Stable equilibrium

A CTIVATION OF C ^LOUD D ^ROPLETS

Heterogeneous nucleation

Cloud Condensation Nuclei (CCN)

activation

Diffusional growth

Condensational growth Collision/coalescence Drizzle formation

Rain

CCN washout

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0,1 1 10 100 1000 µm

Activation Condensational growth

Condensational growth +

collision and coalescence Collision and coalescence

CN, CCN

cloud droplets

drizzle

rain

3

updraft cloud base

maximum

supersatutration updraft

Cloud droplets and aerosol

aerosol

Equilibrium conditions

/48

Stable equilibrium Unstable equilibrium

5

Stable equilibrium

environmental supersaturation

For a droplet with radius r( ) the equilibrium saturation is S.

The droplet is in equilibrium with environment.

r

S

Stable equilibrium

/48 7

environmental supersaturation

S S

r r

If the droplet get bigger ( ), r₊>r, its equilibrium saturation is S+ > S.

The environment is undersaturated relative to the droplet.

The droplet has to evaporate to get back to the equilibrium ( ). S-S₊ < 0

Stable equilibrium

environmental supersaturation

S

S

r r

If the droplet get smaller ( ), r_-<r, its equilibrium saturation is S_-< S.

The environment is supersaturated relative to the droplet.

S-S_- > 0

Stable equilibrium

/48 9

environmental supersaturation

In stable regime of the Köhler curve the droplet can grow by condensation only if the environmental saturation increases.

For a fixed environmental supersaturation the size of the droplet oscillates around r ( ).

r

S

Unstable equilibrium

environmental supersaturation

S

r*

S

r

Droplets ( ) having size r₊>r*, have equilibrium saturation S₊> S.

The environment is supersaturated relative to these droplets.

S-S₊ > 0

Unstable equilibrium

/48 11

environmental supersaturation

S

r*

If S < S* there are two equilibrium points ( ).

Environmental supersaturation (S) is lower than the equilibrium supersaturation (S_eq) for droplets having size r* < r < r₂ .

Droplets will evaporate until they reach a new equilibrium at r₁.

S*

r

r

S-S_eq < 0

Droplet activation; cloud condensational nuclei

• Activation

– represents a change from stable to unstable growth in response to increasing ambient humidity.

•

Process illustrates the conditions required for growth to droplets.

• Cloud condensation nuclei (CCN) – those particles which have large enough

radii and enough solute content to activate to particles at a prescribed

supersaturation.

•

The concept of activation is crucial to our understanding of how aerosol

particles act as CCN and establish the initial microstructure of clouds.

Activation

/48 13

S*

S

For droplets r < r* to grow the environmental supersaturation has to increase.

r < r*

Activation

S* S

Droplets r > r* grow spontaneously even for constant environmental supersaturation S> S_eq. Droplets r > r* are activated and are called cloud droplets.

r* < r

𝑆 − 1 _!" = 𝐴 𝑇

𝑟 − 𝐵_# 𝑟^$

Activation

/48 15

r*

S*

cloud droplets

solution droplets

Droplets r > r* are activated and are called cloud droplets.

Activation

If the environmental saturation increases droplets formed on bigger CCN are activated first. With further increase of environmental saturation progressively droplets formed on

k -Köhler theory

Köhler curve without linear approximations

𝑎_% = 𝑛_&

𝑛_& + 𝑛_# = 𝑟^$ − 𝑟_#^$ 𝜌_&

𝑀_&

𝑟^$ − 𝑟_#^$ 𝜌_&

𝑀_& + 𝑖Φ_#𝑟_#^$ 𝜌_# 𝑀_#

= 𝑟^$ − 𝑟_#^$

𝑟^$ − 𝑟_#^$ + 𝐵_# = 𝑟^$ − 𝑟_#^$ 𝑟^$ − 1 − 𝐵_#

𝑟_#^$ 𝑟_#^$

𝑛_# = 𝑖 0 Φ_#𝑚_#

𝑀_# 𝑚_# = 4

3𝜋𝑟_#^$𝜌_#

𝑛_& = 𝑚_&

𝑀_& 𝑚_& = 4

3𝜋 𝑟^$ − 𝑟_#^$ 𝜌_&

𝑆 𝑟, 𝐵_#, 𝑇 = 𝑎_% exp 𝐴(𝑇) 𝑟

Description of saturation

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For a description of equilibrium saturation conditions over solution droplets we need to know 5 parameters:

• s - surface tension coefficient

• i - number of ions of dissociated molecule

• F_s – osmotic coefficient (usually put to 1)

• M_s – molecular mass of solute substance

• r_s – density of solute

k-Köhler parameterization allows to describe the saturation state using smaller number of parameters.

19

𝐵_# = 𝑖 0 Φ_#𝑟_#^$ 𝜌_# 𝜌_&

𝑀_&

𝑀_# 𝐴 𝑇 = 2𝜎

𝜌_&𝑅_'𝑇 𝑎_% = 𝑛_&

𝑛_& + 𝑛_# = 𝑓 𝑟,𝐵_# 𝑆 𝑟, 𝐵_#, 𝑇 = 𝑎_% exp 𝐴(𝑇)

𝑟

k - Köhler theory

𝜅 - hygroscopicity parameter

V_s – volume of dry particle V_l– volume of water droplet

If many different solutes then simple mixing rule applies:

𝑆 𝑟, 𝑥_#, 𝑇 = 𝑎_% exp 𝐴(𝑇) 𝑟 1

𝑎_% = 1 + 𝜿 0 𝑉_# 𝑉_&

𝑎_% = 𝑟^$ − 𝑟_#^$ 𝑟^$ − 1 −𝜅 𝑟_#^$

𝜅 = C

(

𝜀₍𝜅₎

r_s is often called a ‘dry radius’, r_d.

𝑉_# = 4 3𝜋𝑟_#^$ 𝑉_& = 4

3𝜋 𝑟^$ − 𝑟_#^$

k - Köhler theory

/48

Petters, M.D., and S.M. Kreidenweis, 2007: A single parameter representation of hygroscopic growth and 21

cloud condensation nucleus activity. Atmospheric Chemistry and Physics, 7, 1961-1971.

𝑎_% = 𝑟^$ − 𝑟_#^$

𝑟^$ − 1 − 𝜅 𝑟_#^$ ≈ 1 − 𝜅𝑟_#^$ 𝑟^$

𝜅 = 𝐵_#

𝑟_#^$ = 𝑖 0 Φ_# 𝜌_# 𝜌_&

𝑀_&

𝑀_#

𝑆 𝑟, 𝐵_#, 𝑇 − 1 = 𝐴 𝑇

𝑟 − 𝐵_# 𝑟^$ For 𝜅 > 0.2 a linear approximation is valid

𝑆 𝑟, 𝜅, 𝑇 − 1 = 𝐴 𝑇

𝑟 − 𝜅𝑟_#^$ 𝑟^$

Atmospheric particulate matter is typically characterized by 𝜅 > 0.2, with lower values sometimes observed for particular locations and periods

Critical supersaturation versus dry diameter and k

-3/2 slope in log 𝑆_! − log 𝐷_" for κ > 0.2

𝑆 𝑟, 𝐵_#, 𝑇 − 1 = 𝐴 𝑇

𝑟 −𝐵_# 𝑟^$ Equation

leads to -3/2 slope in

log 𝑆_! − log 𝐷_" for all choices of B_𝑠 > 0

From measured CCN data we can infer the hygroscopicity, k, of the aerosol

/48 23

Pettersand Kreidenweis, ACP 2007 (Fig. 2)

• S_c – D_d data for pure compounds, organic mixtures and organic- inorganic mixtures.

• Dashed lines indicate best-fit κ values for each particle type, as shown in the legend.

• Shaded area indicates range of values for amonium sulfate.

• κ values were computed for

• σ=0.072 J m^-2 and T=298.15K.

Ranked hygroscopicity based on CCN measurements for atmospheric aerosols

/48 25

Log-normal distribution

𝑛 𝑟 = 𝑑𝑁(𝑟)

𝑑𝑟 = 𝑁

2𝜋 𝑟 ln 𝜎 exp − ln 𝑟 − ln 𝑟_* ⁺

2 𝑙𝑛⁺𝜎 𝑐𝑚^,$𝜇𝑚^,-

Log-normal distribution

/48 27

𝑛_& 𝑟 = 𝑑𝑁(𝑟)

𝑑 log 𝑟 = 𝑟𝑛(𝑟)ln 10 = 𝑁 ln 10

2𝜋 ln 𝜎 exp − ln 𝑟 − ln 𝑟_* ⁺

2 𝑙𝑛⁺𝜎 𝑐𝑚^,$

CN condensation nuclei

CCN cloud condensation nuclei

CN (condensation nuclei) aerosol particles that can become water drops for supersaturation <400%

CCN (cloud condensation nuclei) are defined for a given supersaturation S

Critical supersaturation S^* 𝑆^∗ = 1 + 4𝐴^$⁄27𝐵_# 𝜅 = 𝐵_#

𝑟_#^$

𝑟_/0 = 4𝐴^$ 27𝜅 𝑆 − 1 ⁺

-1

$

All particles for which r_s>r_cr will be activated

CN condensation nuclei

CCN cloud condensation nuclei

/48 29

CN (condensation nuclei) aerosol particles that can become water drops for supersaturation <400%

CCN (cloud condensation nuclei) are defined for a given supersaturation S

/48 31

ACTIVATION SPECTRUM

It is a useful way to describe the cloud forming propensity of an aerosol population.

It is the number of particles per unit volume that are activated to

become cloud droplets, expressed as a function of the supersaturation.

Such spectra are measured using cloud chambers in which slight

supersaturations can be achieved and accurately controlled.

Activation spectrum

/48 33

R

0_"#

2

𝑛 𝑟 𝑑𝑟 = 𝑁

2 1 + erfln U𝑟_* 𝑟_/0 2 ln 𝜎

𝑛 𝑟 = 𝑁

2𝜋 𝑟 ln 𝜎 exp − ln 𝑟 − ln 𝑟_* ⁺ 2 𝑙𝑛⁺𝜎

𝑟_/0 = 4𝐴^$

27𝜅 𝑆^∗ − 1 ⁺

-1

$

𝑁 = 𝐶 0 𝑆³

Activation spectrum

/48 35

Activation spectrum

𝑁 = 𝐶 0 𝑆³

Activation spectrum

/48 37

Activation spectrum

Activation spectrum

/48 39

Activation spectrum

Activation – where it happens ?

• Droplets tend to originate at cloud base where an updraught typically produces a peak in the

• CCN activation is generally confined to the first 30-50 m above the cloud base except in vigorous convective clouds with vertical velocities of order of 10 m/s, where the supersaturation can reach levels higher than 1%.

• The peak value of the supersaturation determines the fraction of available

•

/48

•

depends on the

• Clouds growing in a continental or polluted environment typically show higher droplet concentrations than those growing in a marine or pristine environment

41

Aerosol Characterization

Experiment ACE2

ACE2

/48 43

Pawlowska, H., and J. L. Brenguier, 2000: Microphysical properties of stratocumulus clouds during ACE2, Tellus, vol. Vol. 52, Issue 2 , pp. 867-886

Pristine Polluted

Aerosol

Collins et al., 2000: In-situ aerosol size distribution and clear-column radiative closure during ACE2. Tellus, vol. Vol. 52, Issue 2

More aerosols in the boundary layer in polluted case

PRISTINE POLLUTED

Aerosol

/48

Collins et.al. 2000

More aerosol in the boundary layer compared to

the free troposphere ₄₅

PRISTINE POLLUTED

Second Aerosol Characterization Experiment (ACE2)

June-July 1997,

Stratocumulus clouds over the Atlantic

Cloud divided into 5 layers.

Cloud droplet concentration reflects fairly well the activation process at the cloud base.

/48

Cloud droplets number concentration

47

PRISTINE POLLUTED

0,1 1 10 100 1000 µm Activation

Condensational growth

Condensational growth +

collision and coalescence Collision and coalescence

CN, CCN

cloud droplets

drizzle

rain S, CCN

P