Life Cycle of Numerically Simulated Life Cycle of Numerically Simulated Shallow Cumulus CloudsShallow Cumulus Clouds

Ming Zhao and Philip H. AustinDepartment of Earth and Ocean Sciences

The University of British Columbia Canada

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3. Life Cycle of Simulated Individual Clouds

4. Conclusions

2. A Large Eddy Simulation

1. Motivation

Outline

5. Future Work

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1. MotivationAssumption: 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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LCL

LNB

LCT

LFC

Adiabatic cloud modelConceptual Models of Shallow Cumulus Clouds

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LCL

Entraining plume model (EPM)

LFC

LNB

LCT

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Cumulus clouds are highly inhomogeneous; cumulus Cumulus clouds are highly inhomogeneous; cumulus cloudcloud--top is determined by nearly top is determined by nearly undiluteundilute subcloudsubcloud air.air.

Weakness:Weakness:

Warner’s Paradox (1970).Warner’s Paradox (1970).

correctcorrectcloudcloud--top height top height

overover--estimate cloud estimate cloud liquid water content liquid water content

correct liquid correct liquid water content water content

underunder--estimate estimate cloudcloud--top height top height

This was a problem 30 years ago, this is a problem now. This was a problem 30 years ago, this is a problem now. But many people still use But many people still use EPMsEPMs due to their simplicity.due to their simplicity.

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LCL

LFC

LNB

LCT

Episodic mixing and buoyancy-sorting model (EMBS)(Raymond and Blyth 1986, Emanuel 1991, 1999)

saturated positively buoyantsaturated negatively buoyantunsaturated negatively buoyant

Warner’s paradox

Advantages:

downdrafts

mixing line

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2. A Large Eddy Simulation2. A Large Eddy Simulation

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The points to be addressed include:The points to be addressed include:

Cloud life cycles and their impact on convective mass flux.

Buoyancy effects in cumulus convective transport.

Cloud evaporation and the role of the invisible part of cumulus convection.

The role of cloud size in the redistribution of heat and moisture and the effect of cloud size distribution on cloud ensemble transport.

Cloud inhomogeneity and cloud-top determination.

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Colorado State University LES/CRM model

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.

(Khairoutdinov and Randall 2002)

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Model domain: 256x256x128 grid points

Resolution: 25 m uniform in all 3 dimensions

Time step is 1.5 s

Case setup Case setup ---- BOMEXBOMEXSounding and forcings, details at http://www.knmi.nl/~siebesma/gcss/bomex.html

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Simulated cloud field (6.4km x 6.4km)Simulated cloud field (6.4km x 6.4km)

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Simulated cloud field after removing mean windSimulated cloud field after removing mean wind

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3D animation of simulated cloud field3D animation of simulated cloud field

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LES cloud ensemble statisticsLES cloud ensemble statistics

http://roc.eos.ubc.ca/users/zming/bomex/

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3. Life Cycle of Simulated Individual 3. Life Cycle of Simulated Individual CloudsClouds

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Tracer techniqueTracer technique

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liquid waterliquid water tracertracer

Isolated individual cloud (E)Isolated individual cloud (E)

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tracertracer

If no cloud If no cloud

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General characteristics: cloudGeneral characteristics: cloud--top evolutiontop evolution

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Cloud Cloud inhomogeneityinhomogeneity: animation on variable space: animation on variable space

red: saturated positively buoyant; green: saturated negatively buoyant; blue: unsaturated negatively buoyant;black:unsaturated positively buoyant

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Cloud intermittency: pulsating ascentCloud intermittency: pulsating ascenthe

ight

timet1 t2 t3 t4

decay

difference between cloud and environment at level 1250 m from cloud E.

lθ vθtq w

decay1250 m

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CloudCloud--top determinationtop determination

time

heig

ht

t1 t2 t3 t4

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.

t1t2t3

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Comparison of buoyancy: 6 cloudsComparison of buoyancy: 6 cloudsred: 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 cloudVertical velocity of ascending cloud--topstops

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.

pp Bzw

=∂

∂ 2

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ppp wBzw

ε−=∂

∂

(1)

(2)

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Ascending cloudAscending cloud--top mixture distributiontop mixture distribution

t1t2t3

(K) lθ

(kg/kg) tq

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 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 categoriesMass 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 transport of air mass.

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Life cycle of vertical mass flux profile for each cloudLife 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 mass fluxes.

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Partitioned buoyancy fluxesPartitioned 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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lθ∆

tq∆

red: saturated positively buoyant; green: saturated negatively buoyant; blue: unsaturated negatively buoyant;black:unsaturated positively buoyant

Unsaturated downdrafts are systematically cooler andmoister than the environment and therefore must be associated withcloud evaporation.

The nature of The nature of downdraftsdowndrafts

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Cloud lifetime averaged thermodynamic fluxesCloud lifetime averaged thermodynamic fluxes

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Convective tendencies produced by individual cloudsConvective tendencies produced by individual clouds

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The role of cloud size in cloud ensemble transportThe role of cloud size in cloud ensemble transportSmall 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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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.

4. Conclusion (1)

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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 awhole 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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1. Implement and test an episodic mixing and buoyancy-sorting parameterization in Canadian GCM-SCM.

Available papers:

5. Future Work

2. Extend the 3D simulations to deep convection.

Episodic Mixing and Buoyancy-sorting Representation of Shallow Convection: A Diagnostic Study (accepted for publication in JAS)(accepted for publication in JAS)

Life Cycle of Numerically Simulated Shallow Cumulus Clouds(to be submitted to JAS)(to be submitted to JAS)