remote sensing
Article
Aerosol Retrievals from CALIPSO Lidar Ocean
Surface Returns
Srikanth L. Venkata and John A. Reagan *
Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ 85721, USA;
[email protected]
* Correspondence: [email protected]; Tel.: +1-520-343-1105
Academic Editors: Raphael M. Kudela, Xiaofeng Li and Prasad S. Thenkabail
Received: 3 August 2016; Accepted: 28 November 2016; Published: 9 December 2016
Abstract: This paper describes approaches to retrieve important aerosol results from the strong lidar
return signals that are received by the space-borne CALIPSO lidar system after reflecting off-ocean
surfaces. Relations, from which the theoretically expected values of area under ocean surface returns
can be computed, are presented. A detailed description of the lidar system response to the ocean
surface returns and the processes of sampling and averaging of lidar return signals are provided.
An effective technique that reconstructs the lidar response to surface returns—starting from
down-linked samples—and calculates the area under it, has been developed and described.
The calculated area values are validated after comparing them to their theoretically predicted
counterpart values. Methods to retrieve aerosol optical depths (AODs) from these calculated areas
are described and retrieval results are presented, including retrieval comparison with independent
AOD measurements made by an airborne High Spectral Resolution Lidar (HSRL) that yielded quite
good agreement. Techniques and results are also presented on using the spectral ratios of the surface
response areas to determine spectral ratios of aerosol round-trip transmission and AOD spectral
difference, without need of a specific/accurate ocean-surface reflectance model.
Keywords: lidar; CALIPSO; ocean surface reflectance; aerosol transmittance; aerosol optical depth
1. Introduction
LIght Detection And Ranging (lidar) is an optical remote sensing technology which is very often
used in the study of atmospheric aerosols. Similar in concept to radar, lidar emits highly coherent,
ultra-short laser pulses at wavelengths which are comparable to the dimensions of atmospheric aerosol
particles. This permits lidar pulses to physically interact fairly strongly with aerosols such as dust,
pollen, smoke, etc. The inability of in situ instruments to make aerosol measurements on a global scale
and the high variability of both spatial and temporal distributions of tropospheric aerosols drive the
necessity for space-borne observations.
Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) is a satellite lidar
system that was launched by NASA on 28 April 2006 to improve our knowledge and understanding of
the roles played by cloud and aerosol particles on Earth’s climate change. Being the first space-borne
lidar dedicated to the study of aerosols, CALIPSO can make observations and measurements on
a global scale that help provide insight into the factors that regulate Earth’s radiation budget.
The principal goals of the CALIPSO mission are to provide global, vertically resolved aerosol
microphysical properties and spatial distributions, perform height-resolved discrimination of aerosols
into several types, to provide vertical layers of single and multi-layer transmissive clouds and to
determine vertical distributions of cloud ice and water [1–3].
Laser pulses transmitted from the lidar system into the atmosphere are reflected back to the
system as a result of back-scattering by various particles present in the propagation path of the
Remote Sens. 2016, 8, 1006; doi:10.3390/rs8121006
www.mdpi.com/journal/remotesensing
Remote Sens. 2016, 8, 1006
Remote Sens. 2016, 8, 1006
2 of 27
2 of 27
pulse.
Backscatter
hard targets
targetssuch
suchasasland
landand
andocean
ocean
surfaces
pulse.
Backscatterofofthe
thelaser
laserpulses
pulsesalso
also occurs
occurs from
from hard
surfaces
which
result
in
what
are
referred
to
as
“surface
returns.”
Surface
returns
are
expected
to
be
much
which result in what are referred to as “surface returns.” Surface returns are expected to be much
stronger
than
thethe
atmospheric
returns
and
carry
in in
them
qualitative
and
quantitative
stronger
than
atmospheric
returns
and
carry
them
qualitative
and
quantitativefactors
factorsabout
aboutthe
material
medium
presentpresent
in the atmosphere
throughthrough
which the
transmitted
lidar pulses
travelled.
the material
medium
in the atmosphere
which
the transmitted
lidar have
pulses
have
This
paper
includes
an
in-depth
analysis
of
surface
returns
from
ocean
surfaces
and
presents
ways
travelled. This paper includes an in-depth analysis of surface returns from ocean surfaces and
to retrieve
optical
these
returns.
It is returns.
a summary,
somewith
revisions
and additions,
presents ways
to depths
retrieve from
optical
depths
from these
It is a with
summary,
some revisions
and
additions,
of the workby
completed
by the first
author
his M.S.
of the
work completed
the first author
for his
M.S.for
thesis
[4]. thesis [4].
2. Materials
and
Methods
2. Materials
and
Methods
2.1.2.1.
Low-Pass
Filter
Low-Pass
Filter
The
lidar
system
on board
CALIPSO
is calledisCloud-Aerosol
LIdar with
Orthogonal
Polarization
The
lidar
system
on board
CALIPSO
called Cloud-Aerosol
LIdar
with Orthogonal
(CALIOP).
CALIOP
employs
a third-order
Bessel
filter Bessel
with afilter
bandwidth
~2.44 MHz,
Polarization
(CALIOP).
CALIOP
employs alow-pass
third-order
low-pass
with a bandwidth
as ~2.44
a partMHz,
of its as
post-detection
electronics following
thefollowing
PMT detector
for the
532 nm
[5–7].
a part of its post-detection
electronics
the PMT
detector
for channel
the 532 nm
channel
[5–7]. Similarelectronics,
post-detection
electronics,
the same
low-pass
filter,
the photodiode
avalanche
Similar
post-detection
with
the samewith
low-pass
filter,
follows
the follows
avalanche
photodiode
the 1064
nmimportant
channel. feature
A very ofimportant
of filter
this Bessel
(APD)
detector (APD)
for the detector
1064 nm for
channel.
A very
this Besselfeature
low-pass
(LPF) is
low-pass
filterreturn
(LPF)signal
is that(as
foroccurs
a pulse
return
signal (asreflection)
occurs from
a hard-target
reflection)
that
for a pulse
from
a hard-target
it preserves
the area
under itthe
preserves
the
area under
theenters
pulse.this
Thus,
if aitsnarrow
pulse enters
this filter,
itsthe
peak
amplitude
is
pulse.
Thus, if
a narrow
pulse
filter,
peak amplitude
is reduced
but
pulse
is stretched
reduced
but
the
pulse
is
stretched
in
time
so
as
to
preserve
the
area
under
the
original
narrow
pulse.
in time so as to preserve the area under the original narrow pulse. This enables accurate capture of the
This
enables
accurate
capture
of theathard
target
ocean
surfacerate
response
the 10 MHz
digitation
rate
hard
target
ocean
surface
response
the 10
MHz
digitation
of theatdigitizers
following
the
LPF.
digitizers
followingtime
the input
LPF. For
a Dirac
function timeintegral
input toof
the
LPF,
thefunction
convolution
Forofa the
Dirac
delta function
to the
LPF,delta
the convolution
the
delta
input
integral of
the the
delta
function
input convolved
with
the LPFyields
output-to-input
transfer
function
yields
convolved
with
LPF
output-to-input
transfer
function
the transient
output
known
as the
the
transient
output
known
as
the
Impulse
Response
Function
(IRF).
If
the
input
is
not
a
Impulse Response Function (IRF). If the input is not a delta function, but a short pulse compareddelta
to the
function, but a short pulse compared to the IRF response time, as is the case for the short-duration
IRF response time, as is the case for the short-duration transmitted lidar pulse (~20 ns), the convolution
transmitted lidar pulse (~20 ns), the convolution with the LPF transfer function still yields the ideal
with the LPF transfer function still yields the ideal IRF to a very close approximation (simulations
IRF to a very close approximation (simulations showed that the impulse response of the LPF for an
showed that the impulse response of the LPF for an input pulse of duration of the transmitted lidar
input pulse of duration of the transmitted lidar pulse yielded a response within ~0.1% of the ideal
pulse yielded a response within ~0.1% of the ideal IRF). As with any linear time-invariant (LTI) system,
IRF). As with any linear time-invariant (LTI) system, the third-order Bessel filter can be completely
the third-order Bessel filter can be completely characterized by its IRF.
characterized by its IRF.
Impulse
response measurements were made on flight hardware replicas of the CALIOP detector
Impulse response measurements were made on flight hardware replicas of the CALIOP
anddetector
post-detection
electronics electronics
where the detector
was
exposed
optical pulses
of about
duration
and post-detection
where the
detector
wastoexposed
to optical
pulses20
ofns
about
20
to mimic
the
laser
pulse
transmitted
by
CALIOP
[5].
The
measured
impulse
response,
averaged
over
ns duration to mimic the laser pulse transmitted by CALIOP [5]. The measured impulse response,
many
measurements,
to unity area
is shown
in area
Figure
1 [5]. The
circles 1are
digitized
samples
averaged
over manyscaled
measurements,
scaled
to unity
is shown
in Figure
[5].the
The
circles are
the
(at digitized
the 10 MHz
sample
thesample
solid line
is an
analytical
a hyperbolic
samples
(at rate),
the 10and
MHz
rate),
and
the solidbest-fit
line is using
an analytical
best-fittangent
using afor
thehyperbolic
rising parttangent
of the pulse
a Gaussian
curve
the
falling part
[5]. for the falling part [5].
for theand
rising
part of the
pulsefor
and
a Gaussian
curve
Figure
Theimpulse
impulseresponse
responseas
asdetermined
determined by
by lab
Figure
1. 1.
The
lab measurements
measurementsscaled
scaledtotounity
unityarea.
area.
As the transfer functions of Bessel filters are very well characterized, using the control system
As the transfer functions of Bessel filters are very well characterized, using the control system
tool-box of MATLAB, the ideal impulse response shape was generated (assuming the ~2.44 MHz
tool-box of MATLAB, the ideal impulse response shape was generated (assuming the ~2.44 MHz
Remote Sens. 2016, 8, 1006
3 of 27
Remote Sens. 2016, 8, 1006
3 of 27
bandwidth
exhibited
by the
response).
To compare
the two
responses
(lab measured
bandwidth
exhibited
bymeasured
the measured
response).
To compare
theimpulse
two impulse
responses
(lab
measured and
MATLABthey
generated),
they to
arehave
scaled
to same
have the
same
area (unity)
and
are plotted
in
and MATLAB
generated),
are scaled
the
area
(unity)
and are
plotted
in Figure
2.
Figure
2.
It
can
be
concluded
that,
within
a
very
close
approximation,
the
impulse
response
of
the
It can be concluded that, within a very close approximation, the impulse response of the CALIOP
CALIOP
receiver
electronics
does indeed
replicate the
IRF for Bessel
a third-order
Bessel
receiver
electronics
does
indeed replicate
the theoretical
IRFtheoretical
for a third-order
low-pass
transfer
low-pass
transfer
function
(and
the
areas
found
using
either
impulse
response
curve
to
obtain
areas
function (and the areas found using either impulse response curve to obtain areas under CALIPSO
under CALIPSO ocean surface returns were found to be the same within ~1%). For the work
ocean surface returns were found to be the same within ~1%). For the work reported in this paper,
reported in this paper, the impulse response is assumed to be the fit made to the lab measurements
the impulse response is assumed to be the fit made to the lab measurements (solid curve in Figure 1).
(solid curve in Figure 1). It should be noted that should subsequent investigations determine a
It should
be noted
that
shouldmodel
subsequent
determine
a somewhat
more accurate
model
somewhat
more
accurate
for the investigations
impulse response,
the difference
in determining
the area
for the
impulse
response,
difference
in determining
themodel
area under
the lidar
surface
response (SR)
under
the lidar
surfacethe
response
(SR) with
the improved
would only
be a small,
fractionally
with the
improved
model
would
only be a small, fractionally fixed bias that could easily be corrected.
fixed
bias that could
easily
be corrected.
5
Impulse Response from Lab Measurements
Ideal Impulse Response for a 3rd order Bessel Filter
4.5
4
Amplitude
3.5
3
2.5
2
1.5
1
0.5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Time
Figure
2. Comparing
the
twoimpulse
impulse responses.
responses. Time
in μsec
units.
Figure
2. Comparing
the
two
Timeisismeasured
measured
in µsec
units.
2.2. Area under Surface Return Pulse
2.2. Area under Surface Return Pulse
The lidar equation for the instantaneous return signal from a distributed source such as the
The
lidar equation
for the as
instantaneous
return signal from a distributed source such as the
atmosphere
can be expressed
[8]
atmosphere can be expressed as [8]
V (z) =
CE β (z)T (z)
,
z
2
(1)
CEo βλ (z)Tλ (z)
,
(1)
Vλsignal
(z) =from range
where Vλ represents the lidar return
z2z expressed as a voltage level, z is the range
from the lidar increasing downward towards the Earth’s surface, Eo represents the transmitted pulse
whereenergy,
Vλ represents
the lidar
return signal
from at
range
z expressed
as a voltage
level,
z −1is, the
β represents
the backscatter
coefficient
wavelength
λ expressed
in units of
m−1·sr
T (z)range
from is
the
increasing
downward
the Earth’s
surface,
Eozrepresents
the λ
transmitted
thelidar
atmospheric
round-trip
pathtowards
transmittance
to and from
range
at wavelength
and C is thepulse
calibration
constant.
signalscoefficient
from the atmosphere
are mostly
slowly varying
energy,
βλ represents
theReturn
backscatter
at wavelength
λ expressed
in unitsand
of have
m−1 ·longer
sr−1 , T2λ (z)
durations
than
the
impulse
response
of
the
LPF.
Hence
the
LPF
has
little
effect
on
the
atmospheric
is the atmospheric round-trip path transmittance to and from range z at wavelength λ and C is the
returnsconstant.
and the output
the LPFfrom
can the
be well
approximated
by Equation
However,
lidar
calibration
Returnofsignals
atmosphere
are mostly
slowly(1).
varying
andthe
have
longer
response to surface returns Vλs, before entering the LPF, is a pulse which is a replica of the originally
durations than the impulse response of the LPF. Hence the LPF has little effect on the atmospheric
transmitted Gaussian-shaped lidar pulse of duration tp (tp ≈ 20 ns). As this pulse is much narrower
returns and the output of the LPF can be well approximated by Equation (1). However, the lidar
than the impulse response of the LPF, the output of the filter can be assumed to be the ideal impulse
response to surface returns Vλs , before entering the LPF, is a pulse which is a replica of the originally
response IRF of the filter itself. Hence, the time integrated output of the LPF “VλS LPF” for the surface
transmitted
Gaussian-shaped
lidar
return response
“Vλs” is given
by pulse of duration tp (tp ≈ 20 ns). As this pulse is much narrower
than the impulse response of the LPF, the output of the filter can be assumed to be the ideal impulse
response IRF of the filter itself. Hence, the time integrated output of the LPF “VλS LPF ” for the surface
(2)
V dt =
V (t)dt ,
return response “Vλs ” is given by
0
where tp’ is the duration of the output
impulse response duration). Defining “zs” to be
p
wtp of the LPFwt(the
range to the surface, from Equations (1)
and
(2)
we
have
VλS dt = VλS LPF (t)dt ,
0
(2)
0
where tp ’ is the duration of the output of the LPF (the impulse response duration). Defining “zs ” to be
range to the surface, from Equations (1) and (2) we have
Remote Sens. 2016, 8, 1006
4 of 27
wtp
0
tp0
C E0 T2 (zs ) w
VλS dt = λ 2
β(t)dt,
zS
Taking the round-trip propagation time t into account, dt can be written as
wtp
0
(3)
0
z0
2E0 T2 (zs )Cλ w
VλS dt =
β(z)dz,
cz2S
2dz
c
so that
(4)
0
R z0
For a hard target we replace 0 β(z)dz with Rλ , the retro or backscatter reflectance (sr−1 ) of
the surface. Hence, the expected surface return area, ALPF , after being normalized by the calibration
constant, peak energy and range squared (just as the lidar equation, Equation (1), is normalized for the
CALIPSO level 1 data product) is given by
ALPF =
2T2 (zs )Rλ
,
c
(5)
The area under the surface-return response pulse thus depends on the product of the surface
reflectance and total round-trip transmission. In other words, the response of the lidar receiver
to ocean-surface return signals is a scaled version of the impulse response shown in Figure 1,
and the magnitude of the scaling depends on the amount of atmospheric attenuation and the reflectance
value of the ocean surface. With the normalizations, ALPF does not actually have the units of area,
but will be referred to as an area in subsequent discussions. Also, c must be evaluated in units
of km/µsec (c = 0.3 km/µsec) in Equation (5) to yield ALPF values consistent with the CALIPSO
data product sample values of the surface response signals, and the ALPF inferred from the samples,
per/characterized by the similarly normalized lidar equation.
2.3. Ocean Surface Reflectance
Considerable effort ([9–12], to name a few) has been directed over the years to develop a model
that can relate the surface reflectance to the surface wind speed (WS) and wave facet characteristics
and accurately determine it. The ocean-surface reflectance model used in this paper was developed
in [13]. This model is a revised and updated version of the model developed by Cox and Munk [9]
and is presented below. In general, the ocean-surface backscatter reflectance, Rλ , units of sr−1 , can be
modeled by
Rλ = (1 − W) × Retro_Fresnel_Reflectance + W × 0.2 ,
(6)
where “W” represents the fraction of the surface covered with whitecaps and “Retro_Fresnel_Reflectance”
is the Fresnel reflectance of the ocean-surface at nadir (e.g., [14]). They are given by
Whitecap Fraction = 2.95 × 10−6 × WindSpeed3.37 ,
(7)
Fresnel Coeficient
,
4πhwave_slopei2
(8)
Retro_Fresnel_Reflectance =
Here, as the name suggests, “WindSpeed” refers to surface wind speed (WS). The Fresnel Coefficient
($) is spectrally dependent and at 532 nm and 1064 nm has estimated values of $532 = 0.0205 and
$1064 = 0.019 and hwave_slopei2 represents the variance of the distribution of wave slopes and is
given by
hwave_slopei2 = −0.006 + 7.95 × 10−3 × WindSpeed,
(9)
Thus, with known surface wind speeds (WS), the terms in Equations (7)–(9) can be calculated
and the final reflectance can be determined using Equation (6). Figure 3 shows the variation of the
ocean-surface reflectance at 532 nm wavelength, R532 , with surface wind speed (WS). As the reflectance
Remote Sens. 2016, 8, 1006
5 of 27
Sens. at
2016,
8, 1006
5 ofdata
27
rises Remote
sharply
low
wind speeds (WS < ~3 m/s), use of the reflectance model/input WS
in
estimating ALPF must be limited to higher WS, but also be cut off at too high a wind speed where the
data in estimating ALPF must be limited to higher WS, but also be cut off at too high a wind speed
reflectance model becomes less accurate (to be on the conservative side, analysis of CALIPSO data to
where the reflectance model becomes less accurate (to be on the conservative side, analysis of
retrieve
ALPF presented
here Ahas
been limited to WS between ~4 m/s to ~8 m/s).
CALIPSO
data to retrieve
LPF presented here has been limited to WS between ~4 m/s to ~8 m/s).
0.9
Ocean Surface Retro-Reflectance
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
9
Surface Wind Speed
Figure 3. Ocean Surface Reflectance (sr−1) at 532 nm vs. Wind Speed (m/s).
Figure 3. Ocean Surface Reflectance (sr−1 ) at 532 nm vs. Wind Speed (m/s).
2.4. Signal Acquisition and Post-Filtering Processing
2.4. Signal Acquisition and Post-Filtering Processing
The lidar response, generated after photon detection of the received signal and post-detection
The
lidar response,
generated
after photon
of the filtered.
receivedThe
signal
and post-detection
amplification,
is sampled
and digitized
after detection
being low-pass
generated
samples
amplification,
sampled and
digitized afteraveraging
being low-pass
The generated
samples
undergo aiswavelength
channel-specific
schemefiltered.
before being
down-linked
from undergo
the
satellite [6].
Thus, down-linked
samples
corresponding
to ocean
surface returns
are satellite
the result
a wavelength
channel-specific
averaging
scheme
before being
down-linked
from the
[6].ofThus,
samplingsamples
and averaging
a scaled version
of the
LPF’sreturns
impulseare
response.
down-linked
corresponding
to ocean
surface
the result of sampling and averaging
a scaled version of the LPF’s impulse response.
2.4.1. Sampling and Generation of Down-Linked Samples
2.4.1. Sampling
and Generation
of of
Down-Linked
Samples
The fundamental
sampling
the filter output
for both wavelength channels occurs at 10 MHz
frequency (consecutive samples hence separated by 0.1 μsec), insuring that samples meet the
The
fundamental sampling of the filter output for both wavelength channels occurs at 10 MHz
sampling theorem requirement for reconstructing the sampled signal (bandwidth of the LPF is ~2.5
frequency (consecutive samples hence separated by 0.1 µsec), insuring that samples meet the sampling
MHz). Sampling at this frequency essentially means that the vertical decimation of the atmosphere is
theorem requirement for reconstructing the sampled signal (bandwidth of the LPF is ~2.5 MHz).
performed in such a manner that the return signal is collected every 15 m along the transmission
Sampling
this
frequency
essentially
meansthe
that
the vertical
ofand
thethe
atmosphere
is
path ofatthe
lidar
pulse. Figure
4 below shows
impulse
responsedecimation
(in solid blue)
primary
performed
in
such
a
manner
that
the
return
signal
is
collected
every
15
m
along
the
transmission
samples (shown in black) separated by 0.1 μsec. For the 532 nm channel, every down-linked sample
path is
ofgenerated
the lidar by
pulse.
Figure
4 belowprimary
shows samples
the impulse
response them
(in solid
blue)
andand
thetheir
primary
pairing
consecutive
and averaging
in both
value
samples
by 0.1 µsec.
Forfor
thethe
532down-linked
nm channel,
every The
down-linked
sample
time(shown
instantsin
toblack)
obtainseparated
the corresponding
values
sample.
down-linked
is generated
by shown
pairinginconsecutive
samples
and averaging
themdown-linked
in both value
and their
samples are
red in Figure primary
4 and it can
be observed
that consecutive
samples
separated
by 0.2 μsec,
which means thatvalues
the effective
vertical
range resolution
is reduced
to 30 m
time are
instants
to obtain
the corresponding
for the
down-linked
sample.
The down-linked
for
the
532
nm
channel.
samples are shown in red in Figure 4 and it can be observed that consecutive down-linked samples are
1064 which
nm channel,
samples
are obtained
after averaging
consecutive
separatedFor
by the
0.2 µsec,
meansdown-linked
that the effective
vertical
range resolution
is reduced
to 30 m for
primary
samples
in
groups
of
four.
Figure
5
describes
this
process
by
showing
the
original
impulse
the 532 nm channel.
response, its primary samples and the final down-linked samples. Since the 1064 nm channel
For
the 1064 nm channel, down-linked samples are obtained after averaging consecutive primary
requires twice the number of primary samples to be averaged to generate the down-linked sample
samples in groups of four. Figure 5 describes this process by showing the original impulse response,
when compared to the 532 nm channel, the total number of down-linked samples for the 1064 nm
its primary samples and the final down-linked samples. Since the 1064 nm channel requires twice the
channel is half that of the 532 nm channel. However, the CALIPSO data product, from where the
number
of primary
samples
to bechannels
averaged
generateduplicates
the down-linked
sample when
compared
to
down-linked
samples
for both
aretoretrieved,
every down-linked
sample
of the
the 532
nmnm
channel,
number
of down-linked
samples
for theto1064
is half of
that of
1064
channelthe
andtotal
stores
it beside
the original sample
in order
storenm
thechannel
same number
the 532
nm
channel.
However,
the
CALIPSO
data
product,
from
where
the
down-linked
samples
down-linked samples for both the 1064 nm and 532 nm channels. Hence, while the 1064 nm for
both channel-duplicated
channels are retrieved,
duplicates
everyindown-linked
sample
ofinthe
channel filtering
and stores it
samples
are separated
time by 0.2 μsec
just as
the1064
532 nm
nm channel,
beside the original sample in order to store the same number of down-linked samples for both the
1064 nm and 532 nm channels. Hence, while the 1064 nm channel-duplicated samples are separated in
Remote Sens. 2016, 8, 1006
6 of 27
Remote Sens. 2016, 8, 1006
6 of 27
time by
just assamples
in the 532
nmbehind
channel,
filtering
out the
duplicated
out0.2
theµsec
duplicated
leaves
only
the original
samples
(shownsamples
in red inleaves
Figurebehind
5) that only
the original
samples
(shown
in
red
in
Figure
5)
that
are
separated
by
0.4
µsec
which
corresponds
are separated by 0.4 μsec which corresponds to an effective vertical range resolution of 60 m. All to an
effective
vertical
resolution
of 60was
m. done
All analysis
theoriginal
1064 nm
channel
wasout
done
analysis
of therange
1064 nm
channel data
with onlyofthe
samples
afterdata
filtering
the with
duplicate
samples.
only the
original
samples after filtering out the duplicate samples.
5
Impulse Response
Original Samples
Downlinked Samples
4.5
4
Amplitude
3.5
3
2.5
2
1.5
1
0.5
0
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time in usec
Figure
4. Process
generatingdown-linked
down-linked samples
thethe
532532
nmnm
channel.
Figure
4. Process
ofof
generating
samplesforfor
channel.
5
Impulse Response
Original Samples
Downlinked Samples
4.5
4
Amplitude
3.5
3
2.5
2
1.5
1
0.5
0
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time in usec
Figure
5. Process
ofof
generating
samplesfor
for
the
1064
channel.
Figure
5. Process
generatingdown-linked
down-linked samples
the
1064
nmnm
channel.
Effect
of Sampling
Delay
Down-Linked Samples
Samples
2.4.2.2.4.2.
Effect
of Sampling
Delay
onon
Down-Linked
As the primary samples are uniformly spaced with 0.1 μsec separation, the time instant of the
As the primary samples are uniformly spaced with 0.1 µsec separation, the time instant of the
first sample of the impulse response determines the time instances and hence the magnitudes of the
first sample of the impulse response determines the time instances and hence the magnitudes of
remaining samples that follow. On board CALIOP, the starting sampling instant is variable (e.g., due
the remaining
that follow.
board
CALIOP,
the starting
sampling
is variable
to digitizer samples
jitter, difference
in ocean On
surface
elevation
at different
locations/sea
states,instant
and imperfect
(e.g., pointing,
due to digitizer
jitter,
difference
in ocean
surface
elevation
at different
locations/sea
states,
position and
orbit
propagation
knowledge
on board
the satellite)
[7]. Thus,
different lidar
and imperfect
pointing,
position
and
orbit propagation
knowledge
on samples
board the
satellite) [7].toThus,
shots can have
different
starting
sampling
instances and
hence surface
corresponding
different
lidarshot
shots
can “delayed”
have different
starting
instances inand
hence surface
samples
one lidar
maybe
and, thus,
may sampling
differ in magnitudes
comparison
to samples
obtained
from
another
lidar
shot.
This
process
is
depicted
at
532
nm
in
Figure
6.
Similarly,
Figure
7
corresponding to one lidar shot maybe “delayed” and, thus, may differ in magnitudes in comparison
shows
the
influence
of
sampling
delay
on
the
magnitude
of
the
down-linked
samples
for
the
1064
to samples obtained from another lidar shot. This process is depicted at 532 nm in Figure 6. Similarly,
nm
Figure
7 channel.
shows the influence of sampling delay on the magnitude of the down-linked samples for the
1064 nm channel.
results are shown in Figure 8. For the 532 nm channel, the remaining two samples are 0.2 μsec and 0.4
μsec away from the first sample. For the 1064 nm channel, the second sample is 0.4 μsec away from the
first sample. Hence, for every lidar shot, time instances may be assigned to all the surface return
samples at both wavelengths. It should be noted that, regardless of the time delay, the sum of the
down-linked samples (sum value) that make up a given SR pulse is very nearly constant (within ~2%),
Remote Sens. 2016, 8, 1006
7 of 27
for no noise present, and, as discussed later, can be used as a quality check to reject bad shots.
Sampling Delay = 0 usec
5
Impulse Response
Original Samples
Downlinked Samples
4.5
4
Amplitude
3.5
3
2.5
2
1.5
1
0.5
0
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time in usec
Sampling Delay = 0.05 usec
5
4
3
2
1
0
-0.5
Impulse Response
Original Samples
Downlinked Samples
4
Amplitude
Amplitude
Sampling Delay = 0.1 usec
5
Impulse Response
Original Samples
Downlinked Samples
3
2
1
0
0.5
1
0
-0.4
-0.2
Time in usec
0.4
0.6
0.8
1
Sampling Delay = 0.2 usec
Sampling Delay = 0.15 usec
5
Impulse Response
Original Samples
Downlinked Samples
4
3
2
Impulse Response
Original Samples
Downlinked Samples
4
Amplitude
Amplitude
0.2
Time in usec
5
3
2
1
1
0
-0.5
0
0
0.5
Time in usec
1
0
-0.5
0
0.5
Time in usec
1
Figure
6.6.Effect
samplesfor
forthe
the532
532nm
nmchannel.
channel.
Figure
Effectofofsampling
samplingdelay
delay on
on the
the down-linked
down-linked samples
The effect of sampling delay on the magnitude of down-linked samples is quite evident where
it can be seen that the values of the down-linked samples change relative to one another with delay.
The delay must be taken into account in estimating the SR area for any given lidar shot. That is,
the impulse response model used to estimate the area must be positioned under the SR samples for
a given shot for the sampling delay of that shot. The delay can be estimated by the ratio of the first
to second samples for a given shot. Piecewise cubic hermite (shape preserving) interpolation was
performed at both wavelengths so that for every intermediate ratio, a sampling delay is assigned.
The interpolation results are shown in Figure 8. For the 532 nm channel, the remaining two samples
are 0.2 µsec and 0.4 µsec away from the first sample. For the 1064 nm channel, the second sample is
0.4 µsec away from the first sample. Hence, for every lidar shot, time instances may be assigned to
all the surface return samples at both wavelengths. It should be noted that, regardless of the time
delay, the sum of the down-linked samples (sum value) that make up a given SR pulse is very nearly
constant (within ~2%), for no noise present, and, as discussed later, can be used as a quality check to
reject bad shots.
Remote Sens. 2016, 8, 1006
8 of 27
Remote Sens. 2016, 8, 1006
Remote Sens. 2016, 8, 10065
5
Amplitude
3
Impulse Response
Original Samples
Downlinked Samples
4
2
8 of 27
Impulse Response
Original Samples
Downlinked Samples
Sampling Delay = 0 usec
4
Amplitude
8 of 27
Sampling Delay = 0 usec
3
1 2
0 1
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time in usec
0
-0.4
-0.2
0
Sampling Delay = 0.05 usec
0.2
0.4
Time in usec
5
0.6
0.8
1
Sampling Delay = 0.1 usec
5
Impulse Response
Impulse Response
Sampling Delay = 0.05
usecSamples
Original
3
2
2
1
Sampling Delay = 0.1 usec
Original Samples
54
Amplitude
Amplitude
Downlinked Samples
Impulse Response
Original Samples
Downlinked Samples
4
3
Amplitude
Amplitude
4 5
Downlinked Samples
Impulse Response
Original Samples
Downlinked Samples
4
3
3
2
2
1
1
0
-0.5
0
0.5
Time in usec
0
0.5
Time in usec
Sampling Delay = 0.15 usec
0
-0.5
1
1
0
-0.5
1
0
-0.5
5
5
Sampling Delay = 0.15Impulse
usec Response
5
3
2
2
1
1
Impulse Response
Sampling Delay = 0.2 usec
Original Samples
Impulse
Response
Downlinked
Samples
Original Samples
Downlinked Samples
4
4
3
Amplitude
Amplitude
Amplitude
Amplitude
4
3
0.5
Time in usec
0
0.5
Time in usec
Sampling Delay = 0.2 usec
5
Original Samples
Impulse Response
Downlinked
Samples
Original Samples
Downlinked Samples
4
0
3
2
2
1
1
1
1
0
-0.5
0
-0.5
0
0.5
0
Time
in usec 0.5
Time in usec
0
-0.5
1
1
0
0
-0.5
0
0.5
0.5
Time in usec
Time in usec
1
1
Figure 7. Effect of sampling delay on the down-linked samples for the 1064 nm channel.
Figure
on the
thedown-linked
down-linkedsamples
samplesfor
for
the
1064
channel.
Figure7.7.Effect
Effectof
ofsampling
sampling delay on
the
1064
nmnm
channel.
6
5
6
532 nm channel
532 nm channel
6
6
5
4 4
44
Ratio
Ratio Amplitude
Amplitude
5
Ratio Amplitude
Ratio Amplitude
5
3 3
2 2
1 1
0 00
0
1064 nm channel
1064 nm channel
33
22
11
0.05
0.05
0.1
0.15
0.1
0.15
SamplingDelay
Delay
Sampling
0.2
0.2
00
00
0.05
0.05
0.1
0.1
0.15
0.15
Sampling
Delay
Sampling
Delay
0.20.2
Figure
8.8.Interpolation
results. Sampling
Sampling delayisisplotted
plotted in µsec
units.
Figure8.
Interpolationresults.
results.
Figure
Interpolation
Sampling delay
delay is plottedininμsec
μsecunits.
units.
Remote Sens. 2016, 8, 1006
9 of 27
2.4.3.Remote
Down-Linked
Samples
Sens. 2016, 8, 1006
9 of 27
The principle data product that is down-linked from CALIPSO is the attenuated backscatter
2.4.3. Down-Linked Samples
(km−1 ·sr−1 ), which for a range “z” is defined as
The principle data product that is down-linked from CALIPSO is the attenuated backscatter
2
2
2
(km−1·sr−1), which
for a range
“z” is defined
Attenuated
Backscatter
= (βas
(10)
R (z) + βa (z)) × TR (z) × Ta (z) × TOzone ,
AttenuatedBackscatter = β (z) + β (z) × T (z) × T (z) × T
,
(10)
where βa and βR represent the aerosol and Rayleigh components of the backscatter coefficient and T2 a ,
where
βa andrepresent
βR represent
the aerosol
and Rayleigh
components
of the of
backscatter
coefficient
and
T2 R and
T2 Ozone
the aerosol,
Rayleigh
and ozone
components
the round-trip
transmission,
T2a, T2R and T2Ozone represent the aerosol, Rayleigh and ozone components of the round-trip
respectively. It should be noted that the attenuated backscatter data product has been normalized
transmission, respectively. It should be noted that the attenuated backscatter data product has been
to take out the lidar calibration for each wavelength, for the given lidar orbit position, as a part
normalized to take out the lidar calibration for each wavelength, for the given lidar orbit position, as
of CALIPSO standard data processing. For every lidar shot, the CALIPSO data product provides
a part of CALIPSO standard data processing. For every lidar shot, the CALIPSO data product
the attenuated
for 583 altitude
at both
SurfaceSurface
returns
can easily
provides thebackscatter
attenuated backscatter
for 583bins
altitude
binswavelengths.
at both wavelengths.
returns
can be
identified
(so
long
as
the
atmospheric
optical
depth
is
not
too
great
due
to
clouds
or
optically
easily be identified (so long as the atmospheric optical depth is not too great due to clouds or optically thick
aerosol
layers)
amongst
the 583
as they
are
stronger
than
atmospheric
thick
aerosolfrom
layers)
from amongst
the bins
583 bins
as they
aresignificantly
significantly stronger
than
thethe
atmospheric
returns.
The
ocean
surface
returns
were
observed
to
be
made
up
of
three
down-linked
returns. The ocean surface returns were observed to be made up of three down-linked samplessamples
for the for
the 532
and
two
down-linked
samples
the
nm channel,
and almost
they were
almost
532nm
nm channel,
channel, and
two
down-linked
samples
for thefor
1064
nm1064
channel,
and they were
always
found
to lieto
within
bins 561–565
the data in
product
for both
channels.
shows samples
for both
always
found
lie within
bins in
561–565
the data
product
forFigure
both 9channels.
Figure
9 shows
wavelength
corresponding
a typical surface
signal.
It should
besignal.
noted that
the be
samples
for bothchannels
wavelength
channelstocorresponding
to return
a typical
surface
return
It should
scales are not
the are
same
forthe
thesame
two for
channels
(scale
for 1064
nm is
twoisbin
notedhorizontal
that the horizontal
scales
not
the two
channels
(scale
fordouble,
1064 nm
double,
increments).
two bin increments).
0.45
Downlinked Surface Samples at 532 nm
0.45
0.4
0.4
0.35
0.35
0.3
0.3
Magnitude
Magnitude
0.5
0.25
0.2
Downlinked Surface Samples at 1064 nm
0.25
0.2
0.15
0.15
0.1
0.1
0.05
0.05
0
561
562
563
564
565
0
559
566
561
563
565
567
569
Altitude Bin Number
Altitude Bin Number
Figure 9. Typical surface return samples at 532 nm and 1064 nm found in the CALIPSO data product.
Figure 9. Typical surface return samples at 532 nm and 1064 nm found in the CALIPSO data product.
A useful parameter to assess the amount of aerosol loading in the atmosphere is the integral of
A
parameter
to assess
amount
of aerosol
in attenuated
the atmosphere
is the(TIAB),
integral of
theuseful
attenuated
backscatter
downthe
to the
surface,
the total loading
integrated
backscatter
units of sr−1.backscatter
Thus, if “zs” down
is the range
to surface,
the surface
the attenuated
to the
the total integrated attenuated backscatter (TIAB),
units of sr−1 . Thus, if “zs ” is the range to the surface
TIAB = TIAB =
wZS β
+ β
×T
×T
×T
dz,
βAerosol + βRayleigh × T2Aerosol × T2Rayleigh × T2Ozone dz ,
(11)
(11)
From its definition,0 TIAB is expected to increase with increasing aerosol backscatter, although if
βa(z) becomes too large, the corresponding impact on Ta2(z) will cause TIAB to decrease. Even as
TIAB increases,
Ta2(z) TIAB
still decreases
withto
increasing
a (z), causing
the aerosol
strength backscatter,
of observed surface
From
its definition,
is expected
increaseβwith
increasing
although if
2 (z) will
to too
generally
with increasing
TIAB.
very
clear
sky
conditions
(aerosol-free
βa (z)returns
becomes
large, decrease
the corresponding
impact
on TUnder
cause
TIAB
to
decrease.
Even
as TIAB
a
2
atmosphere)
for
532
nm
the
TIAB
reduces
to
increases, Ta (z) still decreases with increasing βa (z), causing the strength of observed surface returns
to generally decrease with increasing TIAB. Under very clear sky conditions (aerosol-free atmosphere)
(12)
TIAB
β
×T
×T
dz ,
for 532 nm the TIAB reduces
to (
) =
TIAB(Clear sky) =
wzs
0
βRayleigh × T2Rayleigh × T2Ozone dz ,
(12)
Remote Sens. 2016, 8, 1006
10 of 27
Using the molecular and ozone density numbers provided in the CALIPSO data product, all the
terms within the integral in Equation (12) can be computed and for the 532 nm channel the TIAB for
clear sky conditions was calculated to be ~0.012. Thus, a TIAB threshold value of 0.0125 was set so
that any 532 nm lidar shot having a TIAB value ≤0.0125 was assumed to have passed through an
essentially aerosol-free atmosphere. The CALIPSO data product also provides, for every lidar shot,
its eastward and westward wind component values (the wind information is provided from NASA’s
Global Modeling and Assimilation Office (GMAO); the wind being estimated from an assimilation
model). The total surface wind speed can be obtained by taking the vector sum of these components,
from which the surface reflectance can be calculated using the model described earlier. Thus,
every lidar shot can be associated with a TIAB and surface reflectance value.
2.5. Reconstruction of Impulse Response and Area Retrieval from Down-Linked Samples
The low-pass filtered lidar responses to ocean-surface signal returns, which are approximated
to be the scaled impulse response of the LPF, have an area that was shown to be proportional to
the product of the surface reflectance and the total round-trip transmittance of the atmosphere.
As the reflectance can be calculated with the knowledge of surface wind speeds, the aerosol round-trip
transmission can be retrieved if the area under the scaled impulse response, ALPF , can be accurately
determined. For every down-linked sample that is identified to be a part of the SR signal, by reversing
this process of averaging and sampling, by using the impulse response model (shown in Figure 1),
the original samples (whose average gives the down-linked sample) and the scaled impulse response
from which the original samples were obtained, can be recovered and the area under it may
be computed.
It can be seen from Figures 6 and 7 that the surface signal is generally made up of two down-linked
samples for the 1064 nm channel and three down-linked samples for the 532 nm channel, amongst
which two of the three seem to be significantly stronger than the third. The first step in the
reconstruction is to determine the time instances of these samples relative to the start of the impulse
response (i.e., the sampling delay), which, as described earlier, can be estimated from the ratio of the
first to second SR samples, using the interpolation curves shown in Figure 8.
As the time instant for every down-linked sample is assigned for 532 nm, the two time instants of
the original samples that upon averaging give the down-linked sample, are also known (0.05 µsec on
either side of the down-linked sample). The impulse response curve based on lab measurements (solid
curve in Figure 1) is varied in area until the average of the values on the curve corresponding to the
two time instants is equal to the value of the down-linked sample. In this manner, area is calculated
for every non-zero down-linked sample. This process is depicted by selecting an arbitrary SR non-zero
sample as shown in red in Figure 10. The down-linked sample is first aligned (i.e., positioned for
the sampling delay estimated for the SR sample) with the impulse response model, which is scaled
initially to have a small area. The initial samples corresponding to this scaled impulse response curve
are located 0.05 µsec on either side of the down-linked sample, and are shown in black. These samples
are then averaged in both their value and their time instances, to produce the sample shown in green
(in Figure 10). As the sample in green is clearly not equal to the down-linked sample in magnitude,
the impulse response curve is scaled to have an increased area. Scaling of the area/curve is increased
(an intermediate scaling is shown in Figure 11) until the average of the samples for the impulse
response curve, found 0.05 µsec on either side of the down-linked sample, is equal in magnitude to the
down-linked sample as shown in Figure 11. The area of the impulse response for this down-linked
sample is stored. The same procedure for estimating area is used on the four-average samples for
1064 nm. The process is repeated for any other non-zero shot samples and these area estimates are
also stored. The resulting areas may be averaged for the area estimate of a given shot (at 532 nm or
1064 nm) or grouped with the areas estimated for similar shots.
Remote
Sens.
2016,
8, 1006
Remote
Sens.
2016,
8, 1006
Remote
Sens.
2016,
8, 1006
0.7
Amplitude
Amplitude
0.6
0.5
0.4
0.3
0.2
0.1
0.8
0.7
0.6
Area
under
Impulse
response
= 0.06
Area
under
Impulse
response
= 0.06
0.80.8
Impulse Response
Impulse Response
Original Sample points of the Curve
Original Sample points of the Curve
Downlinked Sample Point
Downlinked Sample Point
Area
under
Impulse
response
= 0.06
Area
under
Impulse
response
= 0.06
Impulse Response
Impulse Response
Original Sample points of the Curve
Original Sample points of the Curve
Sample resulting from Averaging original sample points
Sample resulting from Averaging original sample points
Downlinked Sample Point
Downlinked Sample Point
0.70.7
0.60.6
0.5
0.50.5
Amplitude
Amplitude
0.8
11 of 27
11 11
of of
27 27
0.4
0.40.4
0.3
0.30.3
0.2
0.20.2
0.1
0.10.1
0
0 0 0.05 0.15
0 0.05 0.15
0.4
0.4
0.6
0.6
0.8
Time
Time
0.8
0 00
0
0.20.2
0.40.4
Time
Time
0.60.6
0.80.8
Figure
Showing
time
instances
original
samples
and
their
average.
Time
is
plotted
in
μsec in
Figure
10.
Showing
time
instances
ofthe
the
original
samples
and
their
average.
is in
plotted
Figure
10.10.
Showing
time
instances
of of
the
original
samples
and
their
average.
Time
is Time
plotted
μsec
units.
units.
µsec
units.
0.8
0.8
0.7
0.7
0.6
0.6
Area under Impulse response = 0.2130
Area under Impulse response = 0.2130
Area under Impulse response = 0.14
Area under Impulse response = 0.14
Impulse Response
Impulse Response
Original Sample points of the Curve
1
Original Sample points of the Curve
1
Sample resulting from Averaging original sample points
Sample resulting from Averaging original sample points
Downlinked Sample Point
Downlinked Sample Point
0.8
0.8
Amplitude
Amplitude
Amplitude
Amplitude
0.5
0.5
0.6
0.6
0.4
0.4
0.3
0.3
0.4
0.4
0.2
0.2
0.2
0.2
0.1
0.1
0
0 0
0
0.2
0.4
0.2
0.4
Time
Time
(a)
(a)
0.6
0.6
0.8
0.8
0
0 0
0
0.2
0.4
0.2
0.4
Time
Time
(b)
0.6
0.6
(b)
0.8
0.8
Figure
Process
scaling
area
until
the
original
impulse
response
down-linked
sample
Figure
11.
Process
ofof
scaling
inin
area
until
the
original
impulse
response
ofthe
the
down-linked
sample
Figure
11.11.
Process
of
scaling
in
area
until
the
original
impulse
response
of of
the
down-linked
sample
is is is
recovered:
(a)
Area
scaled
too
small;
(b)
Area
scaled
to
fit
the
down-linked
sample.
Time
is
plotted
recovered:
scaled too
toosmall;
small;(b)
(b)Area
Areascaled
scaled
down-linked
sample.
Time
is plotted
recovered: (a)
(a) Area
Area scaled
toto
fit the down-linked
sample.
Time
is plotted
in in in
μsec
units.
µsec
μsecunits.
units.
Surface
return
pulses
arising from
surfaces having
reflectance
values
close
one
another
and
Surface
return
pulses
arising
reflectance
values
close
toto
one
another
and
Surface
return
pulses
arisingfrom
fromsurfaces
surfaceshaving
having
reflectance
values
close
to one
another
and
havingthe
thesame
sameatmospheric
atmosphericattenuation
attenuationwill
willapproximately
approximatelyproduce
producethe
thesame
sameoutput
output(i.e.,
(i.e.,the
the
having
having
the same
atmospheric attenuation
will approximately
produce the
same output
(i.e., the
same
same
impulse
response)
from
the
LPF.
the
surface
returns
within
such
a group
produce
nearly
same
impulse
response)
the
LPF.
AsAs
allall
the
surface
returns
within
such
group
produce
nearly
impulse
response)
from from
the LPF.
As all
the
surface
returns
within
such
a agroup
produce
nearly
the
the
same
impulse
response
and
SR
area,
even
if
each
of
them
has
a
different
sampling
delay,
they
are
the same
impulse
response
and
area,even
evenififeach
each of
of them
sampling
delay,
theythey
are
same
impulse
response
and
SRSR
area,
themhas
hasa adifferent
different
sampling
delay,
are
expected
have
approximately
the
same
sum
value
(i.e.,
noted
earlier
the
sum
the
samples
expected
toto
have
approximately
the
same
sum
value
(i.e.,
asas
noted
earlier
the
sum
ofof
the
SRSR
samples
expected
to
have
approximately
the
same
sum
value
(i.e.,
as
noted
earlier
the
sum
of
the
SR
samples
a given
nearly
constant
regardless
sampling
delay).
can
happen
that
the
down-linked
forfor
a given
SRSR
is is
nearly
constant
regardless
ofof
sampling
delay).
It It
can
happen
that
the
down-linked
forsamples
a given corresponding
SR is nearly constant
regardless
of
sampling
delay).
It
can
happen
that
the
down-linked
some
surface
returns
within
the
group
will
spurious
(either
very
strong
samples corresponding toto
some
surface
returns
within
the
group
will
bebe
spurious
(either
very
strong
samples
corresponding
to to
some
surface
returns
within
the
group
will
be
spurious
(either
verycould
strong
or
very
weak
compared
other
samples
of
the
group).
The
source
of
these
spurious
samples
or very weak compared to other samples of the group). The source of these spurious samples could
or very
weak
compared
to
other
samples
of
the
group).
The
source
of
these
spurious
samples
could
the
result
the
return
signal
saturating
the
receiver,
undetected
abrupt
changes
surface
windbe
bebe
the
result
ofof
the
return
signal
saturating
the
receiver,
undetected
abrupt
changes
inin
surface
wind
thespeed
result or
of the
return
signal
saturating
the
receiver,
undetected
abrupt
changes
in
surface
wind
speed
aerosolloading/aerosol
loading/aerosoltype,
type,orordue
duetotothe
thegeneral
generalcorruption
corruptionbybynoise
noiseduring
duringdata
data
speed or aerosol
or aerosol
loading/aerosol
type,
or due to
thevalue
general corruption
by noise
during
data
collection
collection
andsampling.
sampling.The
Thesample
sample
sum
everysurface
surface
returnsignal
signalcan
canbebe
usedasasa and
a
collection
and
sum
value forforevery
return
used
sampling.
The
sample
sum
value
for
every
surface
return
signal
can
be
used
as
a
measure
of
quality
measureofofquality
qualityofofthat
thatsignal.
signal.ToToeliminate
eliminateoutlier
outliersamples,
samples,the
themean
meanand
andstandard
standarddeviation
deviation of
measure
that
signal.
To
eliminate
outlier
samples,
the
mean
and
standard
deviation
values
of
the
sum
values
valuesofofthe
thesum
sumvalues
valuesover
overallallthe
thesurface
surfacereturns
returnsthat
thatconstitute
constitutethe
thegroup
groupare
arecalculated,
calculated,and
and
values
over
all
the
surface
returns
that
constitute
the
group
are
calculated,
and
only
those
surface
returns
only
those
surface
returns
are
retained
whose
sum
values
fall
within
two
standard
deviations
only those surface returns are retained whose sum values fall within two standard deviations ononare
retained
whose
sum
values
fall
within
two standard
deviations
onThe
either
side
of
the mean
sum
value
eitherside
sideofofthe
themean
mean
sum
value
calculated
the
entiregroup.
group.
Thesame
same
criterion
wasused
usedto
to
either
sum
value
calculated
forforthe
entire
criterion
was
calculated
for
the
entire
group.
The
same
criterion
was
used
to
eliminate
outlier
surface
returns
at
eliminate
outlier
surface
returns
at
both
wavelengths.
eliminate outlier surface returns at both wavelengths.
both wavelengths.
Thefinal
finalarea
areaestimate
estimateofofa agroup
groupis iscalculated
calculatedasasthe
themean
meanofofthe
theareas
areascalculated
calculatedforforallall
The
retained
down-linked
samples.
The
impulse
response
scaled
to
the
final
mean-estimated
area
along
The
final
area
estimate
of
a
group
is
calculated
as
the
mean
of
the
areas
calculated
allalong
retained
retained down-linked samples. The impulse response scaled to the final mean-estimatedfor
area
with
retained
down-linked
samples
corresponding
to
an
example
group
is
shown
in
Figure
12.
Also
down-linked
samples.
The
impulse
response
scaled
to
the
final
mean-estimated
area
along
with
with retained down-linked samples corresponding to an example group is shown in Figure 12. Also
shown
is
the
corresponding
area
standard
deviation
value.
Similarly,
for
the
1064
nm
channel,
as
the
retained
samples
corresponding
to an example
group isfor
shown
in Figure
12. Also
shown
shown isdown-linked
the corresponding
area
standard deviation
value. Similarly,
the 1064
nm channel,
as the
is the corresponding area standard deviation value. Similarly, for the 1064 nm channel, as the time
Remote Sens. 2016, 8, 1006
12 of 27
Remote Sens.
Sens. 2016,
2016, 8,
8, 1006
1006
Remote
12 of
of 27
27
12
instant
forinstant
everyfor
down-linked
samplesample
is known,
the time
instances
of the
original
four
samples
time
every down-linked
down-linked
is known,
known,
the time
time
instances
of the
the
original
four
samplesthat
time
instant for
every
sample is
the
instances
of
original
four
samples
uponthat
averaging
give
the
down-linked
sample,
are
also
known.
The
impulse
response
is
varied
in area
upon averaging
averaging give
give the
the down-linked
down-linked sample,
sample, are
are also
also known.
known. The
The impulse
impulse response
response is
is varied
varied
that upon
untilinthe
average
ofaverage
the values
the impulse
response
at these
fourfour
timetime
instances
is isequal
area
until the
the
of the
theofvalues
values
of the
the impulse
impulse
response
at these
these
instances
equalto
tothe
in area
until
average of
of
response
at
four time
instances
is equal
to
valuethe
of value
the
down-linked
sample.
The
area
is
calculated
for
every
down-linked
sample
in
the
group
the
value
of
the
down-linked
sample.
The
area
is
calculated
for
every
down-linked
sample
in
the
of the down-linked sample. The area is calculated for every down-linked sample in the in
this manner
and
finaland
areathe
is final
taken
as the
mean
retained
areas. Figure
13
shows
group
in
this
manner
and
the
final
area
is taken
taken
asof
thethe
mean
of the
the calculated
retained calculated
calculated
areas. Figure
Figure
group in this the
manner
area
is
as
the
mean
of
retained
areas.
13 shows
shows the
the
scatterplot
of the
the
retained down-linked
down-linked
samples
for an
an example
example
1064
nm group,
group,
alongthe
the scatterplot
of scatterplot
the retained
down-linked
samples for
an example
1064 nm1064
group,
along along
with
13
of
retained
samples
for
nm
withresponse
the impulse
impulse
response
scaled
to
the final
final estimated
estimated
area.
impulse
scaled
to thescaled
final to
estimated
area.
with
the
response
the
area.
Final Estimated
Estimated Area
Area == 0.1951,
0.1951, Standard
Standard -- Deviation
Deviation == 0.018
0.018
Final
11
Downlinked Samples
Samples
Downlinked
Impulse Response
Response
Impulse
Amplitude
Amplitude
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
000
0
0.1
0.1
0.2
0.2
0.3
0.3
Time
Time
0.4
0.4
0.5
0.5
0.6
0.6
0.7
0.7
Figure
12. Impulse
Impulse
response
scaled
to
thefinal
finalestimated
estimated area
area and
and
the
down-linked
samples
forfor
thethe
Figure
12. Impulse
response
scaled
toto
the
andthe
thedown-linked
down-linked
samples
Figure
12.
response
scaled
the
final
estimated
samples
for
the
532
nm
channel.
Time
is
measured
in
μsec
units.
532 nm
Time
is measured
in in
µsec
units.
532channel.
nm channel.
Time
is measured
μsec
units.
Final Estimated
Estimated Area
Area == 0.2607,
0.2607, Standard
Standard -- Deviation
Deviation == 0.035
0.035
Final
1.4
1.4
Downlinked Samples
Samples
Downlinked
Impulse Response
Response
Impulse
1.2
1.2
Amplitude
Amplitude
11
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
00
-0.1
-0.1
00
0.1
0.1
0.2
0.2
0.3
0.3
Time
Time
0.4
0.4
0.5
0.5
0.6
0.6
0.7
0.7
0.8
0.8
Figure
13. Impulse
Impulse
response
scaled
to
thefinal
finalestimated
estimated area
area and
and
the
down-linked
samples
forfor
thethe
Figure
13.
response
scaled
the
final
estimated
samples
for
the
Figure
13. Impulse
response
scaled
toto
the
andthe
thedown-linked
down-linked
samples
1064
nm
channel.
Time
is
measured
in
μsec
units.
nm channel.
Time
is measured
μsec
units.
1064 1064
nm channel.
Time
is measured
in in
µsec
units.
Groups for
for averaging
averaging were
were selected
selected by
by binning
binning the
the CALIOP
CALIOP data
data into
into specified
specified small
small increments
increments
Groups
Groups
for
averaging
were
selected
by
binning
the
CALIOP
data
into
small
increments
in
both
wind
speed
(which
then
defines
an
increment
in
reflectance,
R
λ) specified
and
the
total
integrated
in both wind speed (which then defines an increment in reflectance, Rλ) and the total integrated
in both
wind speed
(which
then
defines
increment
in contain
reflectance,
Rλ ) and
the from
total spatially
integrated
attenuated
backscatter,
TIAB.
While
suchan
groups
will likely
likely
contain SR
SR samples
samples
mainly
from
spatially
attenuated
backscatter,
TIAB.
While
such
groups
will
mainly
attenuated
backscatter,
TIAB.
While
such
groups
will
likely
contain
SR
samples
mainly
from
contiguous
lidar
shots,
this
is
neither
required
nor
expected
as
some
shots
may
be
missing
due
tospatially
noise
contiguous lidar shots, this is neither required nor expected as some shots may be missing due to
noise
rejection,
cloud
screening,
abrupt
spatial
change
in
wind
speed
or
TIAB
and
the
like.
Also,
some
shots
contiguous
lidar
shots,
this
is
neither
required
nor
expected
as
some
shots
may
be
missing
due
to noise
rejection, cloud screening, abrupt spatial change in wind speed or TIAB and the like. Also, some shots
from
significantly
different
spatial
locations
could
have
nearly
the
same
TIAB
and
wind
speed
and
be
rejection,
screening,
abrupt
spatial
change
in wind
speedthe
or same
TIABTIAB
and the
shots
from cloud
significantly
different
spatial
locations
could
have nearly
andlike.
windAlso,
speedsome
and be
included
in
the
same
group.
As
presented
in
the
next
section,
the
averaging
groups
were
found
to
be
fromincluded
significantly
spatial
locations in
could
havesection,
nearlythe
theaveraging
same TIAB
and were
windfound
speedtoand
in thedifferent
same group.
As presented
the next
groups
be be
composed
ofsame
anywhere
from
as
many as
as aain
few
hundred
lidar shots
shots
to as
as little
little as
asgroups
few tens
tens
of shots.
shots. As
As
composed
anywhere
from
many
few
lidar
to
aa few
of
included
in theof
group.
Asas
presented
thehundred
next section,
the averaging
were
found
to be
CALIOP
lidar
shots
occur
at
a
surface
separation
of
one-third
of
a
km,
the
group’s
spatial
extents
CALIOP
lidar
shots
occur
at
a
surface
separation
of
one-third
of
a
km,
the
group’s
spatial
extents
composed of anywhere from as many as a few hundred lidar shots to as little as a few tens of shots.
typically ranged
ranged from
from about
about 10
10 km
km up
up to
to 150
150 km
km (could
(could even
even be
be larger
larger depending
depending on
on missing
missing shots
shots and
and
typically
As CALIOP
lidar shots
occur at
a surface
separation
of one-third
of a km, the group’s
spatial extents
shots in
in different
different locations
locations with
with nearly
nearly the
the same
same TIAB
TIAB and
and wind
wind speed).
speed). Grouping
Grouping data
data in
in this
this manner
manner
shots
typically ranged from about 10 km up to 150 km (could even be larger depending on missing shots
proved effective
effective in
in gathering
gathering statistics
statistics on
on the
the range
range and
and variability
variability of
of the
the SR
SR areas.
areas.
proved
and shots in different locations with nearly the same TIAB and wind speed). Grouping data in this
manner proved effective in gathering statistics on the range and variability of the SR areas.
Remote Sens. 2016, 8, 1006
Remote Sens. 2016, 8, 1006
13 of 27
13 of 27
3. Results and Discussion
3. Results and Discussion
3.1. Regions of Study
3.1. Regions of Study
Due to the absence of solar background radiation, the signals collected during the night-time
Dueoftothe
theorbit
absence
of solar
background
radiation,
signalssamples
collectedtoduring
night-time
portion
are less
noisy
and provide
the mostthe
accurate
test thethe
area
retrieval
portion
of
the
orbit
are
less
noisy
and
provide
the
most
accurate
samples
to
test
the
area
retrieval
technique for estimating the area of the CALIOP ocean surface returns. Night-time down-linked
technique
for correspond
estimating the
area of
the CALIOP
oceancollected
surface from
returns.
Night-time
down-linked
samples that
to ocean
surface
returns were
the Southern
Pacific
Ocean (5
samples
that
correspond
to
ocean
surface
returns
were
collected
from
the
Southern
Pacific
May 2011–20 May 2011), Atlantic Ocean (1 May 2011–15 May 2011) and Indian Ocean (1 MayOcean
2011–
(5
2011–20
2011),
Atlantic
Oceandown-linked
(1 May 2011–15
andare
Indian
15 May
May 2011).
TheMay
various
regions
from where
samplesMay
were2011)
collected
shownOcean
in the
(1 May 2011–15 May 2011). The various regions from where down-linked samples were collected
red rectangles (approximately 30 degrees in lat by 40 degrees in lon) of Figure 14. These regions were
are shown in the red rectangles (approximately 30 degrees in lat by 40 degrees in lon) of Figure 14.
chosen on the basis of providing a reasonable fraction of cloud-free situations as well as a variety of
These regions were chosen on the basis of providing a reasonable fraction of cloud-free situations as
aerosol-loading conditions.
well as a variety of aerosol-loading conditions.
Figure 14. The various ocean regions where samples were collected are shown in red, left to right, and
Figure 14. The various ocean regions where samples were collected are shown in red, left to right,
a typical night-time orbit (shown in black) passing through each region is included.
and a typical night-time orbit (shown in black) passing through each region is included.
For
For each
each of
of the
the oceanic
oceanic regions,
regions, aa CALIPSO
CALIPSO orbit
orbit passes
passes over
over the
the region
region of
of study
study during
during
night-time once every 24 h and fires approximately 5000 lidar shots during its time of flight. Thus,
night-time once every 24 h and fires approximately 5000 lidar shots during its time of flight. Thus,
for 15 consecutive days (as the dates suggest), ~5000 × 15 shots are fired by CALIOP over each of
for 15 consecutive days (as the dates suggest), ~5000 × 15 shots are fired by CALIOP over each of the
the regions of study, and surface returns corresponding to each of these lidar shots (determined to
regions of study, and surface returns corresponding to each of these lidar shots (determined to be
be cloud free from the CALIPSO data product) were collected in the form of down-linked samples
cloud
free
data
product) were collected in the form of down-linked samples (for
(for
both
thefrom
532 the
nm CALIPSO
and 1064 nm
channels).
bothAs
thenoted
532 nm
and
1064
nm
channels).
at the end of Section 2.5, averaging groups were defined by binning the CALIOP data
As noted
at the end
of Section
averaging
groups
wereof
defined
by binning
the TIAB
CALIOP
data
into small
increments
in both
wind 2.5,
speed
and TIAB.
For each
the regions
of study,
groups
into small
increments
in bothSR
wind
speedthat
andfell
TIAB.
For TIAB
each of
the regions
study,
were
defined
for the collected
samples
into five
value
ranges ofof0.012
to TIAB
0.0125,groups
0.016
were
defined
for0.024,
the collected
SR samples
that
fell into
five
value speed
rangessub-groups
of 0.012 tofor
0.0125,
to
0.017,
0.022 to
0.028 to 0.031
and 0.034
to 0.036,
units
of TIAB
sr−1 . Wind
each
−1
TIAB
group
were
formed
for
samples
that
fell
into
five
wind
speed
ranges
of
3.7
to
3.9
m/s,
4.4
to
0.016 to 0.017, 0.022 to 0.024, 0.028 to 0.031 and 0.034 to 0.036, units of sr . Wind speed sub-groups
4.6
to 5.3
m/s,were
5.5 to
6.0 m/s
6.6 to that
7.1 m/s
(the wind
speed
increments
so
form/s,
each 5.1
TIAB
group
formed
forand
samples
fell into
five wind
speed
ranges were
of 3.7selected
to 3.9 m/s,
that
the4.6
surface
by more
than6.6
0.005
increment).
The TIAB
upper limit
4.4 to
m/s, reflectance
5.1 to 5.3 did
m/s,not
5.5vary
to 6.0
m/s and
to within
7.1 m/san(the
wind speed
increments
were
was
set toso
0.036
SRsurface
samplesreflectance
above ~0.04
to be
difficult
distinguish
from
atmospheric
selected
thatasthe
didwere
not found
vary by
more
than to
0.005
within an
increment).
The
returns. As noted earlier, the lowest TIAB range of 0.012 to 0.0125 defines samples for lidar shots
TIAB upper limit was set to 0.036 as SR samples above ~0.04 were found to be difficult to distinguish
that passed through essentially aerosol-free atmospheres. The wind speed upper and lower limits
from atmospheric returns. As noted earlier, the lowest TIAB range of 0.012 to 0.0125 defines samples
(3.7 m/s and 7.1 m/s) spanned the range for which the wind speed reflectance model [13] applied to the
for lidar shots that passed through essentially aerosol-free atmospheres. The wind speed upper and
data was deemed reasonably applicable. Neither the TIAB or wind speed groupings are continuous;
lower limits
(3.7 m/s what
and 7.1
m/s)
spanned
the range sampling
for which the
wind speed the
reflectance
model
rather,
they provide
was
deemed
a sufficient
to characterize
continuum
of [13]
SR
applied
to
the
data
was
deemed
reasonably
applicable.
Neither
the
TIAB
or
wind
speed
groupings
samples occurring within the specified TIAB and wind speed limits. The defined groupings contained
are continuous;
rather,
they provide whatinwas
deemed
a sufficient
sampling
characterize
the
numerous
samples
(see results/discussion
following
sub-section)
that
proved to
quite
adequate for
continuum
of
SR
samples
occurring
within
the
specified
TIAB
and
wind
speed
limits.
The
defined
statistically assessing and characterizing the effect of aerosol attenuation and ocean surface reflectance
groupings
contained numerous samples (see results/discussion in following sub-section) that
on
SR area retrievals.
Remote Sens. 2016, 8, 1006
14 of 27
proved quite adequate for statistically assessing and characterizing the effect of aerosol attenuation
Remote
Sens. 2016,
8, 1006
14 of 27
and
ocean
surface
reflectance on SR area retrievals.
3.2. Surface Return Area Retrieval Results
3.2. Surface Return Area Retrieval Results
Example SR impulse response curve fits for data collected from the Southern Pacific Ocean
Example SR impulse response curve fits for data collected from the Southern Pacific Ocean region
region (see area defined in Figure 14) for the 532 nm channel are shown for several groupings in
(see area defined in Figure 14) for the 532 nm channel are shown for several groupings in Figure 15.
Figure 15. As described earlier in the previous section regarding Figures 12 and 13, the response
As described earlier in the previous section regarding Figures 12 and 13, the response curve is the fit to
curve is the fit to the mean area determined from the average of the areas of all the retained
the mean area determined from the average of the areas of all the retained down-linked samples in
down-linked samples in a group. For each grouping, the final estimated mean area and standard
a group. For each grouping, the final estimated mean area and standard deviation, original number
deviation, original number of surface returns/samples in the group and the number of surface
of surface returns/samples in the group and the number of surface returns/samples retained after
returns/samples retained after data screening, are also provided. The areas and standard deviations
data screening, are also provided. The areas and standard deviations for all the Southern Pacific Ocean
for all the Southern Pacific Ocean 532 nm data groupings are given in Table 1, and Figure 16 shows
532 nm data groupings are given in Table 1, and Figure 16 shows plots of these areas versus wind
plots
of these areas versus wind speed for each TIAB range. As expected, it can be seen from the
speed for each TIAB range. As expected, it can be seen from the figure that the areas progressively
figure
that
theincreasing
areas progressively
decrease with
increasing
Corresponding
results
the2
decrease
with
TIAB. Corresponding
results
for the TIAB.
1064 nm
channel are given
in for
Table
1064
nm
channel
are
given
in
Table
2
and
Figure
17.
Similarly,
the
results
for
the
Atlantic
Ocean
data
and Figure 17. Similarly, the results for the Atlantic Ocean data analysis are given in Tables 3 and 4,
analysis
are given
in Tables
and 4,data
andanalysis
the results
theinIndian
are response
given in
and the results
for the
Indian3Ocean
are for
given
TablesOcean
5 and 6data
(theanalysis
SR impulse
Tables
5 and
(the SR
impulse
response
fits likefor
those
given in Figure
are not
for
curve fits
like6those
given
in Figure
15 are curve
not repeated
the Southern
Pacific 15
Ocean
1064repeated
nm channel
the
Southern
Pacific
Ocean
1064
nm
channel
data
or
for
the
two
channels
for
the
other
ocean
regions
data or for the two channels for the other ocean regions as they all proved similar. Also, figures
as
they
all proved
Also,
figures for
likethe
Figures
and regions
17 are not
repeated
the other
ocean
like
Figures
16 andsimilar.
17 are not
repeated
other16
ocean
as they
also for
all proved
similar).
regions
as seen
they in
also
all proved
similar).
As canobtained
be seen in
in the
results
obtained
for
As can be
Figure
15 (and
in the results
forFigure
curve15
fits(and
for all
ocean
regions
and both
curve
fits
for
all
ocean
regions
and
both
wavelengths)
the
greatest
number
of
available
down-linked
wavelengths) the greatest number of available down-linked samples/retained samples occurred at
samples/retained
samples
occurred
at the
lowestoptical
TIAB values
(i.e., thevalues),
lowest indicating
aerosol optical
depth
the lowest TIAB values
(i.e.,
the lowest
aerosol
depth (AOD)
low AODs
(AOD)
values),
indicating
low
AODs
occurred
most
frequently.
occurred most frequently.
TIAB = 0.012 - 0.0125
1
A rea
M ean = 0.2305
S td D eviation = 0.027
0.8
0.6
0.4
1
A rea
M ean = 0.1940
S td D eviation = 0.017
0.8
0.6
0.4
0.2
0.2
0
0
1.2
Down-linked Samples
Magnitude (Area Values)
Magnitude (Area Values)
1.2
Number of Samples = 315
No. of Surface returns after screening = 86
Number of Samples= 258
0.2
0.4
0.6
0.8
Time (usec)
Wind Speed = 3.7 m/s - 3.9 m/s
1.4
Original No. of Surface returns = 431
Number of Samples = 1293
No. of Surface returns after screening = 364
Number of Samples= 1092
0
0
1.2
Magnitude (Area Values)
1.4 Original No. of Surface returns = 105
1
Original No. of Surface returns = 405
Number of Samples = 1215
No. of Surface returns after screening = 342
Number of Samples= 1026
A rea
M ean = 0.1330
S td D eviation = 0.013
0.8
0.6
0.4
0.2
0.2
0.4
0.6
Time (usec)
Wind Speed = 4.4 m/s - 4.6 m/s
Figure 15. Cont.
0
0
0.2
0.4
0.6
Time (usec)
Wind Speed = 6.6 m/s - 7.1 m/s
Remote Sens. 2016, 8, 1006
Remote Sens. 2016, 8, 1006
15 of 27
15 of 27
0.6
0.4
0.3
0.2
0.1
0
0
0.6
0.7
Original No.Aofrea
Surface returns = 41
Number of Samples
123
M ean ==0.
0875
No. of Surface returns after screening = 38
S td D eviation = 0.014
Number of Samples= 114
0.5
Magnitude (Area Values)
0.5
Magnitude (Area Values)
Magnitude (Area Values)
0.7
A rea
M ean = 0.0875
S td D eviation = 0.014
0.5
0.4
0.3
0.4
Original No. of Surface returns = 31
A rea
0.5
Number of Samples = 93
ean = 0.0657
No. of Surface returns afterMscreening
= 30
0.6 Number of Samples= 90 S td D eviation = 0.012
Original No. of Surface returns = 52
Number of Samples
= 156
Down-linked
Samples
A rea
M ean = 0.0781
S td D eviation = 0.01
0.2
0.3
0.1
0.2
0.2
0.1
0.2
0.4
Time (usec)
0
Wind Speed
=
4.4
m/s
4.6
m/s
0
0.2
0.4
0.1
0
0
0.6
0.6
Time (usec)
Wind Speed = 4.4 m/s - 4.6 m/s
0.6
0.2
0.4
Time (usec)
0
Wind
5.1 m/s - 5.3
0 Speed =0.2
0.4 m/s
Time (usec)
Wind Speed = 5.1 m/s - 5.3 m/s
of 27
Original No. of Surface returns15
= 31
Number of Samples = 93
No. of Surface returns after screening = 30
Number of Samples= 90
0.7
0.6 No. of Surface returns after screening = 43
Number of Samples=A 129
rea
0.4
M ean = 0.0781
S
td D eviat
ion = 0.01
0.5
Down-linked
Samples
0.3
0.7
Original No. of Surface returns = 52
Number of Samples = 156
No. of Surface returns after screening = 43
Number ofTIAB
Samples=
129
= 0.028
- 0.031
Magnitude (Area Values)
Number of Samples = 123
No. of Surface returns after screening = 38
Number of Samples= 114
Magnitude (Area Values)
0.6
TIAB = 0.028 - 0.031
0.7
Original
No. 2016,
of Surface
returns = 41
Remote
Sens.
8, 1006
Magnitude (Area Values)
0.7
0.4
0.5
0.4
0.3
0.3
A rea
M ean = 0.0657
S td D eviation = 0.012
0.2
0.2 0.1
0.1
0.6
0
0
0.2
0.4
Time (usec)
0.6
0Wind Speed = 6.6 m/s - 7.1 m/s
0
0.2
0.4
0.6
Time (usec)
Wind Speed = 6.6 m/s - 7.1 m/s
0.6
Figure 15. Example
area
values
at various
TIAB
and and
windwind
speedspeed
values.
Also given
Examplecurve
curvefits
fitsshowing
showing
area
values
at various
TIAB
values.
Also
is number
of15.returns
filtered
out
theby
two
standard
deviation
tests. and
given
is number
of returns
filtered
out
the
two
standard
deviation
tests.
Figure
Example
curve
fits by
showing
area
values
at
various
TIAB
wind speed values. Also
given is number of returns filtered out by the two standard deviation tests.
Table 1.
1. Area under surface returns for various TIAB and surface wind speed values for Southern
Table
1. Area
Pacific
Ocean,
532 under
nm. surface returns for various TIAB and surface wind speed values for Southern
Pacific Ocean, 532 nm.
Wind
Speed
−1
Wind
Speed
TIAB (sr
Wind
Speed
−1 ) ) −1
TIAB (sr
TIAB
(sr )3.7 m/s–3.9 m/s
m/s–3.9
m/s
3.73.7
m/s–3.9
m/s
0.012–0.0125
± 0.027
0.012–0.01250.2305
0.2305
± 0.027
0.012–0.0125
0.2305
± 0.027
0.016–0.017
± 0.026
0.016–0.017 0.2041
0.2041
± 0.026
0.016–0.017
0.2041
± 0.026
0.022–0.024
±±0.027
0.022–0.024 0.1474
0.1474
± 0.027
0.022–0.024
0.1474
0.027
0.028–0.031
0.1174
0.019
0.028–0.031
±±0.019
0.028–0.031 0.1174
0.1174
± 0.019
0.034–0.036
0.0824
0.011
0.034–0.036 0.0824
0.0824
± 0.011
0.034–0.036
±±0.011
0.24
0.24
0.22
Magnitude (Area Values)
Magnitude (Area Values)
0.22
0.2
0.2
0.18
0.18
Wind
Wind
Speed
Wind
Speed
Wind
Speed
WindSpeed
Speed
Wind
Speed Wind
Wind
Wind
Speed
Wind
Speed
Wind
Speed
SpeedSpeedWind Speed
4.4 m/s–4.6 m/s 5.1 m/s–5.3 m/s 5.5 m/s–6.0 m/s 6.6 m/s–7.1 m/s
4.4
m/s–5.3
m/sm/s5.5 m/s–6.0
m/s m/s
6.6 m/s–7.1
4.4m/s–4.6
m/s–4.6 m/s
m/s 5.1 5.1
m/s–5.3
5.5 m/s–6.0
6.6 m/s
m/s–7.1 m/s
0.1940
± 0.017
0.1625±±0.012
0.012
0.1538
± 0.013 0.1330
0.1330
± 0.013
0.1940
0.1625
± 0.013
±0.1330
0.013
0.1940 ±±0.017
0.017
0.1625 ± 0.012 0.15380.1538
± 0.013
± 0.013
0.1675
±±0.016
0.1500±±0.018
0.018 0.1358
0.1358
± 0.016 0.1230
0.1230
± 0.01
0.1675
0.016
0.1500
±
0.016
±
0.01
0.1675 ± 0.016
0.1500 ± 0.018
0.1358 ± 0.016
0.1230 ± 0.01
0.1128
0.1094
0.015
0.0960
± 0.017
± 0.017
0.1128±±±0.023
0.023
0.1094
±±0.015
± 0.017
± 0.017
0.023
0.1094
±
0.015 0.0960
0.0960
± 0.0170.0990.099
0.099
± 0.017
0.014
0.0781
±
0.010 0.0715
0.0715
± 0.012
± 0.012
0.0875
0.0781
0.010
0.0715
± 0.012
0.0657
± 0.012
0.0875±±±0.014
0.014
0.0781
±±0.010
± 0.012
0.0657
±0.0657
0.012
0.0759±±±0.008
0.008
0.0674
±
0.006 0.0589
0.0589
± 0.008
± 0.003
0.0759
0.008
0.0674
±±0.006
± 0.008
0.0565
±0.0565
0.003
0.0759
0.0674
0.006
0.0589
± 0.008
0.0565
± 0.003
TIAB Range = 0.012 - 0.0125
TIAB Range = 0.012 - 0.0125
TIAB Range = 0.016 - 0.017
TIABRange
Range
= 0.016
- 0.017
TIAB
= 0.022
- 0.024
TIABRange
Range
= 0.022
- 0.024
TIAB
= 0.028
- 0.031
TIABRange
Range
= 0.028
- 0.031
TIAB
= 0.034
- 0.036
TIABArea
Range
= 0.034 - 0.036
Mean
Values
Mean Area Values
0.16
0.16
0.14
0.14
0.12
0.120.1
0.08
0.1
0.06
0.08
0.04
3
0.06
0.04
3
4
5
6
Surface Wind Speed (m/s)
4
5
6
Surface Wind Speed (m/s)
7
7
Figure
16. Plots
showing
variation
areawith
withwind
windspeed
speed
and
TIAB
for Southern
Pacific
Figure
16. Plots
showing
variationofofestimated
estimated area
and
TIAB
for Southern
Pacific
Ocean,
532 nm.
Ocean,
532 nm.
Figure 16. Plots showing variation of estimated area with wind speed and TIAB for Southern Pacific
Ocean,
nm.
2.
Area
under
surface
returnsfor
forvarious
various TIAB
wind
speed
values
for Southern
TableTable
2.532
Area
under
surface
returns
TIABand
andsurface
surface
wind
speed
values
for Southern
Pacific
Ocean,
1064
Pacific
Ocean,
1064
nm.nm.
Table 2. Area under surface returns for various TIAB and surface wind speed values for Southern
Wind Speed
Wind Speed
Wind Speed
Wind Speed
Wind Speed
TIABOcean,
(sr−1) 1064
Pacific
nm.Speed
Wind
Speed
Wind Speed
Wind m/s
Speed 6.6 m/s–7.1
Wind
Speed
3.7
m/s–3.9
m/s 4.4Wind
m/s–4.6
m/s 5.1 m/s–5.3
m/s 5.5 m/s–6.0
m/s
TIAB (sr−1 )
0.012–0.0125 Wind
0.2846
± 0.026
3.7
m/s–3.9
m/s
Speed
TIAB0.016–0.017
(sr−1)
0.2493
±
0.04
0.012–0.0125 3.7 m/s–3.9
0.2846 ± 0.026
m/s
0.022–0.024
0.2024±
± 0.037
0.016–0.017
0.2493
0.04
0.012–0.0125
0.2846
±
0.026
0.022–0.024
0.2024
0.028–0.031
0.1525±± 0.037
0.035
0.016–0.017
± ±0.04
0.028–0.031
0.1525
0.034–0.036 0.2493
0.1017
± 0.035
0.003
0.034–0.036
0.1017
± 0.003
0.022–0.024
0.2024
± 0.037
0.028–0.031
0.1525 ± 0.035
0.034–0.036
0.1017 ± 0.003
0.2400
± 0.023
±Speed
0.018m/s
4.4 m/s–4.6
m/s 0.2208
5.1 m/s–5.3
Wind
Speed
Wind
0.2240
±
0.02
0.2066
±
0.018
0.2400 ± 0.023
± 0.018
4.4 m/s–4.6
m/s 5.1 0.2208
m/s–5.3
m/s
0.1609
0.1520
± 0.032
0.2240±±0.03
0.02
0.2066
± 0.018
0.2400
±
0.023
0.2208
±
0.018
0.1609±±
0.03
0.1520
± 0.032
0.1135
0.014
0.096
± 0.003
0.2240
0.2066
0.018
0.1135±±±0.02
0.014
0.096
0.003
0.0825
0.006
0.0833
±±±
0.011
0.0825±±0.03
0.006
0.0833±±
0.011
0.1609
0.1520
0.032
0.1135 ± 0.014
0.096 ± 0.003
0.0825 ± 0.006
0.0833 ± 0.011
0.1944
0.013
± 0.019
5.5 ±m/s–6.0
m/s0.1755
6.6
m/s–7.1
m/s
Wind
Speed
Wind
Speed
0.1766
±
0.028
0.1683
±
0.018
± 0.013
± 0.019
5.50.1944
m/s–6.0
m/s 6.60.1755
m/s–7.1
m/s
0.1219
± 0.026
± 0.019± 0.018
0.1766
± 0.028 0.129 0.1683
0.1944
±
0.013
0.1755
±
0.019
0.1219
± 0.026 0.0893 0.129
± 0.019
0.0916
± 0.016
± 0.012
0.1766
±±0.028
0.1683
±±0.018
0.0916
0.016 0.0561
0.0893
0.012
0.0760
± 0.004
± 0.01
0.0760±±0.026
0.004
0.0561
0.01
0.1219
0.129
±±
0.019
0.0916 ± 0.016
0.0760 ± 0.004
0.0893 ± 0.012
0.0561 ± 0.01
Remote Sens. 2016, 8, 1006
Remote Sens. 2016, 8, 1006
16 of 27
16 of 27
TIAB Range = 0.012 - 0.0125
TIAB Range = 0.016 - 0.017
TIAB Range = 0.022 - 0.024
TIAB Range = 0.028 - 0.031
TIAB Range = 0.034 - 0.036
Mean Area Values
Magnitude (Area Values)
0.3
0.25
0.2
0.15
0.1
0.05
3
4
5
6
Surface Wind Speed (m/s)
7
Figure
Figure 17.
17. Plots
Plots showing
showing variation
variation of
of estimated
estimated area
area with
with wind
wind speed
speed and
and TIAB
TIAB for
for Southern
Southern Pacific
Pacific
Ocean, 1064
1064 nm.
nm.
Ocean,
Table
3. Area
Areaunder
undersurface
surfacereturns
returns
various
TIAB
surface
for Atlantic
Table 3.
forfor
various
TIAB
andand
surface
windwind
speedspeed
valuesvalues
for Atlantic
Ocean,
Ocean,
532 nm.532 nm.
Wind Speed
Wind Speed
Wind Speed
Wind Speed
Wind Speed
0.2250 ± 0.009
0.2250
± 0.009
0.1951
± 0.018
0.1951
±
0.018
0.1380 ± 0.018
0.1380 ± 0.018
0.0945 ± 0.009
0.0945 ± 0.009
0.0727
± 0.009
0.0727
± 0.009
0.2037 ± 0.021
0.2037± ±
0.021
0.1780
0.024
0.1780
±
0.024
0.1097 ± 0.023
0.1097 ± 0.023
0.0854 ± 0.015
0.0854 ± 0.015
0.0637
0.014
0.0637± ±
0.014
0.1865 ± 0.014
0.1865± ±
0.014
0.1585
0.017
0.1585
±
0.017
0.1085 ± 0.016
0.1085 ± 0.016
0.0810 ± 0.016
0.0810 ± 0.016
0.0600
0.009
0.0600± ±
0.009
0.1342 ± 0.012
0.1342±±0.014
0.012
0.1227
0.1227
±
0.014
0.0895 ± 0.009
0.0895 ± 0.009
0.0683 ± 0.01
0.0683 ± 0.01
0.0540
0.0540±±0.009
0.009
0.1283 ± 0.01
0.1283± ±
0.01
0.1181
0.009
0.1181
±
0.009
0.0870 ± 0.003
0.0870 ± 0.003
0.0607 ± 0.01
0.0607 ± 0.01
0.054
0.054±±0.008
0.008
Wind Speed
Wind Speed
Wind Speed
Wind Speed
Wind Speed
TIAB (sr−1 ) 3.7 m/s–3.9 m/s 4.4 m/s–4.6 m/s 5.1 m/s–5.3 m/s 5.5 m/s–6.0 m/s 6.6 m/s–7.1 m/s
3.7 m/s–3.9 m/s 4.4 m/s–4.6 m/s 5.1 m/s–5.3 m/s 5.5 m/s–6.0 m/s 6.6 m/s–7.1 m/s
TIAB (sr−1)
0.012–0.0125
0.012–0.0125
0.016–0.017
0.016–0.017
0.022–0.024
0.022–0.024
0.028–0.031
0.028–0.031
0.034–0.036
0.034–0.036
Table 4. Area under surface returns for various TIAB and surface wind speed values for Atlantic
Table 4. Area under surface returns for various TIAB and surface wind speed values for Atlantic Ocean,
Ocean, 1064 nm.
1064 nm.
Wind Speed
Wind Speed
3.7
m/s–3.9
m/s
TIAB (sr−1 )
3.7 m/s–3.9
0.012–0.0125
0.2861
± 0.027m/s
0.016–0.017
± 0.035
0.012–0.0125 0.2607
0.2861
± 0.027
0.022–0.024
0.1746
0.03
0.016–0.017
0.2607± ±
0.035
0.022–0.024 0.1221
0.1746
± 0.03
0.028–0.031
± 0.022
0.028–0.031
0.1221± ±
0.022
0.034–0.036
0.1005
0.01
0.034–0.036
0.1005 ± 0.01
TIAB (sr−1)
Wind Speed
Wind Speed
4.4 m/s–4.6
m/s
4.4 m/s–4.6
0.2537
± 0.034m/s
0.2374
0.028
0.2537± ±
0.034
0.1523
0.028
0.2374± ±
0.028
0.1523± ±
0.028
0.1083
0.013
0.1083± ±
0.013
0.0890
0.018
0.0890 ± 0.018
Wind Speed
Speed
5.1 Wind
m/s–5.3
m/s
5.1 m/s–5.3
m/s
0.2387
± 0.022
0.2008
0.020
0.2387± ±
0.022
0.1443
0.028
0.2008± ±
0.020
0.1443± ±
0.028
0.0968
0.008
0.0968± ±
0.008
0.0872
0.011
0.0872 ± 0.011
Wind Speed
Wind Speed
Speed
Speed
5.5 Wind
m/s–6.0
m/s 6.6Wind
m/s–7.1
m/s
5.5 m/s–6.0
m/s 0.1608
6.6 m/s–7.1
m/s
0.1820
± 0.015
± 0.013
0.1649
0.152
0.023
0.1820±±0.017
0.015
0.1608± ±
0.013
0.1162
0.1649 ±±0.01
0.017 0.1122
0.152 ±±0.007
0.023
0.1162± ±
0.01
0.1122±±0.016
0.007
0.0935
0.004
0.0888
0.0935±±0.008
0.004
0.0888 ±±0.01
0.016
0.0832
0.0820
0.0832 ± 0.008
0.0820 ± 0.01
Table 5. Area under surface returns for various TIAB and surface wind speed values for Indian
Table 5.532
Area
Ocean,
nm.under surface returns for various TIAB and surface wind speed values for Indian Ocean,
532 nm.
Wind Speed
3.7 m/s–3.9
m/s
Wind Speed
−1 )
TIAB
(sr
0.012–0.0125
0.2315
± 0.01m/s
3.7 m/s–3.9
0.016–0.017
0.2048 ± 0.018
0.012–0.0125
0.2315 ± 0.01
0.022–0.024
0.1472 ± 0.026
0.016–0.017
0.2048 ± 0.018
0.028–0.031
0.0989
0.01
0.022–0.024
0.1472± ±
0.026
0.034–0.036
0.0835
±
0.009
0.028–0.031
0.0989 ± 0.01
0.034–0.036
0.0835 ± 0.009
TIAB (sr−1)
Wind Speed
4.4 m/s–4.6
m/s
Wind Speed
0.2092
± 0.02m/s
4.4 m/s–4.6
0.1801 ± 0.022
0.2092 ± 0.02
0.1173 ± 0.021
0.1801 ± 0.022
0.0871
0.017
0.1173± ±
0.021
0.0678
±
0.008
0.0871 ± 0.017
0.0678 ± 0.008
Wind Speed
5.1 Wind
m/s–5.3
m/s
Speed
0.1791
± 0.017
5.1 m/s–5.3
m/s
0.152 ± 0.018
0.1791 ± 0.017
0.1193 ± 0.008
0.152 ± 0.018
0.0778
0.014
0.1193± ±
0.008
0.0654
±
0.008
0.0778 ±
0.014
0.0654 ± 0.008
Wind Speed
Wind Speed
5.5 Wind
m/s–6.0
m/s
6.6
m/s–7.1
m/s
Speed
Wind
Speed
0.1538
± 0.016
± 0.008
5.5 m/s–6.0
m/s 0.1262
6.6 m/s–7.1
m/s
0.14 ± 0.015
0.121 ± 0.007
0.1538 ± 0.016
0.1262 ± 0.008
0.1036 ± 0.021
0.0755 ± 0.011
0.14 ± 0.015
0.121 ± 0.007
0.0688
0.1036 ±±0.01
0.021 0.0554
0.0755±±0.005
0.011
0.0594
0.008
0.0493
0.0688± ±
0.01
0.0554±±0.005
0.005
0.0594 ± 0.008
0.0493 ± 0.005
Remote Sens. 2016, 8, 1006
17 of 27
Table 6. Area under surface returns for various TIAB and surface wind speed values for Indian Ocean, 1064 nm.
TIAB (sr−1 )
0.012–0.0125
0.016–0.017
0.022–0.024
0.028–0.031
0.034–0.036
Wind Speed
Wind Speed
Wind Speed
Wind Speed
Wind Speed
3.7 m/s–3.9 m/s
4.4 m/s–4.6 m/s
5.1 m/s–5.3 m/s
5.5 m/s–6.0 m/s
6.6 m/s–7.1 m/s
0.2704 ± 0.022
0.2436 ± 0.029
0.187 ± 0.032
0.1273 ± 0.019
0.1134 ± 0.012
0.248 ± 0.034
0.228 ± 0.018
0.1462 ± 0.032
0.1133 ± 0.011
0.0928 ± 0.015
0.2223 ± 0.018
0.1945 ± 0.022
0.1398 ± 0.017
0.0963 ± 0.003
0.0878 ± 0.015
0.2147 ± 0.026
0.1885 ± 0.026
0.132 ± 0.023
0.0973 ± 0.016
0.0813 ± 0.009
0.158 ± 0.009
0.152 ± 0.011
0.0938 ± 0.011
0.0813 ± 0.008
0.067 ± 0.005
From the several tables and figures, it can be seen that the data binning increments yielded tightly
clustered areas for all groupings, the percent standard deviations for which ranged from a high of
~20% (one was as high as 23%) to a low of ~3%. For each channel/ocean region, the percent standard
deviation of the areas was less than 12% for more than half the groupings (anywhere from 52% to 68%).
The percentage of samples retained for the groupings was generally >~75%. The number of retained
samples was >~100 for over 70% of the groupings, with only four groupings having <~50 samples
(28 being the lowest). Thus, there were enough samples for good statistics in almost all cases.
No trends of note were exhibited in the area standard deviations insofar as retained sample size,
TIAB value and wind speed value. The estimated area statistics were found to be quite similar for both
channels and all three ocean regions. Here it important to emphasize that the area standard deviations
stem from a number contributions including (a) random signal noise; (b) temporal-spatial variability in
signals assigned to a given finite size bin (recall that signals in a bin are not necessarily contiguous in
space, time or stem from one aerosol type); (c) possible uncertainty in the wind speeds used to assign
signals to a given bin; and (d) any error in calibration normalized out of the attenuated backscatter
signals that were analyzed to obtain the areas. The fact noted above that the estimated area percent
standard deviation was <12% for the majority of the groupings is relevant in that it implies the same
fractional uncertainty (±0.12) for retrieving the aerosol round-trip transmittance, T2a (z), which in turn
implies half that uncertainty for retrieving the Aerosol Optical Depth (AOD), or ±0.06; there will be
more on this in a later sub-section. One would expect these uncertainties to be lower for a collection of
contiguous/nearly contiguous shots from a localized spatial region with constant wind speed and
fixed aerosol loading. To what extent such conditions may be met can be assessed by examining
the statistics of areas retrieved for individual shots and running mean areas for various averaging
intervals. Example retrievals along short orbit segments given later in the paper demonstrate that such
averaging over fairly homogeneous aerosol regions indeed yields significantly lower uncertainties in
the averaged AOD retrievals (although bias error may still be present).
3.3. Verification of Area Retrievals
The SR area retrievals presented in the previous sub-section were estimated by a fitting procedure,
described earlier in Section 2.5, wherein an assumed normalized impulse response curve was
positioned and fitted to the down-linked SR samples for each shot, the curve fit determining the
SR area for the shot. The individual estimated shot areas were grouped with areas for other shots
with nearly the same TIAB and wind speed and, after screening for outliers, the retained group areas
were averaged to obtain the estimated SR mean area for the group and associated standard deviation.
Alternatively, SR areas may be predicted by the derived analytic relation for ALPF given in Equation (5),
repeated here below with the round-trip transmission, T2λ (zs ), resolved into the aerosol, Rayleigh and
ozone components as was done in Equation (10).
ALPF =
2T2 (z)T2R (z)T2Ozone (z)Rλ
2T2λ (z)Rλ
= a
c
c
(13)
To predict ALPF from this analytic relation requires specification of Rλ , which can be computed
from the wind speed model and the wind speed data for a given shot in the CALIPSO data base, as
well as T2λ (zs ). The Rayleigh and ozone round-trip transmissions are fairly constant over oceans and
Remote Sens. 2016, 8, 1006
18 of 27
can be computed from the information in the CALIPSO data base, the product of which for 532 nm
is to a very close approximation T2R (zs ) × T2Ozone (zs ) = 0.798 × 0.96 = 0.76. The Rayleigh and ozone
attenuations for 1064 nm are quite small so that T2R (zs ) × T2Ozone (zs ) = ~1 is a reasonable approximation.
T2a (zs ) is generally unknown, but by selecting data for the aerosol free, clean atmospheres (for 532 nm
TIAB < 0.0125), it can be approximated as unity. Thus, for data with TIAB < 0.0125, ALPF may be
approximated for 532 nm as
ALPF =
2T2a × T2R × T2Ozone × R532
2 × 1 × 0.76 × R532
2T2 R532
=
=
c
c
c
(14)
2 × T2a × T2R × R1064
2T2 R1064
2 × 1 × 1 × R1064
=
=
c
c
c
(15)
and for 1064 nm as
ALPF =
Computing analytically predicted areas (APA) by these relations for the various wind speed bins
defined earlier (mean wind of each wind speed bin used to calculate Rλ ) and using the data-estimated
areas (DEA) presented earlier (e.g., Table 1) for these wind speed bins and TIAB < 0.0125, a comparison
may be made of the two sets of area determinations as shown in Table 7 for the Southern Pacific Ocean
data collection.
It can be seen that the ratios of DEA/APA are close to one and well within the DEA standard
deviations. Similar results were found for the Atlantic and Indian Ocean ratios as shown in Table 8
(The DEA bin values are not repeated, but can be found in Tables 3–6 nor are the APA bin values as
they are same for all oceans). Averaging the ratios over all wind speeds yields the results shown in
Tables 9 and 10.
Table 7. Comparing analytically predicted and data-estimated areas under surface returns for the
Southern Pacific oceanic region for clean atmospheric conditions.
Wind Speed
Analytically Predicted
Surface Return area
APA at 532 nm
Data-Estimated
Area DEA at
532 nm
Ratio
DEA/APA
for 532 nm
Analytically Predicted
Surface Return Area
APA at 1064 nm
Data-Estimated
Area DEA at
1064 nm
Ratio
DEA/APA
for 1064 nm
3.7 m/s–3.9 m/s
4.4 m/s–4.6 m/s
5.1 m/s–5.3 m/s
5.5 m/s–6.0 m/s
6.6 m/s–7.1 m/s
0.2334
0.1979
0.1747
0.1612
0.1380
0.2305 ± 0.027
0.1940 ± 0.017
0.1625 ± 0.012
0.1538 ± 0.013
0.1330 ± 0.013
0.9875
0.9802
0.9301
0.9539
0.9640
0.2891
0.2452
0.2164
0.1998
0.1710
0.2846 ± 0.026
0.2400 ± 0.023
0.2208 ± 0.018
0.1944 ± 0.013
0.1755 ± 0.019
0.9844
0.9787
1.0203
0.9729
1.026
Table 8. Ratios of analytically predicted and data-estimated areas under surface returns for the Atlantic
and Indian Ocean regions for clean atmospheric conditions.
Wind Speed
3.7 m/s–3.9 m/s
4.4 m/s–4.6 m/s
5.1 m/s–5.3 m/s
5.5 m/s–6.0 m/s
6.6 m/s–7.1 m/s
Ratio DEA/APA
for 532 nm
Ratio DEA/APA
for 1064 nm
Ratio DEA/APA
for 532 nm
Ratio DEA/APA
for 1064 nm
(Atlantic Ocean)
(Atlantic Ocean)
(Indian Ocean)
(Indian Ocean)
0.9640
1.0292
1.0675
0.8323
0.9299
0.9896
1.0346
1.1030
0.9109
0.9403
0.9918
1.0570
1.0251
0.9539
0.9147
0.9353
1.0114
1.0272
1.0745
0.9240
It can be seen for the 1064 nm channel that the ratios for all oceans are within 1% of unity, while
the results for the 532 nm channel fall within 4% of unity, indicating perhaps a slight bias off-set to
lower DEA values, although the ratios are generally within their standard deviations. Such a bias
could arise due to some aerosol contamination in the 532 nm signals assumed to be aerosol free for
TIAB < 0.0125, or if the impulse response assumed for the 532 nm channel was slightly different
than the actual impulse response for that channel, or possible error either in the lidar calibration
or the reflectance model/wind speed input to the model. No such bias is suggested for the
1064 nm channel, indicating an absence of any significant effect from lidar calibration error or the
reflectance model/wind speed input to the model having caused a bias (which would also affect
the 532 nm results, thereby seemingly removing these errors as the source of the 532 nm off-set). Hence,
Remote Sens. 2016, 8, 1006
19 of 27
the slight deviations from unity for either wavelength, being within there standard deviations, may
just stem from normally expected variability. All in all, the agreement between the data estimated
and analytically predicted areas is excellent, indicating corroboration of the technique and results
presented earlier for estimating the area of SR signals from the down-linked SR samples.
Table 9. Mean and standard deviation of DEA/APA ratios calculated over all wind speeds for each
oceanic region at 532 nm wavelength for clean atmospheric conditions.
Region
Mean Ratio (Overall Wind Speeds)
Standard Deviation
Southern Pacific
Atlantic
Indian
0.9631
0.9646
0.9885
0.0227
0.0915
0.0563
Table 10. Mean and standard deviation of DEA/APA ratios calculated over all wind speeds for each
oceanic region at 1064 nm wavelength for clean atmospheric conditions.
Region
Mean Ratio (Overall Wind Speeds)
Standard Deviation
Southern Pacific
Atlantic
Indian
0.9965
0.9957
0.9945
0.0017
0.0763
0.0637
3.4. Aerosol Retrievals
Rearranging Equation (13), T2a (zs ) is given by
T2a (zs ) =
cALPF
2Rλ T2R (zs )T2Ozone (zs )
(16)
Using the approximations given earlier for T2R (zs ) × T2Ozone (zs ), Equation (16) reduces, for both
wavelengths, to
cALPF
T2a (zs ) =
(17)
2 × R532 × 0.76
T2a (zs ) =
cALPF
2 × R1064
(18)
In turn, the aerosol optical depth (AOD), τa , is given by
τa = −
loge T2a (zs )
2
(19)
By differential analysis, the fractional uncertainty in T2a due to uncertainty in ALPF is
∆ T2a
∆ ALPF
=
2
ALPF
Ta
(20)
and the corresponding uncertainty in AOD is half that,
∆τa = −0.5 ×
∆ ALPF
ALPF
(21)
Example retrievals of T2a and AOD by Equations (16) and (19) applied to the ALPF retrievals
given earlier (Tables 1–6), for one wind speed bin (5.1–5.3 m/s) and two TIAB bins (0.016–0.017 and
0.028–0.031), for all three ocean regions, are given in Tables 11–13. Also given in the tables are retrievals
by an alternate method, called the High/Low method.
Remote Sens. 2016, 8, 1006
20 of 27
Table 11. Representative example retrievals of aerosol round-trip transmission and AOD for Southern Pacific Ocean region.
TIAB (sr−1 )
0.016–0.017
0.028–0.031
Ta 2
AOD
Ta 2
AOD
Ta 2
AOD
Ta 2
AOD
(532 nm,
High/Low Method)
(532 nm,
High/Low Method)
(532 nm,
Analytic Method)
(532 nm,
Analytic Method)
(1064 nm,
High/Low Method)
(1064 nm,
High/Low Method)
(1064 nm,
Analytic Method)
(1064 nm,
Analytic Method)
0.9281 ± 0.131
0.4832 ± 0.071
0.037 ± 0.07
0.364 ± 0.073
0.8558 ± 0.103
0.4456 ± 0.057
0.078 ± 0.0601
0.404 ± 0.0639
0.9357 ± 0.112
0.4348 ± 0.038
0.033 ± 0.059
0.416 ± 0.043
0.9654 ± 0.084
0.4486 ± 0.014
0.018 ± 0.043
0.401 ± 0.015
Table 12. Representative example retrievals of aerosol round-trip transmission and AOD for Atlantic Ocean region.
TIAB (sr−1 )
0.016–0.017
0.028–0.031
Ta 2
AOD
Ta 2
AOD
Ta 2
AOD
Ta 2
AOD
(532 nm,
High Low Method)
(532 nm,
High Low Method
(532 nm,
Analytic Method)
(532 nm,
Analytic Method)
(1064 nm,
High Low Method)
(1064 nm,
High Low Method
(1064 nm,
Analytic Method)
(1064 nm,
Analytic Method)
0.8500 ± 0.111
0.4343 ± 0.092
0.081 ± 0.065
0.417 ± 0.105
0.9043 ± 0.097
0.4621 ± 0.091
0.050 ± 0.053
0.386 ± 0.098
0.8412 ± 0.114
0.4055 ± 0.053
0.086 ± 0.067
0.451 ± 0.065
0.9383 ± 0.086
0.4523 ± 0.042
0.032 ± 0.045
0.397 ± 0.046
Table 13. Representative example retrievals of aerosol round-trip transmission and AOD for Indian Ocean region.
TIAB (sr−1 )
0.016–0.017
0.028–0.031
Ta 2
AOD
Ta 2
AOD
Ta 2
AOD
Ta 2
AOD
(532 nm,
High Low Method)
(532 nm,
High Low Method
(532 nm,
Analytic Method)
(532 nm,
Analytic Method)
(1064 nm,
High Low Method)
(1064 nm,
High Low Method
(1064 nm,
Analytic Method)
(1064 nm,
Analytic Method)
0.8487 ± 0.129
0.4344 ± 0.088
0.082 ± 0.075
0.417 ± 0.101
0.8672 ± 0.102
0.4439 ± 0.080
0.071 ± 0.058
0.406 ± 0.090
0.8749 ± 0.122
0.4332 ± 0.038
0.067 ± 0.064
0.418 ± 0.043
0.9089 ± 0.103
0.4500 ± 0.014
0.048 ± 0.056
0.399 ± 0.015
Remote Sens. 2016, 8, 1006
21 of 27
As the ratio of ALPF for two different TIAB values and the same wind speed equals the
corresponding ratio of T2a , the aerosol round-trip transmission for a high TIAB, T2a (high TIAB),
is given by
A (High TIAB)
T2a (High TIAB) = LPF
× T2a (Low TIAB)
(22)
ALPF (Low TIAB)
Selecting the low TIAB to be for the clean, aerosol-free atmosphere case (TIAB < 0.0125) for
which the aerosol round-trip transmission is approximated as unity, T2a (High TIAB) simply equals the
ratio ALPF (High TIAB)/ALPF (Clean Atmosphere). An advantage of the High/Low method is that it
eliminates the need for an accurate surface reflectance-wind speed model as the reflectance cancels
in the area ratio, although the standard deviation for the retrieved aerosol round-trip transmission is
generally a little higher than for the analytic method because the standard deviation of each of the
areas in the ratio must be taken into account. It can be seen from the tables that the T2a retrievals for
both methods agree well within their respective standard deviations (most within ~0.05) and the AODs
agree within ~0.05 (most within ~0.03). This, as with the results in Tables 9 and 10, again suggests that
errors in either the reflectance model/wind speed inputs to the model for determining the analytically
determined AODs or lidar calibration error (which could affect the High/Low determinations) were
not significant. The results for the other wind speed and TIAB bins are similar insofar as having about
the same variability/uncertainty in retrieved T2a and AOD. The AOD uncertainty is comparable to the
AOD retrievals for the lower TIAB (0.016 to 0.017), making it difficult to quantitatively interpret these
AOD, but the higher TIAB (0.028 to 0.031) AODs generally appear good enough to be quantitatively
useful. Examination of the AOD spectral ratio (532/1064) revealed that this ratio ranged from about
1.05 to 1.2, most being 1.1 or greater, which is within the range of the ratios for dust and marine aerosol
models (e.g., [15]). The CALIPSO browse images for the ~15 days and regions for the observations
investigated here revealed that the aerosols were mainly identified as marine aerosols.
Equations (16) and (19) were used to retrieve the AOD for a sample collection of ~50
nearly contiguous lidar shots for an orbit segment over the Atlantic Ocean. These shots were
for a 9 May 2011 segment between the lat-lon positions (−3.3 lat, −16.96 lon) and (−2.85 lat,
−16.86 lon), which corresponds to about ~75 shots, amongst which ~50 had detectable surface returns
(with 0.0125 < TIAB < 0.035). Figure 18 shows the per-shot retrievals of T2a and AOD for both
wavelengths, and the TIAB times 20 (to be on scale) is also shown. The correlation of TIAB with
AOD and anti-correlation with T2a is clearly evident. The mean AODs are about the same for both
wavelengths (0.155 for 532 nm and 0.148 for 1064 nm, each with a standard deviation uncertainty
of ±0.045). The AOD is fairly flat over the segment for 532 nm, but displays a slight rising trend
for 1064 nm. As such, averaging over several shots should reduce the per-shot AOD uncertainty
(~±0.05); averaging over six consecutive shots (2 km averaging) reduced the AOD uncertainty
to <±0.02 for the averaged AODs. The spectral ratio (1064/532) of T2a has a mean of ~1.01, ranging
from ~0.96 to ~1.12, while for AOD the mean spectral ratio is ~1.04, ranging from ~0.70 to ~1.15
(rather variable). Clearly, the mean spectral ratios are fairly neutral, and the mean AOD ratio is close to
the range that applies to dust and marine aerosols (e.g., [15]). Examining the CALIPSO browse image
for this segment revealed that the aerosols present were indeed mainly identified as marine aerosols.
Remote Sens. 2016, 8, 1006
Remote Sens. 2016, 8, x FOR PEER REVIEW
22 of 27
22 of 27
532 nm Channel
Aerosol Optical Depth
Round Transmission
TIAB x 20
1.2
1
Magnitude
0.8
0.6
0.4
0.2
0
-0.2
Lattitude
-3.2
-3.15
-3.1
-16.90
-16.91
Longitude -16.93
-3.05
-16.89
-3
-16.88
-2.95
-16.88
-2.9
-16.87
-2.85
-16.86
1064 nm Channel
Aerosol Optical Depth
Round Transmission
TIAB x 20
1.2
1
Magnitude
0.8
0.6
0.4
0.2
0
-0.2
Lattitude -3.25
Longitude -16.95
-3.2
-3.15
-3.1
-3.05
-16.93
-16.9
-16.89
-16.88
-3
-2.95
-2.9
-2.85
-16.87
-16.87
-16.87
-16.86
Figure 18.
18. Aerosol
Aerosolround-trip
round-triptransmission,
transmission,AOD
AOD
and
TIAB
each
retained
sample
point
for nm
532
Figure
and
TIAB
forfor
each
retained
sample
point
for 532
nm
and
1064
nm
channels.
and 1064 nm channels.
The spectral ratio of aerosol round-trip transmission is of further interest because it can be
The spectral ratio of aerosol round-trip transmission is of further interest because it can be
estimated directly from the spectral ratio of the A
without having to assume a particular wind
estimated directly from the spectral ratio of the ALPF without having to assume a particular wind
speed model, save accounting for the difference in Fresnel reflectance due to the ocean refractive
speed model, save accounting for the difference in Fresnel reflectance due to the ocean refractive index
index difference at the two wavelengths. From Equation (13), the spectral ratio (1064/532) of A ,
difference at the two wavelengths. From Equation (13), the spectral ratio (1064/532) of ALPF , using the
using the numerical estimates for the round-trip Rayleigh and ozone transmittances given earlier,
numerical estimates for the round-trip Rayleigh and ozone transmittances given earlier, reduces to
reduces to
T2T
ALPF
1 1 RR
A 1064
= = × ×1064 × × a2 1064
ALPF
0.76
TaT532
0.76 R532
A 532
R
(23)
(23)
Assuming the
thereflectances
reflectances
equal
at wavelength,
each wavelength,
except
for the refractive
index
Assuming
areare
equal
at each
except for
the refractive
index difference
difference
in the
Fresnel reflectances,
havingratio
a spectral
ratio(for
of ~1/1.06
1064
to 532),(23)
Equation
in
the Fresnel
reflectances,
having a spectral
of ~1/1.06
1064 to(for
532),
Equation
reduces(23)
to
reduces to
T2
T2
T2
ALPF 1064
1
R
1
1
A =
R × a 1064
T =
1×
1× aT1064 = 1.241 × Ta 1064
×1 1064
(24)
(24)
=
×2
=
×
×2
= 1.241 ×T2
A
0.76
R×
0.76 1.06
LPF 532
0.76 532R Ta 532
0.76 1.06 TaT532
A T
Ta 532
For
For the
the clean,
clean, aerosol-free
aerosol-free situation
situation (TIAB
(TIAB << 0.0125),
0.0125), the
the aerosol
aerosol transmission
transmission spectral
spectral ratio
ratio
reduces
reduces to unity and the A
ALPF spectral
spectral ratio
ratio is
is simply
simply 1.241.
1.241. Examining the A
ALPF values
values for
for 1064
1064 nm
nm
and
532
nm
given
earlier
in
Tables
1–6,
for
TIAB
<
0.0125
and
averaging
overall
wind
speeds
and
nm given earlier in Tables 1–6, for TIAB < 0.0125 and averaging overall wind speeds per
per
ocean
region,
yields
spectral
, of 1.281
1.283,and
1.281
andfor
1.248
ocean
region,
yields
meanmean
area area
spectral
ratios,ratios,
A ALPF
/A1064 /A,LPF
of 532
1.283,
1.248
the
for
the
Southern
Pacific
Ocean,
Atlantic
Ocean
and
Indian
Ocean,
respectively,
all
within
~3%
of
Southern Pacific Ocean, Atlantic Ocean and Indian Ocean, respectively, all within ~3% of the 1.241
the
1.241
value, substantiating
theofvalidity
of therelation
analytic
relation
given in(24).
Equation
(24).difference,
This ~3%
value,
substantiating
the validity
the analytic
given
in Equation
This ~3%
as with the ~4% difference noted regarding the 532 nm results in Table 7, could arise due to some
aerosol contamination or the assumed impulse response curve for the 532 nm channel being slightly
Remote Sens. 2016, 8, 1006
23 of 27
difference, as with the ~4% difference noted regarding the 532 nm results in Table 7, could arise due
to some aerosol contamination or the assumed impulse response curve for the 532 nm channel being
slightly different than the actual impulse response for that channel. Examining the ALPF spectral
ratios for all wind speed bins and for bins with TIAB > 0.0125 in Tables 1–6, shows that ~90% of
the T2a 1064 /T2a 532 ratios are >1, meaning AOD532 > AOD1064 almost always, and that these ratios are
bounded by ~0.80 < T2a 1064 /T2a 532 < ~1.2 (with ~70% being between 1.0 and 1.1). Note that retrieving
the spectral aerosol round-trip transmittance ratio does not yield the individual wavelength AODs, just
the difference, AOD532 − AOD1064 [8]. Nevertheless, if AOD can be retrieved at only one wavelength,
the other can be found knowing this difference, and knowing the difference could be a useful constraint
with other techniques for retrieving AOD or identifying aerosol types.
A final example of AOD retrieval along a CALIPSO orbit segment on 22 August 2010 is shown
in Figure 19 from combined CALIPSO and under-orbit airborne HSRL measurements during the
Caribbean Campaign [16] in August 2010. The NASA Langley airborne HSRL [17] can retrieve the
AOD at 532 nm directly by the high spectral resolution lidar (HSRL) technique, providing a truth
comparison with the lidar surface return AOD retrieval technique (HSRL uncertainty in AOD retrievals
given in Figure 19 is estimated to be <±0.005 based on HSRL retrieval comparisons with both airborne
sun-photometer and ground-based AERONET measurements [16], and this is the uncertainty obtained
by averaging the HSRL retrievals over the latitude range shown in Figure 19). The shot-by-shot
CALIOP AOD retrievals displayed some large spiking (8 of the ~120 shots in the segment), likely due
to pre-cloud/cloud-forming effects as is typical of the Caribbean and as seen in the CALIPSO browse
image for this segment (which also showed that the aerosol present was likely from an intrusion of
dust), so these were screened and a 15-shot (5 km) average was formed for the CALIPSO-derived curve
shown in the figure (yielding a standard deviation of ±0.015). The two retrieval curves track fairly well,
and their means agree within ~0.05. As CALIPSO passed over this surface segment within seconds,
while the HSRL aircraft took upwards of ~15 min to complete the segment, some spatial-temporal
variation between the curves could occur (perhaps as seen in the lat region between 13.9 to 14 degrees),
although results by Rogers et al. [16] indicate negligible difference should occur due to such a small
temporal mismatch. This preliminary result of the lidar surface return AOD retrieval technique being
capable of retrieving AOD within ~0.05 is regarded as a good start. It compares favorably with the
accuracy first reported by Josset et al. [18] for their retrieval approach using combined CALIPSO
and CloudSat ocean surface returns. It is also within the statistically determined difference between
CALIPSO-derived AODs, using assumed aerosol models, and HSRL-determined AODs (i.e., standard
deviation of CALIPSO model-derived AODs fell within the HSRL AOD determinations for 50% of
the comparisons), for many comparisons [16]. However, an additional point to note regarding this
comparison is that subsequent investigation of measurements made of flight hardware replicas of the
CALIOP detector and post-detection electronics [5], as well as on-orbit investigations of surface return
signals [6,7], when examined on a log scale revealed a slight after-pulsing tail on the measured 532 nm
impulse response (such after-pulsing is not uncommon in photomultiplier tube (PMT) detectors),
which, if included in the impulse response area integration, could bias ALPF higher and AOD lower.
Preliminary investigations to characterize and remove the tail effect by limiting the area determination
under the impulse response curve to about the first 400 nanoseconds after the pulse start yielded a
higher AOD determination of 0.125 [19], an AOD increase of 0.021 (or an ALPF area decrease of 4.2%),
which brings the tail-corrected AOD (0.125) to about 0.03 below the HSRL AOD retrieval of 0.158.
Another possible effect which can also bias the ALPF retrieval too high is a contribution from
backscattering in the water below the air-water interface. This effect was not assessed in the initially
submitted manuscript, but one of the authors (J. Reagan) was made aware of this possible area
contribution (by Chris Hostetler) during a visit to NASA Langley Research Center on 3 November
2016. While water is opaque to 1064 nm light, it is slightly transmissive/transparent at 532 nm,
although light at this wavelength is largely extinguished within a few tens of meters below the water
surface. To estimate the water backscattering area contribution, Aw , in a form directly comparable to
Remote Sens. 2016, 8, 1006
24 of 27
the water reflectance contribution, ALPF , a number of effects must be taken into account. First of all, the
total backscattering from the transmitted lidar pulse as it propagates downward in the water is given
Remote
2016,Total
8, x FOR
PEER REVIEW
24 ofz27
by theSens.
water
Integrated
Attenuated Backscatter, TIABw , for an integration in-water distance,
w,
from 0 at the surface to a distance below the surface where backscattering is effectively nil (a few 10 s of
distance,
zw, from the
0 atwater
the surface
to a distance
below the constant
surface where
backscattering
is effectively
meters). Treating
backscatter,
βw , as effectively
over the
short penetration
distance
nil
(a
few
10
s
of
meters).
Treating
the
water
backscatter,
β
w, as effectively constant over the short
and the water extinction as Sw βw , where Sw is the water extinction-to-backscatter ratio, TIABw reduces
penetration
distance
and the water extinction as Swβw, where Sw is the water
to simply 1/2S
w . As the propagation is in water, the speed of propagation is 2c/n; where n is the
extinction-to-backscatter
ratio,
TIABwofreduces
to simply
1/2Sw. Astimes
the propagation
is in water,
water refractive index (1.33),
a factor
2n/c should
be multiplied
TIABw , analogous
to the the
2/c
speed
of
propagation
is
2c/n;
where
n
is
the
water
refractive
index
(1.33),
a
factor
of
2n/c
should
be
term in Equation (5) for ALPF . A transmission loss occurs as the laser pulse transmits into water and
multiplied
TIAB
w, analogous to the 2/c term in Equation (5) for ALPF. A transmission loss
backscattertimes
exits the
water
because the air-water transmittance, Taw = (1 − R532 ), is <1, causing an
2
occurs
as
the
laser
pulse
transmits
into water
andthe
backscatter
exits transmittance,
the water because
air-water
additional loss (1 − R532 ) to be multiplied
times
air round-trip
T2 (zsthe
). Finally,
the
transmittance,
T
aw = (1 − R532), is <1, causing an additional loss (1 − R532)2 to be multiplied times the air
backscatter exiting water to air is refracted causing a beam-spreading effect that reduces the radiance
2 s). Finally,
2 . Hence,
round-trip
thethe
backscatter
exiting to
water
to air is lidar
refracted
causing
a
seen by thetransmittance,
lidar receiver T
by(z1/n
Aw contribution
the received
signal,
directly
2. Hence, the Aw
beam-spreading
effect
that
reduces
the
radiance
seen
by
the
lidar
receiver
by
1/n
comparable to ALPF in Equation (5), is given by
contribution to the received lidar signal, directly comparable to ALPF in Equation (5), is given by
2
2
2
2nT2 (zs ) ((1 −
)( R532 )) TIABW
( T )((zs ) (1) − R532 )
AW = A = =
,
(25)
=
,
(25)
ncSW
n2 c
w. The ratio of Aw over ALPF is then simply
including
including the
the result
result that
that TIAB
TIABwwevaluates
evaluatesto
to1/2S
1/2S
w . The ratio of Aw over ALPF is then simply
(1 − R )
A
(26)
= (1 − R532 )2
AAW = 2nS
R
(26)
ALPF
2nSW R532
Using water parameter values representative of relatively clean open ocean water as given by
−1·sr−1,ocean
Using[20]
water
representative
of relatively
water
as R
given
observation
site time (i.e.,
βw = ~3 × clean
10−4 mopen
Sw = 175
sr and
532 =
Churnside
andparameter
R532 for thevalues
−4 m−1 ·sr−1 ,
by Churnside
[20] (5)
and
R532a for
theof observation
site time
(i.e.,
=
~3
×
10
~0.03
sr−1), Equation
yields
value
~0.067 (indicating
a 6.7%
areaβenhancement
to
A
LPF
due
to
w
−
1
Sw = backscatter),
175 sr and Rindicating
sr AOD
), Equation
yields~0.034
a value
~0.067
(indicating
6.7% area
water
retrieval (5)
is biased
toooflow.
For the
assumedaparameter
532 = ~0.03the
enhancement
to ALPF due to water
backscatter),
indicating
the AOD
retrieval
is biased
~0.034 too
values,
the water-attenuated
backscatter
is reduced
effectively
to zero
(within
0.1%) within
twolow.
of
For
the
assumed
parameter
values,
the
water-attenuated
backscatter
is
reduced
effectively
to
zero
the 532 nm down-linked samples (within 45 m below the surface), meaning the Aw contribution is
(within 0.1%)
withinintwo
thesamples
532 nm determining
down-linkedAsamples
(within
below
surface),
effectively
captured
the of
same
LPF. Adding
both 45
themtail
effectthe
and
water
meaning the
Aw contribution
is =effectively
captured
in the sameAOD
samples
determining
.
Adding
backscatter
biases
(0.021 + 0.034
0.055) yields
a bias-corrected
(0.104
+ 0.055) of A
0.159,
almost
LPF
both theequal
tail effect
and
waterAOD
backscatter
biases
(0.021Allowing
+ 0.034 = for
0.055)
yields
a bias-corrected
exactly
to the
HSRL
retrieval
of 0.158.
even
a ±25%
variation inAOD
the
(0.104 + 0.055)
0.159,
exactly
equal
to the HSRL AOD retrieval
of 0.158.
Allowing for
even
estimated
0.055of
bias
(duealmost
to some
possible
variation/uncertainty
in the assumed
parameters)
yields
a
a ±25% variation
thethe
estimated
some still
possible
in the
bias-corrected
AODin in
range of0.055
0.145bias
to (due
0.173,towhich
falls variation/uncertainty
within the ±0.015 standard
assumed parameters)
yields
a bias-corrected
AODfor
in the
0.145 to 0.173,
stillvalue
falls within
deviation
estimated (from
the
15-shot averaging)
the range
initialof
CALIPSO
AOD which
retrieval
(0.104
±0.015
standard
estimated
(from the
averaging)
for the initial
AOD
±the
0.015).
Thus,
with deviation
bias correction,
the HSRL
and15-shot
CALIPSO
AOD retrievals
are CALIPSO
found to agree
retrieval
value
(0.104
±
0.015).
Thus,
with
bias
correction,
the
HSRL
and
CALIPSO
AOD
retrievals
are
within <±0.02.
found to agree within <±0.02.
HSRL Derived AOD = 0.158 ± 0.005
CALIPSO Derived AOD = 0.104 ± 0.015
Figure19.
19.Comparison
Comparisonof
ofCALIPSO
CALIPSOocean
oceansurface
surfacereturn
returnand
andairborne
airborneHSRL
HSRLAOD
AOD retrievals.
retrievals.
Figure
4. Conclusions
A technique has been presented and applied to numerous Cloud-Aerosol Lidar and Infrared
Pathfinder Satellite Observation (CALIPSO)/Cloud-Aerosol Lidar with Orthogonal Polarization
(CALIOP) observations for estimating from signal samples the normalized area, A , under the
Remote Sens. 2016, 8, 1006
25 of 27
4. Conclusions
A technique has been presented and applied to numerous Cloud-Aerosol Lidar and Infrared
Pathfinder Satellite Observation (CALIPSO)/Cloud-Aerosol Lidar with Orthogonal Polarization
(CALIOP) observations for estimating from signal samples the normalized area, ALPF , under the
received surface response from CALIOP-transmitted lidar pulses reflected from ocean surfaces.
An analytic relation for ALPF has also been developed which shows that this area is proportional
to the product of round-trip atmospheric transmission to the ocean surface, T2 (zs ), times the
ocean surface backscatter reflectance, Rλ . The total integrated attenuated backscatter down to the
ocean surface (TIAB), one of the CALIPSO data products, was demonstrated to be useful, along
with ocean reflectance, for binning the ALPF estimates into sub-groups with similar properties
and for demonstrating that the technique for estimating ALPF was in very good to excellent
agreement with the analytic prediction for clean, aerosol-free cases, defined by TIAB values <0.0125
(indicating T2a = ~1.0).
Groupings of ALPF defined by binning the areas in small increments of TIAB and wind speed
(which in turn defined Rλ increments using an assumed reflectance model) yielded tightly clustered
groups (majority of group ALPF having percent standard deviations within 12%) with similar statistics
for both wavelength channels (532 and 1064 nm) and all three ocean regions that were investigated.
Using Rλ predicted by the assumed ocean reflectance/wind speed model permitted retrieval of the
aerosol round-trip transmittance, T2a , from the group ALPF values, and, in turn, the aerosol optical
depth, AOD. As shown, the fractional uncertainty in the retrieved T2a due to uncertainty in ALPF
equaled the fractional uncertainty in ALPF , while the AOD uncertainty equaled half that. An alternate
High/Low method for retrieving T2a and AOD from ratios of ALPF for high and low TIABs, for the
same wind speed, was also presented and demonstrated to be in very good agreement with results
obtained by the analytic method. From the statistics for the retrieved ALPF , it was estimated that the
uncertainty in AOD retrievals from the group ALPF should be less than ±0.06 in the majority of cases.
Example AOD retrievals presented for two CALIPSO orbit track segments yielded similarly good
results with per-shot AOD standard deviations within ±0.05. With multi-shot spatial averaging over
a few km (2 to 5 km), the AOD retrieval uncertainty was reduced to <±0.02. One of the cases was
concurrent with an under-orbit flight with an HSRL lidar at 532 nm that provided an independent
AOD retrieval, and the means of the two 532 nm AOD retrievals were found to agree within 0.05,
seemingly too high to be really useful except in cases of high AOD. However, two bias effects
(PMT tail effect and underwater backscattering) were identified, both of which produce an
enhancement in the data-estimated ALPF . Applying bias corrections for both of these effects yielded
a bias-corrected CALIPSO AOD retrieval within 0.001 of the HSRL AOD retrieval. Allowing for
reasonable uncertainty, the bias corrections still yielded a corrected AOD agreeing with the HSRL
retrieval within ±0.015, which equals the uncertainty associated with the initial, uncorrected CALIPSO
AOD retrieval. Thus, with bias corrections, the technique presented appears capable of retrieving AODs
with an accuracy within ~±0.02 (corresponding to an error within ~±4% for the ALPF determination).
It should be noted that the retrieval results were for CALIPSO observations over a limited global
region (see Figure 14), and results might not be as good over other ocean regions; e.g., due to the lidar
calibrations perhaps being more uncertain in regions more poleward. But it should also be noted
that the analysis results for the regions investigated did not suggest any significant effect due to lidar
calibration error or error in the wind speed model/wind speed input to the model.
The spectral ratio of the aerosol round-trip transmission, T2a 1064 /T2a 532 , which can be determined
without need of a specific wind speed–reflectance model, was also demonstrated to be useful in
validating the expected ratio value for clean, aerosol-free conditions (TIAB < 0.0125), in retrieving the
difference in aerosol optical depths (AOD) between the two wavelengths (AOD532 − AOD1064 ), and in
providing a parameter potentially useful in aiding/constraining methods for typing aerosols. If AOD
is retrieved at both wavelengths, the resulting AOD spectral ratio provides a more direct parameter for
aiding aerosol typing. However, given AOD retrieved at just one wavelength, the retrieved spectral
Remote Sens. 2016, 8, 1006
26 of 27
ratio of the aerosol round-trip transmission (yielding AOD532 − AOD1064 ) can be used to obtain the
AOD at the other wavelength. AOD spectral ratios (532/1064) obtained for the area groups and one
of the orbit track segment retrieval examples (9 May 2011) yielded ratios close to/within the range
of ratios specified for marine and dust aerosol models (generally agreeing with the aerosol types
identified in the CALIPSO browse images).
The results of this investigation, although admittedly preliminary, argue strongly for
implementing the technique presented here to retrieve atmospheric AODs from CALIOP ocean
surface returns to form a CALIPSO database of global over ocean AOD at both 532 nm and 1064 nm.
Such a database would be valuable in itself for monitoring changes in aerosols over time, investigating
episodic aerosol events (e.g., dust and smoke layers) and in providing information useful in the
development of predictive models of aerosols and their effects on climate. The surface-derived AOD
retrievals at 532 nm and 1064 nm can also be used in combination with aerosol typing schemes presently
used in producing CALIPSO backscatter and extinction data products to further confirm and enhance
these products. The surface-derived spectral AOD information used in conjunction with CALIOP
dual-wavelength atmospheric attenuated backscatter should also aid in differentiating aerosol types,
or defining additional types, to obtain greater self-consistency between CALIOP profile retrievals and
the surface-derived AOD product. The results presented here indicate that AOD retrievals, with bias
corrections, may be accurate within ~±0.02, which is sufficient to be quite useful for most observed
AODs. To confirm the capability for achieving this level of accuracy, a number of things/effects
should be further investigated, particularly before using the technique to produce a CALIPSO global
over-ocean data product. These include: modifying the impulse response model to remove the PMT
tail effect bias; formulating a correction for the under-water backscattering bias on ALPF that is easy
to implement; investigating possible improvements in the water reflectance model and wind speed
estimates used in the model; formulating standard screening/saturated signal-rejection/multi-shot
averaging procedures to apply to the data; using improved CALIPSO data product versions (i.e., newly
issued version 4); confirming CALIPSO lidar calibration accuracies are sufficient to not significantly
bias AOD retrievals in other ocean regions (or flag retrievals in regions where the calibrations are too
uncertain), and testing the aforementioned on more CALIPSO data both within and outside the regions
investigated in this paper. That said, the results presented here are considered very encouraging
and warrant developing (along the lines suggested above) the presented AOD retrieval technique for
widespread application.
Acknowledgments: The authors gratefully acknowledge the support of the NASA CALIPSO Project and in
particular the Algorithm Development and Data Management teams at the Langley Research Center. Discussions
with and data provided by these teams, and in particular with Mark Vaughan, were a great benefit to accomplishing
the work reported here. Special thanks also to William Hunt for providing information and assessments,
and many useful discussions, of the results of lab tests made on flight hardware replicas of the CALIOP
detector/post-detection electronics. NASA funding in support of much of this work was provided by sub-contracts
through Science Systems and Applications, Inc. both to the University of Arizona and directly to the second author.
Author Contributions: The results presented in this paper, in principle, constitute the thesis submitted by
Srikanth Lolla Venkata (first author) as a part his master’s degree requirement at the University of Arizona.
John A Reagan (second author) conceived the title and acted as the thesis advisor. The methodology was
conceived and designed by both authors. The data collection was performed by Srikanth Lolla Venkata.
The data was analyzed by both of the authors, and John A Reagan wrote most of the paper, drawing heavily on
the information and results in Srikanth Lolla Venkata’s M.S. Thesis.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
2.
Hostetler, C.A.; Liu, Z.; Reagan, J.; Vaughan, M.; Winker, D.; Osborn, M.; Hunt, W.H.; Powell, K.A.; Trepte, C.
CALIOP Algorithm Theoretical Basis Document; PC-SCI-201, Release 1.0; National Aeronautics and Space
Administration (NASA): Washington, DC, USA, 2006.
Winker, D.M.; Vaughan, M.; Omar, A.; Hu, Y.; Powell, K.A. Overview of the CALIPSO mission and CALIOP
data processing algorithms. J. Atmos. Ocean. Technol. 2009, 26, 2310–2323. [CrossRef]
Remote Sens. 2016, 8, 1006
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
27 of 27
Winker, D.M.; Pelon, J.; Coakley, J.A.; Ackerman, S.A.; Charlson, R.J.; Colarco, P.R.; Flamant, P.; Fu, Q.;
Hoff, R.M.; Kittaka, C.; et al. The CALIPSO mission: A global 3D view of aerosols and clouds. Bull. Am.
Meteorol. Soc. 2010, 91, 1211–1229. [CrossRef]
Srikanth, L.V. Aerosol Retrievals from CALIPSO Lidar Ocean Surface Returns. Master’s Thesis,
University of Arizona, Tucson, AZ, USA, 2012.
Hunt, W.; NASA Langley Research Center, Langley, VA, USA. Personal communications, 2012–2014.
Hunt, W.H.; Winker, D.M.; Vaughan, M.; Powell, K.; Lucker, P.L.; Weimer, C. CALIPSO lidar description and
performance assessment. J. Atmos. Ocean. Technol. 2009, 26, 1214–1228. [CrossRef]
Hu, Y.; Vaughan, M.A.; Liu, Z.; Lin, B.; Yang, P.; Flittner, D.; Hunt, B.; Kuehn, R.; Huang, J.; Wu, D.; et al.
The depolarization-attenuated backscatter relation: CALIPSO lidar measurements vs. theory. Opt. Express
2007, 15, 5327–5332. [CrossRef] [PubMed]
Reagan, J.A.; Zielinskie, D.A. Space-borne lidar remote sensing techniques aided by surface returns.
Opt. Eng. 1991, 30, 96–102. [CrossRef]
Cox, C.; Munk, W. Measurement of the roughness of the sea surface from photographs of the sun’s glitter.
J. Opt. Soc. Am. 1954, 44, 838–850. [CrossRef]
Kodis, R.D. A note on the theory of scattering from an irregular surface. IEEE Trans. Antennas Propag. 1966,
14, 77–82. [CrossRef]
Barrick, D.E. Rough surface scattering based on the specular point theory. IEEE Trans. Antennas Propag. 1968,
14, 449–454. [CrossRef]
Menzies, R.T.; Tratt, D.M.; Hunt, W.H. Lidar in-space technology experiment measurements of sea surface
directional reflectance and the link to surface wind speed. Appl. Opt. 1998, 37, 5550–5559. [CrossRef]
[PubMed]
Lancaster, R.S.; Spinhirne, J.D.; Palm, S.P. Laser pulse reflectance of the ocean surface from the GLAS satellite
lidar. Geophys. Res. Lett. 2005, 32. [CrossRef]
Klein, M.V.; Furtak, T.E. Optics, 2nd ed.; John Wiley and Sons: New York, NY, USA, 1986; pp. 80–81.
Cattrall, C.; Reagan, J.; Thome, K.; Dubovik, O. Variability of aerosol and spectral lidar and backscatter and
extinction ratios of key aerosol types derived from selected aerosol robotic network locations. J. Geophys. Res.
2005, 110, D10S11. [CrossRef]
Rogers, R.R.; Vaughan, M.A.; Hostetler, C.A.; Burton, S.P.; Ferrare, R.A.; Young, S.A.; Hair, J.W.; Obland, M.D.;
Harper, D.B.; et al. Looking through the haze: Evaluating the CALIPSO level 2 aerosol optical depth using
airborne high spectral resolution lidar data. Atmos. Meas. Tech. 2014, 7, 4317–4340. [CrossRef]
Hair, J.W.; Hostetler, C.A.; Cook, A.L.; Harper, D.B.; Ferrare, R.A.; Mack, T.L.; Welch, W.; Izquierdo, L.R.;
Hovis, F.E. Airborne high spectral resolution lidar for profiling aerosol optical properties. Appl. Opt. 2008,
47, 6734–6752. [CrossRef] [PubMed]
Josset, D.; Pelon, J.; Protat, A.; Flamant, C. New approach to determine aerosol optical depth from combined
CALIPSO and CloudSat ocean surface echoes. Geophys. Res. Lett. 2008, 35. [CrossRef]
Guilmo, A.; Tyo, J.S.; Reagan, J. CALIOP high resolution IRF modeling based on in-situ observations
and application to AOD retrieval. In Presented at 2014 Fall AGU Meeting, San Francisco, CA, USA,
3–5 December 2014.
Churnside, J.H.; Sullivan, J.M.; Twardowski, M.S. Lidar extinction to backscatter ratio of the ocean.
Opt. Express 2014, 22, 18698–18706. [CrossRef] [PubMed]
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC-BY) license (http://creativecommons.org/licenses/by/4.0/).