Evaluation of MAX-DOAS aerosol retrievals by coincident observations using CRDS , lidar , and sky radiometer in Tsukuba , Japan

H. Irie, T. Nakayama, A. Shimizu, A. Yamazaki, T. Nagai, A. Uchiyama, Y. Zaizen, S. Kagamitani, and Y. Matsumi Center for Environmental Remote Sensing, Chiba University, 1-33 Yayoicho, Inage-ku, Chiba 263-8522, Japan National Institute for Environmental Studies, 16-2, Onogawa, Tsukuba, Ibaraki 305-8506, Japan Climate Research Department, Meteorological Research Institute, Japan Meteorological Agency, 1-1 Nagamine, Tsukuba 305-0052, Japan Solar-Terrestrial Environment Laboratory, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan


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 (NO 2 ) and sulfur dioxide (SO 2 ), 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., 2008aIrie et al., , b, 2009Irie et al., , 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 NO 2 , 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 R 2 of 0.62-0.78,but the AECs from MAX-DOAS were a factor of 1.5-3.4larger 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 (O 4 or O 2 -O 2 ) 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 O 4 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 O 4 absorption.Potential practical solutions to achieve agreement of the MAX-DOAS observations with the three other observations are discussed.

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 NO 2 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 ( SCD), 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 H 2 O, we used the 2009 edition of the High-Resolution Transmission (HITRAN) database.For O 4 , Hermans' cross-section data at 296 K (Herman, 2011) were used.Results obtained using the newly available O 4 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 O 4 -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 O 4 and NO 2 .NO 2 is the primary target gas for our MAX-DOAS observations (Irie et al., 2011).The retrieved quantity, SCD of O 4 , is referred to as the SCD for quadratic O 2 concentration (molecules 2 cm −5 ) and therefore contains the equilibrium constant between O 4 and two O 2 molecules (Greenblatt et al., 1990).
A set of O 4 SCD 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 O 4 SCD 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 O 4 SCD values at all α for a full α scanning time of 30 min.Here, the O 4 SCD value derived from observations is denoted as O 4 SCD (obs) and that calculated by the forward model is denoted as O 4 SCD (mdl).If the inversion was perfectly finished, the O 4 SCD (mdl) should be identical to O 4 SCD (obs) within the range corresponding to measurement noises.However, if the systematic residual remained, these two quantities could be linked by the following: or where f O 4 is the correction factor for O 4 SCD (mdl).This factor was introduced to compensate for a possible discrepancy between O 4 SCD (obs) and O 4 SCD (mdl).For instance, a discrepancy could occur if there were a bias in O 4 SCD (mdl) due to a bias in O 4 absorption cross-section data.For the CINDI campaign, the adopted f O 4 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).
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 (3) 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 ×F 1 , AOD ×(1 − F 1 )F 2 , and AOD ×(1 − F 1 )(1 − F 2 )F 3 , respectively, and the partial AOD above 3 km as AOD 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 F 1 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 F 1 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, F 1 = 0.60 ± 0.05, F 2 = 0.80 ± 0.03, and F 3 = 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/−1.94km −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 O 4 SCD values.Larger residuals could occur when the above-mentioned method of construct-

H. Irie et al.: Evaluation of MAX-DOAS aerosol retrievals by coincident observations
ing 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 O 4 SCD (obs) in each 30 min interval.

CRDS
The CRDS instrument typically consists of two highreflectivity 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 PM 10 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 thermohygrometers (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: where AEC RH 1 (λ) and AEC RH 2 (λ) are AEC values measured at RH 1 and RH 2 , when aerosols were passed through the humidifier.The AECs (AEC amb (λ)) corresponding to the ambient RH (RH amb ), temperature, and pressure conditions were then calculated using the γ values: AEC amb (λ) = (T cell P amb /T amb P cell ) (5) where T cell and T amb are temperatures, and P cell and P amb are pressures in the cell and ambient air, respectively.The 60 min averaged AEC amb (476 nm) was estimated from the obtained AEC amb (355 nm) and AEC amb (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 AEC amb (476 nm) values was estimated to be 11(± 7)% from the un-certainties 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 (R 2 = 0.94) and 1.00 (R 2 = 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.

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.packversion 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.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 f O 4 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 nearsurface 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.
As a physical reason for applying this correction factor is unclear, other comparisons were made assuming f O 4 = 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 f O 4 = 1.00  brought MAX-DOAS AEC values closer to CRDS and lidar data than those assuming f O 4 = 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 R 2 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 f O 4 = 1.25 (N = 157).This is due to poor O 4 SCD fitting results with relatively high residuals, particularly at high α, as discussed in detail below.
To search for the cause, we focused on median values of residuals for profile retrievals, O 4 SCD (obs) minus O 4 SCD (mdl), as a function of α.As shown in Fig. 8, we found that the residuals were very small (< 10 42 molecules 2 cm −5 ) at α ≤ 10 • .However, the residuals were relatively large at α of 20 and 30 • .In particular, for retrievals As found in MAX-DOAS/CRDS comparisons made earlier, applying a single number for the correction factor (f O 4 = 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 O 4 SCDs that arose from individual retrievals for the case of f O 4 = 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 f O 4 = 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 O 4 SCD (obs).
In principle, the O 4 SCD (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 O 4 SCD (mdl) values is approximated to correspond to conditions of very low aerosols above the near-ground aerosol layer.When the O 4 SCD (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 O 4 SCD (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 O 4 SCDs (obs) to O 4 SCDs (mdl).An R ratio close to unity means that the O 4 SCD (obs) is explained by the O 4 SCD (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.
Here, we make the hypothesis that a correction factor is needed.If so, the correction factor f O 4 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.
From these results, we derived the α-dependent correction factor as 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 R 2 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.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 O 4 SCD (obs) is less accurate (more overestimated) at higher α.In fact, the nature of molecular interactions in O 4 is still under discussion (e.g., Sneep et al., 2006).Recently, Thalman and Volkamer (2013) performed laboratory measurements of the absorption cross section of O 4 , σ (O 4 ) at a pressure close to ambient (825 hPa).Their σ (O 4 ) data at 295 K agreed with Hermans (2011) σ (O 4 ) at 296 K within instrumental measurement errors.The Hermans (2011) σ (O 4 ) 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 O 4 cross sections for the 477 nm absorption band (10 −46 cm 5 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 O 4 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 SCD (obs) due to the use of smaller O 4 cross-section values at a T higher than the actual one can be compensated for by the same magnitude of f O 4 , according to Eq. ( 1).Based on atmospheric direct sun observations, there was no pressure de- pendence of the O 4 cross section within their measurement error of 3 % (Spinei et al., 2015).
In contrast, we estimated the SCD (SCD)-based effective temperature (T eff ) 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 T eff also varies by 7 K under conditions given in the caption of Table 1.However, T eff differences at different α angles become much smaller.The T eff values for α of 3-30 • ranged from 283 (277) to 271 (268) K, yielding a reduction of T eff by 12 K, when α increased from 3 • to 30 • .Using Eq. ( 6), the rate is translated to an increase of f O 4 by a factor of 1.45 per 12 K reduction in temperature.Thus, the tendency for a larger f O 4 to be needed at a colder T eff 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 O 4 SCD (obs), additional DOAS fitting was performed.Adopting Thalman and Volkamer (2013) O 4 absorption cross-section data for 295 K increased O 4 SCD (obs) by 2 % on average.Adopting the data for 203 K decreased O 4 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 O 4 SCD (obs).Systematic biases might occur particularly at high α due to a relatively thin optical depth of O 4 .
The other potential cause of uncertainty is that the O 4 SCD (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.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., f O 4 = 1.00) or 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 f O 4 (α) were likely more reasonable (their respective R 2 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 (R 2 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 f O 4 (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 SCD 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.

Conclusions
Coincident aerosol observations of MAX-DOAS with those of CRDS, lidar, and sky radiometer at Tsukuba, Japan, on 5-18 October 2010 were used to evaluate the MAX-DOAS aerosol retrieval from the viewpoint of the need for a correction factor for O 4 absorption (f O 4 ).After applying a f O 4 of 1.25 to all of the elevation angles, the retrieved near-surface AEC values were found to be significantly larger than those from the surface observations by CRDS.These results are consistent with those of Zieger et al. (2011), who analyzed data from the CINDI campaign with similar correction factors.Without any correction factor, agreement was improved.However, significant characterized residuals were left, particularly at relatively high elevation angles of 20 and 30 • .From detailed analysis of residuals, we empirically deduced an elevation-angle-dependent correction factor (Eq. 6) that describes a larger correction factor at a higher elevation angle.This worked well to improve agreements for all comparisons with CRDS, lidar, and sky radiometer.Equation ( 6) accounts for the T dependence of O 4 absorption cross sections measured by Thalman and Volkamer (2013) qualitatively but is insufficient quantitatively.Another potential reason for the need of a correction factor is that O 4 SCDs derived from DOAS fit might be less accurate at higher elevation angles.Although more investigation is encouraged to quantitatively identify the cause, for minimizing such po-tential effects we propose to limit the set of elevation angles to ≤ 10 • and to adopt an elevation-angle-dependent correction factor for practical profile retrievals with scattered light observations by the ground-based MAX-DOAS.

Figure 1 .
Figure 1.Examples of aerosol extinction coefficient (AEC) profiles retrieved from MAX-DOAS observations.These are derived from four parameters of AOD, F 1 , F 2 , and F 3 , as described in detail in the text.Parameters used are given in the plot.

Figure 2 .
Figure 2. 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.

Figure 3 .
Figure 3. 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.

Figure 4 .
Figure 4. 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 f O 4 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.

Figure 5 .
Figure 5. 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 f O 4 of 1.25 is assumed.

Figure 6 .
Figure 6.Same as Fig. 4, but a f O 4 of 1.00 is assumed in the MAX-DOAS retrieval.

Figure 7 .
Figure 7. Same as Fig. 5, but a f O 4 of 1.00 is assumed in the MAX-DOAS retrieval.

Figure 8 .
Figure 8. Median values of residuals, O 4 SCD (obs) minus O 4 SCD (mdl), as a function of elevation angle.Values for retrievals with f O 4 = 1.00 and f O 4 = 1.25 are plotted with circles and squares, respectively.Error bars represent 67 % ranges.

Figure 11 .
Figure 11.Same as Fig. 4, but f O 4 is assumed to be a function of α in the MAX-DOAS retrieval.

Figure 12 .
Figure 12.Same as Fig. 5, but f O 4 is assumed to be a function of α in the MAX-DOAS retrieval.

Figure 13 .
Figure 13.Same as Fig. 4, but a f O 4 = 1.00 is assumed in the MAX-DOAS retrieval.α used in the retrieval was limited to ≤ 10 • .

Figure 14 .
Figure 14.Same as Fig. 5, but a f O 4 = 1.00 is assumed in the MAX-DOAS retrieval.α used in the retrieval was limited to ≤ 10 • .

Figure 15 .
Figure 15.Same as Fig. 4, but f O 4 is assumed to be a function of α in the MAX-DOAS retrieval.α used in the retrieval has been limited to ≤ 10 • .

Figure 16 .
Figure 16.Same as Fig. 5, but f O 4 is assumed to be a function of α in the MAX-DOAS retrieval.α used in the retrieval has been limited to ≤ 10 • .

Table 1 .
Estimates of effective temperatures (T eff ) for O 4 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.