AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus GmbHGöttingen, Germany10.5194/amt-8-4295-2015A new method of measuring aerosol optical properties from digital
twilight photographsSaitoM.masanori@caos-a.geophys.tohoku.ac.jpIwabuchiH.https://orcid.org/0000-0002-9311-8598Center for Atmospheric and Oceanic Studies, Graduate
School of Science, Tohoku University, Aoba-ku, Sendai, Miyagi
980-8578, JapanM. Saito (masanori@caos-a.geophys.tohoku.ac.jp)14October20158104295431119October20146January201512September20155October2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://amt.copernicus.org/articles/8/4295/2015/amt-8-4295-2015.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/8/4295/2015/amt-8-4295-2015.pdf
An optimal-estimation algorithm for inferring aerosol optical properties
from digital twilight photographs is proposed. The sensitivity of
atmospheric components and surface characteristics to brightness and color
of twilight sky is investigated, and the results suggest that tropospheric
and stratospheric aerosol optical thickness (AOT) are sensitive to condition
of the twilight sky. The coarse–fine particle volume ratio is moderately
sensitive to the sky condition near the horizon under a clean-atmosphere
condition. A radiative transfer model that takes into account a
spherical-shell atmosphere, refraction, and multiple scattering is used as a
forward model. Error analysis shows that the tropospheric and stratospheric
AOT can be retrieved without significant bias. Comparisons with results from
other ground-based instruments exhibit reasonable agreement on AOT. A case
study suggests that the AOT retrieval method can be applied to atmospheric
conditions with varying aerosol vertical profiles and vertically
inhomogeneous species in the troposphere.
Introduction
Twilight sky, one of the most beautiful sights in our daily life, varies
from day to day. The color of the sky under clear-sky conditions gradates
from orange-red and salmon red near the horizon to blue-gray and blue at
zenith. This gradation results from Rayleigh scattering caused by molecules
(Minnaert, 1993). Twilight sky has been studied for more than a half
century, elucidating the effects of ozone and stratospheric aerosol on
twilight sky colors. As an example, ozone has the Chappuis band, an
absorption band with a peak wavelength of about 550 to 600 nm. Hulburt (1953)
simulated twilight sky brightness at zenith with a radiative transfer
model (RTM) based on the Rayleigh scattering theory and taking into account
ozone absorption. Hulburt's results showed that the contribution of ozone
absorption is more important than that of Rayleigh scattering in providing
the blue color at zenith. Lee et al. (2011) measured twilight sky in
Antarctica with a digital still camera to investigate ozone effects on
twilight sky at zenith and the anti-solar horizon, with the results
suggesting that scattering light by aerosols is as important as ozone
absorption in explaining the color of twilight. These results are consistent
with simulation results by Adams et al. (1974).
In 1963, Mt. Agung in Bali, Indonesia, erupted and injected a massive amount
of volcanic ash into the stratosphere. After the eruption, stratospheric
aerosol effects on twilight sky have been investigated by many researchers.
Volz (1964, 1965) suggested that a persistent purple light in the twilight
term seen during 1963 was caused by an increase of stratospheric aerosol as
a result of the eruption, using twilight sky measurements and geometrical
calculations to support this. Dave and Mateer (1968) demonstrated that
stratospheric aerosol was more important than ozone as a mechanism for
creating purple light, showing this by simulations with RTM taking into
account a spherical-shell atmosphere, dust, and ozone effects.
The general radiative transfer process for radiance at a large viewing
zenith angle (VZA) in the twilight sky is more complicated. Because of this,
the effects on twilight sky color near the horizon of atmospheric components
have not been investigated. To properly do so, an RTM must incorporate a
spherical-shell atmosphere, multiple scattering, and refraction effects.
Shaw (1981) investigated the dependence of stratospheric aerosol vertical
profiles on twilight sky at VZA of 70∘ by using a
single-scattering analytical RTM with a spherical-shell atmosphere.
Recently, an RTM for calculating spectral radiation according to a
complicated radiative transfer process has been developed (Iwabuchi and
Suzuki, 2009); this model achieves realistic simulation of twilight sky near
the horizon. Saito et al. (2013) showed that tropospheric aerosol optical
thickness (AOT) was sensitive to twilight sky brightness near the horizon by
analyzing photographic data and RTM simulations. Those results suggest that
multiply scattered light is dominant in twilight sky color and brightness
near the horizon.
Some researchers have tried to retrieve aerosol information from twilight
sky data. Wu and Lu (1988) developed a method to infer stratospheric aerosol
vertical profiles from twilight sky brightness and degree of polarization
measurements at a wavelength of 700 nm at zenith. Mateshvili et al. (2013)
developed a method that uses optimal estimation to infer the upper
tropospheric and stratospheric aerosol vertical profiles from spectral at
zenith during twilight, providing stratospheric AOT both pre- and
post-eruption of the volcano Nabro. Zerefos et al. (2014) tried to retrieve
AOT using a color ratio (R/G), given by digital counts in the red, green, and
blue (R, G, and B) channels, from digital photographs and digitalized
paintings drawn during the time around sunset in the past hundreds years.
The results agree well with other ground-based observations. The aerosol
information obtained from these twilight measurements was consistent with
that from other measurements, showing that twilight sky measurement is a
useful tool for gathering information on aerosols.
It is well known that tropospheric and stratospheric aerosol contributes to
climate change. The optical and radiative properties of aerosol can vary
strongly according to relative amount, chemical components, and particle
sizes. This results in high uncertainty of climate change prediction in
terms of radiation budget (IPCC, 2013). Aerosol measurement is carried out
with satellite- and ground-based instruments such as the MODerate-resolution
Imaging Spectroradiometer (MODIS) devices on-board the Terra and Aqua
satellites and the AErosol RObotic NETwork (AERONET) system. This provide on
solar and sky measurements (Remer et al., 2005; Holben et al., 1998).
However, most of the instruments useful for aerosol measurement require
passive remote-sensing techniques, meaning that these instruments cannot
infer aerosol properties in regions without direct sunlight. In addition,
satellite-based instruments with passive sensors cannot infer aerosol
properties in deserts and snow-covered regions because of high surface
reflectivity. Particularly in the polar region during winter, aerosol
measurements and their data are very limited because of the length of the
polar twilight (sunless condition in all day). In the region, a few
measurements are carried out by active remote-sensing techniques, in situ
sampling, and difficult aerosol measurements that use direct light from the
moon and stars as a substitute for direct sunlight transmittance methods
(Herber et al., 2002; Berkoff et al., 2011).
Recently, digital cameras have begun being used as measurement instruments
(e.g., Lee and Andres, 2003; Lee et al., 2011). Ehrlich et al. (2012)
provided a method for constructing a bi-directional reflectance distribution
function for cloud from data obtained by a digital single-lens reflex (DSLR)
camera installed on an airplane. Kataoka et al. (2013) developed a method
for estimating the altitude of visible aurorae from data obtained by a pair
of DSLR cameras. Hioki and Iwabuchi (2014) demonstrated a method to find the
particle radius of pollen and its column number density from a solar corona
image taken with a digital still camera. A two-dimensional brightness
distribution can be obtained by digital camera, an ability that is likely to
be useful in many scientific fields. The aim of the present study is to
infer aerosol optical properties, such as tropospheric and stratospheric AOT
and particle size information, from twilight photographs taken with a DSLR
camera. This paper is organized into six sections. Section 2 presents the
photographic measurement and camera characteristics. Section 3 shows the
forward model and the tests to determine the sensitivity of aerosol optical
properties to twilight sky. In Sect. 4, the method of aerosol retrieval
and the error analysis are explained. Section 5 discusses the retrieval
results and presents some case studies. The results are compared with those
inferred from other ground- and satellite-based instruments. Section 6
summarizes the study and discusses a few points of interest from the
retrieval results.
Camera equipment characteristics.
EquipmentPeriod of observationCoordinatesISOf-stopNikon D7000 equippedJan 2013–Sendai, Japan200f2.8with a fisheye lensAug 2014(38∘15′ N, 140∘50′ E)Measurements from a digital camera
The instrument for photographic observations in twilight was a Nikon D7000
DSLR camera equipped with a Nikkor equisolid angle-type full-frame fisheye
lens (AF DX Fisheye-Nikkor, 10.5 mm f/2.8G ED). The camera configuration
simulated an International Organization for Standardization (ISO) film speed
of 200 and had an aperture of f2.8. These values were set low enough to
reduce complementary metal oxide semiconductor (CMOS) noise and to gain high
exposure, even in the dark conditions of twilight. The camera was fixed on a
tripod. Table 1 summarizes the measurement setup and the camera
characteristics. Photographic observations of twilight sky have been carried
out at the Graduate School of Science, Tohoku University (38.26 ∘N,
140.84 ∘E; 208 m elevation), Sendai, Japan, since January 2013.
Various instruments for aerosol measurements are collocated at the site.
These include a Mie scattering lidar system operated by the National
Institute for Environmental Studies, a sky radiometer operated by SKYNET and
a sun photometer (PREDE PGS-100) originally managed by Tohoku University
(Shimizu et al., 2010; Takamura and Nakajima, 2004). The twilight
observation criteria are (1) the absence of clouds at the zenith during the
twilight, measured by the Mie scattering lidar, and (2) the absence of
clouds over a 200 km area on the solar side of the observation site,
measured by infrared imagery from the Multifunctional Transport Satellite
(MTSAT), a geostationary meteorological satellite. Table 2 describes the
VZAs, solar zenith angles (SZAs), and relative azimuth angles (RAAs). The
RAAs are the differential angle between the viewing azimuth and the solar
azimuth for data used in aerosol retrievals derived from photographic
observations. The measurements are carried out for an SZA ranging from
90 to 96∘ in intervals of 1∘. The camera
exposure time is changed according to SZA so as to be suitable for imaging.
To obtain the color and brightness distribution of a twilight sky from a RAW
image file, we first extract the digital numbers for the three spectral
channels (RGB) in groups of 12×6 pixels at corresponding angles
(see Table 2 for details). After that, the averaged digital counts for each
channel are used to eliminate pixel-level CMOS noise. The RAW format data
provide a wider dynamic range than the 8-bit JPG format does, which is
sufficient to provide brightness information. To read the Nikon D7000
manufacturer-specific RAW format (for the Nikon D7000 the exact format is
NEF), we employed the useful open-source tool DCRAW. DCRAW has been
described in Ehrlich et al. (2012). Figure 1 shows twilight photographs
taken under typical atmospheric conditions.
Viewing and solar directions used for aerosol retrievals.
An example of a twilight sky photograph taken on 23 March 2012 in the morning.
The color matching functions (CMFs) of the camera for each RGB channels were
determined at the National Institute of Polar Research (NIPR) to quantify
the spectral radiation from the digital numbers. The details of the method
for determining the CMF for a specific camera are given in Saito et al. (2015).
This paper briefly describes the methods. The experiment setup is
described in detail in Sigernes et al. (2008). The camera and
spectroradiometer detect narrowband (i) light in visible wavelengths of
380–740 nm at intervals of 5 nm, which are separated by a grating
monochromator, obtaining camera RAW counts u′k,i and the corresponding
spectral radiance Ii(λ). The camera spectral channels and
wavelengths are defined as k and λ, respectively. To enable
comparison between the values, the values of u′k,i are normalized by the
photon flux density convert radiance-proportional RAW counts uk,i and
uk,i, which can be defined as
uk,i=∫0∞Sk(λ)Ii(λ)dλ,
where the function Sk(λ) is the relative CMF. The optimal-estimation-based inverse calculation is applied to Eq. (1), yielding
determining Sk(λ) with some associated uncertainty. In this
experiment, the same camera configurations are used for all photographic
observations, and an exposure time of 8 s is used. The CMFs for the Nikon
D200, as determined by Sigarnes et al. (2008), are used as prior
information. The vignetting characteristics of the fisheye lens have been
investigated by Saito et al. (2015). We tried to eliminate the effects of
vignetting from the image digital counts by an experiment using integrated
sphere and Halogen light source that enables to generate homogeneous light.
In the experiment, the intensity of integrated light at an edge is usually
lower by 1 % than that at the center so that the vignetting correction
parameter has such biases near the edge of photographs, which does not
significantly influence the aerosol retrievals. Therefore, we assume that
the vignetting effect is totally eliminated for our purposes. Figure 2 shows
the relative CMFs of the Nikon D7000. The center wavelength of each channel
(i.e., the most sensitive wavelength) is shifted to a shorter wavelength, by
about 10 nm for R channel and 20 nm for the B channel, relative to those of
the Nikon D200. Moreover, the shape of the spectral sensitivity on the G
channel of the D7000 is broader in shape than that of the D200.
Inferred color-matching functions of Nikon D7000 in this
study (solid lines) and of D200 (dotted lines) from Sigarnes et al. (2008).
For photographic observation in twilight, exposure times are optimized to
sky brightness levels, which make the digital counts on the pixel used for
the retrievals in a dynamic range of the camera. For example, we used the
exposure time of 1/2048, 1/512, and 1/4 s in the SZAs of 90,
93, and 96∘, respectively, in clean atmospheric
conditions. The RAW counts u′k are converted to radiance-proportional RAW
counts uk, which can be rewritten as cIk, where Ik is
channel-averaged spectral radiance weighted by the camera spectral response
of the channel k. The parameter c is the absolute calibration factor that can
be defined as independent of wavelength, because the wavelength-dependence
of CMOS detector is considered in the CMFs. Finally, the color ratios
(R/G, B/G) are obtained by dividing each of cIR and cIB by cIG, and the
normalized brightness Gn is obtained by dividing the value of cIG by
the value of cIG measured at VZA of 70∘ and RAA of 0∘
for all VZAs, SZAs, and RAAs in the twilight sky. This process results in an
840-dimensional measurement for each photographic observation. For prior
knowledge, this method requires only the relative CMFs of the camera;
absolute calibration is unnecessary because the unknown parameter c can be
excluded from the data analysis. Absolute calibration can be used to
estimate the parameter c, but this is beyond the scope of the current paper
and is left for future work.
Parameters for the aerosol vertical profile assumed in the
forward model.
Vertical profileξψBackgroundbbg11Boundary layerbbl21Upper layerbup50.8Stratospherebst121.5The forward modelModel setup for twilight simulations
For twilight sky simulations, we use JACOSPAR, a spherical-shell atmosphere
RTM that accounts for refraction and multiple scattering (Iwabuchi and
Suzuki, 2009). The RTM calculates singly scattered light by a
semi-analytical approach and multiply scattered light by a backward Monte
Carlo (BMC) method. The RTM also considers 300 wavelength bands in the range
from 370 to 740 nm and models gaseous absorption by the correlated
k-distribution method used in the RSTAR RTM (Nakajima and Tanaka, 1986;
Sekiguchi and Nakajima, 2008). The earth's surface is assumed to be a
Lambertian surface with an albedo of 0.1. In the model atmosphere, we assume
the presence of 70 atmospheric layers, from ground to an altitude of 120 km,
with geometrically thin layers, particularly in the lower part of the
atmosphere. For simulating their scattering properties at each wavelength
band, aerosols are assumed to be spherical particles and the effects are
calculated according to the Lorenz–Mie theory (Bohren and Huffman, 2008).
The normalized vertical profile of stratospheric aerosol extinction
coefficient bst(z) at a wavelength of 550 nm is assumed to follow a Gamma
distribution b(z), defined as
b(z)=zξ-1e-zψΓ(ξ)ψξ,
where Γ(ξ) denotes the Gamma function, and ξ and ψ
are parameters that depend on the shape and scale, respectively. The
normalized vertical profiles of the tropospheric aerosol extinction
coefficient btr(z) are assumed to be the sum of the vertical profiles of
background aerosol bbg(z), aerosol in boundary layer bbl(z), and upper
tropospheric aerosol bup(z), each of which follows a Gamma distribution.
The shape and scale parameters for each aerosol vertical profile are
summarized in Table 3. By substitution, the tropospheric aerosol vertical
profile btr(z) can be written as
btr(z)=abgbbg(z)+ablbbl(z)+aupbup(z),
where abg, abl, and aup are, respectively, the AOT fraction of
background aerosol, boundary layer aerosol, and upper tropospheric aerosol
relative to total tropospheric AOT at a wavelength of 550 nm. In this study,
the AOT fractions are assumed to be in the proportions
abg:abl:aup=1:1.2:0.4. Figure 3 shows a priori aerosol
vertical profile. In general, the extinction coefficient in the middle-upper
troposphere shrinks exponentially with increasing altitude, and aerosol is
abundant in the boundary layer. The extinction coefficients β(z) can
be calculated by multiplying the AOT by b(z).
A prior vertical profile of aerosol extinction coefficient.
The distribution of aerosol particle volumes dV/dr is assumed to follow a
lognormal distribution:
dVdr=V0,Fr2πlnsFexp-12lnr-lnrmod ,FlnsF2+V0,Cr2πlnsCexp-12lnr-lnrmod ,ClnsC2.
Here, r is particle radius, and rmod, s, and V0 are the mode radius,
geometrical standard deviation, and particle volume, respectively, with
subscript F indicating fine particle mode and subscript C indicating coarse
particle mode. The parameters rmod and s for this aerosol model are taken
from the rural aerosol model proposed by Hänel (1976). To simplify for
aerosol properties representation, this paper introduces the coarse–fine
particle volume ratio ς, defined as
ς=V0,CV0,F.
From the above model setting, the spectral radiance-integrated RGB signals
can be calculated by multiplying the simulated spectral radiance of twilight
sky with the camera CMFs. The normalized brightness Gn and the color
ratios (R/G, B/G) can then be obtained in the way described in Sect. 2.
Sensitivity tests
The sensitivities of the color ratios and normalized brightness in twilight
sky to tropospheric AOT τtr, stratospheric AOT τst,
coarse–fine particle volume ratio ς, and other
atmosphere–surface characteristics were tested. For the sensitivity tests,
the complex refractive indices of aerosol were assumed to be 1.5 for the
real part and 0.01 for the imaginary part. The results are described in
Figs. 4, 5, and 6. In the twilight sky, and particularly near the horizon,
as τtr increases, Gn and R/G decrease and B/G increases
(Fig. 4a, b). These relations suggest that the twilight sky becomes dark and blue
near the horizon, which is consistent with the results of Saito et al. (2013).
Figure 4c and d show the sensitivities of the twilight sky to
τst. With large τst, the value of Gn at VZAs of
75–85∘ increases and all R/G (B/G) values increase (decrease),
so that the reddened twilight glow is represented. These results are
consistent with several reports on the very intense twilight glow (the
so-called twilight phenomenon) that results from volcanic aerosol injection
into the stratosphere by volcanic eruptions (Volz, 1964, 1965). The
sensitivity tests show that R/G increases under high ς conditions
only near the horizon (Fig. 4e, f). Figure 5 shows the sensitivities of the
brightness and the color ratios in twilight glow with VZA of 85∘,
SZA of 93∘, and RAA of 0∘. In the R/G–Gn
cross-section (Fig. 5b), Gn depends strongly and inversely on τtr,
decreasing under typical aerosol property condition (ς=1) as τtr increases. In contrast, for R/G, sensitivity to
τst predominates and R/G increases with large τst
(Fig. 5b). The sensitivities of twilight glow are sufficient for modeling with
τtr in 0.01–0.5 and τst in 0.002–0.1, while the
color ratios and normalized brightness in this sector are less sensitive to
ς (Fig. 5c, d). Figure 6 is the same as Fig. 5 except near the
horizon with VZA of 88∘, SZA of 91∘, and RAA of
0∘. The sensitivity of the twilight sky to τst and
ς is weak for τtr=0.13 (Fig. 6a, b). Figure 6c and
d suggest that the sky is more sensitive to ς when
τtr is smaller. In such cases, R/G and Gn increase with increasing
ς. As above, twilight sky is sensitive to ς in the
range of 0.2 to 5 under the clean atmospheric condition (τtr<∼0.1). To summarize this section, the sensitivity
tests showed that the normalized brightness and the color ratios in the
twilight sky have sufficient sensitivity to tropospheric and stratospheric
AOT and have moderate sensitivity to the coarse–fine particle volume ratio
under small AOT conditions.
Sensitivity test results for normalized brightness
(Gn) and color ratios (B/G, R/G) of twilight sky: (a, b) sensitivities to
tropospheric aerosol optical thickness; (c ,d) sensitivity to stratospheric
aerosol optical thickness; (e, f) sensitivity to coarse–fine particle volume
ratio. Panels on the right side (b, d, f) show the dependence of normalized
brightness variations along with the viewing zenith angles. Panels on the
left side (a, c, e) show the dependence of color ratio variations along with
the viewing zenith angles on R/G–B/G cross sections. The SZA and RAA are
93 and 0∘, respectively.
Sensitivity test results for color ratio values of the
twilight glow (VZA of 85∘ and SZA of 93∘ at the solar
azimuth angle). (a, b) show the he dependence of color ratio variations on the R/G–B/G
cross section; (c, d) show the dependence of normalized brightness variations
on the R/G–Gn cross section. Dashed curves in the panels on the
right (b, d) are isolines of coarse–fine particle volume ratio, and solid curves are
isolines of tropospheric aerosol optical thickness. Dashed curves in the
panels on the left (a, c) are isolines of stratospheric aerosol optical
thickness, and solid curves are isolines of tropospheric aerosol optical
thickness.
Sensitivity test results for color ratio values of the
twilight sky near the horizon (VZA of 88∘ and SZA of 91∘
at the solar azimuth angle): (a, b) show the dependence of color ratio
variations on the R/G–B/G cross section; (c, d) show the dependence of normalized
brightness variations on the R/G–Gn cross section. Dashed curves in the
panels on the right (b, d) are isolines of tropospheric aerosol optical
thickness, and solid curves are isolines of coarse–fine particle volume
ratio. Dashed curves in the panels on the left (a, c) are isolines of
coarse–fine particle volume ratio, and solid curves are isolines of
stratospheric aerosol optical thickness.
The sensitivity to other atmospheric and surface characteristics was
investigated, with the results showing that the sensitivity to ozone column
of twilight sky color is moderate, as previously shown by Hulburt (1953).
However, the sensitivities of sky brightness and color to surface albedo,
refractive indices, and water vapor column were found to be very weak (not
shown).
Model setup for aerosol retrievals
To apply the JACOSPAR RTM to the forward model for aerosol retrieval, we
refined the RTM to allow faster computation by semi-analytically calculating
singly scattered light and then linearly interpolating multiply scattered
light from a lookup table (LUT), which was pre-calculated by the BMC method.
Ozone column amount data were taken with the ozone monitoring instruments
(OMIs) on board the Aura satellite and considered in the atmospheric model and
in the LUT of the RTM. We assumed that other surface-atmospheric conditions
(such as: surface albedo, water vapor, and refractive indices) agreed with
climatic values.
Retrieval method and error analysisThe retrieval method
The retrieval method is a maximum a posteriori estimation method based
on optimal estimation (Rodgers, 2000). This method derives an optimal
solution from measurement data under the constraints of prior information
and is presently in use for aerosol and cloud optical property remote
sensing (e.g., Watts et al., 2011; Mateshvili et al., 2013; Iwabuchi et al.,
2014). A measurement vector y is derived from twilight
photographs taken with SZAs of 90–96∘. The color ratios (R/G, B/G) and
the normalized brightness (Gn) around solar direction (VZAs of
60–88∘ and RAAs of 0–30∘) were used in the
elements of the measurement vector. A state vector x that
includes aerosol optical properties as elements, and a set of model
parameters p are defined as
x=lnτtrlnτstlnς,y=y1y2⋮yn,p=ωH2OωO3αmrmi,
where ωH2O is column water vapor amount, ωO3 is
column ozone amount, α is surface albedo, and mr and mi are
the real and imaginary parts, respectively, of the refractive indices of
aerosol. The number of measurement vector elements n is set at 840 because
the number is defined as the number of measurement elements multiplied by
the number of measurement directions (3 of measurement elements and 280 of
measurement directions, which result from 10 VZAs, 7 SZAs, and 4 RAAs). We
can formally describe the physics as the forward model function f(x):
y=f(x,p)+e,
where e is the measurement–model error vector.
Prior information and its error range for the state vector
elements.
Reference values and variabilities assumed for error
analysis.
Error sourceVariableAssumed valueAssumed variability (σ)Measurement errory–Defined by Sy,mForward model approximationAs above–Defined by Sy,fwdModel parameterslnωH2O8.62 kg m-22.58 < ωH2O < 25.8 kg m-2ωO3321 DU280 < ωO3 < 360 DUmr1.51.44 < mr < 1.57lnmi0.010.001 < mi < 0.1lnα0.10.05 < α < 0.3
The cost function J(x) can be described as
J(x)=x-xaTSa-1x-xa+y-f(x,p)TSy-1y-f(x,p),
where xa is an a priori state vector,
Sa is an a priori state error covariance matrix, and
Sy is a measurement–model error covariance matrix.
The derivation of Sy will be described in Sect. 4.2.
We summarize the a priori state and its error variance in Table 4. The
assumed Sa is a diagonal matrix, with the main
diagonal taken as a vector of error variances from prior information. The
prior state and its geometrical standard deviation for τtr are
assumed to be 0.13 and 1.19, respectively, which is taken from the values in
Dubovik et al. (2002) for AOT in urban, continental, and desert regions,
which range from 0.04 to 0.43, as found from ground-based observations. The
a priori value of τst is set to be 0.005 with a geometrical
standard deviation of 1.15 (Hess et al., 1998). The a priori value for
ς is assumed to be that of a rural aerosol model with a bimodal
distribution of particle volume, as proposed by Hänel (1976). The
geometrical standard deviations for the prior information are set to be
large value to avoid overfitting of the state vector x,
which has components lnτtr, lnτst, and lnς. When the state vector becomes optimal, the cost function
should be below the degrees of freedom of the measurement vector (Rodgers,
2000). Therefore, an optimal state xopt gives
J(xopt)≈n.
Because the measurement vector calculated according to the forward model is
nonlinearly dependent on the state vector, we apply the Levenberg–Marquardt
method (LMM) to solve the inverse problem. The LMM can provide a stable
solution for moderately nonlinear problems (Rodgers, 2000). The method is
iteratively applied to find an optimal solution for x. The
state vector at the i+1th iteration,
xi+1, is given by
xi+1=xi+(1+γ)Sa-1+KiTSy-1Ki-1KiTSy-1z-f(x,p)-Sa-1x-xa,
where Ki is the Jacobian of the ith iterative calculation, and
γ represents an adjustment adaptively chosen at each step so as to
minimize the cost function. This construction lets the LMM avoid convergence
at only local minima more readily than the Gauss–Newton method can. When
the cost function is not sufficiently minimized to m, the forward model is
unable to represent the measured twilight sky with the available data under
the given assumptions and a priori constraint in the retrieval method. This
can occur under two conditions: when clouds, fog, and/or haze is present; and
when the values of the state vector and model parameters are out of range
for the retrieval method, which results in underestimation of the
measurement–model error covariance. Simultaneously with obtaining an
optimal solution, the uncertainty can be calculated by the following
equation:
Sx=Sa-1+KTSy-K-1,
where Sx is an error covariance matrix whose diagonal
elements represent the error variances of the solutions.
Measurement–model error
Measurement–model error originates from the measurement error, assumed
errors in the forward model, and uncertainties about model parameters. The
matrix Sy combining these three error components can
be found as
Sy=Sy,m+Sy,p+Sy,fwd,
where Sy,m, Sy,fwd, and
Sy,p are the covariance matrices of the measurement
error, the assumed errors in the forward model, and the uncertainties about
the model parameters, respectively. These errors and the assumptions of the
forward model are listed in Table 5. The real (mr) and imaginary
(mi) parts of the refractive indices are assumed to be 1.5 and 0.01,
respectively, which are taken from Hayasaka et al. (1992) by simplifying from
the annual variation of refractive indices for aerosol optical properties in
Sendai, Japan, as obtained by ground-based measurements (1.44–1.57 real
part and 0.007–0.057 imaginary part). The surface albedo α is
assumed to be 0.1 because of the annual variation of α from 0.05 to
0.3, which was found by Zhou et al. (2003).
Forward model errors (absolute values) in (a, b) R/G,
(c, d) B/G, and (e, f)Gn caused by the model assumptions as functions of SZA and
VZA (see text for details). Panels on the left (a, c, e) have RAA =0∘,
and those on the right (b, d, f) have RAA = 30∘.
The forward model error originates from uncertainties about the particle
size distribution and from the vertical profile shape assumed in the forward
model, and it also includes a smoothing error resulting from linear
interpolation in the LUT. The forward model error is evaluated by adding
Gaussian random noise to the parameters for aerosol particle size
distribution and vertical profile shape (specifically to the mode radii for
the volume particle size distributions and to the scale and shape
parameters of the Gamma distributions for the vertical profile) and running
the forward model and JACOSPAR RTM for perturbed sets of model-assumed
parameters and finally calculating the difference between each model's
output. In general, aerosol vertical profiles are highly variable in the
troposphere. The amount and vertical profile in the boundary layer varied
according to atmospheric condition, and those in upper troposphere are also
variable as typically seen in dust transport events. Considering their
variability, we determined the possible ranges of the shape and scale
parameters in the forward-model-error analysis. The results from JACOSPAR
RTM are taken as ground truth data. The dependence of assumption errors in
the forward model on the measurement angles is shown in Fig. 7. The
root-mean-square (RMS) errors of the color ratios and the normalized
brightness are consistently larger with larger SZAs and are smaller with
smaller VZAs and RAAs. The RMS errors are in the range 1–3 % for R/G,
3–5 % for B/G, and 5–10 % for Gn.
Forward model errors (absolute values) in (a, b) R/G,
(c, d) B/G, and (e, f)Gn caused by uncertainties in the model parameters as
functions of SZA and VZA. Panels on the left (a, c, e) have RAA = 0∘,
and those on the right have RAA = 30∘.
The model parameter errors are evaluated by adding Gaussian random noise to
the model parameters shown in Table 5 and running the forward model for
perturbed sets of model parameters. Aerosol optical properties, such as the
refractive indices and the coarse–fine particle volume ratio, are assumed to
be vertically homogeneous through the entire atmosphere from the
stratosphere to the troposphere. In general, aerosol optical properties in
the troposphere and the stratosphere are essentially different. Most of
stratospheric aerosol is sulfate or sulfuric acid, while
tropospheric aerosol is highly variable. However, aerosol amount in the
troposphere is dominant compared to that in the stratosphere under the
present normal conditions. The retrieved optical property, namely
coarse–fine particle volume ratio, is representative as a tropospheric one.
Furthermore, the twilight sky color and brightness are not very sensitive to
the refractive indices of aerosol according to a sensitivity test,
suggesting that the assumption of constant refractive indices leads to
insignificant uncertainties. We show the dependence of the model parameter
errors on the measurement angles in Fig. 8. The color ratio errors depend
weakly on the value of RAAs and SZAs and are moderately larger with larger
values of VZAs. In contrast, the error in Gn rapidly increases with
increasing SZAs and is slightly larger with smaller values of RAAs and larger
values of VZAs. The RMS errors for R/G and B/G are in the range 3–5 %. The RMS
error for Gn is below 5 % for SZAs of 90–94∘ but in the
range 20–80 % for SZAs of 95–96∘. The model parameter errors
are the largest errors and are dominant in the model–measurement error. The
covariance matrices for errors in the forward model assumptions and the
model parameters are taken as constant matrices for the aerosol retrievals
in this study. The applied algorithm could be improved by accounting for the
effects of the state vector and model parameter values on these matrices.
This is left for future work.
The measurement errors include CMOS noise and biases, uncertainties in the
inferred camera response functions, camera-orientation errors, and time-lag
error while taking the photographs. The dark current also leads relatively
small bias in digital counts in the twilight photographs used in this study:
less than 0.5 % (0.1 %) for the camera signal corresponding to the
twilight sky at VZA of 60∘ (88∘). CMOS biases can arise
from exposure time, aperture, and temperature. CMOS noise errors for each
angle are determined by the variance of RAW counts among pixels taken from
the corresponding angles. The time-lag error is assumed to be normally
distributed with standard deviation 5 s, which gives an uncertainty of
∼0.015∘ for SZA, and the camera-orientation error
is assumed to be normally distributed with standard deviation 0.5∘
for the VZA and 0.3∘ for the RAA. The inclined camera orientation leads to
biases in the normalized brightness and color ratios especially in pixels
with large RAAs and small VZAs even when we use a spirit level. Uncertainty of
orientation angle is approximately 0.8∘. Moreover, a stray light,
which may affect the camera digital counts, is caused by multi-reflected
light among the lenses and reflection on near-Lambertian surface, namely a
plastic part installed in the equipped lens. The dynamic range of twilight
sky brightness is large, and bright light might cause a stray light in the dark
part of the photograph. We have experimentally investigated the order of
magnitude of a stray light effect on digital counts in twilight photographs.
It was found that the stray light effect provided small biases, which became
significantly smaller towered to larger angle from a bright light:
approximately 1, 0.1, and below 0.05 % at angle of 1,
5, and > 15∘, respectively, from the light
source.
Furthermore, the above errors are estimated by running the forward model with
Gaussian random noise perturbation of the camera angles. As a result, the
CMOS noise is on the order of 3–5 %, and other errors including
lens characteristics and angle uncertainties are on the order of 5 % for
the color ratios and 10 % for Gn. The distortion of a fisheye lens may
lead to uncertainties in VZA and RAA estimation. Currently, several
researchers investigated and showed that the recent lenses for consumers had
very slight distortion, leading to a difference between ideal and
distorted optical path within a pixel (Schneider et al., 2009; Shahriar
et al., 2009). Rabaza et al. (2010) showed that the distortion effect for a
Nikkor fisheye lens was considered negligible. For this reason, we assumed
the lens distortion did not influence our results.
Retrieval-error analysis
The errors in retrieved aerosol properties originate from the
measurement–model error and the sensitivity of the state vector of the sky
to atmospheric conditions. For the error sources in Table 3, the retrieval
error is evaluated by retrieval simulations. First, after assuming a state
x and model parameters
pnoise and adding Gaussian random noise, the
forward-model-simulated measurements ynoise are
calculated, and Gaussian random noise is added to simulate measurement error
and the forward model error. Second, we try to retrieve the state vector
xnoise from ynoise with this
algorithm. Finally, the truth–retrieval difference
xnoise–x is obtained. Each state
was simulated 200 times and the retrieval error was taken as the average
error. The retrieval results with filtering (J(x) < 1000)
are shown in Fig. 9. The value of τtr is accurately
retrieved, with RMS error of 54.5 % (absolute RMS error of 0.025) in the
range of 0.01–0.5, and positive biases are found particularly under small
AOT conditions (Fig. 9a). The retrieval uncertainty is small under the clean
and moderately turbid atmospheric conditions for τtr from 0.01 to
0.3, suggesting that this method can retrieve tropospheric AOT with high
precision. In the more turbid atmospheric conditions (τtr > 0.3),
the uncertainty in the retrieved τtr is around
±0.15. The value of τst is also correctly retrieved with a
RMS error of 53.2 % (absolute RMS error of 0.005) and slightly positive
bias (13 %) (Fig. 9b). The retrieved value of τst is
overestimated under small tropospheric AOT conditions as a result of the
particular characteristics of this retrieval method (not shown). The
uncertainties for τst retrieval are small for large values of
τst and are slightly larger for small values of τst,
suggesting that the value of τst can be retrieved under the dense
τst conditions caused by volcanic eruption, such as the Mt.
Pinatubo eruption in 1991.
Initial and retrieved (a) tropospheric aerosol optical
thickness, (b) stratospheric aerosol optical thickness, and (c) coarse–fine
particle volume ratio ς in the retrieval-error analysis. Black
and gray marks (circles) show ς retrievals with ς > 1
(ς≤1) under very and moderately clean
conditions, respectively.
From Fig. 9c, it seems difficult to retrieve the
value of ς under typical atmospheric conditions and under
fine-particle-dominance conditions. The RMS error is large, and the
retrieved values of ς are scattered, centered mostly around the a
priori assumption even under clean atmospheric conditions. This occurs
because the sensitivity of ς on twilight sky is too low to
overcome the measurement–model error. When coarse particles dominate in the
atmosphere (ς > 1) under clean atmospheric conditions,
the value of ς might be retrieved, and the RMS error and bias are
62.7 and 8.8 %, respectively. In addition, the averaging kernel
A=KTSy-1K+Sa-1KTSy-1K,
shows a sensitivity of retrievals to the true states, demonstrating whether
the measurement with associate uncertainties contains enough information to
retrieve the state vector or not (Rodgers, 2000). The diagonal elements of
the averaging kernel are 0.92, 0.74, and 0.94 (0.94, 0.94, and 0.95)
corresponding to tropospheric AOT, stratospheric AOT, and coarse–fine
particle volume ratio under the atmospheric condition with tropospheric AOT
of ∼0.1 (0.3), while the non-diagonal elements are relatively
significantly small (below 0.05) except for the sensitivity of coarse–fine
particle volume ratio on the true stratospheric AOT state (around 0.3) under
small tropospheric AOT condition. Furthermore, the degree of freedom for
signal given by trace of the A shows above 2.5 under the general
atmospheric conditions. Therefore, it is reasonable to retrieve the three
state variables under clean atmospheric condition and at least tropospheric
and stratospheric AOT when AOT is large.
Comparison of aerosol property retrievals from camera
measurements and sky radiometer measurements. Error bars show uncertainty of
retrievals. Color scales show total retrieval cost J(x). The
vertical axis and horizontal axis show retrievals from a camera and those
from other instruments, respectively: (a) aerosol optical thickness, from
camera and sky radiometer, with correlation coefficient r at 0.94 and 18
trials; (b) stratospheric aerosol optical thickness from camera and OSIRIS
on board the Odin satellite; (c) coarse–fine particle volume ratio from
camera and sky radiometer.
ResultsValidation
To validate this retrieval method, the retrievals from photographic
observations were compared with those from the sky radiometer measurements
located at the same site and with satellite-based measurements (Fig. 10).
The comparison is limited to selected results with J(x) < 3000.
The sky radiometer and an the software tool Skyrad.pack
developed by Nakajima et al. (1996) were used as the measurement system and
tool to infer aerosol optical properties, such as AOTs and distributions of
particle volumes, from direct and diffused sunlight. For twilight,
sky radiometer measurements are not available because of the absence of
direct sunlight. Typically, aerosol optical properties do not vary much
within a few hours except when a strong emission source (e.g., forest fire)
is present near the site. For this reason, we used the sky radiometer data
obtained 1 h before sunset and 1 h after sunrise for comparison in
this study. Figure 10a shows the comparison of AOTs (τtr+τst) retrieved from the photographic observations and the
sky radiometer measurements. Mostly, the retrieved AOTs from the digital
camera were consistent with those from the sky radiometer, with little
uncertainty and a correlation coefficient of 0.94. The values of τst
retrieved from the camera data were compared with those from the
Canadian optical stratospheric and infrared imaging system (OSIRIS) on board
the Swedish satellite Odin (Murtagh et al., 2002; Llewellyn, et al., 2004).
OSIRIS measures atmospheric limb radiance of scattered sunlight across
visible and near-infrared wavelengths as well as optical thickness, and the
vertical profiles of the extinction coefficient at 750 nm in stratospheric
aerosol were inferred by the use of the algorithm given by Bourassa et al. (2007).
The photographic observations are carried out under the background
stratospheric aerosol conditions, in other words, without any effects of
volcanic eruptions in the stratosphere. Figure 10b shows the scatter plot of
τst retrieved from the camera and from OSIRIS. Note that we
compare stratospheric AOTs at 750 nm from OSIRIS and those at 550 nm from
the photographic observations. For stratospheric aerosol particle size, the
Ångström coefficient is generally in a range of 0–2, resulting in the
stratospheric AOT at 750 nm being smaller than that at 550 nm by
0–26 %. It is shown that average stratospheric AOT from the photographic
observations is in the same order of magnitude but positively biased by
10–50% compared with those from OSIRIS, and no correlation exists for
this measurement period. The variability is in the same order of magnitude
compared with the RMS error in τst retrievals from photographic
observations according to the retrieval-error tests. The values of
ς retrieved from the camera are compared with those calculated
from particle volume distributions retrieved from the sky radiometer (Fig. 10c).
The retrieved value of ς tends to be close to the a priori
assumption, and thereby no correlation between the camera and the
sky radiometer is found.
Photographs of twilight sky on the solar side, for the
case studies of (a) 31 January, (b) 23 May, and (c) 3 June 2013. In
all cases, SZA is uniformly 94∘, and VZA is 90.45∘ at
the horizon, 91.5∘ at the bottoms of the images, and 30∘
at the tops of the photographs.
Retrieval results and SPRINTARS model simulation results
for case studies.
Retrievals DateCamera Sky radiometer Sun photometerSPRINTARS AOT AOTςAOTςAOTSulfateDust(a)31 Jan 2013, morning0.056±0.0282.52±0.340.1081.1160.0830–0.020–0.02(b)23 May 2013, morning0.091±0.0060.99±0.110.1121.1930.1220.03–0.050.1–0.2(c)3 Jun 2013, morning0.261±0.007NA0.2961.3660.3110.03–0.050.1–0.2
NA: not available
Case studies
To test the flexibility under various aerosol conditions (e.g., vertical
profiles and aerosol species) of this retrieval method, we chose three
characteristic cases and analyzed the simulation results in detail with
respect to the vertical profiles of the aerosol extinction coefficients.
Figure 11 shows photographs of the twilight sky taken on (a) 31 January 2013,
(b) 23 May 2013, and (c) 3 June 2013. These photographs were taken at
an SZA of 94∘. In Fig. 11a, a bright red-orange twilight glow is
seen near the horizon, and the twilight sky color gradates from orange to
blue. The brightness rapidly decreases as the VZA decreases. In contrast,
the color in Fig. 11b seems to be dull across the sky in comparison with
Fig. 11a. An orange-to-gray twilight glow is present above a dark-blue
segment that appears near the horizon (Saito et al., 2013). In Fig. 11c, the
range of the twilight sky color is the smallest among the three cases, and a
dark-blue segment can be seen near the horizon, similar to that in Fig. 11b.
Figure 12 shows the vertical profiles of aerosol extinction coefficients in
the troposphere from the ground to an altitude of 6 km; these are derived
from the lidar measurements for each case (Shimizu et al., 2010). In the
lidar products, the lidar ratio of 50 sr is assumed, and the inferred
extinction coefficients are separated into spherical and nonspherical
particles.
Table 6 summarizes the results from the ground-based observations (the
sun photometer and the sky radiometer, collocated at the photographic
observation site) and from the daily means of aerosol optical properties, as
calculated by the aerosol transport model SPRINTARS (Takemura et al., 2000,
2002, 2005). The sun photometer measures direct solar light in the visible to
near infrared wavelengths to infer the AOTs. For 31 January 2013 (case a), a
very clean atmosphere with an AOT of 0.02–0.03 is simulated by the
SPRINTARS and weak backscatter signals are obtained from lidar measurement.
Moreover, spherical particles are dominant in this case. In contrast, the
SPRINTARS products suggest that sulphate and dust particles were transported
from the eastern part of continental China to Japan from 20 May to 26 May 2013.
Consistently, the lidar measurements show the presence of
nonspherical particles at altitudes of 3–6 km and the presence of
spherical/nonspherical mixed particles in the boundary layer for 23 May 2013
(case b). For 3 June 2013 (case c), dust transported from the north
inland area of China to Japan from 2 June to 5 June 2013 is shown by
the model. A spherical/nonspherical mixture of particles is present in the
boundary layer (altitudes of 0–2 km), and nonspherical particles are
dominant above 6 km, according to the lidar measurements.
Vertical profiles of aerosol extinction coefficients for
altitudes from 0 to 6 km, as obtained from lidar measurements for the case
studies. Data for 0 to 150 m are not available.
From the above results, the atmospheric characteristics are clean atmosphere
in case (a), dust-pollutant mixed particles transported from eastern China
in case (b), and yellow sand transported from inland China in case (c).
Additionally, the vertical profiles and aerosol species are vertically
inhomogeneous in cases (b) and (c). A comparison of the results retrieved
from the photographic observations with the corresponding results from other
products shows that the retrieved AOTs are reasonable but slightly lower
than the AOTs obtained from other products for the three cases with AOTs of
0.056±0.029 (a), 0.091±0.006 (b), and 0.261±0.007 (c)
relative to estimates from other ground-based passive instruments. The
retrieved values of ς are 2.52±0.34 (a) and 0.99±0.11 (b). The retrieved value of ς is eliminated in the case (c)
because of low confidence in the ς retrieval, which was predicted
by the retrieval-error analysis (Sect. 4.3) for large AOT conditions. The
main reason for the under estimation might be the temporal–spatial
variability of aerosol optical properties. Specifically, during dust events,
aerosol optical properties showed high variability, and so they varied more
widely during the time lag between camera observations and other
measurements than they did in the other cases, resulting in the difference
in AOTs. The AOTs for those three cases are consistent with the total AOTs
calculated by SPRINTARS. Thus, the case studies demonstrate that the
proposed method can infer AOTs without much dependence on knowing the
vertical inhomogeneity for aerosol species and the extinction coefficients.
Conclusions and discussions
An optimal-estimation-based algorithm was developed to infer aerosol optical
properties from twilight photographs taken with a digital camera at SZAs of
90–96∘. The following advantages are offered by this method and
measurement techniques: (1) tropospheric and stratospheric AOTs can be
retrieved by a passive remote-sensing technique, even in the absence of
direct sunlight conditions; (2) the retrievals and their uncertainties are
simultaneously calculated in the optimal-estimation framework; and 3) a low-cost instrument (a digital camera) can be used.
The measurement vector was set to be the color ratios and the normalized
brightness around the solar direction derived from camera RAW data in RGB
channels. Ozone column data were taken from OMI/Aura. The forward model
includes a spherical-shell atmosphere, refraction, and multiple scattering.
Additionally, in the model, singly scattered radiances are calculated
semi-analytically, and multiply scattered radiances are calculated by linear
interpolation from a pre-calculated LUT. The values of diagonal elements in
the a priori state covariance matrix were assumed to be large in order to
avoid overfitting. The model parameters and their uncertainties were
determined by prior measurement and error analysis. The error sources during
retrieval were chiefly the model parameter uncertainties, with each of CMOS
noise, the assumed distribution of particle volume, and vertical profile
shape contributing some error. The retrieval-error analysis showed that the
tropospheric and stratospheric AOTs can be inferred for τtr in
the range 0.01 to 0.5 and τst in the range 0.001–0.1,
obtaining a small RMS error (around 50–55 % for τtr and
τst). Especially stratospheric AOT retrieval can be outperformed
under dense τst conditions. The retrieved AOT from the digital
camera was compared with those from the sky radiometer measurements, and this
comparison showed consistency between the results, with a correlation
coefficient as large as 0.94. The retrieved stratospheric AOTs from the digital
camera were positively biased compared with that from OSIRIS measurements
with reasonable variability as shown in the retrieval-error analysis. No
correlation was found in the ς comparisons. A case study for
three different atmospheric conditions was presented to demonstrate the
usefulness of the method. Comparison with products provided by other
instruments and results from other model was used to investigate the effects
of vertical inhomogeneity for aerosol species and profiles in detail. This
investigation showed that AOTs can be retrieved with reasonable accuracy
without knowing the details of such properties.
The difficulty in retrieving the coarse–fine particle volume ratio
ς can be explained by the following. In cases with a large AOT,
the following are true: the sensitivity of ς in twilight sky is
weak. In cases with a small AOT, one possible explanation is that
polarization effects cause non-negligible differences between the twilight
sky brightness and color found by the forward model simulations and those
found by measurement. The forward model uses a scalar approximation to model
the radiative transfer. Saito et al. (2013) investigated the contribution of
multiply scattered light to twilight sky near the horizon with the JACOSPAR
RTM, from which the present forward model is descended. The fraction of
multiply scattered light is in the range of 20–50 % near the
horizon for a VZA of 90–85∘ under small AOT conditions (0.05<τtr<0.13). Mishchenko et al. (2006)
demonstrated that scalar approximation leads to biases for calculated
radiance, with the magnitude of the bias in the range of ± 3–5 %
depending on the RAA, relative to the vector RTM outputs for AOTs of
0.1–0.3. This may cause an error in the retrieved brightness and color in
twilight near the horizon. Another possible reason is the seeming
insensitivity of ς in twilight sky when looking near the horizon
(with SZA of ∼90∘), and this sensitivity may be
too low to overcome the uncertainties resulting from model errors and camera
noise. An investigation of this possibility and improvements to the
algorithm to compensate are left for future work.
The retrieval method proposed by this paper can be applied to aerosol
measurements in desert, snow-covered, and polar regions, areas where it is
difficult to apply the conventional solar reflection-based methods.
Particularly in the polar region in winter, aerosol measurements are very
limited, and the present twilight photometry method should be helpful to
increase the availability of aerosol measurements. Furthermore, it is easy
to extend the aerosol observations at many points with this method because
of the use of a digital camera, which is both inexpensive and easily
movable. Digital cameras are widely used in daily life, and many amateur
photographers have the opportunity to take pictures of beautiful sights,
including twilight sky. In addition to their beauty, twilight photographs
have the potential to be used as measurement data for aerosol retrievals.
Therefore, the present aerosol retrieval method has unique characteristics,
and it may complementarily be used in combination with other measurement
techniques.
Acknowledgements
The authors are grateful to M. Ejiri of the National Institute of
Polar Research and I. Murata of Tohoku University for their assistance
in the development of camera measurement techniques and to T. Takemura of
Kyushu University for providing SPRINTARS data. We also thank
SKYNET for the use of sky radiometer data in this research and the OpenCLASTR
project for the use of the RSTAR package to calculate radiative transfer.
This study was partly supported by a grant-in-aid for scientific research
(DC1 262947) from the Japan Society for the Promotion of Science (JSPS).
Edited by: U. Friess
References
Adams, C. N., Plass, G. N., and Kattawar, G. W.: The influence of ozone and aerosols on
the brightness and color of the twilight sky, J. Atmos. Sci., 31, 1662–1674, 1974.
Berkoff, T. A., Sorokin, M., Stone, T., Eck, T. F., Hoff, R., Welton, E., and
Holben, B.: Nocturnal aerosol optical depth measurements with a small-aperture automated
photometer using the moon as a light source, J. Atmos. Ocean.
Tech., 28, 1297–1306, 2011.
Bohren, C. F. and Huffman, D. R.: Absorption and Scattering of Light by Small Particles,
John Wiley & Sons, New York, 2008.Bourassa, A. E., Degenstein, D. A., Gattinger, R. L., and Llewellyn, E. J.:
Stratospheric aerosol retrieval with optical spectrograph and infrared imaging system limb scatter
measurements, J. Geophys. Res., 112, D10217,
10.1029/2006JD008079, 2007.
Dave, J. V. and Mateer, C. L.: The effect of stratospheric dust on the color of the
twilight sky, J. Geophys. Res., 73, 6897–6913, 1968.
Dubovik, O., Holben, B., Eck, T. F., Smirnov, A., Kaufman, Y. J., King, Y. J.,
Tanre, D., and Slutsker, I.: Variability of absorption and optical properties of key aerosol types
observed in worldwide locations, J. Atmos. Sci., 59, 590–608, 2002.Ehrlich, A., Bierwirth, E., Wendisch, M., Herber, A., and Gayet, J.-F.: Airborne
hyperspectral observations of surface and cloud directional reflectivity using a commercial
digital camera, Atmos. Chem. Phys., 12, 3493–3510,
10.5194/acp-12-3493-2012, 2012.
Hänel, G.: The properties of atmospheric aerosol particles as functions of the
relative humidity at thermodynamic equilibrium with the surrounding moist air, Adv. Geophys., 19,
73–188, 1976.
Hayasaka, T., Nakajima, T., Ohta, S., and Tanaka, M.: Optical and chemical properties of
urban aerosols in Sendai and Sapporo, Japan, Atmos.
Environ., 26, 2055–2062, 1992.Herber, A., Thomason, L. W.,, Gernandt, H., Leiterer, U., Nagel, D.,
Schulz, K. H., Kaptur, J., Albrecht, T., and Notholt, J.: Continuous day and
night aerosol optical depth observations in the Arctic between 1991 and 1999,
J. Geophys. Res., 107, 4097, 10.1029/2001JD000536, 2002.
Hess, M., Koepke, P., and Schult, I.: Optical properties of aerosols and
clouds: the software package OPAC, B. Am. Meteorol. Soc., 79, 831–844, 1998.
Hioki, S. and Iwabuchi, H.: Photographic observation and optical simulation
of a pollen corona display in Japan, Appl. Opt., 54, B12–B21, 2015.
Holben, B. N., Eck, T. F., Slutsker, I., Tanré, D., Buis, J. P., Setzer,
A., Vermote, E., Reagan, J. A., Kaufman, Y. J., Nakajima, T., Lavenu, F.,
Jankowiak, I., and Smirnov A.: AERONET – a federated instrument network and
data archive for aerosol characterization, Remote Sens. Environ., 66, 1–16,
1998.
Hulburt, E. O.: Explanation of the brightness and color of the sky,
particularly the twilight sky, J. Opt. Soc. Am., 43, 113–118, 1953.
Intergovernmental Panel on Climate Change (IPCC): Climate Change 2013: The
Physical Science Basis, Contribution of Working Group I to the Fifth
Assessment Report of the IPCC, edited by: Stocker, T. F., Qin, D.,
Plattner, G. K., Tignor, M., Allen, S. K., Boschung, J., Nauels, A., Xia, Y.,
Bex, V., and Midgley, P. M., Cambridge University Press, Cambridge, UK, New
York, NY, USA, 2013.Iwabuchi, H. and Suzuki, T.: Multiple-scaling method for anisotropic
scattering and its applications to radiance calculations, AIP Conf. Proc.,
41, 1100, 10.1063/1.3117009, 2009.
Iwabuchi, H., Yamada, S., Katagiri, S., Yang, P., and Okamoto, H.: Radiative
and microphysical properties of cirrus cloud inferred from the infrared
measurements made by the Moderate Resolution Imaging Spectroradiometer
(MODIS) – Part I: Retrieval method, J. Appl. Meteorol.Clim., 53, 1297–1316,
2014.Kataoka, R., Miyoshi, Y., Shigematsu, K., Hampton, D., Mori, Y., Kubo, T.,
Yamashita, A., Tanaka, M., Takahei, T., Nakai, T., Miyahara, H., and
Shiokawa, K.: Stereoscopic determination of all-sky altitude map of aurora
using two ground-based Nikon DSLR cameras, Ann. Geophys., 31, 1543–1548,
10.5194/angeo-31-1543-2013, 2013.
Lee Jr., R. L. and Andres, J. H.: Measuring and modeling twilight's purple
light, Appl. Optics, 42, 445–457, 2003.
Lee Jr., R. L., Meyer, W., and Hoeppe, G.: Atmospheric ozone and colors of
the Antarctic twilight sky, Appl. Optics, 50, 162–171, 2011.
Llewellyn, E. J., Lloyd, N. D., Degenstein, D. A., Gattinger, R. L.,
Petelina, S. V., Bourassa, A. E., Wiensz, J. T., Ivanov, E. V., McDade, I.
C., Solheim, B. H., McConnell, J. C., Haley, C. S., von Savigny, C., Sioris,
C. E., McLinden, C. A., Griffioen, E., Kaminski, J., Evans, W. F. J.,
Puckrin, E., Strong, K., Wehrle, V., Hum, R. H., Kendall, D. J. W.,
Matsushita, J., Murtagh, D. P., Brohede, S., Stegman, J., Witt, G., Barnes,
G., Payne, W. F., Piché, L., Smith, K., Warshaw, G., Deslauniers, D. -L.,
Marchand, P., Richardson, E. H., King, R. A., Wevers, I., McCreath, W.,
Kyrölä, E., Oikarinen, L., Leppelmeier, G. W., Auvinen, H., Mégie, G.,
Hauchecorne, A., Lefèvre, F., de La Nöe, J., Ricaud, P., Frisk, U.,
Sjoberg, F., von Schéele, F., and Nordh, L.: The OSIRIS instruments on the
Odin spacecraft, Can. J. Phys., 82, 411–422, 2004.Mateshvili, N., Fussen, D., Mateshvili, G., Mateshvili, I., Vanhellemont, F.,
Kyrölä, E., Tukiainen, S., Kujanpää, J., Bingen, C.,
Robert, C., Tétard, C., and Dekemper, E.: Nabro volcano aerosol in the
stratosphere over Georgia, South Caucasus from ground-based spectrometry of
twilight sky brightness, Atmos. Meas. Tech., 6, 2563–2576,
10.5194/amt-6-2563-2013, 2013.
Minnaert, M. G. J.: Light and Color in the Outdoors, vol. 17, Springer
Verlag, 1993.
Mishchenko, M. I., Travis, L. D., and Lacis, A. A.: Multiple Scattering of
Light by Particles: Radiative Transfer and Coherent Backscattering, Cambridge
Univ. Press, New York, 2006.
Murtagh, D., Frisk, U., Merino, F., Ridal, M., Jonsson, A., Stegman, J.,
Witt, G., Eriksson, P., Jiménez, C., Megie, G., de la Noë, J., Ricaud,
P., Baron, P., Pardo, J. R., Hauchcorne, A., Llewellyn, E. J., Degenstein, D.
A., Gattinger, R. L., Lloyd, N. D., Evans, W. F. J., McDade, I. C., Haley, C.
S., Sioris, C., von Savigny, C., Solheim, B. H., McConnell, J. C., Strong,
K., Richardson, E. H., Leppelmeier, G. W., Kyrölä, E., Auvinen, H., and
Oikarinen, L.: Review: an overview of the Odin atmospheric mission, Can. J.
Phys., 80, 309–319, 2002.
Nakajima, T. and Tanaka, M.: Matrix formulations for the transfer of solar
radiation in a plane-parallel scattering atmosphere, J. Quant. Spectrosc.
Ra., 35, 13–21, 1986.
Nakajima, T., Tonna, G., Rao, R., Boi, P., Kaufman, Y., and Holben, B.: Use
of sky brightness measurements from ground for remote sensing of particulate
polydispersions, Appl. Optics, 35, 2672–2686, 1996.
Rabaza, O., Galadi-Enriquez, D., Estrella, A. E., and Dols, F. A.: All-sky
brightness monitoring of light pollution with astronomical methods, J.
Environ. Manage., 91, 1278–1287, 2010.
Remer, L. A., Kaufman, Y. J., Tanre, D., Mattoo, S., Chu, D. A.,
Martins, J. V., Li, R. R., Ichoku, C., Levy, R. C., Kleidman, R. G.,
Eck, T. F., Vermote, E., and Holben, B. N.: The MODIS aerosol algorithm,
products, and validation, J. Atmos. Sci., 62, 947–973, 2005.
Rodgers, C. D.: Inverse Methods for Atmospheric Abounding: Theory and
Practice, Atmospheric, Oceanic and Planetary Physics, vol. 2, World
Scientific, Singapore, 2000.
Saito, M., Iwabuchi, H., and Hayasaka, T.: Physical explanation of
tropospheric aerosol effect on twilight sky color based on photographic
observations and radiative transfer simulations, SOLA, 9, 15–18, 2013.
Saito, M., Iwabuchi, H. and Murata, I.: Estimation of spectral distribution
of sky radiance using a commercial digital camera, Appl. Opt., submitted,
2015.Schneider, D., Schwalbe, E., and Maas, H.-G.: Validation of geometric models
for fisheye lenses, ISPRS J. Photogram. Remote Sens., 64, 259–266,
10.1016/j.isprsjprs.2009.01.001, 2009.Sekiguchi, M. and Nakajima, T.: A k-distribution-based radiation code and
its computational optimization for an atmospheric general circulation model,
J. Quant. Spectrosc. Ra., 109, 2779–2793, 2008.
Shahriar, A. N. M., Hyde, R., and Hayman, S.: Wide-angle image analysis for
sky luminance measurement, Architect. Sci. Rev., 52, 211–220, 2009.
Shaw, G. E.: Radiance and color of the sky at twilight: perturbations caused
by stratospheric haze, Pure. Appl. Optics, 119, 231–247, 1981.
Shimizu, A., Sugimoto, N., and Matsui, I.: Detailed Description of Data
Processing System for LiDAR Network in East Asia, 25th International Laser
Radar Conference, 911–913, 2010.
Sigernes, F., Holmes, J. M., Dyrland, M., Lorentzen, D. A., Svenøe, T.,
Heia, K., Aso, T., and Deehr, C. S.: Sensitivity calibration of digital
colour cameras for auroral imaging, Opt. Express, 16, 15623–15632, 2008.
Takamura, T. and Nakajima, T.: Overview of SKYNET and its activities, Opt.
Pura. Apl., 37, 3303–3308, 2004.
Takemura, T., Okamoto, H., Maruyama, Y., Numaguchi, A., Higurashi, A., and
Nakajima, T.: Global three-dimensional simulation of aerosol optical
thickness distribution of various origins, J. Geophys. Res., 105,
17853–17873, 2000.
Takemura, T., Nakajima, T., Dubovik, O., Holben, B. N., and Kinne, S.:
Single-scattering albedo and radiative forcing of various aerosol species
with a global three-dimensional model, J. Climate, 15, 333–352, 2002.Takemura, T., Nozawa, T., Emori, S., Nakajima, T. Y., and Nakajima, T.:
Simulation of climate response to aerosol direct and indirect effects with
aerosol transport-radiation model, J. Geophys. Res., 110, D02202,
10.1029/2004JD005029, 2005.
Volz, F. E.: Twilight phenomena caused by the eruption of Agung volcano,
Science, 144, 1121–1122, 1964.
Volz, F. E.: Note on the global variation of stratospheric turbidity since
the eruption of Agung volcano, Tellus, 4, 513–515, 1965.Watts, P. D., Bennartz, R., and Fell, F.: Retrieval of two-layer cloud
properties from multispectral observations using optimal estimation, J.
Geophys, Res., 116, D16203, 10.1029/2011JD015883, 2011.
Wu, B. and Lu, D.: Retrieval of stratospheric background aerosol scattering
coefficient from twilight polarization measurements, Appl.
Optics, 27, 4889–4906, 1988.Zerefos, C. S., Tetsis, P., Kazantzidis, A., Amiridis, V., Zerefos, S. C.,
Luterbacher, J., Eleftheratos, K., Gerasopoulos, E., Kazadzis, S., and
Papayannis, A.: Further evidence of important environmental information
content in red-to-green ratios as depicted in paintings by great masters,
Atmos. Chem. Phys., 14, 2987–3015, 10.5194/acp-14-2987-2014, 2014.Zhou, L., Dickinson, E., Tian, Y., Zeng, X., Dai, Y., Yang, Z. -L., Schaaf,
C. B., Gao, F., Jin, Y., Strahle, A., Myneni, B., Yu, H., Wu, W., and Shaikh,
M.: Comparison of seasonal and spatial variations of albedos from
Moderate-resolution Imaging Spectroradiometer (MODIS) and Common Land Model,
J. Geophys. Res., 108, 4488, 10.1029/2002JD003326, 2003.