Laboratory studies of cloud processes
and interpretation with models
Dr Paul Connolly
University of Manchester
Outline
• Ice crystal
y
growth
g
from vapour
p
– Continuum theory
– Elastic and inelastic collisions between
vapour and solid
– Strotski et al (2011)
• Ice growth by aggregation - snowflakes
– Hosler and Halgren
Halgren, Latham
Latham, Hobbs
Hobbs, etc
– Connolly et al (2011)
• Summary
y
Growth from water vapour
Change of phase: vapour to solid.
Heat conduction: `Diffusion’
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.
q = −k∇T
Jean Baptiste
Joseph Fourier (1768-1830)
Fourier believed that keeping
p g the body
y wrapped
pp up
p in blankets was
beneficial 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
smooths out gradients’
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 mass
Philosophical magazine (1855)
Fick's law of diffusion
Adolf Eugen Fick (3 September 1829, Kassel,
Hesse-Kassel – 21 August 1901) was a German
physiologist He started to study mathematics
physiologist.
and physics, but then realized he was more
interested in medicine. He earned his doctorate
in medicine at Marburg in 1851
1851.
In 1855 he introduced Fick's law of
diffusion,, which governs
g
the diffusion of
salts in water and vapour molecules in
air
Fick managed to double-publish his law of
diffusion, as it applied equally to physiology and
physics.
j = − D∇ρ
Adolf Eugen Fick (1829-1901)
Diffusion
us o `smooths
s oo s ou
out’ g
gradients
ad e s
Vapour is transferred from regions of high concentration to low concentration
Hence, b
H
because th
the vapour d
density
it can b
be supersaturated
t t d away ffrom th
the
crystal, but only saturated at the crystals surface, vapour diffuses toward the
crystal
Among his many achievements
(
(e.g.
El
Electromagnetic
i theory,
h
1864), Maxwell (1870) was the first
to combine the laws of diffusion of
mass and
d heat
h t tto write
it down
d
th
the
particle growth equations in the
continuum regime
But this assumed that the vapour
density in moist air is continuous
(no sharp jumps) right up to the
drop surface.
James Clerk Maxwell (1831
(1831–1879)
1879)
Diffusion of vapour to a growing crystal
When the particles have radii
p
to the mean free p
path
comparable
of air it becomes unrealistic
(liberating latent heat)
Diffusion of heat from a crystal
Langmuir made a step forward
1918 paper in Journal Am Chem Soc.
I i Langmuir
Irving
L
i (1881
(1881-1957)
1957)
We now know from the work of
NA Fuchs (1959)
Continuum regime (droplet sizes
much larger than the mean free
path of air)
j ~ gradient in vapour
Kinetic regime (droplet sizes
smaller than the mean free path
of air)
j ~ gradient in vapour × α
α is
i called
ll d th
the accommodation
d ti
coefficient and is unknown
Summary of previous work on the
deposition coefficient
Gierens et al (2003)
Note that the
importance of alpha in
ice nucleation in cirrus
clouds is a
consequence of the
Bergeron-Findeison
process.
Nott sensitive
N
iti iin th
the
range
0.1 < α < 1.0
Ice number concentration very sensitive to choice of the mass
accommodation coefficient
Climate is also sensitive to alpha
Simulation where they changed
the 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
between obs and model
Insert ice crystals into the
model at the observed
rate
Run the model
along the precise
conditions of
temperature and
pressure that
were measured
225 K
217 K
206 K
Our work
191 K
Take the experimental
uncertainty as the range in alpha
that give the best correlations
and the lowest residual
differences
diff
Accommodation coefficient not less than 0.1
This means that it doesn’t appreciably
pp
y affect cloud formation
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
or regelation”
regelation
J
James
Th
Thomson
(1822-1892)
(1822 1892)
Lord Kelvin (1824-1907)
Snowflakes: “Note
Note on Regelation”
Regelation of ice
Michael Faraday (1791-1867)
1860: a `quasi-liquid’ layer exists at the
interface between ice and air, and that
y solidifies only
y when
this layer
sandwiched between two ice surfaces
Hosler Jensen and Goldshlak 1957
Hosler,
Sticking never occurred colder than -25C
The ice spheres were brought in
contact for 1 minute.
minute Clearly this
would not happen in the
atmosphere!
Sintering
g ((Mason 1957, Hobbs 1974))
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
p
pressure 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 aggregation
Aggregation
gg g
rate = number
of sticking events per
second between i and j.
ri
If all collisions resulted in a
sticking event
rj
π
vi
vj
4
(r + r )
2
i
j
vi − v j n j
Aggregation efficiency, Ea,
number 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
Pressure iis responsible
ibl ffor melting
lti iice and
d
forming the ice bond – Thomson (1856).
• Pressure not required, but liquid-like layer
– Faraday
y (1860)
(
) – still not resolved!
• Sintering (molecular diffusion) strengthens
the neck
neck, but liquid like layer responsible
for initial bridging.
• Interlocking ma
may be responsible for
crystals coming in contact (Ohtake, 1969)
Particle size dist. at top
Cloud of drops
Formation of ice causes
the evaporation of drops
Formation of ice
causes the
evaporation of drop
Particle
a ce
Large aggregate
observed first
size
s e dist.
ds a
at bo
bottom
o
An increase toward
the end (largest
aggregates)
A reduction in size
through the course of
the experiment
Single
g crystals
y
at top
p of chamber
-30 deg C
-25 deg C
-20 deg C
-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
gg g
at bottom of chamber
-30 deg C
-25 deg C
-20 deg C
-15 deg C
-10 deg C
-5 deg C
Aggregates grow by adding monomers
Estimating Eagg
Show difference at -15C than previous results.
This supports
pp
the interlocking
g mechanism
Plates were seen at -10, -15, -20, -25C. They do not appear to be responsible for
the differences
Summary
• A
Accommodation
d ti coefficient
ffi i t (F
(Fourier,
i Fi
Fick,
k M
Maxwell,
ll L
Langmuir,
i
Fuch):
– has been controversial, but looks like experimental artefacts could have
given problems.
– Problems with water vapour condensing onto pipes and not actually
measuring 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
efficiency at zero
ero not obser
observed
ed in lab
lab: co
could
ld 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