Scattering of ice clouds in
Infrared
forward RT models
Zhibo Zhang, Ping Yang, and George Kattawar
Texas A&M University
Hung-Lung (Allen) Huang, Thomas Greenwald, and Jun
Li
CIMSS/ University of Wisconsin
Bryan Baum, Danial Zhou, and Yongxiang Hu
NASA Langley Research Center
Outline
„
Bulk scattering properties of ice clouds
„
„
„
The importance of scattering and a simple IR RT
model for cloudy conditions
„
„
„
What determines the bulk scattering properties of ice clouds?
What is our current understanding of those factors?
Is scattering important in IR RT models?
How is scattering treated in ITOA=(1-ε)Iclr+εB(Tc); ε=1-exp(-(1-ω)τ/μ)?
Where/Why does it do a good/bad job?
Rigorous fast IR RT model for cloudy conditions
„
„
Why the adding-doubling method is suitable for hyperspectral
RT model?
FIRTM-AD (Fast Infrared RT model based on the addingdoubling principle)
Outline
„
Bulk scattering properties of ice clouds
„
„
„
The importance of scattering and a simple IR RT
model for cloudy conditions
„
„
„
What determines the bulk scattering properties of ice clouds?
What is our current understanding of those factors?
Is scattering important in IR RT models?
How is scattering treated in ITOA=(1-ε)Iclr+εB(Tc); ε=1-exp[-(1-ω)τ/μ]
? Where/Why does it do a good/bad job?
Rigorous fast IR RT model for cloudy conditions
„
„
Why the adding-doubling method is suitable for hyperspectral
RT model?
FIRTM-AD (Fast Infrared RT model based on the addingdoubling principle)
Outline
„
Bulk scattering properties of ice clouds
„
„
„
The importance of scattering and a simple IR RT
model for cloudy conditions
„
„
„
What determines the bulk scattering properties of ice clouds?
What is our current understanding of those factors?
Is scattering important in IR RT models?
How is scattering treated in ITOA=(1-ε)Iclr+εB(Tc); ε=1-exp(-(1-ω)τ/μ)?
Where/Why does it do a good/bad job?
Rigorous fast IR RT model for cloudy conditions
„
„
Why the adding-doubling method is suitable for hyperspectral
RT model?
FIRTM-AD (Fast Infrared RT model based on the addingdoubling principle)
What controls the
scattering of ice clouds?
„
If a photon hits an ice crystal, how many things
must we know about the ice crystal to determine
the next state of the photon?
¾How large is the ice crystal?
•Particle size distribution
¾What does the crystal look like?
•Ice crystal habit/habit distribution
¾How do ice crystals interact with the photon?
•Single scattering properties of ice crystals
Particle Size Distribution (PSD)
Howmuch
manychance
small/large
crystals
How
for a ice
photon
to hit
in aice
unit
volume
of certain
ice clouds
An
crystals
with
size?
1x10
7
1x10
6
1x10
5
1x10
4
1x10
3
1x10
2
1x10
1
1x10
0
1x10
-1
1x10
-2
1x10
-3
1x10
-4
1x10
-5
Fu 1996, Fu et al. 1998
1
10
100
1000
Maximum Dimension of ice crystal ( μm )
10000
Baum et al. 2005
Ice crystal habits/shapes
„
Ice crystal habits
„
In reality “no two snowflakes are alike”
In practice, 6 habits
are widely used
•Droxtal
•Hexagonal column
•Hollow column
•Hexagonal plate
•Bullet rosette
•Aggregate
http://www.ssec.wisc.edu/~baum/Cirrus/MidlatitudeCirrus.html
Ice crystal
habit distribution
An on-going research topic
25% hollow columns
25% plates
100% droxtal
30% aggregate
30% bullet rosette
20% hollow columns
45% plates
hollow columns
20%
45% solid columns
10% aggregates
5
4
3
2
1
0
3
15% bullet rosettes
50% solid columns
35% plates
4
200
150
100
50
0
-50
-100
-150
-200
-150
-40
-30
-20
-10
0
10
20
30
40
-100
-50
0
50
5
4
3
2
1
0
-1
-2
100
0
1
2
3
-3
-4
-5
-4 -3 -2 -1
0
1
2
4
4
3
2
1
0
-1
-2
-150
-40
-30
-20
-10
0
10
20
30
40
40
30
20150
10
0
-10
-20
-30
-40
-40 -30-20 -10 0 10 20 40
30 40
30
20
10
0
-10
-20
-30
-40
-40 -30-20 -10 0 10 20 30 40
4
-100
-3
-4
-5
-50
0
50
-4 -3 -2 -1
100
0
1
150
2
3
4
-150
-40
-30
-20
-10
0
10
20
30
40
-100
-50
0
50
200
150
100
50
0
-50
-100
-150
-200
100
150
40
30
20
10
0
-10
-20
-30
-40
-40 -30-20 -10 0 10 20 30 40
70μm
60μm
3
5
-3
-4
-5
-4 -3 -2 -1
0
-1
-2
1000μm
Maximum Dimension(μm)
2500μm
Maximum Dimension(μm)
200
150
100
50
0
-50
-100
-150
-200
50
2
4
3
2
1
00
1
5
0
0
0
-50 0
0
50
-4 -3 -2 -1
97% bullet rosette
3% aggregates
00
-4
-5
50
-3
00
-2
0
0
0
-50 0
-1
0
0
0
-50 0
100%
Particle Density (# m-3 μm-1)
Particle Density (# m-3 μm-1)
In current CAM3.0,
all ice crystals are
assumed to be solid
hexagonal columns
MODIS collection04
Baum
et al. 2005
50% bullet rosette
An extensive database of
single-scattering properties of ice
crystals in IR region
Scattering properties
„
The shape of ice crystals:
4
3
2
1
-150
-40
-30
-20
-10
0
10
20
30
40
0
-1
-2
-3
-4
-5
Wavelength:
-4 -3 -2 -1
„
„
„
0
1
2
3
4
-100
-50
0
50
100
200
150
100
50
0
-50
-100
-150
-200
150
50
5
40
30
20
10
0
-10
-20
-30
-40
-40 -30-20 -10 0 10 20 30 40
00
„
Qe ϖ P g
4
0
0
0
-50 0
„
49 wavelengths from 3.08- to 100 μm
Size bin:
„
45 Size bins from 2 μm to 10000 μm
(in maximum dimension of ice crystal)
How do they work together?
If we randomly
upcrystal
an iceactually
crystal
Single scattering
properties:pick
the ice
has
Bulk scattering
ice crystal would most likely
from properties:the
the ice clouds…
have.
Single-scattering albedo
ϖ =
∫
∞
0
Probability of
an
ice crystalPSD
being hit
HD
⎛
⎞
⎜⎝ ∑ ϖ i (D)Qe,i (D)Ai (D)w(D)⎟⎠ n(D)dD
i
∞⎛
⎞
∫0 ⎜⎝ ∑i Qe,i (D)Ai (D)w(D)⎟⎠ n(D)dD
Cloud bulk albedo
Bulk scattering properties of ice clouds in IR region
(Baum et al. J. Appl. Meteor. 2005)
Qe
ϖ
De
g
Forimportant
ice cloud with
large De ,under
An
feature
single-scattering conditions, about
50%of
the incident
¾
At large
effectiveenergy
size(Deis
) Qscattered
e , ϖ and g
and a large
of the
scattered
approach
toportion
2.0,0.5 and
0.9,
Energy is concentrated in the
respectively
“forward direction”
For ice cloud with small De, the
situation is more complex
Summary of Part1
„
„
PSD, HD and single-scattering properties
together determine the bulk scattering
properties of ice clouds.
In-situ observations have substantially
improved our understanding of the
microphysics and bulk scattering properties of
ice clouds
Is scattering important for
IR RT computations?
ϖ
dI
=I−J
IR RTE μ
dτ
source term J =ϖ (scattering) + (1 − ϖ )(emission)
ϖ ≈ 0.5 for most υ and De
Ts and Tats are comparable toTc
Scattering term has the same
order of magnitude as emission.
It can NOT be ignored in IR RT!
A simplification of the
scattering in IR region
1 1
ϖ (scattering) = ϖ ∫ P( μ, μ ')I( μ ')d μ '
2 −1
Interested scattering direction
2D problem
Incidence
Interested scattering direction
1D problem
Incidence
The scattering is concentrated mainly in
the “forward direction”
A simplification o f the
scattering in IR region
Interested scattering direction
From the RTE point of view,
The simplification means
scattering phase
P( μfunction
, μ ') = 2δP( μ= −2δμ(')μ − μ ') Incidence
dI(τ , μ, υ )
μ
= I(τ , μ, υ ) − ϖ I(τ , μ, υ ) − (1 − ϖ )B[T (τ )]
dτ
For a homogenous and isothermal cloud layer with τ *
↑
↑
I top
= (1 − ε )I base
+ ε B(Tc )
ε = 1 − exp ⎡⎣ −(1 − ϖ )τ * / μ ⎤⎦
Isn’t it familiar!
A simple IR RT model for
cloudy conditions
–If the atmosphere above an ice clouds
can be ignored
–If an ice cloud layer is homogenous and
isothermal
I TOA = (1 − ε )I clr + ε B(Tc )
ε = 1 − exp [−(1 − ϖ )τ / μ ]
It is NOT because scattering is ignored(or non-scattering)
but a result of the “forward-scattering”simplification
I TOA = (1 − ε )I clr + ε B(Tc )
Problems ε = 1 − exp [−(1 − ϖ )τ / μ ]
ϖ
g
forward-scattering → no cloud reflection
I TOA tends to be overestimated
particularly for ice clouds with small De .
because g is relatively small and ϖ is realtively
large when De is small.
Errors: How good is it?
log10 (τ )
27045
-1040 -8
15
Lower atmosphere
-4
-2
0
2
26035
ice cloud layer @ 12km
BT (K)
12.5
Height (km)
homogenous and isothermal
log10(τ )
-6
30
250
10
25
24020
15
5
7.5
23010
2.5
800
5
0
175
T(K)
τ (8.5μm)
τ (11μm)
τ (12μm)
²BT (K)
No atmosphere above
-10
-8
-6
-4
-2
0
2
τ vis =502.0;
De = 60 μ m;nadir-viewing angle
3
1.5
T(K)
0
800
1000
τ (8.5μm)
τ (11μm)
τ (12μm)
900
1000
1100
Wavenumber (cm-1 )
1200
1200
= (1−
ε)Iclr325
+ εB(Tc )
DISORT
175 Temperature
200 225
250 Iobs
275
300
(K)
Temperature (K) −(1−ϖ )τ / μ
32 Stream
ε =1− e
0200
225
250
275
300
325
Lambert
Surface
RMS
BT error
generally >2K;~5K for small De
εRelative
= 1.0; T radiance
= 300K difference generally >8%;~15% for small De
Summary of Part2
„
„
„
Scattering term in IR RTE has the same
magnitude as the thermal emission term
ITOA=(1-ε)Iclr+εB(Tc) is a result of the “forward
scattering” simplification. It does a reasonably
good job, except for small De.
To achieve higher accuracy, a rigorous RT model
with is needed.
Challenge for RT model from
hyperspectral remote sensing
„
Speed
„
„
„
„
Thousands of wavelengths
global observations
Accuracy
„
At least more accurate than I TOA = (1 − ε )I clr + ε B(Tc )
„
Clear sky accuracy < 0.1K
General applicability
„
„
Both TOA(space-borne) and
user-defined-levels (air-borne & ground)
Multiple-layered and
vertically inhomogenous clouds
Current fast IR RT models
for cloudy conditions
„
RTTOV
„
„
CHARTS
„
„
Evans (2006)
FIRTM-1,2, and -AD
„
„
Moncet et al. (2001,2003)
SHDOMPPDA
„
„
Moncet and Clough (1997)
OSS
„
„
Eyre and Woolf(1988), Saunders et al.(1999)
Wei et al. (2004), Niu et al. (2006), Zhang et al. (2006)
Many others
FIRTM-AD (Fast IR RT model
based on adding-doubling
principle)
„
„
„
„
why adding-doubling?
Stable and accurate
easy to understand
Applicable to multiple-layered or
vertically inhomogenous clouds
Applicable to computations at
different user-level
FIRTM-AD (Fast IR RT model
based on adding-doubling
principle)
„
Why is it fast?
„
„
Extensive pre-computed look-up library
Efficient interpolation scheme
pre-computed R,T,ε library
Clear Layer
Sub-layers
Cloud Layer
..
Clear Layer
Clear Layer
Cloud Layer
Clear Layer
Suface Layer
In traditional
models,
Sub-layers
In FIRTM-AD,
..
to initialize
the adding-doubling
the R,T and ε of the whole
operation the cloud layer must be first
cloud layer is directly extracted
divided into optically thin layer (τ∼10−3)
τ Space From the pre-computed library
FIRTM-AD errors
BT spectrum @ TOA
single-layered & isothermal
“on-grid” accuracy <0.1K
(both De and τ
on gird of the library No interpolation is needed)
250 times faster than DISORT
single − layer, τ vis = 2, De = 60μm, μ = 0.9947 @12km
0.2
270
a)
²BT (K)
260
-0.2
0.4
240
230
DISORT
FIRTM-AD
210
800
0
-0.1
900
1000 1100 1200
Wavenumber (cm-1)
²Radiance (%)
BT (K)
250
220
b)
0.1
0.3
c)
0.2
0.1
0
-0.1
1300
800
900
1000 1100 1200
Wavenumber (cm-1)
1300
FIRTM-AD errors
BT spectrum @ TOA
single-layered & isothermal
“off-grid” accuracy <0.4K
(both De and τ
off gird of the library, interpolation is needed)
The resolution of the
library is still being
tested to achieve
better accuracy and
smaller size of the
library.
Summary
„
„
„
The adding-doubling method seems a
proper approach for a fast hyperspectral RT
model
The time-consuming initialization step in
the adding-doubling computation can be
replaced by pre-computed look-up libraries
Current FIRTM-AD has 0.1K “on-grid”
accuracy and 0.4K “off-grid” accuracy, and
is 250 times faster than DISORT
Thank you