Numerical Weather Prediction Parametrization of diabatic processes The ECMWF cloud parametrization

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Numerical Weather Prediction Parametrization of
diabatic processesThe ECMWF cloud parametrization

• tompkins_at_ecmwf.int

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The ECMWF Scheme Approach

• 2 Additional prognostic variables
• Cloud mass (liquid ice)
• Cloud fraction
• Sources/Sinks from physical processes
• Deep and shallow convection
• Turbulent mixing
• Cloud top turbulence, Horizontal Eddies
• Diabatic or Adiabatic Cooling or Warming
• Radiation, dynamics...
• Precipitation processes
• Advection

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Basic assumptions

• Clouds fill the whole model layer in the vertical
  (fractioncover)
• Clouds have the same thermal state as the
  environmental air
• rain water/snow falls out instantly but is
  subject to evaporation/sublimation and melting in
  lower levels
• cloud ice and water are distinguished only as a
  function of temperature - only one equation for
  condensate is necessary

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Schematic of Source/Sink terms
cloud
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ECMWF prognostic scheme - Equations
Cloud liquid water/ice ql
Cloud fraction C
A Large Scale Advection S Source/Sink due
to SCV Source/Sink due due to shallow
convection (not post-29r1) SBL Source/Sink
Boundary Layer Processes (not post-29r1) c
Source due to Condensation e Sink due to
Evaporation Gp Precipitation sink D Detrainment
from deep convection Last term in liquid/ice
Cloud top entrainment (not post-29r1)
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Linking clouds and convection

• Basic idea
• use detrained condensate as a source for cloud
  water/ice
• Examples
• Ose, 1993, Tiedtke 1993, DelGenio et al. 1996,
  Fowler et al. 1996
• Source terms for cloud condensate and fraction
  can be derived using the mass-flux approach to
  convection parametrization.

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Convective source terms - Water/Ice
Standard equation for mass flux convection
scheme ECHAM, ECMWF and many others...
(Muqlu)k-1/2
k-1/2
k
Duqlu
k1/2
(Muqlu)k1/2
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Convective source terms - Cloud Fraction
Can write similar equation for the cloud
fraction Factor (1-a) assumes that the
pre-existing cloud is randomly distributed and
thus the probability of the convective event
occurring in cloudy regions is equal to a
k-1/2
k
Du
k1/2
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Stratiform cloud formation
Local criterion for cloud formation q gt qs(T,p)
Two ways to achieve this in an unsaturated
parcel increase q or decrease qs
Processes that can increase q in a gridbox
Advection
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Advection and cloud formation
Advection does not mix air !!! It merely moves it
around conserving its properties, including
clouds.
Because of the non-linearity of qs(T), q2 gt qs(T2)
This is a numerical problem and should not be
used as cloud producing process!
Would also be preferable to advect moist
conserved quantities instead of T and q
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Stratiform cloud formation
Postulate The main (but not only) cloud
production mechanisms for stratiform clouds are
due to changes in qs. Hence we will link
stratiform cloud formation to dqs/dt.
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Stratiform cloud formation
The cloud generation term is split into two
components
Existing clouds
New clouds
And assumes a mixed uniform-delta total water
distribution
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Stratiform cloud formation Existing Clouds
C
G(qt)
qt
Already existing clouds are assumed to be at
saturation at the grid-mean temperature. Any
change in qs will directly lead to condensation.
Note that this term would apply to a variety of
PDFs for the cloudy air (e.g. uniform
distribution)
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Stratiform cloud formation
Formation of new clouds
Due to lack of knowledge concerning the variance
of water vapour in the clear sky regions we have
to resort to the use of a critical relative
humidity
RHgtRHcrit
RHltRHcrit
C
G(qt)
1-C
qt
term inactive
RHcrit 80 is used throughout most of the
troposphere
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Evaporation of clouds
Processes ee1e2

• Large-scale descent and cumulus-induced subsidence

• Diabatic heating

• Turbulent mixing (E2)

Note Incorrectly assumes mixing only reduces
cloud cover and liquid!
GCM grid cell Dx
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Problem Reversible Scheme?
Cooling Increases cloud cover
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Precipitation generation
Mixed Phase and water clouds
Sundqvist, 1978
C010-4s-1
C1100
Collection
C20.5
Bergeron Process
qlcrit0.3 g kg-1
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Precipitation generation Pre 25r3
Pure ice clouds (Tlt250 K)
Two size classes of ice, boundary at 100 mm
Ice falling in cloud below is source for ice in
that layer, ice falling into clear sky is
converted into snow
IWCgt100 falls out as snow within one timestep
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Precipitation generation Post 25r3
Pure ice clouds (Tlt250 K)
Two size classes of ice, boundary at 100 mm
Ice falling in cloud below is source for ice in
that layer, ice falling into clear sky is
converted into snow
IWCgt100 falls according to Heymsfield and Donner
(1990)
Small Ice has fixed fall speed of 0.15 m/s
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Numerical Integration
In both prognostic equations for cloud cover and
cloud water all source and sink terms are treated
either explicitly or Implicitly. E.g
Solve analytically as ordinary differential
equations
(provided Kjgt0)
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Numerical Integration

• How is this accomplished?
• If a term contains a nth power for example

• The first order approximation is used

Beginning of timestep value
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Numerical Aspects Ice fall speeds

• Remember the original ice assumptions?

IWCgt100 falls out as snow within one timestep
Solved implicitly to prevent noise
Can calculate fall speed implied by CFL limit
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Resulting Ice Fall Speed T511 pre-25r3
LARGE ICE
SMALL ICE
IN CLOUD ICE MIXING RATIO (KG/KG)
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Resulting Ice Fall Speed T95 pre-25r3
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Resulting Ice Fall SpeedT95 Post 25r3
SMALL ICE
CFL
LARGE ICE
Fall Speed (m/s)
Fraction Small Ice
MEAN ICE
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Numerical Aspects - Vertical Advection
Problem we neglect vertical subgrid-scales
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Ice sedimentation Further Numerical Problems
Since we only allow ice to fall one layer in a
timestep, and since the cloud fills the layer in
the vertical, the cloud lower boundary is
advected at the CFL rate of Dz / Dt
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Numerical Aspects - Ice settling
Problem A bad assumption and numerics (always
imperfect) lead to a realistic looking result.
Start with single layer ice cloud in level k -
expect that settling moves some of the ice into
the next layer and that some stays in this layer
due to size distribution.
1. We implicitly assume that all particles fall
with the same velocity - wrong
Assume Dt Dz / vice
Perfect numerics in this case - explicit scheme
Correct but not as expected
2. Use analytical integration
as expected but incorrect
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Planned Revision for 29r3 (sept 2005)To tackle
ice settling deficiency
ice fall speed
Advected Quantity (e.g. ice)
Options (i) Implicit numerics (ii) Time
splitting (iii) Semi-Lagrangian
Explicit Source/Sink
Implicit Source/Sink (not required for short
timesteps)
Implicit Upstream forward in time, jvertical
level ntime level
what is short?
Solution
Note For multiple X-bin bulk scheme (Xice,
graupel, snow) with implicit (D above)
cross-terms leads to set of linear algebraic
equations
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Improved Numerics in SCM Cirrus Case
100 vs 50 layer resolution
29r1 Scheme
which is which?
29r3 Scheme
time evolution of cloud cover and ice
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Precipitation evaporation and melting
Evaporation (Kessler 1969, Monogram)
Newtonian Relaxation to saturated conditions
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Precipitation Evaporation
Mimics radiation schemes by using a 2-column
approach of recording both cloud and clear
precipitation fluxes
This allows a more accurate assessment of
precipitation evaporation
NUMERICS Solved Implicitly to avoid numerical
problems
Jakob and Klein (QJRMS, 2000)
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Precipitation Evaporation

• Numerical Limiters have to be applied to
  prevent grid scale saturation

Clear sky region
Grid can not saturate
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Precipitation Evaporation

• Threshold for rainfall evaporation based on
  precipitation cover

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Critical relative humidity for precipitation
evaporation
RHcrit
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Clear sky Precipitation Fraction
0

• Instead can use overlap with clear sky humidity
  distribution
• Humidity in most moist fraction used instead of
  clear sky mean

Clear sky
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Cirrus Clouds, new homogeneous nucleation form
for 29r3

• Want to represent super-saturation and
  homogeneous nucleation
• Include simple diagnostic parameterization in
  existing ECMWF cloud scheme
• Desires
• Supersaturated clear-sky states with respect to
  ice
• Existence of ice crystals in locally subsaturated
  state
• Only possible with extra prognostic equation

GCM gridbox
C
Clear sky
Cloudy region
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Unlike parcel models, or high resolution LES
models, we have to deal with subgrid variability
GCM gridbox
qvcld ?
qvenv?
cloud
clear
I F S
C
Three items of information qv, qi, C (vapour,
cloud ice and cover)

• We know qc occurs in the cloudy part of the
  gridbox
• We know The mean in-cloud cloud ice
• What about the water vapour? In the bad-old-days
  was easy
• Clouds qvcldqs
• Clear sky qvenv(qv-Cqs)/(1-C) (rain evap and
  new cloud formation)

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The good-new-days assume no supersaturation can
exist
GCM gridbox
C
qvcld
qvenv
The bad old days No supersaturation
(qv-Cqs)/(1-C)
qs
1.
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From Mesoscale Model
qvenv
qvcld
GCM gridbox
Critical Scrit reached
uplifted box
qvcld reduces
qvenvqvcld
Artificial flux of vapour from clear sky to
cloudy regions
Assumption ignores fact that difference processes
are occurring on the subgrid-scale, and amounts
to an all-or-nothing scheme
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From GCM perspective
qvenv
qvcld
GCM gridbox
Critical Scrit reached
Difference to standard scheme is that
environmental humidity must exceed Scrit to form
new cloud
uplifted box
qvcld reduces to qs
qvenv unchanged
qi increases
microphysics
qi decreases
qvenvunchanged
No artificial flux of vapour from clear sky
from/to cloudy regions
Assumption seems reasonable BUT! Does not allow
nucleation or sublimation timescales to be
represented, due to hard adjustment
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RH PDFat 250hPaone month average
Aircraft observations
A Numerics and interpolation for default
model B The RH1 microphysics mode C Drop due
to GCM assumption of subgrid fluctuations in
total water
from Gierens et al 99
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The ECMWF cloud parametrization
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Summary of Tiedtke Scheme

• Scheme introduces two prognostic equations for
  cloud water and cloud mass
• Sources and sinks for each physical process -
• Many derived using assumptions concerning
  subgrid-scale PDF for vapour and clouds
• J More simple to implement than a prognostic
  statistical scheme since short cuts are
  possible for some terms. Also nicer for
  assimilation since prognostic quantities are
  directly observable
• L Loss of information (no memory) in clear sky
  (a0) or overcast conditions (a1) (critical
  relative humidities necessary etc). Difficult to
  make reversible processes.
• Nothing to stop solution diverging for cloud
  cover and cloud water. (e.g liquidgt0 while a0).
  More unphysical safety switches necessary.

Last Lecture Validation!
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ExampleProblem
M0 s-1
Gridbox
M1/3600 s-1
M1/3600 s-1

• Convection detrains into a clear-sky grid-box at
  a normalized rate of 1/3600 s-1. This is the
  highest level of convection so there is no
  subsidence from the layer above (see picture).
  How long does it take for the cloud cover to
  reach 50? State the assumptions made.
• The detrained air has a cloud liquid water mass
  mixing ratio of 3 g kg-1. If the conversion to
  precipitation is treated as a simple Newtonian
  relaxation (i.e. dql / dtprecip ql / tau)
  with a timescale of 2 hours, what is the
  equilibrium cloud mass mixing ratio?

Answers (1) 42 minutes (2) 2 g kg-1.