• Description of formation and evolution of cloud

MICROPHYSICS

A matter of scale

100 ^µm 1 cm

1 m

100 m

1 km

1000 km

E Bodenschatz et al. Science 2010;327:970-971 2 /40

Cloud microphysics is the branch of the atmospheric sciences concerned with the many particles that

make up a cloud.

From: Encyclopedia of Atmospheric Sciences (Second Edition), 2015

A cloud is an aggregate of cloud droplets or ice crystals, or a combination of both, suspended in air.

For a cloud to be visible,

the cloud particles need to exist in a sufficiently large concentration.

• Cloud is a medium composed of water and/or ice

immersed in a field of water vapor

• Description of formation and evolution of cloud

is a main goal of what is called

• Spatial coordinates, sizes, and/or shapes of each cloud

at any

instant of time would provide the most exhaustive information on a cloud

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Types and sizes of particles

10^-9 10^-6 10^-3 10^-1 diameter (m) Aerosol

Cloud

Sizes of cloud particles

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10^-9 10^-6 10^-3 10^-1 10^-3

1

10³ 10⁵ (µm)

Aerosol Rain

diameter (m) 100

1

10 200 500

diameter (µm)

Cloud droplets Drizzle drops Rain drops

Snow flakes Ice cristals

1000

Sizes of cloud particles

Hail

Cloud

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10 µm

1 µm 100 µm

1 mm

Cloud particles are divided according to their sizes (diameter):

• Cloud droplets: 1-30 µm

• Drizzle drops: 30 – 600 µm

• Rain drops: > 600 µm

This division reflects processes involved in those particle’s formation.

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Cloud droplets, drizzle, rain drops Concentration, size, distances between

particles

1 cm V=1 cm³

d=2 mm

r=10 µm

d=1 cm

Concentration, N=125 cm^-3 Cloud droplets Size (radius), r=10 µm

Distance between droplets, d=2 mm

Concentration, N=1 cm^-3 Drizzle drops Size (radius), r=100 µm

Distance between drops, d=1 cm

Concentration, N=1 dm^-3 Precipitation/rain drops Size (radius), r=1000 µm

Distance between drops, d=10 cm

x10

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Hailstone… the record

The largest recorded hailstone in the United States by diameter 8 inches (20 cm) and weight 1.93 pounds (0.88 kg). The hailstone fell in Vivian, South Dakota on July 23, 2010.

Image: NOAA

X10

Rain drop, r= 1 mm

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CONCENTRATION AND SIZE

1.

Cloud droplets

Concentration: 10–500 cm^-3 Size (radius): 1–20 µm

2.

Drizzle drops

Concentration: 0.1-1 cm^-3 Size (radius): 30-300 µm 3.

Precipitation/rain drops

Concentration: 1 dcm^-3 Size (radius): 1 mm

HOW TO DESCRIBE CLOUD MICROPHYSICAL

PROPERTIES?

•

Particle Size Distribution, PSD

•

Moments of PSD (concentration, mean radius, mean volume radius…)

•

Integrated cloud characteristics (liquid water path, cloud optical

thickness)

Cloud processes span over wide ranges of scales

• Lower limit:

– cloud droplets sizes – micrometers

– distance between cloud droplets – milimeters and centimeters

Investigation of cloud processes in such scales in natural clouds is very difficult if not impossible

• Upper limit:

– Cloud macroscale – hundreds of meters to tens or hundreds of kilometers

Characterization of clouds in macroscale is a challenge because

• it should reflect mean cloud properties and

• it should reproduce well their global radiative and/or dynamical properties

Characteristics of cloud microphysics always refer to a given volume or mass of air.

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Spatial coordinates, sizes, and/or shapes of each cloud particle at any instant of time provide the most exhaustive

information on a cloud.

Is position of any single cloud particle important for description of cloud microphysics?

NO!!!!!

Because any identical cloud won’t happen any more.

For description of populations of cloud’s particles we need to define distribution functions.

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Warm clouds

Particle size distribution (PSD)

Particle size distribution (particle spectrum) provides information of a number of particles of a given size in a given volume of a cloud.

(N

, r

) –number of particles, N

(cm

), in a unit volume having radius r

(µm).

The most often N

is a number of particles having radii in a bin size (r

, r

+Dr

).

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Δ𝑟_! = 0.5 𝜇𝑚

𝑁_!, 𝑟_!+Δ𝑟_! 𝑁 = +

!𝑁_! = 100 𝑐𝑚^"#

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Δ𝑟_! = 0.5 𝜇𝑚 Δ𝑟_! = 1 𝜇𝑚

𝑁_!, 𝑟_!+Δ𝑟_! 𝑁 = +

!𝑁_! = 100 𝑐𝑚^"#

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Δ𝑟_! = 0.5 𝜇𝑚 Δ𝑟_! = 1 𝜇𝑚 Δ𝑟_! = 2 𝜇𝑚

𝑁_!, 𝑟_!+Δ𝑟_! 𝑁 = +

!𝑁_! = 100 𝑐𝑚^"#

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Particle size distribution (PSD)

Particle size distribution (particle spectrum) provides information of a number of particles of a given size in a given volume of a cloud.

(N

, r

) –number of particles, N

(cm

), in a unit volume having radius r

(µm).

The most often N

is a number of particles having radii in a bin size (r

, r

+Dr

).

n

= N

/ Dr

is particle number density (cm

µm

).

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𝑛_! = 𝑁_!⁄∆𝑟_! 𝑁 = +

!𝑛_! ∆𝑟_!= 100 𝑐𝑚^"#

Δ𝑟_! = 0.5 𝜇𝑚 Δ𝑟_! = 1 𝜇𝑚 Δ𝑟_! = 2 𝜇𝑚

Particle size distribution (PSD)

Particle size distribution (particle spectrum) provides information of a number of particles of a given size in a given volume of a cloud.

(N

, r

) –number of particles, N

(cm

), in a unit volume having radius r

(µm).

The most often N

is a number of particles having radii in a bin size (r

, r

+Dr

).

n

= N

/ Dr

is particle number density (cm

µm

).

For many purposes the particle density function is expressed by a continuous analytical function n(r), where

n(r)dr is the number of particles in the infinitesimal size interval (r,r+dr).

In fact (n

, r

) is also a continuous size distribution.

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𝑛_! = 𝑁_!⁄∆𝑟_! 𝑐𝑚^"#𝜇𝑚^"$ , 𝑁 = +

!𝑛_!∆𝑟_!

Continuous analytical function: 𝑛 𝑟 𝑐𝑚^"#𝜇𝑚^"$ , N=∫_%^&𝑛 𝑟 𝑑𝑟 Cumulative distribution 𝑃 𝑟 = ∫_%^' 𝑛 𝑥 𝑑𝑥

OR probability density distribution 𝑃 𝑟 = _"^! ∫_%^'𝑛 𝑥 𝑑𝑥

Cloud microphysical parameters

• Particle Size Distribution (PSD) encapsulates a complete description of the number of each size of particle in a given spectrum

• In order to characterize the microphysical properties of a cloud volume, it is often only necessary to have

information about the statistical moments of the density function n(r)/N (N is total droplet number concentration)

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Cloud microphysical parameters

j^th moment of particle size distribution

j Parameter Application

1 Mean radius

2 Mean surface

radius Extinction [m^-1]

3 Mean volume

radius Liquid Water Content

Mixing ratio

6 ^{no name} Radar reflectivity

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𝑟⁽ = 1

𝑁+

! 𝑟_!⁽𝑁_! = 1 𝑁6

%

&

𝑟⁽𝑛 𝑟 𝑑𝑟, 𝑗 = 1,2, … .

𝜎_)*+ = 𝑄_)*+𝜋𝑁𝑟_,^- 𝑚^"$

𝐿𝑊𝐶 = 4

3𝜋𝜌_.𝑁𝑟_/^# 𝑔 𝑚^"#

𝑞_. = 𝐿𝑊𝐶 𝜌D ₀ 𝑔 𝑘𝑔^"$

𝑍 ∝ 𝑀₁

̅𝑟 = 𝑟

𝑟_, = 𝑟^{- ⁄$ -} 𝑟_/ = 𝑟^{# ⁄$ #}

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𝑟_! = 1, 2, 2.5, 5

̅𝑟 = 2.62

𝑟_, = 3.01

𝑟_/ = 3.34 All droplets have the same radius

Total droplet surface 𝜋 K 36 Total droplet volume ³_#𝜋 K 150

Total droplet surface 𝜋 K 27 Total droplet volume ³_#𝜋 K 72

Total droplet surface 𝜋 K 36 Total droplet volume ³_#𝜋 K 109

Total droplet surface 𝜋 K 44 Total droplet volume ³_#𝜋 K 150

Effective radius

Parameter used to describe optical properties of aerosols, cloud particles

Liquid Water Content

Extinction

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𝑟₎ = 𝑟_/^# 𝑟_,^-

𝐿𝑊𝐶 = 4

3𝜋𝜌_.𝑁𝑟_/^# ⇒ 𝑟_/^# = 3 K 𝐿𝑊𝐶 4𝜋𝜌_.𝑁

𝜎_)*+ = 𝑄_)*+𝜋𝑁𝑟_,^- ⇒ 𝑟_,^- = 𝜎_)*+

𝑄_)*+𝜋𝑁

𝑟₎ = 𝑟_/^#

𝑟_,^- = 3 4

𝑄_)*+

𝜌_.

𝐿𝑊𝐶 𝜎_)*+

𝜎_)*+ = 3 4

𝑄_)*+

𝜌_.

𝐿𝑊𝐶 𝑟₎

Integrated cloud characteristics Liquid Water Path (LWP)

Liquid Water Path in units of [g/m²] is a measure of the total amount of liquid water present in a column of atmosphere (cloud).

LWPis an important quantity in understanding radiative transfer in the atmosphere. It is defined as the integral of liquid water content between two points in the atmosphere.

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𝐿𝑊𝑃 = 6

4_#$%&

4_'()

𝐿𝑊𝐶 K 𝑑ℎ 𝑔𝑚^"-

𝐿𝑊𝑃 = 6

4_#$%&

4_'()

4

3𝜋𝜌_.𝑁𝑟_/^# K 𝑑ℎ

Liquid Water Path

/40 30 https://climatesciences.jpl.nasa.gov/projects/cloudyboundary/index.html

Integrated cloud characteristics Optical thickness (depth)

/40 31

A measure of extinction (absorption + scattering) of radiation by optically active medium (cloud)

𝐹_%

𝐹

𝐹 = 𝐹_%𝑒^"5

Optical depth is a coordinate transformation. Instead of using physical distance (z) we rescale to a dimensionless coordinate, where optical depth 𝜏=1 means that only

e^-1=0.368 of energy is passed without being scattered.

𝑧

Beer-Lambert law

Integrated cloud characteristics Optical thickness (depth)

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𝜏 = 6

4_#$%&

4_'()

𝜎_)*+ K 𝑑ℎ = 𝜋𝑄_)*+ 6

4_#$%&

4_'()

𝑁𝑟_,^- K 𝑑ℎ

𝑟₎ = 𝑟_/^#

𝑟_,^- ⇒ 𝑟_,^- = 𝑟_/^#

𝑟₎ 𝑟_/^# = 3

4𝜋 K 𝐿𝑊𝐶 𝜌_.

𝜏 = 3𝑄_)*+

4𝜌_. 6

4_#$%&

4_'()

𝐿𝑊𝐶

𝑟₎ K 𝑑ℎ

if 𝑟₎ = 𝑐𝑜𝑛𝑠𝑡 𝜏 = 3𝑄_)*+

4𝜌_.

𝐿𝑊𝑃 𝑟₎

Cloud optical thickness

/40 Siebesma, A., Bony, S., Jakob, C., & Stevens, B. (Eds.). (2020). Clouds and Climate: Climate Science's 33

Greatest Challenge. Cambridge University Press.

Cloud albedo

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𝐴 = 𝜏

𝜏 + 7.7

Cloud albedo

/40 35

𝐴 = 𝜏

𝜏 + 7.7

linear scale

Effective radius ( r _e ) - versus - mean volume radius ( r _v )

/40 36

𝜏 = 3𝑄_)*+

4𝜌_. 6

4_#$%&

4_'()

𝐿𝑊𝐶

𝒓_𝒆 K 𝑑ℎ 𝐿𝑊𝑃 = 6

4_#$%&

4_'()

𝐿𝑊𝐶 K 𝑑ℎ 𝑔𝑚^"- 𝐿𝑊𝑃 = 6

4_#$%&

4_'()

4

3𝜋𝜌_.𝑁𝒓_𝒗^𝟑 K 𝑑ℎ

if 𝑟₎ = 𝑐𝑜𝑛𝑠𝑡 𝜏 = 3𝑄_)*+

4𝜌_.

𝐿𝑊𝑃 𝒓_𝒆

𝑟₎ = 𝑟_/ ? ? ? 𝑟₎^# = 𝑘𝑟_/^# ? ? ?

Effective radius ( r _e ) - versus - mean volume radius ( r _v )

/40 37 Aerosol Characterization Experiment

✓

Effective radius ( r _e ) - versus - mean volume radius ( r _v )

/40 38 Aerosol Characterization Experiment

✓

Formation and growth of

cloud particles

Warm clouds

aerosol - cloud - precipitation

Heterogeneous nucleation

Cloud Condensation Nuclei (CCN)

activation

Diffusional growth

Condensational growth Collision/coalescence Drizzle formation

Rain

CCN washout

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