Laboratory studies of cloud processesLaboratory studies of cloud processes and interpretation with models

Dr Paul ConnollyUniversity of ManchesterUniversity of Manchester

Outline

• Ice crystal growth from vapoury g p– Continuum theory– Elastic and inelastic collisions betweenElastic and inelastic collisions between

vapour and solid– Strotski et al (2011)Strotski et al (2011)

• Ice growth by aggregation - snowflakesHosler and Halgren Latham Hobbs etc– Hosler and Halgren, Latham, Hobbs, etc

– Connolly et al (2011)

• Summaryy

Growth from water vapourGrowth from water vapour

Change of phase: vapour to solid.

Heat conduction: `Diffusion’ of heatHeat conduction: Diffusion of heat

In 1822 Fourier presented his work on heat flow in Théorie analytique de la chaleur (The Analytic Theory of heat), in which he based his reasoning on Newton's law of cooling, namely, that the flow of heat between two adjacent molecules is proportional to the extremely small difference of their temperatures.

Jean Baptiste Joseph Fourier (1768-1830)Tk∇−=q

Fourier believed that keeping the body wrapped up in blankets was

q

p g y pp pbeneficial to the health. He died in 1830 when in this state he tripped and fell down the stairs at his home

Science World Wolfram. http://scienceworld.wolfram.com/biography/Fourier.html. Retrieved 2009-05-06

Heat transfer `smooths out gradients’Heat transfer smooths out gradients

Heat is transferred from warm to cold regions.

So for the growing ice crystal (warmed by latent heat) it is transferred away

Diffusion of massDiffusion of massFick's law of diffusion

Philosophical magazine (1855)

Adolf Eugen Fick (3 September 1829, Kassel, Hesse-Kassel – 21 August 1901) was a German physiologist He started to study mathematicsphysiologist. He started to study mathematics and physics, but then realized he was more interested in medicine. He earned his doctorate in medicine at Marburg in 1851

In 1855 he introduced Fick's law of diffusion, which governs the diffusion of

in medicine at Marburg in 1851.

Adolf Eugen Fick (1829-1901)

, gsalts in water and vapour molecules in air

Fick managed to double-publish his law of diffusion, as it applied equally to physiology and physics.

ρ∇−= Dj

Diffusion `smooths out’ gradientsus o s oo s ou g ad e s

Vapour is transferred from regions of high concentration to low concentration

H b th d it b t t d f thHence, because the vapour density can be supersaturated away from the crystal, but only saturated at the crystals surface, vapour diffuses toward the crystal

Among his many achievements ( El i h(e.g. Electromagnetic theory, 1864), Maxwell (1870) was the first to combine the laws of diffusion of

d h t t it d thmass and heat to write down the particle growth equations in the continuum regime

James Clerk Maxwell (1831 1879)But this assumed that the vapour density in moist air is continuous James Clerk Maxwell (1831–1879)density in moist air is continuous (no sharp jumps) right up to the drop surface.

Diffusion of vapour to a growing crystal

When the particles have radii comparable to the mean free path

Diffusion of vapour to a growing crystal

(liberating latent heat)p p

of air it becomes unrealistic Diffusion of heat from a crystal

Langmuir made a step forwardLangmuir made a step forward1918 paper in Journal Am Chem Soc.

I i L i (1881 1957)Irving Langmuir (1881-1957)

We now know from the work of NA Fuchs (1959)

Continuum regime (droplet sizes much larger than the mean free path of air)path of air)

in vapourgradient ~j

Kinetic regime (droplet sizes smaller than the mean free path of air)of air)

α×in vapourgradient ~j i ll d th d tiα is called the accommodation

coefficient and is unknown

Summary of previous work on theSummary of previous work on the deposition coefficient

Gierens et al (2003)Gierens et al (2003)Note that the importance of alpha in ice nucleation in cirrus clouds is a consequence of the Bergeron-Findeison process.

N t iti i thNot sensitive in the range

0110 0.11.0 << α

Ice number concentration very sensitive to choice of the mass accommodation coefficient

Climate is also sensitive to alphaSimulation where they changed the mass accommodationthe mass accommodation coefficient from 0.5 to 0.006.

Completely dwarfs other `cloud’ sensitivities

Lohmann et al (2008, ERL)

Schematic of AIDA cloud chamber

Allow the ice crystals to grow from the vapour (and therefore deplete the water vapour in the chamber).

To assess `goodness of fit’ look at correlations and residual differences

Insert ice crystals into the

and residual differences between obs and model

model at the observed rate

Run the model along the precisealong the precise conditions of temperature and pressure thatpressure that were measured

Our work225 K 217 K 206 K 191 K

Take the experimental uncertainty as the range in alpha that give the best correlations and the lowest residual diffdifferences

Accommodation coefficient not less than 0.1

This means that it doesn’t appreciably affect cloud formationpp y

In real clouds however, once formed ice crystals also grow by aggregation

ICE CRYSTALS FROM CIRRUS, T<-40C (EMERALD-1)

Images taken from a Cloud Particle Imager

(Facility for Ground-base Atmospheric Measurement)

ICE CRYSTALS FROM ANVIL CIRRUS (EMERALD-2)

Images taken from a Cloud Particle Imager

(Facility for Ground-base Atmospheric Measurement)

ICE CRYSTALS FROM ANVIL CIRRUS (EMERALD-2)

Images taken from a Cloud Particle Imager

(Facility for Ground-base Atmospheric Measurement)

ICE CRYSTALS IN MIXED PHASE, T>-15C (CLACE)

Images taken from a Cloud Particle Imager

(Facility for Ground-base Atmospheric Measurement)

Pressure melting of ice “or regelation”Pressure melting of ice or regelation

J Th (1822 1892)James Thomson (1822-1892)

Lord Kelvin (1824-1907)

Snowflakes: “Note on Regelation” of iceSnowflakes: Note on Regelation of ice

Michael Faraday (1791-1867)

1860: a `quasi-liquid’ layer exists at the interface between ice and air, and that this layer solidifies only when y ysandwiched between two ice surfaces

Hosler Jensen and Goldshlak 1957Hosler, Jensen and Goldshlak 1957

The ice spheres were brought in contact for 1 minute Clearly this

Sticking never occurred colder than -25C

contact for 1 minute. Clearly this would not happen in the atmosphere!

Sintering (Mason 1957, Hobbs 1974)g ( )It is based on atomic diffusion. Diffusion occurs in any material above absolute zero but it occurs much faster at higher temperatures.

The saturation vapour ppressure is lower over a concaved surface so vapour is transported to form a `neck’

Again Hobbs, puzzled about how the spheres could come into contact for bonding to take place

Hobbs (1974): initial bridging between the two ice particles in contact is most likely the result of a quasi-liquid layer.

Efficiency of aggregationEfficiency of aggregationAggregation rate = number gg gof sticking events per second between i and j.

ri rj If all collisions resulted in a sticking event

vi ( ) jjiji nrr vv4

2 −+π

vj4Aggregation efficiency, Ea,number of sticking eventsnumber of sticking events divided by number of collisions

Hosler and Halgren, 1960

Target

Plates were observed at -12C

“experiments indicate that the basal plane is stickier than the planes parallel to the c-axis”

Summary of previous work on snowflakes

P i ibl f lti i d• Pressure is responsible for melting ice and forming the ice bond – Thomson (1856).

• Pressure not required, but liquid-like layer – Faraday (1860) – still not resolved!y ( )

• Sintering (molecular diffusion) strengthens the neck but liquid like layer responsiblethe neck, but liquid like layer responsible for initial bridging.Interlocking ma be responsible for• Interlocking may be responsible for crystals coming in contact (Ohtake, 1969)

Particle size dist. at top

Cloud of dropsFormation of ice causes

Formation of ice causes theFormation of ice causes

the evaporation of dropscauses the evaporation of drop

Particle size dist. at bottomLarge aggregatea c e s e d s a bo oLarge aggregate observed first

An increase toward the end (largest aggregates)

A reduction in size through the course of the experiment

Single crystals at top of chamber-30 deg C -25 deg C -20 deg C

g y p

-15 deg C -10 deg C -5 deg C

Note that plates were seen at -10, -15, -20, -25C. Should be possible to test Hosler and Halgren’s hypothesis.

Aggregates at bottom of chamber-30 deg C -25 deg C -20 deg C

gg g

-15 deg C -10 deg C -5 deg C

Aggregates grow by adding monomersAggregates grow by adding monomers

Estimating EaggEstimating Eagg

Show difference at -15C than previous results.

This supports the interlocking mechanismpp g

Plates were seen at -10, -15, -20, -25C. They do not appear to be responsible for the differences

SummarySummaryA d ti ffi i t (F i Fi k M ll L i• Accommodation coefficient (Fourier, Fick, Maxwell, Langmuir, Fuch):– has been controversial, but looks like experimental artefacts could havehas been controversial, but looks like experimental artefacts could have

given problems.– Problems with water vapour condensing onto pipes and not actually

measuring the relative humiditymeasuring the relative humidity– Laboratory work has definitely improved our knowledge here

• Snowflakes (Faraday, Thomson, Hobbs, Hosler and Halgren):– Evidence that shape is an important factor.

High aggregation efficienc at ero not obser ed in lab co ld be– High aggregation efficiency at zero not observed in lab: could be because in the atmosphere crystals are more complicated and can also interlock – more work needed here.

Difference in vapour pressures almost the same at -15 and -10C