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@uqam.ca
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.
TKE evolution is dependent on subgrid scale vertical fluxes
which in turn are dependent on TKE
D
is dissipation of TKE ( l
is a typical length scale for eddies responsible for TKE loss)
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.
l
h,m
follows ideas of Bougeault and
Lacarrare with wind shear included
Via Richardson number.
Moist conservative turbulence and statistical cloud representation
Turbulence phrased in moist conservative variables (
l
and r
t
) naturally incorporates
phase change effects in buoyancy production term.
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
)
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.
C
f
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
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 (N<0.4) where the buoyancy flux
is increasingly
skewed
(towards values dominated by the incloud portion). In these types of
cloudy boundary Layers (say with N<0.1) the 2nd (clear sky) and 3rd (
non

Gaussian
) terms
dominate the buoyancy flux and by implication TKE evolution and turbulent mixing lengths.
f
NG
expresses the contribution of the non

Gaussian (skewed) fluxes of
l
and q
t
to the total
buoyancy flux.
f
NG
increases rapidly with decreasing N (increasing skewness) and like N and
q
l
can be parameterised in terms of
the normalised saturation deficit Q
1
.
Introducing a variable
s
describing the effect of changes in r
t
and T
l
on the saturation state
of the grid box leads to a formualtion of Q
1
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, q
l
and f
NG
as a function of Q
1
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 rh
crit
in relative humdity fractional cloud schemes and allows
clouds to form when the grid box mean is subsaturated (Q
1
<0)
s
can parameterised in a manner analagous to other subgrid scale correlation terms
(i.e. as a vertical diffusion flux)
l
tke
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 ~>10km we must also include
variance due to convective scale and mesoscale circulations.
SFIX
uses equation A above with
l
tke
fixed to a free tropospheric
value of 250m
Lenderink & Siebsma 2000
Cloud Fraction and normalised cloud water as a function
of the normalised grid box mean saturation deficit Q
1
If
s
is relatively small
Cloud Fraction will be skewed
Towards fraction 1 (Q
1
>0) or
Fraction zero (Q
1
<0) .
This scenario is okay for
very high resolution models
(e.g. dx~2km) 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
Standard cloud schemes (RH based and
RH/q
l
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.
Cloud and turbulence simulations
Improve at high vertical resolution.
But turbulence is a fast process
this can lead to Numerical stability
problems
FIRE

EUROCS 2 day
Stratocumulus simulation
Using 25m vertical resolution
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
0 20 40
0 20 40
800
400
0
800
400
0
Cloud Fraction Cloud Water (g/kg)
TKE Relative Humidity
Vertical cross

section of EUROCS Stratocumulus with moist CBR + statistical clouds
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
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/dt
CBR
are set to zero. Contributions to
s
from convection,
turbulence and above 2xpblh, turbulence using fixed l
tke
=250m
cloud fraction from statistical cloud scheme, dCW/dt=q
l(new)

q
l(old)
diagnosed from
statistical cloud scheme, with RK large scale precipitation active.
KNMI LES
HIRLAM 1D
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
RH
scu
sturb
Variance in s dominated
by contribution from
Convection scheme.
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 q
l
in
calculating the non

Gaussian
contribution to the buoyancy flux.
Relative Humidity KNMI LES
Relative Humidity CBR only dz=25m
Relative Humidity CBR only dz=12m
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 Moist CBR only 25m
Cloud water CBR and KF convection
KNMI LES Cloud Water
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 Moist CBR only and no convective variance of S
RH KNMI LES
Cloud Fraction CBR only
4 day GCSS period of deep convection and associated cloud fields.
Can statistical cloud scheme simulate all cloud types?
Cloud Fraction

3

2

1 0 1 2 3
Upper level cloud
as observed
Convective
events
0 12 24 36 48 60 72
84 96
0 12 24 36 48 60 72
84 96
Areas moistened by
convective detrainment
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 q
tot
/q
sat
(T
liq
)
This area of upper level clouds
occurs after convection has ceased
and is in a region of subsaturation
0 12 24 36 48 60
72
84 96
Where
s
uses the vertical flux
Formulation and a fixed l
tke
=250m
Cloud fraction VERY sensitive in free troposphere to magnitude of
s
term
Which sets Q
1
tern for a given q
t

q
s
(T
liq
)
0 12 24 36 48 60
72 84 96
0 12 24 36 48 60
72 84 96
s
x10

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
SFIX
NOT included
0 12 24 36 48 60
7
2 84 96
0 12 24 36 48 60
7
2 84 96
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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