Figure: ZhuandZhang,MWR,2004 Figure: ZhuandZhang,MWR,2004 Figure: MicrophysicsandHurricanes Simulatedvs.observedHurricaneBonnie’98 Simulatedvs.observedHurricaneBonnie’98

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Institute for Atmospheric and Climate Science

Microphysics and Hurricanes

Figure: Frisius and Hasselbeck, article in preparation RMW: radius of maximum wind

Ulrike Lohmann (IACETH) Microphysics and Hurricanes April 10, 2007 1 / 32

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Motivation Cloud formation Rain formation Mixed-phase clouds Ice outflow from Cb

Simulated vs. observed Hurricane Bonnie ’98

Figure: Zhu and Zhang, MWR, 2004

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stitute for Atmospheric and Climate Science

Simulated vs. observed Hurricane Bonnie ’98

Figure: Zhu and Zhang, MWR, 2004

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Simulated vs. observed Hurricane Bonnie ’98

Figure: Zhu and Zhang, MWR, 2004

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Role of microphysics for TC development

Figure: Zhu and Zhang, JAS, 2006

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CTL: control simulation

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NEVP: no evaporation of rain and cloud water

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NMLT: no melting of ice, snow and graupel

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NGP: no graupel

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NICE: no ice microphysics

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Phase changes

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Are easiest understood in terms thinking that a system wants to minimise its Gibbs free energy G (analogous to a system wanting to maximize its entropy)

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G = u + e

s

α − Ts (1) where u = internal energy, e

s

= saturation vapor pressure, α = specific volume, s = entropy

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nucleation from the vapor phase requires to form a new surface, which needs energy.

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if the vapor is supersaturated and the volume term of the change in Gibbs free energy is larger than the surface term, nucleation has occurred and the particles is said to be activated

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Gibbs free energy for homogeneous nucleation

(Fig. 9.10 Seinfeld and Pandis, 1997)

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Kelvin equation

Vapor pressure enhancement over smaller drops due to surface tension

e

s

(r) = e

s

(∞)exp 2σ

R

v

ρ

w

Tr

(2) where T = temperature, r = particle radius, σ = surface tension ≈ 0.075 N/m, ρ

_w

= water density, R

_v

= gas constant of water vapor (461.5 J kg

⁻¹

K

⁻¹

).

Saturation ratio Critical radius number of molecules

S r

^∗

(µm) n

1 ∞ ∞

1.01 0.12 2.47 x 10

⁸

1.1 0.0126 2.81 x 10

⁵

2 1.73 x 10

⁻³

730 10 5.22 x 10

⁻⁴

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Raoult’s Law

Vapor pressure reduction due to the presence of a non-volatile solute:

e

⁰

e

s

(∞) = n

o

i n + n

o

∼ 1 − i n n

o

= 1 − 3imM

w

4πM

s

ρ

w

r

³

(3)

where e

⁰

= equilibrium vapor pressure over a solution with n

o

water molecules and n solute molecules; i = degree of ionic dissociation; M

w,s

= molecular weight of water or solute; m = mass of solute.

(Seinfeld and Pandis, 1997)

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K¨ ohler curve

Combination of Kelvin and Raoult’s equation:

e

⁰

(r )

e

s

(∞) = 1 + 2σ

ρ

w

R

v

Tr − 3imM

_w

4πM

s

ρ

w

r

³

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Figure: Rogers and Yau, 1989

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Droplet growth equation

r dr

dt = S − 1

L

RvT

− 1

_Lρ

w

KT

+

^ρ^w_De^R^v^T

s

= S − 1

F

_k

+ F

_d

(5) where F

_k

= thermodynamic term, F

_d

= vapor diffusion term, K = thermal conductivity of air, D = diffusion coefficient of water vapor in air

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Growth by collection (=collision-coalescence)

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coalescence = one or two particles merge during contact dR

dt = π 3

Z

R

o

R + r R

2

n(r)[u(R) − u(r)]r

³

E (R, r)dr (6) where R, r = radius of collector and collected drop; n(r) = number of drops with size r

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u(R), u(r) = fall velocity of collector and collected drop

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E (R, r) = collision efficiency (= fraction of drops with radius r in the path swept out by collector drop that actually collide with it):

E (R, r) = x

²

(R + r)

²

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Collision efficiency

Figure: Rogers and Yau, 1989

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Cloud drop/rain fall speed

Figure: Houze, 1993

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Droplet radius 15 mu

time collection

condensation

Figure: Droplet growth by condensation versus collection

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Motivation: seeding of hurricanes (Willoughby, BAMS, 1985)

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Frequency of supercooled clouds

Figure: Pruppacher and Klett, 1998

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Bergeron-Findeisen process

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Ice crystal habits

Relative growth of basal face versus prism face determines habit. It is a function of temperature and supersaturation:

A

A A

A

A A

H

H H j

*

basal growth - column like

prism growth - plate like

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Ice enhancement

Figure: Houze, 1993

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Hallett-Mossop process

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small ice particles are ejected by drops ≥ 25 µm in diameter when they freeze on to an ice particle at between -3 and -8

^◦

C.

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At temperature higher than -3

^◦

C drops tend to spread over the ice surface instead of freezing as discrete drops.

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At temperature colder than -8

^◦

C, the freezing is thought to proceed so rapidly, starting with an outer shell of ice, that disruption does not occur.

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Drops ≤ 25 µm in diameter probably freeze too rapidly to be disrupted.

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Snow crystal fall speed

Figure: Houze, 1993

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Degrees of riming [Courtesy of Eszter Bartazy, IACETH]

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Hail: rimed particles > 1 cm in diameter

Figure:

http : //earthstorm.ocs.ou.edu/materials /graphics/HailstoneLifecycle.gif

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Hail

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Cumulonimbus

(www.ems.psu.edu/∼lno/Meteo437/Cbsmall1.jpg)

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Outflow from cumulonimbus

Figure: 5.32 Houze [1993]

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Collapse of a cumulonimbus anvil

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Outflow from cumulonimbus I

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Is envisioned as a two-stage process

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First outflow undergoes a collapse during which the wake is flattened and spread laterally by the environment

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The upper part of outflow, being denser than the environment, subsides, while the lower part of the outflow, being lighter, rises

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At the same time that this external collapse takes place, an internal collapse occurs, in which the turbulence of the plume is slowly dissipated, its energy being transferred to waves and larger-scale 2D turbulence

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Outflow from cumulonimbus II

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Radiation is the only significant heat source since latent heat release is negligible at these altitudes

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Thus, the anvil can be treated as a dry mixed layer, for which the perturbation form of the first law is given as:

dΘ dt = − ∂

∂z w

⁰

Θ

⁰

+ R

= const. in z (8) where R = radiative flux divergence and w

⁰

Θ

⁰

= heat flux

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