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Phenomenology, Simulation and Parameterization of Atmospheric Convection Pier Siebesma Yesterday: “Dry” Atmospheric Convection Today: “Moist” Convection and (shallow cumulus) clouds Dry Convection 1
1.
Motivation 2. Equations 3. Moist Thermodynamics Concepts 4. LES of shallow cumulus convection 5. Parameterization of cumulus convection 6. Geometry of Cumulus Clouds 7. (PDF cloud schemes) Dry Convection 2
Tropopause 10km Subsidence ~0.5 cm /s 10 m/s Cloud base ~500m Equator 0 o
•Deep Convective Clouds •Precipitation •Vertical turbulent transport • Net latent heat production •Engine Hadley Circulation
inversion E v Trade wind region E v
•Shallow Convective Clouds •Little precipitation •Vertical turbulent transport •No net latent heat production •Fuel Supply Hadley Circulation
North 30 o N
•Stratocumulus •Interaction with radiation
EUROCS intercomparison project on cloud representation in GCM’s in the Eastern Pacific Large Scale Models tend to overestimate Tradewind cumulus cloudiness and underestimate Stratocumulus
Deep cu Shallow cu scu
Siebesma et al. (2005, QJRMS)
1. Motivation 2. Equations 3. Moist Thermodynamics Concepts 4. LES of shallow cumulus convection 5. Parameterization of cumulus convection 6. Geometry of Clouds 7. (PDF cloud schemes) Dry Convection 5
Grid Averaged Equations of thermodynamic variables
t
q v
t
q l
t
v
v
q v
v
q l
w
z w
q v
z w
q l
z
x i u i
x i
x i u i
q v
u i
q l
L
c p
c
e
c
e
c
e
Q rad P r
Large scale advection Large scale subsidence turbulent transport Net Condensation Rate
Introduce moist conserved variables!
l
L c p
q l q t
q v
q l
•
Liquid water potential Temperature
•
Total water specific humidity
t l
q t
t
v
l
v
q t
w w
z l
q t
z
z
z w
w
q t
l
Q rad P r
What happened with the clouds?
Buoyancy is the primary source for the vertical velocity
w
t
g
0
v
With:
v
( 1 0 .
61
q v
q l
)
v
1 .
61
q v
q l
Typical numbers:
= 0.5K
q v = 1~5 g/kg
q l = 0~3 g/kg
0 .
5
K
0 ~ 3
K
0 ~ 1
K
So we need to go back to “down to earth” variables:
{
q l a c
0 , 0 ,
Cloud Scheme in LES: All or Nothing
if q t
q sl
0 {
q l a c
1 , (
q t
q sl
),
if q t
q sl
0 In Climate models we have partial cloud cover so we need a parameterization.
1. Motivation 2. Equations 3.
Moist Thermodynamics Concepts 4. LES of shallow cumulus convection 5. Parameterization of cumulus convection 6. Geometry of Clouds 7. (PDF cloud schemes) Dry Convection 10
Conditional Instability
•
Lift a (un)saturated parcel from a sounding at z0 by dz
•
Check on buoyancy with respect to the sounding:
B
g
0
v
,
p
v
profile
d
z unstable
v
m
5.4K/km
stable Stable for unsaturated parcels Unstable for saturated parcels Conditionally Unstable!!!
d
z v
m
CAPE CIN
Introductory Concepts 1:
CAPE
CAPE = Convective Available Potential Energy.
CIN = Convection Inhibition •
CAPE and CIN unique properties of moist convection
•
Primary Reason why moist convection is so intermittant
Free Energy CAPE and CIN: An Analogue with Chemistry Surf Flux Mixed Layer Activation (triggering) CIN CAPE LFC Parcel Height LS-forcing RAD LS-forcing LNB 1) Large Scale Forcing :
•
Horizontal Advection
•
Vertical Advection (subs)
•
Radiation 2) Large Scale Forcing: slowly builds up CAPE 3) CAPE
•
Consumed by moist convection
•
Transformed in Kinetic Energy
•
Heating due to latent heat release (as measured by the precipitation)
•
Fast Process!!
Free after Brian Mapes
Introductory Concepts 3:
Quasi-Equilibrium
(Arakawa and Schubert JAS 1974)
dCAPE
dt JM b
F LS
0
LS-Forcing that slowly builds up slowly The convective process that stabilizes environment Quasi-equilibrium: near-balance is maintained even when F is varying with time, i.e. cloud ensemble follows the Forcing.
Forfilled if :
t
adj <<
t
F w u a u Used convection closure (explicit or implicit) JM b
t
adj ~ CAPE/
t
adj : hours to a day.
M b =a u w u
r :
Amount of convective vertical motion at cloud base (in an ensemble sense)
Introductory Concepts 4:
Earthly Analogue
Free after Dave Randall:
•
Think of CAPE as the length of the grass
•
Forcing as an irrigation system
•
Convective clouds as sheep
•
Quasi-equilibrium: Sheep eat grass and no matter how quickly it grows, the grass is allways short.
•
Precipitation………..
1. Motivation 2. Equations 3. Moist Thermodynamics Concepts 4.
LES of shallow cumulus convection 5. Parameterization of cumulus convection 6. Geometry of Clouds 7. (PDF cloud schemes) Dry Convection 16
History of LES of cumulus topped PBL
1.
2.
3.
4.
5.
6.
7.
Sommeria, G. (1976) J. Atm Sci. 33, 216-241 Sommeria, G and Lemone, M.A (1978) J. Atm Sci. 35, 25-39 Beniston, M.G. and Sommeria G (1981) J. Atm Sci. 38, 780-797 Bougeault, Ph (1981) J. Atm Sci. 38, 2414-1438 Nicholls, L, Lemone, M.A. and Sommeria, G. (1982) QJRMS 108, 167-190 Cuijpers J,W,M and Duynkerke, P.G, (1993) J. Atm Sci. 50, 2894-3908 Siebesma and Cuijpers J,W,M (1995) J. Atm Sci. 52, 650-666 GCSS; LES intercomparison studies of shallow cumulus:
Experiment BOMEX Case Steady state Trade wind cu year 1997
Siebesma et al. JAS 2003
ATEX Trade wind cu topped with Scu 1998
Stevens et al. JAS 2001
ARM RICO Diurnal Cycle Cumulus Precipitating trade wind cu 2000 2006
Brown et al. QJRMS 2002 Van Zanten et al. in preperation
•
No observations of turbulent fluxes.
•
Use Large Eddy Simulation (LES) based on observations BOMEX ship array (1969)
t
t
large scale
t
LES 0
observed observed To be modeled by LES Nitta and Esbensen 1974 JAS
•
11 different LES models
•
Initial profiles
•
Large scale forcings prescribed
•
6 hours of simulation Is LES capable of reproducing the steady state?
•
Large Scale Forcings
•
Mean profiles after 6 hours
•
Use the last 4 simulation hours for analysis of …….
•
Turbulent Fluxes of the conserved variables qt and
l
w
l
w
L c p w
q l
w
q t
w
q v
Cloud layer looks like a enormous entrainment layer!!
w
q l
LES: “clouds in silico” Convective Mass flux decreasing with height
mass flux = cloud core fraction * core velocity
Siebesma et al JAS 2003
x x =
Recently validated for “Clouds in vivo” (Zhang, Klein and Kollias 2009) clouds “in vivo”
ARM mm-cloud radar Updraft mass flux = updraft fraction * updraft velocity
Conditional Sampling of:
•
Total water qt
•
Liquid water potential temperature
l
Lateral Mixing between clouds and environment
1. Motivation 2. Equations 3. Moist Thermodynamics Concepts 4. LES of shallow cumulus convection 5.
Parameterization of cumulus convection 6. Geometry of Clouds 7. (PDF cloud schemes) Dry Convection 26
Mass Flux decomposition
a
u
u
u u
e
e
e e
a
u u
( 1
a
)
e e
Courtesy : Martin Kohler (ECMWF)
M
w
a w
u u
( 1
a
)
w
e e
a w u
(
u
) sub-core flux env. flux Siebesma and Cuijpers JAS (1995) M-flux
In general: bulk approach:
Cloud ensemble:
approximated by
1 effective cloud:
How to estimate updraft fields and mass flux?
The old working horse: Entraining plume model:
1
M
1 2
z c
M
z
w c
2
z
(
c
b
) for l ,
q t
w c
2
aB
,
B
g
0
v
v
Betts Arakawa&Schubert Tiedtke Gregory & Rowntree Kain & Fritsch And many more……..
1974 JAS 1974 JAS 1988 MWR 1990 MWR 1990 JAS
M
Plus boundary conditions at cloud base.
Different tendency to form cumulus anvils is caused by differences in the vertical structure of model mass flux:
,
values fixed Mixing; Flexible structure M
Tiedtke (1989) in IFS EDMF-DualM
M Siebesma et al 2007 (JAS) Neggers et al 2009 (JAS)
Standard (schizophrenic) parameterization approach:
w
K
z w
M
(
u
)
t
z
S
This unwanted situation has led to:
•
Double counting of processes
•
Problems with transitions between different regimes: dry pbl
shallow cu scu
shallow cu shallow cu
deep cu
Deterministic versus Stochastic Convection (1) •
Traditionally convection parameterizations are deterministic:
•
Instantaneous large scale Forcing and mean state is taken as input and convective response is deterministic
•
One to one correspondency between sub-grid state and resolved state assumed.
•
Conceptually assumes that spatial average is a good proxy for the ensemble mean.
~500 km
Deterministic versus Stochastic Convection (2) •
However: Cloud Resolving Models (CRM’s) indicate that operational resolutions show considerable fluctuations of convective response around the ensemble mean.
•
This suggests that a deterministic (micro-canonical) approach might be too restricitive for most operational resolutions.
pdf Mass Flux
Plant and Craig 2006 JAS
More Sophisticated Parameterization (2) (Plant and Craig 2007)
Parameterization:
•
Select N cloud updrafts stochastically according to the pdf
•
Calculate impact for each updraft by using a cloud updraft model
•
Note : N is a function of the resolution
•
Only tested in 1D setting
1. Motivation 2. Equations 3. Moist Thermodynamics Concepts 4. LES of shallow cumulus convection 5. Parameterization of cumulus convection 6.
Geometry of Clouds 7. (PDF cloud schemes) Dry Convection 35
Is this a Cloud??
….and, how to answer this question?
Fractal Geometry
“Shapes, which are not fractal, are the exception. I love Euclidean geometry, but it is quite clear that it does not give a reasonable presentation of the world. Mountains are not cones, Euclidean”. clouds are not spheres , trees are not cylinders, neither does lightning travel in a straight line. Almost everything around us is non Benoit Mandelbrot
Instead of
Area-Perimeter analyses of cloud patterns (1) Procedure:
•Measure the projected cloud area A p and the perimeter L p of each cloud •Define a linear size through
l
A p
• Perimeter dimension define through:
L p
l D p
For “ordinary” Euclidean objects:
log
L p
Slope: D p = 1 log
l
Area-Perimeter analyses of cloud patterns (2)
•
Pioneered by Lovejoy (Science 1982)
•
Area-perimeter analyses of projected cloud patterns using satellite and radar data
•
Suggest a perimeter dimension Dp=4/3 of projected clouds!!!!!
•
Confirmed in many other studies since then… Instead of Consequences:
•
Cloud perimeter is fractal and hence self-similar in a non-trivial way.
•
Makes it possible to ascribe a (quantitative) number that characterizes the structure
•
Provides a critical test for the realism of the geometrical shape of the LES simulated clouds!!!!
Slope 4/3
Similar analysis with LES clouds
• •
l
V
1
/
3 •
Plot in a log-log plot
S
(
l
)
l D s
•
Assuming isotropy, observations would suggest Ds=Dp+1=7/3
Siebesma and Jonker Phys. Rev Letters (2000)
Result of one cloud field
Repeat over 6000 clouds
Some Direct Consequences Surface area can be written as a function of resolution (measuring stick)
l :
S
(
l
)
S L l L
2
D s
,
l
L D s
7 / 3
S L
L
measured with L.
•
Euclidian area SL underestimates true cloud surface area S(l=
) by a factor
L
2
D s
100 •
LES model resolution of l=50m underestimates cloud surface area still by a factor 5!!!
•
Does this have consequences for the mixing between clouds and the environment???
l
0
T
(
l
0
) Transport = Contact area x Flux
S
(
l
0
)
F
(
l
0
)
S
(
l
0
)
K
(
l
0
)
c
x
turbulence diffusive flux
resolved advection
S
(
l
0
)
Subgrid diffusion
K
(
l
0
)
c
x
Consequences for transport over cloud boundary (2)
T
(
l
0
)
S
(
l
0
)
F
(
l
0
)
S
(
l
0
)
K
(
l
0
)
c l
0
S
(
l
0
)
S L l
0
L
2
D s K
(
l
0
)
l
0
u
(
l
0
)
l
0
u
(
L
)
l
0
L
(Richardson Law) 1
/
3
T
(
l
0
)
c
u
(
L
)
S
(
L
)
l
0
L
7
/
3
D s !
!
!
!
!
No resolution dependancy for Ds=7/3!!
Is this shear luck ????
Not really: Repeat the previous arguments for
l
0
T
( )
c
u
(
L
)
S
(
L
)
L
7
/
3
D s
Re 3/4 7/3 D s
Boundary flux T only Reynolds independent if
D s
7 / 3
which completes a heuristic “proof” why clouds are fractal with a surface dimension of 7/3.
Gradient Percolation Dp=4/3 A stronger underlying mechanism ? (Peters et al JAS 2009) Dry Convection 47
high
Conceptual models Statistical Mechanics Self-Organised Criticality
Level of “understanding ” or conceptualisation low
Direct Interface & microphysical models Numerical Simulati on Large Eddy Simulations Mixed layer models Models/Parameterizations Global Climate Simulations Simulations Laboratory experiments
High
Atmospheric Profiling stations Field campaigns resolution Scale Hierarchy Satellite data Observations
Low