Numerical Weather Prediction Parameterization of diabatic processes Convection III The ECMWF convect

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Numerical Weather Prediction Parameterization of
diabatic processesConvection IIIThe ECMWF
convection scheme

• Christian Jakob and Peter Bechtold

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A bulk mass flux schemeWhat needs to be
considered
Link to cloud parameterization
Entrainment/Detrainment
Type of convection shallow/deep
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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Large-scale budget equations M?w Mugt0 Mdlt0
Heat (dry static energy)
Humidity
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Large-scale budget equations
Momentum
Cloud condensate
Cloud fraction (supposing fraction 1-a of
environment is cloud free)
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Large-scale budget equations
Nota These tendency equations have been written
in flux form which by definition is conservative.
It can be solved either explicitly (just apply
vertical discretisation) or implicitly (see
later). Other forms of this equation can be
obtained by explicitly using the derivatives
(given on Page 10), so that entrainment/detrainmen
t terms appear. The following form is particular
suitable if one wants to solve the mass flux
equations with a Semi-Lagrangien scheme note
that this equation is valid for all variables T,
q, u, v, and that all source terms (apart from
melting term) have cancelled out
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Occurrence of convectionmake a first-guess
parcel ascent

• 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
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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Cloud model equations updraughtsE and D are
positive by definition
Mass (Continuity)
Heat
Humidity
Liquid Water/Ice
Momentum
Kinetic Energy (vertical velocity) use height
coordinates
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Downdraughts
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 downdraughtsE and D are
defined positive
Mass
Heat
Humidity
Momentum
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Entrainment/Detrainment (1)
Updraught
Turbulent entrainment/detrainment
e and d are generally given in units (1/m) since
(Simpson 1971) defined entrainment in plume with
radius R as e0.2/R for convective clouds R
is of order 1500 m for deep and R100 or 50 m for
shallow
However, for shallow convection detrainment
should exceed entrainment (mass flux decreases
with height this possibility is still
experimental
Organized entrainment is linked to moisture
convergence, but only applied in lower part of
the cloud (this part of scheme is questionable)
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Entrainment/Detrainment (2)
Organized detrainment
Only when negative buoyancy (K decreases with
height), compute mass flux at level z?z with
following relation
with
and
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Precipitation
Liquidsolid precipitation fluxes
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
Simple representation of Bergeron process
included in c0 and lcrit
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Precipitation
Fallout of precipitation from updraughts
Evaporation of precipitation
1. Precipitation evaporates to keep downdraughts
saturated
2. Precipitation evaporates below cloud base
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Closure - Deep convection
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) The
quantity required by the parametrization is the
cloud base mass-flux. How can the above
assumption converted into this quantity ?
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Closure - Deep convection
Assume
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Closure - Deep convection
i.e., ignore detrainment
where Mn-1 are the mass fluxes from a previous
first guess updraft/downdraft computation
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Closure - Shallow convection
Based on PBL equilibrium what goes in must go
out - no downdraughts
With
and
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Closure - Midlevel convection
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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Vertical Discretisation
Fluxes on half-levels, state variable and
tendencies on full levels
cu
GP,u
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Numerics solving Tendency advection equation
explicit solution
if ? T,q
Use vertical discretisation with fluxes on half
levels (k1/2), and tendencies on full levels k,
so that
In order to obtain a better and more stable
upstream solution (compensating subsidence,
use shifted half-level values to obtain
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Numerics implicit advection
if ? T,q
Use temporal discretisation with on
RHS taken at future time and not at
current time
For upstream discretisation as before one
obtains
gt Only bi-diagonal linear system, and tendency
is obtained as
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Numerics Semi Lagrangien advection
if ? T,q
Advection velocity
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Convective source terms - Cloud fraction
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Convective source terms - Cloud fraction
Mass-flux concept for transport of cloud mass
Is there any cloud mass produced in the grid box ?
Mu - only transport in the vertical
Du - only transport of cloud mass from updraught
to environment
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Convective source terms - Cloud fraction
Eu - transports environment air into updraughts
(1-a) parts of this air are not cloudy, but will
be converted into cloudy air inside the
updraught, hence
Introduce source and transport term into , use
convection scheme, do a little algebra.
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Tracer transport experiments(1) Single-column
simulations Stability
Surface precipitation continental convection
during ARM
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Tracer transport experiments(1) Stability in
implicit and explicit advection
instabilities

• Implicit solution is stable.
• If mass fluxes increases, mass flux scheme
  behaves like a diffusion scheme well-mixed
  tracer in short time

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Tracer transport experiments(2) Single-column
against CRM
Surface precipitation tropical oceanic
convection during TOGA-COARE
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Tracer transport experiments(2) IFS
Single-column and global model against CRM
Boundary-layer Tracer

• Boundary-layer tracer is quickly transported up
  to tropopause
• Forced SCM and CRM simulations compare
  reasonably well
• In GCM tropopause higher, normal, as forcing in
  other runs had errors in upper troposphere

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Tracer transport experiments(2) IFS
Single-column and global model against CRM
Mid-tropospheric Tracer

• Mid-tropospheric tracer is transported upward by
  convective draughts, but also slowly subsides due
  to cumulus induced environmental subsidence
• IFS SCM (convection parameterization) diffuses
  tracer somewhat more than CRM