Introduction
Atmospheric aerosols play a critical role in controlling the Earth's climate
and air quality (IPCC, 2013). Due to the insufficient understanding of their
complicated formation mechanisms and effects, there is a growing need to
understand and measure their optical properties and precursors. Under these
circumstances, simultaneous measurements of aerosols and their gaseous
precursors, such as nitrogen dioxide (NO2) and sulfur dioxide
(SO2), using the multi-axis differential optical
absorption spectroscopy (MAX-DOAS) technique have been reported, with additional and
significant advantages of vertical profiling, simple setup, low power
consumption, and autonomous operation without absolute radiometric
calibration (Hönninger and Platt 2002; Hönninger et al., 2004;
Wittrock et al., 2004; Irie et al., 2008a, b, 2009, 2011). MAX-DOAS is an application of the well-established
DOAS technique, with which narrow band absorption features are analyzed to
selectively detect and quantify trace gases by applying the Lambert–Beer law
(Platt, 1994; Platt and Stutz, 2008). In general, MAX-DOAS measures
ultraviolet (UV)–visible spectra of scattered sunlight at several elevation
angles (α) between the horizon and zenith. Within the boundary
layer, for instance, observation at a low α yields averaged
information about trace gas concentrations over a distance, which is in the
same order of, or finer than, the horizontal scale usually adopted by models
and measured by satellites but coarser than that of in situ observations. Thereby,
it is expected that MAX-DOAS plays an important role in bridging different
data sets with different spatial resolutions (Irie et al., 2011). Thus,
observations by MAX-DOAS are highly unique and have great potential for
realizing many applied studies, including those on aerosols.
The number of MAX-DOAS instruments has grown considerably in recent years
(e.g., Roscoe et al., 2010; Piters et al., 2012). The increasing use of
MAX-DOAS instruments for tropospheric observations, together with the
diversity of their designs and operation protocols, created the need for
formal comparison. For this purpose, the Cabauw Intercomparison Campaign of
Nitrogen Dioxide measuring Instruments (CINDI) was held at the Cabauw
measurement station (51.97∘ N, 4.93∘ E), the
Netherlands, in June–July 2009. During the CINDI campaign, besides the
intercomparison for NO2, near-surface aerosol extinction coefficients
(AECs) retrieved from observations from four different MAX-DOAS instruments
were compared to those measured by the in situ humidified nephelometer (Zieger et
al., 2011). The comparison showed a tight correlation at a determination
coefficient R2 of 0.62–0.78, but the AECs from MAX-DOAS were a factor
of 1.5–3.4 larger than the in situ values. The systematic differences could have
been caused by the limited vertical resolution of the MAX-DOAS retrieval
overestimating the AECs in the lowest layer, as lofted aerosol layers were
present during the measurement period (Zieger et al., 2011; Irie et al.,
2011). However, sufficient evidence for their causal link was not obtained.
In relation to the discussion below, we note here that a correction factor
for the absorption of oxygen collision complexes (O4 or
O2–O2) was applied to all four participating MAX-DOAS retrievals.
This is based on observations by Wagner et al. (2009) and Clémer et al. (2010), who indicated that retrieved O4 slant column densities (SCDs)
were systematically too high to match the model simulation under near pure
Rayleigh conditions, although a physical explanation for applying the
correction factor was unclear.
In the present study, coincident aerosol observations by MAX-DOAS and those
by cavity ring-down spectroscopy (CRDS), lidar, and sky radiometer were
conducted in Tsukuba, Japan, on 5–18 October 2010. This occasion was used
to evaluate the MAX-DOAS aerosol retrievals of AECs and aerosol optical depth
(AOD) at 476 nm, particularly from the viewpoint of the need for a
correction factor for O4 absorption. Potential practical solutions to
achieve agreement of the MAX-DOAS observations with the three other
observations are discussed.
Observations
MAX-DOAS
We installed our MAX-DOAS system at the Meteorological Research Institute
in Tsukuba, Japan (36.06∘ N, 140.13∘ E), on 1 June 2010. Because the installed MAX-DOAS system (PREDE, Co., Ltd)
is basically the same as the one used for the CINDI campaign (Irie et al.,
2011) and for the MAX-DOAS network of NO2 in Russia and Asia (MADRAS)
(Kanaya et al., 2014), only a brief description is given below. A
miniaturized UV–visible spectrometer (Ocean Optics, Inc., USB4000) was used
to record spectra between 223 and 557 nm. The temperature (T) of the USB4000
spectrometer was kept constant at 40.0 ± 0.1∘C to stabilize
spectrometer characteristics and to prevent possible dew condensation. The
spectral resolution (full width at half maximum) was 0.76 at 450 nm, as
estimated by wavelength calibration using a high-resolution solar spectrum
(Kurucz et al., 1984). The integration time was kept constant throughout the
day at 150 ms. Spectra recorded at a fixed α for a 5 min interval
were averaged and analyzed. The line of sight was directed to an azimuth
angle of 316∘ (northwest). The field of view was < 1∘. Spectra were recoded sequentially at six different
α of 3, 5, 10,
20, 30, and 90∘ using
a movable mirror. This sequence was repeated every 30 min.
Spectral analysis and subsequent profile retrieval were performed using our
new version of the Japanese MAX-DOAS profile retrieval algorithm, version 2,
which is the updated version of the JM1 (Irie et al., 2011) used for CINDI.
Because most parts are the same as the JM1, some detailed descriptions have
been omitted in this paper. The recoded spectra were first analyzed by the
so-called DOAS method (Platt, 1994; Platt and Stutz, 2008), in which
spectral fitting is performed using the nonlinear least-squares method (Irie
et al., 2008a). The DOAS method retrieves the differential slant column
density (ΔSCD), defined as the difference between the SCD along the
path of sunlight for off-axis measurements (α < 90∘) and the SCD for the reference measurement (α = 90∘).
Most of the absorption cross-section data used
here were the same as those used during the CINDI campaign (Roscoe et al.,
2010). For H2O, we used the 2009 edition of the High-Resolution
Transmission (HITRAN) database. For O4, Hermans' cross-section data at
296 K (Herman, 2011) were used. Results obtained using the newly available
O4 cross-section data of Thalman and Volkamer (2013) are discussed
later.
The fitting window of 460–490 nm was analyzed for aerosol retrievals at
476 nm. The wavelength corresponds to the O4-cross-section-weighted mean
wavelengths for the fitting window. The fitting window was chosen to
minimize the wavelength dependence of the air mass factor (AMF) information
between representative wavelengths for O4 and NO2. NO2 is the
primary target gas for our MAX-DOAS observations (Irie et al., 2011). The
retrieved quantity, ΔSCD of O4, is referred to as the ΔSCD for quadratic O2 concentration (molecules2 cm-5) and
therefore contains the equilibrium constant between O4 and two O2
molecules (Greenblatt et al., 1990).
A set of O4ΔSCD data obtained at all α was inverted
into the vertical profile of AECs at 476 nm. The nonlinear inversion problem
was solved by the Optimal Estimation Method (Rodgers, 2000). To create a
lookup table (LUT) of the box-AMF vertical profile, which was required to
calculate O4ΔSCD in the forward model, we used the radiative
transfer model JACOSPAR. The JACOSPAR was developed based on its
predecessor, the Monte Carlo Atmospheric Radiative Transfer Simulator
(MCARaTS) (Iwabuchi, 2006). Box-AMF calculations by MCARaTS have been
validated by other radiative transfer models (Wagner et al., 2007). To
simulate a realistic atmosphere, we considered the surface altitude at the
measurement site (35 m a.s.l.) and the altitude where the instrument was
located (63 m a.s.l). In addition, in the forward model, temporal
variations in ambient temperature and pressure based on National Centers for
Environmental Prediction surface data were considered.
In this inversion, components of the measurement vector were set to O4
ΔSCD values at all α for a full α scanning time of
30 min. Here, the O4 ΔSCD value derived from observations is
denoted as O4 ΔSCD (obs) and that calculated by the forward
model is denoted as O4 ΔSCD (mdl). If the inversion was
perfectly finished, the O4 ΔSCD (mdl) should be identical to
O4 ΔSCD (obs) within the range corresponding to measurement
noises. However, if the systematic residual remained, these two quantities
could be linked by the following:
O4ΔSCDmdl×fO4=O4ΔSCDobs
or
fO4=O4ΔSCDobs/O4ΔSCDmdl,
where fO4 is the correction factor for O4 ΔSCD (mdl). This
factor was introduced to compensate for a possible discrepancy between
O4 ΔSCD (obs) and O4 ΔSCD (mdl). For instance, a
discrepancy could occur if there were a bias in O4 ΔSCD (mdl)
due to a bias in O4 absorption cross-section data. For the CINDI
campaign, the adopted fO4 values (and their reciprocals, as described by
Zieger et al., 2011) ranged from 1.20 (0.83) to 1.33 (0.75), depending on
the participating group (Zieger et al., 2011). Our JM1 algorithm adopted
1.25 (0.80), according to Clémer et al. (2010).
Examples of aerosol extinction coefficient (AEC) profiles retrieved
from MAX-DOAS observations. These are derived from four parameters of AOD,
F1, F2, and F3, as described in detail in the text. Parameters
used are given in the plot.
With the above setup, we retrieved four parameters, which were used to
construct the continuous AEC vertical profile. The state vector (x)
was then defined as
x=AODF1F2F3T.
The F values that range between 0 and 1 are the parameters determining the
shape of the vertical profile. Partial AOD values for 0–1, 1–2, and 2–3
km are given as AOD ×F1, AOD ×(1-F1)F2, and AOD ×(1-F1)(1-F2)F3,
respectively, and the partial AOD above 3 km as AOD ×(1-F1)(1-F2)(1-F3). From the partial AOD above 3 km, we
determined a continuous AEC profile for the layer from 3 to 100 km assuming
an AEC value at the top of the layer (100 km) and an exponential profile
shape. Similarly, we determined continuous profiles for layers of 2–3,
1–2, and 0–1 km. Examples of AEC vertical profiles parameterized in this
way are shown in Fig. 1. The a priori profile is shown in red. When AOD was
doubled, the AEC profile was simply scaled by a factor of 2 (Fig. 1).
Increasing the F1 value, for example, led to a greater fraction of AOD
below 1 km, resulting in a steep gradient of the AEC profile below 1 km.
When the F1 value decreased, the fraction of AOD below 1 km decreased.
This resulted in a reduction of the gradient, and the representation of an
uplifted aerosol profile was possible (Fig. 1).
The a priori values (± error) used in the present study were the same
as those used for CINDI (Irie et al., 2011): AOD = 0.21 ± 3.0,
F1 = 0.60 ± 0.05, F2 = 0.80 ± 0.03, and F3 = 0.80 ± 0.03. These yield an AEC of 0.13 km-1 as the mean values
for the 0–1 km layer. The corresponding error is +2.22/-1.94 km-1,
indicating the allowance for retrieving a wide range of AECs. Non-diagonal
elements of the a priori covariance matrix were set to 0.
Output from the vertical profile retrieval was only available for retrieved
AOD less than 3, which corresponds to the largest value in the LUT. This
excludes large optical depth cases, most of which should be due to optically
thick clouds. Further data screening was made using the root-mean squares of
the residuals of the O4 ΔSCD values. Larger residuals could
occur when the above-mentioned method of constructing a vertical profile was
too simple to represent the true profile, particularly with a very steep
vertical gradient of extinction due to clouds. In addition, rapid changes in
optical depth within the full α scanning time of 30 min could lead
to larger residuals. The threshold for these data screening was set to
10 % of the mean O4 ΔSCD (obs) in each 30 min interval.
CRDS
The CRDS instrument typically consists of two high-reflectivity
plano-concave mirrors set opposite one another. A pulsed or continuous laser
beam is coupled into the cavity from one side, and performs multiple
reflections inside the cavity. A photodetector is placed at the other side
of the cavity and measures the exponential decay of the light intensity
transmitted through the cavity. By comparing the decay rates measured in the
presence and absence of aerosols, the AECs can be determined.
At Tsukuba from 5 to 18 October 2010, the AECs at 355 and 532 nm were
measured using a custom-built 2λ-CRDS (Nakayama et al., 2010a, b). Ambient particles were sampled through the PM10 inlet placed
54 m a.s.l. The decay rates in the absence of aerosols were measured for 5 min
every 20 min by passing the particles through a high efficiency particulate
air filter (Pall). To determine the relative humidity (RH) dependence of the
AEC values, the AECs were measured under high RH conditions (RH = 79.0 ± 0.6 %) by passing the particles through a humidifier (Perma Pure
LLC, MD-110-24S-4) for 20 min every 60 min. The RH and temperature in the
cells were monitored using thermo-hygrometers (Vaisala, HMT-337). The 60 min
average exponential dependence parameter of extinction on RH (γ) was
calculated using a series of 20 min averages of AEC and RH data as follows:
AECRH1(λ)/AECRH2(λ)=[(100-RH1)/(100-RH2)]-γ,
where AECRH1(λ) and AECRH2(λ) are AEC values
measured at RH1 and RH2, when aerosols were passed through the
humidifier. The AECs (AECamb(λ)) corresponding to the ambient
RH (RHamb), temperature, and pressure conditions were then calculated
using the γ values:
AECamb(λ)=(TcellPamb/TambPcell)×AECRHcell(λ)[(100-RHamb)/(100-RHcell)]-γ,
where Tcell and Tamb are temperatures, and Pcell and Pamb
are pressures in the cell and ambient air, respectively. The 60 min averaged
AECamb (476 nm) was estimated from the obtained AECamb (355 nm)
and AECamb (532 nm) using the extinction Ångström exponent
between 355 and 532 nm and was used for comparison with the MAX-DOAS data.
The average (± 1σ) relative uncertainty in the 60 min average
AECamb (476 nm) values was estimated to be 11(± 7)% from
the uncertainties in the AEC measurements at 355 and 532 nm and in the
corrections for RH and wavelength dependence.
During the CRDS measurements, aerosol scattering and absorption coefficients
(ASC and AAC, respectively) were also measured using a 3λ nephelometer (TSI, model 3563, 450, 550, 700 nm) and a 3λ-particle soot absorption photometer (PSAP) (Radiance Research, 467, 530,
660 nm) (Uchiyama et al., 2014). The nephelometer data were corrected using
the scattering Ångström-exponent-dependent correction factors
reported by Anderson and Ogren (1998). The PSAP data were corrected based on
the scheme reported by Ogren (2010). These corrected data were used for
comparison with the CRDS data after taking into account the difference in
the RH, temperature, and pressure in the cells, as well as the difference in
wavelength. The AACs at 450 and 550 nm were estimated using the absorption
Ångström exponent between 462 and 526 nm and between 526 and 650 nm,
respectively, assuming that the AACs were independent of RH. The AECs at 355
and 532 nm obtained by the CRDS were corrected to the values corresponding
to the RH in the cell of nephelometer using the γ values. Then, the
AEC values at 450 and 550 nm were estimated using the extinction
Ångström exponent and used for the comparison with the nephelometer
and PSAP data. The AECs estimated from the CRDS data showed good agreement
with the sum of the ASCs measured by the TSI nephelometer and the AACs
estimated from PSAP data, with a slope of 1.01 (R2=0.94) and 1.00
(R2=0.93) at 450 and 550 nm, respectively.
Lidar
The lidar system operated was a compact Mie-scattering system utilizing the
fundamental and second harmonics of a flashlamp-pumped neodymium-doped
yttrium aluminum garnet (Nd:YAG) laser (1064/532 nm) as the light source
(Shimizu et al., 2004). To solve the lidar equation, we assumed a constant
extinction-to-backscattering ratio (S) of 50 sr. The S ratio can vary by more
than 30 % at Tsukuba, with resulting errors in AEC due to the use of a
fixed S occasionally exceeding 30 % (Irie et al., 2008a). In quantitative
discussion of AEC values near the surface, the lidar aerosol extinction data
at 532 nm were converted into AEC value at 476 nm, which can be compared to
the MAX-DOAS data, using coincident measurements of the Ångström
exponent by the CRDS. During the time period of this comparative
observation, lidar data were sometimes affected by clouds. In cases where
clouds were present below 6 km, an AEC profile was retrieved from data below
the cloud base. This is not the preference for the lidar data analysis and
is potentially the reason for the large uncertainty in derived AEC values
below clouds. Due to the lack of overlap between the laser beam and the
field of view of the telescope, the lowest height of retrieved AECs was 120 m. Thereafter, assuming homogeneous mixing of aerosols below this altitude,
we assumed constant AEC values and their errors in the vertical direction
below 120 m.
Vertical profiles of AEC values at 532 nm derived from lidar
observations. Black indicates the regions between the cloud base and
apparent cloud top. Gray corresponds to invisible regions above clouds.
Mean vertical profiles of lidar AEC data at 532 nm for 5–18 October 2010. Profiles with the original vertical resolution (30 m) and 1 km
mean profiles are shown in black and red, respectively. In this period,
there are significant amounts of AECs even above 2 km. Error bars represent
1σ standard deviations.
Time series of AEC and AOD values at 476 nm on 5–18 October 2010.
(Top) Near-surface AEC values from CRDS and MAX-DOAS; (middle) AEC values
for 0–1 km from lidar and MAX-DOAS; (bottom) AOD values from sky radiometer
and MAX-DOAS are compared in respective plots. For the MAX-DOAS retrieval, a
fO4 of 1.25 is assumed. Error bars for MAX-DOAS represent uncertainty
associated with the retrieval. Error bars for CRDS represent the 1σ
values estimated from the uncertainties in the AEC measurements at 355 and
532 nm and in the corrections for RH and wavelength dependence. Error bars
for lidar represent 1σ standard deviations of original 30 m AEC
values in the 0–1 km layer.
Correlation plots (left) between near-surface AEC values from CRDS
and MAX-DOAS, (center) between mean AEC values for 0–1 km from lidar and
MAX-DOAS, and (right) between AOD values from sky radiometer and MAX-DOAS.
In AEC plots, red symbols show the averages of the MAX-DOAS AEC values for
each 0.05 km-1 bin of CRDS or lidar data. The bin has been optimized
considering the number of bins and the number of data in each bin for all
pairs of comparisons in this study. For the MAX-DOAS retrieval, a fO4 of
1.25 is assumed.
Sky radiometer
A scanning sun–sky photometer called the sky radiometer (Prede Co., Ltd,
Tokyo, Japan) is the main instrument in the ground-based observation network
SKYNET (Nakajima et al., 2007). A set of measurements of the direct solar
irradiance and the solar radiance distributions was made with the sky
radiometer in 30 s to 2 min, depending on the solar zenith angle. This
was repeated every 10 min. The data were analyzed to derive the aerosol
optical properties (such as AOD) at 340, 380, 400, 500, 675, 870, and 1020 nm using the SKYRAD.pack version 4.2 software package (Nakajima et al.,
1996). The Ångström exponent was calculated from these AOD values
and was used to derive AOD values at 476 nm. Aerosol optical properties
retrieved from sky radiometers/SKYNET have been used to investigate regional
and seasonal characteristics of aerosols for climate and environmental
studies and to validate satellite remote sensing results (Higurashi and
Nakajima, 2002; Kim et al., 2005; Sohn et al., 2007; Pandithurai et al.,
2009; Campanelli et al., 2010; Khatri et al., 2010; Takenaka et al., 2011).
There are several reports that the AOD values obtained have high accuracy
compared to those of the standard Langley method and those from AERONET
(Campanelli et al., 2007; Che et al., 2008).
Results and discussion
Temporal variations in vertical profiles of AECs at 532 nm derived from
lidar observations at Tsukuba for the period of 5–18 October 2010 are
shown in Fig. 2. This time period can be characterized as a rather ordinary
period with moderate cloud occurrence. In addition, it can be seen that most
aerosols were located below an altitude of ∼ 2 km, and
significant, prolonged uplifted aerosols were not observed. This differs
from the situation during the CINDI campaign period, when the uplifted
aerosols could be attributed to the discrepancy found in comparisons between
MAX-DOAS and the ground-based humidified nephelometer (Zieger et al., 2011;
Irie et al., 2011). In Fig. 3, the mean vertical profile of lidar AEC data
taken on 5–18 October is plotted. Mean AECs above 3 km were about 0.03 km-1. Above 3 km, MAX-DOAS has a weak sensitivity to aerosols and the
JM2 vertical profile retrieval algorithm employs a parameterization that
does not allow a significant number of AECs (Fig. 1). This easily results in
the underestimation of AECs above 3 km and AOD.
Same as Fig. 4, but a fO4 of 1.00 is assumed in the MAX-DOAS
retrieval.
In Figs. 4 and 5, MAX-DOAS aerosol data are compared to CRDS AECs, lidar
AECs, and sky radiometer AOD data. The comparisons were made for a
wavelength of 476 nm. In the MAX-DOAS retrieval, a fO4 of 1.25 was
assumed, following the procedure taken in the CINDI campaign (Irie et al.,
2011). In general, temporal variation showed very similar patterns (Fig. 4).
A problem found in the comparisons is that most of the MAX-DOAS AEC values
at the near-surface level show values larger than CRDS values (Fig. 5). The
AECs from MAX-DOAS were larger than CRDS values by a factor of
∼ 1–4, which is comparable to that found by Zieger et al.
(2011) from similar comparisons during CINDI (a factor of 1.5–3.4). The
important point is that the systematic differences seen in the MAX-DOAS/CRDS
comparisons occurred even when uplifted aerosol layers were not often
present during the observation period of this study (Fig. 1). This indicates
that the occurrence of uplifted aerosols is not the major reason causing
significant differences.
Same as Fig. 5, but a fO4 of 1.00 is assumed in the MAX-DOAS
retrieval.
As a physical reason for applying this correction factor is unclear, other
comparisons were made assuming fO4 = 1.00 (i.e., no correction
applied) for MAX-DOAS retrievals (Figs. 6 and 7). For comparisons made at
the near surface and at 0–1 km, the retrievals assuming
fO4 = 1.00 brought MAX-DOAS AEC values closer to CRDS and lidar data than those
assuming fO4 = 1.25. The mean differences of MAX-DOAS AEC values from
CRDS and lidar data were improved from +0.07 ± 0.09 and +0.03 ± 0.10 km-1 to +0.04 ± 0.08 and
-0.02 ± 0.07 km-1, respectively. At the same time, however, almost all of the
MAX-DOAS AOD values showed underestimation. In addition, simple linear
regression analyses show rather poor correlations with CRDS and lidar AEC
data at R2 of ∼ 0.4 and 0.7, respectively. Furthermore,
the number of MAX-DOAS aerosol data that survived after retrievals and
data screening becomes much smaller (N=107) compared to that for
retrievals with fO4 = 1.25 (N=157). This is due to poor O4
ΔSCD fitting results with relatively high residuals, particularly at
high α, as discussed in detail below.
Median values of residuals, O4 ΔSCD (obs) minus O4
ΔSCD (mdl), as a function of elevation angle. Values for retrievals
with fO4 = 1.00 and fO4 = 1.25 are plotted with circles and
squares, respectively. Error bars represent 67 % ranges.
To search for the cause, we focused on median values of residuals for
profile retrievals, O4 ΔSCD (obs) minus O4 ΔSCD
(mdl), as a function of α. As shown in Fig. 8, we found that the
residuals were very small (< 1042 molecules2 cm-5) at
α≤10∘. However, the residuals were
relatively large at α of 20 and 30∘. In particular, for retrievals adopting fO4 = 1.00,
O4 ΔSCD (obs) values tended to be systematically larger than O4 ΔSCD (mdl) values, indicating that the model values were underestimated.
Clémer et al. (2010) compared the measured and simulated O4 ΔSCDs at α of 15 and 30∘ and found
that values of the ΔSCD (mdl) values were systematically 25 ± 10 % smaller than the measured ones.
Individual profile retrieval residuals, O4 ΔSCD (obs)
minus O4 ΔSCD (mdl), as a function of O4 ΔSCD
(obs). Values for retrievals with fO4 = 1.00 are plotted. Values for
α of 3, 5, 10, 20, and 30∘ are shown in black, blue,
green orange, and red, respectively.
As found in MAX-DOAS/CRDS comparisons made earlier, applying a single number
for the correction factor (fO4 = 1.25) to all α yielded
significant deviations in MAX-DOAS AEC values from the CRDS data. In
contrast, when no correction factor was applied, agreement was improved.
These results gave us an idea that a different magnitude of correction
factor should be applied for different α, if a correction factor is
needed.
To check if the correction factor is needed and to further estimate
empirically the required correction factor from measurements, we analyzed
the residuals of O4 ΔSCDs that arose from individual retrievals
for the case of fO4 = 1.00. As also seen from analysis of their median
values (Fig. 8), the individual residual was usually small at the lowest
α (3∘) (Fig. 9). While the lowest α is
usually most important in determining near-surface AEC, the MAX-DOAS AECs
retrieved with a fO4 = 1.00 agreed well with the CRDS values, as
discussed above. This may suggest that no significant correction factor is
needed (i.e., the correction factor would be close to unity) for the lowest
α. In contrast, the residuals tended to be greater at higher α. In particular, as clearly seen at α of 10,
20, and 30∘, the residual increases with
an increase in O4 ΔSCD (obs).
Relationships of 80, 90, and 95th percentiles of O4
ΔSCD (obs)/O4 ΔSCD (mdl) with α.
In principle, the O4 ΔSCD (mdl) has the upper limit that
corresponds to pure Rayleigh conditions. Under ambient conditions with a
certain amount of aerosols near the ground, the upper limit for the O4
ΔSCD (mdl) values is approximated to correspond to conditions of
very low aerosols above the near-ground aerosol layer. When the O4
ΔSCD (obs) values are greater than the upper limit, their difference
emerges as the residual. This happened in our retrievals, as indicated by
the clear linear correlations between the residual and the O4 ΔSCD (obs) for high α in Fig. 9.
To estimate the correction factor needed to explain the discrepancy found in
the fitting residuals, we investigated the ratio (R) of O4 ΔSCDs
(obs) to O4 ΔSCDs (mdl). An R ratio close to unity means that
the O4 ΔSCD (obs) is explained by the O4 ΔSCD
(mdl) with retrieved aerosol profiles. An R ratio smaller than unity is
potentially explained by artificially adding more aerosols in the retrieved
aerosol profiles, when AEC values are underestimated in the retrieved
profiles. Similarly, an R ratio larger than unity can be explained by
artificially lowering AEC values.
Same as Fig. 4, but fO4 is assumed to be a function of α in the MAX-DOAS retrieval.
Here, we make the hypothesis that a correction factor is needed. If so, the
correction factor fO4 should correspond to the largest R to compensate
for as much residuals as possible. Considering that the estimate of R itself
had uncertainty, the largest R was estimated to be approximate to the 80th,
90th, and 95th percentiles for each α. The largest R values estimated
in this way are plotted as a function of α in Fig. 10. We found
clear relationships between the largest R and α. Interestingly, the
regression lines pass over the point of R at ∼ 1.25 at an
α of 15∘, consistent with the estimate of the
correction factor by Clémer et al. (2010) for the α of
15∘. This strongly supports the hypothesis that a
correction factor is needed, particularly for high α.
Same as Fig. 5, but fO4 is assumed to be a function of α in the MAX-DOAS retrieval.
From these results, we derived the α-dependent correction factor as
fO4=fO4α=1+α/60.
Using this empirical equation, retrievals of AEC and AOD were performed.
Updated results for comparisons with CRDS AECs, lidar AECs, and sky
radiometer AOD data are shown in Figs. 11 and 12. Compared to the results
presented earlier, reasonable agreements can be seen for the three
comparisons with CRDS, lidar, and sky radiometer. For comparisons with CRDS
and lidar AEC data, the values of determination coefficient R2 were as
high as 0.96 and 0.89, respectively. The mean differences of MAX-DOAS AEC
values from CRDS and lidar data were as small as +0.01 ± 0.04 and
-0.03 ± 0.05 km-1, respectively.
Estimates of effective temperatures (Teff) for O4
absorption for an AOD (476 nm) of 0.1, a solar zenith angle of
45∘, and a relative azimuth angle of 180∘.
Surface temperature and pressure are assumed to be 292 K and 986 hPa,
respectively, according to mean values at Tsukuba during the observation
period.
Elevation angle (∘)
3
5
10
20
30
SCD-based Teff (K)
277
275
272
270
268
ΔSCD-based Teff (K)
283
279
276
274
271
However, this empirical equation for the correction factor should be used
with caution, unless the physical explanations underpinning it are
clarified. One potential reason for the need for the correction factor is
that O4 ΔSCD (obs) is less accurate (more overestimated) at
higher α. In fact, the nature of molecular interactions in O4
is still under discussion (e.g., Sneep et al., 2006). Recently, Thalman and
Volkamer (2013) performed laboratory measurements of the absorption cross
section of O4, σ(O4) at a pressure close to ambient (825 hPa). Their σ(O4) data at 295 K agreed with Hermans (2011)
σ(O4) at 296 K within instrumental measurement errors. The
Hermans (2011) σ(O4) data were recommended for MAX-DOAS aerosol
retrievals during the CINDI campaign and were also adopted in the present
study. Thalman and Volkamer (2013) found that the peak O4 cross
sections for the 477 nm absorption band (10-46 cm5 molec-2)
were temperature dependent and were 6.60, 6.91, and 7.67 at 293, 253, and
203 K, respectively. Values relative to 293 K are 1.00, 1.05, and 1.16,
respectively. Thus, the peak O4 cross section increases by a factor of
1.05 per 40 K reduction of temperature from 293 to 253 K or ∼ 1.09 ± 0.025 per 44 K reduction from 275 to 231 K (Thalman
and Volkamer, 2013; Spinei et al., 2015). The potential
overestimation in ΔSCD (obs) due to the use of smaller O4 cross-section values at a T higher than the actual one can be compensated for by
the same magnitude of fO4, according to Eq. (1). Based on atmospheric
direct sun observations, there was no pressure dependence of the O4
cross section within their measurement error of 3 % (Spinei et al.,
2015).
Same as Fig. 4, but a fO4 = 1.00 is assumed in the MAX-DOAS
retrieval. α used in the retrieval was limited to ≤ 10∘.
Same as Fig. 5, but a fO4 = 1.00 is assumed in the MAX-DOAS
retrieval. α used in the retrieval was limited to ≤ 10∘.
In contrast, we estimated the ΔSCD (SCD)-based effective
temperature (Teff) for observations in the present study (Table 1). For
observations of this study, the mean surface temperature was 292 K with a
standard deviation of 7 K. When the surface temperature varies by 7 K, the
estimated Teff also varies by 7 K under conditions given in the caption
of Table 1. However, Teff differences at different α angles
become much smaller. The Teff values for α of 3–30∘ ranged from 283 (277) to 271 (268) K, yielding a
reduction of Teff by 12 K, when α increased from
3∘to 30∘. Using Eq. (6), the rate is
translated to an increase of fO4 by a factor of 1.45 per 12 K reduction
in temperature. Thus, the tendency for a larger fO4 to be needed at a
colder Teff is consistent with that deduced from experiments by Thalman
and Volkamer (2013) and Spinei et al. (2015), although the magnitude is
different. A similar discussion has been made in the study by Spinei et al. (2015).
To investigate uncertainty in the retrieved ΔO4 SCD (obs),
additional DOAS fitting was performed. Adopting Thalman and Volkamer (2013)
O4 absorption cross-section data for 295 K increased ΔO4
SCD (obs) by 2 % on average. Adopting the data for 203 K decreased ΔO4 SCD (obs) by 14 % on average, which is comparable to the 16 %
change in the peak cross sections between 295 and 203 K. In this case,
however, residuals significantly increased. The combined use of the
two-temperature cross-section data of Thalman and Volkamer (2013) at 295 and
203 K resulted in a 2 % increase on average. The impact of changing the
degree of polynomial and the degree of offset polynomial by ± 1 was
within ± 3 %. All of these tests were insufficient to quantitatively
explain Eq. (6). However, we note here that the results from these tests
do not support the accuracy of ΔO4 SCD (obs). Systematic biases
might occur particularly at high α due to a relatively thin optical
depth of O4.
The other potential cause of uncertainty is that the O4 ΔSCD
(mdl) may be less accurate at higher α. However, calculations of the
box AMF by various radiative transfer models were validated by Wagner et al. (2009), and larger differences among them were seen at very low
α. Therefore, this is not likely a cause. In addition, there is the
fact that direct sunlight observations do not need a correction factor
(Spinei et al., 2015), suggesting that this issue is only for scattered
light observations. These discussions would help us identify a physical
explanation of the need for a correction factor in the future.
Same as Fig. 4, but fO4 is assumed to be a function of α in the MAX-DOAS retrieval. α used in the retrieval has been
limited to ≤ 10∘.
Same as Fig. 5, but fO4 is assumed to be a function of α in the MAX-DOAS retrieval. α used in the retrieval has been
limited to ≤ 10∘.
Although the definitive physical explanations behind Eq. (6) are unclear,
it is clear that problems tend to occur at relatively large α.
Considering this, as a practical solution we propose limiting the set of
α to ≤ 10∘ to minimize the above-mentioned
potential impacts and to keep a sufficient number of α for each
profile retrieval. Under these conditions, we tested two retrievals without
(i.e., fO4 = 1.00) or with the correction factor (fO4 = fO4(α)). The respective results are shown in Figs. 13–14 and
Figs. 15–16.
Although a set of α is limited to ≤ 10∘, we
obtain overall reasonable agreements similar to those seen for retrievals
using all α. As the most significant difference between results from
retrievals with and without the correction factor, we can see that almost
all of the MAX-DOAS AOD values underestimated the sky radiometer AOD when
the retrievals were performed without any correction factor (Fig. 14). In
addition, for comparisons with CRDS and lidar AECs, correlations for
retrievals adopting fO4(α) were likely more reasonable (their
respective R2 values of 0.84 and 0.80, and mean differences of +0.02 ± 0.04 and -0.01 ± 0.08 km-1) than those without a
correction factor (R2 of 0.75 and 0.70, and mean differences of +0.03
± 0.05 and -0.03 ± 0.08 km-1). Therefore, we propose
limiting the set of α to ≤ 10∘and adopting
fO4(α) for practical profile retrievals. These are encouraged to
be tested by other MAX-DOAS aerosol profile retrieval algorithms.
Limiting the set of α to ≤ 10∘ lowers degrees of freedom for signal (DOFS) but increases the number of available data (Table 2). The former means that
observations at α larger than 10∘ can contribute to an
increase in DOFS. Such observations at high α should be added when
reasons for the large ΔSCD fitting residuals found in Figs. 8 and 9
are quantitatively understood. The increased number of data again
supports the tendency that fitting for α≤ 10∘ is less subject to the
correction factor than that for α=20∘ and
30∘. The increase in the number of data is partly due to the fact
that more data under cloudy conditions became available. Excluding α
of 20 and 30∘ leads to the loss of
sensitivity to extinction at high altitudes, where clouds are usually more
dominant than aerosols. As a result, although the DOFS decreases, the
capability for observing the boundary layer by MAX-DOAS is expected to be
enhanced.
DOFS and the number of available data (N) for each case of
correction factor.
Correction factor and α range
DOFS
N
fO4 = 1.25 and all α
2.5±0.4
157
fO4 = 1.00 and all α
2.2±0.4
107
fO4=fO4(α) and all α
2.4±0.4
159
fO4 = 1.00 and α≤10∘
2.0±0.3
207
fO4=fO4(α) and α≤10∘
2.1±0.3
229