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Transcript of 1 Dry Convection Phenomenology, Simulation and Parameterization of Atmospheric Convection Pier...
1Dry Convection
Phenomenology, Simulation and Parameterization of Atmospheric Convection
Pier Siebesma
Yesterday: “Dry” Atmospheric Convection
Today: “Moist” Convection and (shallow cumulus) clouds
2Dry Convection
o0
Equator
N30
Northoregion
windTrade
Subsidence
~0.5 cm/s
10 m/s
vE vE
inversion
Cloud base
~500m
Tropopause 10km
•Stratocumulus
•Interaction with radiation
•Shallow Convective Clouds
•Little precipitation
•Vertical turbulent transport
•No net latent heat production
•Fuel Supply Hadley Circulation
•Deep Convective Clouds
•Precipitation
•Vertical turbulent transport
• Net latent heat production
•Engine Hadley Circulation
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
Siebesma et al. (2005, QJRMS)
scuShallow cuDeep cu
5Dry Convection
rlii
ll
l
vii
vv
v
radp
ii
Pecquxz
qwq
t
q
ecquxz
qwq
t
q
Qecc
Lu
xzw
t
v
v
v
Large scale Large scale
advectionadvection
Large scale Large scale
subsidencesubsidence
turbulent turbulent transporttransport
Net Net Condensation Condensation RateRate
Grid Averaged Equations of thermodynamic variables
Introduce moist conserved variables!
lp
l qcL
•Liquid water potential Temperature
lvt qqq •Total water specific humidity
rtt
tt
radll
ll
Pqwzz
qwq
t
q
Qwzz
wt
v
v
What happened with the clouds?
Buoyancy is the primary source for the vertical velocity
v
gtw
0
With: )61.01( lvv qq
lvv qq 61.1
K5.0 K3~0 K1~0
Typical numbers: = 0.5K
qv= 1~5 g/kg
ql= 0~3 g/kg
So we need to go back to “down to earth” variables:
{
{ 0),(
,1
0,0
,0
sltsltl
sltl
qqifqqq
a
qqifq
a
c
c
Cloud Scheme in LES: All or Nothing
In Climate models we have partial cloud cover so we need a parameterization.
10Dry Convection
Conditional Instability
•Lift a (un)saturated parcel from a sounding at z0 by dz
•Check on buoyancy with respect to the sounding: vpv
gB
,
0
Stable for unsaturated parcels
Unstable for saturated parcels
Conditionally Unstable!!!
mv
d z
z
dm
v
profile
stableunstable
5.4K/km
CIN
Introductory Concepts 1: Introductory Concepts 1: CAPECAPE
CAPE = Convective Available Potential Energy.
CIN = Convection Inhibition
CAPE
•CAPE and CIN unique properties of moist convection
•Primary Reason why moist convection is so intermittant
CAPE and CIN: An Analogue with ChemistryCAPE and CIN: An Analogue with Chemistry
Free
Energy
Surf Flux
Mixed Layer
CAPE
CIN
Activation (triggering)
LS-forcing
LS-forcing
RAD
LFC LNB
Parcel Height
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: Introductory Concepts 3: Quasi-EquilibriumQuasi-Equilibrium
0 LSb FJMdt
dCAPE
au
wu
Mb=au wu Amount of convective vertical motion at cloud base (in an ensemble sense)
The convective process that stabilizes environment
LS-Forcing that slowly builds up slowly
Quasi-equilibrium: near-balance is maintained even when F is varying with time, i.e. cloud ensemble follows the Forcing.
Forfilled if :adj << F
Used convection closure (explicit or implicit) JMb ~ CAPE/ adj
adj : hours to a day.
(Arakawa and Schubert JAS 1974)
Introductory Concepts 4: Introductory Concepts 4: Earthly AnalogueEarthly Analogue
•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………..
Free after Dave Randall:
16Dry Convection
History of LES of cumulus topped PBL
1. Sommeria, G. (1976) J. Atm Sci. 33, 216-241
2. Sommeria, G and Lemone, M.A (1978) J. Atm Sci. 35, 25-39
3. Beniston, M.G. and Sommeria G (1981) J. Atm Sci. 38, 780-797
4. Bougeault, Ph (1981) J. Atm Sci. 38, 2414-1438
5. Nicholls, L, Lemone, M.A. and Sommeria, G. (1982) QJRMS 108, 167-190
6. Cuijpers J,W,M and Duynkerke, P.G, (1993) J. Atm Sci. 50, 2894-3908
7. Siebesma and Cuijpers J,W,M (1995) J. Atm Sci. 52, 650-666
GCSS; LES intercomparison studies of shallow cumulus:
2006Precipitating trade wind cu
RICO
2000Diurnal Cycle Cumulus
ARM
1998Trade wind cu topped with Scu
ATEX
1997Steady state Trade wind cu
BOMEX
yearCaseExperiment
Siebesma et al. JAS 2003
Stevens et al. JAS 2001
Brown et al. QJRMS 2002
Van Zanten et al. in preperation
0LESscale
large
ttt
0LESscale
large
ttt
BOMEX ship array (1969)
•No observations of turbulent fluxes.
•Use Large Eddy Simulation (LES)
based on observations
•No observations of turbulent fluxes.
•Use Large Eddy Simulation (LES)
based on observations
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
•11 different LES models
•Initial profiles
•Large scale forcings prescribed
•6 hours of simulation
Is LES capable of reproducing the steady state?
Is LES capable of reproducing the steady state?
•Large Scale Forcings•Large Scale Forcings
•Mean profiles after 6 hours•Mean profiles after 6 hours
•Use the last 4 simulation hours for analysis of …….•Use the last 4 simulation hours for analysis of …….
•Turbulent Fluxes of the conserved variables qt and l
•Turbulent Fluxes of the conserved variables qt and l
Cloud layer looks like a enormous entrainment layer!!
lp
l qwc
Lww lvt qwqwqw
LES: “clouds in silico”
mass flux = cloud core fraction * core velocity
Convective Mass flux decreasing with height
xx =
Siebesma et al JAS 2003
Updraft mass flux = updraft fraction * updraft velocity
clouds “in vivo”
Recently validated for “Clouds in vivo” (Zhang, Klein and Kollias 2009)
ARM mm-cloud radar
Conditional Sampling of:
•Total water qt
•Liquid water potential temperature l
Conditional Sampling of:
•Total water qt
•Liquid water potential temperature l
Lateral Mixing between clouds and environment
26Dry Convection
Mass Flux decomposition
u
uuu e
eee
e
e
u
u aa )1(
a
)()1( uu
e
e
u
u wawawaw
M
M-fluxenv. fluxsub-core flux
Courtesy : Martin Kohler (ECMWF)
Siebesma and Cuijpers JAS (1995)
Cloud ensemble:
approximated by
1 effective cloud:
In general: bulk approach:
vvcc
tcc
gBaBwb
z
w
z
M
M
qz
0
22
l
,2
1
1
,for)(
vvcc
tcc
gBaBwb
z
w
z
M
M
qz
0
22
l
,2
1
1
,for)(
M
The old working horse:
Entraining plume model:
Plus boundary conditions
at cloud base.
How to estimate updraft fields and mass
flux? Betts 1974 JAS
Arakawa&Schubert 1974 JAS
Tiedtke 1988 MWR
Gregory & Rowntree 1990 MWR
Kain & Fritsch 1990 JAS
And many more……..
Different tendency to form cumulus anvils is caused by differences in the vertical structure of model mass flux:
M M
, values fixed Mixing; Flexible structure
Tiedtke (1989) in IFS EDMF-DualMSiebesma et al 2007 (JAS)
Neggers et al 2009 (JAS)
•Double counting of processes
•Problems with transitions between different regimes:
dry pbl shallow cu
scu shallow cu
shallow cu deep cu
This unwanted situation has led to:
Swzt
zKw
)( uMw
Standard (schizophrenic) parameterization approach:
Deterministic versus Stochastic Convection (1)Deterministic versus Stochastic Convection (1)
~500 km
•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.
Deterministic versus Stochastic Convection (2)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.
Mass Flux
Plant and Craig 2006 JAS
More Sophisticated Parameterization (2)More Sophisticated Parameterization (2)(Plant and Craig 2007)(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
35Dry Convection
Is this a Cloud??
….and, how to answer this question?
“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, clouds are not spheres, trees are not cylinders, neither does lightning travel in a straight line. Almost everything around us is non-Euclidean”.
Fractal Geometry
Benoit Mandelbrot
Instead of
Area-Perimeter analyses of cloud patterns (1)
Procedure:
•Measure the projected cloud area Ap and the perimeter Lp of each cloud
•Define a linear size through
• Perimeter dimension define through:
pAl
llog
pLlog
Slope: Dp= 1
pDp lL
For “ordinary” Euclidean objects:
•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…
Area-Perimeter analyses of cloud patterns (2)
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
•Measure Surface As and linear size of each cloud
•Plot in a log-log plot
• sDllS )(
•Assuming isotropy, observations would suggest Ds=Dp+1=7/3
31/Vl
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 :
3/7,)(2
s
D
L DLlL
lSlS
s
•Euclidian area SL underestimates true cloud surface area S(l=) by a factor
•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???
1002 sDL
With L=outer scale (i.e. diameter of the cloud) and the normalizing area if measured with L.
2LSL
Transport = Contact area x Flux
x
clKlSlFlSlT
)()()()()( 00000
turbulence diffusive flux
)( 0lSx
clK
)( 0
0l Resolution dependence for transport over cloud boundary (1)
resolved advection
Subgrid diffusion
Consequences for transport over cloud boundary (2)
000000 l
clKlSlFlSlT
)()()()()(
sD
L L
lSlS
2
00 )(
(Richardson Law)
31
00000
/
)()()(
L
lLullullK
!!!!!
D/ s
L
lLSLuclT
370
0 )()()(
No resolution dependancy for Ds=7/3!!
Is this shear luck ????
sD-7/33/4Re
37
)()()(
sD/
LLSLucT
Not really:
Repeat the previous arguments for 0l
Boundary flux T only Reynolds independent if 3/7sD
which completes a heuristic “proof” why clouds are fractal with a surface dimension of 7/3.
47Dry Convection
Gradient Percolation
A stronger underlying mechanism ? (Peters et al JAS 2009)
Dp=4/3
Scale Hierarchy
High Low
low
high
Direct
Numerical
Simulation
Conceptual models
Statistical Mechanics
Self-Organised Criticality
Level of
“understanding”
or
conceptualisation Large
Eddy
Simulations
Global
Climate
SimulationsSimulations
Laboratory
experiments
Atmospheric
Profiling
stations
Field
campaignsSatellite
data
Observations
Models/Parameterizations
resolution
Mixed layer
models
Interface &
microphysical
models