30 25 20 15 10 5 0 180 Scattering angle (deg)...above Salt Lake City, Utah. Shown from top to bottom...
8
0 5 10 15 20 25 30 Size parameter (a) Prolate, a/b = 1/1.4 0 5 10 15 20 25 30 (b) Oblate, 0 5 10 15 20 25 30 Size parameter (c) Prolate, 0 5 10 15 20 25 30 (d) Oblate, 0 30 60 90 120 150 180 Scattering angle (deg) 0 5 10 15 20 25 30 Size parameter (e) Prolate, 0 30 60 90 120 150 180 Scattering angle (deg) 0 5 10 15 20 25 30 (f) Oblate, -100 - 50 0 50 100 a/b = 1.4 a/b = 1/1.7 a/b = 1.7 a/b = 1/2 a/b = 2 0 5 10 15 20 25 30 Size parameter (g) Prolate, 0 5 10 15 20 25 30 (h) Oblate, 0 5 10 15 20 25 30 Size parameter (i) Prolate, 0 5 10 15 20 25 30 (j) Oblate, 0 30 60 90 120 150 180 Scattering angle (deg) 0 5 10 15 20 25 30 Size parameter (k) Prolate, 0 30 60 90 120 150 180 Scattering angle (deg) 0 5 10 15 20 25 30 (l) Oblate, <0.25 0.4 0.5 0.7 1 1.4 2 2.5 >4 a/b = 1.7 a/b = 1/1.4 a/b = 1.4 a/b = 1/1.7 a/b = 1/2 a/b = 2 Plate 10.2. Two left-hand columns: –b 1 a 1 (in %) versus scattering angle and effective size parameter for polydisperse randomly oriented spheroids with various axis ratios and a fixed relative refractive index m = 1.53 + i0.008. The distribution of surface-equivalent-sphere radii is given by Eq. (5.246) with α = –3 and v eff = 0.1. Two right-hand columns: as in the two left-hand columns, but for the ratio of the phase function a 1 for randomly oriented polydisperse spheroids and that for surface-equivalent spheres.
Transcript of 30 25 20 15 10 5 0 180 Scattering angle (deg)...above Salt Lake City, Utah. Shown from top to bottom...
051015202530
Size parameter
(a)
Pro
late
, a/
b =
1/1
.4
051015202530
(b
) O
blat
e,
051015202530
Size parameter
(c)
Pro
late
,
051015202530
(d
) O
blat
e,
030
6090
120
150
180
Sca
tterin
g an
gle
(deg
)
051015202530
Size parameter
(e
) P
rola
te,
030
6090
120
150
180
Sca
tterin
g an
gle
(deg
)
051015202530
(f
) O
blat
e,
−100
−50
050
100
a/b
= 1
.4
a/b
= 1
/1.7
a/b
= 1
.7
a/b
= 1
/2a/
b =
2
051015202530
Size parameter
(g)
Pro
late
,
051015202530
(h
) O
blat
e,
051015202530
Size parameter
(i) P
rola
te,
051015202530
(j)
Obl
ate,
030
6090
120
150
180
Sca
tterin
g an
gle
(deg
)
051015202530
Size parameter
(k)
Pro
late
,
030
6090
120
150
180
Sca
tterin
g an
gle
(deg
)
051015202530
(l)
Obl
ate,
<0.
250.
40.
50.
71
1.4
22.
5>
4
a/b
= 1
.7
a/b
= 1
/1.4
a/b
= 1
.4
a/b
= 1
/1.7
a/b
= 1
/2a/
b =
2
Plat
e 10
.2.
Two
left-
hand
col
umns
: –b 1
�a1 (
in %
) ver
sus s
catte
ring
angl
e an
d ef
fect
ive
size
par
amet
er fo
r pol
ydis
pers
e ra
ndom
ly o
rient
ed sp
hero
ids w
ithva
rious
axi
s rat
ios a
nd a
fixe
d re
lativ
e re
frac
tive
inde
x m
= 1
.53
+ i0
.008
. Th
e di
strib
utio
n of
surf
ace-
equi
vale
nt-s
pher
e ra
dii i
s giv
en b
y Eq
. (5.
246)
with
α =
–3 a
nd v
eff =
0.1
. Tw
o rig
ht-h
and
colu
mns
: as i
n th
e tw
o le
ft-ha
nd c
olum
ns, b
ut fo
r the
ratio
of t
he p
hase
func
tion
a 1 fo
r ran
dom
ly o
rient
ed p
olyd
ispe
rse
s phe
roid
s and
that
for s
urfa
ce-e
quiv
alen
t sph
eres
.
051015202530
Size parameter
(a)
Pro
late
,
051015202530
(b
) O
blat
e,
051015202530
Size parameter
(c)
Pro
late
,
051015202530
(d
) O
blat
e,
030
6090
120
150
180
Sca
tterin
g an
gle
(deg
)
051015202530
Size parameter
(e
) P
rola
te,
030
6090
120
150
180
Sca
tterin
g an
gle
(deg
)
051015202530
(f
) O
blat
e,
025
5075
100
a/b
= 1
/1.4
a/b
= 1
/1.7
a/b
= 1
.4
a/b
= 1
.7
a/b
= 2
a/b
= 1
/2
051015202530
Size parameter
(g)
Pro
late
,
051015202530
(h
) O
blat
e,
051015202530
Size parameter
(i) P
rola
te,
051015202530
(j)
Obl
ate,
030
6090
120
150
180
Sca
tterin
g an
gle
(deg
)
051015202530
Size parameter
(k)
Pro
late
,
030
6090
120
150
180
Sca
tterin
g an
gle
(deg
)
051015202530
(l)
Obl
ate,
−100
−50
050
100
a/b
= 1
/1.4
a/b
= 1
.4
a/b
= 1
/1.7
a/b
= 1
.7
a/b
= 1
/2a/
b =
2
Plat
e 10
.3.
As i
n th
e tw
o le
ft-ha
nd c
olum
ns o
f Pla
te 1
0.2,
but
for a
2�a 1
(the
two
left-
hand
col
umns
) and
a3�
a 1 (t
he tw
o rig
ht-h
and
colu
mns
).
051015202530
Size parameter
(a)
Pro
late
,
051015202530
(b
) O
blat
e,
051015202530
Size parameter
(c)
Pro
late
,
051015202530
(d
) O
blat
e,
030
6090
120
150
180
Sca
tterin
g an
gle
(deg
)
051015202530
Size parameter
(e
) P
rola
te,
030
6090
120
150
180
Sca
tterin
g an
gle
(deg
)
051015202530
(f
) O
blat
e,
−100
−50
050
100
a/b
= 1
/1.4
a/b
= 1
.4
a/b
= 1
/1.7
a/b
= 1
.7
a/b
= 1
/2a/
b =
2
051015202530
Size parameter
(g)
Pro
late
,
051015202530
(h
) O
blat
e,
051015202530
Size parameter
(i) P
rola
te,
051015202530
(j)
Obl
ate,
030
6090
120
150
180
Sca
tterin
g an
gle
(deg
)
051015202530
Size parameter
(k)
Pro
late
,
030
6090
120
150
180
Sca
tterin
g an
gle
(deg
)
051015202530
(l)
Obl
ate,
−100
−50
050
100
a/b
= 1
/1.4
a/b
= 1
.4
a/b
= 1
/1.7
a/b
= 1
.7
a/b
= 1
/2a/
b =
2
Plat
e 10
.4.
As i
n th
e tw
o le
ft co
lum
ns o
f Pla
te 1
0.2,
but
for a
4�a 1
(the
two
left-
hand
col
umns
) and
b2�
a 1 (t
he tw
o rig
ht-h
and
colu
mns
).
0
5
10
15
20
25
Siz
e pa
ram
eter
Sphe
res
0
5
10
15
20
25
Siz
e pa
ram
eter
0
5
10
15
20
25
Siz
e pa
ram
eter
0 30 60 90 120 150 180Scattering angle (deg)
0
5
10
15
20
25
Siz
e pa
ram
eter
0 30 60 90 120 150 180Scattering angle (deg)
0 30 60 90 120 150 180Scattering angle (deg)
<−1 −0.5 0 0.5 >1
<0.25 0.5 0.7 1 1.4 2 3 >4
−100 −50 0 50 100
log10[a1(S)] a3 /a1 (%) a4 /a1 (%)
D/L
=1
D/L
=1/
2D
/L=
2
a1(C)/a1(S) a3 /a1, a4 /a1 (%)log10[a1(S)]
a1(C)/a1(S)
Plate 10.5. The top left panel shows the logarithm of the phase function versus scattering angle and effective sizeparameter for polydisperse spheres. The three lower diagrams in the left-hand column show the ratio of the phasefunction )C(1a for polydisperse randomly oriented cylinders with LD = 1, 1/2, and 2 and the phase function
)S(1a for surface-equivalent spheres. The middle and right-hand columns show 13 aa and 14 aa for spheres (toppanels) and for surface-equivalent cylinders (lower three pairs of panels). Each diagram is quantified by thecorresponding color bar at the bottom of the plate. All particles have the same relative refractive index, 1.53 +i0.008. The distribution of surface-equivalent-sphere radii is given by Eq. (5.246) with 3−=α and .1.0eff =v
0
5
10
15
20
25
Siz
e pa
ram
eter
Sphe
res
0
5
10
15
20
25
Siz
e pa
ram
eter
D/L
=1
0
5
10
15
20
25
Siz
e pa
ram
eter
0 30 60 90 120 150 180Scattering angle (deg)
0
5
10
15
20
25
Siz
e pa
ram
eter
0 30 60 90 120 150 180Scattering angle (deg)
0 30 60 90 120 150 180Scattering angle (deg)
0 25 50 75 100
−100 −50 0 50 100
−100 −50 0 50 100
D/L
=1/
2D
/L=
2
a2 /a1 (%) −b1 /a1 (%) b2 /a1 (%)
Plate 10.6. The ratios ,12 aa ,11 ab− and 12 ab for polydisperse spheres and for surface-equivalent randomlyoriented cylinders with LD = 1, 1/2, and 2. The diagrams in each column are quantified using the color bar belowthe column. All particles have the same relative refractive index, 1.53 + i0.008. The distribution of surface-equivalent-sphere radii is given by Eq. (5.246) with 3−=α and .1.0eff =v
0.01
0.1
1
10
100P
hase
func
tion
Monodisperse spheroids
0.01
300
Spheres= 1.2= 1.4= 1.6= 1.8= 2= 2.2= 2.4
(a)
0.1
1
10
100
Pha
se fu
nctio
n
Polydisperse spheroids
0.06
300
Spheres= 1.2= 1.4= 1.6= 1.8= 2= 2.2= 2.4
(b)
0 60 120 180 Scattering angle (deg)
0.1
1
Pha
se fu
nctio
n
0.06
5
Spheres= 1.2 − 2.4= 1.3 − 2.3= 1.4 − 2.2= 1.5 − 2.1= 1.6 − 2.0= 1.7 − 1.9= 1.8
Shape mixtures
(c)
0 60 120 180 00Scattering angle (deg)
0.1
1
10
100
Pha
se fu
nctio
n
0.06
300
Spheres
Prolate spheroids
Oblate spheroids
All spheroids
(d)
ε ε ε ε ε ε ε
ε ε ε ε ε ε ε
ε ε ε ε ε ε ε
Plate 10.7. T-matrix computations of phase function versus scattering angle for monodisperse and polydispersespheres and randomly oriented spheroids with a relative refractive index 1.53 + i0.008 at a wavelength 443 nm.Panel (a) shows results for a monodisperse sphere with a radius 1.163 µm and for surface-equivalent prolatespheroids with aspect ratios ranging from 1.2 to 2.4. Panel (b) shows similar computations but for a log normal sizedistribution with an effective radius 1.163 µm and an effective variance 0.168. Panel (c) demonstrates the effect ofusing a spheroid aspect-ratio distribution of finite width; it shows the ensemble-averaged phase functions forequiprobable shape mixtures of polydisperse prolate spheroids with different aspect-ratio ranges, all centered on
.8.1=ε Panel (d) shows the phase functions for polydisperse spheres and ensemble-averaged phase functions forequiprobable shape mixtures of prolate spheroids (green curve), oblate spheroids (blue curve), and prolate andoblate spheroids together (red curve) with aspect ratios ranging from 1.2 to 2.4 in steps of 0.1. (After Mishchenkoet al. 1997a.)
0
5
10
15
20
25
30
Siz
e pa
ram
eter
(a) Spheres
0
5
10
15
20
25
30
(b) Bispheres (fixed orientation)
0 30 60 90 120 150 180Scattering angle (deg)
0
5
10
15
20
25
30
Siz
e pa
ram
eter
(c) Bispheres (fixed orientation)
0 30 60 90 120 150 180Scattering angle (deg)
0
5
10
15
20
25
30
(d) Bispheres (random orientation)
−100 −50 0 50 100
Plate 10.8. Panel (a): the ratio )0,0;0,()0,0;0,( incincscasca11
incincscasca21 ======− ϕϑϕϑϕϑϕϑ ZZ in % versus
scaϑ and size parameter for monodisperse single spheres. Panels (b)–(d): the same ratio versus scaϑ andconstituent-sphere size parameter for monodisperse bispheres with equal touching components in fixed and randomorientations. In panels (b) and (c) the bisphere axis is oriented respectively along the z-axis and along the x-axis ofthe laboratory reference frame. The relative refractive index is 1.5 + i0.005.
Plate 10.9. Compilation of data for the case study on 5 March 1999 of cirrus, contrails, and an Asian dust layerabove Salt Lake City, Utah. Shown from top to bottom are: three fish-eye photographs of all-sky cloud conditions,obtained at 1808, 1826, and 1905 UTC (from left to right); backscattered intensity and linear depolarization time-height displays measured by an upward-looking lidar at a wavelength µm,694.0 the broadband visible andinfrared hemispherical fluxes, and the mid-infrared column brightness temperatures ;bT and, at the bottom,expanded views of backscattered intensity (black and white images) and linear depolarization (colored images) atwavelengths µm 532.0 (bottom left panel) and µm06.1 (bottom right panel) for a time range near the end of themeasurement period. The depolarization displays can be quantified using the inserted color bar. (From Sassen etal. 2001.)
L
