.9 2005
Comparison Analysis Forecast for African 850
hPa winds (easterly waves). No filtering
required
from a series of 2-day Forecasts
26
Wavenumber frequency Diagrams of OLR
27
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 lt1K/1000 km and in the absence
  of precipitation the vertical motions(subsidence)
  tend to balance the cooling through IR radiation
  loss w d?/dz d?/dt_rad -1-2 K/day gt 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 gt 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

28
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
29
Midlatitude Convection (2)Its 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
30
Midlatitude Convection (3) European MCSs (Morel
and Sénési, 2001)Density Map of Triggering ..
over Orography
31
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)
32
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
33
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
34
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.

35
Midlatitude Convection (8a) Conceptual model of
a rotating mesoscale convective system tornadic
thunderstorm (from Lemon and Doswell, 1979)
36
Midlatitude Convection (8b) Origin and mechanism
of generation of vertical vorticity
A useful quantity in estimating the storm
intensity is the bulk Richardson number
RCAPE/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
37
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 -gt 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 RN H/f (NBrunt Vaisala Freq,
  fCoriolis parameter, Htropopause height) is
  infinite, and therefore the effects are not
  locally bounded, but spread globally via gravity
  waves throwing a stone in a lake

38
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 !
39
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 F0 and non-hydrostatic contribution,
then the non-hydrostatic vertical acceleration
can be expressed through a perturbation term
where
40
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.
41
Buoyancy - physics of Archimedes (1)
Body in a fluid
Forces
Emanuel, 1994
42
Buoyancy (2)
Vertical momentum equation
Neglect second order terms
43
Buoyancy (3)
44
Buoyancy (4)Contributions
Dry air
45
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
46
Non-hydrostat. Pressure gradient effects
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
47
Convective Available Potential Energy (CAPE)
Definition
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.
48
Thermodynamic diagrams
Tephigram
49
Convection in thermodynamic diagrams (1)using
Tephigram/Emagram
Idealised Profile
50
Convection in thermodynamic diagrams (2)using
equivalent Potential Temperature and saturated
equivalent Potential Temperature
GATE Sounding
?
Te is conserved during moist adiabatic ascent
CAPE
Tesat(T)
Te(T,q)
Note that no CAPE is available for parcels
ascending above 900 hPa and that the tropical
atmosphere is stable above 600 hPa (?e increases)
downdrafts often originate at the minimum level
of ?e in the mid-troposphere.
51
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
52
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
53
Mixing and 3D flowsubcloud and cloud-layer
Circulations
54
Mixing models
after Raymond,1993
55
Effect of mixing on parcel ascent
56
Large-scale effects of convection (1) Q1 and Q2
Thermodynamic equation (dry static energy)
why use s and not T s CpTgz ds/dz CpdT/dzg If
dT/dz-g/Cp (dry adiabatic lapse rate), then ds0
large-scale observable terms
57
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.
58
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
59
Large-scale effects of convection (3)Deep
convection
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
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
61
Effects of mesoscale organization The two modes
of convective heating
Effects on heating
62
Zonal average convective Q1 in IFS
P (hPa)
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
GARP Atlantic Tropical Experiment (1974)
Thompson et al., JAS, 1979
64
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)