Retrieval Accuracy of HCHO Vertical Column Density from Ground-Based Direct-Sun Measurement and First HCHO Column Measurement Using Pandora

In the present study, we investigate the effects of signal to noise (SNR), slit function (FWHM), and aerosol optical depth (AOD) on the accuracy of formaldehyde (HCHO) vertical column density (HCHOVCD) using the ground-based direct-sun synthetic radiance based on differential optical absorption spectroscopy (DOAS). We found that the effect of SNR on HCHO retrieval accuracy is larger than those of FWHM and AOD. When SNR = 650 (1300), FWHM = 0.6, and AOD = 0.2, the absolute percentage difference (APD) between the true HCHOVCD values and those retrieved ranges from 54 (30%) to 5% (1%) for the HCHOVCD of 5.0 × 1015 and 1.1 × 1017 molecules cm−2, respectively. Interestingly, the maximum AOD effect on the HCHO accuracy was found for the HCHOVCD of 3.0× 1016 molecules cm−2. In addition, we carried out the first ground-based direct-sun measurements in the ultraviolet (UV) wavelength range to retrieve the HCHOVCD using Pandora in Seoul. The HCHOVCD was low at 12:00 p.m. local time (LT) in all seasons, whereas it was high in the morning (10:00 a.m. LT) and late afternoon (4:00 p.m. LT), except in winter. The maximum HCHOVCD values were 2.68 × 1016, 3.19 × 1016, 2.00 × 1016, and 1.63 × 1016 molecules cm−2 at 10:00 a.m. LT in spring, 10:00 a.m. LT in summer, 1:00 p.m. LT in autumn, and 9:00 a.m. LT in winter, respectively. The minimum values of Pandora HCHOVCD were 1.63 × 1016, 2.23 × 1016, 1.26 × 1016, and 0.82 × 1016 molecules cm−2 at around 1:45 p.m. LT in spring, summer, autumn, and winter, respectively. This seasonal pattern of high values in summer and low values in winter implies that photo-oxidation plays an important role in HCHO production. The correlation coefficient (R) between the monthly HCHOVCD values from Pandora and those from the Ozone Monitoring Instrument (OMI) is 0.61, and the slope is 1.25.


Introduction
Despite its relatively short atmospheric lifetime [1][2][3], which is less than five hours near the surface [4], formaldehyde (HCHO) is one of the most abundant carbonyl compounds in the atmosphere.HCHO in the atmosphere has a surface mixing ratio of several tens of ppbv in a polluted atmosphere [5][6][7][8]; in an uncontaminated atmosphere, it has a background concentration of several tens of pptv [9][10][11][12].
Atmospheric HCHO levels have been measured for more than 15 years using satellite sensors from the Global Ozone Monitoring Experiment (GOME) onboard the European Remote Sensing-2 satellite (ERS-2) launched in April 1995, the SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY) onboard the European Environment Satellite (ENVISAT) launched in March 2002, the Atmospheric Chemistry Experiment-Fourier Transform Spectrometer (ACE-FTS) onboard the Science Satellite (SCISAT-1) launched in August 2003, the Ozone Monitoring Instrument (OMI) on the Aura satellite launched in June 2004, GOME-2 onboard the Meteorological Operational satellites launched in January 2007 (MetOp-A) and September 2012 (MetOp-B), and the Ozone Mapping and Profiler Suite (OMPS) on the Suomi National Polar-orbiting Partnership (Suomi NPP) satellite launched in October 2011.Each of these satellites uses a different fitting window to retrieve the HCHO data.The GOME, SCIAMACHY, OMI, GOME-2, and OMPS sensors have fitting windows of 337.0-359.0,334.0-348.0,328.5-356.5, 328.5-346, and 328.5-356.5 nm, respectively.
Chance et al. [13] retrieved HCHO data for North America from GOME measurements.De Smedt et al. [14] calculated the global tropospheric vertical column density (VCD) of HCHO (HCHO VCD ) based on the GOME and SCIAMACHY measurements and reported the temporal trend in HCHO between 1997 and 2009.To investigate the spatiotemporal characteristics of the HCHO column between 2004 and 2014, De Smedt et al. [15] used data from SCIAMACHY, GOME-2, and OMI to develop a new version (v14) of the BIRA-IASB algorithm for HCHO retrieval.
A number of ground-based HCHO retrieval studies have also been conducted to validate the satellite-based HCHO observations using various ground-based remote sensing techniques.In particular, Multi-AXis Differential Optical Absorption Spectroscopy (MAX-DOAS), which is highly sensitive to trace gases in the planetary boundary layer (PBL) and uses scattered sunlight as a light source to retrieve the column density of HCHO in the atmosphere, has been used successfully in several studies.Among these MAX-DOAS studies of HCHO, Li et al. [16] retrieved the vertical HCHO distribution using a fitting window of 335.0-358.0nm based on MAX-DOAS data from Shanghai, and reported the summertime diurnal characteristics of HCHO VCD .Lee et al. [17] investigated diurnal variations in the vertical distribution of HCHO using a fitting window of 335.0-357.0nm based on MAX-DOAS data from Beijing in summer, and compared these retrieved HCHO data with OMI HCHO data.Franco et al. [18] retrieved the vertical HCHO distribution using a fitting window of 328.5-358.0nm with MAX-DOAS data and Fourier Transform InfraRed (FTIR) measurements from Jungfraujoch in Switzerland, and investigated the sensitivity difference of the vertical HCHO distribution between the two ground-based instruments.Previous HCHO-related MAX-DOAS studies are summarized in Table 1.Among the instruments that use direct ultraviolet (UV) and visible sunlight as a light source, MultiFunction Differential Optical Absorption Spectroscopy (MFDOAS) has been used to measure NO 2 VCD at the Goddard Space Flight Center [24].The Pandora Spectrometer Instrument (PSI) has also been used to retrieve O 3 VCD in Boulder, USA, and to retrieve NO 2 VCD in Maryland, USA, and in Thessaloniki, Greece [24,25].Fioletov et al. [26] retrieved SO 2 VCD data from Pandora measurements in the Canadian oil sands region.To date, no studies have measured the HCHO column using MFDOAS or Pandora.
To use a ground-based instrument as a tool to validate satellite products, the accuracy of the data obtained from the ground-based instrument must be quantified and understood.We understand some of the retrieval uncertainty associated with MAX-DOAS measurement since there have been many studies that reported the retrieval accuracy of MAX-DOAS [22,27,28].However, although there are either no, or negligible, air mass factor (AMF) errors in ground-based direct-sun measurements, the light absorption path length of direct-sun measurements is generally shorter than that of scattered-sun light measurements made using MAX-DOAS in most regions, which implies that the retrieval sensitivity of direct-sun measurements with respect to trace gases in PBL such as HCHO is lower than that of MAX-DOAS.Unfortunately, there is no information available regarding the errors associated with the products retrieved from such ground-based direct-sun measurements using the DOAS technique.
Therefore, the aims of this study are as follows: (1) to quantify the effects of signal-to-noise ratios (SNR), slit function (FWHM), and aerosol optical depth (AOD) on the HCHO VCD accuracy of DOAS HCHO retrieval at various HCHO levels obtained from ground-based direct-sun measurement; (2) to retrieve, for the first time, HCHO VCD using Pandora data and compare this with the values retrieved from the OMI in Seoul, South Korea; (3) to analyze the seasonal and diurnal characteristics of the retrieved HCHO columns from Seoul.

Estimation of HCHO VCD Retrieval Accuracy
Figure 1 shows a flowchart of the HCHO VCD retrieval accuracy test.We used a four-step process to determine which parameters affect the HCHO VCD retrieval accuracy.First, a total 135 of synthetic radiances were generated using the linearized pseudo-spherical scalar and vector discrete ordinate radiative transfer (VLIDORT, version 2.6) model [29] between 290 and 510 nm and with a 0.2 nm sampling resolution under various SNR, FWHM, AOD, and HCHO VCD .Here, the HCHO vertical profile was assumed to be a box profile [30] (Figure 2).The values of the HCHO VCD and HCHO vertical upper limit, model input parameters such as aerosol properties (aerosol type, AOD, and aerosol peak height (APH)), and the geometry information (solar zenith angle (SZA) and surface reflectance) are summarized in Table 2. Other gas vertical profiles, such as ozone (O 3 ) and nitrogen dioxide (NO 2 ), were obtained from the Deriving Information of Surface Conditions from Column and Vertically Resolved Observations Relevant to Air Quality (Discover-AQ) dataset [31,32].

The aerosol profile is based on a Gaussian distribution function (GDF), as used by Jeong et al. [33]
and Hong et al. [34], and the GDF equation is as follows: where z n1 and z n2 are the aerosol lower and upper limits, respectively, W is a normalization constant related to total aerosol loading, h is related to the half width η, and z p is the APH [29,33,34].
Second, random noise (SNR from 650, 920, and 1300) was added to the simulated synthetic radiances.Herman et al. [25] reported that the Pandora spectrometer system is not noise limited when measuring under clear-sky conditions [25].Moreover, Herman et al. [25] assume that, if the entire variability were instrument noise, the signal-to-noise ratio would be 650:1.SNRs of 920 and 1300 calculated when the exposure time is doubled and quadrupled, respectively.These synthetic radiances were convolved using various Gaussian slit functions with a full-width-half-maximums (FWHMs) of 0.2, 0.6, and 1.0.The SNR of each synthetic radiance was calculated using the following equation [35]: where SNR i (λ) and I i (λ) are the i-th SNR and radiance at wavelength λ, respectively, I a is the average value of all synthetic radiances from 290 to 510 nm, and SNR a is its corresponding SNR.
Third, in the present study, the AMF G was used as the AMF because Pandora takes ground-based direct-sun measurements [25].The AMF G is calculated as follows: Then, the retrieved HCHO Slant Column Densities (HCHO SCDs ) were divided by the AMF G to convert them to HCHO VCD values.The spectral fitting method used to retrieve HCHO SCD is described in Section 2.2.2.
Finally, the retrieved HCHO VCD values were compared with the true HCHO VCD values.Here, the true HCHO VCD denotes the line-integrated value of the HCHO vertical profile data, which are inputted in the RTM to calculate the synthetic radiances (Figure 1).The absolute percentage difference (APD) was calculated through the difference between the true HCHO VCD retrieved from the HCHO vertical profile, which are inputted in the RTM to calculate the synthetic radiances and the HCHO VCD retrieved by the spectral fitting method and AMF G described above.The HCHO VCD error, which is the difference between the retrieved and true HCHO VCD values, occurs only due to the spectral fitting because we used AMF G values in this study.The Pandora measurements were made on the rooftop of the Science Building at Yonsei University in Seoul (37.56 • N, 126.94 • E) between March 2012 and December 2014.The PSI consists of a two filter wheel optical head sensor mounted on a computer-controlled sun tracker and sky scanner connected via a 400-micron core diameter single-strand multi-mode optical fiber to an Avantes symmetric Czerny-Turner 2048 × 64 pixels charge-coupled device (CCD) detector maintained at a temperature of 1 • C to reduce the dark current noise.This spectrometer operates in the 280-530 nm spectral range with a 0.6 nm slit function width (full width at half maximum).A fiber optic cable allows the temperature-sensitive spectrometer to be stored away from the sun in an insulated box equipped with a thermoelectric heating and cooling system that maintains the temperature within ±1 • C of 20 • C. The sensor head has a multiply baffled collimating tube with a 1.6 • FOV (field of view).Light passing through the collimator then passes through a filter wheel assembly that contains the two UV band-pass filters (280-320 and 280-380 nm) used for SO 2 and O 3 measurements, respectively, an open hole, and a blocked region for measuring the dark current after each measurement.In addition, there is a circuit board for controlling the filter wheel and a sun-tracking device connected through an RS-232 serial computer interface.A flat quartz window constitutes the first optical element, which protects the intimal optical and electrical components from rain, dust, and humidity.Herman et al. [24,25] provided a detailed description of the instrument.

Spectral Analysis (Retrieval of HCHO Slant Column Density)
To derive the slant column density (SCD) of HCHO (HCHO SCD ), we analyzed the PSI data using QDOAS software [36], which is based on difference optical absorption spectroscopy (DOAS) [37,38].The noise signals, including the dark current and offset signals from the Pandora CCD detector, were recorded during each measurement routine and then removed from the direct sunlight spectra.The wavelengths of the spectra recorded by the Pandora system were calibrated by fitting the raw spectra to a solar reference spectrum [39].The DOAS fitting was carried out over the wavelength interval (332.5-350nm).This spectral interval, with three strong HCHO absorption bands, was found to have the smallest fitting residual.A spectrum recorded at ~12:00 p.m. LT on 9 September was used as the reference spectrum (RS).The minimum HCHO SCD was calculated from the RS via DOAS spectral fitting.The RS and the absorption cross sections of HCHO, NO 2 , O 3 , and O 4 were simultaneously fitted to the measurement spectra using a nonlinear least squares method [37,38] and QDOAS software.We used the HCHO absorption cross section [40], NO 2 absorption cross sections (220 K and 296 K; [41]), O 3 absorption cross sections (223 K and 243 K; [42]), and the O 4 absorption cross section [43] to perform the DOAS fitting.The BrO absorption cross section was excluded from the spectral fitting since no (or negligible) BrO absorption features were found during the spectral fitting process.All reference absorption cross-sectional spectra were convolved with the measured Pandora slit function.The NO 2 and O 3 spectra were I o -corrected using QDOAS software.We used the third-order polynomial to eliminate the effects of Rayleigh and Mie scattering.Figure 3 shows an example of the deconvolution of the DOAS spectrum that was used to evaluate the HCHO SCD at 12:00 p.m. LT on 13 March 2012.Finally, the HCHO SCD obtained from the DOAS technique was converted to the HCHO VCD by dividing the SCD by the AMF G (described in Section 2.1).

Ozone Monitoring Instrument (OMI) Data
To compare the Pandora HCHO VCD values with those from the OMI measurements, we used the OMI/Aura HCHO total column global 0.25 • latitude/longitude grid (V003) HCHO level 2G data [44].The OMI is onboard NASA's Earth Observing System (EOS)/Aura satellite [45] that was launched on 15 July 2004 into a sun-synchronous ascending polar orbit at an altitude of 705 km and with a local equator crossing time of 1:45 p.m.A detailed description of the OMI HCHO algorithm can be found in Chance [46].The OMI HCHO data used here were cloud-free (cloud fraction < 0.2) and flagged as "0" (quality flag = 0), which indicates a good quality level [47,48].The use of quality flagged as "0" only uses the data that passes all quality checks including the row anomaly.Table 3 summarizes the product name, filter flags, and the condition of the OMI HCHO product that we used [47].We used the Pandora and OMI data in the cloud-free condition, which is determined on the basis of the cloud observation data [49] of the Korea Meteorological Administration (KMA) and the OMI cloud data (cloud fraction < 0.2; quality flag = 0) [47,48].

HCHO Precision Estimations
To investigate the effects of SNR, slit function (FWHM), and AOD on the accuracy on the HCHO VCD values obtained from the ground-based direct-sun measurements, the HCHO SCDs were retrieved using the DOAS method from synthetic radiances.The retrieved SCDs were converted into VCDs by divided them by the AMF G (described in Section 2.1), which we assumed to have no errors.
Figure 4 shows the APD between the true and retrieved HCHO VCD values as a function of HCHO VCD values under various SNR conditions (SNRs of 650, 920, and 1300) with an FWHM of 0.6 nm and an AOD of 0.2.A significant increase in the APDs was found for the HCHO VCD values less than 3 × 10 16 molecules cm −2 (molec.cm −2 ).In particular, when SNR = 650, the APDs were found to be larger than those of high SNR conditions (SNR = 920 and 1300).In Figure 4, for an SNR of 1300, the APD ranges from 1 to 3% for HCHO VCD values equal to or greater than 3 × 10 16 molec.cm −2 , whereas the APD is between 3 and 30% for HCHO VCD values less than 3 × 10 16 molec.cm −2 .However, the APD for an SNR of 650 ranges from 5 to 11% for HCHO VCD values equal to or greater than 3 × 10 16 molec.cm −2 , whereas the APD is between 11 and 53% for HCHO VCD values less than 3 × 10 16 molec.cm −2 .[17,50] with covariance between the HCHO SCD error and the AMF G error.No error is assumed for AMF G in the present study due to negligible scattering effects for the direct-sun measurement.
Figure 5 shows the slit function (FWHM) effects as a function of HCHO VCD values for an SNR of 650.The effects of small and large FWHM values on the APD are found to be small.The APDs of FWHM 0.2 (0.6) ranges from 3 (5%) to 10% (12%) for HCHO VCD values equal to or greater than 3 × 10 16 molec.cm −2 and ranges from 10 (12%) to 53% (57%) for HCHO VCD values less than 3 × 10 16 molec.cm −2 .The average APD of all three FWHM (0.2, 0.6, and 1.0) conditions is 8% for HCHO VCD values equal to or greater than 3 × 10 16 molec.cm −2 , while it is 46% for HCHO VCD values less than 3 × 10 16 molec.cm −2 .The APDs were not calculated for HCHO VCD values of 5 × 10 15 and 9 × 10 15 molec.cm −2 at an FWHM of 1.0 due to the spectral fitting failure.[17,50] with covariance between HCHO SCD error and AMF G error.No error is assumed for AMF G in the present study due to negligible scattering effects for the direct-sun measurement.
Figure 6 shows the effect of AOD variation as a function of HCHO VCD values for an SNR = 650, SZA = 30, and FWHM = 0.6.An increasing AOD leads to an increase in APD.For an AOD of 0.2, the APD ranges from 4 to 8% when HCHO VCD values are equal to or greater than 3 × 10 16 molec.cm −2 .However, the APD is between 8 and 55% when HCHO VCD values are less than 3 × 10 16 molec.cm −2 .For an AOD of 0.6 (1.0), the APD ranges from 4 (5%) to 9% (15%) when HCHO VCD values are equal to or greater than 3 × 10 16 molec.cm −2 .However, the APD is between 9 (15%) and 57% (57%) when the HCHO VCD values are less than 3 × 10 16 molec.cm −2 .For the small HCHO VCD values (5 × 10 15 molec.cm −2 ), the APD of low AOD (AOD = 0.2) was found to be similar to that of high AOD (AOD = 1.5), which implies that the large noise associated with the poor SNR (650) dominantly influences the APD compared to the AOD effect for the small HCHO VCD values.As shown in Figure 5, we found that the APDs are similar between the various FWHM values at the poor SNR condition (650), which supports that the large noise with the poor SNR is dominant on the APD for the small HCHO VCD values.Meanwhile, for the large HCHO VCD values (1.1 × 10 17 molec.cm −2 ), the APD of low AOD (AOD = 0.2) was found to be similar to that of high AOD (AOD = 1.5), which implies that the sensitivity of the Pandora to this high HCHO VCD value was so great that the AOD effect was negligible.Therefore, we found, interestingly, that the maximum AOD effect on HCHO accuracy for the HCHO VCD value was 3.0 × 10 16 molecules cm −2 , for which both the noise effect at small HCHO VCD values and the high sensitivity effect at high HCHO VCD values are minimal.HCHO VCD values using a radiance with various AOD (0.2, 0.6, and 1.5) and under conditions of SZA = 30, SNR = 650, FWHM = 0.6.Y-axis error bars represent the HCHO VCD errors calculated using the error propagation equation [17,50] with covariance between HCHO SCD error and AMF G error.No error is assumed for AMF G in the present study due to negligible scattering effects for the direct-sun measurement.

HCHO VCD Retrieval in Seoul Using Pandora
Figure 7 shows the diurnal variations in HCHO VCD for each season based on the Pandora data from Seoul.The maximum (minimum) values of Pandora HCHO VCD were 2.68 × 10 16 (1.63× 10 16 ), 3.19 × 10 16 (2.23 × 10 16 ), 2.00 × 10 16 (1.26× 10 16 ), and 1.63 × 10 16 (0.82 × 10 16 ) molec.cm −2 for spring, summer, autumn, and winter, respectively.Figure 7 shows that the Pandora HCHO VCD value tends to be high between 9:00 and 10:00 a.m. in the morning in all seasons.We interpret these high Pandora HCHO VCD levels in Seoul in the morning to be associated with significant increases in the emissions of volatile organic compounds (VOCs) and their subsequent photo-oxidation from traffic during the rush hour.A small contribution may also be derived from direct HCHO emissions during this time [51].The Pandora HCHO VCD is low throughout the late morning between 10:00 a.m. and 12:00 p.m. LT in all seasons.An increase in HCHO VCD is also evident in Figure 7 sometime in the afternoon for all seasons except winter, but the specific time varies with the season (i.e., 2:00 p.m. in spring, 3:00 p.m. in summer, and 1:00 p.m. in autumn).These increases in all seasons except winter can be attributed to the photolysis of VOCs and hydrocarbon photo-oxidation by the OH • radical and ozone [52].However, there is no peak on winter afternoons, possibly due to the weak UV solar radiation at that time, even in the afternoon, and an increase in wind speed compared with the summer.
The diurnal pattern of Pandora HCHO VCD shown in Figure 7 is similar to that of the HCHO mixing ratio near the ground seen in the MAX-DOAS and Long-Path DOAS (LP-DOAS) measurements from several cities including Seoul and Beijing [52][53][54].However, previous studies [55,56] have reported high HCHO levels at noon and low HCHO levels in the morning from the Houston-Galveston Airshed (HGA) and Southern China, which are opposite to the diurnal pattern found in Seoul in this study.As discussed in [52], the different diurnal variations of HCHO seen among various urban areas might be related to differences in the HCHO sources and loss mechanisms at each site.Figure 8 shows the monthly (Figure 8a) and seasonally averaged (Figure 8b) variations in the Pandora HCHO VCD and OMI HCHO VCD from Seoul during the study period when both OMI HCHO column and Pandora HCHO data are available, and the error bars represent the calculated HCHO VCD uncertainties for each measurement.The monthly Pandora HCHO VCD values were unavailable for some months due to instrument malfunctions.Figure 8 shows that both the Pandora HCHO VCD and OMI HCHO VCD are high in summer, whereas they are low in winter, with similar HCHO VCD patterns in both the Pandora and OMI data.This high-in-summer, low-in-winter pattern of HCHO VCD implies that the solar radiation energy leads to photo-oxidation that plays a key role in the seasonal HCHO pattern in Seoul.Biogenic species, especially isoprene, may also influence the seasonal HCHO pattern in Seoul.The monthly and seasonal HCHO patterns in Seoul are similar to those reported previously [52,53] in studies carried out in urban areas.
Figure 9 shows a scatter plot of the monthly Pandora and OMI HCHO VCD levels from Seoul between 2012 and 2014.To determine the Pandora HCHO VCD retrieval errors, we calculated the error covariance of the spectral fitting errors, but with no errors associated with the direct-sun AMF G calculation (Figures 8 and 9).Then, the error covariance was used in the error propagation equation [17,50].The error bars of the OMI HCHO VCD in Figure 9 were obtained from the OMI Level 2G product.The HCHO retrieval uncertainty of the OMI Level 2G product varies between 50 and 105% (https://www.cfa.harvard.edu/atmosphere/Instruments/OMI/PGEReleases/READMEs/OMHCHO_README_v3.0.pdf).In Figure 9, the average spectral fitting error of the Pandora (OMI) data was 85% (157%).Given the Pandora SNR of 950 in Seoul and the HCHO VCD interval in Figure 9, the APD may range from 11 to 34%, as shown in Figure 4. Nevertheless, the correlation coefficient (R) between the Pandora HCHO VCD and OMI HCHO VCD was 0.61, with a slope of 1.25.The Pandora HCHO VCD values generally tend to be larger than those of the OMI HCHO VCD (Figure 9) over the study period of 2012-2014.This tendency for the Pandora HCHO VCD values to be greater than the OMI HCHO VCD values could be associated with differences in the sensitivities as well as bias to the true HCHO value between the ground-based Pandora and satellite-based OMI instruments.We found a positive bias trend in the Pandora HCHO VCD to the true HCHO value, which is partly in agreement with the tendency for the Pandora HCHO VCD values to be greater than the OMI HCHO VCD values in Figure 9, if we assume that the OMI HCHO VCD is true.However, in order to identify the reasons for the relationship between the HCHO VCD values retrieved from Pandora and OMI in Figure 9, additional synthetic and field validation studies need to be carried out to understand the information, such as the accuracy and bias of the OMI HCHO measurements.

Discussion
To use a ground-based instrument as a tool to validate satellite products, the accuracy of the data obtained from the ground-based instrument need to be quantified and understood.In the present study, we quantified the accuracy of DOAS HCHO retrieval using ground-based direct-sun measurements.The most important finding of this HCHO accuracy study was that the APDs always significantly increase for HCHO VCD values less than 3 × 10 16 molec.cm −2 under various SNR, FWHM, and AOD conditions.The APD of a low SNR (SNR = 650) is much larger than that of a high SNR (SNR = 1300) for HCHO VCD values less than 3 × 10 16 molec.cm −2 .When Pandora HCHO data are compared to those of satellite data, one should be aware that the HCHO VCD error may be larger than about 55% in the condition of SNR = 650.In order to enhance Pandora HCHO accuracy, especially over low HCHO conditions less than 2 × 10 16 molec.cm −2 , the SNR of the Pandora needs to be increased to 1300.For example, as the SNR increases from 650 to 1300, the average APD decreases from 53 (34%) to 30% (10%) under the HCHO VCD of 5 × 10 15 (9 × 10 15 ) molec.cm −2 .
In addition, we retrieved the HCHO VCD values using Pandora in a megacity and here report its diurnal and seasonal variations.The diurnal variation found in the present study is similar to that of the HCHO mixing ratio near the ground seen in the MAX-DOAS and Long-Path DOAS (LP-DOAS) measurements in Seoul and Beijing [52][53][54].However, Pang et al. [55] and Rappenglück et al. [56] reported high HCHO levels at noon and low HCHO levels in the morning from the Houston-Galveston Airshed (HGA) and Southern China, which are different from the diurnal characteristics found in Seoul in the present study.As discussed by Lee et al. [52], the different diurnal variations of HCHO seen among various urban areas might be related to differences in the HCHO sources and loss mechanisms at each site.These high-in-summer, low-in-winter patterns found in both Pandora and OMI HCHO VCD values in Seoul are similar to those reported by Lee et al. [52] and Pang et al. [53] carried out in Seoul and Beijing.The HCHO VCD and its temporal pattern reported in the present study are thought to be useful in validating the HCHO VCD data produced by both satellite observations and CTMs, since the temporal characteristics of HCHO VCD values are different among observations sites.

Conclusions
In the present study, for the first time, we investigate the sensitivity of HCHO retrieval under various SNR, FWHM, AOD, and HCHO VCD conditions based on ground-based direct-sun measurement.Increasing SNR leads to a significant increase in the APD under various AOD and FWHM conditions.In a high-HCHO condition (HCHO VCD = 1.1 × 10 17 molec.cm −2 ) and a low-HCHO condition (HCHO VCD = 5.0 × 10 15 molec.cm −2 ), the APD of low AOD (AOD = 0.2) is found to be similar to that of high AOD (AOD = 1.5).We found the maximum AOD effect when the HCHO VCD is 3.0 × 10 16 molec.cm −2 .In terms of first-time HCHO measurements using Pandora, the HCHO VCD tends to be higher in the morning (9:00 a.m.-10:00 a.m.LT) but lower through the late morning (10:00 a.m.-12:00 p.m. LT) in all seasons in Seoul.An increase in HCHO VCD occurred in the afternoon for all seasons except winter.Both Pandora HCHO VCD and OMI HCHO are high in summer and low in winter.The correlation coefficient between Pandora HCHO VCD and OMI HCHO VCD is 0.61.The Pandora HCHO VCD values generally tend to be larger than those derived from the OMI observations.

Figure 1 .
Figure 1.Flow charts for the air mass factor (AMF) and synthetic radiance calculation, and the absolute percentage difference (APD) calculation.

Figure 2 .
Figure 2. HCHO mixing ratio profiles between the surface and 2 km as a function of HCHO VCD , as used to calculate synthetic radiance.

Figure 3 .
Figure 3. Example of deconvolution of the DOAS spectrum for evaluating HCHO slant column densities.Black lines represents the absorption signal and red lines represent the sum of the absorption signal and the fit residual.The residual is small compared with HCHO absorption.The example measured spectrum was obtained at 12:00 p.m. LT on 13 March 2012.Reference spectrum (RS) represents the spectrum measured at 12:00 p.m. LT on 9 September 2012.Measured spectrum (MS) represents the spectrum measured at 12:00 p.m. LT on 13 March 2012.

Figure 4 .
Figure 4. Absolute percentage difference (APD) between the retrieved HCHO VCD values and true HCHO VCD values using a radiance with various random SNR values (650, 920, and 1300) and under conditions of SZA = 30, AOD = 0.2, and FWHM = 0.6.Y-axis error bars represent the HCHO VCD errors calculated using the error propagation equation[17,50] with covariance between the HCHO SCD error and the AMF G error.No error is assumed for AMF G in the present study due to negligible scattering effects for the direct-sun measurement.

Figure 5 .
Figure 5. Absolute percentage difference (APD) between the retrieved HCHO VCD values and true HCHO VCD values using a radiance with various FWHM (0.2, 0.6, and 1.0) and under conditions of SZA = 30, AOD = 0.2, and SNR = 650.Y-axis error bars represent the HCHO VCD errors calculated using the error propagation equation[17,50] with covariance between HCHO SCD error and AMF G error.No error is assumed for AMF G in the present study due to negligible scattering effects for the direct-sun measurement.

Figure 6 .
Figure 6.Absolute percentage difference (APD) between the retrieved HCHO VCD values and true HCHO VCD values using a radiance with various AOD (0.2, 0.6, and 1.5) and under conditions of SZA = 30, SNR = 650, FWHM = 0.6.Y-axis error bars represent the HCHO VCD errors calculated using the error propagation equation[17,50] with covariance between HCHO SCD error and AMF G error.No error is assumed for AMF G in the present study due to negligible scattering effects for the direct-sun measurement.

Figure 7 .
Figure 7.Diurnal variations in seasonal HCHO VCD over Seoul between 2012 and 2014.

Figure 8 .
Figure 8.(a) Monthly variations in HCHO VCD obtained from the Pandora and OMI measurements in Seoul between 2012 and 2014.(b) Seasonal (spring, summer, autumn, and winter) variations in HCHO VCD in Seoul between 2012 and 2014.The blue and red error bars represent the monthly averaged retrieval errors associated with the Pandora HCHO VCD and monthly averaged retrieval uncertainty associated with the OMI HCHO VCD , respectively.

Figure 9 .
Figure 9. Correlation between monthly averaged HCHO VCD retrieved from Pandora measurements and those obtained from OMI measurements in Seoul between 2012 and 2014.The Pandora error bars represent the errors calculated using the error propagation equation, whereas the OMI error bars represent the retrieval uncertainties [17,50].X-axis error bar represents the monthly averaged retrieval errors of Pandora HCHO VCD .Y-axis error bar represents the retrieval uncertainties obtained from the OMI Level 2G product (https://www.cfa.harvard.edu/atmosphere/Instruments/OMI/PGEReleases/READMEs/OMHCHO_README_v3.0.pdf).The red lines represent major axis regression between Pandora HCHO VCD and OMI HCHO VCD .

Table 1 .
Summary of previous studies using Multi-AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) measurements.

Table 2 .
Variables and constant used to calculate synthetic radiances.

Table 3 .
Ozone monitoring instrument (OMI) data and flags considered.