Defining aerosol layer height for UVAI interpretation using aerosol vertical distributions characterized by MERRA-2

Aerosol vertical distributions are important for aerosol radiative forcing assessments and atmospheric remote sensing research. From our perspective, the aerosol layer height (ALH) is one of the major concerns in quantifying aerosol 15 absorption from the ultra-violet aerosol index (UVAI). The UVAI has a global daily record since 1978, whereas a corresponding ALH data set is still limited. In this paper, we attempted to construct such an ALH data set from aerosol extinction profiles provided by the MERRA-2 aerosol reanalysis, meanwhile we evaluated them, together with several satellite ALH products in terms of the UVAI sensitivity to ALH. In the first part of this paper, we derived ALHs from the MERRA-2 aerosol profiles by four definitions. Through the sensitivity studies, we found that the definition of top boundary 20 aerosol layer height (H"#$ % ) is more robust to the changes in extinction profile properties than others. The spatial and temporal variation of H"#$ % are also well associated with the major aerosol sources and the atmospheric dynamics. In the second part, we further evaluated the UVAI altitude dependence on the MERRA-2 ALH as well as several satellite ALH. Among all the satellite ALH products in this paper, the correlation between the TROPOMI oxygen (O2) A-band ALH and UVAI, and that between the GOME-2 absorbing aerosol layer height (AAH) and UVAI are in agreement with our a-priori 25 knowledge that the altitude dependence of UVAI increases with aerosol loadings. The correlation between the MERRA-2 H"#$ % and UVAI also matches well with what we found from observational data sets. This implies the top boundary of the aerosol layer derived from MERRA-2 can be an alternative in case there is no observational ALH data available for quantitively aerosol absorption from UVAI and other UVAI-related applications.


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There are various methods to derive an ALH value from a given aerosol extinction profile. One can calculate the aerosol effective heights, for example, the aerosol mean height weighted by the aerosol properties (aerosol properties-weighted mean height), or the aerosol scale height at which the aerosol profile or the cumulative profile passes a pre-determined threshold.
One can also detect the geometric boundary or center (aerosol geometric height), the so-called aerosol layer real height. In this section, we introduce the above ALH definitions in detail and apply them to the MERRA-2 aerosol extinction profiles.
135 Table 1 lists the above representative ALH definitions. Note that all ALHs are calculated from full profiles from the surface to the top of atmosphere (TOA) and they are relative to the terrain height by default unless it is mentioned precisely.

Aerosol optical properties-weighted mean height
Given an aerosol extinction coefficient profile ( ( )) with layers, a common way to derive the ALH is calculating the mean height weighted by the extinction coefficient in each atmospheric height interval (Eq.(1), Koffi et al., 2012;Chimot et 140 al., 2018;Kylling et al., 2018;Liu et al., 2019) or by the AOD in each atmospheric height interval (Eq. (2), Wu et al., 2016).
, where ( A ) and A are the extinction coefficient and the geometric thickness of each atmospheric height interval . The superscript and of "#$ indicate the averaging weight is extinction coefficients or AOD. If the atmospheric layers are evenly gridded in vertical direction, then the "#$ E and "#$ F will give the same result.

Aerosol geometric height
The above ALH definitions are 'effective' heights where aerosol loading should be placed to be representative of the aerosol radiative properties, while the aerosol geometric height describes the 'real' aerosol layer location (Kylling et al., 2018). The For a box-shape profile, "#$ % is explicitly indicated by a clear sharp decrease of the extinction coefficient in the transition layer. For other profile types, there is no uniform method to determine "#$ % . Welton et al. (2002) found the top boundary if the lidar signal strength is greater than the Rayleigh signal by a predetermined threshold setting. The mean signal over the next 500 m is also checked in order to avoid effect from noise. Leon et al. (2009) detected the top layer boundary by retaining the first altitude below TOA at which the signal is 3 times of the standard deviation larger than the average in the reference altitude (6.5 to 7 km). CALIOP employs a much more comprehensive layer detection algorithm (SIBYL, Vaughan et al., 2009), where the magnitude of the threshold is adapted according to the characteristics of the signal (Winker et al., For an extinction profile provided by MERRA-2, we attempt to find the top border of an aerosol layer with help of the extinction coefficient lapse rate ( #U% , unit: km -2 ), which is defined as: , where ( ) is the extinction coefficient difference between two continuous layers and is the atmospheric interval geometric thickness. The concept of #U% is proposed by Huang et al. (2017) to explore the relationship between atmospheric 170 stability and aerosol vertical distributions. The stable meteorological conditions lead to a large positive #U% , while the elevated aerosol layers result in a negative value. Given an aerosol extinction profile, we search upwards from the surface and retain the first height at which the magnitude of #U% above this height is always smaller than a certain value. We set up a sensitivity study in Appendix C and find the threshold of 0.01 km -2 is most suitable to determine the aerosol layer top boundary.

MERRA-2 aerosol layer height sensitivity studies
The derived ALHs using above methods may depend on the attributes of given aerosol extinction profiles. For instance, whether an extinction profile is evenly gridded in vertical direction, to which altitude an extinction profile extends and what is the minimum level of an extinction coefficient is used (i.e. background values in a model or detection limit of an instrument) may influence the value of derived ALHs. Therefore, we explore the sensitivities of ALHs to the above aspects.
The sensitivity studies are based on a subset of the daily MERRA-2 aerosol profiles during the period from 2006-01-01 to 2016-12-31. For each day, we randomly select 100 profiles, a total of 401800 profiles are selected. For each profile, we modify the profile by changing its vertical grid size, truncating it to a certain height (the profile top height), or resetting the minimum extinction coefficient. Then we compare the ALHs derived from the original MERRA-2 profiles and that derived from the modified profiles by making difference between them (the latter minus the former). Fig.1 shows the statistics of each ALH quantity. The original vertical grid in MERRA-2 is irregular, i.e. denser grids in the lower part of the atmosphere and coarser grids in the upper. This has a significant influence on "#$ E , though the effect of vertical resolution is limited as its calculation is independent to the grid size of each layer. The bias of other ALH definitions is small if the vertical resolution is less than 0.5 km. Compared with "#$ % , the other ALH definitions are more sensitive to the top height of the profile, as their calculation depends on the full profile. If the profile only contains information within 190 the troposphere (say less than 15 km), the derived ALHs may be significantly underestimated compared with that derived from the full profile. The influence of profile top height is negligible above 20 km as there exists little aerosol. The minimum extinction coefficient has an obvious effect on the derived ALHs only if it is larger than 0.001 km -1 . Nevertheless, "#$ is almost insensitive to the minimum extinction.
The sensitivity studies give us several implications which may useful when one wants to derive an ALH from a given 195 extinction profile: whether a profile is evenly gridded in vertical direction or not may lead to significant difference in "#$ E ; the profile vertical resolution is suggested to be better than 0.5 km; obtaining full profiles from the surface to the top of the atmosphere is generally not necessary, but it is suggested the profile top height should not be lower than 20 km; the minimum extinction coefficient matters if it is over 0.001 km -1 . Generally, among all ALH definitions, "#$ seems to be the most robust that is not vary significantly due to the changes in the given aerosol profile.

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2.4 Spatial and temporal distribution of MERRA-2 aerosol layer heights Fig.2 shows the global seasonal climatology maps of MERRA-2 ALHs averaged over the selected period. The magnitude of "#$ E is lowest, with most values less than 2 km. This is because the aerosol extinction is usually higher at the lower part of the atmosphere and the maximum extinction coefficient often appears at or near the ground, as we can tell from the zonal extinction profile climatology (Fig.B1)  example, the dust belt and biomass burning regions, these three quantities are significantly higher in the rest of the world, particularly in high-latitude clean regions. The seasonal variations also show that the effective heights are more variable over low AOD regions than aerosol source regions. By contrast, the spatial-temporal variation of "#$ % is better associated with AOD. One can easily recognize the seasonal aerosol sources from the spatial and temporal variation of "#$ % , e.g. the 215 biomass burning regions in the central Africa during winter, the Sahara dust and its outflows over the Northern Atlantic during summer, etc. Compared with "#$ % , it is difficult to recognize aerosol sources from both the spatial maps and the zonal profiles of "#$ E , "#$ F and "#$ RS . The reason is that they are sensitive to where most photons extinct (the location of the peak extinction layers), how prominent those layers compared to the rest (the magnitude of the peak extinction layers), and how fast the extinction coefficient decay ( #U% ). Here, we take four representative extinction coefficient profiles as examples to explain 230 the behavior of these ALH definitions. Fig.4 shows the representative extinction profiles (black lines). They are obtained from the average extinction profiles during the selected period for East China, North Africa, Antarctica and South Africa.
For each region, we also provide the standard deviation to show the variation of the mean profiles (gray bars), and #U% to show how fast the extinction profiles changes with height (blue lines).
Although both the mean profile of East China (Fig.4a) and North Africa (Fig.4b) monotonically decrease with altitude, the 235 magnitude of #U% of North Africa is much smaller. The extinction coefficient of East China is no longer significant above 3 km due to the fast decay, whereas at the same altitude, the extinction coefficient of North Africa still plays an important role in ALH calculations. As a result, the derived ALHs for North Africa are slightly higher than that of East China. The mean profile of Antarctica also decays with altitude ( Fig.4c), however the peak extinction is only slightly higher than extinction in other layers. As the weights given to each atmospheric layer are not significantly different in this case, the role of extinction extinction coefficients below this altitude, the derived "#$ E , "#$ F and "#$ RS are higher than other cases (Fig.4a-c) where their peak extinctions layers are at the surface.

Satellite aerosol layer height products
In this section, we focus on the introduction and pre-processing of several satellite ALH products which also have corresponding UVAI available. As listed in Table 2, the candidate products are the ALH reported in the OMAERUV, the OMI O2-O2 neural network ALH, the TROPOMI O2 A-band ALH and the GOME-2 Absorbing aerosol layer height. It is 250 noted that the OMAERUV ALH is not an independent product retrieved based on physical processes, but a best guess based on satellite and CTM climatology. The reason we include it in this paper is because that the OMAERUV ALH is designed to retrieve accurate aerosol properties of absorbing aerosols in the UV channel (Torres et al., 2013), and it has a long-term global record since 2006.

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The ALH provided by the official OMI/Aura level 2 OMAERUV product (http://dx.doi.org/10.5067/Aura/OMI/DATA2004, last access: 12 August 2019) is a best guess to retrieve accurate aerosol properties of absorbing aerosols in the UV channel (Torres et al., 2013), which is the main reason we include this ALH data set in this paper. The ALH is either given by the CALIOP climatology, a CTM provided climatology (for dust), or a-priori assumptions (for carbonaceous and sulphate aerosols) according to aerosol types and geolocations if the CALIOP entry is not available. The aerosol types in OMAERUV 260 are determined by the corresponding UVAI, the carbon monoxide data from the Atmospheric Infrared Sounder (AIRS) and the scene type from the International Geosphere/Biosphere Programme (IGBP) database. One can refer to Torres et al. (2013) for more detailed information.
The OMAERUV data used in this paper are from the same period as MERRA-2, i.e. 2006-01-01 to 2016-12-31. Satellite pixels with solar zenith angle (SZA) larger than 70°, or contaminated by clouds (cloud fraction larger than 0.3), sun-glint 265 (glint angle larger than 20° over water) or the so-called row anomaly (XTrackQualityFlags is not 0) are removed before analysis. remote oceans, etc. Thus, to ensure the quality of OMAERUV ALH in the further analysis, we employ the ground network

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AERONET data as an additional quality control, which will be described later in Section 4.2.

OMI O2-O2 neural network aerosol layer height
The O2-O2 ALH retrieval algorithm is based on the OMI slant column density ( The O2-O2 ALH global data set used in this study is available only for year 2006 (the data is not publicly assessible, last access: 15 July 2019). It is trained by the MODIS AOD at 550 nm of the combined dark target and deep blue products, and the O2-O2 SCD originally from the OMICLDO2 product. As the algorithm is exclusively trained under cloud-free scenes, we filter out pixels with MODIS geometric cloud fraction larger than 0.02 or OMI cloud fraction larger than 0.1. Besides, pixels 295 with low aerosol loading (AOD smaller than 0.5) are abandoned as the aerosol shielding effect on O2-O2 is negligible (Chimot et al., 2018). To avoid the large errors triggered by NN extrapolation, i.e. samples with feature values outside the range in the training data set, we only retain samples satisfying the following criteria: surface albedo is less than 0.1, surface height is less than 400 m, SZA is between 9° and 65°, the viewing zenith angle (VZA) is between 0° and 45° and retrieved aerosol layer pressure is between 150 and 975 hPa. More information can refer to the Table 1   Australia. The O2-O2 ALH trained with aerosol SSA of 0.95 is generally higher than that trained by SSA of 0.90, since the

TROPOMI O2 A-band aerosol layer height
The TROPOMI O2 A-band ALH is developed to detect vertically localized aerosol layers in the free troposphere under clean sky, i.e. dust storms, biomass burning or volcanic plumes (Sanders A.F.J. and de Haan J.F., 2016). The ALH is based on the O2 absorption in the near-infrared (758 -770 nm). Similar to OMI O2-O2 absorption at 477 nm, a higher O2 absorption 310 indicates a longer absorption light path as the aerosol layer is close to the surface (Sanders et al., 2015).
To accelerate the computational efficiency in operation, a NN algorithm is implemented to replace the line-by-line radiative transfer method during the retrieval procedure and to generate the official TROPOMI ALH product (Nanda et al., 2019a).
The training process is also based on radiative transfer simulations but only for a fixed Henyey-Greenstein aerosol type (SSA at 550 nm = 0.95, Ångström Exponent = 0 and asymmetry factor = 0.7). The aerosol layer is assumed to be distributed in a 315 homogeneous layer with constant thickness of 50 hPa. Other input features of the radiative transfer simulations are satellite measurement geometry, aerosol optical properties, meteorological parameters and surface conditions. For more detailed information on this algorithm one can refer to . The validation study shows that TROPOMI ALH is generally in good agreement with collocated CALIOP level 2 data. The CALIOP ALH is generally higher than TROPOMI (1 km higher over ocean and 2.4 km higher over land) as CALIOP is more sensitive to the top of the aerosol layer where 320 most of the signal comes from (Nanda et al., 2019, AMTD).
In this study, we collect the TROPOMI ALH level 2 offline data from 2018-11-03 to 2019-08-31 (https://s5phub.copernicus.eu/dhus/#/home , last access: 18 November 2019). The TROPOMI UVAI and FRESCO cloud fraction are enclosed in this product. The data product also retrieves AOD as a diagnostic tool indicating influence of bright surfaces and undetected clouds. Similar to the pre-processing of the OMI O2-O2 ALH, to avoid NN extrapolation due to 325 scenes not included in the training process, samples are kept only if they satisfy the following criteria: AOD between 0.05 and 5, SZA between 8.2° and 70°, ALP between 75 and 1000 hPa, surface pressure between 520 and 1048.5 hPa and surface albedo smaller than 0.7. For more details, one can refer to Table 2 in . To exclude out ALH quality, we only retain pixels with only successful retrievals (Processing Quality Flags = 0) and full quality data (qa_value = 1). This procedure automatically excludes pixels affected sun-glints, clouds, bright surfaces (snow and ice) and UVAI (calculated by 330 354-388 nm wavelength pair) smaller than 1. Besides, as aerosols transported from a certain distance are assumed smoothly distributed, to avoid sub-pixel cloud contamination, a local standard deviation for a pixel and its nearest surrounding 8 pixels is calculated. A pixel is excluded if its local standard deviation of ALH is higher than 0.2 km or its standard deviation of AOD at 758 nm is higher than 10.

GOME-2 absorbing aerosol layer height
The GOME-2 AAH is derived based on the GOME-2 UVAI product (Tilstra et al., 2010) and the FRESCO cloud product (Wang et al., 2008). FRESCO retrieves effective cloud pressure and cloud fraction using the reflectance of the O2 A-band at 340 760 nm. Since this wavelength is suitable to retrieve ALH for cloud-free cases (Boesche et al., 2009;Dubuisson et al., 2009;Sanders et al., 2015) and aerosols are treated in the same way as clouds in FRESCO, Wang et al. (2012) attempted to derive and interpret information on aerosol layer pressure from the FRESCO cloud product. Their findings led to the operational GOME-2 AAH algorithm (Tilstra et al., 2019). The algorithm retrieves ALH only for pixels with UVAI larger than 2 with two methods. In the first approach, cloud pressure is retrieved along with effective cloud fraction by assuming a constant 345 cloud albedo of 0.8. Another approach retrieves scene pressure and scene albedo if the cloud/aerosol layer is assumed to cover the entire scene. If the retrieved cloud fraction is below 0.25 or higher than 0.75, the retrieved cloud pressure can better represent the aerosol layer pressure. In other situations, the best estimate of ALH is the higher value between cloud pressure and scene pressure. For more detailed algorithm description one can refer to Tilstra et al. (2019).
We collect the AAH provided by the GOME-2 on-board the Metop-A/B/C from 2018-08-01 to 2019-10-31 (the data are not

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publicly accessible yet, last access: 24 November 2019). Pixels with SZA larger than 70°, or those affected by sun-glint or solar eclipse events are abandoned (AAH_Error_Flag = 0). The GOME-2 AAH retrieves ALH only for pixels with UVAI larger than 2 (Tilstra et al., 2019). Besides, unconverging pixels with AAH set to be 15 km are also excluded. Fig.5m and 5n presents the distribution of GOME-2 AAH and the corresponding level 2 GOME-2 UVAI (calculated by 340-380 nm wavelength pair) product. The distribution of AAH is similar to that of the TROPOMI ALH as they are available 355 during a similar period and they are retrieved in the same band. The fire events reflected by TROPOMI ALH also appears in the GOME-2 AAH map. While the TROPOMI ALH has more observations of dust and smoke outflows over the Atlantic Ocean, the GOME-2 AAH has better availability over desert regions and remote oceans as its retrieval has no constraint on surface albedo and cloud fraction.

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In previous sections, we have obtained four MERRA-2 ALHs using different definitions and four pre-processed satellite ALH products. A direct comparison between above ALH data sets is not very meaningful as these definitions represent different aspects of the aerosol vertical distribution (Torres et al., 2013). Furthermore, the aerosol vertical profile parameterizations, the retrieval principles, the measurement techniques are not the same. Instead, we focus on the comparison in terms of the relationship between ALH and UVAI. This section starts with introducing UVAI and its 365 dependence on ALH. Next, as CMTs do not have corresponding UVAI fields, we assign the OMAERUV UVAI data set to the MERRA-2 ALHs with quality assurance using independent AERONET records. Lastly, we discuss the performances of the MERRA-2 ALHs and satellite ALH products in terms of UVAI dependence on them.

UVAI and its dependence on ALH
UVAI is a long-term record of aerosol absorption since 1978 (Herman et al., 1997). It detects the change of the radiance or 370 reflectance contrast between two UV channels ( Z and [ ) due to the presence of absorbing aerosols: , where obs and Ray indicate measured and simulated for a Rayleigh atmosphere, respectively. fZ k"l is simulated at the surface albedo that satisfies f[ hij = f[ k"l . A positive UVAI value represents the presence of absorbing aerosols while a negative value indicates the non-absorbing components.
The UVAI dependence on ALH is well-studied by radiative transfer simulations, no matter which aerosol profile assumption   6 shows the results. UVAI increases with ALH due to more molecular radiation coming from below is absorbed by 385 aerosols. The higher aerosol loadings, the stronger the UVAI dependence on ALH (Fig.6a). However, the dependence becomes weaker over brighter surfaces, particularly under low aerosol loading (Fig.6b). On the other hand, little altitude dependence is found for scattering aerosols (Fig.6c). The above features of UVAI-ALH relationship can be used to validate the performances of MERRA-2 ALHs and satellite ALH products. As the influence of surface albedo is negligible compared with that of AOD, in the following analysis, we only focus on the UVAI dependence to ALH under different aerosol 390 loadings.

Assignment of the OMAERUV UVAI to the MERRA-2 ALHs
The UVAI data we use to examine the MERRA-2 ALHs is provided by the OMI/Aura level 2 OMAERUV product  Jethva et al., 2014;Lacagnina et al., 2015): given an AERONET record, a time window (±30 minute for AOD and ±3 hour for SSA) and a spatial threshold (≤50 km) is applied to the OMAERUV-MERRA-2 data set. The joint satellite-model pixels 400 are averaged if they both pass the quality control on both AOD and SSA (Dubovik et al., 2000;Remer, 2005): , where is the wavelength which is 500 nm for OMAERUV and 550 nm for MERRA-2. For AERONET sites do not report AOD at 500 nm or 550 nm, the •€€ or ••€ is estimated by the Ångström Exponent and AOD at other channels. The •€€ or ••€ is linearly interpolated by the nearest values (usually 440 nm and 675 nm, but the exact wavelength may slightly vary from site to site). The result of this section is a co-located data sets of 2704 samples, which consists of 405 MERRA-2 ALHs and OMAERUV observations that are quality-assured by the AERONET records. The performances of the three effective heights ( "#$ E , "#$ F and "#$ RS ) are similar to each other. They all show relatively strong but negative correlation (R is around -0.4) with UVAI in the first AOD group (AOD smaller than 0.2). As discussed in Section 2.4, the effective heights show more variabilities at low AOD situations. The negative correlation may be caused 415 by that the effective heights tend to get extremely high values for very low aerosol loading cases, for instance, the aerosol profiles in Antarctic as explained in Fig.4c. The correlation coefficients and the slope between the UVAI and the three effective heights increase with aerosol loading in the next two AOD regimes, however, barely no correlation is found under the last AOD group. Although the UVAI varies from 0 to 5, the effective heights are less variable in the highest AOD regime. It is because that the peak extinctions are most likely to appear in the lower part of the atmosphere (below 3 km, Fig.3), resulting in the derived ALHs are limited below this altitude.

UVAI dependence on MERRA-2 ALHs
Compared with effective counterparts, the overall correlation between UVAI and "#$ % is higher. Its correlation with UVAI increases with aerosol loading and so does the linear fitting slope, which is consistent with our knowledge that UVAI dependence on ALH increases with AOD as explained in Section 4.1. But whether this UVAI dependence on ALH is realistic needs further validation with observations, which will be discussed in the following sections. Fig.8-11 present the relationship between the selected satellite ALH products and their corresponding UVAI. Similar to Fig.7, we group the data into four regimes by the AOD values. Note that the AOD thresholds for each group differ from one product to another. Fig.8 presents the OMAERUV ALH from the AERONET quality-screened OMAERUV-MERRA-2 joint data set (as described in Section 4.2). The OMAERUV ALH is overall positively correlated with UVAI, and both the correlation and the slope increase with AOD. It is noted that the correlation between OMAERUV ALH and UVAI is strong (R is larger than 0.6). As described in Section 3.1, the OMAERUV ALH is specifically designed to detect the height of absorbing aerosol layers, and the UVAI information also involves in the determination of ALH (Torres et al., 2013). Furthermore, the quality control by the AERONET records may further enhance the correlation between UVAI and ALH. Consequently, the 435 correlation may be overestimated compared to the reality. Fig.9 shows the relationship between the OMI O2-O2 ALH trained for SSA of 0.90 and 0.95 and the corresponding OMAERUV UVAI. The AOD here is accompanied with the OMI O2-O2 ALH products, which is the co-located MODIS AOD used in NN prediction. Although we only use samples with AOD larger than 1 in order to exclude potential outliers in the retrieved ALH due to the low O2-O2 absorption signal, there are still some extreme values (above 10 km), especially for 440 the lowest AOD regime. The likely reasons could be the mismatch of aerosol models between the training and prediction process, and/or the clouds contamination in sub-pixels. The magnitude of the correlation and slope between the O2-O2 ALH and UVAI are negligible until the last AOD group. Apart from the outliers, this may be caused by that the product excludes majority of dust aerosols over land (one of the most important absorbing aerosol sources) due to the bright surface.

UVAI dependence on satellite ALH products
Moreover, unlike other ALH products that more or less use UVAI as an entry in retrieval algorithms, the O2-O2 ALH 445 retrieval is purely independent to information of UVAI.
Since currently there is no operational AOD product for TROPOMI, we use the Dark Target Fig.10. Note that the TROPOMI ALH is only retrieved for pixels with UVAI (calculated by 354-388 nm wavelength pair) larger than 1. The overall UVAI altitude dependence is lower than that of OMAERUV. Nevertheless, both the correlation and the slope increase with AOD from 0.05 to 0.39 and 0.08 to 0.96, respectively.
Similar to TROPOMI, as there is no operational AOD product of GOME-2, we co-locate the Dark Target  GOME-2 UVAI (calculated by 340-380 nm wavelength pair) larger than 2 though, it is suggested to use pixels with UVAI larger than 4 to assure reliable retrievals. Besides, only samples with could fraction lower than 0.25 are retained due to effective heights ( "#$ E , "#$ F and "#$ RS ) show high variabilities and sometimes predict extremely high ALH for low AOD cases, while they are less variable when the aerosol loading is high. Consequently, all these three parameters show strong negative correlation between UVAI and ALH in the lowest AOD regimes, while little correlation for high aerosol loading conditions.
In summary, among the selected ALH products, the TROPOMI ALH and the GOME-2 AAH are the two preferred candidate 495 products for UVAI analysis. Their correlation with UVAI is generally positive and increases with aerosol loading, which agrees with our theoretical knowledge on UVAI as described in Section 4.1. By comparing the MERRA-2 ALHs with the satellite products, we find that the relationship between "#$ % and the corresponding UVAI is most similar to the two satellite ALH products. In other words, the MERRA-2 "#$ % can be an alternative data set to interpret aerosol absorption from UVAI in case that there is no observational aerosol vertical distribution available.

Conclusions
Aerosol vertical distributions are important to aerosol radiative forcing assessments and atmospheric remote sensing research. From our perspective, ALH is necessary to quantitively analyze aerosol absorption from UVAI. Facing the problem that observations of aerosol vertical distributions are still limited, this paper attempts to find an ALH data set for UVAI analysis using aerosol extinction profiles provided by the MERRA-2 aerosol reanalysis.

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We proposed four methods to derive ALH from given aerosol extinction profiles: (1) the extinction-weighted mean height ( "#$ E ), (2) the AOD-weighted mean height ( "#$ F ), (3) the scale height ( "#$ RS ) and (4) the top boundary height ( "#$ % ). We tested their sensitivity to the extinction profiles and found that the "#$ % is the most robust. The test also provided the following implications which may be useful for deriving ALH from aerosol extinction profiles in future studies: (1) Whether an aerosol extinction profile is evenly gridded in vertical direction has a significant impact on "#$ E ;

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(2) A coarse vertical grid resolution (larger than 0.5 km) may bias all the ALH quantities; (3) If an aerosol extinction profile only covers troposphere, the derived ALH may differ from that derived from a full profile.
If there are no major volcanic eruptions, aerosol loadings above 20 km is negligible; (4) The minimum extinction coefficient (detection limit of instruments or background values of models) matters when it is over 0.001 km -1 .

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The spatial-temporal patterns of MERRA-2 "#$ % is generally in agreement with variations in AOD. The major aerosol sources, however, are not reflected by the distribution of "#$ E , "#$ F and "#$ RS . The three effective ALH quantities tend to predict a high altitude where little aerosol exists, or an altitude close to the surface under high aerosol loading. The reason is that their calculations are sensitive to the extinction lapse rate, the magnitude and location of peak extinction layers.
In the second part of this paper, we examined the MERRA-2 ALHs and four satellite ALH products in terms of their O2 ALH has a relatively weaker correlation with UVAI than others, especially when AOD is low, since it is sensitive to outliers at low O2 absorption signals. Besides, the OMI O2-O2 ALH excludes most of dust aerosols over land and its retrieval does not depends on UVAI information. By contrast, the ALH reported in the official OMAERUV product shows the highest correlation with UVAI which may be considered to be overestimated. This is because the OMAERUV ALH is intentionally 525 designed for absorbing aerosols and uses UVAI as an input in its retrieval. The quality assurance procedure by the AERONET records also enhances the correlation. The TROPOMI ALH and the GOME-2 AAH behaves similarly as they are retrieved in the same band and use the same cloud inputs. These two considered as preferred candidate ALH products, since they both show a gradually stronger correlation with UVAI as AOD increases, which agrees with our a-priori knowledge of UVAI altitude dependence. The correlation coefficients are moderate (R is around 0.4-0.5) in the highest AOD 530 regime, which is more reasonable compared with the strong correlation between the OMAERUV UVAI and ALH. Among all MERRA-2 ALH parameters, only the aerosol layer top boundary height ( "#$ % ) matches the behavior of the TROPOMI ALH and the GOME-2 AAH.
In summary, the definition of the MERRA-2 aerosol layer top boundary height ( "#$ % ) proposed in this paper is robust to changes in the given aerosol extinction profiles. In other words, this method can be applied to aerosol profiles provided by 535 other data sets. The spatial distribution and temporal variation of "#$ % derived from the MERRA-2 aerosol fields are well associated aerosol sources and atmospheric dynamics. More importantly, UVAI dependence on this quantity increases with AOD, and the magnitude of their correlation coefficient matches that we found from the observational data sets, i.e. the TROPOMI ALH and the GOME-2 AAH. This means in case that there is no ALH information provided by TROPOMI or GOME-2, "#$ % derived from MERRA-2 can be an alternative ALH data source and contribute to interpret the aerosol 540 absorption from UVAI observations.

Appendix A: converting from aerosol mass concentration profiles to aerosol extinction coefficient profiles
The MERRA-2 3-hourly instantaneous aerosol mass mixing ratio (MERRA-2 inst3_3d_aer_Nv, 10.5067/LTVB4GPCOTK2 , last access: 7 June 2019) provides mass mixing ratio profiles for 15 aerosol sub-species. The conversion from mass concentrations to extinction coefficients is as follows: , where U ( ) is the mass mixing ratio (unit: kg kg -1 ) of an aerosol type at altitude (unit: m). "A$ ( ) and U ( ) are the mass density (unit: kg m -3 ) of air and the aerosol species . †,U ( ) and U ( ) are the mass extinction coefficients (unit: m 2 kg -1 ) and extinction coefficients (unit: m -1 ) for the aerosol species . The aerosol mass extinction coefficient †,U ( ) is a function of relative humidity, whose values are provided in the supplementary document of Randles et al. (2017). The total extinction profile ( ) is the summation of aerosol species.

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To prove that the MERRA-2 aerosol fields are realistic, we validate them with CALIOP measurements. CALIOP is designed to measure vertical profiles of elastic backscatter at two wavelengths (1064 nm and 532 nm) from a near nadir-viewing geometry during both daytime and nighttime. Accurate aerosol and cloud heights and the high-resolution (

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Fig .B1 shows the seasonal zonal aerosol extinction coefficient profiles ( ( )) as a function of latitude and Fig.B2 shows the seasonal AOD maps calculated from the extinction coefficients below 12 km. The magnitude of the MERRA-2 extinction coefficients in the free troposphere and AOD are generally higher than that of CALIOP. It may because that the MERRA-2 aerosol fields seem to have higher background level of extinction coefficients. Besides, the CALIOP measurements suffer from problems of missing data or attenuated signal due to presence of clouds or over bright surfaces, etc. The largest 570 differences occur at the Sahara region and biomass burning region in south Africa during fall, and smoke plume over the southern Atlantic Ocean during summer and fall. Nevertheless, the spatial distribution and temporal variation of MERRA-2 aerosol fields generally agree well with that of CALIOP, indicating the MERRA-2 aerosol assimilation system works properly.
Both MERRA-2 and CALIOP data show that, in most situations, aerosols are located near the ground (below 3 km).   distributions from CALIPSO lidar measurements and GOCART simulations: Regional and seasonal variations, J. Geophys.   895 Figure.11 The GOME-2 AAH against the GOME-2 UVAI as a function of the MODIS AOD. The marker size indicates the magnitude of AOD. For each AOD regime, the number of samples (N), the spearman correlation coefficient (R) and the slope of 900 linear regression (k) between ALH and UVAI are provided. Figure.12 Spearman correlation coefficients between ALH and UVAI as a function of AOD. The magnitude of AOD is monotonically increasing from group 1 to group 4.