Three-Dimensional Radiative
Transfer in Clouds
Warren Wiscombe
NASA Goddard
See new book, edited by Marshak and
Davis, published late 2004
mainly
shortwave
(sunlight)
dedicated to Gerry Pomraning
and Georgii Titov
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A motivation: Clouds cause 2–5 C range in predicted
global average temperature increase for 2xCO2
1979 Report on
CO2 and Climate,
Woods Hole:
“... the equilibrium
surface global
warming due to
2xCO2 will be in
the range 1.5 to
4.5 C”.
2001 IPCC:
Essentially the
same as above.
temperature range is pretty uniformly filled!
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99% of atmospheric radiative transfer
approximate{d,s} 3D clouds as 1D slabs
Constraints were: slow computers, and inability to
(a) specify cloud in 3D, (b) test models (cloud or radiation)
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There’s an approximately 1D world
overhead on a mountaintop on a clear day
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But the real world of cloud radiation looks
nothing like the tame, peaceful 1D world
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What are the unique aspects of Earth
atmospheric radiative transfer?
Clouds & vegetation — extreme 3D, big scale range
Strong, dense absorption lines
Forward-peaked scattering phase function
Surface BRDF important
specular reflection, hot spot!
Polarization — Rayleigh, aerosol, glint
Beams from inside, outside
Rapid variation — turbulent
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Real cloud radiation looks turbulent, with
occasional excursions above the 1D envelope
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and it still looks
intermittent for a
3–hr subset of
total flux!
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1D radiative transfer history in the
atmospheric sciences
Chandrasekhar (1950):
– polarized radiative transfer
Sekera & students (1950s) inspired by Chandrasekhar
to study Rayleigh scattering atmosphere w. aerosol
– polarized r.t. survived only in microwave until POLDER
reinvigorated field
van de Hulst, Twomey (1960s): adding-doubling
Dave and others: spherical harmonics w. polarization
– 1968 code still survives in UV project at Goddard!
Dave: Mie scattering
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Peaks of 1D theory were reached with
Grant-Hunt version of adding-doubling (1969)
Stamnes et al. discrete ordinates (DISORT, 1988)
k-distributions (Lacis/Hansen and others, 1980s)
Atmospheric radiative transfer field focused
on the wavelength rather than the x-y spatial
dimension. Lab spectroscopy measurements
led to an hubris that models were correct
without testing them in the open air. Thus
the field became largely an indoor activity...
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Thus, when theoreticians emerged into the
open air, they were puzzled...
“What is this strange alien object?”
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I started in 3D and 1D-spherical r.t.,
devolved to 1D-slab...
In 1970, the 3D world I entered was dominated by
–
–
–
–
Monte Carlo methods
discretize everything
spectral-expand some things, discretize others
diffusion, Eddington methods & variants
First two were severely computer-constrained
– random number generators were mediocre
– linear algebra algorithms for large matrices were poor
(this was even before LINPACK!)
Atmospheric science inherited these methods but
eventually improved on them considerably
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then I rode the 1D to 3D transition in
cloud radiation, mainly funded by ARM
In radiative transfer methodology, the transition
was somewhat predictable:
– more photons in Monte Carlo (finally, enough!)
– various stews of discrete vs. spectral for
both angle and space dimensions, with some
computationally hopeless, now-dead methods
– avoidance of brute force methods because
matrices can become so large (a small problem
of 100x100x20 w. 80 discrete angles could
lead to matrices of 16Mx16M)
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The full range of 3D radiative transfer
options are now used in cloud studies
Diffusion and other approximations
Analytical-numerical (quintessence: SHDOM, 1998)
Monte Carlo
Cases:
- step cloud
- 2D field from ARM radar
- 3D field derived from Landsat
- Sc and shallow Cu, Large Eddy model
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Emerging subject, cloud micro-3D radiative
transfer, challenges “elementary-volume”
assumption embodied in phase function p
Monochromatic Radiative Transfer Equation
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What assumptions are being challenged?
NumberOfDrops(radius r) = c x Volume
According to high-time-resolution aircraft data,
above a critical radius of ~14 mm:
(1) NumberOfDrops(radius r) = c(r) x VolumeD(r)
where 0 < D(r) < 1
(2) the larger drops are, the more they cluster
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This is a numerical simulation of drop
clustering based on aircraft data
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But if we give up “elementary volume”,
what can we do, radiative transfer-wise?
First-principles Monte Carlo: each photon interacts
with actual drops at specific spatial locations, rather
than with a fictitious elementary volume.
(At the outermost limit of what we can do computationally)
Fractional differential equations: in the very
simplest case of pure transmission through a
fractal-clustered drop distribution, must solve:
dI (x)   small I(x) dx   large large (x) I(x) (dx)D
0 no large drop at x
0  D  1,  large (x)  
1 large drop at x
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Many details of 3D radiative transfer will be
covered in the following talks, so because the 1D
to 3D transition in cloud structure modeling was
more unexpected, I will focus instead on:
(1) cloud structure — theoreti-empirical, and
instruments for measuring it
(2) tentative steps toward incorporating 3D
into routine activities of our field
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Clouds are highly variable in x, y, z & t
“Immense chaos amid immense order” (turbulence
produces chaos, reigned in by overall physical
controls that create & sustain large cloud systems)
Clouds are the tip of the water vapor iceberg!
– Typically <3% of water vapor in column condenses.
Clouds represent only the tail of the relative
humidity probability distribution; this already
ensures high variability.
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Real regularity in clouds happens when
waves overpower turbulence, and is rare
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This deep tropical convection from Shuttle
is more typical of the “immense chaos”
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Coast of Holland shows how surface
variability adds to cloud variability
Landsat image
These cloud waves would cause
mild bump in power spectrum
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Nevertheless, following Occam’s Razor,
clouds were modeled as cubes, 1975-90
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the ultimate Euclidean cloud...
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Lovejoy (1982)
showed that clouds
have a fractal not
Euclidean character
if Euclidean:
area perim 2
the data show:
area  perim 1.5
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What other
evidence of
fractality
was found?
Cloud liquid water
power spectra
from field
campaigns:
- scaling behavior
over a range 10 m
to ~50 km!
- no preferred scale
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How was the idea of modeling clouds as
fractals received?
Euclidean cloud papers survived into the early 1990s
Fractal models not taken seriously until extended:
– beyond the monofractals in Mandelbrot’s book
– beyond cloud geometry, to cloud liquid water
Two attractive features finally won the day:
– simpler than Euclidean models (fewer
parameters)
– better connected to the underlying scaling
physics exemplified in Kolmogorov approach to
turbulence
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Nowadays we routinely model statistical
clouds using empirical information
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Scaling
analysis for
Landsat cloud
radiances
revealed a
scale break at
~0.5 km...
not seen in
cloud optical
depth.
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3D radiative smoothing has three regimes
Analysis of
the Landsat
scale break
led to the
basic ideas
underlying
multiple
scattering
lidar
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Another way to specify a cloud is to use a
“cloud-resolving model”
Dynamical and dynamical/microphysical cloud models
were mainly for thunderstorms.
Models for more horizontally extensive cloud forms
remained primitive through the 1980s, but have
matured since then and are now routinely used to
provide input to 3D radiative transfer models.
Most 3D radiation modelers use both fractal and
cloud-resolving models for specifying clouds,
according to the situation.
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Ron Welch, Bill Hall and I pioneered
radiation-cloud physics collaboration
Hall/Clark model:
- 2D thunderstorm!
- explicit drop size
categories
We horizontally
averaged Hall’s
results to use in
a 1D radiation
model — ugh...
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I3RC (Intercomparison of 3D Radiation Codes)
uses cloud-resolving model input for some cases
http://i3rc.gsfc.nasa.gov/
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What simple ways have been put forward
to deal with or account for 3D variability
in climate models?
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1D error has two very different natures
depending on pixel size
Independent Column
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Plane-Parallel
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Cubic clouds gave an
extreme view of the
perils of ignoring 3D
cloudy cubes
have optical
depth 50
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The simplest and oldest method for
dealing with 3D is “cloud fraction”
Cloud fraction (“oktas”)
has sentimental and
historical value in
meteorology.
Cloud fraction Ac is
used as a linear weight:
(1D)
(1D)
I  Ac I cloudy
 (1 Ac ) I clear
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So what’s wrong with cloud fraction?
Stephens (1988), showed that
Ac (radiative)  Ac (true)
(equality only when no correlations between
fluctuations in the radiation and cloud fields)
This inequality makes it impossible to test
retrievals of Ac(radiative) against an
alternative, non-radiative definition. (done still)
Sometimes Ac(radiative) < 0 to get the
radiation right!
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The next
band-aid
beyond cloud
fraction was
cloud overlap
random,
maximum,
and maxrandom were
all tried...but
none seem to
work well
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The first decent 1D approximation to 3D was the
Independent Column Approximation (ICA)
Requires the probability
distribution of optical depth
pdf(t)
in the cloudy part of the
scene, instead of just the
mean optical depth.
Since the low-t part of
pdf(t) is very hard to get, in
practice we still fall back on
cloud fraction...
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Application to Global Climate Models
100-500 km
Approximations to
incorporate 3D effects into a
1D framework:
-Cahalan,
-Barker/Oreopoulis,
-Cairns,
-Pincus/Barker.
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Serious limitation of slab model is
partitioning of space into two disjoint halfspaces, one containing Sun, other the Earth
so from any point, can view reflected or transmitted light, not both
Davis has
proposed a
spherical cloud
model more in
accord with
everyday
experience
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Davis uses illuminated and shaded sides of
each cloud to retrieve “optical diameter”
t eff
2  Robs

1  g Tobs
generalization of familiar 2-stream
theory with redefintion of R, T, t
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How do 3D effects impact typical 1D
retrievals of cloud properties?
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1D retrieval of cloud optical depth at
increasingly oblique angles shows 3D effect
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Remote retrieval of
cloud optical depth t
using 1D algorithms
incurs considerable
bias
Each dot
corresponds to a
50x50 km area
with t averaged
separately over
all illuminated vs
all shaded pixels
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Cahalan inhomogeneity parameter  is rough
measure of 3D bias in optical depth

exp(ln t )
t
where t is cloud
optical depth
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What instruments do we currently use to
probe and characterize clouds?
Major categories are passive & active (probes)
We must extrapolate 1D or 2D data into 4D:
– ground-based probes: t-z
– aircraft-based probes: mix of t–z and x–z
– space-based probes: x-z
– all are dimensionally challenged!
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Current aircraft cloud sampling probes
PMS FSSP-100 (Forward
Scattering Spectrometer Probe)
Rosemount total
temperature probe
PMS 2D-P
optical array probe
King liquid water probe
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Aircraft cloud probes sample cm3 volumes
Remote sensing instruments sample much bigger
volumes:
– > m3 for radars
– approaching km3 for satellites
Other problems:
– aircraft fly horizontally ; cloud radars point vertically
– clouds evolve while aircraft fly through them
To match aircraft scale with radar and/or satellite
scale (both time and space!), aircraft would need to
perform “long-range scans”!
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ARM Oklahoma:
A “Field of Beams”
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ARM let theoreticians do things like...
help lead field programs (“IOPs”)
suggest new instruments
and take observations!
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Lidar can detect cloud base but usually not
cloud top (except for cirrus)
Micropulse lidar (Spinhirne) inside
trailer at ARM Oklahoma site
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We prefer to remote-sense in the microwave spectrum
because clouds are relatively transparent there...
and also
because
(a) gases do
not dominate
absorption;
(b) scattering,
except by ice,
is relatively
negligible.
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Passive microwave radiometers can retrieve
cloud liquid water path directly
Microwaves satisfy a simple radiative transfer
equation with only thermal emission, but:
– ice is invisible
– clouds of low optical depth are invisible
– rte-based retrieval has been less successful than empirical
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mm radar can see through most clouds but
is confused by drizzle and insects
MilliMeter Cloud Radar at
ARM Oklahoma site (35
GHz ~ 1 cm wavelength)
2D time-height slice but not whole 4-D cloud field
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In sum, active cloud-probing instruments
struggle to characterize a single 4-D cloud
Lidars and radars are “dimensionally challenged”
Lidars can’t see deeply into a cloud
Space lidar beams are ~100 m wide at cloud level;
creates multiple scattering artifacts
Passive microwaves can’t see ice or thin clouds
Cloud radars are sensitive to drizzle, insects, ...
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Only by combining different kinds of instruments can we hope to characterize clouds
Whole Sky Imager
IR thermometer atop
microwave radiometer
Experimental Nephelo;
rotates to scan sky
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Some new instruments and methods
to capitalize on advances in 3D
radiative transfer understanding
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Now: Two-channel 3D cloud optical depth
retrieval uses these two instruments
Cimel (French); designed for aerosol
but now has added a “cloud mode”;
over 100 deployed in global network
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Two-channel NFOV
(Narrow Field of View)
62
Now: THOR lidar shoots lidar straight down then
measures time-resolved scattered photons in
bulls-eye rings around central spot
THOR retrieves
geometric thickness
of op. thick clouds
THOR was based on advances in Green’s function
theory and radiative smoothing in 3D clouds
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Now: IceSat lidar getting Equator to pole cloud
topography & some internal structure
(and apparently IceSat is showing cloud fraction ~ 70%
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European 4-D Clouds Project: 2–mm cloud
radar and 22–channel microwave radiometer
can scan clouds fast, simultaneously
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Future: Understand EOS 1D cloud
property retrievals from a 3D perspective
1D cloud
optical depth
from two
solar
channels
(MODIS)
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Future: In situ lidar
senses extinction in
expanding spheres
around aircraft
One of new class of
instruments designed
using extensive Monte
Carlo simulations
curve steepens
when light bubble
hits edge of cloud
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Future: CloudSat radar will see cloud
drops (not just rain drops like TRMM)
with complementary
measurements from
other cars on “the
A-train”:
- CALIPSO: lidar
- PARASOL: polarized
radiances (French)
- Aqua, Aura: last great
multi-instrument Eos
platforms
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Future: Cloud tomography was pioneered
by cloud physicist Warner in the 1980s
69
Warner’s 1986 tomography from two surface
microwave radiometers
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In summary, 3D cloud radiative transfer exploded
in the 1990s and has many applications
Publicly available 3D models like SHDOM and Pincus or Mayer
Monte Carlo build on a solid foundation of 1D models like
DISORT, SBDART, CHARTS, etc.
Can simulate realistic cloud structures using fractals, wavelets,
and statistical methods from turbulence
Quantum leaps in dynamical/microphysical cloud models
A new breed of cloud experiments: SUCCESS, SHEBA, ARM,
4D Clouds,...
New instrumental concepts exploiting the time dimension and
multiple scattering (Davis WAIL, Cahalan THOR lidars)
Instruments and measurement strategies for field campaigns
simulated in advance with 3D radiation models
Discussion time!
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