Utilization of O 4 slant column density to derive aerosol layer height 1 from a spaceborne UV-Visible hyperspectral sensor : Sensitivity and 2 case study 3 4

The sensitivities of oxygen-dimer (O4) slant column densities (SCDs) to changes in aerosol layer height are investigated using the simulated radiances by a radiative transfer model, the Linearlized pseudo-spherical vector discrete ordinate radiative transfer (VLIDORT), and the Differential Optical Absorption Spectroscopy (DOAS) technique. The sensitivities of the O4 index (O4I), which is defined as dividing O4 SCD by 1040 molecules2cm-5, to aerosol types and optical properties are also evaluated and compared. Among the O4 absorption bands at 340, 360, 380, and 477 nm, the O4 absorption band at 477 nm is found to be the most suitable to retrieve the aerosol effective height. However, the O4I at 477 nm is significantly influenced not only by the aerosol layer effective height but also by aerosol vertical profiles, optical properties including single scattering albedo (SSA), aerosol optical depth (AOD), particle size, and surface albedo. Overall, the error of the retrieved aerosol effective height is estimated to be 1276, 846, and 739 m for dust, non-absorbing, and absorbing aerosol, respectively, assuming knowledge on the aerosol vertical distribution shape. Using radiance data from the Ozone Monitoring Instrument (OMI), a new algorithm is developed to derive the aerosol effective height over East Asia after the determination of the aerosol type and AOD from the MODerate resolution Imaging Spectroradiometer (MODIS). About 80% of retrieved aerosol effective heights are within the error range of 1 km compared to those obtained from the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) measurements on thick aerosol layer cases.

On the other hand, the O4I from OMI standard product of cloud (OMCLDO2) and Ballard (1998) considering the temperature dependence by interpolating to 234 representative atmospheric temperature of 253 K (Accarreta et al., 2004). For this 235 reason, there can be systematic difference between the O4I from OMCLDO2 and 236 direct estimation from the observed radiance spectra in this present study. Figure 2   237 shows the O 4 SCD from OMCLDO2 and those directly retrieved from radiance 238 spectrum over all observed OMI pixels on March 31, 2007 over East Asia. Similar to 239 the DOAS analysis using the simulated spectra for a look-up table (LUT) calculation, 240 OMI observed radiance spectra are fitted with the Ring spectrum and the FRS in 241 addition to the absorption cross sections in Table 1 within the same wavelength 242 window. Before the spectral fitting, the NO 2 and O 3 cross sections are I 0 corrected, and 243 the Ring spectrum (Fish and Jones, 1995), accounting for the effects of the rotational 244 Raman scattering due to air molecules, is calculated using the WinDOAS software 245 (van Roozendael and Fayt, 2001). After the fitting, the noise level of residual spectrum 246 is estimated to be on the order of 10 -3 for the radiance spectrum at 477 nm from OMI 247 measurements. The O 4 SCDs with the fitting error less than 1% is used for the 248 comparison. From this figure, a systematic difference between the two different fitting 249 results is less than 1%, although the cross section databases for fitting are different.

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From this result, the effect of cross section database difference is negligible when the 251 same observation data was used. Furthermore, the DOAS analysis for LUT calculation 252 can be used to compare the O 4 SCD from OMCLDO2. 253 Figure 3 shows the comparison of the O 4 SCD at 477 nm from LUT with the 254 dimension as in Table 2  Kleipool et al., 2008). Because the standard product of the O 4 SCD is only estimated at 261 the 477 nm band, the results can be compared only at this band. To minimize the 262 DOAS fitting error, the observed data from OMI is selected by the fitting precision less 263 than 2% and the quality flags for spectral fitting are also considered. As shown in ground-based measurements adopted the correction factors to cross section database.
while the negative bias is removed to 0.98±0.05 and the regression line slope is 1.123.

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Although the comparison result is not perfect, the calculation by the VLIDORT  The sensitivity of the O4I to the AEH is investigated for its absorption bands at 292 340, 360, 380, and 477 nm. Figure 4 shows the O4I as a function of the AEH and the 293 three different aerosol types of MITR, WASO and COPO at 360,380,and 477 nm,294 respectively. The vertical error bar represents the fitting error estimated by the residual 295 spectra from the DOAS fitting (e.g., Stutz and Platt, 1996). For the calculation shown 296 in the figures, the following geometries are assumed: solar zenith angle (SZA) of 30 297 degrees, viewing zenith angle (VZA) of 30 degrees, and relative azimuth angle (RAA) 298 of 100 degrees. Note that insignificant SCD value was estimated at 340 nm due to the 299 large spectra fitting error. In these three figures, the O4Is show the AEHs ranging from 300 1.0 to 5.0 km for the AODs of 1.0 and 2.5 at 500 nm, which could be due to the 301 existence of thick aerosol layers. For the sensitivity result, the decrease rate of the O4I 302 value in the 1 km interval of AEH (-dO 4 /dZ) is defined as equivalent O4I difference 303 converting from O4I difference between neighbor AEH in same AOD condition.

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The O4I is significantly decreased with increasing AEH at 360 and 380 nm for all 306 aerosol types. However negative O4Is are occasionally estimated at 360 nm.

307
Furthermore the fitting errors are too large to estimate the AEH, which range from 160 308 to 410 at 360 nm and from 350 to 1060 at 380 nm. From large fitting error with small 309 O4I, the fitting results are insignificant at these two absorption bands.

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On the other hand, the sensitivity of the O4I at 477 nm is a significant variable to O4I sensitivity to AEH is generally increased to increasing optical path length to the 325 viewing geometries. From this result, the accuracy for the AEH retrieval is potentially 326 better for large zenith angle cases than for low zenith angle cases.

Error analysis
Errors are also estimated in terms of key variables in the estimation of the O4I at 330 477 nm, with the variables and their dimensions as summarized in Table 3. For the 331 error analysis of AEH retrieval, characteristics for all of extinction properties are 332 essential to consider. In this study, errors are analyzed in terms of AOD, aerosol 333 vertical distribution, particle size and SSA for aerosol amount and properties. Surface 334 albedo variation is also considered to represent surface condition. To estimate the error 335 amount, the AEH error is converted from the half of O4I difference between adding 336 and deducting perturbation of variables as shown in equation (1).
where ε(Z) is the AEH error amount due to variable of error source, x, in AEH 339 of Z, and δx is perturbation of AEH retrieval error source. The ε(Z) value also 340 depends on viewing geometries. Therefore ε(Z) is represented for specific geometries 341 together with averaging over all geometries. AODs ( a ), the O4I at AEHs of 1.0 and 3.0 km is shown in Figure 6 for the same 348 geometry assumed in Figure 4. From OMI standard products, the expected error of the 349 AOD over ocean is the larger of 0.1 or 30% for absorbing aerosol, and the larger of 0.1 350 or 20% for non-absorbing aerosol (Torres et al., 1998(Torres et al., , 2002. For this reason, the 351 uncertainty of AOD is assumed to be 0.1 in this study, although uncertainty of AOD would be larger than the assumed value for large AOD. The decreasing rate of the O4I 353 (-dO 4 /d a ), which defines O4I reduction with AOD increase by 0.1, is found to be 354 larger for the AEH at 3.0 km than for that at 1.0 km. Among the three aerosol types, 355 the -dO 4 /d a is found to be the least for the WASO, which has stronger scattering 356 characteristics than other two aerosol types. In addition, the sensitivity for WASO 357 showed negative -dO 4 /d a for small AOD at low AEH, which has small shielding 358 effect with large enhancement effect, due to the large SSA of WASO. The mean -359 dO 4 /d a values are estimated to be 1.2%, 0.9%, and -0.1% for the AEH of 1.0 km as 360 the AOD changes by 0.1 for the MITR, COPO, and WASO, respectively, whereas they 361 are estimated to be 2.3%, 2.1%, and 1.0% for the AEH of 3.0 km with respect to the 362 same AOD changes for the three different type, respectively. 363 Figure 7 shows the expected error in AEH due to retrieval uncertainty of AOD 364 from observation. Because O 4 concentration exponentially decreases as the 365 atmospheric altitude increases, the sensitivity to AEH becomes weak at high AEHs. In 366 addition, aerosol signal is relatively weak for low AOD. From these reasons, the AEH 367 retrieval error due to AOD uncertainty is maximized for the high AEH with low AOD 368 cases for all aerosol types. The maximum retrieval error is 2.0, 0.7, and 4.4 km for 369 COPO, WASO, and MITR for the case at AEH of 4.0 km and AOD of 0.4, which is 370 least sensitive case for AEH. For AOD of 0.4, however, the retrieval error due to AOD 371 uncertainty is 0.3, 0.2, and 0.4 km for COPO, WASO, and MITR for the case at AEH 372 of 1.0 km. Except for AEH lower than 4 km and AOD larger than 0.4, the retrieval 373 error of AEH is less than 1.0 km for all viewing geometries and all aerosol types.  Table 5 shows the mean AEH errors between the two vertical profiles of aerosol 478 as AOD changes. As the aerosol vertical profile is changed with increasing its widths,  Table 6 shows the summary of the total error budget for the AEH estimation with 489 a list of the major error sources and their values, assuming errors in each variable in 490 OMI standard products. To convert the O4I difference to the AEH error, the difference 491 of O4I due to the respective error source is divided by that from the change of the AEH 492 in each bin of the AOD and AEH as shown in section 3.2, with the simulation cases 493 over 58,800 runs listed in Table 3 to calculate mean and standard deviation of errors.

494
Because of weak signal sensitivity to AEH for AOD of 0.4 and AEH at 5.0 km as 495 shown in the previous section, this simulation case is omitted in calculating statistical values for error budget. In summary, the total number of aerosol simulations for the 497 combination of AOD and AEH includes 39 cases.

498
The mean errors from 10% variation in the SSA for all of the variable conditions 499 in Table 3 correspond to 726, 576, and 1047 m for the MITR, COPO, and WASO, 500 respectively. For the total error budget calculations, however, SSA change by 5% was 501 used according to Torres et al. (2007), which reported the variation of the SSA less 502 than 0.03 for the given aerosol type. The error from the vertical distribution is 503 estimated to be 720, 1480, and 690 m for the COPO, MITR and WASO, respectively.

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The errors from SSA and aerosol profile shape are the two important error sources 505 in estimating the AEH, followed by the errors related to AOD and surface albedo.

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From these results, the errors of the AEH due to the error from OMI AOD of 0.1 and 507 the surface albedo of 0.02 are less than 300 m for WASO and COPO, and about 400 m 508 for MITR. However, the AEH error from surface albedo is important for cases with 509 low AOD at high AEH, which is surface reflectance dominant case. (3-sigma) hPa from NCEP Reanalysis 2 data since 2004. In clear case, the difference 521 of O4I due to the ±3% for pressure variation is 3.4±0.1% in all geometries.

522
Furthermore, the AEH error in terms of inaccurate spectral wavelength calibration 523 is estimated based on the assumed errors of ±0.02 nm, which corresponds to 0.1 pixels 524 for OMI. Although it is well known that the accuracy in the spectral wavelength 525 calibration before the DOAS fitting affects the trace gas SCD retrieval, the errors in the 526 O4I associated with the wavelength shift of the sub-pixel scale are estimated to be 527 negligible due to the broad O 4 absorption band width around 477 nm.

528
Finally, the total error budget in the AEH retrieval is estimated based on the error 529 analysis with respect to error sources. Note that the result of error analysis explains 530 about 50% for SSA and 25% for size parameter in calculating the total error budget.

531
Overall, the total error budget in the AEH retrieval is estimated to be 739, 1276, and  (Levelt et al., 2006). The 542 spatial resolution is 13 km × 24 km at nadir in "Global Mode". In the present study, the nm and the AEH information. 545 Figure 12 shows an AEH retrieval algorithm for the case study. In retrieving AEH, 546 AOD is obtained from MODIS standard product (e.g., Levy et al., 2007). Although 547 OMI aerosol product provides AOD at 500 nm, AOD from OMI was partially affected 548 by aerosol height and suffered from cloud contamination due to its large footprint 549 (Torres et al., 2002). For this reason, AOD from MODIS was allocated to the OMI 550 pixels as a reference AOD for the AEH retrieval. For type selection, the AE from 551 MODIS and AI from OMI is respectively used for the information of size and 552 absorptivity, to classify aerosol type into four following the method from Kim et al.  Table 7. Due to the limitation of the accuracy of aerosol type classification and those of 558 AOD over land, this study estimates the AEH only over ocean surface. Although 559 temporal and spatial variation of surface albedo influences the AEH result from error 560 study, surface albedo is assumed to be a fixed value of 0.10, which is used in the 561 sensitivity study. Even if the surface albedo is changed but known, the qualitative 562 conclusion here is not affected. For case study, the LUT of O4I is developed by the   Figure 15 shows the scatter plot of AEH between CALIOP and OMI on the dates 591 in Table 8, which lists aerosol transport cases over East Asia with simultaneous observations by OMI and CALIOP in 2007 and 2008. The AEH from CALIOP is 593 estimated by the data from vertical profile of aerosol extinction coefficient at 532 nm. 594 differential optical absorption spectroscopy measurements with least-squares 898 methods, Applied Optics, 35, 30, 6041-6053, 1996. 899 Torres, O., Bhartia, P. K., Herman, J. R., Ahmad, Z., and Gleason, J.: Derivation of 900 aerosol properties from satellite measurements of backscattered ultraviolet 901 radiation: Theoretical basis, J. Geophys. Res.,103(14), 17099-17110, 1998. 902 Torres, O., Decae, R., Veefkind, P., and de Leeuw, G.: OMI Aerosol Retrieval Algorithm,  Table 8. List of aerosol transport cases and its period for comparison.     Table 8. List of aerosol transport cases and its period for comparison.