OMI, a nadir-viewing imaging spectrograph developed by the Netherlands and Finland, was launched in 2004 aboard NASA's Earth Observing System (EOS) Aura satellite . Operating in an ascending Sun-synchronous polar orbit, OMI crosses the Equator at approximately 13:40 LT (local time). It measures solar radiation backscattered by the Earth's atmosphere and surface, covering a wavelength range of 270–500 nm with a spectral resolution of roughly 0.5 nm. With a 114° viewing angle, OMI provides a 2600 km swath width, enabling daily global coverage. The individual ground pixels measure 13 km (along-track) by 24 km (across-track) at the center of the swath, increasing to about 150 km towards the edges. The swath is divided into 60 across-track ground pixels, with incoming light depolarized by a scrambler and split into three spectral channels: two UV channels (UV1 and UV2, covering 270–380 nm) and one visible channel (350–500 nm).

TROPOMI, aboard the Copernicus Sentinel-5 Precursor (S5P) satellite , is a four-channel, nadir-viewing grating spectrometer that measures solar backscattered radiances across the UV, visible, near-infrared (NIR), and shortwave infrared (SWIR) spectra. Like OMI, TROPOMI operates from an ascending Sun-synchronous polar orbit, crossing the Equator at about 13:30 LT. It retains comparable spectral resolution and radiometric performance in the ultraviolet and visible ranges but offers enhanced spatial resolution. At the center of the swath, the ground pixels measure 7 km along-track (reduced to 5.6 km as of 6 August 2019) and vary from 3.5 to 25 km across-track, depending on the wavelength band. With a 2600 km swath width, TROPOMI achieves near-global daily coverage, excluding narrow strips approximately 0.5° wide between orbits at the Equator. The swath is divided into 77 to 450 rows, with the binning factor adjusted to ensure similar spatial size for each row, The exact number of rows depends on the spectral band.

The BIRA-IASB O₂–O₂ cloud product for OMI utilizes the OML1BIRR and OML1BRVG product from the OMI Collection 4 dataset (processor version: 2.0.8.4/24861), which is publicly accessible through NASA's Goddard Earth Sciences Data and Information Services Center (GES DISC). This dataset employs a newly developed L0-1b processor, based on the TROPOMI L0-1b processor at the OMI Science Investigator-led Processing System (OMI SIPS). The advanced processor converts raw sensor data into radiometrically calibrated and geolocated solar irradiances and earthshine radiances. Building on 17 years of experience with OMI Collection 3 data, significant improvements have been made to address issues related to optical and electronic aging and to enhance pixel quality flagging. Detailed information about the upgrade from Collection 3 to Collection 4 is provided in . The OML1BIRR contains daily-averaged irradiance measurements, while the OML1BRVG product contains Earth-view spectral radiances recorded in global mode from the visible detector.

Since 2007, OMI has experienced a field-of-view blockage known as the “row anomaly”, which affects data quality across all retrieval wavelengths for certain rows . The row anomaly has been analyzed for the entire mission for the UV2 and VIS channels, determining affected rows for each day at two wavelengths per channel. Based on these analyses, a dynamic map is generated and used by the Collection 4 L0-1b processor to flag rows accordingly over time. The row anomaly initially affected two rows in June 2007 but eventually extended to approximately 50 % of the sensor's 60 rows. Moreover, the row anomaly is not static and evolves slowly over both long and short timescales.

The initial version of the TROPOMI L1b spectra, based on pre-launch calibration, is described in detail by , while subsequent improvements informed by in-flight calibration are comprehensively documented in . This study uses the updated version of the L1b (ir)radiance dataset (processor version: 2.1.0.25042), which has been reprocessed since 2022.

TROPOMI measurements can experience saturation in band 4 (visible) and band 6 (NIR) detectors when observing intensely bright scenes, such as high clouds in tropical regions. This saturation can affect the O₂–O₂ cloud retrievals, which rely on measurements from band 4. To mitigate this, spectral pixels flagged as saturated are excluded from data analysis. Saturation can lead to anomalously low radiances for certain spectral pixels. Significant saturation can also cause “blooming”, where excess charge from saturated pixels spills into adjacent ground pixels along the row direction, leading to anomalously high radiances for some spectral pixels. Both saturation and blooming are identified and flagged under a single error flag, as documented by . The revised irradiance product includes corrections for optical degradation, improvements in absolute irradiance calibration, and adjustments for the solar radiation angle dependence of the irradiance signal. Additionally, degradation correction is applied to the radiance data.

The O₂–O₂ cloud algorithm, developed by KNMI and known as OMCLDO2, was specifically designed for OMI measurements, as OMI does not cover the spectral range of the O₂ A-band at 760 nm . This algorithm utilizes satellite measurements of O₂–O₂ collision complex absorption near 477 nm to retrieve essential cloud parameters. The procedure involves two main steps. First, a DOAS fit is applied to determine the O₂–O₂ slant column amount, with reflectance calculated at the center of the fitting window. Second, these parameters are converted into effective cloud fraction and effective cloud pressure using a Lambertian cloud model, which assumes that clouds act as Lambertian reflectors with a fixed albedo of 0.8 . This cloud product is designed to mitigate cloud effects in trace gas retrievals, and the cloud model assumptions are consistent across both cloud and NO₂ retrievals. Validation indicates that the retrieved cloud pressure corresponds to the mid-level of the cloud rather than the cloud-top pressure . It is important to note that this algorithm does not distinguish between clouds and aerosols. Consequently, in the computation of the air mass factor (AMF) for trace gas retrieval, aerosol-induced cloud parameters can implicitly correct part of the aerosol effects .

The OMCLDO2 algorithm was first described by , and further improved the retrieval approach. The improvements primarily involve correcting differences in the temperature profile and consequently in the absorption coefficient due to density changes between the GEOS-5 Forward Processing for Instrument Teams (FP-IT) model profile and the fixed model profile used in the forward calculations. Additionally, the look-up table (LUT), which is pre-inverted, has also been updated. The OMI OMCLDO2 product used in this study is based on the most recent version of the OMI L1b dataset Collection 4 data;. Since the release of the TROPOMI operational NO₂ processor version 2.2, the O₂–O₂ cloud product has been included in the NO₂ data product files . However, it has not yet been utilized in trace gas retrievals.

The BIRA-IASB O₂–O₂ cloud retrieval algorithm, though similar in many aspects to OMCLDO2, incorporates several enhancements to improve accuracy and consistency across different sensors:

The DOAS slant column fitting employs a larger fitting window, capturing two O₂–O₂ absorption bands at 446 and 477 nm.

The following section details the BIRA-IASB O₂–O₂ cloud retrieval approach, with an emphasis on these improvements relative to the OMCLDO2 algorithm.

Table  summarizes the absorption cross-sections and settings used for retrieving O₂–O₂ slant columns. Several improvements have been made to the DOAS fitting compared to the OMCLDO2 algorithm. While OMCLDO2 performs the DOAS fit over a spectral range of 460–490 nm, accounting for the absorption effects of NO₂, O₃, and O₂–O₂, the BIRA-IASB approach employs a wider fitting window of 435–495 nm. This expanded range includes both a strong absorption band centered at 477 nm and a weaker absorption band around 447 nm. The wider fitting range improves the stability of the retrieval by reducing the sensitivity of O₂–O₂ SCD retrievals to the polynomial order chosen in the DOAS settings. The inclusion of this broader range necessitates additional spectral analysis adjustments. For example, the fitting now incorporates gas species like water vapor, along with a liquid water absorption cross-section , to mitigate systematic errors over oceans. Importantly, this revised DOAS approach aligns closely with NO₂ DOAS retrievals 405–465 nm,, owing to the substantial overlap between the O₂–O₂ and NO₂ fitting windows.

The latest available cross-sections for species absorbing within the selected fitting window are utilized in the analysis. The absorption cross-sections of the oxygen dimer, which are crucial for this analysis, are depicted in Fig. . It should be noted that there is a systematic 3 % difference in the O₂–O₂ slant columns between the retrieval using the O₂–O₂ cross-sections from and . The fitting residuals using these two O₂–O₂ cross-sections are generally similar; however, the latter exhibits larger residuals in cases influenced by liquid water. Additionally, the dataset from includes cross-sections at a greater number of temperatures, allowing for a more detailed investigation of temperature dependence. In the slant column density fit, an absorption cross-section with a fixed temperature is used. Changing the temperature of O₂–O₂ cross-section from 293 to 253 K results in a reduction of approximately 4 % in the retrieved O₂–O₂ slant columns. This temperature dependence is subsequently corrected in the calculations using a similar approach to the one described in , which will be discussed in Sect. .

Intensity offsets in the spectra, caused by factors such as residual stray light, are corrected by fitting the inverse of the solar reference spectrum see Eq. 5.6 of. In addition, the DOAS fit procedure includes a spike removal scheme as described in , which allows us to filter out individual corrupted radiance measurements from the fit and hence reduce the noise in the retrieval. This approach is also included in the OMCLDO2 algorithm . In this study, the slant columns are derived using the QDOAS software developed at BIRA-IASB .

Figure  presents O₂–O₂ retrievals based on the BIRA-IASB approach and a comparison with OMCLDO2. The data shown are based on OMI measurements on 1 October 2004 and TROPOMI measurements on 1 October 2018. The OMI OMCLDO2 data use the Product Generation Executive (PGE) version 4.0.0.308, based on the OMI Collection 4 L1 dataset, while the TROPOMI OMCLDO2 data come from the operational NO₂ product processor version 2.2, based on TROPOMI Collection 3 Level 1 data. Although the observations are from different times, a comparison of Fig. a and d shows that TROPOMI SCDs are slightly higher than OMI SCDs for low SCD values. For OMI, the differences between BIRA-IASB and OMCLDO2 algorithms indicate a relatively large negative bias over land and a positive bias at high latitudes. For TROPOMI, the biases are predominantly negative, particularly over land regions. The across-track dependence visible in the OMI difference map is likely caused by calibration issues in the OMI L1b data, which introduce across-track variability in trace gas retrievals , and this effect varies depending on the retrieval approach used. A correction methodology for this effect will be detailed in the following section. The dependence on cloud fraction, as shown in Fig. c and f, indicates that the significant biases are primarily associated with cases for small cloud fraction.

The TOA reflectance is calculated at the central wavelength of the fitting window (465 nm) with a bandwidth of 1 nm. For TROPOMI, the solar irradiance reference is derived from daily solar irradiance measurements. In contrast, for OMI, the limited quality of the daily solar measurements necessitates using a 100 d running mean of solar irradiance data, further smoothed to enhance accuracy . However, this approach still does not satisfy the precision requirement of the DOAS fitting. Consequently, a fixed annual average irradiance spectrum from 2005 is applied.

OMI data reveal systematic biases in retrievals, appearing as a striped pattern across cross-track positions – an issue commonly observed in satellite sensors equipped with 2-D detector arrays . To mitigate this artifact, a “de-striping” correction can be applied . Alternatively, the reference sector method offers another approach to mitigate this issue .

To evaluate the across-track variability of O₂–O₂ slant column retrievals for OMI and TROPOMI, we analyze data collected between 50° S and 50° N, focusing specifically on ocean pixels. For each row, 7 d median O₂–O₂ SCD values are computed and plotted as a function of the tangent of the viewing zenith angle (tan⁡(θ)), as shown in Fig. a. Negative viewing zenith angle (VZA) values correspond to satellite measurements on the west side of the swath. OMI results are analyzed across multiple years to explore interannual variability over the same time period. The results reveal that TROPOMI SCDs display significantly smoother across-track variability compared to OMI, consistent with findings from previous NO₂ retrieval studies .

Compared to trace gas retrievals, identifying suitable reference data for correcting stripe patterns in O₂–O₂ is more challenging. In this work, we present a “de-striping” approach to eliminate across-track biases in O₂–O₂ SCDs for OMI measurement across different viewing angles:

We compute the median O₂–O₂ SCD for each row over ocean pixels using 7 consecutive days of measurements between 50° S and 50° N. These median values are plotted as a function of tan⁡(θ).

The O₂–O₂ SCD is highly sensitive to variations in both along-track and across-track solar and viewing zenith angles, as well as to surface albedo, surface pressure, and cloud parameters. The data selection method used in Fig. a excludes land regions due to the significant spatial and temporal variations in surface albedo and surface pressure, as these factors strongly affect the O₂–O₂ SCD. Additionally, using median values helps mitigate the effects of clouds on the O₂–O₂ SCDs, allowing the observed variations to be primarily attributed to geometric factors, particularly viewing zenith angles. As shown in Fig. a, TROPOMI SCDs exhibit an almost linear dependence on tan⁡(θ) for both the west and east sides of the swath. Therefore, we propose using the described method to smooth the O₂–O₂ SCD.

After 2007, an anomaly began affecting OMI radiances in certain cross-track positions, making the second step of the smoothing process inapplicable. However, Fig. b demonstrates that the smoothed SCDs exhibit minimal interannual variation. This finding has been further confirmed for other periods, indicating interannual differences of up to 0.1 × 10⁴³ molec.² cm⁻⁵ (not shown). Thus, we use the average from 2004 to 2007 as a reference. Additionally, an offset is calculated based on the measurements from rows 2–21 (0-based), which remain unaffected by the anomaly throughout all periods, and this offset correction is applied to further mitigate small interannual variations.

Figure c illustrates the across-track variability corrections for 1–7 October for selected years for both OMI and TROPOMI. The correction for TROPOMI follows the same methodology as described above, using the 2018 average as a reference. The OMI amplitudes reach up to 0.3 × 10⁴³ molec.² cm⁻⁵, with a slight increase observed over time, whereas the TROPOMI amplitudes are much lower, remaining below 0.05 × 10⁴³ molec.² cm⁻⁵. The typical precision of O₂–O₂ SCD from DOAS fits is approximately 0.07 × 10⁴³ to 0.1 × 10⁴³ molec.² cm⁻⁵ for OMI in 2004 and 2018, which is lower than the observed amplitude variations. In contrast, for TROPOMI, the O₂–O₂ precision is around 0.05 × 10⁴³ molec.² cm⁻⁵, making it comparable to the amplitude variations. As a result, this correction is currently applied only to OMI data.

As illustrated in Fig. , a stripe pattern is visible in the cloud pressure retrievals, particularly over nearly cloud-free scenes. The de-striping correction effectively reduces cloud pressure variability across the track. As shown in Fig. d, the differences in cloud pressure due to this correction are generally within ±30 hPa, with significantly larger deviations observed when the cloud fraction approaches zero. Additionally, this impact on cloud fraction retrieval is negligible (not shown).

To further validate the O₂–O₂ SCD retrieval, we compared the measured O₂–O₂ SCDs with those simulated using a radiative transfer model. For ground-based measurements, a scaling factor is often required to align measured and modeled O₂–O₂ absorptions . assess various sources of uncertainty in both measurements and simulations, emphasizing the importance of accurately characterizing the atmospheric state, measurement conditions, and spectral analysis to minimize discrepancies.

To accurately simulate O₂–O₂ absorption, we adopt the method described in Eq. (8) of with an improvement to calculate the O₂–O₂ slant column under clear-sky conditions, as follows: 1NSO2–O2=0.2094762⋅RgMgkB2∫p0pTOAm(p)⋅c(T(p))⋅pT(p)dp, where Rg is the gas constant, M is the mean molecular mass of dry air, g is the gravity acceleration, kB is Boltzmann's constant, and m represents the clear-sky box-AMF calculated at 465 nm. The mixing ratio of oxygen is assumed to be 20.9476 %. Compared to Eq. (8) of , a correction factor c is included to account for the temperature effect on the O₂–O₂ cross-section. Since the O₂–O₂ SCD retrieval uses an absorption cross-section at a fixed temperature, this factor aligns the retrieved and modeled O₂–O₂ absorption, compensating for the variation of O₂–O₂ absorption due to temperature changes. Details on the calculation of the correction factor c will be discussed in Sect. . For temperature profiles, we use the CAMS reanalysis data – the latest global atmospheric composition reanalysis produced by the Copernicus Atmosphere Monitoring Service (CAMS). The data are provided at 3 h intervals and include 60 vertical hybrid sigma–pressure levels, with the top level at 0.1 hPa. Additionally, surface reflectance is obtained from the TROPOMI monthly DLER database , which is used for the AMF calculations.

Figure  shows the ratio of retrieved O₂–O₂ SCD to simulated clear-sky O₂–O₂ SCD as a function of cloud fraction over two remote regions, where aerosol effects can be neglected. The analysis is based on 1 month of OMI measurements from October 2004 and TROPOMI from October 2018, considering only pixels with a VZA below 60°, For OMI data, the de-striping correction is applied. The results indicate that the OMI ratios approach 1 when the cloud fractions are near zero, consistent with our expectations. Additionally, as the cloud fraction increases, median ratio values rise over the ocean and fall over land, suggesting that low clouds are more prevalent over ocean, while high clouds are more frequent over land, consistent with previous findings . TROPOMI ratios are systematically higher than those of OMI. When an offset of -0.08 × 10⁴³ molec.² cm⁻⁵ is applied to the TROPOMI SCDs, the ratios align more closely with OMI results. This offset reflects the difference in the mean O₂–O₂ SCD values between OMI and TROPOMI for scenes with cloud fractions between 0 and 0.05 in the two study regions. Further tests, such as restricting pixels to nadir measurements (θ<30°), adjusting spectral fitting settings, and analyzing data from other time periods, yielded similar conclusions (not shown). Although factors like surface reflectance precision and aerosol effects may influence the O₂–O₂ simulation and although DOAS settings may affect the accuracy of the O₂–O₂ SCD retrieval, the bias between OMI and TROPOMI remains unchanged. A potential explanation for this discrepancy is the difference in the solar reference spectrum. While further investigation is needed, it lies beyond the scope of this study. To ensure consistency between OMI and TROPOMI in this study, an offset of -0.08 × 10⁴³ molec.² cm⁻⁵ is applied to the TROPOMI data. This adjustment leads to a cloud pressure retrieval approximately 50 hPa higher in nearly cloud-free scenes, with the effect diminishing as the cloud fraction increases.

Surface albedo is an important parameter for accurately retrieving cloud properties. In the OMI OMCLDO2 product, surface albedo is derived from a 5-year climatology of the OMI LER , based on OMI L1b Collection 3 data, provided on a grid of 0.5° × 0.5° . Recently, a dedicated TROPOMI surface albedo climatology has been developed using TROPOMI measurements . This new climatology offers both a traditional LER and a directionally dependent LER (DLER), similar to the version derived from GOME-2 measurements by , with a finer spatial resolution of 0.125° × 0.125°. The differences in the visible band between the OMI and TROPOMI LER databases are generally small, with a slightly high bias over high latitudes and some land regions . The DLER dataset has been implemented in version 2.4 of operational processing for cloud retrievals (FRESCO and OMCLDO2) and NO₂ retrievals .

For OMI, the “mode LER” is used, representing the most frequently observed value derived through a statistical method, which is particularly effective for improving surface albedo retrieval over scenes with snow, ice, or desert cover . In contrast, for TROPOMI, the surface albedo is determined using the minimum surface LER for snow- and/or ice-free scenes, parameterized as a function of the viewing zenith angle . The OMI mode LER is systematically higher than the TROPOMI minimum LER, especially over bright surfaces (see Fig. ), mainly due to differences in the statistical analysis methods used. Over land-covered surfaces, the TROPOMI DLER values at the east edge of the swath are 0.02–0.03 higher than those at the west edge of the swath and are comparable to OMI mode LER (Fig. ). Over water surfaces, the DLER is identical to the corresponding LER, representing the diffuse component of reflection from the water surface .

The BIRA-IASB approach uses version 2.1 of the TROPOMI DLER dataset for retrievals in both OMI and TROPOMI, taking advantage of TROPOMI's overpass time, which closely aligns with that of OMI. Compared to version 1.0, which was used in the NO₂ processor version 2.4 and based on 3 years of Collection 1 L1 data; version 2.1 is based on 5 years of Collection 3 L1 data. It also includes enhancements for detecting and handling snow/ice contamination and excludes measurements affected by cloud shadows from the analysis . It should be noted that there are still some geometric differences between OMI and TROPOMI, which can introduce biases in DLER. Additionally, interannual variability is not accounted for. However, these differences are expected to be smaller than the discrepancy between OMI LER and TROPOMI LER in most scenarios, particularly for snow- and/or ice-free pixels.

In OMCLDO2 retrievals, surface albedo values are calculated as the average of the albedo at 463 and 494 nm . In contrast, the BIRA-IASB approach directly uses albedo values from the surface albedo dataset at 463 nm, which is close to the center of the O₂–O₂ fitting window. Additionally, the current cloud retrieval approach is only valid when the surface albedo is below 0.6. As surface albedo approaches 0.8, the cloud retrieval becomes unstable, making it challenging for the algorithm to distinguish between clouds and the surface. This issue commonly occurs over snow- and ice-covered surfaces . In such cases, OMCLDO2 performs the retrieval using the LER method. This method models the scene by assuming a Lambertian surface that covers the entire pixel, fitting only the scene albedo and scene pressure. Consequently, it eliminates the need to distinguish between clouds and the surface. On the other hand, this study focuses on the cloud parameters for tropospheric trace gas retrievals in snow/ice-free scenes.

Figure  compares cloud fraction retrievals using various surface albedo datasets. Since cloud fraction retrievals can be influenced by variations in viewing geometries for cloudy scenes, we calculate the 1st percentile of cloud fraction values for each row to minimize the impact of clouds. These values, representing retrievals over cloud-free scenes, are plotted as a function of tan⁡(θ). The results indicate that TROPOMI cloud fractions using TROPOMI DLER are generally close to 0, with slightly lower values at the nadir and relatively higher towards the edge of the swath, with minimal west–east bias. An exception is the enhancement around tan⁡(θ) of -0.5 over the Pacific Ocean, attributed to sun-glint effects. OMI cloud fractions using TROPOMI DLER exhibit similar patterns to TROPOMI values but display a consistently high bias. The OMI cloud fraction values are comparable between 2004 (green) and 2018 (brown), except at the edges of the OMI swath over the eastern USA, where the 2004 values are relatively higher. This difference may be related to changes in land vegetation over time, which could have influenced the DLER values. When using TROPOMI LER, the cloud fractions are 0.02–0.04 higher on the east side of the OMI swath compared to those using TROPOMI DLER over land regions. In contrast, cloud fractions derived using OMI LER are systematically lower, particularly for nadir measurements.

The satellite NO₂ retrieval algorithm employs the DOAS approach, which consists of three main steps: (1) the NO₂ SCDs are retrieved by spectral fitting within a predefined wavelength window, matching the satellite-measured reflectance spectrum to a set of relevant reference spectra; (2) the stratospheric contribution is estimated and removed from the NO₂ slant column; and (3) the residual tropospheric slant column is converted into a VCD using a tropospheric AMF. Cloud retrievals mainly influence the calculation of the AMF, which relies on the independent pixel approximation (IPA). The AMF is expressed as a linear combination of clear-sky and cloudy AMFs, with the retrieved cloud fraction and cloud pressure used to determine the cloudy AMF.

In this study, we use the OMI QA4ECV NO₂ product version 1.1 and the TROPOMI operational NO₂ product version 2.4 to evaluate the impact of changes in cloud correction methods on the derived tropospheric NO₂ VCDs. The NO₂ SCDs and stratospheric components are directly obtained from these products, while the calculation of the NO₂ AMF follows the approach described in , using scripts developed at BIRA-IASB. The box-AMF and TOA reflectance LUTs are pre-calculated at 437.5 nm using VLIDORT v2.8. Surface albedo data are taken from the TROPOMI DLER climatology dataset v2.1 at 440 nm, and a priori NO₂ profiles are obtained from the TM5-MP model , providing vertical profiles simulated at a 1°×1° spatial resolution for 34 atmospheric layers, ranging from the surface up to 0.1 hPa.

Figure  presents monthly mean tropospheric NO₂ VCDs from OMI and TROPOMI, using BIRA-IASB cloud corrections, for October 2018. The lower noise level of TROPOMI is evident, particularly for low NO₂ levels, such as over ocean. Note that approximately half of the OMI measurements are excluded from the analysis due to a detector row anomaly . Overall, we observe a good agreement in both the magnitude and spatial distribution of the NO₂ columns.

The uncertainty in the tropospheric NO₂ is primarily driven by spectral fitting uncertainty in clean areas, whereas in regions with high NO₂ columns the uncertainty is largely dominated by the estimation of the tropospheric AMF . For quantitative comparisons, we calculate the monthly-averaged AMFs and NO₂ columns for five regions (large black boxes in Fig. ) representing some of the most polluted areas globally. To assess the impact of cloud corrections on NO₂ retrievals, we compare the cloud-corrected AMFs with the clear-sky AMFs, as well as the NO₂ retrievals using AMFs with and without cloud correction; results are presented in Fig. . In addition to the BIRA-IASB and OMCLDO2 clouds, the analysis implements the cloud correction approach used in the TROPOMI operational NO₂ product. This correction is based on an effective cloud fraction calculated in the NO₂ fitting window at 440 nm, combined with a cloud pressure derived from the dedicated TROPOMI FRESCO-S algorithm version 2.4;. As shown in Fig. , the 440 nm cloud fractions agree well with the results from our O₂–O₂ algorithm. In contrast, the cloud fractions derived from the O₂–O₂ and O₂–A band measurements exhibit larger discrepancies, and these differences are particularly evident for low cloud fractions, with differences more pronounced over land. For cloudy scenes, there is generally good agreement in cloud pressure retrieval between our O₂–O₂ results and FRESCO (Fig. ). However, in scenes with low cloud fractions, the figures show substantial scatter. FRESCO tends to retrieve relatively lower cloud pressure for high cloud cases over ocean and slightly higher over land.

The impact of cloud corrections on the NO₂ AMF is generally within ±20 % (see Fig. ). All corrections exhibit a systematic positive bias over ocean, whereas over land the effect is comparatively minor, except in tropical regions, where most cloud products introduce a negative bias. As shown in Fig. a, the average impact of cloud correction for the selected polluted regions ranges from -6 % to 11 %, depending on the cloud product used. The AMF difference resulting from various cloud corrections can exceed 10 %. However, these values remain well below the typical uncertainty associated with tropospheric NO₂ AMFs . The AMFs show little variation when using OMI BIRA-IASB, OMI OMCLDO2, or TROPOMI BIRA-IASB cloud corrections. However, the AMF obtained with the TROPOMI OMCLDO2 cloud correction is systematically higher compared to the others, while the AMF based on the cloud correction used in the TROPOMI operational process generally falls between these values, except for a deviation in Western Europe. Additionally, the cloud correction effect over Southern Africa is smaller compared to other regions, likely due to the relatively higher clouds in this area. The NO₂ VCDs generally exhibit an inverse relationship with the effect of cloud corrections, particularly for the three TROPOMI retrievals. This correlation is somewhat weaker when comparing OMI and TROPOMI, which may be influenced by sampling differences between the two sensors. The difference in NO₂ VCDs resulting from the use of different cloud corrections can be as large as 15 %. In general, the TROPOMI NO₂ retrieval based on BIRA-IASB cloud correction aligns more closely with OMI NO₂ retrievals compared to TROPOMI NO₂ retrievals using other correction methods.

In this section, we assess the consistency of BIRA-IASB cloud retrievals between OMI and TROPOMI. Additionally, we compare NO₂ retrievals that utilize the cloud correction based on the BIRA-IASB cloud products. The analysis relies on OMI and TROPOMI measurements from October 2018. To illustrate the improved consistency achieved with the new cloud retrievals, the OMCLDO2 cloud retrievals are also included in the analysis.