AMT - Efficient multi-angle polarimetric inversion of aerosols and ocean color powered by a deep neural network forward model

AMT - Efficient multi-angle polarimetric inversion of aerosols and ocean color powered by a deep neural network forward model
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04 Jun 2021
Research article |
04 Jun 2021
Efficient multi-angle polarimetric inversion of aerosols and ocean color powered by a deep neural network forward model
Efficient multi-angle polarimetric inversion of aerosols and ocean color powered by a deep neural network forward model
Efficient multi-angle polarimetric inversion of aerosols and ocean color powered by a deep...
Meng Gao et al.
Meng Gao
Bryan A. Franz
Kirk Knobelspiesse
Peng-Wang Zhai
Vanderlei Martins
Sharon Burton
Brian Cairns
Richard Ferrare
Joel Gales
Otto Hasekamp
Yongxiang Hu
Amir Ibrahim
Brent McBride
Anin Puthukkudy
P. Jeremy Werdell
and
Xiaoguang Xu
Meng Gao
CORRESPONDING AUTHOR
meng.gao@nasa.gov
Ocean Ecology Laboratory – Code 616, NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
Science Systems and Applications, Inc., Greenbelt, MD, USA
Bryan A. Franz
Ocean Ecology Laboratory – Code 616, NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
Kirk Knobelspiesse
Ocean Ecology Laboratory – Code 616, NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
Peng-Wang Zhai
JCET and Physics Department, University of Maryland, Baltimore County, Baltimore, MD 21250, USA
Vanderlei Martins
JCET and Physics Department, University of Maryland, Baltimore County, Baltimore, MD 21250, USA
Sharon Burton
MS 475, NASA Langley Research Center, Hampton, VA 23681-2199, USA
Brian Cairns
NASA Goddard Institute for Space Studies, New York, NY 10025, USA
Richard Ferrare
MS 475, NASA Langley Research Center, Hampton, VA 23681-2199, USA
Joel Gales
Ocean Ecology Laboratory – Code 616, NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
Science Applications International Corp., Greenbelt, MD, USA
Otto Hasekamp
Netherlands Institute for Space Research (SRON, NWO-I), Utrecht, the Netherlands
Yongxiang Hu
MS 475, NASA Langley Research Center, Hampton, VA 23681-2199, USA
Amir Ibrahim
Ocean Ecology Laboratory – Code 616, NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
Science Systems and Applications, Inc., Greenbelt, MD, USA
Brent McBride
JCET and Physics Department, University of Maryland, Baltimore County, Baltimore, MD 21250, USA
Science Systems and Applications, Inc., Greenbelt, MD, USA
Anin Puthukkudy
JCET and Physics Department, University of Maryland, Baltimore County, Baltimore, MD 21250, USA
P. Jeremy Werdell
Ocean Ecology Laboratory – Code 616, NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
Xiaoguang Xu
JCET and Physics Department, University of Maryland, Baltimore County, Baltimore, MD 21250, USA
Abstract
NASA's Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission, scheduled for
launch in the timeframe of 2023, will carry a hyperspectral scanning
radiometer named the Ocean Color Instrument (OCI) and two multi-angle
polarimeters (MAPs): the UMBC Hyper-Angular Rainbow Polarimeter (HARP2) and the
SRON Spectro-Polarimeter for Planetary EXploration one (SPEXone). The MAP
measurements contain rich information on the microphysical properties of
aerosols and hydrosols and therefore can be used to retrieve accurate aerosol
properties for complex atmosphere and ocean systems. Most polarimetric aerosol
retrieval algorithms utilize vector radiative transfer models iteratively in
an optimization approach, which leads to high computational costs that limit
their usage in the operational processing of large data volumes acquired by
the MAP imagers. In this work, we propose a deep neural network (NN) forward
model to represent the radiative transfer simulation of coupled atmosphere and
ocean systems for applications to the HARP2 instrument and its
predecessors. Through the evaluation of synthetic datasets for AirHARP
(airborne version of HARP2), the NN model achieves a numerical accuracy
smaller than the instrument uncertainties, with a running time of
0.01
in a single CPU core or 1
ms
in a GPU. Using the NN as a
forward model, we built an efficient joint aerosol and ocean color retrieval
algorithm called FastMAPOL, evolved from the well-validated Multi-Angular
Polarimetric Ocean coLor (MAPOL) algorithm. Retrievals of aerosol properties
and water-leaving signals were conducted on both the synthetic data and the
AirHARP field measurements from the Aerosol Characterization from Polarimeter
and Lidar (ACEPOL) campaign in 2017. From the validation with the synthetic
data and the collocated High Spectral Resolution Lidar (HSRL) aerosol
products, we demonstrated that the aerosol microphysical properties and water-leaving signals can be retrieved efficiently and within acceptable
error. Comparing to the retrieval speed using a conventional radiative transfer
forward model, the computational acceleration is
10
times faster with CPU
or
10
times with GPU processors. The FastMAPOL algorithm can be used to
operationally process the large volume of polarimetric data acquired by PACE
and other future Earth-observing satellite missions with similar capabilities.
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Gao, M., Franz, B. A., Knobelspiesse, K., Zhai, P.-W., Martins, V., Burton, S., Cairns, B., Ferrare, R., Gales, J., Hasekamp, O., Hu, Y., Ibrahim, A., McBride, B., Puthukkudy, A., Werdell, P. J., and Xu, X.: Efficient multi-angle polarimetric inversion of aerosols and ocean color powered by a deep neural network forward model, Atmos. Meas. Tech., 14, 4083–4110, https://doi.org/10.5194/amt-14-4083-2021, 2021.
Received: 21 Dec 2020
Discussion started: 09 Feb 2021
Revised: 28 Apr 2021
Accepted: 30 Apr 2021
Published: 04 Jun 2021
Introduction
Atmospheric aerosols are tiny particles suspended in the
atmosphere, such as dust, sea salt, and volcanic ash, that play important
roles in air quality
Shiraiwa et al.
2017
Li et al.
2017
and Earth's climate
Boucher et al.
2013
. Aerosols influence the Earth's reflectivity directly
through scattering and absorption of solar light and indirectly through
interactions with clouds. The radiative forcing from aerosols is one of the
main uncertainties in studies of global climate change
Boucher et al.
2013
. When deposited into ocean waters, aerosols also
contribute to the availability of nutrients needed for phytoplankton growth
and thereby influence ocean ecosystems
Westberry et al.
2019
. Accurate
knowledge of aerosol optical properties is also important for atmospheric
correction in ocean color remote sensing, wherein the spectral water-leaving
radiances are retrieved by subtracting the contributions of the atmosphere and
ocean surface from the spaceborne or airborne measurements made at the top of
atmosphere
(TOA;
Mobley et al.
2016
. The resulting water-leaving signals provide
valuable information to derive biogeochemical quantities for monitoring the
global ocean ecosystem
Dierssen and Randolph
2013
and for quantifying ocean
biochemical processes
Platt et al.
2008
. Accurate assessments of aerosol
optical and microphysical properties are thus important for both atmospheric
and oceanic studies.
Multi-angle polarimeters (MAPs) measure polarized light at continuous or
discrete spectral bands and at multiple viewing angles, providing rich
information on aerosol optical and microphysical properties
Mishchenko and Travis
1997
Chowdhary et al.
2001
Hasekamp and Landgraf
2007
Knobelspiesse et al.
2012
. The
Polarization and Directionality of the Earth's Reflectances (POLDER) instrument
pioneered the spaceborne MAP, which was hosted on Advanced Earth Observing
Satellite missions (ADEOS-I; 1996–1997 and ADEOS-II; 2002–2003) and the
Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled
with Observations from a Lidar (PARASOL; 2004–2013) mission
Tanré et al.
2011
. The Hyper-Angular Rainbow Polarimeter (HARP) CubeSat, a
small satellite with 3U (10 cm
10 cm
30 cm) volume, was launched from the International Space
Station on February of 2020 and has captured scientific images
UMBC Earth and Space Institute
2021
. Several satellite missions
plan to carry MAP instruments, which are scheduled to be launched in the timeframe of 2023–2024, including the European Space Agency's (ESA) Multi-viewing
Multi-channel Multi-polarisation Imager (3MI) on board the MetOp-SG satellites
Fougnie et al.
2018
, the National Aeronautics and Space Administration's
(NASA) Multi-Angle Imager for Aerosols (MAIA)
Diner et al.
2018
, and
Plankton, Aerosol, Cloud, ocean Ecosystem (PACE)
Werdell et al.
2019
missions. A thorough review of the MAP instruments and algorithms can be
found in
Dubovik et al.
2019
The PACE mission will carry a hyperspectral scanning radiometer named the
Ocean Color Instrument (OCI) and two MAPs: a next-generation UMBC (University
of Maryland, Baltimore County) Hyper-Angular Rainbow Polarimeter (HARP2)
Martins et al.
2018
and the SRON (Netherlands Institute for Space
Research) Spectro-Polarimeter for Planetary EXploration one (SPEXone)
Hasekamp et al.
2019
. OCI will provide continuous spectral measurements
from the ultraviolet (340
nm
) to near-infrared (890
nm
) with
full width at half maximum of 5
nm
resolution and sampling every
2.5
nm
, plus a set of seven discrete shortwave infrared (SWIR) bands
centered at 940, 1038, 1250, 1378, 1615, 2130, and 2260
nm
. SPEXone
performs multi-angle measurements at five along-track viewing angles of
20
, and
58
, with a surface swath of
100
km
and a continuous spectral range spanning 385–770
nm
at resolutions of 2–3
nm
for intensity and 10–40
nm
for
polarization
Rietjens et al.
2019
. HARP2 is a wide field-of-view imager
that measures the polarized radiances at 440, 550, 670, and 870
nm
where the 670
nm
band will measure 60 viewing angles and the other
bands 10 viewing angles, with a swath of 1556
km
at nadir on the Earth's
surface. To facilitate cross calibrations and validations, a PACE Level-1C
common data format has been developed, with the purpose of projecting all
three PACE instruments onto an uniform spatial grid
Plankton, Aerosol, Cloud, ocean Ecosystem – PACE
2020
. The
PACE instruments will provide an unprecedented opportunity to improve the
characterization of the atmosphere and ocean states
Remer et al.
2019
Frouin et al.
2019
To retrieve the aerosol information from polarimetric measurements over
oceans, several advanced aerosol retrieval algorithms have been developed for
both airborne and spaceborne MAPs, such as
POLDER/PARASOL
Hasekamp et al.
2011
Dubovik et al.
2011
2014
Li et al.
2019
Hasekamp et al.
2019
Chen et al.
2020
, the Airborne Multiangle
SpectroPolarimetric Imager (AirMSPI)
Xu et al.
2016
2019
, SPEX
airborne (the airborne version of SPEXone)
Fu and Hasekamp
2018
Fu et al.
2020
Fan et al.
2019
, the Research Scanning Polarimeter
(RSP)
Chowdhary et al.
2005
Wu et al.
2015
Stamnes et al.
2018
Gao et al.
2018
2019
2020
, and the Directional Polarimetric Camera (DPC) on board Gaofen-5
Wang et al.
2014
Li et al.
2018
. The retrieval algorithms are mostly based on
iterative optimization approaches that utilize vector radiative transfer (RT)
models as the forward model. The high computational costs of the RT simulations
pose great challenges in the operational processing of the large data volumes
acquired by the MAP imagers. To alleviate this issue, the SPEX team
represented the polarimetric reflectance for an open-ocean system using a deep
neural network (NN) and coupled it with a radiative transfer model for the
atmosphere
Fan et al.
2019
. This hybrid forward model avoids the direct
calculation of the scattering and absorption properties inside the ocean and
still maintains high accuracy, therefore enabling sufficient efficiency for
SPEXone data retrieval. For coastal waters,
Mukherjee et al.
2020
developed
a NN model to predict the polarimetric reflectance associated with complex
water optical properties. This NN model can be combined with a flexible
atmosphere model for MAP aerosol retrievals over complex waters.
For non-polarimetric remote sensing studies, several NN approaches have been
developed to derive aerosol and ocean properties simultaneously
Fan et al.
2017
Shi et al.
2020
, and references therein).
Fan et al.
2017
developed NN models to directly invert the aerosol optical depth (AOD) and
remote sensing reflectance
rs
sr
−1
) from the NASA
Moderate Resolution Imaging Spectroradiometer (MODIS)
measurements.
Shi et al.
2020
developed a NN radiative transfer scheme for
coupled atmosphere and ocean systems including both open and coastal waters,
which is then applied in an optimal estimation algorithm for the Cloud and
Aerosol Imager-2 (CAI-2) hosted on the Greenhouse gases Observing Satellite-2
(GOSAT-2).
A number of NN models have been developed to directly invert the aerosol
microphysical properties from MAP measurements.
Di Noia et al.
2015
discusses the NN employed to retrieve aerosol refractive index, size, and
optical depth (AOD) from groundSPEX (a ground version of SPEX instrument)
measurements.
Di Noia et al.
2017
developed a NN inversion method for
airborne MAP measurement over land from RSP. In both works, the results from
the NN inversion are further used as initial values for iterative
optimization, and both efficiency and the retrieval accuracy are shown to be
improved. Using NN to conduct direct inversion is efficient, but it is often
viewed as a black box, and it is difficult to account for measurement
uncertainties. The combination of a NN inversion with an iterative
optimization method shows promise for MAP retrievals.
Even with such ample progress, it is still challenging for current
state-of-the-art algorithms to process MAP data operationally through
iterative optimization. In this work, we present a joint retrieval algorithm
for aerosol properties and water-leaving signals that uses a deep NN model to
replace the radiative transfer forward model for simulation of the
polarimetric reflectances. This approach is one step further than
Fan et al.
2019
, as both the atmospheric and oceanic radiative transfer
processes are represented by the NN. The NN forward model is then used in an
iterative retrieval algorithm that is significantly more computationally
efficient than approaches that use traditional radiative transfer. The
benefits of using a NN model as the forward model in retrieval algorithms can
be summarized as follows with details provided in later sections.
Fast.
NN models involve matrix operations that can be evaluated efficiently.
Accurate.
Given sufficient training data volumes and accuracies, NN models can be trained with high precision.
Differentiable.
The Jacobian matrix of NN models can be represented analytically and therefore further improves efficiency and accuracy in retrievals.
Transferable.
The parameters of a NN can be exported and implemented into existing retrieval algorithms.
The retrieval algorithm we developed is called FastMAPOL, which is evolved
from the well-validated Multi-Angular Polarimetric Ocean coLor (MAPOL)
algorithm
Gao et al.
2018
2019
2020
by replacing its forward
model with NN models. To validate the retrieval algorithm, we applied
FastMAPOL to both synthetic and field measurements from AirHARP (the airborne
version of HARP2 and HARP CubeSat) for the Aerosol Characterization from
Polarimeter and Lidar (ACEPOL) campaign in 2017
Knobelspiesse et al.
2020
. The synthetic AirHARP data are a supplement of
the field measurements with a wider range of aerosol and ocean optical
properties, as well as solar and viewing geometries. The AODs derived from coincident
High Spectral Resolution Lidar (HSRL,
Hair et al.
2008
) and Aerosol
Robotic Network (AERONET,
Holben et al.
1998
) measurements are used to
evaluate the performance of the AOD retrieval from the AirHARP field
measurements. Using the retrieved aerosol properties, atmospheric correction
is applied to the AirHARP measurements to derive the water-leaving signal at
four AirHARP bands. The retrieved aerosol products from MAP can also assist
hyperspectral atmospheric correction on instruments such as PACE OCI as
previously demonstrated using the aerosol properties retrieved from RSP and
hyperspectral measurements from SPEX airborne
Gao et al.
2020
Hannadige et al.
2021
. Retrieval uncertainties of both aerosol and water-leaving
signals under various aerosol loadings are also discussed in this study. The
retrieval algorithm powered by the NN forward model provides a practical
approach for operational applications of polarimetric aerosol and ocean color
retrieval for PACE, as well as other satellite missions that utilize polarimeters in
the retrieval of geophysical properties from Earth observations.
The paper is organized into seven sections: Sect. 2 reviews the retrieval
algorithm and its radiative transfer forward model, Sect. 3 discusses the
training and accuracy of the NN forward model, Sect. 4. applies the NN forward
model to aerosol and water-leaving signal retrievals from the synthetic
AirHARP data, Sect. 5. discusses the retrievals on AirHARP field measurements
from the ACEPOL campaign, and Sects. 6 and 7 provide discussions and conclusions.
Joint aerosol and ocean color retrieval algorithm
In this section, we will discuss the MAPOL retrieval algorithm based on
multi-angle polarimetric measurements and the associated radiative transfer
forward model. The retrieval algorithm has been validated using both synthetic
data
Gao et al.
2018
and RSP field measurements
Gao et al.
2019
2020
. To apply the retrieval algorithm to AirHARP measurements, we
will first discuss the AirHARP instrument characteristics.
AirHARP measures the total and linearly polarized radiance at 60 viewing
angles at the 660
nm
band and at 20 viewing angles at the 440, 550,
and 870
nm
bands. Different from AirHARP, HARP2 reduces the number of
viewing angles to 10 at 440, 550, and 870
nm
and maintains 20 viewing
angles at 660
nm
in order to fulfill the bandwidth requirement and
preserve information content as much as possible. HARP instruments (AirHARP,
HARP CubeSat, and HARP2) use a modified three-way Phillips prism located after the front lens to split the incident light into the three orthogonal linear
polarization states (0
, 45
, and 90
), which can be recombined to
obtain the Stokes parameters
, and
at the observational
altitude
Puthukkudy et al.
2020
. Circular polarization (Stokes parameter V)
is not measured by any of the polarimeters in ACEPOL as it is negligible for
atmospheric studies
Kawata
1978
. We use the total measured
reflectance (
) and degree of linear polarization (DoLP,
) at the height of
the aircraft with spectral dependencies hereafter implied, which are defined
as
(1)
(2)
where
is the extraterrestrial solar irradiance,
is the cosine of
the solar zenith angle, and
is the Sun–Earth distance correction factor in
astronomical units.
Based on the MAP measurements, the MAPOL retrieval algorithm is developed to
derive both the aerosol properties and the water-leaving signal
simultaneously. The retrieval algorithm minimizes the difference between the
MAP measurements and the forward model simulations computed from vector
radiative transfer simulations
Zhai et al.
2009
2010
. By assuming
the measurement and modeling uncertainties follow Gaussian statistical
distributions, the retrieval parameters can be estimated through Bayesian
theory using the cost function
to quantify the difference between the
measurement and the forward model simulation
Rogers
2000
(3)
where
and
are the measured reflectance and DoLP as defined in
Eqs. (
) and (
), and
and
are the corresponding quantities computed from the forward
model. The state vector
contains all retrieval
parameters, such as the aerosol size and refractive indices; the subscript
stands for the index of the measurements at different viewing angles and
wavelengths; and
is the total number of the measurements used in the
retrieval. For AirHARP measurements, the maximum value of
is 240, twice of the total number of viewing angles. The total uncertainties of the
reflectance and DoLP used in the algorithm are denoted as
and
, which are contributed by both the measurement uncertainties
and the forward model uncertainties
(more details in
Sect.
3.3
):
(4)
(5)
One important component of
is the calibration
uncertainty. AirHARP was calibrated in the lab with an accuracy of
–5
for reflectance and 0.005 for DoLP
McBride et al.
2019
. In-flight uncertainty for the AirHARP DoLP is
conservatively estimated to be at most 0.01 without an onboard calibrator. In
this study, we adopted the calibration uncertainty for reflectance as
cal
and for DoLP as
cal
0.01
for all four bands. The accuracy of the HARP2 measurements can be further improved through onboard
calibration
McBride et al.
2020
Puthukkudy et al.
2020
In this study, we considered the total measurement uncertainties as the contributions only from the calibration (
cal
):
(6)
cal
However, other contributions such as spatial variability of the geophysical
properties may also contribute to the measurement uncertainties, which will be
discussed in Sect.
. Furthermore, noise correlation is an
import influence on the retrieval accuracy
Knobelspiesse et al.
2012
that
is ignored in this study due to the lack of knowledge on this characteristic
for AirHARP.
As observed by AirHARP
Puthukkudy et al.
2020
and RSP measurements
Gao et al.
2020
, the sunglint angular pattern cannot be well modeled by an
isotropic Cox–Munk model. Using these data will require characterization of
the corresponding measurement and model uncertainties. To minimize the impact
of sunglint in our discussions, we removed the signals within an angle range
of 0
to 40
relative to the solar specular reflection direction.
The forward model uncertainties
include the
uncertainties of the radiative transfer calculation and uncertainties due to
the incompleteness of the model to describe the system. However, the latter are difficult to quantify; we will discuss the possible sources for them in the next section. For convenience, we will only consider the uncertainties of
the NN forward model (
NN
) and the radiative transfer
simulation used for generating the NN training data (
RT
) as
(7)
RT
NN
NN
is evaluated by comparing with synthetic multi-angle
AirHARP measurements discussed in Sect.
3.3
To fully utilize the information contained in the AirHARP measurements, the
forward model needs to achieve an accuracy level much better than the
measurement uncertainties. This becomes the goal of the NN training in the
next section. Detailed comparisons of the forward
model uncertainties and the measurement uncertainties will be provided in the
next section. To minimize the cost function defined in Eq.
),
we use an optimization method, called the subspace trust-region interior
reflective (STIR) approach
Branch et al.
1999
as implemented in the Python
SciPy package
Virtanen et al.
2020
, to solve the state parameters
iteratively. The method is based upon the Levenberg–Marquardt method
Moré
1978
and shows good stability for the boundary constraints.
2.1
Forward model
We used a vector radiative transfer model based on the successive order of
scattering method for coupled atmosphere and ocean systems
Zhai et al.
2009
2010
to model the measured reflectance and DoLP. The atmosphere is
configured as three layers: a top molecular layer above the aircraft, a
molecular layer below the aircraft in the middle, and an aerosol and molecular
mixing layer on the bottom with a height of 2
km
. Aerosols are assumed
to be uniformly distributed in the mixing layer as shown in the left panel of
Fig.
. The same
vertical structure of the atmosphere was successfully used in the inversion of
RSP data
Gao et al.
2019
2020
Figure 1
Panel
(a)
shows the coupled atmosphere and ocean system used in FastMAPOL including the atmosphere, ocean surface, and ocean body.
Panel
(b)
represents a system used for atmospheric correction which only has atmosphere and ocean surface without scattering in the ocean body. The atmospheres in both systems are modeled as the same three layers. TOA indicates the top of the atmosphere. The bottom of the atmosphere (BOA) and the top of the ocean (TOO) indicate the locations just above and below the ocean surface, respectively. All quantities shown in the figures need to be computed from the forward model and represented by the NN for efficient calculations. Symbols are defined in Table
The atmospheric surface pressure is assumed to be 1 atm (standard atmosphere pressure), which is consistent with the value discussed in Sect.
. Anisotropic molecular Rayleigh scatterings are
accounted for in
Hansen and Travis
1974
. The molecular absorption properties are
computed by the hyperspectral line-by-line atmospheric radiative transfer
simulator (ARTS)
Buehler et al.
2005
with the molecular absorption
parameters of oxygen, water vapor, methane, and carbon dioxide from the HITRAN
database
Gordon et al.
2017
. The gas absorption of ozone and nitrogen
dioxide are from
Gorshelev et al.
2014
Serdyuchenko et al.
2014
, and
Bogumil et al.
2003
, respectively. The hyperspectral absorption coefficients are
then averaged within the instrument spectral response function and used in the
multiple scattering radiative transfer simulation
Zhai et al.
2009
2010
2018
. The molecular profile used is the US standard
atmospheric constituent profiles
Anderson et al.
1986
. Ozone is the most
important gas that influences the absorption transmittance at the AirHARP
bands of 550 and 660
nm
. For the application to AirHARP measurements
in ACEPOL, we use the ozone column density as a free parameter with values
from the Modern-Era Retrospective analysis for Research and Applications,
Version 2 (MERRA-2) developed by NASA's Global Modeling and Assimilation
Office
Gelaro et al.
2017
to rescale the molecular absorption optical depth
calculated under the abovementioned standard atmospheric profile.
Aerosols are diverse in size, composition, and morphology. To capture their
variation in the atmosphere, we modeled the size and refractive index for both
fine and coarse modes. The aerosol size is represented by the volume density
distribution as a combination of five lognormal distributions:
(8)
ln
exp
ln
ln
where
is the column volume density for each submode; the mean radius
is fixed with values of 0.1, 0.1732,
0.3, 1.0, and 2.9
µm
; and the standard deviation
is fixed with values of 0.35, 0.35, 0.35, 0.5, and 0.5
Dubovik et al.
2006
Xu et al.
2016
. The first three submodes are categorized as
the fine-mode aerosol, while the last two submodes are the coarse mode. All
aerosols are assumed to be spherical in the current forward model. The
nonspherical particle shape is important in the aerosol model
Dubovik et al.
2006
and will be considered in future studies. The aerosol
refractive index spectra for the fine and coarse modes are represented by the
principal component analysis in MAPOL
Wu et al.
2015
Gao et al.
2018
as
(9)
where
is the first-order principal component computed from the
aerosol refractive index dataset including water, sea salt, dust-like
particles, biomass burning, soot, sulfate, water-soluble aerosols, and industrial
aerosols
Shettle and Fenn
1979
d'Almeida et al.
1991
and
are two
coefficients to determine the spectrum. For the application to AirHARP bands,
for the real part of the refractive index is approximately
spectrally flat for both the fine- and coarse-mode aerosols within the AirHARP
spectral range. We further assume the spectral shape for the imaginary
refractive spectra is also flat. Two parameters can be combined into one to
represent the refractive index. Hereafter, we only refer one independent
parameter for each refractive index spectrum. Therefore, only four
independent parameters are required to determine the real and imaginary
refractive index spectra for the fine and coarse modes. With the aerosol size
and refractive index, the polarimetric single scattering properties are
modeled by the Lorenz–Mie theory and computed by the code developed by
Mishchenko et al.
2002
For the ocean layer shown in Fig.
, two ocean bio-optical
models are implemented in the forward model of MAPOL: one with chlorophyll
concentration (Chl
mg m
−3
) as the single parameter applicable to
open-ocean optical properties and the other with seven parameters more
suitable to fully describe complex coastal waters
Gao et al.
2019
. Since
the waters are generally clear within the ocean scenes in this
study
Gao et al.
2020
, an open-ocean model is used for both NN training and
retrievals. The optical properties of open-ocean waters include contributions
from pure seawater, colored dissolved organic matter (CDOM), and
phytoplankton, where the CDOM and phytoplankton absorption coefficients as well as
the phytoplankton scattering coefficient and phase function are parameterized by
Chl
Gao et al.
2019
. A complex costal water model for NN trainings will
be investigated in separate studies. The ocean surface roughness
is modeled
by the isotropic Cox–Munk model with a scalar wind speed. Whitecap is not
considered in the current study.
In summary, the parameters used to represent the forward model include five
volume densities (one for each submode); four independent parameters for the
refractive indices of fine and coarse modes; and one parameter for wind speed,
ozone column density, and Chl
, respectively. Three additional geometric parameters are
used to set up the system, including the solar zenith angle, viewing zenith
angle, and relative viewing azimuth angle. Therefore, it requires a total of
15 parameters to conduct the radiative transfer calculation, with a total of
11 independent state parameters that can be retrieved from optimizing the cost
function as defined in Eq. (
).
2.2
Remote sensing reflectance
An important task for the joint retrievals is to obtain the water-leaving
signal, which is often represented in ocean color studies by the spectral
remote sensing reflectance defined as
rs
where
is the downwelling irradiance and
is the
water-leaving radiance just above the ocean surface
Mobley et al.
2016
. The
remote sensing reflectance can be derived from the water-leaving reflectance
reaching the sensor (
) via
(10)
rs
BRDF
where
and
are the solar and viewing zenith
angles, and
is the relative viewing azimuth
angle.
represents the signals originating from scattering
in the ocean that reached the sensor, which can be derived from the
atmospheric correction process as
(11)
atm
sfc
where
is the measured total reflectance as defined in
Eq. (
), and
atm
sfc
is the
reflectance from a system with only atmosphere and ocean surface
Mobley et al.
2016
as represented in the right panel of
Fig.
. The same formalism has been used to derive
rs
from RSP measurements
Gao et al.
2019
2020
Table 1
Definition of the symbols for the quantities computed from the forward model (indicated by the superscript f) as shown in Fig.
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The downwelling irradiance transmittance
is for
the solar irradiance from TOA to the surface, and the upwelling radiance
transmittance
is for the water-leaving
radiance from BOA to the sensor
Gao et al.
2019
. Both
and
are denoted
in Fig.
and represented as follows:
(12)
(13)
atm
sfc
atm
sfc
where
and
atm
sfc
are reflectance just above
ocean surface also denoted in Fig.
and
Table
To remove the dependency of
rs
on the solar and viewing
geometries, a bidirectional reflectance distribution function (BRDF) correction
BRDF
is applied to adjust
rs
to the observation with a zenith sun and a nadir viewing
direction as defined by
Morel et al.
2002
(14)
BRDF
accounts for reflection and refraction effects
when light propagates through the ocean interface. (
) is the direction of the upwelling radiance beneath the sea
surface, where
is defined through Snell's law:
(15)
sin
sin
with water refractive index
BRDF
in its
original form is defined using the radiance and irradiance just below the
ocean surface
Morel et al.
2002
; here we have converted all quantities into
the radiance reflectance
and the irradiance
transmittance
similar to
Eqs. (
) and (
12
).
To compute the remote sensing reflectance from the multi-angle AirHARP
measurement, we only consider the reflectance at the minimum viewing zenith
angle for each wavelength and apply the atmospheric correction and BRDF
correction as discussed above. For
15
20
), the
factor is approximately a constant value of 1, but for larger
angles, the ratio increases with both wind speed and
Morel and Gentili
1996
Morel et al.
2002
. In this study we
ignored the
factor in Eq. (
14
), which
will not impact
rs
calculation from synthetic data due to the
small viewing zenith angle used but may cause underestimation of
rs
at the edge of the image, as will be discussed in
Sects.
and
. All quantities denoted in
Fig.
and Table
need to be determined for the forward model and the
calculation of remote sensing reflectance and will be represented by NN
models.
Neural network for forward model
Deep NN models are developing rapidly due to the advancement in machine-learning infrastructure and demands in broad applications
Goodfellow et al.
2016
and are demonstrated to be efficient in
approximating physical functions
Lin et al.
2017
. In this study, we
employed the deep feed-forward NN
Goodfellow et al.
2016
to represent the
MAP measurements. In this section, we will discuss the procedures to train the
NN forward models for reflectance and DoLP respectively, with their
performance evaluated.
3.1
Training data
To train a NN that can represent the forward model accurately for the AirHARP
measurements from the ACEPOL field campaign, we generated the training data
according to the average aircraft height of 20.1
km
on the day of 23 October 2017 from ACEPOL. We simulated 21 000 cases according to the forward
model as discussed in the previous section by considering general aerosol and
ocean properties, as well as a large range of solar and viewing geometries
with the minimum and maximum values of all parameters summarized in
Table
. The ranges of solar zenith angle
, viewing
zenith angle
, and relative viewing azimuth angle
are from 0
to 70
, 60
and 180
, respectively. The reflectance and DoLP with a viewing azimuth angle larger
than
180
can be evaluated by the corresponding value less than
180
due to symmetry with respect to the principal plane (defined by
and
180
). For each
solar zenith angle, the polarized reflectance is calculated for all viewing
angles within the aforementioned ranges with an angular resolution of
. The solar zenith angle, ozone column density, refractive index,
and wind speed are randomly sampled from a uniform distribution. Chl
is
randomly sampled from a log-uniform distribution. The fine-mode volume
fraction is sampled uniformly within [0, 1], which is then randomly
partitioned to each submode. To maintain a uniform distribution of the total
AOD, we sampled the AOD at 550
nm
within [0, 0.5] in a linear
scale. The volume density
of each submode is determined by the total
aerosol optical depth and volume fraction for each mode.
Figure
shows one example simulation dataset for the angular distribution of reflectance and DoLP.
Table 2
Parameters used to represent the atmosphere and ocean system for the radiative transfer simulation and NN training.
and
are the solar and viewing zenith angles.
is the relative viewing azimuth angle.
denotes the five volume densities defined in Eq. (
).
and
are the real and imaginary parts of the refractive index. Ozone column density (
) in the atmosphere, ocean surface wind speed, and Chl
are also provided. The minimum
(min)
and maximum (max) values determine the parameter ranges used to generate NN training data, which are also the constraints in the retrieval algorithm. The initial values are the ones used
in the retrieval optimization algorithm, where
, and
are assumed to be known from inputs.
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Figure 2
The reflectance
(a)
and DoLP
(b)
from radiative transfer simulation with the wind speed of 4.13
m s
−1
, the aerosol optical depth of 0.26, Chl
of 0.05
mg m
−3
, and ozone column density of 196 DU. The antisolar point is indicated by the red asterisk with a solar zenith angle
46.41
and
indicate the viewing zenith and relative azimuth angles. The principal plane is defined by the viewing azimuth angle of 0
and 180
We randomly selected 20 000 cases out of the total 21 000 simulated cases
for the training and validation processes, and
the remaining 1000 random cases
will be used as test cases to evaluate the NN accuracy, which will be
discussed in the next section. To enable the NNs to predict reflectance and
DoLP at any given viewing geometry, for each case, we sampled 100 random pairs
of viewing zenith and azimuth angles. If the sampled angles fall outside of
the predefined angular grids, values from spline interpolation are used. The
sunglint angles within an angle of 40
to the solar specular
reflection direction are removed. Approximately 1 million data points are
obtained for each wavelength for training.
To maintain both flexibility and efficiency, we trained two NN models for
reflectance and DoLP respectively in the next section. Reflectance and DoLP
have different accuracy requirements as discussed in Sect.
and also differ in angular variations as shown in the Fig.
therefore, it is convenient to control their accuracy through separated
training procedures.
3.2
Neural network training
A feed-forward NN can be defined recursively with one input layer, one output layer, and
hidden layers
Aggarwal
2018
(16)
(17)
(18)
where
is the input parameter vector including all 15 parameters
needed to define the forward model as listed in Table
. Here
not only contains the retrieval parameters in the state vector
defined in Eq. (
) but also includes additional non-retrieval
parameters such as the solar zenith angle, viewing zenith and azimuth angles,
and the ozone column density.
is a four-dimensional output vector
for reflectance or DoLP at the four AirHARP bands. The weight matrix
+1
connects the
th and (
+1
)th NN layers. The bias vector
for the (
+1
) layer is defined as
+1
. The output of each
layer
+1
becomes the input of the next layer as shown in
Eq. (
17
).
is the number of hidden layers, and
+1
refers to the output
layer. In this study, we tested several NN architectures and eventually chose
three hidden layers with the number of nodes of 1024, 256, and 128 as shown in
Table
. The nonlinear activation function
used in this
model is the Leaky ReLU function, which is defined as
(19)
max
0.01
min
Both Leaky ReLU and ReLU (defined as
max
) activation functions are simple
in their mathematical forms and are tested in our NN trainings. Leaky ReLU is
eventually chosen due to its slightly better accuracy achieved than the NN
with ReLU.
Table 3
The accuracy of the NN for the corresponding quantities in terms of the RMSE (
NN
) of the difference between the NN-predicted values and the truth values from radiative transfer simulation. The NN architecture denotes the number of the nodes in each layer. The corresponding NN data sizes are indicated.
Remote sensing reflectance is computed by Eq. (
10
) using the NNs for
atm
sfc
and
BRDF
as discussed in Sect.
3.4
. (The percentage values listed below in the parenthesis are the percentage uncertainties defined as the RMSE of the percentage difference between the RT simulation and NN predictions.). n/a means not applicable.
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The training process is to minimize the cost function defined as the mean
square error between the training data generated from radiative transfer
simulations and the NN-predicted values
Aggarwal
2018
. All
parameters in the neural network weight matrices and bias vectors, over
670 000 numbers, need to be trained. With this large number of parameters, it
is a challenging task to avoid overfitting where the model works well for the
training dataset but poorly for the dataset not used in the training
process. Several training procedures are performed for reflectance and DoLP
data to avoid overfitting and improve NN performance.
Both input and output data are normalized before training. We normalize the input data into the range of [0, 1] using the minimum and maximum values from the datasets as listed in Table
. The reflectance and DoLP in the output layers are normalized by dividing their standard deviation of the training data at each wavelength.
The Adam (short for Adaptive Moment Estimation) optimization algorithm
Kingma and Ba
2015
with weight decay regularization
Loshchilov and Hutter
2019
is used to update the weights and bias of the NN.
The training dataset is divided into multiple mini-batches, each with 1024 random samples.
The training iterations loop through all mini-batches in the training data (each loop is called an epoch). Convergence requires training through multiple epochs, where mini-batches are resampled in each epoch.
The learning rate determines the step size in the parameter update. We use an exponential decay schedule to reduce the learning rate: we start with a learning rate of 0.005 and reduce the learning rate by a factor of 10 every 200 epochs.
To monitor overfitting in the training process, we split the data into 70
for training and 30
for validation. We conduct the optimization based on the training dataset, and in the meantime we monitor the performance of training by applying the NN model to the validation dataset. To avoid overfitting, the early-stopping approach is employed where the training is stopped when the cost function on the validation dataset stops to reduce for a threshold of 50 epochs.
The machine-learning Python library PyTorch is used for the training
Paszke et al.
2019
. The trained NN model is used to replace the radiative
transfer model to compute the reflectance and DoLP in the retrieval
algorithm. The Jacobian matrix used in the optimization is computed by the
finite difference approximation of the partial derivatives of reflectance and
DoLP with respect to the retrieval parameters. Here central difference method
is used. Note that the Jacobian matrix can also be computed analytically from
the NN model using the automatic differentiation techniques based on the chain
rule of differentiation
Baydin et al.
2018
. This will be a topic in our
future studies.
3.3
Neural network accuracy
After training the NN model, we evaluated its accuracy using synthetic AirHARP
measurements generated from the 1000 simulation cases which have not been used
in the training and validation process. Each simulation dataset includes
polarized reflectance on regular viewing angle grids, which are interpolated
to the viewing geometry of AirHARP to create synthetic measurement data and
compare with the NN predictions. Glint angles are excluded from the comparison
because the NNs are not trained over these angles. As the example shown in
Fig.
, both the reflectance and DoLP are in good agreement
between the synthetic data and the NN results, where the maximum absolute
differences for reflectance and DoLP are within 0.001 and 0.0025. This
translates to a difference for both reflectance and DoLP mostly less than
for bands 440, 550, and 670
nm
. The maximum percentage
difference can be as large as 3
for 870
nm
bands due to the
small reflectance magnitude.
Figure 3
The synthetic HARP reflectance
(a)
and DoLP
(b)
sampled from the radiative transfer data shown in Fig. 2. Panels
(c)
and
(d)
indicate the difference between the NN predictions and RT simulations. Panels
(e)
and
(f)
indicate their percentage differences. The positive and negative signs of the viewing
zenith angles indicate the azimuth angles of
116.2
and
180
Figure 4
Comparison between the radiative transfer simulation and NN prediction:
(a, c, e)
reflectance (
) and
(b, d, f)
DoLP (
).
The scatter plots are shown in panels
(a)
and
(b)
, the difference in panels
(c)
and
(d)
, and the percentage difference in panels
(e)
and
(f)
. For each plot, the data points for the 550, 660, and 870
nm
bands are shifted upward by constant offsets consecutively as indicated by the solid cyan lines.
The comparison with all 1000 synthetic datasets and their NN predictions are
shown in Fig.
. The mean absolute error (MAE) and the root
mean square error (RMSE) between the simulation data (
) and the NN-predicted data (
) shown in Fig.
are defined as
(20)
MAE
(21)
RMSE
Both MAE and RMSE are useful metrics, where MAE is less dependent on
outliers compared to RMSE.
Analysis shows that the statistics of the differences between the NN
prediction and the RT simulations as shown in Fig.
can be
well modeled by Gaussian distributions and characterized by RMSE. Therefore
the RMSE is used to represent the NN uncertainties for both reflectance
,NN
) and DoLP (
,NN
) and will be
incorporated into the total uncertainties in the cost
function. Table
summarizes the uncertainties of the NN models.
The
,NN
at 440
nm
is 0.0006, which decreases to
0.0004 at 870
nm
. However, due to the smaller reflectance magnitude at
870
nm
, the corresponding RMSE for the percentage reflectance
difference as shown in Fig.
is increased from 0.4
at 440
nm
to 1.0
at 870
nm
. For DoLP, the maximum
,NN
is 0.003 at 870
nm
, which decreases to 0.0016 at
440
nm
. The uncertainties can be further improved with more training
data points. For the readers' information, RMSE of the NN model trained with
20 000 cases (1 million data points) decreases by a factor of
in
comparison with the one using 10 000 cases (0.5 million data points). It
takes 0.01
in a single-core CPU (AMD EPYC processor) or 1
ms
in a GPU (GeForce GTX 1060) to predict all 120 angles for both reflectance and
DoLP in the NN forward model.
Furthermore, the data sizes for the NNs are minimal, which are 1.2 MB for the reflectance and DoLP and less than 100 KB for the factor
BRDF
(details in Sect.
3.4
as shown in Table
).
The assessment of the NN accuracy is relative to the synthetic measurements
simulated by the vector radiative transfer simulations. To account for the
modeling uncertainties of the forward model
, we consider
both the NN accuracy
NN
and the numerical accuracy of the
radiative transfer simulations
RT
for reflectance and DoLP,
respectively. Uncertainties due to incomplete assumptions in the forward model
are not considered. Several internal parameters determine the numerical
accuracy of the radiative transfer simulations. In the framework of the
successive order of scattering
Zhai et al.
2008
2009
, these
parameters include the number of scattering orders (
), the number of
Gaussian quadratures for discretizing the viewing zenith angle in the
atmosphere (
) and ocean (
), the order of Fourier decomposition
) for the viewing azimuth angle, and the order of Legendre expansion (
of the single scattering phase function. In this study, we chose
=20
=32
=64
=32
, and
=32
which has a higher accuracy than the
radiative transfer forward model directly used in our previous retrieval
studies
Gao et al.
2020
To quantify the accuracy of the radiative transfer calculation used for
generating training data (
RT
), we simulated an additional
1000 synthetic AirHARP datasets with all internal parameters doubled as the
most rigorous calculations, and the viewing angular resolution was reduced
from 1
to
0.5
in order to reduce interpolation
errors. The resultant reflectance and DoLP values are compared between these
two sets of radiative transfer calculations. The RMSE for each band can be
used as a measure of the accuracy for the radiative transfer calculation used
to generate the training data (
RT
). The uncertainties
RT
for reflectance and DoLP are summarized in
Table
, with reflectance uncertainties less than 0.00015 and
DoLP uncertainties less than 0.0007 for all AirHARP
bands.
,RT
is about 4 times smaller than the NN
uncertainties, and
,RT
is about 4 to 10 times smaller.
The measurement uncertainties from calibration (
cal
) are also summarized in Table
. The total forward model uncertainties
RT
NN
as in Eq. (
) are much smaller than
cal
. The overall uncertainties used in the retrieval cost function in Eq. (
) are dominated by the measurement contributions.
Table 4
Comparisons of the uncertainties for reflectance (
) and DoLP (
) for both measurement and forward model including calibration uncertainty (
cal
), the radiative transfer simulation uncertainty (
RT
), and the NN uncertainty (
NN
). The same
,NN
and
,NN
have been shown in Table
and are repeated here for comparisons. (As in Table
, the percentage values listed in the table indicate the percentage uncertainties.)
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Furthermore, in this study higher accuracies from the radiative transfer
simulations are used for the NN training for comparison with the accuracies
from the radiative transfer model directly used in our previous retrieval
algorithm. Since the simulations of the training data can be conducted
independent of the retrieval algorithm, higher computational costs can be
accommodated to improve NN forward model accuracy. After the NN model is
trained, the model can be applied to the retrieval algorithm through efficient
matrix operations.
3.4
Neural network model for remote sensing reflectance
As discussed in Sect.
2.2
, the water-leaving signals are represented
by the remote sensing reflectance as defined in Eq. (
10
Mobley et al.
2016
. To conduct the atmospheric correction in
Eq. (
11
), we need to determine the reflectance
atm
sfc
at the aircraft level, transmittance
and
, and the BRDF correction coefficient
BRDF
. Based on Eq. (
10
), we combined
, and
BRDF
into a single term denoted as
BRDF
. To efficiently determine
rs
, two NNs need to be trained to represent
atm
sfc
, and
BRDF
, respectively.
Following similar NN training schemes as discussed previously, we conducted
10 000 simulations to determine the reflectance at aircraft altitude
atm
sfc
from a system with only atmosphere and ocean surface
(right panel of Fig.
) and trained the NN for
atm
sfc
in the same way as
. Since this system only
includes the atmosphere and ocean surface but without the ocean body, there are a total of
14 input parameters (without Chl
). To train a NN for
BRDF
with
, and
BRDF
defined in Eqs. (
12
)–(
14
), we obtained five additional quantities corresponding to the
abovementioned 10 000 cases with and without ocean body: for the fully
coupled system with atmosphere, ocean surface, and ocean body (left panel of
Fig.
), we computed the reflectance just above and below the
ocean surface (
and
) and
irradiance transmittance just above and below the ocean surface
and
); for the
system without ocean body but with ocean surface (right panel of
Fig.
), we computed the reflectance just above the ocean
surface (
atm
sfc
). The accuracies of
the NNs for
atm
sfc
and
BRDF
are evaluated and shown in
Table
, which has an accuracy around 1
similar to
other quantities.
To evaluate the overall accuracy for the
rs
after the BRDF
correction, we conducted radiative transfer simulations with a zenith sun and
a nadir viewing direction and obtained the truth remote sensing reflectance
using the upwelling radiance and downwelling irradiance just above the ocean
surface as the examples shown in Fig.
. The predicted
rs
values
were computed from Eq. (
10
) after the application of two NNs. The
RMSEs of the difference between the simulated and NN-predicted
rs
are shown in Table
, with a maximum value of 0.0004 at wavelength
440
nm
and smaller than 0.0002 in other bands.
Figure 5
Comparison of the truth
rs
(RT) and the neural network (NN) computed
rs
. The truth
rs
is computed from radiative transfer simulations with a zenith sun and nadir viewing direction. The NN computed
rs
follows Eq. (
10
).
Joint retrieval results on synthetic AirHARP measurements
The NN forward models for reflectance (
) and DoLP
) are used in the FastMAPOL retrieval algorithm as
discussed in Sect.
. To evaluate the performance of the
retrieval algorithm, we conducted retrievals on the synthetic AirHARP
data. The creation of the synthetic data is discussed in
Sect.
3.3
. To account for the measurement uncertainties,
random noise is added to the simulated data according to the calibration
uncertainties as listed in Table
. The total uncertainties in
the cost function include contributions from calibration
cal
), radiative transfer simulation (
RT
),
and NN model (
NN
).
Using the initial values as listed in Table
, a total of 1000
synthetic AirHARP cases are retrieved with the cost function values (
summarized in Fig.
. Retrievals with
<1.5
are chosen
in our following discussion, which includes 96
of all retrieval
cases.
Gao et al.
2020
showed that the retrieval results depend on the
initial values. Testing with several random sets of initial values shows that
the statistics of the retrieval results from the 1000 synthetic cases are
robust. As demonstrated by
Di Noia et al.
2015
and
Di Noia et al.
2017
, a
better choice of initial values for each pixel in the optimization may further
improve the overall retrieval accuracy.
Figure 6
Histogram of the cost function values (
) with initial values as specified in Table 3 with a total of 1000 cases. The most probable
is 0.82.
A threshold of
<1.5
is used in the discussion.
Figure 7
The comparisons of the retrieved and truth values for total AOD (550
nm
), SSA (550
nm
), wind speed, and Chl
are shown in the top panels. The dashed line indicates the linear regression fitting with
, where
is the slope and
is the intercept. The lower panels show the difference between the retrieved and truth values of the corresponding upper panel parameters as a function of the total AOD at 550
nm
Figure 8
The comparisons of the retrieved and truth values for the fine-mode aerosol parameters including AOD, SSA, refractive index (
), and effective radius (
eff
) and variance (
eff
).
With the directly retrieved aerosol refractive index and volume densities (see
Table
) as inputs, the aerosol optical depth (AOD) and single
scattering albedo (SSA) for both the fine and coarse modes were computed
using additional NNs to represent the Lorenz–Mie calculations in
Appendix
. The retrieved total AOD, SSA, wind speed, and
Chl
are compared with the truth values as shown in
Fig.
. Total AOD indicates the summation of the fine- and
coarse-mode AODs, and total SSA is the ratio of the total scattering and
extinction cross sections; both are specified in Appendix
For fine aerosol, the AOD, SSA, refractive index (
), and effective
radius (
eff
) and variance (
eff
) are shown in
Fig.
. The color plots indicate the data point density
(normalized by its maximum value) approximated by a kernel density estimation
method
Silverman
1986
Figure 9
The retrieval uncertainties at various aerosol loadings for AOD, SSA, refractive index (
), effective radius (
eff
) and variance (
eff
), wind speed, and Chl
AOD values at the
axis from 0.1 to 0.5 indicate the five ranges of total
AOD including [0.01, 0.1], [0.1, 0.2], [0.2, 0.3], [0.3, 0.4], and [0.4, 0.5], which are used to compute the corresponding uncertainties.
Chl
uncertainties are evaluated in terms of MAE in log scale (see Eq.
22
), and all other parameters are evaluated in terms of RMSE.
AOD (%) indicates the percentage AOD uncertainties comparing to the truth AOD.
In order to quantify the variation of the retrieval uncertainties with respect
to different aerosol loadings, we computed the RMSE between the retrieved
and truth values at five AOD ranges including [0.01, 0.1], [0.1, 0.2],
[0.2, 0.3], [0.3, 0.4], and [0.4, 0.5]. Each AOD range includes
approximately 200 cases. Note that as discussed in Sect.
3.3
the total AOD and the fine-mode volume fraction are uniformly sampled for the
simulated data; therefore, there is an equal mixing fraction of fine- and
coarse-mode aerosol for each AOD range. The retrieval uncertainties for
aerosols are shown in Fig.
, with the
corresponding ranges indicated by AOD values from 0.1 to 0.5. All discussions
regarding the AOD and SSA are for a wavelength of 550
nm
in this
section.
As shown in Figs.
and
, the
errors of the retrieved total AOD increase with aerosol loadings: the
uncertainty (evaluated using RMSE) is 0.008 and 0.015 for the AOD range
[0.01, 0.1] and [0.1, 0.2] and increases to 0.035 for the AOD range
[0.4, 0.5]. Similar absolute uncertainties are found for both the fine- and
coarse-mode AODs, with a slightly smaller value. In percentage, the total AOD
uncertainties is 28.3
at the AOD range [0.01, 0.1], where the large
uncertainties are due to the cases with small AODs. For the AOD range from
[0.1, 0.2] to [0.4, 0.5], the AOD uncertainties further decrease from
14.4
to 5.6
Similar to the total AOD uncertainties, the total SSA uncertainties decreases
with AOD from 0.05 to 0.02. The fine-mode SSA uncertainties reduce similarly
from 0.05 to 0.03. The uncertainties for coarse-mode SSA reduces slightly from
0.1 to 0.08, which is more than twice as large as the fine-mode SSA
uncertainties. The uncertainties for the fine-mode
eff
, and
eff
show a larger value in the AOD bin of
[0.01, 0.1] of 0.06, 0.024
µm
, and 0.08 and then remain close to a constant at larger AOD ranges with a smaller value of 0.03, 0.01
µm
, and 0.03 respectively. The
averaged uncertainties for coarse-mode
eff
, and
eff
are approximately 0.08, 0.5
µm
, and 0.15 respectively with less AOD dependency at all AOD ranges. The coarse-mode
uncertainty is more than twice the fine-mode uncertainty. The larger
uncertainty values for coarse-mode
eff
and
eff
are
also related to their large particle size.
For wind speed retrievals as shown in Fig.
, the
agreements between the truth and retrievals depend strongly on the wind speed
value itself: when the wind speed is small, there is less retrieval
sensitivity due to the removal of glint; for a higher wind speed, the agreements
are improved, likely due to the larger range of angles influenced by wind
speed. The retrieval uncertainties are shown in
Fig.
; for a wind speed (WS) lower than
m s
−1
, the
uncertainty increases from 1.5 to 2.1
m s
−1
for AOD ranges from
[0.1, 0.2] to [0.4, 0.5]. For wind speed higher than 3
m s
−1
, the
averaged retrieval uncertainty is 1.2
m s
−1
with a small variation
of less than 0.1
m s
−1
The retrieved and truth Chl
is compared in Fig.
where the MAE in log scale is used with the definition
(22)
MAE(log)
10
where
log
10
log
10
where
and
denote the retrieval and truth values. MAE(log) is
recommended by
Seegers et al.
2018
as a better metric for Chl
, which
indicates the averaged ratio between the retrieval and truth values. The
dependency of the MAE(log) for Chl
with the aerosol loadings is shown in
Fig.
. The Chl
retrieval performance depends
on the magnitude of the Chl
. In this work, we chose four ranges of Chl
according to the trophic regions discussed in
Seegers et al.
2018
. Note
that Chl
from in situ measurements is typically larger than
0.01 mg m
−3
, and we chose a broader range of Chl
with its
minimum value of
0.001 mg m
−3
as listed in Table
for sensitivity studies. For
0.01
mg
Chl
0.1
mg
and
0.1
mg
Chl
mg
, Chl
retrieval uncertainties vary within 1.3 to 1.6
when AOD
0.3 and then increase to 2.3 at AOD range [0.4, 0.5]. For
Chl
mg
and
Chl
0.01
mg
, the uncertainties are generally larger, with a value
around 2 to 3.
With the retrieved aerosol and ocean properties, the atmospheric correction
procedures can be applied to compute the remote sensing reflectance as
discussed in Sect.
3.4
. The comparison of the retrieved
rs
with the truth data is shown in Fig.
. To account
for the various solar geometries, the BRDF correction has been applied to the
retrieved
rs
as discussed in Sect.
3.4
. Note that
the
factor will not impact the BRDF correction
in computing
rs
for the synthetic data, because of the small
viewing zenith angles used at the four AirHARP bands, which are
1.22
, 1.17
, 0.03
, and 3.52
respectively. The truth
rs
was computed with a zenith sun and a
nadir viewing direction, emphasizing the need for the latter correction to the
MAP observations. Overall
rs
uncertainties for the four bands are
0.007, 0.0004, 0.0002, and 0.0002 as shown by the RMSE in
Fig.
10
. MAE showed values of 0.0006, 0.0003, 0.0002, and
0.0001, which are less sensitive to outliers. Note that the atmospheric
correction is applied to the synthetic measurements without adding additional
random noise in order to evaluate the impacts on
rs
uncertainties
from only aerosol and ocean surface property retrievals. The retrieval
uncertainties for
rs
for each AirHARP bands are shown in
Fig.
10
depending on the aerosol loadings: larger
uncertainties are found with larger aerosol optical depth.
Figure 10
The difference between the retrieval and truth
rs
with respect to AOD.
The truth
rs
is computed with a zenith sun and a nadir viewing direction. The retrieved
rs
follows Eq. (
10
) with the BRDF correction considered.
RMSE and MAE are for all retrievals cases at each wavelength.
The PACE accuracy requirements on ocean color are specified in terms of the
water-leaving reflectance, which can be converted to those of
rs
by dividing them by a factor of
. The resultant requirements in terms of
rs
are 0.0006
sr
−1
or 5
from 400 to
600
nm
and 0.0002
sr
−1
or 10
from 600 to
710
nm
Werdell et al.
2019
. As shown in Fig.
11
rs
values at 550
nm
are within the requirement of
0.0006
sr
−1
for all AOD ranges. For the 440
nm
band, when AOD
is less than 0.3, the
rs
retrieval uncertainties are less than
0.0005
sr
−1
, but the uncertainties become as high as
0.001
sr
−1
at a larger AOD of 0.5.
rs
at 670 and
870
nm
varies in a very small dynamical range and is less impacted by
the aerosol retrievals.
rs
uncertainties at 670 and
870
nm
are slightly larger than the requirement of
0.0002
sr
−1
when AOD (550
nm
) is larger than 0.4 and 0.3
respectively. Further work is needed to understand how the uncertainties of
the retrieved aerosol properties influence the retrievals. Note that from
Table
, the uncertainties of the
rs
computed using
NNs have an uncertainty of 0.0004 to 0.0001 from 440 to 870
nm
, which
may be further minimized with better training and help to reduce the
rs
retrieval uncertainties.
Figure 11
Retrieval uncertainties for
rs
at the four AirHARP bands. The uncertainties are computed in the same way as for Fig.
in terms of RMSE.
Joint retrieval results on AirHARP measurements from ACEPOL
The ACEPOL field campaign, conducted from October to November of 2017,
included a total of six passive and active instruments on the NASA ER-2
high-altitude aircraft
Knobelspiesse et al.
2020
with four MAPs – AirHARP
McBride et al.
2020
, AirMSPI
Diner et al.
2013
, SPEX airborne
Smit et al.
2019
, and the RSP
Cairns et al.
1999
– and two lidars – HSRL-2
Burton et al.
2015
and CPL (the Cloud Physics Lidar)
McGill et al.
2002
. Aerosol retrieval algorithms have been applied for all
four MAPs
Fu et al.
2020
Puthukkudy et al.
2020
Gao et al.
2020
. The measurement
datasets are available from the ACEPOL data portal
Knobelspiesse et al.
2020
. In this work, we focus on the study of the
AirHARP measurements over ocean scenes as shown in Fig.
12
on
23 October 2017. The viewing angles are within
57
along the track
and
47
across the track as shown in the polar plots in
Fig.
12
. Figure
13
shows the RGB images (670, 550, and
440
nm
) for the three scenes at near-nadir viewing direction. AirHARP
conducted high-spatial-resolution measurements with a grid size of
55
and swath width of 42
km
at nadir (up to 60
km
at
far angles). We averaged the reflectance and DoLP respectively within a bin
box of
10×10
pixels (
550 m×550
).
Figure 12
The location of the three ocean scenes from AirHARP from ACEPOL on 23 October
2017. The flight track color shows the UTC time along the flight path. The aircraft flew at an
altitude of 20.1
km
. The viewing zenith and relative azimuth angle
(relative to the solar azimuth angle) for the 440
nm
band from all
pixels in the corresponding scene are shown in the bottom polar plots. The central portion of viewing angle plot is removed due to water condensation on the lens.
The averaged solar zenith angles for the three scenes are 47.0
, 45.6
, and 52.9
, respectively, as indicated in the polar plots by the red asterisks.
Figure 13
The RGB images (670, 550, and 440
nm
bands) for the three scenes at near-nadir viewing directions. Scene 1 and Scene 2 observe only ocean, while Scene 3 observes both ocean and land. Sparse thin clouds are visible from Scene 1 and Scene 2. Sunglint can be observed at the lower portion of the Scene 2 image.
The HSRL-2 instrument from ACEPOL provided useful aerosol optical depth ground
truth at 355 and 532
nm
Hair et al.
2008
Burton et al.
2016
, which was
used for the validation of the aerosol retrieval algorithm using the AirHARP
data. The HSRL-2 measures the pixels along the track as shown in
Fig.
12
, where an assumed lidar ratio of 40
sr
is
multiplied by the aerosol backscatter coefficient derived from the HSRL
technique to produce aerosol extinction and AOD at 532
nm
. For the
low-aerosol-loading cases considered in this study, the assumed lidar ratio
approach produces a systematic uncertainty of
±50 %
Fu et al.
2020
. In Scene 3, the aircraft also flew over an AERONET
USC_SEAPRISM site (33.564
N, 118.118
W) which is equipped
with a CIMEL-based system called the Sea-viewing Wide Field-of-view Sensor
(SeaWiFS) Photometer Revision for Incident Surface Measurements (SeaPRISM)
that collects radiances at eight wavelengths of 412, 443, 490, 532, 550, 667,
870, and 1020
nm
Zibordi et al.
2009
. AOD from the AERONET data
product version 3 level 2.0 data was used in this study, which is also
consistent with the HSRL-2 AOD at 532
nm
as shown latter in
Fig.
20
. The estimated AERONET AOD uncertainty is from 0.01 to
0.02, with the maximum uncertainty in the UV channels
Giles et al.
2019
. We
compared AOD from AirHARP retrievals with those from both HSRL and
AERONET. Furthermore, to validate the atmospheric correction procedure in the
retrieval algorithm, we compared the retrieved remote sensing reflectance with
the AERONET ocean color (OC) products as reported by the SeaPRISM measurements
at the USC_SEAPRISM site.
Table 5
The standard deviations of the reflectance (
,avg
) and DoLP (
,avg
) are calculated within a
10×10
pixel box and averaged over all angle and pixels from the three scenes (over ocean pixels only). The percentage values listed in the table indicate the percentage uncertainties.
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To assess the spatial variability of field measurement, we computed the
standard deviations for the reflectance (
,avg
) and DoLP
,avg
) within the bin box. Representative values are
provided in Table
. The values of
,avg
and
,avg
at the 870
nm
band
are 4.5
and 0.05, respectively, which suggest larger measurement
uncertainties at 870
nm
than other bands probably due to small
radiometric magnitudes. Meanwhile, our retrieval tests showed larger coarse-mode retrieval uncertainties than synthetic data results. To better constraint
retrievals, we assume the coarse-mode aerosol as sea salt by setting its
imaginary refractive index to zero. All other retrieval parameter ranges are
kept the same as in Table
Furthermore, we found our forward model cannot predict the angular variation of DoLP in the 440
nm
band well (with an estimated MAE of 0.04), which contributes a major portion to the cost function and increases both fine- and coarse-mode retrieval uncertainties. Therefore, we exclude DoLP in the 440
nm
band from our retrievals in this study.
Figure 14
The histograms of the cost function values over the three scenes as shown in Fig.
12
with total pixel numbers of 13 491, 13 226, and 9159. Only pixels over ocean are considered.
We conducted retrievals with similar procedures as discussed for synthetic
data. The solar and viewing geometries as shown in Fig.
12
and the
ozone column density (
) are assumed to be known inputs to the retrieval
algorithm. The averaged values of
from MERRA2 over each of
the three scenes are obtained, which are 277.5, 278.6, and 281.3 DU
respectively. The averaged surface pressures from MERRA2 over the three scenes
are 1.008, 1.006 and 1.003 atm, which is
consistent with our assumption in the atmosphere model as discussed in
Sect.
. The histograms of
for all pixels retrieved in
each scene are shown in Fig.
14
. The most probable
values
are 1.1, 1.7, and 1.1 respectively.
Figure 15
The number of viewing angles used in the retrieval (
), the cost function value (
), the retrieved AOD (550
nm
), and
rs
(550
nm
) for all pixels in Scene 1.
The HSRL AODs at 532
nm
are indicated by the colored dots in the AOD plot.
Figure 16
Same as Fig.
15
but for Scene 2.
For
rs
, viewing angles at least
40
away from the solar specular reflection direction are used to avoid sunglint as shown in Fig.
13
Figure 17
Same as Fig.
15
but for Scene 3. The pixels with large
are mostly influenced by the land (upper region) and island (lower left). The retrieved AOD and
rs
over land pixels are not shown. The location of the AERONET USC_SEAPRISM site is indicated by a red star symbol.
To evaluate the retrieval performance, we plotted the map of the total number
of viewing angles used in the retrieval (
), the cost function
, the retrieved AOD (550
nm
), and
rs
for each
scene in Figs.
15
17
. As discussed
in Sect.
, the maximum number of viewing angles is 120 for
AirHARP measurements. Figures
15
17
show the number of available viewing angles vary from 0 to 120
due to the removal of glint and other data quality control
measures. Discontinuity in the number of angles can be seen as a stripe, due
to the removal of angles influenced by water condensation on the lens, which
can also be observed in the polar plots in Fig.
12
with the nadir
region removed. All three figures show that the number of viewing angles are
smaller at the edges parallel to the flight track, where small
can be
achieved but may be less reliable.
For pixels with large
as shown in Fig.
14
, the
forward model cannot fit the measured reflectance or DoLP well, which may be
due to cloud contamination
Stap et al.
2015
, land, or residuals of
glint. In Scene 1, the top region with large
values is impacted by
the thin cloud which is visible from Fig.
13
. Larger residuals in
the 870
nm
band between
measurement and forward model are also
observed. The retrieved AOD are overestimated in this region. In Scene 2, the
region with
>3
correlates closely with the thin clouds
(Fig.
13
), which influence nearby AOD and
rs
retrievals. For Scene 3,
become larger than 2 when close to the
coast. This may be due to complex water properties which are not well
represented by the open-water bio-optical model used in the simulation
Gao et al.
2019
. The pixels near the coast are also potentially impacted by
the bottom effect and adjacency effect of land pixels.
Figure 18
Comparison of the retrieved AOD (550
nm
) from AirHARP measurement with the AOD (532
nm
) from HSRL for Scene 1 to 3. The AOD (550
nm
) from the AERONET USC_SeaPRISM site is shown in Scene 3. The AirHARP retrieved AOD is averaged with
4×4
pixels (
2.2 km×2.2 km
). The averaged AODs and their standard deviations for both AirHARP retrievals and HSRL products are provided in the text. Pixels with
>30
and
<10
are considered.
To compare with the HSRL AOD in the along-track direction, the retrieved AOD
(550
nm
) is averaged within a box of
4×4
pixels
(2.2
km
×2.2
km
). The averaged AOD (550
nm
values and the corresponding standard deviations are shown in
Fig.
18
. Pixels with
>30
and
<10
are
considered. The overall averaged AODs and their standard deviation are also
computed and indicated in the plots. The averaged HSRL AODs are 0.079, 0.071,
and 0.037 for Scene 1 to 3. The averaged retrieved AOD (550
nm
) are
0.096, 0.078, and 0.049, with relatively larger retrieval variation of 0.02 to
0.03. For Scene 1, most
values are larger than 2, while for the
other two scenes, more pixels are less than 2 except for those pixels very close to
cloud and coast. In Scene 1, the retrieved AOD is larger than that of the HSRL AOD by 0.03
in the overlapped region, which may be influenced by the remaining effect of
water condensation. In Scene 2, the peaks of the retrieved AOD values
correspond to the
values larger than 2, which are influenced by the
nearby thin cloud. There are no overlapped pixels except the ones associated
with high AOD peaks, but the general trend of the retrieved AOD agrees with the
HSRL results. For Scene 3, the retrieved AOD values agree well with the HSRL
AOD with an average difference of less than 0.01 and
mostly less than 2.
However when the pixels are close to the coast, both
and AOD
increased significantly as discussed previously.
Figure 19
Similar to Fig.
18
, the retrieved
rs
values are computed for the AirHARP band of 440, 550, and 670
nm
bands. The averaged
rs
and its standard deviation are shown in the legends. For Scene 3,
rs
values from the AERONET USC_SeaPRISM site at wavelengths corresponding to AirHARP bands are indicated by the star symbols.
Figure
19
shows the mean value and standard deviation of
rs
averaged in the same way as AOD discussed above. There is
similar spatial variation between the retrieved
rs
and
AOD. Pixels with large
rs
uncertainties are mostly associated
with the large AOD uncertainties shown in Fig.
18
. The
rs
values at 440
nm
for the three scenes are 0.0055,
0.0072, and 0.0030
sr
−1
, where the decrease in
rs
from
Scene 2 to Scene 3 may be due to the increase in CDOM close to the coast as
demonstrated in Fig.
. Moreover,
rs
values at Scene 1 are
likely to be underestimated due to the large
and retrieved AOD over
the center of Scene 1. The averaged
rs
values at 550
nm
remain approximately constant with a value of 0.0003
sr
−1
over all
three scenes.
rs
values from the AERONET USC_SeaPRISM site are indicated in
Scene 3 of Fig.
19
and also compared in
Fig.
20
. As discussed in Sect.
2.2
, we chose the
minimum viewing zenith angle available from the measurements after removing
the sunglint. The removal of sunglint improves the
rs
calculation for Scene 2
as shown in Fig.
16
. Moreover, we have ignored the
factor in Eq. (
14
), which may cause
underestimation of the
rs
at the edge of the image where
can reach as large as
60
. However it is
challenging to analyze its impact at large
angles.
has a strong dependency on wind speed,
but the retrieved wind speeds from current retrievals show large
uncertainties. Further work may require a better treatment of sunglint and
improved accuracy in wind speed.
Figure 20
Comparisons of the AOD and
rs
from AirHARP retrievals with AERONET products. The retrieval results are averaged with
4×4
pixels (
2.2 km×2.2 km
) around the AERONET USC_SeaPRISM site. This is similar to Figs.
18
and
19
, with error bars indicating the standard deviations, but only pixels with
<2
are considered.
The AERONET AOD and
rs
spectra are taken from 23 October 2017, with the error bars indicating daily variations. HSRL AOD at 532
nm
is also shown.
To better compare with AERONET results, we only considered the pixels with
<2
and conducted the same averaging (
4×4
pixels) around the
USC_SeaPRISM site for the retrieved AOD and
rs
. The averaged
values and their standard deviations are plotted in
Fig.
20
. The overall retrieved AOD spectrum is similar to
AERONET results with a difference smaller than 0.01. The results are similar
to the retrieval results from the Research Scanning Polarimeter as reported by
Gao et al.
2020
. The retrieved
rs
agrees well with the AERONET
rs
, with a difference of less than 0.001
sr
−1
. Note that
this study is done with a possible AirHARP measurement uncertainty of
in reflectance, which may impact the atmospheric correction
accuracy.
The complete retrieval results, including the aerosol microphysical
properties, wind speed, Chl
, and atmospheric-correction-related datasets,
are provided in the “Data availability” section. The retrieval uncertainties for aerosol
microphysical properties are relatively large due to the small aerosol optical
depths. Chl
retrievals are sensitive to the aerosol retrievals and are
more challenging to retrieve accurately at small values as discussed in
Sect.
Discussion
The NN model greatly improved the speed of the forward model used in the
iterative optimization approach and boosted the efficiency of the FastMAPOL
retrievals. The average retrieval speed for one pixel with FastMAPOL is
approximately 3
with a single CPU core, or approximately
0.3
with a GPU using the same hardware as mentioned in
Sect.
3.3
. Comparing to the retrieval speed of approximately
per pixel using conventional radiative transfer forward model, the
computational acceleration is
10
times faster with CPU or
10
times
with GPU processors. Meanwhile, the NN model maintains a high accuracy as
shown in Tables
and
. For retrieval algorithms
running the radiative transfer simulation, the accuracy is often tuned down to
reduce the simulation time. By training a NN, however, the high accuracy of the
radiative transfer model simulation can be achieved, as has been demonstrated
in this work. Thus, despite the one-time high computational costs in
generating the training datasets and conducting the training, the trained NN
can be applied efficiently to large observational datasets in the retrieval
algorithm.
In the retrieval of the AirHARP field measurement, each pixel has multiple
viewing angles that are aggregated from measurements at different times with
slightly different solar zenith angles. The NN used in FastMAPOL computes the
polarimetric measurement for specific solar zenith angles for each viewing
direction, and, therefore, the variation of the solar zenith angle can be
captured. These effects may be small for AirHARP measurement in ACEPOL, with a
maximum solar zenith angle difference within 0.6
. However, this
capability can help to minimize the impacts of the solar angle for HARP2 in
spaceborne measurements, which can reach to a maximum difference of
1.5
for HARP2 observations.
With the efficient retrievals from FastMAPOL, we have discussed the retrieval
performance and uncertainties for the aerosol properties, including AOD, SSA,
refractive index, and particle sizes. Since the AirHARP measurements share
many similar characteristics with HARP2 as planned for the PACE mission, the
knowledge from the retrieval analysis can help to understand the retrieval
performance for the HARP2 instrument in spaceborne measurements. Note that
HARP2 is likely to have higher accuracy due to the onboard calibration
capability and the potential to conduct cross calibration with the OCI
instrument. For the development of the NN forward model for spaceborne
measurements, similar training procedures can be applied with the sensor
altitude at the top of the atmosphere instead of the aircraft altitude used in
this study. Due to the impact of retrieval capability by geometry
Fougnie et al.
2020
, solar and viewing geometries according to the PACE
orbits need to be considered.
The water-leaving reflectance is obtained from the atmospheric correction
process using the aerosol and ocean properties retrieved from the AirHARP
measurements, and a similar procedure can be applied to future HARP2
retrievals. Since the hyperspectral OCI in PACE will provide high-accuracy
measurements, the retrieved information can be applied to OCI and therefore
assist hyperspectral atmosphere corrections as demonstrated by
Gao et al.
2020
and
Hannadige et al.
2021
. However, aerosol retrieval and
atmospheric correction are challenging in the UV spectral range
Remer et al.
2019
. For the ocean bio-optical model in this study, the water
properties are modeled as open-ocean waters parameterized by a single Chl
value. For complex coastal water, complex bio-optical models are preferred in
the retrieval of both accurate aerosol properties and water-leaving signals as
demonstrated by
Gao et al.
2019
Conclusions
We have demonstrated the application of a NN for highly accurate forward model
calculations of polarimetric measurements for AirHARP. Additional NN models
were used to conduct atmospheric correction. These models are used in the
FastMAPOL joint retrieval algorithm to conduct simultaneous aerosol property
and water-leaving signal retrieval. Applications to both the synthetic AirHARP
data and field measurements from ACEPOL are discussed. The uncertainties of
the retrieved aerosol properties and remote sensing reflectance are discussed
for different aerosol loadings. These results from AirHARP retrievals can help
to evaluate the retrieval capabilities for the HARP2 instrument on PACE. In
the application to field measurements from ACEPOL, the impacts of the number of
viewing angles and the value of cost function to the retrieval quality are
discussed. Further comparison with the HSRL and AERONET OC data shows good
performance in the retrieval of AOD and remote sensing
reflectance. Furthermore, the NN forward model and the associated retrieval
algorithm enable fast and practical retrievals of the polarimetric
measurement, thus making the algorithm practical for analysis of large data
volumes expected from spaceborne imagers such as HARP2. The experience and
methodology can be used to help the algorithm development of other satellite
instruments in polarimetric remote sensing.
Appendix A:
Neural networks for AOD and SSA
As summarized in Table
, we have discussed the NNs used to
represent the total reflectance (
) and DoLP
), which are then used as the forward model in the retrieval
algorithm. Using the retrieved aerosol parameters, NNs for
atm
sfc
and
BRDF
are used to compute
remote sensing reflectance. To expedite and simplify the calculation of
aerosol single scattering properties such as AOD and SSA as discussed in
Sect.
, we developed four additional NNs to represent the AOD and SSA for both fine and coarse modes, respectively. These NNs are
only used to analyze the retrieved aerosol properties and are not used in the
retrieval process. The NN architectures and accuracy are shown in
Table
A1
. The input parameters for the fine-mode SSA and AOD
are the three submode volume densities and the real and imaginary parts of
refractive index, with a total of five parameter. For coarse-mode aerosols, there
are a total of four parameters with only two submodes used. The outputs are the
AOD and SSA at the four AirHARP bands.
A total of 10 000 training data points are generated in the same way as in
Sect.
3.1
using the Lorenz–Mie code discussed in
Sect.
. The NN model accuracy is evaluated with an additional
1000 data points not used in the training. As shown in
Table
A1
, the accuracy is much smaller than the retrieval
uncertainties shown in Fig.
; therefore, the NNs
for AOD and SSA provide sufficient accuracy to evaluate the aerosol single
scattering properties.
Table A1
The accuracy of the NN for the corresponding quantities in terms of the RMSE (
) between the NN-predicted values and the truth values from the Lorenz–Mie calculations.
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With the fine- and coarse-mode AOD and SSA evaluated, the total AOD and SSA can
be derived. The total AOD (
) is the summation of the fine- and coarse-mode AODs as
(A1)
where
and
are the fine- and coarse-mode AODs.
The total (or averaged) SSA (
) is defined as the ratio of the total scattering cross section and the total extinction cross section for both fine and coarse modes, which can be computed as
(A2)
where
and
are the fine- and coarse-mode SSA.
Data availability
The data files for AirHARP and HSRL-2 used in this study are available from the ACEPOL website
ACEPOL Science Team
2017
). Complete retrieval results as well as data related to atmospheric correction from the three AirHARP scenes discussed in Sect.
are available from NASA Open Data Portal:
Gao
2021
Author contributions
MG, BAF, KK, and PWZ formulated
the original concept for this study.
MG developed the NN model and generated the scientific data. PWZ
developed the radiative transfer code. KK, PWZ, BC, OH, and YH advised
on the uncertainty model and retrieval algorithm. BAF, AI, and PJW
advised on the atmospheric correction. KK, AI, and YH advised on the NN
model. JG supported the parallel computing of the training data.
VM, XX, BM, and AP provided and advised on the AirHARP data. RF and SB
provided and advised on the HSRL-2 data. All authors participated in
reviewing and editing this paper.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
The authors would like to thank the ACEPOL science team for conducting the field campaign and providing the data, as well as the AERONET principal investigators and their teams for establishing and operating the USC_SEAPRISM site. We thank the NASA Ocean Biology Processing Group (OBPG) system team for support in high-performance computing (HPC) and the NASA Advanced Software Technologies Group (ASTG) for Python and machine-learning trainings. We appreciate the constructive discussions with Frederick Patt, Andy Sayer, and George Kattawar, as well as the valuable comments from Yingxi Shi and Reed Espinosa.
Meng Gao, Bryan A. Franz, Kirk Knobelspiesse, Brian Cairns, Amir Ibrahim, Joel Gales, and P. Jeremy Werdell have been supported by the NASA PACE project. Peng-Wang Zhai has been supported by NASA (grants 80NSSC18K0345 and 80NSSC20M0227). Funding for the ACEPOL field campaign came from NASA (ACE and CALIPSO missions) and SRON. Part of this work has been funded by the NWO/NSO project ACEPOL (project no. ALW-GO/16-09). The ACEPOL campaign has been supported by the Radiation Sciences Program.
Financial support
This research has been supported by the NASA PACE project, NASA (grant nos. 80NSSC18K0345 and 80NSSC20M0227), NASA (ACE and CALIPSO missions), SRON, NWO/NSO project ACEPOL (project no. ALW-GO/16-09), and the Radiation Sciences Program.
Review statement
This paper was edited by Alexander Kokhanovsky and reviewed by Yingxi Shi and Reed Espinosa.
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Articles
Abstract
Introduction
Joint aerosol and ocean color retrieval algorithm
Neural network for forward model
Joint retrieval results on synthetic AirHARP measurements
Joint retrieval results on AirHARP measurements from ACEPOL
Discussion
Conclusions
Appendix A:
Neural networks for AOD and SSA
Data availability
Author contributions
Competing interests
Acknowledgements
Financial support
Review statement
References
Article
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Short summary
Multi-angle polarimetric measurements can retrieve accurate aerosol properties over complex atmosphere and ocean systems; however, most retrieval algorithms require high computational costs. We propose a deep neural network (NN) forward model to represent the radiative transfer simulation of coupled atmosphere and ocean systems and then conduct simultaneous aerosol and ocean color retrievals on AirHARP measurements. The computational acceleration is 10
times with CPU or 10
times with GPU.
Multi-angle polarimetric measurements can retrieve accurate aerosol properties over complex...
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Sections
Abstract
Introduction
Joint aerosol and ocean color retrieval algorithm
Neural network for forward model
Joint retrieval results on synthetic AirHARP measurements
Joint retrieval results on AirHARP measurements from ACEPOL
Discussion
Conclusions
Appendix A:
Neural networks for AOD and SSA
Data availability
Author contributions
Competing interests
Acknowledgements
Financial support
Review statement
References