The role of aerosol layer height in quantifying aerosol absorption from ultraviolet satellite observations

Abstract. The purpose of this study is to demonstrate the role of
aerosol layer height (ALH) in quantifying the single scattering albedo (SSA)
from ultraviolet satellite observations for biomass burning aerosols. In the
first experiment, we retrieve SSA by minimizing the near-ultraviolet (near-UV) absorbing aerosol index (UVAI) difference between
observed values and those simulated by a radiative transfer model. With the
recently released S-5P TROPOMI ALH product constraining forward
simulations, a significant gap in the retrieved SSA (0.25) is found between
radiative transfer simulations with spectral flat aerosols and those with strong spectrally dependent aerosols, implying that inappropriate assumptions regarding aerosol absorption spectral dependence may cause severe misinterpretations
of the aerosol absorption. In the second part of this paper, we propose an
alternative method to retrieve SSA based on a long-term record of co-located satellite and ground-based measurements using the support vector regression
(SVR) approach. This empirical method is free from the uncertainties due to the
imperfection of a priori assumptions on aerosol microphysics seen in the
first experiment. We present the potential capabilities of SVR using
several fire events that have occurred in recent years. For all cases, the difference
between SVR-retrieved SSA and AERONET are generally within ±0.05, and
over half of the samples are within ±0.03. The results are encouraging,
although in the current phase the model tends to overestimate the SSA for
relatively absorbing cases and fails to predict SSA for some extreme
situations. The spatial contrast in SSA retrieved by radiative transfer
simulations is significantly higher than that retrieved by SVR, and the latter better
agrees with SSA from MERRA-2 reanalysis. In the future, more sophisticated
feature selection procedures and kernel functions should be taken into
consideration to improve the SVR model accuracy. Moreover, the high-resolution TROPOMI UVAI and co-located ALH products will guide us to more
reliable training data sets and more powerful algorithms to quantify aerosol
absorption from UVAI records.



Introduction
The concept of the near-ultraviolet (near-UV) absorbing aerosol index (UVAI) initially came along with the ozone product 25 of the Nimbus 7/Total Ozone Mapping Spectrometers (TOMS). It detects UV-absorbing aerosols by measuring the spectral contrast difference between a satellite observed and a model simulated Rayleigh atmosphere for a given wavelength pair ( and # ) The over four-decade heritage UVAI observations (1978 to present) has been widely used for aerosol research. It would be beneficial to have a quantitative relationship between UVAI and other aerosol absorption properties that do not have such 30 long-term global records, e.g. the single scattering albedo (SSA), which is the ratio of aerosol scattering to aerosol extinction. Aerosols are considered as the largest error source in radiative forcing assessments (IPCC, 2014), and SSA is one of the key parameters to reduce this uncertainty (Haywood and Shine, 1995).
The most straightforward approach to derive a relationship between UVAI and quantitative aerosol absorption properties like SSA is through forward radiative transfer simulations. Lookup tables (LUTs) of simulated UVAI for various measuring 35 geometries, aerosol properties, atmospheric and surface conditions are constructed by radiative transfer models (RTMs).
Then SSA is derived by minimizing the difference between pre-calculated UVAI and satellite observed ones (Colarco et al., 2002;Hu et al., 2007;Jeong and Hsu, 2008;Sun et al., 2018). Hereafter, we refer to this method as the RTM-based retrieval.
Apart from pre-assumed aerosol micro-physics, the aerosol loading and the aerosol vertical distribution are two key parameters in forward simulations of UVAI. The former is usually provided in terms of the aerosol optical depth (AOD). 40 There are plentiful AOD products providing wide spatial-temporal coverage with various spectral choices. By contrast, only little information on the aerosol vertical distribution is available. The most well-known aerosol profile product is offered by the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP), but the number of measurements is limited because of its narrow tracks (Winker et al., 2009). Passive sensors only measure columnar quantities but, in some cases, also provide the aerosol layer height (ALH), a compact form of aerosol profile information indicating where most aerosols are located. 45 Chimot et al. (2017) present the feasibility of ALH retrieval using the oxygen (O2-O2) band at 447 nm of the Ozone Monitoring Instrument (OMI), but so far it has not been run operationally yet.
Recently, a new ALH algorithm based on the near-Infrared (NIR) O2 A-band has been developed for the TROPOspheric Monitoring Instrument (TROPOMI) on board the Copernicus Sentinel-5 Precursor (S-5P) (Sanders et al., 2015). TROPOMI was launched on 13 October 2017. The instrument is equipped with both the UV-visible (270-500 nm) and the near-infrared 50 (NIR) (675-775 nm) channels (Veefkind et al., 2015), which makes it possible to interpret UVAI using corresponding ALH measurements. Furthermore, TROPOMI has a wide swath of 2600 km, providing daily global coverage with a high spatial resolution of 7×3.5 km 2 in nadir.
The purpose of this paper is to demonstrate the potential of the TROPOMI ALH product for quantifying aerosol absorption.
As the TROPOMI ALH product is not operationally available yet, we focus on the data of one of the largest wildfires that 55 happened in southern California in 2017, i.e. the Thomas Fire (http://www.fire.ca.gov/current_incidents/incidentdetails/Index/1922 ). Ignited on 4 December 2017, the fire was expanded quickly northwest by the strong and persistent Santa Ana winds and was fully under control on 12 January 2018. The precise cause of the fire remains unknown, but a prolonged period of heat and absence of precipitation definitely contributed to this devastating fire (https://inciweb.nwcg.gov/incident/5670/ ). We selected one day (12 December 2017) for our case study. As 60 shown in Fig.1, a brown smoke plume produced by the Thomas Fire was blown away from the continent and transported northwards. The major part of the plume was over the ocean with cloud free conditions, which is favorable for space-borne aerosol observations. We conduct two experiments to investigate the potential of TROPOMI ALH for quantifying aerosol absorption of the smoke plume generated by the Thomas Fire. First, as concluded in our previous study (Sun et al., 2018), the absence of aerosol 65 vertical distribution information and an improper spectral dependence of aerosol absorption in the near-UV region can be responsible for a large difference between estimated and measured SSA. Now with the TROPOMI ALH as a constraint, we are able to quantitatively determine the influences of assumed wavelength dependent aerosol absorption on retrieved SSA. Similar to our previous study (Sun et al., 2018), SSA retrieval in the first experiment is conducted by the RTM-based method. 70 In the second part of this paper, we propose a statistics-based machine learning (ML) approach to predict aerosol absorption.
ML algorithms are data-driven and they learn the underlying behavior of a system from a given training data set. Another advantage of this kind of method is that no a priori knowledge about the relationship between data is needed. Hence, ML algorithms are particularly useful to address ill-defined inversion problems in the field of geosciences and remote sensing, where theoretical understanding is incomplete but there is a significant amount of observations (Lary et al., 2015). Various 75 algorithms have been developed to deal with classification or regression problems, among which artificial neural networks (ANNs) and support vector machines (SVMs) are most common. In this study we choose the latter due to relatively limited availability of training data (nevertheless it is still large enough to apply ML techniques).
SVMs is a non-parametric statistical algorithm initially devised by Vapnik (1995) to solve classification problems, and later extended to its regression variant, i.e. support vector regression (SVR) (Drucker et al., 1997). An extensive introduction on 80 SVR can be found in (Alex J. Smola and Scholkopf, 2004). In summary, SVMs algorithm is suitable to solve problems of Atmos. Meas. Tech. Discuss., https://doi.org/10.5194/amt-2019-96 Manuscript under review for journal Atmos. Meas. Tech. Discussion started: 5 April 2019 c Author(s) 2019. CC BY 4.0 License. small training data sets with a high-dimensional feature space and can provide excellent generalization performance (Durbha et al., 2007;Yao et al., 2008). Besides, SVMs can efficiently avoid overfitting problems as it only depends on a subset of the training data ( -insensitive loss). The wide choice of kernel functions also allows it to solve different non-linear problems.
SVMs have been applied extensively to solve remote sensing problems (Lary et al., 2009;Mountrakis et al., 2011;Noia and 85 Hasekamp, 2018). Our second experiment is constructing a training data set consist of existing measurements of UVAI, AOD and ALH, from which the SVR learns the underlying relationship of the system and predicts the SSA. We will present the efficiency and accuracy of this empirical method by comparing it with the results of the RTM-based method. This paper is organized as follows: section 2 introduces the data sets involved in this study; the first part of section 3 expresses the setup of the RTM-based method and the first experiment, i.e. a sensitivity study of SSA examining 90 assumptions on the spectral dependence of near-UV aerosol absorption; the second part of section 3 focuses on the second experiment: how the training data set is prepared and how SVR parameters are determined; results and main conclusions are presented in sections 4 and 5, respectively.

Data sets
Data sets listed in this section are either used by the RTM-based method or the SVR-based method, or both. The pre-processing 95 and detailed usage of those data are explained in section 3.

TROPOMI satellite data
In this study, we employ the TROPOMI Level 2 reprocessed UVAI product to quantify aerosol absorption for the target fire event (TROPOMI UVAI data on 12 December 2017 is only internally available, last access: 19 June 2018. UVAI offline data can be accessed via http://doi.org/10.5270/S5P-0wafvaf). The TROPOMI UVAI is calculated for two different 100 wavelength pairs. One uses the conventional 340 and 380 nm to continue the heritage of UVAI records from multiple sensors, and the other uses 354 and 388 nm in order to allow comparison with OMI measurements (D.C. Stein Zweers, 2016). In this study we retrieve the SSA based on the latter pair. Satellite measurement geometries (solar/viewing zenith angle # / @ , solar/viewing azimuth angle # / @ ) and the surface pressure (Ps) included in the UVAI product are input for the radiative transfer calculations. The scene albedo (Asc) from the same product is also used in the pre-processing as will be 105 described later.
TROPOMI ALH retrieval is based on the pattern of a highly structured spectrum with strong absorption of O2 in the A-band (759~770 nm), which is particularly suitable for elevated optically dense aerosol layers (Sanders et al., 2015;A.F.J. Sanders and J.F. de Haan, 2016). The TROPOMI ALH data is still in a pre-operational phase of development and only internally available (last access: 22 June 2018). The ALH is reported in both altitude and pressure. The ALH data for this fire event is 110 available for pixels with UVAI values (calculated for the wavelength pair of 340 and 380 nm) larger than 1 to exclude pixels dominated by non-absorbing aerosols. For the forward radiative transfer calculations, the input aerosol profile is parameterized as a one-layered box shape profile, with central layer height derived from TROPOMI and an assumed constant pressure thickness of 50 hPa.
Note that in the second experiment, the MODIS AOD at 550 nm is converted to 500 nm using the Ångström Exponent (a) provided by the nearby AERONET site (i.e. UCSB, see section 3.4), as AOD in the training data set is reported at 500 nm.
The training data set will be described in subsection 3.2.

OMI satellite data
Surface reflectance (As) is currently not provided in the TROPOMI UVAI product. Instead, we use the Aura/OMI Level 3 125 Lambertian equivalent reflectance (LER) monthly climatology calculated from measurements between 2005 and 2009 (Kleipool et al., 2008) (Kleipool, 2010)  TROPOMI on S-5P and OMI on Aura have similar overpass times (both are approximately at 13:30 local time) and measuring geometries (Levelt and Noordhoek, 2002) (Veefkind et al., 2015). A spectrally flat As is assumed between 354 and 388 nm according to   . 130 The OMAERUV is currently the only product containing a long-term UVAI with corresponding ALH (Torres et al., 2007) ( Torres et al., 2013). It is noted that the ALH reported in the OMAERUV product is not derived from the OMI observations, but from a combination of climatology derived from the CALIPSO data and from a chemical transport model. In order to construct the training data set from which the SVR algorithm can learn, we collect the Level 2 OMAERUV version 3 product (http://dx.doi.org/10.5067/Aura/OMI/DATA2004 , last access: 17 October 2018) from 1 January 2005 to 31 135 December 2017. The training data set will be described in subsection 3.2.

AERONET data
The retrieved aerosol absorption is evaluated with the version 2 Level 1.5 inversion product (https://aeronet.gsfc.nasa.gov, last access: 13 October 2018) (Holben et al., 1998)   In addition, we collect the AERONET version 2 Level 1.5 direct sun and inversion product for all stations for the same period as OMAERUV (1 January 2005 to 31 December 2017), to construct the training data set for the SVR-based method.
The training data set will be described in detail in subsection 3.2.

Methodology
This section introduces the procedure and technical concerns of the RTM-based method and the SVR-based method. The pre-150 processing and detailed usage of data sets mentioned in section 2 are also explained.

The RTM-based method
Forward radiative transfer simulations are conducted by the KNMI developed radiative transfer model DISAMAR (Determining Instrument Specifications and Analyzing Methods for Atmospheric Retrieval) (de Haan, 2011). Fig.3 illustrates the main inputs and the procedure. For each pixel, first, aerosol optical properties are computed by Mie theory for 155 pre-defined aerosol models. Then DISAMAR calculates UVAI using the corresponding AOD, ALH, satellite measuring geometries ( # , @ , # and @ ), surface and environmental conditions (As and Ps) of the target pixel. For the detailed implementation of these forward simulations, please refer to Sun et al. (2018). The output of the forward simulations is a LUT of UVAI as a function of the input SSA at 500 nm (determined by the pre-defined aerosol models), which is fit by a Atmos. Meas. Tech. Discuss., https://doi.org/10.5194/amt-2019-96 Manuscript under review for journal Atmos. Meas. Tech. Discussion started: 5 April 2019 c Author(s) 2019. CC BY 4.0 License. second order polynomial function. Finally, by specifying the corresponding satellite observed UVAI, the SSA of the target 160 pixel is estimated from the UVAI-SSA relationship. The retrieved SSA is reported at 500 nm in order to compare with the results of the SVR method.

Pre-processing of the satellite inputs
Due to different spatial resolutions, TROPOMI ALH, OMI As climatology and MODIS AOD are resampled onto the TROPOMI UVAI grid. Before implementing radiative transfer calculations, pre-processing excludes pixels meeting at least 165 one of the following criteria: # larger than 75°, UVAI340,380 smaller than 1 (corresponding UVAI354,388 smaller than 0.8) or AOD550 smaller than 0.5. As shown in Fig.1, the north part of the plume may be contaminated by underlying clouds, thus pixels in this region (latitude over 36°N) with Asc larger than 0.15 are also removed. In the end there 4808 plume pixels are left. The pre-processed satellite data are presented in Fig.4 (the TROPOMI measurement geometries are given in terms of the scattering angle, Θ). The south part of the plume is the most absorbing region, where the aerosol loading is high (AOD larger 170 than 2) and the aerosol layer has risen to about 4 km.

Aerosol models and sensitivity study construction
The aerosol models used in this study for the Mie calculations are a combination of the ESA Aerosol_cci project (T. Holzer- Popp et al., 2013) and the OMAERUV algorithm (Torres et al., 2007;Torres et al., 2013). We assume a fine mode smoke aerosol type and further divide it into 7 subtypes (Table 1). The particle size distribution employs the fine mode strongly 175 absorbing aerosol of ESA Aerosol_cci project: a geometric radius ( E ) of 0.07 µm (effective radius FGG of 0.14 µm) and a geometric standard deviation ( E ) of 1.7 (logarithm variance E of 0.53). The real refractive index ( ) uses the same value as in the OMAERUV algorithm, which is set to be 1.5 for all subtypes and spectrally flat. We adopt the imaginary refractive index at 388 nm ( KLL ) of the OMAERUV smoke subtypes (except for BIO-1) in our study and add a subtype with KLL equal to 0.06. 180 Many studies have shown evidence that a strong spectral dependence in the near-UV band of absorption by biomass burning aerosols (Kirchstetter et al., 2004;Bergstrom et al., 2007;Russell et al., 2010). Accordingly, a constant 20% ∆ has been applied to all smoke subtypes in the recent OMAERUV algorithm (Jethva and Torres, 2011), where ∆ is defined as the relative difference between KNO and KLL . In this study, we investigate how the retrieved SSA responds to the assumed spectral dependence by considering 9 different ∆ values from 0% (i.e. 'grey' aerosols) to 40% (Table 1). This corresponds 185 to an Absorbing Ångström Exponent ( :78 ) from 1 to 3.4 and from 1.3 to 4.7, depending on aerosol subtype. Note that the ∆ is only applied between KNO and KLL . Aerosol absorption at wavelengths larger than 388 nm is set equal to that at 388 nm.
To summarize, the first experiment to explore the SSA sensitivity to the spectral dependence of aerosol absorption in the near-UV band consists of 9 cases represented by different ∆ . Within each case, there are 7 pre-defined aerosol subtypes 190 with varying KLL . Thus, we perform 63 forward simulations in total for each pixel.

The SVR-based retrieval
In this subsection, we propose an SVR-based method to derive SSA from existing measurements of UVAI, AOD and ALH as a replacement of the RTM-based retrieval. The procedure is presented in Fig.5. As many other ML algorithms, the major steps of SVR consist of feature selection, training and testing data preparation, hyper-parameters tuning and 195 application. We first collect parameters relevant for the derivation of SSA from UVAI, from which we then select a subset based on our knowledge to construct the SVR model (feature selection). The SVR model is then fit to a training data set containing the selected parameters (training process). The SVR model hyper-parameters are tuned until the generalization performance of the SVR evaluated by the testing data set is satisfied (hyper-parameters tuning). Finally, the tuned SVR model is used to predict the SSA for our target event (case application). Detailed descriptions on these procedures are 200 provided in the following subsections.

Feature selection based on OMI and AERONET observations
Although SVR is able to cope with high-dimensional input features, feature selection is still important for generalization performance, computational efficiency and interpretational issues (Weston et al., 2001). Many sophisticated approaches have been devised for feature selection (Guyon and Elisseeff, 2003). In this study we choose features based on the Pearson 205 correlation coefficients ( ) between various parameters in collocated OMAERUV and AERONET measurements and our empirical knowledge on aerosol absorption.
To start with, we collect the 13-year measurement OMAERUV and AERONET measurements as described in section 2.
OMI pixels with # larger than 75°, or cloud fraction larger than 0.1, or UVAI354,388 smaller than 0.8, or pixels with extreme high ALH but low UVAI are excluded. Then an OMI pixel is collocated with an AERONET site if their spatial distance is 210 within 50 km and their temporal difference is within 3 hours. To ensure consistency between the different measurement techniques (ground-based and space-borne), samples are also excluded if the SSA difference between OMI and AERONET is larger than 0.03, or the AOD difference between OMI and AERONET is larger than 5%. The AERONET SSA and AAOD are linearly interpolated to 500 nm as OMAERUV reports AOD at this wavelength. In total 4003 samples are left. Fig.A1 and A2 in the Supplement, part A show the global distribution and the statistical distribution of the OMI-AERONET joint 215 measurements, respectively. Note that these are not restricted to biomass burning areas, but may also contain other aerosol types.
The parameters in OMI-AERONET joint data set for feature selection consists of UVAI, geometries, surface conditions and ALH from OMI, and SSA, AOD and AAOD from AERONET. Fig.6 presents the correlation coefficients matrix (absolute values, |r|) of those parameters. Geometries and surface conditions show little correlation with aerosol absorption quantities. 220 Hence, we will not focus on them. Except for AAOD, SSA is barely dependent on any of the other parameters. This also points out that the one-to-one numerical relationship between UVAI and SSA in the RTM-based method does not have a firm physical basis. On the contrary, AAOD is correlated with UVAI and AOD, as it carries information on both aerosol absorption and aerosol loading. Therefore, it is decided to predict AAOD from given UVAI and AOD and to derive SSA via the relationship in Eq.(2) rather than to directly predict SSA from UVAI. 225 One may also notice that the UVAI dependence on ALH in Fig.6 is insignificant (the correlation coefficient |r| is only 0.3).
This is because the ALH from the OMAERUV product is either as pre-described as other aerosol properties in LUTs or based on the monthly CALIOP ALH climatology. Another possible reason is the presence of non-smoke aerosols in the joint data set, for which the relationship between UVAI and ALH may differ from that for biomass burning aerosols. By contrast, the independently observed TROPOMI UVAI and ALH of our target case reveals a much higher correlation (|r| is 0.63). 230 Although this value may be overestimated as it is calculated for a specific case, it seems more reasonable since a strong UVAI dependence on ALH is well documented (de Graaf et al., 2005;Sun et al., 2018). Under the same conditions, a higher aerosol layer can shield more Rayleigh scattering beneath the layer, resulting in larger UVAI. Thus, ALH is a necessary parameter to prevent misinterpretations of aerosol absorption.
Based on the above analysis, we construct an SVR model with UVAI, AOD and ALH as input features and AAOD as output 235 to be predicted. Then the SSA is derived by Eq.(2).

Preparing training and testing data sets
As described in the previous section, the selected features consist of UVAI, ALH, AOD (inputs) and AAOD (output). A good training data set is crucial to ML algorithms, because they learn the underlying behavior of the system from it. One problem we are facing in this study is that the ALH from the OMAERUV product may not have sufficient quality to use. 240 The influence of OMI ALH can be seen by comparing the relationship between 3 input features from TROPOMI-MODIS measurements (Fig.7a) and that from OMI-AERONET measurements (Fig.7b). One may recall that the OMI ALH is climatological whereas the TROPOMI ALH is directly derived from observations. As a result, we propose to create a 'more observational' ALH to replace the OMI ALH in the original OMI-AERONET joint data set. We numerically adjust the OMI ALH to the TROPOMI ALH to make the relationship between UVAI, AOD and ALH of OMI-AERONET joint data 245 ( Fig.7b) more similar to that of TROPOMI-MODIS data (Fig.7a). This is realized by an extra SVR model, where TROPOMI-MODIS data is the training data set and the ALH in the OMI-AERONET data is the target output to be predicted. We call this intermediate step the SVR for ALH prediction. It should be noted that this SVR is trained on the Thomas fire case, which has no overlap with the training data set for the other SVR.
As can be seen in Fig.5  observations. There is no necessity to do this anymore once a reliable ALH product is accessible to build up training data 255 sets, e.g. the TROPOMI ALH product that will be released in the near future.
The ALH predicted by the extra SVR replaces the OMI ALH in the original OMI-AERONET joint data set. Both the original and adjusted OMI-AERONET joint data are partitioned into a training data set and a testing data set, respectively.
The rule of thumb ratio is 70% versus 30%. The training data set containing the original OMAERUV ALH and the adjusted ALH are referred to as the original and adjusted training data set, respectively. We fit the SVR for AAOD prediction to both 260 training data sets in order to investigate the importance of a reliable ALH input.
To summarize this section, 3 SVR models are applied in this paper: first, an SVR is used to predict ALH in an intermediate step to improve the quality of the original training data set. This is a temporary solution only applied in this paper due to the lack of observational information concerning aerosol vertical distribution. The remaining 2 SVR models are used to predict AAOD with the original OMI ALH and the adjusted ALH, respectively. Fig.5 shows the procedure of the SVRs for ALH 265 (indicated in purple) and AAOD (indicated in green) prediction. Table 2 also summarizes the input features, output parameter and the corresponding data sources of the 3 SVR models discussed in this sub-section. All input features are scaled into the range between 0 and 1 (min-max normalization) before training.

SVR training process and hyper-parameters tuning
For the mathematical formulation of SVR algorithm one can refer to Smola and Scholkopf (2004). Briefly, SVR tries to find 270 the coefficient and the bias b of a linear model by minimizing the function: , where is true value and (•) is the nonlinear transformation that maps x onto a m-dimensional feature space. The loss function in SVR is -insensitive loss (Eq.(4)), where is the width of insensitive zone within which the error is ignored (Vapnik, 1995).
SVR can be solved by specifying a kernel function Ky , | = ( ) y | which is positive defined so that the Mercer's 275 theorem is satisfied (Tuia et al., 2011).
It is clear that the generalization performance of the SVR depends on the following hyper-parameters: (1) the width of insensitive zone . The cost function does not consider errors in the training data as long as their deviation is smaller than , by which SVR can efficiently avoid overfitting issues; (2) the regularization constant C that determines the trade-off between model complexity and the degree to which deviations larger than are penalized; (3) the kernel parameter that concerns 280 the influencing area of support vectors. We adopt the methodology from (Cherkassky and Ma, 2004), where SVR parameter C and can be directly determined from the training data (Eq.(B1) and (B2) in the Supplement). We employ a radial basis function (RBF) kernel to take into account the non-linearity of the SVR models applied in this paper. The kernel parameter is determined by hyper-tuning on a testing data set (Durbha et al., 2007). More information on the SVR tuning procedure is given in Part B of the Supplement. 285 The values chosen by the above methods are robust in our case (Fig.B1-B3 in the Supplement, part B), i.e. retaining a relatively low error while preventing overfitting. Table 3 summaries the settings of the SVR models determined by tuning procedure and the evaluation of the algorithm performance. All 3 SVR models present good generalization capabilities as the differences in root mean square error (RMSE) between the training data and the testing data are minor. The accuracy of the SVR model for ALH prediction is 0.26 km. Fig.7c shows the relationship of UVAI, AOD and the SVR predicted ALH. The 290 structure is more similar to that in Fig.7a and |r| between UVAI and ALH increases from 0.30 to 0.61, which is sufficient to mitigate the impact of uncertainties of ALH in the OMAERUV product. Note that this value may be overestimated as the SVR for ALH prediction is only trained by a specific case due to the limited availability of TROPOMI ALH, but it is more reasonable compared with the original UVAI and ALH relationship in the OMI-AERONET data. The predicted ALH, together with OMI UVAI, AERONET AOD and AAOD provides a new training data set for AAOD prediction, i.e. the 295 adjusted training data set. The accuracy of SVR models for AAOD prediction trained by the original and the adjusted training data set are 0.01.

Data for case application
After determining the hyper-parameters, the SVR is applied to predict aerosol absorption in the case of the smoke plume generated by the Thomas Fire event. The input UVAI, ALH and AOD are taken from TROPOMI UVAI from near-UV band, 300 TROPOMI ALH from O2 A-band and MODIS AOD from visible band, respectively. The predicted AAOD is further used to derive the SSA according to Eq.(2). The retrieved SSA within 50 km from AERONET site (UCSB) is validated. Information about each data product can be found in the corresponding sub-sections in Section 2.

Evaluating the retrieved SSA with AERONET measurements 305
We first analyze the results of the RTM-based method. Fig.8a displays the mean SSA of all plume pixels retrieved by the RTM-based method as a function of ∆ . The retrieved aerosol absorption decreases with ∆ . This finding is in good agreement with Jethva and Torres (2011). 'Gray' aerosols require stronger absorption to reach the same level of UVAI than 'colored' aerosols. This also explains the high SSA standard deviation (filled area) in the cases with little or no spectral The retrieved aerosol absorption is evaluated with the nearby AERONET site (UCSB), whose SSA at 500 nm at 19:55:07 UTC is 0.96. There are 24 TROPOMI pixels located within 50 km from the UCSB site. Hereafter we call them validation pixels. As illustrated in Fig.8b, the mean SSA of the validation pixels also increases with ∆ and eventually levels off at 315 around 0.96. The extremely low SSA (0.53) and high variation (±0.37) retrieved for 'gray' aerosols prove that the spectral independence assumption is not recommended for smoke aerosols (at least in this case). The differences between the mean SSA of the validation pixels and the AERONET measurement are shown in Fig.8c. The retrieved SSA falls inside the uncertainty range of AERONET (±0.03) (Holben et al., 2006) when ∆ is larger than 15%. This indicates that the assumption of a 20% ∆ in the OMAERUV algorithm to describe the spectral dependence of aerosol absorption is adequate. 320 Only a slightly better estimate is found when ∆ equals to 25%, where the mean SSA of validation pixels is 0.002 lower than that of AERONET (Table 3).
On the other hand, the results from both SVR models are also in agreement with the ground-based measurements. SSA retrieved with the original training data set is approximately 0.01 lower than that of AERONET, whereas that predicted by the adjusted training data set shows barely any difference to the AERONET measurements. It is apparent that the adjustment 325 in OMAERUV ALH data leads to an improvement of the performance of SVR algorithm.

Comparing the results of the RTM-based method and the SVR-based method
From the small set of validation pixels, it is difficult to distinguish the RTM or SVR method is superior, because their results are all satisfactory if one considers the typical AERONET uncertainty (±0.03). We further investigate the SSA retrieved by the different methods for the entire plume. 330 As listed in Table 4, the significant difference between the mean SSA of the plume pixels and the validation pixels (0.896 vs 0.957) and the large plume standard deviation (±0.045) reveal a large spatial variability in the RTM-retrieved results. By contrast, the SSA estimated by SVR presents a more homogeneous spatial feature. The plume mean SSA is similar to that of the validation pixels and both have small variabilities of about 0.01. The difference in spatial pattern is also reflected in Fig.9. The RTM-estimated SSA (Fig.9a) shows strong heterogeneity in the horizontal direction. Although enhancing the 335 spectral dependence of aerosol absorption can reduce the SSA standard deviation to some extent, the spatial variability is still considerable even when applying a ∆ of 40% (±0.03, Fig.8b). Conversely, only small spatial variability is observed in the SSA predicted by the SVR-based method ( Fig.9b and 9c).
The strong spatial variability in the RTM-retrieved SSA is mainly controlled by the heterogeneity of the UVAI (Fig.4a).
UVAI is a comprehensive variable dependent to many factors, as listed in Fig.3. The spatial pattern of UVAI is passed to the 340 SSA through the one-to-one numerical relationship. This relationship may differ from one pixel to another as the algorithm focuses on one-pixel retrieval each time. However, in the SVR-based algorithms, the spatial variability of the intermediate output AAOD is cancelled out by the 3 input features, rather than dominated by UVAI alone. Furthermore, SVR predicts SSA for each pixel based on the common relationship between UVAI, AOD and ALH in the training data set.
SSA is an inherent aerosol attribute that is only determined by the size distribution and the refractive indices. In cloud-free 345 cases, it is expected that micro-physical properties of smoke particles within the plume should be similar over short time periods as they were originated from the same source and generated under the same conditions. We therefore conclude that the empirical SVR-based models outperform the conventional RTM-based retrieval as the SVR-predicted SSA shows a more homogeneous spatial distribution.
To summarize, the validation results of both methods are satisfactory with respect to the AERONET uncertainty (±0.03), 350 nevertheless, the higher homogeneity in SVR-retrieved SSA shows that the SVR-based method is superior to the RTM-based method. The SVR trained by the adjusted ALH also shows a better retrieval compared with that trained by the original OMAERUV ALH. This reveals the feasibility to quantify aerosol absorption based on data-driven methods such as SVR, as Atmos. Meas. Tech. Discuss., https://doi.org/10.5194/amt-2019-96 Manuscript under review for journal Atmos. Meas. Tech. Discussion started: 5 April 2019 c Author(s) 2019. CC BY 4.0 License. a replacement of radiative transfer calculations. The operational TROPOMI ALH product that is becoming available in the near future will be the key to widely apply this empirical method and to build up a long-term global SSA data set. 355

Conclusions
The purpose of this paper was to investigate the potential role of the TROPOMI ALH product in quantitatively interpreting the absorption of biomass burning aerosols from near-UV satellite observations. Firstly, we used the TROPOMI ALH to quantify the influences of assumed spectral dependence of near-UV aerosol absorption (represented by the relative difference between KNO and KLL ) on the retrieved SSA. A significant gap in SSA (0.24) between 'gray' and 'colored' aerosols 360 (∆ =0% and 40%, respectively) demonstrates that inappropriate spectral dependences may significantly bias the retrieved smoke aerosol absorption.
The TROPOMI ALH product also provides the opportunity to propose an alternative SSA retrieval method. This is a statistical method based on the correlation between UVAI, AOD and ALH, and requires no a priori assumptions on aerosol micro-physics, which is considered as one of the major error sources in RTM-based method. The new method was realized 365 by SVR, a representative ML algorithm. The SVR models were trained using 4003 co-located observations from OMI and AERONET during the period from 2005 to 2017 throughout the world. An adjustment on OMI ALH was implemented to enhance the quality of training data set. The results of the SVR-based retrieval are more convincing than that of the RTMbased in terms of retrieved values as well as spatial features. According to the SVR algorithm, the mean SSA of the smoke plume generated by the Thomas Fire on 12 December 2017 is 0.96 ±0.01. 370 The successful SSA retrieval in this study demonstrates the feasibility to quantify aerosol absorption directly from existing measurements. So far, we have realized this retrieval method by applying SVR which is suitable to the relatively small training data size. We choose input features based on Pearson correlation coefficients and our knowledge of the subject, and analytically determined parameters of SVR models from training data set. In the future, more sophisticated feature selection and SVR parameter tuning should be considered to investigate the robustness the algorithm. Moreover, individual training 375 data sets for different aerosol types may be necessary to enhance the retrieval accuracy. But the most important factor determining the performance of this method is the availability of qualified training data. We believe that the upcoming TROPOMI ALH product is key to construct a reliable training data set and will contribute greatly to construct a long-term global SSA database. Its large amount observations will also boost the possibilities to explore other aerosol SSA retrieving algorithms using ML techniques. 380