Life Cycle of Numerically Simulated
Shallow Cumulus Clouds
Ming Zhao and Philip H. Austin
Department of Earth and Ocean Sciences
The University of British Columbia
Canada
Outline
1. Motivation
2. A Large Eddy Simulation
3. Life Cycle of Simulated Individual Clouds
4. Conclusions
5. Future Work
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1. Motivation
Assumption: Accurate representation of the statistical
properties of cumulus convection requires accurate
representation of the convective elements.
Use LES approach to examine the properties of convective
elements and evaluate conceptual models of shallow
cumulus clouds
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Conceptual Models of Shallow Cumulus Clouds
Adiabatic cloud model
LCT
LNB
LFC
LCL
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Entraining plume model (EPM)
LCT
LNB
LFC
LCL
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Weakness:
Cumulus clouds are highly inhomogeneous; cumulus
cloud-top is determined by nearly undilute subcloud air.
Warner’s Paradox (1970).
correct
cloud-top height
over-estimate cloud
liquid water content
correct liquid
water content
under-estimate
cloud-top height
This was a problem 30 years ago, this is a problem now.
But many people still use EPMs due to their simplicity.
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Episodic mixing and buoyancy-sorting model (EMBS)
(Raymond and Blyth 1986, Emanuel 1991, 1999)
Advantages:
LCT
Warner’s paradox
downdrafts
LNB
mixing line
LFC
LCL
saturated positively buoyant
saturated negatively buoyant
unsaturated negatively buoyant
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2. A Large Eddy Simulation
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The points to be addressed include:
‰ Cloud inhomogeneity and cloud-top determination.
‰ Cloud evaporation and the role of the invisible part of
cumulus convection.
‰ Cloud life cycles and their impact on convective mass
flux.
‰ Buoyancy effects in cumulus convective transport.
‰ The role of cloud size in the redistribution of heat and
moisture and the effect of cloud size distribution on cloud
ensemble transport.
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Colorado State University LES/CRM model
(Khairoutdinov and Randall 2002)
‰ Dynamics approximation: anelastic
‰ Subgrid scale parameterization: 1.5-order with a
prognostic subgrid-scale TKE
‰ Advection of momentum: second-order finite differences
in flux form with kinetic energy conservation.
‰ Advection of scalar: fully three-dimensional positive
definite and monotonic scheme of Smolarkiewicz and
Grawboski (1990).
‰ Time integration: third-order Adams-Bashforth scheme
with a variable time step.
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Case setup -- BOMEX
‰ Sounding and forcings, details at http://www.knmi.nl/~siebesma/gcss/bomex.html
‰ Model domain: 256x256x128 grid points
‰ Resolution: 25 m uniform in all 3 dimensions
‰ Time step is 1.5 s
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Simulated cloud field (6.4km x 6.4km)
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Simulated cloud field after removing mean wind
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3D animation of simulated cloud field
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LES cloud ensemble statistics
http://roc.eos.ubc.ca/users/zming/bomex/
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3. Life Cycle of Simulated Individual
Clouds
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Tracer technique
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Isolated individual cloud (E)
liquid water
tracer
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If no cloud
tracer
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General characteristics: cloud-top evolution
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Cloud inhomogeneity: animation on variable space
red: saturated positively buoyant; green: saturated negatively buoyant;
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blue: unsaturated negatively buoyant;black:unsaturated positively buoyant
height
Cloud intermittency: pulsating ascent
decay
1250 m
decay
t1
t2
time
t3
t4
θl qt θv w
difference
between cloud
and environment
at level 1250 m
from cloud E.
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height
Cloud-top determination
t1
t2
time
t3
Cloud ascent is non-steady and consists
of a series of pulses. Cloud maximum
ascending height should be determined by
ascending cloud-top (ACT) properties
rather than cloud mean properties.
t4
t3
t2
t1
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Comparison of buoyancy: 6 clouds
red: cloud mean;
green: cloud-top
mean;
blue: the most
undilute parcel
in cloud-top.
Ascending cloud-top is more buoyant and less diluted than the cloud
mean property.
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Vertical velocity of ascending cloud-tops
2
∂
w
1 p
2 ∂z
2
∂
w
1 p
2 ∂z
= Bp
(1)
= Bp − εw2p
(2)
red: simulated ascending cloud-top mean vertical velocity w.
black: predicted w using (1) and cloud-mean B.
green: predicted w using (1) and cloud-top mean B.
blue: predicted w using (2) and cloud-top mean B.
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Ascending cloud-top mixture distribution
t3
t2
t1
θl (K)
qt (kg/kg)
Ascending cloud-top has mixture distribution peaking at properties of
nearly undilute subcloud air and maintains a core structure.
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Cloud lifetime averaged vertical mass flux
Individual clouds produce net downward mass flux in the upper 1/3 of
their depth. Small clouds tend to have downward mass flux extend to
lower level.
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Mass fluxes partitioned into 4 categories
red: saturated
positively buoyant;
green: saturated
negatively buoyant;
blue:unsaturated
negatively buoyant;
black:unsaturated
positively buoyant
Saturated positively buoyant mixtures dominate upward mass flux;
unsaturated negatively buoyant mixtures dominate downward mass.
However, there also exist significant amount counter-buoyancy
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transport of air mass.
Life cycle of vertical mass flux profile for each cloud
During the developing stage the clouds produce on-average upward mass
fluxes while at the dissipating stage the clouds produce net downward
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mass fluxes.
Partitioned buoyancy fluxes
red: saturated
positively buoyant;
green: saturated
negatively buoyant;
blue: unsaturated
negatively buoyant;
black:unsaturated
positively buoyant
Unsaturated negatively buoyant mixtures dominate the buoyancy flux
near the upper 1/3 of cloud depth.
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The nature of
downdrafts
∆θl
Unsaturated downdrafts are
systematically cooler and
moister than the
environment and therefore
must be associated with
cloud evaporation.
∆qt
red: saturated positively buoyant;
green: saturated negatively
buoyant;
blue: unsaturated negatively
buoyant;
black:unsaturated positively
buoyant
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Cloud lifetime averaged thermodynamic fluxes
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Convective tendencies produced by individual clouds
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The role of cloud size in cloud ensemble transport
Small clouds only moisten and cool
their environment throughout their
depth
Large clouds moisten and cool their
environment near their tops but dry and
warm it near their bases
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4. Conclusion (1)
1.
Simulated clouds are inhomogeneous and ascend in a series of
pulses. Ascending cloud-top maintains a core structure, which is
less diluted and determines cloud maximum ascending height. The
mixing behavior of ascending cloud-top is consistent with shedding
thermal models rather than entraining plume models.
2.
Individual clouds produce net downward mass flux in the upper 1/3
of their depth. The downward mass flux comes primarily from the
unsaturated cloud mixed-region and at the dissipating stage.
Unsaturated downdrafts are systematically cooler and moister than
their environment and therefore must be associated with cloud
evaporation. Unsaturated cloud mixtures dominate the mass and
buoyancy fluxes near cloud-top region and therefore are important
in mass flux parameterization.
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Conclusion (2)
3.
The vertical profile of convective tendencies produced by individual
clouds depends on cloud size/height; Large clouds warm and dry
their environment at the lower half of their depth and cool and
moisten it at the upper half of their depth, while small clouds tend to
cool and moisten throughout their depths. The varying effect of
cloud size on the redistribution of heat and moisture requires a
whole population of clouds to achieve the ensemble transport,
which balances the large-scale forcing. The observed cloud size
distribution can be explained by individual cloud dynamics and the
large-scale forcing.
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5. Future Work
1.
Implement and test an episodic mixing and buoyancy-sorting
parameterization in Canadian GCM-SCM.
2.
Extend the 3D simulations to deep convection.
Available papers:
Episodic Mixing and Buoyancy-sorting Representation of Shallow
Convection: A Diagnostic Study (accepted for publication in JAS)
Life Cycle of Numerically Simulated Shallow Cumulus Clouds
(to be submitted to JAS)
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