Particle Scattering

1
Particle Scattering Single Dipole scattering
(tiny particles)
Rayleigh Scattering Multiple
dipole scattering larger particles
(Mie
scattering) Extinction
Rayleigh particles and the example
of microwave measurement of cloud
liquid water
Microwave precipitation
Scattering phase function radar/lidar
equation
backscattering properties
e.g. Rayleigh backscatter
calibration
of lidar, radar reflectivity

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Analogy between slab and particle scattering
Insert 13.10/ 14.1
slab
particle
Slab properties are governed by oscillations (of
dipoles) that coherently interfere with one
another creating scattered radiation in only two
distinct directions - particles scatter radiation
in the same way but the interference are
less coherent producing scattered stream of
uneven magnitude in all directions
3
Radiation from a single dipole
Scattered wave is spherical in wave form (but
amplitude not even in all directions) Scattered
wave is proportional to the local dipole moment
(p?E)
Basic concept of polarization

• Key points to note
• parallel perpendicular
• polarizations
• scattering angle

Any polarization state can be represented by two
linearly polarized fields superimposed in an
orthogonal manner on one another
Referred to as Rayleigh scattering
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Rayleigh scattering
Polarizability p?E
Spherical wave form
(2?/?)4 ? ?-4
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The degree of polarization is affected by
multiple scattering. Position of neutral points
contain information about the nature of the
multiple scattering and in principle the
aerosol content of the atmosphere (since the
Rayleigh component can be predicted with models).
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Rayleigh scattering as observed POLDER
Radiance
Strong spatial variability
Scattering angle
Pol. Rad 650 nm
Smooth pattern Signal governed by
scattering angle
(Deuz? et al., 1993, Herman et al., 1997)
Proportional to Q
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Radiation from a multiple dipole particle
r
ignore dipole-dipole interactions
?
rcos?
At P, the scattered field is composed on an EM
field from both particles
size parameter
P
For those conditions for which ??0, fields
reinforce each other such that I?4E2
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Scattering in the forward corresponds to ??0
always constructively add Larger the particle
(more dipoles and the larger is 2?r/? ), the
larger is the forward scattering The more larger
is 2?r/?, the more convoluted (greater of
max-min) is the scattering pattern
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size parameter
10
0
180
P(?)
forward scattering increase with x rainbow
and glory smoothing of scattering function by
polydispersion
single particle
Properties of the phase function
fig. 14.19
asymmetry parameter g1 pure forward scatter g0
isotropic or symmetric (e.g
Rayleigh) g-1 pure backscatter
poly-dispersion
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Particle Extinction
Particle scattering is defined in terms of
cross-sectional areas efficiency factors Cext
effective area projected by the
particle that determines
extinction Similarly Csca, Cabs
Geometric cross-section ?r2
The efficiency factor then follows
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Particle Extinction (single particle)
Note how the spectrum exhibits both coarse and
fine oscillations Implications of these for
color of scattered light How Qext?2 as 2?r/???
extinction paradox
insert 14.8
?1
Rayleigh limit x ?0 (xltlt1)
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Extinction Paradox
shadow area ?r2
combines the effects of absorption and any
reflections (scattering) off the sphere.
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insert 14.10
Poisson spot occupies a unique place in science
by mathematically demonstrating the
non-sensical existence of such a spot, Poisson
hoped to disprove the wave theory of light.
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Scattering Size Parameter
(Spheres only)
From Petty (2004)
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Particle Extinction (single particle)
Note how the spectrum exhibits both coarse and
fine oscillations Implications of these for
color of scattered light How Qext?2 as 2?r/???
extinction paradox
insert 14.8
?1
Rayleigh limit x ?0 (xltlt1)
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Volumes containing clouds of many particles
Extinctions, absorptions and scatterings by all
particles simply add- volume coefficents
half of 14.9
L-4
L
L-1
L2
n( r) the particle size distribution
particles per unit volume per unit
size
r
Exponential distribution (rain)
Modified Gamma distribution (clouds)
Lognormal distribution (aerosols, sometimes
clouds)
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Effective Radius Variance
Mean particle radius doesnt have much physical
relevance for radiative effects
For large range of particle sizes, light
scattering goes like pr2. Defines an effective
radius
Effective variance
Modified Gamma distribution
a effective radius b effective variance
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Scattering/extinction properties
Cloud optical depths (visible/nir ?s)
Microwave (Rayleigh) scattering x?0
W
w?z
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Polydisperse Cloud Optical Depth, Effective
Radius, and Water Path
(visible/nir ?s)
Cloud Optical Depth
Volume Extinction Coefficient km-1
Cloud Optical Depth
Local Cloud Density kg/m3
Cloud Effective Radius µm
1st indirect aerosol effect! (Twomey Effect)
w?z
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Microwave (Rayleigh) scattering x?0

• Cloud droplets with xltlt1 for all droplets
• Optical depth t through some depth ?z
• t depends only on total water path L, the index
  of refraction of water or ice (through ?), and
  the density of water/ice.

Ex 37 GHz, 0.5 kg/m2 Water K 0.11 Ice K
3.1e-4 twat 0.13 tice 4e-4
Cloud Ice can be neglected in most microwave RT!
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Example Retrieving path integrated water vapor
and cloud liquid water from microwave radiances
Fig. 7.6
Microwave spectrum around the 22 GHZ water vapor
absorption line
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Measurement of ?T at two frequencies (19GHz, 37
GHz), estimation of RV/H ?kw/l, and Trox allows
for simultaneous solution for W and L,
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Increase of Water Vapor over time
Trenberth et al. (2005)
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20 yrs Cloud Water from Multiple Satellites
ODell et al. (2008)
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Diurnal cycle of Cloud Water from Multiple
Satellites
Wood et al. (2002) ODell et al. (2008)
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Scattering phase function
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spheres
spherical
Non spherical with plane of symmetry
non spheres
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Particle Backscatter
Cd(?)I0 is the power scattered into ? per unit
solid angle
Differential cross-section Bi-static
cross-section Backscattering cross-section
CbI0 is the total power assuming a particle
scatters isotropically by the amount is scatters
at ?180
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Polarimetric Backscatter LIDAR depolarization

• Transmit linear
• Receive parallel/perpendicular

Ice
Water/Ice/Mix
0 for spheres
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Polarimetric Backscatter RADAR ZDR

• Transmit both horizontal vertical
• Receive horizontal vertical

for spheres, ZDR0
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Lidar Calibration using Rayleigh scattering
Laser backscattering Crossection as
measured During the LITE experiment
For Rayleigh scattering
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Lidar Calibration using Rayleigh scattering
Rayleigh scattering is well-understood and easily
calculable anywhere in the atmosphere!
ns 1 a (1 b ?-2)
Stephens et al. (2001)