Can we use a statistical cloud scheme coupled to

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Can we use a statistical cloud scheme coupled to
convection and moist turbulence parameterisations
to simulate all cloud types? Colin
Jones CRCM/UQAM jones.colin_at_uqam.ca
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1-D TKE equation used in HIRLAM
A
B
C
D
A is buoyant production
B is shear production
C is transport (vertical diffusion of TKE) and
pressure force term.
D is dissipation of TKE ( l? is a typical length
scale for eddies responsible for TKE loss)
TKE evolution is dependent on subgrid scale
vertical fluxes which in turn are dependent on
TKE
lh,m follows ideas of Bougeault and Lacarrare
with wind shear included Via Richardson number.
Turbulence (and subgrid scale vertical transport)
is often larger inside clouds than in the
surrounding atmosphere. This is due to latent
heat release and cloud top radiative cooling
and/or entrainment which are strong sources of
turbulence inside clouds through the buoyant
production term A. It is important this term is
modelled correctly for an accurate description
of subgrid scale vertical transport by boundary
layer clouds.
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Moist conservative turbulence and statistical
cloud representation Turbulence phrased in moist
conservative variables (?l and rt) naturally
incorporates phase change effects in buoyancy
production term.
In the HIRLAM moist TKE scheme atmospheric static
stability plays a key role in determining
the Mixing length scales used in determining the
vertical fluxes of the conserved
variables. Atmospheric stability is calculated
relative to clear and cloudy portions of the
model grid box.
Cf is cloud fraction and appears in the vertical
stability and thus vertical eddy flux term
through both the resolved gradient and in
determining the mixing length
Cloud fraction can be calculated by the present
cloud scheme (external to Turbulence scheme) but
due to the fast nature of incloud turbulent
mixing this risks mis-matches in time and/or
space between moist turbulence and cloud fields
leading to potential numerical instability.
Better to use a cloud fraction embedded within
the turbulence scheme and directly influenced by
the degree of turbulent mixing, using the same
stability measures as used for calculating the
turbulent length scales and vertical fluxes.
(e.g. Statistical Clouds)
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The buoyancy flux term is the main generator of
TKE in boundary layer clouds and therefore is
crucial to model accurately. Following Cuijpers
Bechtold (1995) the buoyancy flux in a (partly)
cloud layer can be schematically represented by
N is cloud fraction and the 3rd term on the RHS
plays an important role in the buoyancy flux in
cloudy boundary layers with small cloud fractions
(Nlt0.4) where the buoyancy flux is increasingly
skewed (towards values dominated by the incloud
portion). In these types of cloudy boundary
Layers (say with Nlt0.1) the 2nd (clear sky) and
3rd (non-Gaussian) terms dominate the buoyancy
flux and by implication TKE evolution and
turbulent mixing lengths. fNG expresses the
contribution of the non-Gaussian (skewed) fluxes
of ?l and qt to the total buoyancy flux. fNG
increases rapidly with decreasing N (increasing
skewness) and like N and ql can be parameterised
in terms of the normalised saturation deficit Q1.
Introducing a variable s describing the effect of
changes in rt and Tl on the saturation state of
the grid box leads to a formualtion of Q1
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CRM and LES models can be used to explicitly
simulated cloud scale turbulence in a variety Of
cloud situations. These results can be used to
estimate ?s and develop expressions for N, ql and
fNG as a function of Q1
In these expressions ?s is the term linking the
subgrid scale variability in the saturation state
of the model grid box to the mean (sub)
saturation conditions. It plays the role of
rhcrit in relative humdity fractional cloud
schemes and allows clouds to form when the grid
box mean is subsaturated (Q1lt0)
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?s can parameterised in a manner analagous to
other subgrid scale correlation terms (i.e. as a
vertical diffusion flux)
ltke is a length scale from the turbulence scheme
and links the cloud terms to the turbulence. ?s
is a measure of the subgrid scale variability of
saturation characteristics in a grid box due to
fluctuations not resolved by the model. In
HIRLAM ?sturb as defined is from (classical small
scale) PBL turbulence only. In models at
resolutions 2km this may be the only unresolved
variance. But for models at gt10km we must also
include variance due to convective scale and
mesoscale circulations.
Lenderink Siebsma 2000
?SFIX uses equation A above with ltke fixed to a
free tropospheric value of 250m
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Cloud Fraction and normalised cloud water as a
function of the normalised grid box mean
saturation deficit Q1
If ?s is relatively small Cloud Fraction will be
skewed Towards fraction 1 (Q1gt0) or Fraction zero
(Q1lt0) . This scenario is okay for very high
resolution models (e.g. dx2km) where
only typical boundary layer turbulence is not
resolved. At lower resolutions we need to
develop parameterisations of mesoscale and
convective scale variance (in r and T). We need
to include all factors contributing to subgrid
scale variance in the term s
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FIRE-EUROCS 2 day Stratocumulus simulation Using
25m vertical resolution
Cloud and turbulence simulations Improve at high
vertical resolution. But turbulence is a fast
process this can lead to Numerical stability
problems
Standard cloud schemes (RH based and RH/ql based)
exhibit large instability at high vertical
resolution, when coupled to a moist TKE mixing
scheme. This motivated us to build a
statistical cloud scheme within the moist
turbulence parameterisation. Cloud amounts and
cloud buoyancy contribution to TKE generation are
then in phase and resulting simulation is far
more stable.
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With high vertical resolution moist CBR plus
statistical cloud scheme produces An accurate and
stable simulation of cloud water, cloud fraction
and drizzle For the FIRE-EUROCS stratocumulusc
case
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Vertical cross-section of EUROCS Stratocumulus
with moist CBR statistical clouds
Cloud Fraction
Cloud Water (g/kg)
800 400 0
TKE
Relative Humidity
800 400 0
0 20 40
0 20 40
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Can we use the same statistical cloud scheme to
diagnose cloud fraction and Cloud water in
ARM-EUROCS shallow cumulus case? Initial results
using a seperate treatment for shallow
convective cloud fraction and cloud water and
large scale clouds. Problem with this approach
is deciding which cloud fraction and cloud water
to use convective or large scale, it would be
easier with a single common estimate of both terms
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KNMI LES and HIRLAM 1D cloud water evolution for
ARM shallow cumulus case. Kain-Fritsch convection
provides tendencies of heat and water vapour. In
regions of active convection d/dtCBR are set to
zero. Contributions to ?s from convection, turbule
nce and above 2xpblh, turbulence using fixed
ltke250m cloud fraction from statistical cloud
scheme, dCW/dtql(new)-ql(old) diagnosed
from statistical cloud scheme, with RK large
scale precipitation active.
HIRLAM 1D
KNMI LES
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HIRLAM and KNMI LES Relative Humidity for ARM
shallow cumulus case. Magnitude of RH mixing
slightly underestimated leading to slightly less
deep cloud in HIRLAM
HIRLAM
KNMI LES
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RH
??scu
Variance in s dominated by contribution from
Convection scheme.
??sturb
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Relative Humidity KNMI LES
In the original ARM shallow Cumulus integrations
KF convection accounted for mixing of heat and
water vapour where cumulus convection
was diagnosed. At these points vertical fluxes
due to CBR were set to zero. But statistical
cloud scheme (within CBR) using the variance
terms from both CBR and convection was used to
diagnose cloud fraction and cloud water. New
integrations here reset all KF convection
thermodynamic tendencies to zero. All vertical
mixing done only by moist CBR. Using convective
turbulent variance terms for statistical cloud
fraction calculation and ql in calculating the
non-Gaussian contribution to the buoyancy flux.
Relative Humidity CBR only dz25m
Relative Humidity CBR only dz12m
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Cloud Water Moist CBR only 25m
Presently cloud scheme very sensitive to small
combined errors in over-estimation of vertical
flux and saturation state, plus
(possible) underestimate of variance near cloud
top. But depth and overall character of mixing
by moist CBR including skewness term in buoyancy
production term not completely wrong!!
Cloud water CBR and KF convection
KNMI LES Cloud Water
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RH Moist CBR only and no convective variance of S
Without inclusion of KF convection generated
variance of s (saturation measure of the grid
box), the variance term appears underestimated
and the model simulation goes between 0 and 1 too
much, with strong evaporation of diagnosed cloud
water. More work is needed to understand how to
parameterise the variance of water within the
moist CBR using the skewness term.
RH KNMI LES
Cloud Fraction CBR only
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4 day GCSS period of deep convection and
associated cloud fields. Can statistical cloud
scheme simulate all cloud types?
Cloud Fraction
Convective events
Upper level cloud as observed
0 12 24
36 48 60
72 84
96
0 12 24
36 48 60
72 84
96
-3 -2 -1
0 1 2
3

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4 day simulation with of GCSS deep convection
case using KF convection and statistical cloud
diagnosis of cloud Fraction and cloud liquid/ice
water. Shown is qtot/qsat(Tliq)
This area of upper level clouds occurs after
convection has ceased and is in a region of
subsaturation
Areas moistened by convective detrainment
0 12 24
36 48
60 72 84
96
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Cloud fraction VERY sensitive in free troposphere
to magnitude of ?s term Which sets Q1 tern for a
given qt-qs(Tliq)
Where ?s uses the vertical flux Formulation and a
fixed ltke250m
0 12 24
36 48
60 72
84 96
0 12 24
36 48
60 72
84 96
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?sx10-4 the 4-day GCSS deep convection case.
Cloud fraction and cloud water amounts are very
sensitive to free tropospheric variance of s term
?SFIX included
0 12 24
36 48
60 72
84 96
?SFIX NOT included
0 12 24
36 48
60 72
84 96
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Summary Statistical cloud scheme within moist
turbulence parameterisation seems a promising
way to simulate all cloud types (both fraction
and water/ice content) Moreover the simulated
clouds are well balanced with the prognosed
turbulence and thus allow for stble integrations
at high vertical resolution. But the simulated
clouds are critically sensitive to the accurate
representation of the variance of water variable
s around the grid box mean value. While using
solely moist turbulent mixing and statistical
cloud scheme for all aspects of shallow cumulus
mixing and cloud formation is not yet
successful, results seem encouraging enough to
pursue the idea further. More work is needed to
carefully evaluate the skewness contribution to
the buoyancy production term in the TKE
equation. This will lead to a better
understanding/simulation of the mixing length in
partially cloudy boundary layers and by
impliciation the variance of water term. It may
be necessary to calculate mixing lengths and
vertical diffusion seperately for clear and
cloudy fractions before averaging.
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