What LES tell us about the parameterisation of  and  - Convection

COST ES0905
What LES tell us about the
parameterisation of and
An attempt to stimulate convergence in
parameterisation approaches
Wim de Rooy et al.
Entrainment and detrainment in cumulus convection: an overview.
Wim C. de Rooy, Peter Bechtold, Kristina Fröhlich, Cathy Hohenegger, Harm Jonker, Dmitrii
Mironov, A. Pier Siebesma, Joao Teixeira, and Jun-Ichi Yano
(Pending minor revisions QJRMS)

COST ES0905
Parameterisations of detrainment and entrainment are
extremely important in NWP and Climate models.
(see e.g. Murphy et al. 2004).
They should have a sound physical bases:
–Observations (e.g. Jonas 1990, Rodts et al. 2003)
-LES
Direct translation from observation to parameterisation is
cumbersome
Most important tool to evaluate and diagnose and

Why are LES so important?
LES domain NWP gridbox
NWP- or Climate model:
)
t
(
' '
w
z
F
w ' '
= total turbulent transport
(sub grid for NWP models)
'
w ww
'
w'
'
LES
domain

= cloudy LES gridbox
Convective transport
c
w'
'
a w'
'
(1
a
) w'
'
a
(1 a
)( w
c
c
e
c
c
1
A
c
c cloudy
area
c
c
dxdy
w)(
)
Define cloud with a conditional
sampling, e.g.: 0 w
0
aw
c
v v
(Siebesma & Cuijpers 95)
q l
c
e)
M
( c
)
c( e
Convective transport
e
c
e
Investigate bulk mass flux
approach in LES

LES provide the experimental environment to investigate
your (bulk) mass flux parametersation including all the
relevant processes like and
Determine:
Maw
c
z
M
(
M
z
c c
)
c e
describes the
updraft dilution
and describe the
mass flux profile
•How well do your and compare to LES?
•How do they vary in LES and with what?
•Can you capture the most important dependencies?
LES should be leading in parameterisation development!
However, in reality………….

Direct comparison of (dilution) with LES: Kain Fritsch
BOMEX case: Kain Fritsch with optimal 0
0.004
KF
2
0 c
=0.02* c
2
0.003
0.002
0.001
KF
2
0 c
0.000
0.000 0.001 0.002 0.003 0.004
+2h
+3h
+4h
+5h
+6h
+7h
+8h
+9h
+10h
+11h
+12h
+13h
+14h
+15h
LES
+1h
=1/(z-z i
+500)
0.004
BOMEX case: =(z-z i +500) -1
+1h
+2h
+3h
+4h
0.003
+5h
+6h
+7h
+8h
+9h
+10h
0.002
+11h
+12h
+13h
+14h
+15h
0.001
0.000
0.000 0.001 0.002 0.003 0.004
LES
Kain Fritsch not very suitable for describing the dilution (cloud top!)

COST ES0905
Dependence of on RH of the environment?
Two operational
parameterisations:
KF
2
0
c
0(1.3
RH)f
Bechtold
scale
Increasing with RH e !
Decreasing with RH e !
Setup RH experiment: Derbyshire et al. 2004
Bechtold et al. (2008)
Dependency RH e
Not yet established

There is another very important feature
that should be represented correctly:
The mass flux profile
and both influence the mass flux profile
However
•Variations in the mass flux profile are strongly
dominated by !
•Empirical arguments
•Theoretical arguments
De Rooy & Siebesma 2008, 2010

Empirical arguments
Much larger variation in from case to case, hour to hour, different cloud sizes
Jonker et al., 2006 Hohenegger, 2011

Empirical arguments
Optimal fixed and LES
Optimal fixed and LES
ARM
ARM
De Rooy & Siebesma, 2008

Cloud layer
Theoretical arguments
Based on general in-cloud budget eq. for q t and making a distinction
between small and large-scale lateral mixing (de Rooy & Siebesma 2010)
Cloud ensemble
(divergent condition)
turb
dyn
turb
dyn
~
1
M
1
M
M
z
M
~
z
1
~
z
Included in:
de Rooy & Siebesma 08
Neggers et al. 09

What are the consequences?
As far as variations in the (non-dim) mass-flux profile concerns:
Use a (simple) fixed function for but a flexible
=
Parameterise the mass-flux profile
So no explicit and for M profile!
Unconventional:
Separate entrainment (dilution) and mass flux profile!
De Rooy & Siebesma 2008 (RACMO, Harmonie) and Neggers et al. 2009

Parameterising the mass flux profile
LES
large c
High RH e (friendly environment)
Very buoyant updraft(s)
Slow decrease M with height
small c
Low RH e (hostile environment)
Marginally buoyant updraft(s)
Fast decrease M with height
Model parameterisation
Parameterisation mass flux profile (or ) is dependent
on properties of the environment and the updraft itself!
De Rooy & Siebesma, 2008

0 (1.3 RH)
Bechtold f scale
Traditional scheme
Bechtold et al. 2008
COST ES0905
Setup RH experiment: Derbyshire et al. 2004

Conclusions/Recommendations
• LES are very important:
– Fundamental studies and (Romps, Dawe & Austin)
– Investigate and in bulk (model) framework
• Parameterisations of , should be based on LES (i.o. tuned in
model) describing the right processes.
• Detrainment is responsible for variations in the mass flux profile
(due to variations in cloudlayer depth, environment and updraft).
Separate parameterisation of mass flux and dilution ()
– Theoretical and empirical arguments
– More flexibility
– Robustness
• Keep parameterizations as simple as possible.
Just enough complexity to include the most relevant processes

A popular traditional scheme:
Kain Fritsch (buoyancy sorting)
(1-)θ vu
()θ ve
vu
c
1
v
positive buoyant
mixtures
negative buoyant
mixtures
ve
Courtesy: Stephan de Roode
0
fraction environmental air ()