A Statistical Algorithm for Retrieving Background Value of Absorbing Aerosol Index Based on TROPOMI Measurements

Aerosols are a complex mixture of small liquid and solid particles suspended in the atmosphere. According to the optical properties of aerosols in solar ultraviolet (UV) to near-infrared wavelengths, aerosols can be divided into absorbing and scattering aerosols, depending on their properties to absorb and scatter solar radiation (Torres et al., 1998; Penner et al., 2001). It is widely acknowledged that the UV aerosol index (UVAI) can be used to indicate UV absorbing aerosols, including biomass burning plumes (Jost et al., 2004; Guan et al., 2010), desert dust (Chiapello et al., 2005; Engelstaedter et al., 2006), volcanic ash (Krotkov et al., 1997; Seftor et al., 1997), and anthropogenically produced soot (Haywood and Shine, 1995) in remote sensing. These absorbing aerosols play an important role in global warming (Torres et al., 1998; Randerson et al., 2006), substantially altering the radiation and chemical balance of the atmosphere (Penner et al., 2001).

Initially, UVAI was used to qualitatively estimate the effects of absorbing aerosols in the Total Ozone Mapping Spectrometer (TOMS) ozone retrieval algorithm (Herman et al., 1997; Torres et al., 1998). Moreover, UVAI was also applied to indicate the presence of UV-absorbing aerosols and to retrieve atmospheric concentration of absorbing aerosols. On a wider scale, applications of the UVAI using several satellite data products can be used to monitor the transport of absorbing aerosol plumes produced by large aerosols events such as wildfires and volcanic eruption. For instance, UVAI has been used to examine the aerosol effects on climate and to study the global spatio-temporal distribution of absorbing aerosols in heavy aerosol events (Li et al., 2009; Balarabe et al., 2016). Numerous satellite instruments, such as the TOMS, global ozone monitoring experiment (GOME), scanning imaging absorption spectrometer for atmospheric chartography(SCIAMACHY/ ENVISAT), ozone monitoring instrument (OMI/Aura), and TROPOspheric monitoring instrument (TROPOMI/Sentinel-5 Precursor) continuously provide the UVAI data product (Hsu et al., 1996; de Graaf et al., 2004, 2005; Trees et al., 2021). The long-term data record of UVAI can provide continuity and effectiveness for spaceborne aerosol monitoring (Anuforom et al., 2007; Torres et al., 2018).

There are a number of influential factors associated with the accuracy of UVAI. Typical satellite products such as aerosol optical depth (AOD) (Buchard et al., 2015) and the column density of trace gases (Boersma et al., 2007) are independent of the viewing geometry, but the UVAI is different in such cases. Although UVAI can reflect the presence of absorbing aerosols (Herman et al., 1997), it depends on the viewing geometry (de Graaf et al., 2005) and the degradation of the instrument (de Graaf and Stammes, 2005). The TROPOMI instrument began production of the UVAI data products on 28 June 2018. The trends due to instrument degradation and reflectance were affected by severe calibration errors in the UV band, as reported by Tilstra et al, 2020. Since 1 July 2021, a positive offset has been applied to the operational TROPOMI UVAI official data products due to the recent update of the L1b data including a correction for observed degradation of the irradiance (Zweers et al., 2021). These biases caused by the viewing geometry and the instrument’s radiometric temporal drift, which appeared in the initial UVAI results, need to be removed from the background UVAI to improve the comparability and long-term consistency of the UVAI data under different viewing geometries and observation times. The background UVAI is a statistical value that includes the calibration errors of the instrument and its dependence on viewing geometry.

Therefore, it is necessary to investigate the temporal and spatial distribution of the background UVAI over the Pacific Ocean under clear sky conditions. To this end, our study presents a statistical method that calculates the background value of the UVAI using operational TROPOMI observation data over the Pacific Ocean under clear-sky scenes. The objectives of this study are (1) to reduce the effects of viewing geometry on the UVAI distribution by introducing a background UVAI, and (2) to examine the temporal change of background UVAI by using radiative transfer calculations.

In section 2, we describe the definition of UVAI and the retrieval approach of UVAI in the presence of clouds. In section 3, we discuss the enhanced UVAI features in the spatial distribution of UVAI and simulate the dependence of viewing geometry on the UVAI using a radiative transfer model. Section 4 introduces the background UVAI, describes the method for calculating the background UVAI, and elucidates the spatio-temporal nature of the background UVAI. Section 5 presents the application of the background UVAI and section 6 provides a summary of the work and prospects for future UVAI retrieval on the EMI instrument.

TROPOMI is a push-broom spectrometer onboard the Sentinel-5 Precursor (S5P) satellite. The S5P satellite flies in a near-polar, sun-synchronous orbit with an orbital altitude of 824 km and an equator crossing time of 13:30 (Zweers et al., 2021). TROPOMI has achieved daily global coverage of aerosol measurements for monitoring aerosol events. Moreover, there is a relatively high clear-sky frequency over the southern part of the tropical Pacific Ocean throughout the year (Apituley et al., 2022). We performed cloud screening by using the TROPOMI Level 2 cloud product (https://s5phub.copernicus.eu/dhus/#/home, accessed on 1 March 2021). Realizing that the Pacific Ocean would not be affected by the absorbing aerosols without significant absorbing aerosol events, the Pacific Ocean was selected as an ideal region for retrieving the background UVAI because we anticipated the overall UVAI mean to be zero or a negative value over this region. Accordingly, we selected the TROPOMI offline Level 2 aerosol index data (https://s5phub.copernicus.eu/dhus/#/home, accessed on 1 February 2021) for March 2019, 2020, and 2021 over the Pacific Ocean (Zweers et al., 2021). The selection of the same month can ensure the consistency of the sun angle. The TROPOMI background UVAI calculation exploits the data at latitudes between 60°S and 60°N. The scene albedo at 380 nm was < 0.2 to avoid extreme viewing geometry and to screen the cloudy pixels.

UVAI is a dimensionless qualitative indicator (Eguchi and Yokota, 2008), which calculates the difference between the measured reflectance of 340 and 380 nm and simulated reflectance from the radiative transfer calculation for a Rayleigh molecular atmosphere-surface system without aerosols (de Graaf and Stammes, 2005;). UVAI is formalized according to Eq. (1) (Herman et al., 1997):

where R₃₄₀ and R₃₈₀ are the reflectance at the top of the atmosphere (TOA) at 340 and 380 nm, respectively, and R^meas and R^Ray represent the measured TOA reflectance with aerosols and the calculated reflectance without aerosols, respectively.

The reflectance is defined by Eq. (2)

where I is the Earth radiance at the TOA, E is the solar irradiance at the TOA perpendicular to the direction of the incident solar beam, and the parameter µ₀ is the cosine of the solar zenith angle. Figure 1 shows the reflectance spectra, measured by TROPOMI over the Pacific Ocean at UV band 3 (320–405 nm) on 16 March 2019. The R₃₄₀ and R₃₈₀ are not affected by O₃ and other trace gas absorption nor the Fraunhofer lines. The ozone absorption is weak and does not affect the interaction between aerosols and the molecular atmosphere (Torres et al., 1998; Penning et al., 2009).

Figure 1.  Reflectance spectra measured by TROPOMI in the cloudless scenes on 16 March 2019, while observing the Pacific Ocean at various wavelengths.

In this study, the Rayleigh reflectance in the simulations was retrieved using a homogeneous Lambertian surface with wavelength-independent surface albedo (A_sc) composed of surfaces, clouds, and aerosols. By assuming that the simulated reflectance equals the measured reflectance at a wavelength of 380 nm, $ R_{{\text{380}}}^{{\text{meas}}}{\text{ = }}R_{{\text{380}}}^{{\text{Ray}}}{A_{{\text{sc}}}} $ ,we can derive the surface albedo (A_sc).

where the term R is the Lambertian surface contribution to the reflectance at TOA, the term R₀ is the pathreflectance, which is the atmospheric contribution to the reflectance, T is the total atmosphere transmission, and A is the spherical albedo of the atmosphere.

Further, Eq. (1) can be modified to Eq. (4):

Fundamentally, UVAI reflects the difference in the aerosol absorption characteristics of the two channels. The higher the absorbing aerosol concentration, the larger is the UVAI value. The UVAI value is ≤ 0 when there is no absorbing aerosol (Torres et al., 1998; de Graaf and Stammes, 2005).

In the UVAI retrieval, a look-up table (LUT) was created using the radiative transfer model SCIATRAN (Rozanov et al., 2005). In a pseudospherical atmosphere, reflectance estimates were calculated using the scalar discrete ordinate method without considering polarization. The LUTs for the reflectance at the two wavelengths contain the solar zenith angle (SZA), viewing zenith angle (VZA), relative azimuth angle (RAA), surface altitude, and cloud height. Note that the standard mid-latitude summer atmosphere was utilized for the atmospheric gas and temperature profiles (Anderson et al., 1986; Ahmad et al., 2006). The nodes of these parameters are listed in Table 1.

Starting from 1 July 2021, the offset of the operational TROPOMI UVAI official data products have been added following the offset factor applied to the UVAI for the degradation of radiance and irradiance at each wavelength (Zweers et al., 2021). Figure 2 displays the global operational TROPOMI observation on 10 March 2019 and 15 July 2021. Upon comparing this display to Fig. 2a, it is seen that the enhanced UVAI values are shown near the orbit edges in Fig. 2b, while the Pacific Ocean is mostly devoid of aerosols. We surmise that the enhanced UVAI on the left side of the orbit is caused by clouds or viewing geometry. The TROPOMI-based scene albedo at 380 nm indicates that a cloud is not the main driver behind the large positive UVAI value (Kooreman et al., 2020). Viewing geometry can be responsible for the asymmetry features.

Figure 2.  Global distribution of the TROPOMI UVAI on 10 March 2019 and 15 July 2021.

Figure 3 displays the average UVAI values of TROPOMI orbits over the Pacific in March 2019 and November 2021 with cloudless scenes. The UVAI values should be near zero, or positive, for this clear and low aerosol level. However, the UVAI values were larger than 1.0 at the edge of the orbit over the Pacific Ocean even after correcting the degradation in the TROPOMI irradiance data, which is adverse to the trending analysis of absorbing aerosols. Overall, the average UVAI values increased with time and the viewing geometry effect on the UVAI became more obvious after 1 July 2021.

Figure 3.  TROPOMI UVAI as a function of ground pixels in March 2019 and November 2021 with cloudless scenes.

In this study, we introduced the background UVAI to mitigate the viewing geometry effect on the UVAI and the effect of degradation in irradiance on the operational TROPOMI UVAI, and retain the absorbing aerosol signal. The degradation is independent of viewing geometry (Kooreman et al., 2020).

To examine the features of the high positive UVAI values over the Pacific Ocean, we simulated the UVAI for observation geometry of the TROPOMI measurements for a series of scenes under clear sky conditions. We quantified the TOA reflectance by using the SCIATRAN radiative transfer model. The calculations were performed for maritime aerosols by using AOD from MODIS. These results reveal that the viewing zenith angle and solar zenith angle are symmetric, as has been previously discussed by de Graaf et al. (de Graaf and Stammes, 2005). Here, we investigated the sensitivity of the UVAI to the different observation geometries and latitudes. Note that any of these parameters should be generally reflected in the UVAI results.

The change in the maritime aerosol index with the TROPOMI geometry including SZA, VZA, and RAA at the equator, 15°, 30°, 45°, and 60° south-north latitude is shown in Fig. 4. The range of ground pixels of 0–30 yields the UVAI bias of +0.6, compared to ground pixel 225 (nadir view). The UVAI bias is caused by the change of viewing geometry. The 60°S latitude shows a +0.2 AAI value higher than 45°S. Higher latitudes mean that higher SZA yields higher UVAI errors (de Graaf et al., 2005). The simulation results show that UVAI exhibits a severe asymmetry across the orbit, and the UVAI increases with latitude, indicating the dependence of UVAI and the viewing geometry. To reduce the effects of viewing geometry on the UVAI, the background UVAI (namely, UVAI with the same viewing geometry under cloudless scenes over the Pacific Ocean) must be applied to the initial UVAI retrieval.

Figure 4.  Simulated UVAI of maritime aerosol inside the atmosphere as a function of ground pixels for different latitudes with cloudless scenes.

An aerosol filter was applied by using the AOD from the Moderate Resolution Imaging Spectroradiometer (MODIS) on board the Earth Observing System Terra and Aqua platforms, which is the best available instrument for monitoring real-time aerosols. MODIS has 36 spectral channels with spatial resolution ranges from 250 m to 2500 m within the wavelength ranges from 400 nm to 1440 nm (King et al., 1992; Parkinson, 2003). The average AOD over ocean was taken from the MODIS MOD08_M3 product (https://search.earthdata.nasa.gov/search, accessed on 20 August 2021). There are no significant natural sources of absorbing aerosols according to the operational TROPOMI official UVAI data product. It can prove the Pacific scenes without the concentrations of absorbing aerosols for March 2019, 2020, and 2021. Figure 5 shows the frequency distribution of the MODIS AOD at 550 nm over the ocean for March 2019, 2020, and 2021. The color data rectangles and curves represent the AOD histogram and the normal distribution, respectively. The mean AOD is 0.18, 0.18, and 0.19 for March 2019, 2020, and 2021, respectively. The standard deviation exhibits similar results, which are nearly 0.10. The mean value and standard deviation of AOD remain constant, which indicates that the distribution of aerosol is homogenous. This finding also suggests that there was no prominent change in the aerosol level over the Pacific Ocean.

Figure 5.  Frequency distribution of the monthly average MODIS AOD at 550 nm over ocean for March 2019, 2020, and 2021.

The effects of clouds on the quantitative application of UVAI are complicated because the clouds are three-dimensional structures, whereas completely cloud-free scenes are rare in the atmosphere (Krijger et al., 2006). Notably, Penning et al. (2009) have introduced a way to describe how clouds affect the UVAI.

The effects of clouds on the calculation of the background UVAI can be reduced by applying a cloud filter. The TROPOMI Level 2 cloud product provides the cloud fraction. However, errors originating from the cloud retrieval algorithm adversely affect the selection of suitable clear-sky scenes. The simple cloud fraction threshold is not a robust filter for small and/or thin clouds (Penning et al., 2009). Therefore, two steps are introduced to confidently filter out the cloudy pixels. First, cloud screening was performed using the cloud fraction from the TROPOMI cloud products. The threshold of the value was set to 0.2. This only allows removing scenes containing the highest cloud concentrations. Moreover, to reduce a gap with the clear sky scene, we added a geometric criterion defined as the ratio of the measured TOA reflectance to the Rayleigh scattering reflectance at the wavelength($ \lambda $) of 340 nm or 380 nm:

As mentioned earlier, the simulations were conducted by the SCIATRAN radiative transfer model to derive the relationship between the ratio and cloud fraction. As shown in Fig. 6, the ratio (8) exhibits a linearly increasing response to the cloud fraction at the wavelengths of 340 nm and 380 nm. The lowest value of the ratio at the corresponding pixels was confirmed to be cloud-free pixels.

Figure 6.  The ratio of the measured top of the atmosphere (TOA) reflectance to the Rayleigh scattering reflectance at the 340 nm and 380 nm for variations in cloud fraction.

To improve the accuracy of the distribution of aerosol characteristics, the instrumental background UVAI was derived by using a statistical method over the Pacific Ocean. Two factors need to be considered for this process. First, one should select the appropriate days. The effect of the solar zenith angle on the background UVAI can be reduced by using shorter days of data. However, another issue emerges because large volumes of data are lost by filtering out cloudy pixels for shorter days. In turn, this increases the random error of the background UVAI. The simulations (Fig. 4) showed that the effect of latitude within ±10° on the UVAI is minor, and therefore can be ignored. We found that the direct sun angle equals to ~7° change per month. Due to this, a period of one month was chosen to extract the background UVAI.

Second, one should filter out cloudy pixels. We retrieved the cloud-free pixels by the method introduced in section 3.2. At the same time, we also needed to remove the pixels satisfying the sun glint condition. Note that a sun glint is a commonly-observed phenomenon, driven by specular reflection of direct sunlight from the ocean surface (Torres et al., 1998; de Graaf and Stammes, 2005; Tilstra, 2012). The sun glint generates a high UVAI value. The sun glint deviation angle ($ \Theta $) can be defined for each pixel by using Eq. (9):

We calculated the sun glint deviation angle for each individual TROPOMI pixel in the process of UVAI retrieval. An ocean surface pixel with a sun glint deviation angle of < 18^o was determined to satisfy the sun glint condition.

Figure 7 shows the distribution of TROPOMI orbits over the Pacific in November 2021. The range of the UVAI values in Fig. 7 suggests that the operational TROPOMI official UVAI data products feature elevated UVAI near the orbit edges, located on both sides of the orbit. After correction for the degradation of irradiance, a positive offset was introduced to the operational TROPOMI UVAI data. Moreover, positive UVAI values were observed near the left side of the orbit for the cloudless scenes, caused by viewing geometry (Kooreman et al., 2020). At the intersection of the equator and ground pixel of 150, a distinct UVAI population is visible, which virtually reflects the sun glint caused by the ocean surface reflection effects. The positive structural features indicate that the operational TROPOMI UVAI is associated with the viewing geometry and instrument degradation.

Figure 7.  Orbital distribution of TROPOMI over the Pacific Ocean in November 2021. The x-axis “ground pixel” represents the viewing direction, whereas the y-axis “latitude” represents the solar position. The color bar links the colors given to the AAI value.

The operational TROPOMI official UVAI data products include the calibration errors of the instrument and the dependence of viewing geometry. The initial UVAI results that we retrieved using the UVAI algorithm also include these factors, which can be removed from the operational TROPOMI UVAI and the initial UVAI retrieval results by applying the background UVAI. The background UVAI is a statistical value that includes the calibration errors of the instrument and the dependence of viewing geometry, which is computed as a function of time, latitude, and ground pixel. This study investigates these effects on the initial UVAI retrieval values. These investigations also applied to the operational TROPOMI UVAI.

In Fig. 8, we show the background UVAI from our UVAI retrieval, namely, the statistics of 30 retrieved UVAI orbits over the Pacific in March 2019, 2020, and 2021 in panels (a)−(b), (c)−(d) and (e)−(f), respectively. The statistical method yielded the spatial distribution of the background UVAI between latitudes 60°S and 60°N by selecting 30 days, filtering out cloudy scenes, and discarding the sun glint pixels.

Figure 8.  The left panels for orbital distribution of retrieved UVAI and the right panels for UVAI after interpolation over the Pacific for (a, b) March 2019 (c, d) 2020 and (e, f) 2021, respectively. Red color represents positive UVAI value, but the Pacific is devoid of absorbing aerosols. Thus, the UVAI retrieval is severely affected by viewing geometries.

Note that an empty area in Fig. 8 occurs on the equator, which is due to the sun glint in this region. The background UVAI of the sun glint pixels can be retrieved by applying a spline interpolation, which can also reduce the random errors of the background UVAI. The region of negative UVAI value might relate to ocean anisotropy (Kooreman et al., 2020).

The spatial distribution of the background UVAI and the retrieved UVAI from 2019 (Fig. 8a) agrees well with those of 2020 (Fig. 8b) and 2021(Fig. 8c). Also, the viewing geometry dependency is pronounced near the left side of the orbits. However, a clear declining angle dependency can be identified until March 2021, compared to the global mean background UVAI for 2019 (−0.7739), 2020 (−1.121), and 2021 (−1.426). This indicates that on average, a lower index point can be related to the radiometric calibration offset and degradation in the TROPOMI irradiance data (Kooreman et al., 2020; Ludewig et al., 2020). Therefore, we need to update the background UVAI for UVAI retrieval every month.

The spatial distribution of the background UVAI from the UVAI retrieval is displayed in Fig. 8, which also shows the annual aerosol variations. The Pacific average background UVAI was much higher in early 2019, but subsequently exhibited a clear decrease after two years. To analyze the time variation of the background UVAI, we once again examined the time series of the monthly Pacific average UVAI retrieval value. The data that was selected was the mean of the retrieved UVAI value per month between latitudes 10°N and 10°S to reduce the effect of high latitudes on the UVAI value. The background UVAI is averaged along the latitudinal direction to obtain the variations of the background UVAI in the across-track direction for each ground pixel. Figure 9 illustrates the retrieval orbital monthly average background UVAI as a function of a ground pixel for each year over the Pacific. The curve is characterized by the same features as the spatial distribution of the background UVAI. The left side reveals an enhanced UVAI value, given the viewing geometry dependence of the UVAI. The steep peak between the ground pixels 100 and 200 indicates that the sun glint feature exhibits similar patters except for the overall decrease from 2019 to 2021. A clear decrease in the average background UVAI was identified in 2020 and 2021, compared with that of 2019. This result reflects the status of the instrument, which will be discussed further in the next section.

Figure 9.  The average background value of retrieved UVAI as a function of ground pixels for three years.

Figure 10 shows the UVAI on 10 March 2019. A strong dust aerosol signal is captured in the imagery with spatial patterns similar in the Sahara Desert from the retrieved UVAI (Fig. 10a) according to the level 1 ancillary data and the operational TROPOMI official UVAI data product (Fig. 2a). The effects of viewing geometry on UVAI reflect in the initial UVAI appear near the left side of the orbit, as shown in Fig. 10a. The dependence of viewing geometry on the UVAI is reduced after the background UVAI correction was applied as shown in Fig. 10b. Also, the results from Fig. 10b reveal a more homogeneous distribution of aerosols. The distribution of absorbing aerosols in the Sahara Desert can be detected as a positive UVAI, while the ocean and land areas without absorbing aerosols give a neutral UVAI close to zero or slightly positive.

Figure 10.  Distribution of the initial UVAI retrieval (a) before, and (b) after background UVAI correction on 10 March 2019.

The correlation coefficient (r²) of UVAI after background UVAI correction and operational TROPOMI (0.95) is higher than the initial UVAI retrieval and operational TROPOMI (0.83) over the Sahara Desert area, as shown in Fig. 11. As expected, the background UVAI mitigates the viewing geometry effects on UVAI.

Figure 11.  UVAI comparisons between TROPOMI and (a)UVAI retrieval and (b) UVAI background UVAI correction over the Sahara Desert region on 10 March 2019.

Since 1 July 2021, special structures with high UVAI values near the orbit have been observed. For example, when the operational TROPOMI UVAI map of a scene across Taklimakan and northern India was observed on 6 November 2021 (Fig. 12a), a plume of desert air from Taklimakan sandstorms was also observed. The UVAI values were larger than 1.0 in the area even without absorbing aerosol events. The effects of degradation in irradiance and viewing geometry on UVAI were also observed in the distribution of operational TROPOMI UVAI. After correction of the background UVAI, the primary desert aerosol plumes were captured, as shown in Fig.12b, which improved the identification of absorbing aerosols. The corrected TROPOMI UVAI can be used to avoid confusion caused by the enhanced UVAI.

Figure 12.  Distribution of the TROPOMI official UVAI data product (a) before and (b) after background UVAI correction(b) across the Taklimakan and northern India on 6 November 2021.

The UVAI is a physical quantity that is very sensitive to the reflectance and degradation of the instrument (de Graaf and Stammes, 2005; Tilstra et al., 2012). This implies that the background UVAI can be used as a sensitive indicator of the satellite instrument changes. In this section, we analyze the changes in the background UVAI of the TROPOMI instrument. The analysis is based on the average reflectance at 340 and 380 nm over the Pacific.

We used the TOA reflectance at 340 and 380 nm to elucidate the driver behind the variation in the instrumental background UVAI for three years. The mean reflectance was retrieved from the TROPOMI reflectance measurements between the latitudes of 10°S and 10°N in March 2019, 2020, and 2021. The data for the same season efficiently removes the effect of the Sun-Earth distance variation on the reflectance.

Figure 13 shows the results for the TOA reflectance at 340 and 380 nm. In particular, the curves represent the monthly average reflectance of each ground pixel. At 380 nm, no clear trend was observed. There was a small upward trend as the time increased at 340 nm, exhibiting a stable periodic change. The sun glint feature does not exhibit any difference between the time series at 340 and 380 nm.

Figure 13.  TROPOMI reflectance as a function of ground pixels at 340 nm (a) and 380 nm (b) for 2019, 2020, and 2021

To analyze the time series, we assume that the mean reflectance (ave) for every pixel (pixel), denoted by $ {R}_{\lambda ，\text{pixel}}^{\text{ave}}(t) $, representative of an annual periodic may be described by: $ {c_\lambda }(t){\text{ = }}{{R_\lambda ^{{\text{ave}}}(t + 1)} \mathord{\left/ {\vphantom {{R_\lambda ^{{\text{ave}}}(t + 1)} {R_\lambda ^{{\text{ave}}}(t)}}} \right. } {R_\lambda ^{{\text{ave}}}(t)}} $, which expresses the reflectance change due to instrument change at the wavelength λ. The parameter t is the time expressed (years). Figure 13 indicates that the factor c_λ at 340 nm is 1.013 and 1.0232 for 2019−20 and for 2020–21 periods, respectively.

We applied the SCIATRAN radiative transfer model to simulate the contribution of periodic variations in reflectance to UVAI at 340 nm. The model computes the TOA reflectance without the influence of clouds and aerosols by utilizing the viewing geometry data of the equator from TROPOMI measurements over the Pacific.

Figure 14 shows the results of simulating the upward trend of the reflectance at 340 nm. The reflectance only increased by 1.0% and 1.9%, in 2019−20, and 2020−21, respectively. A strong decline in Fig. 14b in cross-track was identified for UVAI with 197% and 341% reduction in 2020 and 2021 (compared with 2019), respectively. We compared this graph with the results from Fig. 13 and found that the variation of the simulated UVAI in across-track exhibited a somewhat consistent trend with the average background UVAI of the retrieved UVAI, changing with ground pixels. The simulation of the contribution of relative variations in the reflectance to UVAI confirms that the UVAI is very sensitive to reflectance. Thus, the background UVAI is also sensitive to reflectance and can be used as a sensitive indicator of instrument status.

Figure 14.  The simulated reflectance at 340 nm (a) and UVAI (b) as a function of ground pixels for 2019, 2020 and 2021.

Instruments can be adversely affected in different ways: (1) an instrument is exposed to UV light and cosmic radiation, potentially causing degradation of optical and electronic parts; (2) the existence of potential radiometric calibration errors, compared with the standard value in the laboratory before the launch of the satellite, and (3) the presence of electronic drift. These effects plague both the radiometric accuracy of radiance and irradiance (Ludewig et al., 2020).

Further analyses were performed to determine whether the annual variations in the background UVAI were related to instrumental variations. We quantified the reflectance using the ratio of Earth and solar radiance, where the radiance variations are reflected in the degradation of the spectrometers. The irradiance variations are expressed in the degradation of the spectrometers and quasi volume diffusers (QVD), depending on the wavelength.

The TROPOMI instrumental degradation in bands 3 and 4 has been previously identified to be strongest for the UV wavelength bands (Tilstra et al., 2020). In-flight measurements revealed the degradation of the UV spectrometer and internal solar diffusers (Ludewig et al., 2020). The irradiance retrieved from TROPOMI shown in Fig. 15 clearly exhibits a reduction of 2% and 1% at 340 and 380 nm, respectively, in 2020. The variation of the background UVAI is about 0.3 per year in 2020. A degradation in the TROPOMI radiance data indicates the degradation of the spectrometers and QVDs at 340 and 380 nm. Therefore, a decline in the background UVAI can be regarded as the degradation of the instrument at 340 and 380 nm.

Figure 15.  Annual variation of the TROPOMI Irradiance at 340 and 380 nm in 2020.

This study introduced a statistical method consisting of calculations made of the background value of UVAI by using TROPOMI (TROPOspheric Monitoring Instrument) observation data over the Pacific Ocean under clear-sky scenes (as there are assumed to be no absorbing aerosols in this scenario). We showed that the enhanced UVAI value on the side of the orbit can be traced to the geometry dependence of the UVAI and the degradation of radiance and irradiance at the wavelength. Notably, this feature is the same with regard to the simulation result that the maritime UVAI is characterized by the severe asymmetry across the orbit. We reduced the effects of viewing geometry and the instrumental degradation on the UVAI distribution along the orbit by introducing a background UVAI. To this end, we introduced the statistical method of the background UVAI over the Pacific Ocean for cloudless scenes. The spatio-temporal distributions of the background UVAI were reconstructed. We found that the background UVAI decreased with time under the same viewing geometry and aerosol concentration.

The applications of the background UVAI to the UVAI have efficiently reduced these effects. A more homogenous UVAI distribution can be retrieved by the background UVAI correction. Notably, the spatial distribution of UVAI retrieval agreed well with the operational TROPOMI official UVAI data product. The correlation coefficient between operational TROPOMI and the initial UVAI retrieval was 0.83, whereas that of the UVAI after the background UVAI correction was 0.95 using data over the Sahara Desert on 10 March 2019. The correlations were improved for UVAI retrieval after background UVAI correction. The background UVAI also can mitigate the effect of viewing geometry and degradation in irradiance on the operational TROPOMI UVAI after 1 July 2021.

To investigate the change in the background UVAI over time, we performed radiative transfer calculations and found that the variation of the background UVAI efficiently reflects the variation in reflectance. The simulation results indicate that UVAI also depends on the instrument status. Therefore, the background UVAI can be used as a sensitive indicator to represent the change in instrument status.

The background UVAI includes the viewing geometric characteristics of the UVAI and the instrumental state. The UVAI following the correction of the background UVAI can diminish the effects of viewing geometry and instrument status on the UVAI. We can also monitor the change in the TROPOMI instrument by using the background UVAI.

Overall, our results can be applied to the EMI instruments onboard the Chinese GaoFen-5 satellite as it will produce the UVAI product as well. One can also calculate the background UVAI as a sensitive indicator to monitor the state of the EMI instrument in future.

Acknowledgements. The authors thank the Institute of Environmental Physics and University of Bremen for providing the SCIATRAN software. We are thankful to NASA for the provisions of TROPOMI and MODIS products.