The parameterization of moist convection

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The parameterization of moist convection

• Peter Bechtold, Christian Jakob, David Gregory
• With contributions from J. Kain (NOAA/NSLL)
• Original ECMWF lecture has been adjusted to fit
  into todays schedule
• Roel Neggers, KNMI

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Outline of second hour

• Parameterizing moist convection
• Aspects triggering, vertical distribution,
  closure
• Types of convection schemes
• The mass-flux approach
• The ECMWF convection scheme
• Flow chart
• Main equations
• Behavior

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Task of convection parameterization total Q1 and
Q2
To calculate the collective effects of an
ensemble of convective clouds in a model column
as a function of grid-scale variables. Hence
parameterization needs to describe
Condensation/Evaporation and Transport
Apparent heat source
Condensation/ Evaporation
Radiation
Transport
Apparent moisture sink
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Task of convection parameterizationin practice
this means
Determine occurrence/localisation of convection
Trigger
Determine vertical distribution of heating,
moistening and momentum changes
Determine the overall amount / intensity of the
energy conversion, convective precipitationheat
release
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Constraints for convection parameterization

• Physical
• remove convective instability and produce
  subgrid-scale convective precipitation
  (heating/drying) in unsaturated model grids
• produce a realistic mean tropical climate
• maintain a realistic variability on a wide range
  of time-scales
• produce a realistic response to changes in
  boundary conditions (e.g., El Nino)
• be applicable to a wide range of scales (typical
  10 200 km) and types of convection (deep
  tropical, shallow, midlatitude and
  front/post-frontal convection)
• Computational
• be simple and efficient for different
  model/forecast configurations (T799 (25 km), EPS,
  seasonal prediction T159 (125 km) )

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Types of convection schemes

• Moisture budget schemes
• Kuo, 1965, 1974, J. Atmos. Sci.
• Adjustment schemes
• moist convective adjustement, Manabe, 1965, Mon.
  Wea. Rev.
• penetrative adjustment scheme, Betts and Miller,
  1986, Quart. J. Roy. Met. Soc.,
  Betts-Miller-Janic
• Mass-flux schemes (bulkspectral)
• Entraining plume - spectral model, Arakawa and
  Schubert, 1974, Fraedrich (1973,1976), Neggers et
  al (2002), Cheinet (2004), all J. Atmos. Sci. ,
• Entraining/detraining plume - bulk model, e.g.,
  Bougeault, 1985, Mon. Wea. Rev., Tiedtke, 1989,
  Mon. Wea. Rev., Gregory and Rowntree, 1990, Mon.
  Wea . Rev., Kain and Fritsch, 1990, J. Atmos.
  Sci., Donner , 1993, J. Atmos. Sci., Bechtold et
  al 2001, Quart. J. Roy. Met. Soc.
• Episodic mixing, Emanuel, 1991, J. Atmos. Sci.

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Type I Kuo schemes
Closure Convective activity is linked to
large-scale moisture convergence what comes in
must rain out
Vertical distribution of heating and moistening
adjust grid-mean to moist adiabat
Main problem here convection is assumed to
consume water and not energy -gt . Positive
feedback loop of moisture convergence
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Type II Adjustment schemes
e.g. Betts and Miller, 1986, QJRMS
When atmosphere is unstable to parcel lifted from
PBL and there is a deep moist layer - adjust
state back to reference profile over some
time-scale, i.e.,
Tref is constructed from moist adiabat from cloud
base but no universal reference profiles for q
exist. However, scheme is robust and produces
smooth fields.
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Procedure followed by BMJ scheme
T
Tdew
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Type III Mass-flux schemes
Condensation term
Eddy transport term
Aim Look for a simple expression of the eddy
transport term
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The mass-flux approach
Reminder Reynolds averaging (boundary layer
lecture)
Hence
and therefore
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The mass-flux approachCloud Environment
decomposition
Fractional coverage with cumulus elements
Define area average
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The mass-flux approach

• Neglect subplume correlations
• Small area approximation

Make some assumptions
Then
Define convective mass-flux
Then
Mass flux
Excess of plume over enviroment
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The mass-flux approach
Plume model
With the above we can rewrite
To predict the influence of convection on the
large-scale with this approach we now need to
describe the convective mass-flux, the values of
the thermodynamic (and momentum) variables inside
the convective elements and the
condensation/evaporation term. This requires a
plume model and a closure.
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The entraining plume model
Entraining plume model
Mass
Detrainment rate
Entrainment rate
Interaction (mixing) with the plume environment
Area
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Bulk entraining plume models
Simplifying assumptions
1. Steady state plumes, i.e.,
Most mass-flux convection parametrizations today
still make that assumption, some however are
prognostic
2. Bulk mass-flux approach
A single bulk plume describes the effect of a
whole ensemble of clouds
Sum over all cumulus elements
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Substitution of bulk mass flux model into Q1 and
Q2
Combine
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Interpretation
I
II
III
Convection affects the large scales by
Heating through compensating subsidence between
cumulus elements (term I)
The detrainment of cloud air into the environment
(term II)
Evaporation of cloud and precipitation (term III)
Note The condensation heating does not appear
directly in Q1. It is however a crucial part of
the cloud model, where this heat is transformed
in kinetic energy of the updrafts.
Similar derivations are possible for Q2.
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Closures in mass-flux parameterizations
The plume model determines the vertical structure
of convective heating and moistening
(microphysics, variation of mass flux with
height, entrainment/detrainment assumptions). The
determination of the overall magnitude of the
heating (i.e., surface precipitation in deep
convection) requires the determination of the
mass-flux at cloud base. - Closure problem Types
of closures Deep convection Equilibrium in CAPE
or similar quantity (e.g., cloud work
function) Shallow convection Boundary-layer
equilibrium Mixed-layer turbulence closures
(e.g. Grant 2001 Neggers 2008,2009)
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CAPE closure - the basic idea
Find the magnitude of Mbc so that profile is
adjusted to reference profile
Principle can also be applied to boundary-layer
humidity / moist static energy
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Turbulence closures - the basic idea
Tie the magnitude of Mbc to sub-cloud layer
turbulence
Motivation cumulus thermals are observed to be
deeply rooted in the sub-cloud layer
Grant (2001)
wBsurface buoyancy flux hsubcloud
mixed-layer height a0.05 is updraft fraction
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Summary (1)

• Convection parameterizations need to provide a
  physically realistic forcing/response on the
  resolved model scales and need to be practical
• a number of approaches to convection
  parameterization exist
• basic ingredients to present convection
  parameterizations are a method to trigger
  convection, a cloud model and a closure
  assumption
• the mass-flux approach has been successfully
  applied to both interpretation of data and
  convection parameterization .

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The ECMWF convection schemeLets get technical

• Peter Bechtold and Christian Jakob
• Original ECMWF lecture has been adjusted to fit
  into todays schedule
• Roel Neggers, KNMI

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A bulk mass flux schemeWhat needs to be
considered
Link to cloud parameterization
Entrainment/Detrainment
Type of convection shallow/deep/midlevel
Cloud base mass flux - Closure
Downdraughts
Generation and fallout of precipitation
Where does convection occur
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Basic Features

• Bulk mass-flux scheme
• Entraining/detraining plume cloud model
• 3 types of convection deep, shallow and
  mid-level - mutually exclusive
• saturated downdraughts
• simple microphysics scheme
• closure dependent on type of convection
• deep CAPE adjustment
• shallow PBL equilibrium
• strong link to cloud parameterization -
  convection provides source for cloud condensate

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Main flow chart
callpar
IFS Documentation, Part IV Physical processes
Chapter V Convection
cucall
satur
cuini
cumastrn
cubasen
cuascn
cubasemcn
cuentr
cudlfsn
cuddrafn
cuascn
cubasemcn
cuentr
cuflxn
cudtdqn
cuccdia
cududv
custrat
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Convective terms in LS budget equations M?w
Mugt0 Mdlt0
cudtdqn
Heat (dry static energy)
Humidity
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Convective terms in LS budget equations
cududv
Momentum
Cloud condensate
Source terms in cloud-scheme
Cloud fraction (supposing fraction 1-a of
environment is cloud free)
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Occurrence of convection (triggering)make a
first-guess parcel ascent
cubasen
cubasemcn

1. Test for shallow convection add T and q
   perturbation based on turbulence theory to
   surface parcel. Do ascent with w-equation and
   strong entrainment, check for LCL, continue
   ascent until wlt0. If w(LCL)gt0 and
   P(CTL)-P(LCL)lt200 hPa shallow convection

2) Now test for deep convection with similar
procedure. Start close to surface, form a 30hPa
mixed-layer, lift to LCL, do cloud ascent with
small entrainmentwater fallout. Deep convection
when P(LCL)-P(CTL)gt200 hPa. If not . test
subsequent mixed-layer, lift to LCL etc. and so
on until 700 hPa
T
Tdew
3) If neither shallow nor deep convection is
found a third type of convection midlevel
is activated, originating from any model level
above 500 m if large-scale ascent and RHgt80.
LCL
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Plume model equations updraftsE and D are
positive by definition
cuascn
Mass (Continuity)
Heat
Humidity
Liquid Water/Ice
Momentum
Kinetic Energy (vertical velocity) use height
coordinates
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Downdrafts
cudlfsn
cuddrafn
1. Find level of free sinking (LFS) highest model
level for which an equal saturated mixture of
cloud and environmental air becomes negatively
buoyant
2. Closure
3. Entrainment/Detrainment turbulent and
organized part similar to updraughts (but
simpler)
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Cloud model equations downdraftsE and D are
defined positive
cuddrafn
Mass
Heat
Humidity
Momentum
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Entrainment/Detrainment (1)
cuentr
e and d are generally given in units (m-1) since
(Simpson 1971) defined entrainment in plume with
radius R as e0.2/R for convective clouds R
is of order 500-1000 m for deep and R50-100 m
for shallow
?
?
Scaling function to mimick a cloud ensemble
Constants
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Entrainment/Detrainment (2)
cuentr
Organized detrainment
Only when negative buoyancy (K decreases with
height), compute mass flux at level z?z with
following relation
?org
?org
Mu
with
Updraft mass flux
and
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Precipitation fluxes
cuflxn
Two interacting shafts Liquid (rain) and solid
(snow)
Where Prain and Psnow are the fluxes of precip in
form of rain and snow at pressure level p. Grain
and Gsnow are the conversion rates from cloud
water into rain and cloud ice into snow. The
evaporation of precip in the downdraughts edown,
and below cloud base esubcld, has been split
further into water and ice components. Melt
denotes melting of snow.
Generation of precipitation in updraughts
(Sundqvist)
Simple representation of Bergeron process
included in c0 and lcrit
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Precipitation
cuflxn
Fallout of precipitation from updraughts
Evaporation of precipitation (Kessler)
1. Precipitation evaporates to keep downdraughts
saturated
2. Precipitation evaporates below cloud base
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Closure - Deep convection
cumastrn
Convection counteracts destabilization of the
atmosphere by large-scale processes and radiation
- Stability measure used CAPE Assume that
convection reduces CAPE to 0 over a given
timescale, i.e.,

• Originally proposed by Fritsch and Chappel,
  1980, JAS
• Implemented at ECMWF in December 1997 by Gregory
  (Gregory et al., 2000, QJRMS), using a constant
  time-scale that varies only as function of model
  resolution (720s T799, 1h T159)
• The time-scale is a very important quantity and
  has been changed in Nov. 2007 to be
• equivalent to the convective turnover
  time-scale which is
  defined by the cloud thickness divided by the
  cloud average vertical velocity, and further
  scaled by a factor depending linearly on
  horizontal model resolution (it is typically of
  order 1.3 for T799 and 2.6 for T159)
• Purpose Estimate the cloud base mass-flux. How
  can we get this?

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Closure - Deep convection
cumastrn
Assume
Now use this equation to back out the cloud base
mass flux Mu,b
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Closure - Deep convection
cumastrn
The idea assume stabilization is mainly caused
by compensating subsidence
?v
i.e., ignore detrainment
Me
Mc
where Mt-1 are the mass fluxes from a previous
first guess updraft/downdraft computation
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Closure - Shallow convection
cumastrn
Based on PBL equilibrium for moist static energy
h what goes in must go out - including
downdraughts
Mu,b
cbase
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Closure - Midlevel convection
cumastrn
Roots of clouds originate outside PBL assume
midlevel convection exists if there is
large-scale ascent, RHgt80 and there is a
convectively unstable layer Closure
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Studying model behavior at process level
Single column model (SCM) simulation
Time-integration of a single column of sub-grid
parameterizations in isolated mode, using
prescribed large-scale forcings
sw
lw
free troposphere
subsidence
cloud layer
PBL
advection
mixed layer
Advantages computational efficiency
model transparency good for studying
interactions between fast parameterized physics
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Behavior Single column model (SCM) experiments
Surface precipitation continental convection
during ARM
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Behavior Single column model (SCM) experiments
SCM simulation at Cabauw, 12-15 May 2008
Deep convective plume, depositing cloud water at
8km
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Behavior Single column model (SCM) experiments
SCM simulation at Cabauw, 31 May 3 June 2008
Deep convective plumes
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