Numerical Weather Prediction Numerical Weather Prediction Parametrization of Diabatic ProcessesParametrization of Diabatic Processes

Clouds (1)Clouds (1)Cloud MicrophysicsCloud Microphysics

Richard Forbes

and Adrian Tompkins

forbes@ecmwf.int

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OutlineOutline

• LECTURE 1: Cloud Microphysics1. Overview of GCM cloud parametrization issues

2. Microphysical processes

2.1 Warm phase

2.2 Cold phase

3. Summary

• LECTURE 2: Cloud Cover in GCMs

• LECTURE 3: The ECMWF Cloud Scheme

• LECTURE 4: Validation of Cloud Schemes

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1. Overview of GCM Cloud 1. Overview of GCM Cloud Parametrization IssuesParametrization Issues

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1. Water Cycle

2. Radiative Impacts

3. Dynamical Impacts

The Importance of Clouds

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Clouds in GCMs - What are the Clouds in GCMs - What are the problems ?problems ?

convection

Clouds are the result of complex interactions between a large number of processes

radiation

turbulence

dynamics

microphysics

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Clouds in GCMs - What are the Clouds in GCMs - What are the problems ?problems ?

Many of these processes are only poorly understood - For example, the interaction with radiation

Cloud-radiation interaction

Cloud macrophysics Cloud microphysics “External” influence

Cloud fraction and overlap

Cloud top and base height Amount of

condensate

In-cloud conden-sate distribution

Phase of condensate Cloud particle

size

Cloud particle shape

Cloud environment

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Cloud Parametrization Issues:Cloud Parametrization Issues:

• Microphysical processes

• Macro-physical – subgrid heterogeneity

• Numerical issues )()()( llll qDqSqAt

q

Cloud Parametrization Issues:Cloud Parametrization Issues:Which quantities to represent ?Which quantities to represent ?

• Cloud water droplets• Rain drops• Pristine ice crystals• Aggregate snow flakes• Graupel pellets• Hailstones

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• Note for ice phase particles: Additional latent heat. Terminal fall speed of ice hydrometeors significantly less (lower density). Optical properties are different (important for radiation).

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Cloud Parametrization Issues:Cloud Parametrization Issues:Complexity ?Complexity ?

Ice mass

Ice number

Small ice

Medium ice

Large ice

Most GCMs only have simple single-moment schemes

Ice Mass

Liquid Mass

CloudMass

Complexity

“Single Moment”Schemes

“Double Moment”Schemes

“Spectral/Bin”Microphysics

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Cloud Parametrization Issues:Cloud Parametrization Issues:Diagnostic or prognostic Diagnostic or prognostic variables ?variables ?

Cloud condensate mass (cloud water and/or ice), ql.

Diagnostic approach

,, 11 tt

fq nnl

Prognostic approach

)()()( llll qDqSqAt

q

CAN HAVE MIXTURE OF APPROACHES

Advection + sedimentation

Sources

Sinks

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Simple Bulk MicrophysicsSimple Bulk Microphysics

VAPOUR (prognostic)

CLOUD (prognostic)

RAIN (diagnostic)

Evaporation

Autoconversion

Evaporation

Condensation

Why ?

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Microphysics - a “complex” Microphysics - a “complex” GCM schemeGCM scheme

Fowler et al., JCL, 1996

Similar complexity to many schemes in use

in CRMs

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2. Microphysical Processes2. Microphysical Processes

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Cloud microphysical processesCloud microphysical processes

• We would like to include into our models:– Formation of clouds– Release of precipitation– Evaporation of both clouds and precipitation

• Therefore we need to describe– Nucleation of water droplets and ice crystals from water vapour– Diffusional growth of cloud droplets (condensation) and ice crystals

(deposition)– Collection processes for cloud drops (collision-coalescence), ice crystals

(aggregation) and ice and liquid (riming) leading precipitation sized particles

– The advection and sedimentation (falling) of particles– the evaporation/sublimation/melting of cloud and precipitation size

particles

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Microphysics: Microphysics: A complex A complex system!system!

Overview of(1) Warm Phase Microphysics T > 273K(2) Mixed Phase Microphysics ~250K < T < 273K(3) Pure ice Microphysics T < ~250K

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2. Microphysical Processes 2. Microphysical Processes 2.1 Warm Phase 2.1 Warm Phase

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Droplet ClassificationDroplet Classification

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Nucleation of cloud droplets:Nucleation of cloud droplets:Important effects for particle Important effects for particle activationactivation

TrRe

re

lvs

s

2

exp)(

)(

Planar surface: Equilibrium when e=es and number of molecules impinging on surface equals rate of evaporation

Curved surface: saturation vapour pressure increases with smaller drop size since surface molecules have fewer binding neighbours.

Surface molecule has fewer neighbours

radius drop

droplet of tension Surface

r

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Nucleation of cloud droplets:Nucleation of cloud droplets:Homogeneous NucleationHomogeneous Nucleation

• Drop of pure water forms from vapour

• Small drops require much higher super saturations

• Kelvin’s formula for critical radius for initial droplet to “survive”

• Strongly dependent on supersaturation

• Would require several hundred percent supersaturation (not observed in the atmosphere).

sLv

vlc

eeTR

Rln

2

droplet of tension Surface

Radius Critical

cR

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Nucleation of cloud droplets:Nucleation of cloud droplets:Heterogeneous NucleationHeterogeneous Nucleation

• Collection of water molecules on a foreign substance, RH > ~80% (Haze particles)

• These (hydrophilic) soluble particles are called Cloud Condensation Nuclei (CCN)

• CCN always present in sufficient numbers in lower and middle troposphere

• Nucleation of droplets (i.e. from stable haze particle to unstable regime of diffusive growth) at very small supersaturations.

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Nucleation of cloud droplets:Nucleation of cloud droplets:Important effects for particle Important effects for particle activationactivation

Planar surface: Equilibrium when e=es and number of molecules impinging on surface equals rate of evaporation

Curved surface: saturation vapour pressure increases with smaller drop size since surface molecules have fewer binding neighbours.Effect proportional to 1/r (curvature effect)

Presence of dissolved substance: saturation vapour pressure reduces with smaller drop size due to solute molecules replacing solvent on drop surface (assuming esollute<ev)Effect proportional to 1/r3 (solution effect)

Surface molecule has fewer neighbours

Dissolved substance reduces vapour pressure

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Nucleation of cloud droplets:Nucleation of cloud droplets:Heterogeneous NucleationHeterogeneous Nucleation

“Curvature term”Small drop – high radius of curvature

easier for molecule to escape

“Solution term”Reduction in

vapour pressure due to dissolved

substance

activated"" 12.0

,01.1/

mr

ese

e/e s

equi

libriu

m

Haze particle in equilibrium

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Diffusional growthDiffusional growthof cloud water dropletsof cloud water droplets

)1(1

STR

De

rdt

dr

vL

s

For r > 1 m and neglecting diffusion of heat

D=Diffusion coefficient, S=SupersaturationNote inverse radius dependency

Once droplet is activated, water vapour diffuses towards it = condensation

Reverse process = evaporation

Droplets that are formed by diffusion growth attain a typical size of 0.1 to 10 m

Rain drops are much larger

-drizzle: 50 to 100 m

-rain: >100 m

Other processes must also act in precipitating clouds

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CollectionCollectionCollision-coalescence of water dropsCollision-coalescence of water drops

• Drops of different size move with different fall speeds - collision and coalescence

• Large drops grow at the expense of small droplets

• Collection efficiency low for small drops

• Process depends on width of droplet spectrum and is more efficient for broader spectra – paradox

• Large drops can only be produced in clouds of large vertical extent – Aided by turbulence (differential evaporation), giant CCNs ?

Rain drop shape Chuang and Beard (1990)

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Parameterizing nucleation and Parameterizing nucleation and droplet growthdroplet growth

• Nucleation: Since “Activation” occurs at supersaturations less than 1%, most schemes assumes all supersaturation is immediately removed as liquid water

• Note that this assumption means that models can just use one “prognostic” equation for the total water mass, the sum of vapour and liquid

• Usually, the growth equation is not explicitly solved, and in single-moment schemes simple (diagnostic) assumptions are made concerning the droplet number concentration when needed (e.g. radiation). These often assume more CCN in polluted air over land.

27Microphysics - ECMWF Seminar on Parametrization 1-4 Sep 2008 27

Microphysical Parametrization Microphysical Parametrization “Autoconversion” of cloud drops to “Autoconversion” of cloud drops to raindropsraindrops

qlqlcrit

Gp

qlqlcrit

Gp

• Linear function of ql (Kessler, 1969)

• Function of ql with additional term to avoid singular threshold and non-local precipitation term (Sundqvist 1978)

• Or, for example, for a more complex double-moment parametrization (Seifert and Beheng,2001), derived directly from the stochastic collection equation.

Kessler

Sundqvist

otherwise0

if0critcrit

lllll qqqqc

t

q

2

0 1 critl

l

q

q

ll eqct

q1F

1F

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Heterogeneous NucleationHeterogeneous NucleationRH>78% (Haze)RH>78% (Haze)

Schematic of Warm Rain Schematic of Warm Rain ProcessesProcesses

CCN

~10 microns~10 microns

RH>100.6%RH>100.6%““Activation”Activation”DiffusionalDiffusional

GrowthGrowth

Different fall speedsDifferent fall speeds

Coalescence

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2. Microphysical Processes2. Microphysical Processes2.2 Cold Phase 2.2 Cold Phase

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Kepler (1611) “On the Six-Kepler (1611) “On the Six-Cornered Snowflake”Cornered Snowflake”

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““The Six-Cornered Snowflake”The Six-Cornered Snowflake”

www.snowcrystals.comKen Libbricht

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• Ice nucleation

• Depositional Growth (and sublimation)

• Collection (aggregation/riming)

• Splintering

• Melting

Ice Microphysical ProcessesIce Microphysical Processes

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Ice NucleationIce Nucleation

• Droplets do not freeze at 0oC !

• Ice nucleation processes can also be split into Homogeneous and Heterogeneous processes, but complex and not well understood.

• Homogeneous freezing of water droplets occurs below about -38oC,

• Homogeneous nucleation of ice crystals dependent on a critical relative humidity (fn of T, Koop et al. 2000).

• Frequent observation of ice between 0oC and colder temperatures indicates heterogeneous processes active.

• Number of activated ice nuclei increases with decreasing temperature.

Fletcher 1962

• Observations: – < -20oC Ice free clouds are rare– > -5oC ice is unlikely (unless ice falling from above!)– ice supersaturation ( > 10% ) observations are

common

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Ice Nucleation:Ice Nucleation:Heterogeneous nucleationHeterogeneous nucleation

Supercooled drop

aerosol

I will not discuss heterogeneous ice nucleation in great detail in this course due to lack of time and the fact that

these processes are only starting to be tackled in Large-

scale models. See recent work of Ulrike Lohmann for more

details

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Pure ice Phase: Homogeneous Pure ice Phase: Homogeneous Ice NucleationIce Nucleation

• At cold temperature (e.g. upper troposphere) difference between liquid and ice saturation vapour pressures is large.

• If air mass is lifted, and does not contain significant liquid particles or ice nuclei, high supersaturations with respect to ice can occur, reaching 160 to 170%.

• Long lasting contrails are a signature of supersaturation

Institute of Geography, University of Copenhagen

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4( )

1s s

a si

CsFS D

L L RTRT k T Xe

Equation for the rate of change of mass for an ice particle of diameter D due to deposition (diffusional growth), or evaporation

Diffusional growth of ice crystalsDiffusional growth of ice crystalsDepositionDeposition

• Deposition rate depends primarily on• the supersaturation, s • the particle shape (habit), C • the ventilation factor, F

• The particular mode of growth (edge growth vs corner growth) is sensitive to the temperature and supersaturation

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Diffusional growth of ice crystalsDiffusional growth of ice crystalsIce HabitsIce Habits

Ice habits can be complex, depend on temperature: influences fall speeds and radiative properties

http://www.its.caltech.edu/~atomic/snowcrystals/

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Diffusional growth of ice crystalsDiffusional growth of ice crystalsAnimationAnimation

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Ice Saturation

Homogeneous Freezing Temperature

Water S

aturationDiffusional growth of ice crystalsDiffusional growth of ice crystalsMixed Phase Clouds: Bergeron Process Mixed Phase Clouds: Bergeron Process (I)(I)

The saturation water vapour pressure with respect to ice is smaller than with respect to water

A cloud, which is saturated with respect to water is supersaturated with respect to ice !

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Diffusional growth of ice crystalsDiffusional growth of ice crystalsMixed phase cloud Bergeron process Mixed phase cloud Bergeron process (II)(II)

Ice particle enters water cloud

Cloud is supersaturated with respect to ice

Diffusion of water vapour onto ice particle

Cloud will become sub-saturated with respect to water

Water droplets evaporate to increase water vapour

Ice particles grow at the expense of water

droplets

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• Ice crystals can aggregate together to form “snow”

• “Sticking” efficiency increases as temperature exceeds –5C

• Irregular crystals are most commonly observed in the atmosphere (e.g. Korolev et al. 1999, Heymsfield 2003)

Collection processes:Collection processes:Ice Crystal AggregationIce Crystal Aggregation

Lawson, JAS’99

Field & Heymsfield ‘03

500 m

CPI Model

T=-46oC

Westbrook et al. (2008)

• Some schemes represent ice processes very simply, removing ice super-saturation (as for warm rain process).

• Others, have a slightly more complex representation allowing ice supersaturation (e.g. current ECMWF scheme).

• Increasingly common are schemes which represent ice, supersaturation and the diffusional growth equation, and aggregation represented as an autoconversion to snow or parametrization of an evolving particle size distribution (e.g. Wilson and Ballard, 1999). See Lohmann and Karcher JGR 2002(a,b) for another example of including ice microphysics in a GCM.

Parametrization of ice crystal Parametrization of ice crystal diffusion growth and aggregationdiffusion growth and aggregation

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Collection processes:Collection processes:Riming Riming –– capture of water drops by capture of water drops by ice ice

• Graupel formed by collecting liquid water drops in mixed phased clouds (“riming”), particulaly when at water saturation in strong updraughts (convection). Round ice crystals with higher densities and fall speeds than snow dendrites

• Hail forms if particle temperature close to 273K, since the liquid water “spreads out” before freezing. Generally referred to as “Hail” – The higher fall speed (up to 40 m/s) imply hail only forms in convection with strong updraughts able to support the particle long enough for growth

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Rimed IRimed Icce Crystalse Crystals

http://www.its.caltech.edu/~atomic/snowcrystals

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Rimed Ice CrystalRimed Ice Crystal

emu.arsusda.gov

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Heavily Rimed Ice CrystalHeavily Rimed Ice Crystal

emu.arsusda.gov

• Most GCMs with parametrized convection don’t explicitly represent graupel or hail (too small scale)

• In cloud resolving models, traditional split between ice, snow and graupel and hail but this split is rather artificial.

• Degree of riming can be light or heavy.

• Alternative approach:– Morrison and Grabowski (2008) have three ice prognostics, ice

number concentration, mixing ratio from deposition, mixing ratio from riming.

– Avoids artificial thresholds between different categories.

Parametrization of rimed ice Parametrization of rimed ice particlesparticles

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Other microphysical processesOther microphysical processesSplintering, Shedding Evaporation, MeltingSplintering, Shedding Evaporation, Melting

• Other processes include evaporation (reverse of condensation), ice sublimation (reverse of deposition) and melting.

• Shedding: Large rain drops break up – shedding to form smaller drops, places a limit on rain drop size.

• Splintering of ice crystals, Hallet-Mossop splintering through riming around -5°C. Leads to increased numbers of smaller crystals.

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Particle Size DistributionsParticle Size Distributions

Mass DistributionSize Distribution

From Fleishauer et al (2002, JAS) Field (2000), Field and Heymsfield (2003)

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Falling PrecipitationFalling Precipitation

• Need to know size distribution• For ice also affected by ice habit• Poses problem for numerics

From R Hogan www.met.rdg.ac.uk/radar

Cou

rtes

y: R

Hog

an,

U.

Re

adin

g

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Image from Robin Hogan. Data from RCRU RAL.

Typical time-height cross section of a front from the vertically pointing 94GHz radar at Chilbolton, UK

Microphysics at the Cloud ScaleMicrophysics at the Cloud Scale

Melting

Ice Nucleation and diffusion growth Aggregation

Warm phase

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3. Summary3. Summary

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Summary: Warm CloudSummary: Warm Cloud

E.g: Stratocumulus

Condensation

(Rain formation - Fall Speeds - Evaporation of rain)

Evaporation

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Summary: Deep Summary: Deep Convective CloudConvective Cloud

• Precipitation Falls Speeds• Evaporation in Sub-Cloud Layer

• Heteorogeneous Nucleation of ice• Splintering/Bergeron Process

• Melting of Snow and Graupel

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Summary: Cirrus cloudSummary: Cirrus cloud

Homogeneous Nucleation(representation of supersaturation)

Heterogeneous Nucleation(representation of nuclei type and concentration)

Diffusional growth, Aggregation Sedimentation of ice crystals

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Simple Bulk MicrophysicsSimple Bulk Microphysics

VAPOUR (prognostic)

CLOUD (prognostic)

RAIN (diagnostic)

Evaporation

Autoconversion

Evaporation

Condensation

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Microphysics - a “complex” Microphysics - a “complex” GCM schemeGCM scheme

Fowler et al., JCL, 1996

Similar complexity to many schemes in use in CRMs

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Summary 1: A complex system!Summary 1: A complex system!

• Molecular Scale– Nucleation/activation, Diffusion/condensation/evaporation

• Particle Scale– Collection/collision-coalescence/aggegation, Shedding/splintering

• Parcel Scale– Particle Size Distributions

• Cloud Scale– Heterogeneity– Interaction with the dynamics (latent heating)

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Summary 2: Simplifying Summary 2: Simplifying assumptionsassumptions• Parametrization of cloud and precipitation microphysical

processes:– Need to simplify a complex system– Accuracy vs. complexity vs. computational efficiency trade off– Appropriate for the application and no more complexity than can be

constrained and understood– Dynamical interactions (latent heating), radiative interactions– Still many uncertainties (particularly ice phase)– Particular active area of research is aerosol-microphysics interactions.– Microphysics often driven by small scale dynamics…..

• Next lecture: Cloud Cover– Sub-grid scale heterogeneity– Linking the micro-scale to the macro-scale

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ReferencesReferences

Reference books for cloud and precipitation microphysics:

Pruppacher. H. R. and J. D. Klett (1998). Microphysics of Clouds and Precipitation (2nd Ed). Kluwer Academic Publishers.

Rogers, R. R. and M. K. Yau, (1989). A Short Course in Cloud Physics (3rd Ed.) Butterworth-Heinemann Publications.

Mason, B. J., (1971). The Physics of Clouds. Oxford University Press.

Hobbs, P. V., (1993). Aerosol-Cloud-Climate Interactions. Academic Press.

Houze, Jr., R. A., (1994). Cloud Dynamics. Academic Press.

Straka, J., (2009). Cloud and Precipitation Microphysics: Principles and Parameterizations. Cambridge University Press. Not yet released!