Rethinking the correction for absorbing aerosols in the satellite-based surface UV products

Satellite estimates of surface UV irradiance have been available since 1978 from TOMS UV spectrometer and continued with significantly improved ground resolution using Ozone Monitoring Instrument (OMI 2004-current) and Sentinel 5 Precursor (S5P 2017-current). The surface UV retrieval algorithm remains essentially the same: it first estimates the clear-sky UV irradiance based on measured ozone and then accounts for the attenuation by clouds and aerosols applying two consecutive 5 correction factors. When estimating the total aerosol effect in surface UV irradiance, there are two major classes of aerosols to be considered: 1) aerosols that only scatter UV radiation and 2) aerosols that both scatter and absorb UV radiation. The former effect is implicitly included in the measured effective Lambertian Equivalent scene reflectivity (LER), so the scattering aerosol influence is estimated through cloud correction factor. Aerosols that absorb UV radiation attenuate the surface UV radiation more strongly than non-absorbing aerosols of the same extinction optical depth (AOD). Moreover, since these aerosols 10 also attenuate the outgoing satellite-measured radiance, the cloud correction factor that treats these aerosols as purely scattering underestimates their AOD causing underestimation of LER and overestimation of surface UV irradiance. Therefore, for correction of aerosol absorption additional information is needed, such as the UV absorbing Aerosol Index (UVAI) or a model-based monthly climatology of aerosol absorption optical depth (AAOD). A correction for absorbing aerosols was proposed almost a decade ago and later implemented in the operational OMI and TROPOMI UV algorithms. In this study, however, we show that 15 there is still room for an improvement to better account for the solar zenith angle dependence and non-linearity in the absorbing aerosol attenuation and as a result we propose an improved correction scheme. There are two main differences between the new proposed correction and the one that is currently operational in OMI and TROPOMI UV-algorithms. First, the currently operational correction for absorbing aerosols is a function of AAOD only, while the new correction takes additionally the solar zenith angle dependence into account. Second, the 2nd order polynomial of the new correction takes better into account the 20 non-linearity in the correction as a function of AAOD, if compared to the currently operational one, and thus better describes the effect by absorbing aerosols over larger range of AAOD. To illustrate the potential impact of the new correction in the global UV estimates, we applied the current and new proposed correction for global fields of AAOD from the aerosol clima1 https://doi.org/10.5194/amt-2021-17 Preprint. Discussion started: 1 March 2021 c © Author(s) 2021. CC BY 4.0 License.

UV irradiance, there are two major classes of aerosols to be considered: 1) aerosols that only scatter UV radiation and 2) aerosols that both scatter and absorb UV radiation. The former effect is included in the measured Lambertian Equivalent reflectivity (LER) scene reflectivity, so the scattering aerosol attenuation is estimated through OMI cloud correction scheme, approximating the aerosol reflectivity by clouds of equivalent reflectivity. On the other hand, for the correction of absorbing 60 aerosols, ancillary information is needed and currently a monthly climatology is used to obtain the necessary information for the attenuation by absorbing aerosols. Aerosols that absorb UV radiation attenuate the surface UV radiation more strongly than non-absorbing aerosols of the same optical depth. Moreover, since these aerosols also attenuate the outgoing satellitemeasured radiance, the cloud correction algorithm that treats these aerosols as purely scattering underestimates their optical depth causing overestimation of UV irradiance (Krotkov et al. , 1998). Therefore, it is a complex and difficult task to properly estimate the overall total effect by scattering and absorbing aerosols. In this study, however, we show that there is still room for an improvement to better account for the solar zenith angle dependence and non-linearity in the absorbing aerosol attenuation and we propose a modified correction scheme. And more specifically, the innovation is to explicitly include the solar zenith angle dependence and moreover have a functional form for the correction, which can better account for the true non-linearity in the correction over wider range in the aerosol absorption optical depth, if compared to the currently operational correction. 70 This paper is organized as follows. Section 2.1 first introduces the background and principle in the correction for absorbing aerosols, which is currently operational in OMI and TROPOMI surface-UV algorithms. Then in the Section 2.2, the radiative transfer simulations and assumptions are described, followed then by the specific details used to derive a new correction for absorbing aerosols in the Section 2.3. In the Section 3 some examples of differences between new proposed correction and the currently operational one are shown as global maps at noon-time conditions. Finally, Section 4 summarizes our study and main 75 findings.

Principle of the correction for absorbing aerosols
The OMI surface UV algorithm first estimates the clear-sky surface irradiance using the OMI-measured total column ozone, climatological surface albedo (Tanskanen, A. , 2004), elevation above sea level, solar zenith angle (SZA), and latitude-dependent 80 climatological ozone and temperatures profiles. In the next step, the clear-sky irradiance is multiplied by cloud correction C c , which also accounts for scattering aerosols and also by correction factor for aerosol absorption. If we denote the clear-sky UV as U V clear , and the correction factors for cloud/scattering aerosol and absorbing aerosol as C c and C a , respectively, we can write the equation for the cloudy sky U V cloud as: The wavelength dependence for all terms in Eq. (1) was omitted for clarity. In the OMI surface UV algorithm, effective cloud and scattering aerosol optical depth (COD) is retrieved using 360nm channel reflectance. Although COD is assumed spectrally constant, the C c factor has characteristic spectral dependence with broad maximum at 330-340nm due to interaction between Rayleigh scattering and cloud layer, decreasing at shorter UVB wavelengths due to ozone absorption. The cloud correction of OMI surface UV is based on radiative transfer calculations for a homogeneous, plane-parallel water-cloud model embedded in 90 a scattering molecular atmosphere with ozone absorption (Krotkov et al. , 2001). The cloud optical depth, which is assumed to be spectrally constant with the angular scattering corresponding to the C1-cloud model (Deirmendjian , 1969), is derived from OMI-measured 360 nm radiance assuming aerosol-free atmosphere.
Estimates of surface UV fluxes are further corrected for the effects of absorbing aerosols by applying an additional correction factor C a as described by Arola et al. (2009). This correction factor is based on monthly aerosol climatology of aerosol 95 absorption optical depth (AAOD) by Kinne et al. (2013) at 1x1 degree latitude-longitude resolution. Different correction factors are estimated for each wavelength of the surface UV product, using wavelength dependent aerosol absorption optical depth (AAOD). In the following, however, we use 360nm to derive the new correction, since it is then consistent with the wavelength of reflectance used for the scattering aerosol correction, as described in the above paragraph.
There is a new version of the aerosol climatology available and published recently (Kinne , 2019) and we plan to include it where C OM I a is the post-correction factor, to account for absorbing aerosols in Equation 1. It is denoted here additionally 105 by word "OMI" to distinguish it from the new parameterization developed in this study, which in turn is denoted hereafter as C N EW a . The part 1 + K * τ abs of this equation, with a slope term K, describes the overestimation factor of satellite-based UV due to aerosol absorption, i.e., (U V clear * C c /U V cloud ).
Previous studies (Arola et al. , 2005;Krotkov et al. , 2005) acknowledged that the slope K depends on solar zenith angle (SZA) and τ abs but neglected these dependencies using average value of K = 3 with the Equation 2 as suggested by Krotkov et 110 al. (2005) and Arola et al. (2009). This choice was mainly based on limited validation results that included ground UV measuring stations with moderate level of absorbing aerosols. However, in this study we revisited this assumption and developed a modified algorithm to account for both SZA and τ abs dependency in the absorbing aerosol correction. This was considered as an important step to enhance the applicability of the correction globally, also in regions of high seasonal biomass burning, for instance.

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The new correction scheme was developed with the aid of radiative transfer (RT) simulations with LibRadtran RT package (Emde et al. , 2016) and compared to the current simpler correction. In the following sections, these simulations are described and explained.

Radiative transfer simulations to build up the new correction
To establish a new correction for absorbing aerosols, which accounts for both SZA and AAOD dependencies, we carried out a comprehensive set of RT simulations. Since the aerosol correction is divided into two separate terms in the satellite-UV algorithm (corrections for aerosol scattering by C c and for aerosol absorption by C a ), we needed to estimate "OMI-like" COD and thus estimate C c that the satellite-UV algorithm would assume for any given aerosol conditions. In addition, "true correction" of full aerosol effect (effect of both aerosol scattering and absorption), C true , was estimated as a ratio of surface UV flux from two RT model runs: run with aerosols and U V clear (see Equation 1). Since our goal was to derive a new correction 125 for absorbing aerosols, which should be directly applicable in those surface-UV algorithms that use a similar principle than OMI and TROPOMI (described by the Equation 1), the following should be emphasized. It was indeed crucial that for our C c estimation we included water clouds only, to be consistent with the scattering aerosol treatment in those algorithms. Moreover, although these algorithms do not distinguish between water clouds, haze, ice clouds and non-absorbing aerosols, sensitivity studies have shown that for AOD of 0.5 at 360 nm for instance, the error in estimating the C C for these varying conditions 130 through water cloud assumption is relatively small, about 1% (Krotkov et al. , 2002).
According to the Equation 1, with a perfect algorithm C c * C a = C true , in which case C a = C true /C c : ratio between the "true correction" and the correction if only the scattering aerosol correction was applied (C c only, as in OMI cloud correction algorithm). These RT simulated ratios of C a = C true /C c formed the basic source of information to find a suitable new parameterization to describe the correction factor for absorbing aerosols as a function of SZA and AAOD, C N EW a .

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The assumption in the cloud correction, C c , is that it also accounts for scattering aerosols. However, scattering aerosols and cloud droplets differ by size and thus also by their scattering angular dependence, cloud droplets being more forward-scattering.
This means that, for instance, for a scene of purely scattering aerosols in cloud-free conditions OMI-retrieved effective COD should be larger than the true AOD. To put this slightly differently: in cloud-free conditions with scattering aerosols of a given aerosol optical depth (AOD), the effective cloud optical depth must be larger than the AOD to cause the same reflectance at 140 top of the atmosphere. In general, this difference between COD and true AOD depends on the aerosol optical properties, most strongly on single scattering albedo (SSA). In order to properly estimate C c , we created a following simulation set up. First, we simulated top-of-atmosphere (TOA) radiance measurements at 360nm for clear-sky (no clouds) atmosphere that nadir-looking satellite instrument would measure from varying aerosol conditions (so varying AOD and SSA, and assuming a constant value of 0.7 for the aerosol asymmetry parameter at 360nm). Then in the second step, radiancies were similarly simulated, but for 145 the case of aerosol-free atmosphere with clouds (and varying COD in this case). The latter case corresponds to the OMI cloud correction, which assumes homogeneous C1 cloud model without aerosols. Therefore, we can find effective COD that OMI would retrieve for a given cloud-free scene including aerosols with varying AOD and SSA. We can then estimate C c as a ratio of simulated surface UV flux with "OMI-like" COD and U V clear . This correction factor then reduces the surface UV to the extent that is due to the aerosol scattering.

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Similarly to OMI, we assume only water clouds in our simulations. We also evaluated the influence of the satellite viewing zenith angle (VZA) on the correction factor, but found only a minor influence. In these nadir view simulations, we then only varied solar zenith angle (SZA) and used fixed atmospheric profile of AFGL (Air Force Geophysical Laboratory) mid-latitude summer from the LibRadtran library and disort with 16 streams as the RT solver. The cloud layer was placed between 2 and 4km and default aerosol profile of LibRadtran was used, therefore placing the main fraction of aerosols close to surface and 155 in the boundary layer. In addition, fixed surface albedo of 0.03 was assumed. The main goal in our work here was to develop a new correction that properly accounts for both SZA and AAOD dependence, while preserving the level of sophistication regarding the secondary factors similar to the previous method.
To develop a new correction for absorbing aerosols, the actual total aerosol effect on surface UV needs to be taken into account. In other words, two-fold effect by absorbing aerosols needs to be considered, to account for both the possible influence of absorbing aerosols in the satellite-measured TOA radiance (thus for the possible low bias in COD) and also for the impact of aerosol absorption in atmospheric attenuation of surface UV. For this reason, the impact in total transmission is assessed by C true /C c . This is the quantity, for which the new correction for absorbing aerosols, is to be developed. However, it is illustrative to show first the ratio of true correction and the current correction for absorbing aerosols, which was suggested in In these simulations, there were a small number of cases when negative COD was retrieved. In other words, these are cases when the aerosol absorption was so strong, relative to the aerosol scattering, that it diminished the TOA reflectance to such a low level that the signal by aerosol scattering vanished. These few cases were in the left bottom corner of the plot, when both AOD and SSA were very low. In the Figure 1 these cases are now included as zero COD and thus with C c of 1. Moreover, it 170 is to be noted that the range covers very high cases of aerosol absorption, up to AAOD of about 0.35. Those absorption levels do not occur often but are nonetheless possible in some regions during the seasons of biomass burning or dust aerosols, for instance.
As mentioned above, in case of ideal perfect algorithm C a * C c would equal C true , thus with such an algorithm the ratios shown in the Figure 1 would be always one. However, since C OM I a is a rather simple parameterization, Figure 1 illustrates both 175 the apparent SZA and AAOD dependency of "true correction", if compared to the current operational one. On the other hand, these results also confirm that for purely scattering aerosols (SSA=1), the current version of the algorithm properly accounts for the overall aerosol effect for all SZA. In the current correction, there is no SZA dependence and the constant slope of 3 has been estimated using a data set including a range of SZA values, and as a result it over-corrects (under-corrects) at low SZA (at high SZA). This SZA dependency is the reason why the ratios shown are mostly larger than 1 in the upper plot, while they are 180 lower than 1 in the lower plot when SZA is higher. There is also another major influence to be considered when interpreting the results in the Figure 1, that is the AAOD dependence in the correction, which in turn includes two types of effects. First, absorbing aerosols cause attenuation in the surface irradiance. Second, the satellite-measured reflectance is decreased due to the aerosol absorption, which leads to the underestimation of COD and C c . Both effects are increasing with increasing AAOD and are not fully accounted for by the current correction (Equation 2) in higher AAOD. In the conditions of SZA of 20 •

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(lower plot), there is an overall over-correction due to the SZA effect by the Equation 2, however when AAOD is increasing (AOD increasing and/or SSA decreasing), there is simultaneously increasing under-correction due to the true non-linear AAOD dependence, and as a result the overall effect maximum maximizes around AOD of 1 and diminishes then for larger AOD. On the other hand, with the case of SZA of 60 • , both the neglected SZA dependence and AAOD influence are responsible for under-correction, as can be interpreted also from the lower plot. Both SZA and AAOD impacts are further illustrated later by 190 Figure 2, when new correction is compared against current correction.

Derivation of the new enhanced correction for absorbing aerosols
Our RT simulations covered a wide range of SZAs from 0 to 80 • , as well as a broad range of AOD and SSA, as discussed above. The ultimate objective was to establish a new correction, C true /C c as a function of AAOD and SZA. The current operational formula (Equation 2) is a function of AAOD only. Moreover, the denominator (1+K*AAOD) is linear with respect 195 to AAOD, while in our analysis we found that it does not properly describe the non-linearity of the actual correction factor with respect to AAOD. Moreover, clear SZA dependency exists in the correction factor that the earlier approach did not take into account. Therefore, our goal was two-fold: to keep the formula still as simple as possible, but to account for AAOD and SZA dependencies.The final parameterization was found after an extensive search for the most appropriate form, so essentially by an "trial and error" approach, resulting in the following equation: where f describes the SZA dependent part in the correction factor, for which the suitable form was the following: f=(1.27 + sin(SZA)) * τ abs . This formula provides the best fit for the overall range of SZA, AOD, and SSA of our simulations for the true correction factor, C true /C c . In addition, the following constants were found to best describe the correction factor for these various conditions of AAOD and SZA: c1=-1. 43, c2=1.20, c3=-0.56. 205 The upper plot of the Figure  It is possible that one would interpret the results in the Figure 1 so that the differences between new and current aerosol corrections do not appear significant. Indeed, the differences are in the range of ±5% for realistic conditions. They can be larger in rather extreme SZA, for instance, but then the UV intensities themselves are small and the correction factor itself becomes less relevant. Also, the differences can be larger for some exceptionally high AAOD levels that are not unusual seasonally (e.g., biomass burning events in South-America or South-Africa). However, it is emphasized that these are systematic errors 220 (biases). For instance, the current correction overestimates the absorption effect in the noontime UV index (thus underestimates the surface UV) in regions where noontime SZA values are below 40-50 • . Therefore, it is of importance to correct also for these systematic AAOD and SZA effects.
To illustrate the potential impact of the new correction in the global UV estimates, we applied the current and new proposed correction for global fields of AAOD from the aerosol climatology currently used in OMI UV algorithm (Kinne et al. , 2013).

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In the following Figures 3 and 4, we show the ratio of the corrections at noon time and for two example months of January and June. It is obvious that the difference is in the range of ±5%. It illustrates how systematic over-and underestimation of absorbing aerosol influence can be reduced by the new proposed algorithm, which is planned to be included in the new OMI UV re-processing, planned for early 2021. The relatively sharp change from over-to under-correction in the current OMI correction close to Sahel region, where there is a very strong spatial gradient in C OM I a and thus in AAOD, is an interesting 230 spatial feature to demonstrate how both AAOD and SZA indeed influence the C N EW a .
In addition to these two months shown, other months were investigated (not shown). For instance in September and October during the biomass burning season both in South-America and South-Africa, when climatological AAOD levels are quite high, similar differences of ±5% were observed when comparing the new correction and the current operational correction for absorbing aerosols in the OMI surface UV algorithm. However, since now these examples were produced by using monthly 235 climatology, it is obvious that the impact would be larger in episodic cases of higher true AAOD. Moreover, as illustrated by the Figure 2 above, the influence can be also larger, in particular for cases of higher SZA than shown here at local solar noon.
It can be also concluded from these global maps that it will be likely challenging, if not entirely impossible, to see and confirm this improved performance through the possible future validation studies against ground-based UV measurements for two reasons. First, the differences are largest in those regions where there are no ground-based UV measurements available