Numerical Weather Prediction Numerical Weather Prediction Parametrization of diabatic processesParametrization of diabatic processes

Cloud ParametrizationCloud Parametrization

Adrian Tompkins

OutlineOutline

• LECTURE 1: Introduction to Cloud Issues– Physical processes to represent– What are the potential problems in GCMs?– History of cloud schemes

• LECTURE 2: Cloud Cover in GCMs

• LECTURE 3: The ECMWF cloud scheme

• LECTURE 4: Validation of cloud schemes

GCMs: Issues and GCMs: Issues and approachesapproaches

Clouds in GCMs - What are the Clouds in GCMs - What are the problems ?problems ?Many of the observed clouds and especially the processes within them are of subgrid-scale size (both horizontally and vertically)

GCM Grid cell 40-400km

~50

0m

~100km

Macroscale Issues of Macroscale Issues of ParameterizationParameterization

VERTICAL COVERAGEMost models assume that this is 1

This can be a poor assumption with coarse vertical grids.Many climate models still use fewer than 30 vertical levels

currently, some recent examples still use only 9 levels

~50

0m

~100km

Macroscale Issues of Macroscale Issues of ParameterizationParameterization

HORIZONTAL COVERAGE, a

~50

0m

~100km

Macroscale Issues of Macroscale Issues of ParameterizationParameterization

Vertical Overlap of cloudImportant for Radiation and Microphysics Interaction

~50

0m

~100km

Macroscale Issues of Macroscale Issues of ParameterizationParameterization

In cloud inhomogeneity in terms of cloud particle size and number

~50

0m

~100km

Macroscale Issues of Macroscale Issues of ParameterizationParameterization

Just these issues can become very complex!!!

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

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

What do we want to What do we want to represent?represent?

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

Clouds in GCMs - How ?Clouds in GCMs - How ?

Main variables:

Cloud fraction, a - refers to horizontal cover since cloud fills vertical

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

Diagnostic approach

,, 111 tt

fa nn

,, 112 tt

fq nnl

Prognostic approach

)()()( aDaSaAt

a

)()()( llll qDqSqA

t

q

NOT DISTINCT - CAN HAVE MIXTURE OF APPROACHES

Cloud microphysical Cloud microphysical processesprocesses• 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– the change of phase from water vapour to water droplets and

ice crystals– the transformation of small cloud droplets/ice crystals to

larger rain drops/ice particles– the evaporation/sublimation of cloud and precipitation size

particles

Microphysical processes and Microphysical processes and water substanceswater substances• Nucleation of particles• Diffusion growth• Collision-Coalescence • Collection• Breakup of drops• Sedimentation• Ice enhancement• Melting• Evaporation/sublimation

• Involving:• Water vapour• Cloud liquid water• Precipitation liquid water• Cloud ice• Precipitation ice

Processes Uncertain - Parameterization often highly simplified

Reference: “Microphysics of Clouds and Precipitation” by H.R.Pruppacher and J. D. Kett and “A short course in Cloud Physics” by Rogers and Yau

(all subsequent diagrams from latter text unless otherwise stated)

Microphysics: Microphysics: Complex Complex System!System!

Overview of(1) Warm Phase Microphysics T>273K(2) Mixed Phase Microphysics 235K<T<273K(3) Pure ice Microphysics T<235K

Droplet ClassificationDroplet Classification

Nucleation of Water:Nucleation of Water:Homogeneous NucleationHomogeneous Nucleation

• Drop of pure water forms from vapour

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

• strongly dependent on supersaturation

• requires several hundred percent supersaturation (not observed in the atmosphere),

sLv

vlc

eeTR

Rln

2

Nucleation of Water:Nucleation of Water:Heterogeneous NucleationHeterogeneous Nucleation

• Collection of water molecules on a foreign substance, RH > ~80% (Haze particles) (Note, not same when drying)

• Particles are called Cloud Condensation Nuclei (CCN)• CCN always present in sufficient numbers in lower and

middle troposphere• Activation at supersaturations of <1%• Therefore we assume that condensation occurs if

RH>100% (n.b. deep convection)

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

Diffusion growth (water)Diffusion growth (water)

• Nucleation small droplets• 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 than that

– drizzle: 50 to 100 m– rain: >100 m

• other processes must also act in precipitating clouds

)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

Parameterizing Nucleation Parameterizing Nucleation and droplet growthand droplet 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)

Collision-CoalescenceCollision-Coalescence

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

• 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 and entrainment

• important process for low latitudes where deep clouds of high water content are present

Parameterizating Parameterizating “Autoconversion” of cloud drops “Autoconversion” of cloud drops to raindropsto raindrops

Autoconversion (Kessler, AMS monogram 1969)

otherwise0

if0critcrit

lllll qqqqc

t

q

qlqlcrit

Gp

Sundqvist, QJRMS, 1978

2

0 1 crit

l

l

q

q

ll eqc

t

q

qlqlcrit

Gp“Non-local” collectionPcF 11 1

1F1F

P=Precipitation Flux

what are the issues for data assim

ilation?

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

Ice NucleationIce Nucleation

• Ice processes complex and poorly understood• Droplets do not freeze at 0oC! • Can also be split into Homogeneous and

Heterogeneous processes• Processes depend on temperature and history of cloud• Homogeneous freezing of water droplet occurs between

–35 and –40oC (often used assumption in microphysical schemes).

• Frequent observation of ice above these temperatures indicates role for heterogeneous processes

Ice NucleationIce Nucleation

• Spontaneous freezing of liquid droplets smaller than 5 m requires temperature less than -40oC.

• Observations of liquid in cloud are common at -20oC.

• Ice crystals start to appear in appreciable numbers below around -15oC.

• Heterogenous Nucleation responsible: Process less clear

• Ice nuclei: Become active at various temperatures less than 0oC, many fewer

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

common

Fletcher 1962

Heterogeneous NucleationHeterogeneous Nucleation

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

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

Mixed Phase clouds: Bergeron Mixed Phase clouds: Bergeron Process (I)Process (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 !

Bergeron process (II)Bergeron process (II)

Ice particle enters water cloud

Cloud is supersturated 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

Modification of Sundqvist to take Modification of Sundqvist to take Bergeron Process into accountBergeron Process into account

Sundqvist, QJRMS, 1978

2

0 1 crit

l

l

q

q

lP eqcG

qlqlcrit

Gp

Collection

Bergeron Process

PcF 11 1

TcF 2681 22

21FF21FF

Otherwise, most schemes have neglected ice processes, removing ice super-saturation “al la Warm rain” – See Lohman and Karcher JGR 2002(a,b) for first

attempts to include ice microphysics in GCM

AggregationAggregation

• Ice crystals can aggregate together to form snow• Temperature dependent, process increases in efficiency

as temperature exceeds –5C, when ice surface becomes sticky

• Also a secondary peak between –10 and –16C when dendrite arms get entangled

RimingRiming

• If vapour exceeds the water saturation mixing ratio, water can condense on ice crystal, and then subsequently freeze to form “graupel”: Round ice crystals with higher densities and fall speeds than snow dendrites

• Graupel and Hail are also formed by aggregating liquid water drops in mixed phased clouds (“riming”)

– If the Latent heat of condensation and fusion keeps temperature close to 273K, then high density hail particle forms, 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

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

Aggregation and Riming: Aggregation and Riming: Simple stratified picture Simple stratified picture

Ice HabitsIce Habits Ice habits can be complex: influences fall speeds and radiative properties

From Fleishauer et al 2002, JAS

Note shape/diameter distribution not monotonic with height, Turbulence!

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

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g

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

Homogeneous/heterogeneous Homogeneous/heterogeneous nucleation nucleation

• However even in “polluted” NH air, homogeneous nucleation can dominate in strong updraughts

• However wind fluctuations can occur on mesoscale length-scales comparible or smaller to grid length.

– Upscale cascade from turbulence– Gravity waves– Subgrid instabilities (cloud top

instabilities)……

• It is clear that models are deficient in representing these

• E.g: Lohmann shows inadequacy of ECMWF model, and how enhancement of turbulence activity can produce improved spectra

From

haag and Kaerchner

ECMWF resolved motions only

aircraft

Limb Sounder and Mozaic DataLimb Sounder and Mozaic Data(Pictures courtesy of Klaus Gierens and Peter Spichtinger, DLR)(Pictures courtesy of Klaus Gierens and Peter Spichtinger, DLR)

• Recent observations (e.g. Mozaic aircraft and Microwave sounders) have revealed such values are common.

3000 km supersaturated segment observed ahead of front

Heteorogeneous NucleationHeteorogeneous Nucleation

• On the other hand, in air polluted by organic and mineral dust, supersaturation achieve perhaps 130%.

• Research is ongoing to determine the nature of ice nuclei at these colder temperatures

• This process probably more prevalent in NH where air is less ‘clean’

22nd April 2003: Modis Image from http://modis.gsfc.nasa.gov

Summary: Warm CloudSummary: Warm Cloud

E.g: Stratocumulus

Condensation

(Rain formation - Fall Speeds - Evaporation of rain)

Evaporation

Summary: Deep Convective Summary: Deep Convective CloudCloud

• Precipitation Falls Speeds• Evaporation in Sub-Cloud Layer

• Heteorogeneous Nucleation of ice• Splintering/Bergeron Process• Melting of Snow and Graupel

Summary: Cirrus cloudSummary: Cirrus cloud

Homogeneous Nucleation(representation of supersaturation)

Heterogeneous Nucleation(representation of nuclei type and concentration)

Sedimentation of Ice crystals?Size distribution and formation of snow?

Cloud Schemes - A Brief Cloud Schemes - A Brief HistoryHistory

60s

Condensation(non-convective)

qv > qs

Radiationeffects

Prescribedzonal meanalbedo andemissivity

Convection No cloudinteraction

Microphysics none

60s 70s

Condensation(non-convective)

qv > qs qv > qs

Radiationeffects

Prescribedzonal meanalbedo andemissivity

a diagnostic[usually f(RH)]ql prescribed

Convection No cloudinteraction

acu = f(CP)ql cu prescribed

Microphysics none none

60s 70s 80s

Condensation(non-convective)

qv > qs qv > qs ql prognostica diagnostic

Radiationeffects

Prescribedzonal meanalbedo andemissivity

a diagnostic[usually f(RH)]ql prescribed

a = as cloudscheme

Convection No cloudinteraction

acu = f(CP)ql cu prescribed

acu = f(CP)ql cu prescribed

Microphysics none none Simple bulkmicrophysics

60s 70s 80s 90s-

Condensation(non-convective)

qv > qs qv > qs ql prognostica diagnostic

ql prognostica prognostic(directly orindirectly)

Radiationeffects

Prescribedzonal meanalbedo andemissivity

a diagnostic[usually f(RH)]ql prescribed

a = as cloudscheme

a = as cloudscheme

Convection No cloudinteraction

acu = f(CP)ql cu prescribed

acu = f(CP)ql cu prescribed

Direct link toa and ql

Microphysics none none Simple bulkmicrophysics

Complex bulkmicrophysics(ice)

Simple Bulk MicrophysicsSimple Bulk Microphysics

VAPOUR (prognostic)

CLOUD (prognostic)

RAIN (diagnostic)

WHY?

Evaporation

Autoconversion

Evaporation

Condensation

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

Fowler et al., JCL, 1996

Similar complexity to many schemes in use in CRMs

Mostly treated as instant“No supersaturation

assumption”

“Threshold” linear or exponential terms

with efficiency adjustments

)( vsat qqKR

Cloud Cover: Why Important?Cloud Cover: Why Important?

In addition to the influence on radiation, the cloud cover is important for the representation of microphysics

Imagine a cloud with a liquid condensate mass ql

The incloud mass mixing ratio is ql/a

a largea small

GC

M g

rid b

ox

precipitation not equal in each case sinceautoconversion is nonlinear

Reminder: Autoconversion (Kessler, 1969)

otherwise0

if0critcrit

llllP

qqqqcG

Complex microphysics perhaps a wasted effort if assessment of a is poor