to simulate all cloud types?

earsplittinggoodbeeInternet and Web Development

Nov 3, 2013 (3 years and 7 months ago)

63 views

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.