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M.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD, Belfield.

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Page 1: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

M.Sc. in Meteorology

Synoptic Meteorology[MAPH P312]

Prof Peter Lynch

Second Semester, 2004–2005Seminar Room

Dept. of Maths. Physics, UCD, Belfield.

Page 2: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Part 6

Cloud Microphysics

These lectures follow closely the text of Wallace & Hobbs.

2

Page 3: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Introduction

3

Page 4: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

IntroductionWater vapour condensing on a condensation nucleus mayform a droplet of radius 1 µm. To form a raindrop, thisdroplet will have to increase to radius of, say, 1mm. Thatis an increase in mass of one billion (109).

3

Page 5: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

IntroductionWater vapour condensing on a condensation nucleus mayform a droplet of radius 1 µm. To form a raindrop, thisdroplet will have to increase to radius of, say, 1mm. Thatis an increase in mass of one billion (109).

To account for growth through such a wide range of sizes intime periods as short as ten minutes or so for some convec-tive clouds, it is necessary to consider a number of physicalprocesses.

3

Page 6: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

IntroductionWater vapour condensing on a condensation nucleus mayform a droplet of radius 1 µm. To form a raindrop, thisdroplet will have to increase to radius of, say, 1mm. Thatis an increase in mass of one billion (109).

To account for growth through such a wide range of sizes intime periods as short as ten minutes or so for some convec-tive clouds, it is necessary to consider a number of physicalprocesses.

Scientific investigations of these processes is the domain ofcloud microphysics.

3

Page 7: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Cloud Microphysics will be considered under eight headings:

4

Page 8: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Cloud Microphysics will be considered under eight headings:

1. Nucleation of Water Vapour Condensation

4

Page 9: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Cloud Microphysics will be considered under eight headings:

1. Nucleation of Water Vapour Condensation

2. Microstructures of Warm Clouds

4

Page 10: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Cloud Microphysics will be considered under eight headings:

1. Nucleation of Water Vapour Condensation

2. Microstructures of Warm Clouds

3. Cloud Liquid Water Content and Entrainment

4

Page 11: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Cloud Microphysics will be considered under eight headings:

1. Nucleation of Water Vapour Condensation

2. Microstructures of Warm Clouds

3. Cloud Liquid Water Content and Entrainment

4. Growth of Cloud Droplets in Warm Clouds

4

Page 12: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Cloud Microphysics will be considered under eight headings:

1. Nucleation of Water Vapour Condensation

2. Microstructures of Warm Clouds

3. Cloud Liquid Water Content and Entrainment

4. Growth of Cloud Droplets in Warm Clouds

5. Microphysics of Cold Clouds

4

Page 13: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Cloud Microphysics will be considered under eight headings:

1. Nucleation of Water Vapour Condensation

2. Microstructures of Warm Clouds

3. Cloud Liquid Water Content and Entrainment

4. Growth of Cloud Droplets in Warm Clouds

5. Microphysics of Cold Clouds

6. Artificial Modification of Clouds and Precipitation

4

Page 14: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Cloud Microphysics will be considered under eight headings:

1. Nucleation of Water Vapour Condensation

2. Microstructures of Warm Clouds

3. Cloud Liquid Water Content and Entrainment

4. Growth of Cloud Droplets in Warm Clouds

5. Microphysics of Cold Clouds

6. Artificial Modification of Clouds and Precipitation

7. Thunderstorm Electrification

4

Page 15: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Cloud Microphysics will be considered under eight headings:

1. Nucleation of Water Vapour Condensation

2. Microstructures of Warm Clouds

3. Cloud Liquid Water Content and Entrainment

4. Growth of Cloud Droplets in Warm Clouds

5. Microphysics of Cold Clouds

6. Artificial Modification of Clouds and Precipitation

7. Thunderstorm Electrification

8. Cloud and Precipitation Chemistry

4

Page 16: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

1. Nucleation of Condensation

5

Page 17: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

1. Nucleation of CondensationIf the water vapour pressure in the air is e, thesupersaturation (in percent) with respect to liquid water is(

e

es− 1

)× 100

where es is the saturation vapour pressure.

5

Page 18: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

1. Nucleation of CondensationIf the water vapour pressure in the air is e, thesupersaturation (in percent) with respect to liquid water is(

e

es− 1

)× 100

where es is the saturation vapour pressure.

Clouds form when air becomes supersaturated. The mostcommon means by which supersaturation is produced isthrough the ascent of air parcels, which results in the ex-pansion of the air and adiabatic cooling.

5

Page 19: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

1. Nucleation of CondensationIf the water vapour pressure in the air is e, thesupersaturation (in percent) with respect to liquid water is(

e

es− 1

)× 100

where es is the saturation vapour pressure.

Clouds form when air becomes supersaturated. The mostcommon means by which supersaturation is produced isthrough the ascent of air parcels, which results in the ex-pansion of the air and adiabatic cooling.

Under these conditions, water vapour condenses onto someof the particles in the air to form a cloud of small waterdroplets or ice particles.

5

Page 20: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

1. Nucleation of CondensationIf the water vapour pressure in the air is e, thesupersaturation (in percent) with respect to liquid water is(

e

es− 1

)× 100

where es is the saturation vapour pressure.

Clouds form when air becomes supersaturated. The mostcommon means by which supersaturation is produced isthrough the ascent of air parcels, which results in the ex-pansion of the air and adiabatic cooling.

Under these conditions, water vapour condenses onto someof the particles in the air to form a cloud of small waterdroplets or ice particles.

We are concerned with the formation of water droplets fromthe condensation of water vapour.

5

Page 21: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Kelvin’s Equation

6

Page 22: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Kelvin’s EquationWe consider first the hypothetical problem of the formationof a pure water droplet by condensation from a supersatu-rated vapour without the aid of particles in the air.

6

Page 23: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Kelvin’s EquationWe consider first the hypothetical problem of the formationof a pure water droplet by condensation from a supersatu-rated vapour without the aid of particles in the air.

In this process, which is referred to as homogeneous nucle-ation of condensation, the first stage is the chance collisionsof a number of water molecules in the vapour phase to formsmall embryonic water droplets that are large enough toremain intact.

6

Page 24: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Kelvin’s EquationWe consider first the hypothetical problem of the formationof a pure water droplet by condensation from a supersatu-rated vapour without the aid of particles in the air.

In this process, which is referred to as homogeneous nucle-ation of condensation, the first stage is the chance collisionsof a number of water molecules in the vapour phase to formsmall embryonic water droplets that are large enough toremain intact.

Let us suppose that a small embryonic water droplet of vol-ume V and surface area A forms from pure supersaturatedwater vapour at constant temperature and pressure. Workis done in creating the surface area of the droplet.

6

Page 25: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Kelvin’s EquationWe consider first the hypothetical problem of the formationof a pure water droplet by condensation from a supersatu-rated vapour without the aid of particles in the air.

In this process, which is referred to as homogeneous nucle-ation of condensation, the first stage is the chance collisionsof a number of water molecules in the vapour phase to formsmall embryonic water droplets that are large enough toremain intact.

Let us suppose that a small embryonic water droplet of vol-ume V and surface area A forms from pure supersaturatedwater vapour at constant temperature and pressure. Workis done in creating the surface area of the droplet.

This work may be written as Aσ, where σ is the work re-quired to create a unit area of vapour-liquid interface (calledthe surface energy of the liquid).

6

Page 26: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

It is possible to demonstrate that the surface energy of aliquid has the same numerical value as its surface tension(denoted σ).

7

Page 27: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

It is possible to demonstrate that the surface energy of aliquid has the same numerical value as its surface tension(denoted σ).

Let ∆E be the net increase in the energy of the system due

to the formation of the droplet. It can be shown that

∆E = Aσ − nV kT loge

es

7

Page 28: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

It is possible to demonstrate that the surface energy of aliquid has the same numerical value as its surface tension(denoted σ).

Let ∆E be the net increase in the energy of the system due

to the formation of the droplet. It can be shown that

∆E = Aσ − nV kT loge

es

Here n is the number of water molecules per unit volume ofliquid, e and T are the vapour pressure and temperature ofthe system, es the saturation vapour pressure and k is theBoltzmann constant.

7

Page 29: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

It is possible to demonstrate that the surface energy of aliquid has the same numerical value as its surface tension(denoted σ).

Let ∆E be the net increase in the energy of the system due

to the formation of the droplet. It can be shown that

∆E = Aσ − nV kT loge

es

Here n is the number of water molecules per unit volume ofliquid, e and T are the vapour pressure and temperature ofthe system, es the saturation vapour pressure and k is theBoltzmann constant.

For a droplet of radius R, this becomes

∆E = 4πR2σ − 4

3πR3n kT log

e

es

7

Page 30: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

It is possible to demonstrate that the surface energy of aliquid has the same numerical value as its surface tension(denoted σ).

Let ∆E be the net increase in the energy of the system due

to the formation of the droplet. It can be shown that

∆E = Aσ − nV kT loge

es

Here n is the number of water molecules per unit volume ofliquid, e and T are the vapour pressure and temperature ofthe system, es the saturation vapour pressure and k is theBoltzmann constant.

For a droplet of radius R, this becomes

∆E = 4πR2σ − 4

3πR3n kT log

e

es

Under subsaturated conditions, e < es and ln(e/es) is nega-tive. Thus, ∆E is always positive and increases with R.

7

Page 31: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Increase ∆E in the energy of a system due to the forma-tion of a water droplet of radius R from water vapour withpressure e.

8

Page 32: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

In other words, the larger the embryonic droplet that formsin a subsaturated vapour the greater is the increase in theenergy, ∆E, of the system.

9

Page 33: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

In other words, the larger the embryonic droplet that formsin a subsaturated vapour the greater is the increase in theenergy, ∆E, of the system.

Since a system approaches an equilibrium state by reducingits energy, the formation of droplets is clearly not favouredunder subsaturated conditions.

9

Page 34: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

In other words, the larger the embryonic droplet that formsin a subsaturated vapour the greater is the increase in theenergy, ∆E, of the system.

Since a system approaches an equilibrium state by reducingits energy, the formation of droplets is clearly not favouredunder subsaturated conditions.

Even so, due to random collisions of water molecules, verysmall embryonic droplets continually form (and evaporate)in a subsaturated vapour, but they do not grow large enoughto become visible as a cloud of droplets.

9

Page 35: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

In other words, the larger the embryonic droplet that formsin a subsaturated vapour the greater is the increase in theenergy, ∆E, of the system.

Since a system approaches an equilibrium state by reducingits energy, the formation of droplets is clearly not favouredunder subsaturated conditions.

Even so, due to random collisions of water molecules, verysmall embryonic droplets continually form (and evaporate)in a subsaturated vapour, but they do not grow large enoughto become visible as a cloud of droplets.

Under supersaturated conditions, e > es and so ln(e/es) ispositive. In this case, ∆E can be either positive or negative,depending upon the value of R.

9

Page 36: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

In other words, the larger the embryonic droplet that formsin a subsaturated vapour the greater is the increase in theenergy, ∆E, of the system.

Since a system approaches an equilibrium state by reducingits energy, the formation of droplets is clearly not favouredunder subsaturated conditions.

Even so, due to random collisions of water molecules, verysmall embryonic droplets continually form (and evaporate)in a subsaturated vapour, but they do not grow large enoughto become visible as a cloud of droplets.

Under supersaturated conditions, e > es and so ln(e/es) ispositive. In this case, ∆E can be either positive or negative,depending upon the value of R.

The variation of ∆E with R for e > es is also shown in theFigure (red curve), where it can be seen that ∆E initiallyincreases with increasing R, reaches a maximum value atR = r, and then decreases with increasing R.

9

Page 37: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Increase ∆E in the energy of a system due to the forma-tion of a water droplet of radius R from water vapour withpressure e.

10

Page 38: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Hence, under supersaturated conditions, small embryonicdroplets, with R < r, tend to evaporate, since by so doingthey decrease ∆E.

11

Page 39: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Hence, under supersaturated conditions, small embryonicdroplets, with R < r, tend to evaporate, since by so doingthey decrease ∆E.

However, larger droplets, that manage to grow by chancecollisions to a radius that just exceeds r, will continue togrow spontaneously by condensation from the vapour phase,since this will produce a decrease in ∆E.

11

Page 40: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Hence, under supersaturated conditions, small embryonicdroplets, with R < r, tend to evaporate, since by so doingthey decrease ∆E.

However, larger droplets, that manage to grow by chancecollisions to a radius that just exceeds r, will continue togrow spontaneously by condensation from the vapour phase,since this will produce a decrease in ∆E.

At R = r, a droplet can grow or evaporate infinitesimallywithout any change in ∆E. We can obtain an expression forr in terms of e by setting ∂(∆E)/∂R = 0 at R = r.

11

Page 41: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Hence, under supersaturated conditions, small embryonicdroplets, with R < r, tend to evaporate, since by so doingthey decrease ∆E.

However, larger droplets, that manage to grow by chancecollisions to a radius that just exceeds r, will continue togrow spontaneously by condensation from the vapour phase,since this will produce a decrease in ∆E.

At R = r, a droplet can grow or evaporate infinitesimallywithout any change in ∆E. We can obtain an expression forr in terms of e by setting ∂(∆E)/∂R = 0 at R = r.

Hence, from the above equation for ∆E, we get

r =2σ

nkT log(e/es)or e = es exp

(2σ

nkTr

)

11

Page 42: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Hence, under supersaturated conditions, small embryonicdroplets, with R < r, tend to evaporate, since by so doingthey decrease ∆E.

However, larger droplets, that manage to grow by chancecollisions to a radius that just exceeds r, will continue togrow spontaneously by condensation from the vapour phase,since this will produce a decrease in ∆E.

At R = r, a droplet can grow or evaporate infinitesimallywithout any change in ∆E. We can obtain an expression forr in terms of e by setting ∂(∆E)/∂R = 0 at R = r.

Hence, from the above equation for ∆E, we get

r =2σ

nkT log(e/es)or e = es exp

(2σ

nkTr

)This is referred to as Kelvin’s Equation, after Lord Kelvinwho first derived it.

11

Page 43: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

We can use Kelvin’s Equation in two ways.

12

Page 44: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

We can use Kelvin’s Equation in two ways.

1. It can be used to calculate the radius r of a droplet thatis in (unstable) equilibrium with a given water vapourpressure e.

12

Page 45: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

We can use Kelvin’s Equation in two ways.

1. It can be used to calculate the radius r of a droplet thatis in (unstable) equilibrium with a given water vapourpressure e.

2. It can be used to determine the saturation vapour pres-sure e over a droplet of specified radius r.

12

Page 46: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

We can use Kelvin’s Equation in two ways.

1. It can be used to calculate the radius r of a droplet thatis in (unstable) equilibrium with a given water vapourpressure e.

2. It can be used to determine the saturation vapour pres-sure e over a droplet of specified radius r.

The relative humidity at which a droplet of radius r is in(unstable) equilibrium is 100× (e/es), where e/es is given byKelvin’s Equation.

12

Page 47: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

We can use Kelvin’s Equation in two ways.

1. It can be used to calculate the radius r of a droplet thatis in (unstable) equilibrium with a given water vapourpressure e.

2. It can be used to determine the saturation vapour pres-sure e over a droplet of specified radius r.

The relative humidity at which a droplet of radius r is in(unstable) equilibrium is 100× (e/es), where e/es is given byKelvin’s Equation.

The variation of the equilibrium relative humidity withdroplet radius is shown in the Figure that follows.

12

Page 48: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

The relative humidity and supersaturation at which purewater droplets are in (unstable) equilibrium at 5◦C.

13

Page 49: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

A pure water droplet of radius 0.01 µm requires a relativehumidity of 112% (i.e., a supersaturation of 12%) to be in(unstable) equilibrium with its environment.

A droplet of radius 1 µm requires a relative humidity of only100.12% (i.e., a supersaturation of 0.12%).

14

Page 50: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

A pure water droplet of radius 0.01 µm requires a relativehumidity of 112% (i.e., a supersaturation of 12%) to be in(unstable) equilibrium with its environment.

A droplet of radius 1 µm requires a relative humidity of only100.12% (i.e., a supersaturation of 0.12%).

The supersaturations that develop in natural clouds due tothe adiabatic ascent of air rarely exceed a few percent.

14

Page 51: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

A pure water droplet of radius 0.01 µm requires a relativehumidity of 112% (i.e., a supersaturation of 12%) to be in(unstable) equilibrium with its environment.

A droplet of radius 1 µm requires a relative humidity of only100.12% (i.e., a supersaturation of 0.12%).

The supersaturations that develop in natural clouds due tothe adiabatic ascent of air rarely exceed a few percent.

It follows that, even if embryonic droplets of pure wateras large as 0.01 µm in radius formed by the chance collisionof water molecules, they would be well below the criticalradius required for survival in air that is just a few percentsupersaturated.

14

Page 52: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

A pure water droplet of radius 0.01 µm requires a relativehumidity of 112% (i.e., a supersaturation of 12%) to be in(unstable) equilibrium with its environment.

A droplet of radius 1 µm requires a relative humidity of only100.12% (i.e., a supersaturation of 0.12%).

The supersaturations that develop in natural clouds due tothe adiabatic ascent of air rarely exceed a few percent.

It follows that, even if embryonic droplets of pure wateras large as 0.01 µm in radius formed by the chance collisionof water molecules, they would be well below the criticalradius required for survival in air that is just a few percentsupersaturated.

Consequently, droplets do not form in natural clouds byhomogeneous nucleation of pure water.

14

Page 53: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Heterogeneous NucleationDroplets form on atmospheric aerosol by what is known asheterogeneous nucleation.

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Page 54: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Heterogeneous NucleationDroplets form on atmospheric aerosol by what is known asheterogeneous nucleation.

A surface is said to be perfectly wettable (hydrophilic) if itallows water to spread out on it as a horizontal film (deter-gents are used for this purpose).

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Page 55: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Heterogeneous NucleationDroplets form on atmospheric aerosol by what is known asheterogeneous nucleation.

A surface is said to be perfectly wettable (hydrophilic) if itallows water to spread out on it as a horizontal film (deter-gents are used for this purpose).

A surface is completely unwettable (hydrophobic) if waterforms spherical drops on its surface (cars are waxed to makethem hydrophobic).

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Page 56: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Heterogeneous NucleationDroplets form on atmospheric aerosol by what is known asheterogeneous nucleation.

A surface is said to be perfectly wettable (hydrophilic) if itallows water to spread out on it as a horizontal film (deter-gents are used for this purpose).

A surface is completely unwettable (hydrophobic) if waterforms spherical drops on its surface (cars are waxed to makethem hydrophobic).

The atmosphere contains many particles that range in sizefrom submicrometer to several tens of micrometers. Thoseparticles that are wettable can serve as centers upon whichwater vapour condenses.

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Page 57: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Heterogeneous NucleationDroplets form on atmospheric aerosol by what is known asheterogeneous nucleation.

A surface is said to be perfectly wettable (hydrophilic) if itallows water to spread out on it as a horizontal film (deter-gents are used for this purpose).

A surface is completely unwettable (hydrophobic) if waterforms spherical drops on its surface (cars are waxed to makethem hydrophobic).

The atmosphere contains many particles that range in sizefrom submicrometer to several tens of micrometers. Thoseparticles that are wettable can serve as centers upon whichwater vapour condenses.

Moreover, droplets can form and grow on these particles atmuch lower supersaturations than those required for homo-geneous nucleation.

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Page 58: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

For example, if sufficient water condenses onto a completelywettable particle 0.3 µm in radius to form a thin film of waterover the surface of the particle, we see from the Figure thatthe water film will be in (unstable) equilibrium with air thathas a supersaturation of 0.4%.

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Page 59: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

For example, if sufficient water condenses onto a completelywettable particle 0.3 µm in radius to form a thin film of waterover the surface of the particle, we see from the Figure thatthe water film will be in (unstable) equilibrium with air thathas a supersaturation of 0.4%.

If the supersaturation were slightly greater than 0.4%, waterwould condense onto the film of water and the droplet wouldincrease in size.

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Page 60: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

For example, if sufficient water condenses onto a completelywettable particle 0.3 µm in radius to form a thin film of waterover the surface of the particle, we see from the Figure thatthe water film will be in (unstable) equilibrium with air thathas a supersaturation of 0.4%.

If the supersaturation were slightly greater than 0.4%, waterwould condense onto the film of water and the droplet wouldincrease in size.

Some of the particles in air are soluble in water. Conse-quently, they dissolve, wholly or in part, when water con-denses onto them, so that a solution (rather than a purewater) droplet is formed.

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Page 61: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Cloud Condensation NucleiA small fraction of the atmospheric aerosol serve as particlesupon which water vapour condenses.

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Page 62: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Cloud Condensation NucleiA small fraction of the atmospheric aerosol serve as particlesupon which water vapour condenses.

These form droplets that are activated and grow by con-densation to form cloud droplets at the supersaturationsachieved in clouds (∼ 0.1− 1%).

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Page 63: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Cloud Condensation NucleiA small fraction of the atmospheric aerosol serve as particlesupon which water vapour condenses.

These form droplets that are activated and grow by con-densation to form cloud droplets at the supersaturationsachieved in clouds (∼ 0.1− 1%).

These particles are called cloud condensation nuclei (CCN).

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Page 64: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Cloud Condensation NucleiA small fraction of the atmospheric aerosol serve as particlesupon which water vapour condenses.

These form droplets that are activated and grow by con-densation to form cloud droplets at the supersaturationsachieved in clouds (∼ 0.1− 1%).

These particles are called cloud condensation nuclei (CCN).

The larger the size of a particle, the more readily it is wettedby water, and the greater its solubility, the lower will be thesupersaturation at which the particle can serve as a CCN.

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Page 65: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Cloud Condensation NucleiA small fraction of the atmospheric aerosol serve as particlesupon which water vapour condenses.

These form droplets that are activated and grow by con-densation to form cloud droplets at the supersaturationsachieved in clouds (∼ 0.1− 1%).

These particles are called cloud condensation nuclei (CCN).

The larger the size of a particle, the more readily it is wettedby water, and the greater its solubility, the lower will be thesupersaturation at which the particle can serve as a CCN.

For example, to serve as a CCN at 1% supersaturation,completely wettable but water insoluble particles need tobe at least ∼ 0.1 µm in radius, whereas soluble particles canserve as CCN at 1% supersaturation even if they are assmall as ∼ 0.01 µm in radius.

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Page 66: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Most CCN consist of a mixture of soluble and insolublecomponents (called mixed nuclei).

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Page 67: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Most CCN consist of a mixture of soluble and insolublecomponents (called mixed nuclei).

World-wide measurements of CCN concentrations have notrevealed any systematic latitudinal or seasonal variations.

However, near the Earth’s surface continental air massesgenerally contain larger concentrations of CCN than marineair masses.

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Page 68: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Most CCN consist of a mixture of soluble and insolublecomponents (called mixed nuclei).

World-wide measurements of CCN concentrations have notrevealed any systematic latitudinal or seasonal variations.

However, near the Earth’s surface continental air massesgenerally contain larger concentrations of CCN than marineair masses.

The concentration of CCN in the continental air mass overthe Azores, is about 300 cm−3 at 1% supersaturation, whilein the marine air mass over Florida it is about 100 cm−3,and in clean Arctic air it is only about 30 cm−3.(Figure follows)

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Page 69: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

CCN spectra in the boundary layer from measurements near the

Azores in a polluted continental air mass (brown), in Florida in a

marine air mass (green), and in clean Arctic air (blue).

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Page 70: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Concentrations of CCN over land decline by about a factorof five between the planetary boundary layer and the freetroposphere.

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Page 71: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Concentrations of CCN over land decline by about a factorof five between the planetary boundary layer and the freetroposphere.

Concentrations over the ocean remain fairly constant, oreven increase with height reaching a maximum concentra-tion just above the mean cloud height.

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Page 72: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Concentrations of CCN over land decline by about a factorof five between the planetary boundary layer and the freetroposphere.

Concentrations over the ocean remain fairly constant, oreven increase with height reaching a maximum concentra-tion just above the mean cloud height.

Ground-based measurements indicate that there is a diurnalvariation in CCN concentrations, with a minimum at about6 a.m. and a maximum at about 6 p.m.

? ? ?

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Page 73: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Origins of CCNThe observations provide clues as to the origins of CCN.

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Page 74: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Origins of CCNThe observations provide clues as to the origins of CCN.

The land acts as a source of CCN and thus concentrationsof CCN are higher over land and decrease with altitude.

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Page 75: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Origins of CCNThe observations provide clues as to the origins of CCN.

The land acts as a source of CCN and thus concentrationsof CCN are higher over land and decrease with altitude.

The rate of production of CCN from burning vegetable mat-ter is on the order of 1012−1015 per kg of material consumed.Thus, forest fires are a source of CCN.

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Page 76: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Origins of CCNThe observations provide clues as to the origins of CCN.

The land acts as a source of CCN and thus concentrationsof CCN are higher over land and decrease with altitude.

The rate of production of CCN from burning vegetable mat-ter is on the order of 1012−1015 per kg of material consumed.Thus, forest fires are a source of CCN.

About 80% of the particles emitted by idling diesel enginesare CCN at 1% supersaturation.

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Page 77: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Origins of CCNThe observations provide clues as to the origins of CCN.

The land acts as a source of CCN and thus concentrationsof CCN are higher over land and decrease with altitude.

The rate of production of CCN from burning vegetable mat-ter is on the order of 1012−1015 per kg of material consumed.Thus, forest fires are a source of CCN.

About 80% of the particles emitted by idling diesel enginesare CCN at 1% supersaturation.

About 70% of the particles emitted by the 1991 Kuwait oilfires were CCN at 1% supersaturation.

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Page 78: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

Origins of CCNThe observations provide clues as to the origins of CCN.

The land acts as a source of CCN and thus concentrationsof CCN are higher over land and decrease with altitude.

The rate of production of CCN from burning vegetable mat-ter is on the order of 1012−1015 per kg of material consumed.Thus, forest fires are a source of CCN.

About 80% of the particles emitted by idling diesel enginesare CCN at 1% supersaturation.

About 70% of the particles emitted by the 1991 Kuwait oilfires were CCN at 1% supersaturation.

Although sea-salt particles enter the air over the oceans,they do not appear to be a dominant source of CCN, evenover the oceans.

? ? ?

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Page 79: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

There appears to be a widespread and probably a fairlyuniform source of CCN over both the oceans and the land,the nature of which has not been definitely established.

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Page 80: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

There appears to be a widespread and probably a fairlyuniform source of CCN over both the oceans and the land,the nature of which has not been definitely established.

A likely candidate is gas-to-particle conversion, which canproduce particles up to a few tenths of a micrometer indiameter that can act as CCN if they are soluble or wettable.

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Page 81: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

There appears to be a widespread and probably a fairlyuniform source of CCN over both the oceans and the land,the nature of which has not been definitely established.

A likely candidate is gas-to-particle conversion, which canproduce particles up to a few tenths of a micrometer indiameter that can act as CCN if they are soluble or wettable.

Gas-to-particle conversion mechanisms that require solar ra-diation might be responsible for the observed peak in CCNconcentrations at around 6 p.m.

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Page 82: M.Sc. in Meteorology Synoptic MeteorologyM.Sc. in Meteorology Synoptic Meteorology [MAPH P312] Prof Peter Lynch Second Semester, 2004–2005 Seminar Room Dept. of Maths. Physics, UCD,

There appears to be a widespread and probably a fairlyuniform source of CCN over both the oceans and the land,the nature of which has not been definitely established.

A likely candidate is gas-to-particle conversion, which canproduce particles up to a few tenths of a micrometer indiameter that can act as CCN if they are soluble or wettable.

Gas-to-particle conversion mechanisms that require solar ra-diation might be responsible for the observed peak in CCNconcentrations at around 6 p.m.

Many CCN consist of sulfates. Over the oceans, organicsulfur from the ocean (in the form of the gases dimethyl-sulfide (DMS) and methane sulfonic acid (MSA)) provide asource of CCN, with the DMS and MSA being convertedto sulfate in the atmosphere.

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