The TROPOMI instrument is a push-broom spectrometer on board the dedicated Sentinel-5 Precursor satellite maintaining a polar orbit with an ascending node Equator crossing at 13:30 local solar time. The TROPOMI AER_AI AAI retrieval uses level 1b earth radiance measurements converted to reflectances using the ultraviolet–visible–near-infrared band solar irradiance measurements, which have a spectral resolution of 0.5 nm . This study uses a selection of 54 TROPOMI orbits between 6 August and 4 September 2019 over the Pacific Ocean, overlaid and averaged based on the Equator crossing time. The orbits have been chosen in such a way that 178∘ E <η< -140∘ E, where η is the longitude of dayside nadir Equator crossing. We use the TROPOMI offline level 2 AER_AI aerosol index product from the 340 nm/380 nm pair, version 1.2.0, rather than the 354 nm/388 nm pair because of continuity with TOMS, GOME, SCIAMACHY, and GOME-2. However, we do not expect a significant difference in results between the two wavelength pairs. Data are only used if the retrieved scene albedo at 380 nm is between 0 and 1, the solar zenith angle is smaller than 80∘, and the qa_value is > 0.8. This quality assurance value is a continuous quality descriptor, varying between 0 (no data) and 1 (full-quality data). The value is changed based on observation conditions and retrieval flags, and users are recommended to at least ignore data with qa_value < 0.5 (for details see ).

When one zooms in on a TROPOMI AAI map of a scene with broken clouds, one can always see structures of clouds with high and low AAI values. An example is given in Fig. , which is a TROPOMI observation over the South Pacific Ocean on 30 August 2018. Please note that no absorbing aerosols are present in this ocean scene, so only clouds can be responsible for the AAI effects.

The small-scale effects show that clouds have sides with high and low AAI. This is related to the small (nadir) pixel size of TROPOMI (3.5 km× 5.5 km), which is in the order of the size of clouds, and not observed by GOME-2 (40 km× 80 km pixels) and OMI (13 km× 24 km pixels).

Figure  shows the AAI in a cloudy scene over the Pacific Ocean on 30 August 2018 measured by TROPOMI (Fig. a). Large positive AAI values are found next to negative AAI values. Comparing the AAI map to the true-color image of Visible Infrared Imaging Radiometer Suite (VIIRS; Fig. b), the TROPOMI top of the atmosphere reflectance (Fig. c) and the TROPOMI calculated scene albedo at 380 nm (Fig. d) shows that the large positive AAI pixels are located at the brightest cloud patches. Stronger negative values are found on the self-shadow side of the clouds (to the right of the cloud tops in this image). Clouds reflect incident sunlight anisotropically, causing a solar illumination and the viewing geometry dependence of the AAI. In Sect. , we investigate the directional effect of cloud reflection on the AAI.

Negative AAI values are found in the partly clouded area between the thicker clouds. showed with plane-parallel cloud modeling that scenes with thin clouds or small geometrical cloud fractions may cause a more negative AAI than cloud-free or fully clouded scenes. In Fig. , large negative AAI values are also found on top of the clouds. Indeed, clouds have 3D structures which may induce a self-shadow (i.e., the part of the cloud which is not illuminated by direct light) or a cast shadow (i.e., a shadow on another cloud, the atmosphere, or the surface below the cloud) . At the right side of the brightest cloud patch in Fig , the cloud’s self-shadows and cast shadows on lower clouds decrease the AAI. In this work, we will investigate the large-scale cloud effect on the AAI and leave the in-depth analysis of the effect of small-scale and 3D cloud features on the TROPOMI AAI for a future study.

To provide a useful AAI product, the AAI algorithm ideally performs consistently over the orbit, independent of non-aerosol variables, such as solar-viewing geometry, surface properties, cloud presence, and instrumental features. The consistency of the AAI distribution over the Earth can be evaluated by compiling a multi-orbit mean image. This removes the small-scale variability of individual overpasses and reveals structural biases. The Pacific Ocean is mostly devoid of aerosols as it does not harbor any significant natural sources of absorbing aerosols. Any orbits with aerosol plumes from volcanic eruptions or smoke events are not included in the Pacific Ocean data used. The large-scale effect of persistent aerosol contamination is illustrated in Fig.  which displays the Pacific multi-orbit AAI on the right and the global AAI on the left. A band of elevated AAI values is seen in the global plot, which can be attributed to plumes of Saharan dust over the Atlantic Ocean. The Pacific is therefore an ideal test environment for AAI features of clouds as we expect the overall AAI mean to be near zero over this region.

Figure  shows the mean of 54 TROPOMI orbits. The range of values in Fig.  immediately shows us that AAI values are mostly negative. This is partly due to the scattering effect of clouds but also due to a radiometric calibration offset and a degradation in the TROPOMI irradiance data. Due to the degradation, the 340 nm/380 nm wavelength pair AAI has dropped by about 0.5 units over the period of 20 months. After sensor commissioning in early 2018, the global average AAI was much higher (∼-0.2). An update of the level 1b product includes an irradiance degradation correction which will alleviate the problem. Activation of the version 2.0.0 level 1b processor is foreseen for late 2020. As the degradation is expected to be independent of viewing geometry, it does not affect the relative AAI values of the orbital features of interest in this work.

The AAI blob in Fig.  at the intersection of scanline 2200 and ground pixel 150 is caused by the sunglint which shows up in scenes where the sea surface is visible. The circular pattern intersecting the sunglint can be traced back to the cloud bow when looking at the corresponding single scattering angles. In Fig. , the single scattering angle is shown to clarify the geometry-dependence of the AAI. The single scattering angle Θ is defined as the following: 1cos⁡Θ=-μμ0+1-μ21-μ02cos⁡ϕ-ϕ0, where ϕ-ϕ0 is the relative azimuth angle of viewing and solar directions. Respectively, μ0 and μ are the cosines of the solar and viewing zenith angles.

In Fig. a, positive AAI features are found near the orbit edges, especially near the orbit start and end, located at the intersections of ground pixel 0 and scanlines 600 and 3600. The origin of these features is unknown, and we hypothesize that they are caused by a combination of clouds and extreme solar and viewing geometries (i.e., high solar zenith angle, SZA, and viewing zenith angle, VZA).

In Fig. , the mean orbital distribution of the AAI is shown for scenes with few to no clouds, in which the retrieved scene albedo is small (0.0 < Asc < 0.2), and for cloudy scenes, in which the scene albedo is high (0.6 < Asc < 1.0). The cloudless scenes in Fig. a show AAI features due to ocean surface reflection effects, especially the sunglint (the positive AAI blob at ground pixel 130 and scanline 2200), and mildly higher AAI at more extreme viewing angles. The area of strongly negative AAI north and south of the sunglint (around scanlines 1000 and 3000) might also be related to ocean anisotropy (bidirectional reflectance distribution function, BRDF).

The cloudy scenes in Fig. b show that clouds play a large role in systematic AAI offsets. Especially the cloud-bow is a prominent feature (centered at ground pixel 280 and scanline 2200 with a radius of approximately 800 scanlines), but we also see enhanced AAI values at more extreme viewing angles. Moreover, a clear increase is seen in the eastern part of the orbit, which is related to the anisotropy of light reflection by clouds.

To assess this hypothesis, we used two more elaborate atmospheric models that compensate for the approximate effect of clouds, similar to . This is described in the next section.

The AAI is defined as the difference between the ratio of measured reflectances at 340 and 380 nm and the ratio of simulated reflectances at those two wavelengths. 2AAI=-100⋅log⁡10R340R380meas-log⁡10R340R380sim Here the simulated reflectances are calculated for a purely Rayleigh scattering atmosphere without aerosols but including ozone, which is absorbing at these wavelengths. We note that the correction for absorption by ozone, which mainly resides in the stratosphere, can be done accurately since in this part of the UV spectrum (340–400 nm), ozone absorption is weak and does not affect the interaction between aerosols and the molecular atmosphere. For the simulation required in Eq. (), the albedo of the lower boundary of the atmosphere, called the scene albedo Asc, is adjusted such that the simulated top of atmosphere (TOA) reflectance at 380 nm equals the measured reflectance at 380 nm. 3R380simAsc=R380meas So the scene albedo is the Rayleigh-corrected scene reflectance for an assumed model of the lower boundary, where the default is a Lambertian model. In reality, the scene is generally composed of surface, clouds, and aerosols. The assumption in the AAI retrieval is that the scene albedo is spectrally independent in the spectral window between λ = 380 nm and λ = 340 nm. Thus, the scene albedo that is found at 380 nm is also used for the simulation at 340 nm. 4Asc(340)=Asc(380) This makes it possible to determine R340sim for all scene-specific solar-viewing geometries in order to calculate the AAI according to Eq. ().

We call the default model for the simulation the Lambertian scene model (LSM). In this model, the surface, clouds, and aerosols in the scene are together represented by one Lambertian surface with albedo Asc. This model is used operationally by TROPOMI  and is used to obtain the results of Sect. . The LSM and two other models are further described in Sect. .

We note that the wavelength pair 340 nm/380 nm can be replaced by another wavelength pair, i.e., 354 nm/388 nm, which is used for OMI . The longest wavelength of the pair is called the reference wavelength since for that wavelength, the scene albedo is found which is then used for the simulation at the shorter wavelength.

An important assumption in the default AAI retrieval described above is that the surface is Lambertian, i.e., it reflects isotropically. This means that the directionality of the radiation incident on the surface does not affect the amount of reflection by the surface; direct solar irradiance coming from one direction or diffuse skylight radiation coming from all directions are reflected in the same way. So the assumption is that the total albedo (also called plane albedo) of the surface, averaged over all outgoing directions, does not depend on the directionality of the illumination. However, in reality most surfaces and objects, like clouds, are not Lambertian but reflect anisotropically; they have a bidirectional reflectance distribution function (BRDF) with more reflection in certain directions and less reflection in other directions. According to symmetry considerations, this means that the total albedo of the surface or the cloud layer depends on the directionality of the illumination; for some incident directions the total albedo of the surface or cloud layer is higher than for other incident directions. Thus, an important assumption of the default AAI model breaks down.

The effect of the BRDF on the AAI can be understood as follows. In the UV spectrum, there is a strong spectral dependence of direct and diffuse illumination on the surface since the Rayleigh optical thickness τRay is large and strongly varying: at 340 nm τRay=0.714 and at 380 nm τRay=0.447, which is a ratio of 1.597. The ratio between direct and diffuse downwelling irradiances at the surface (normalized to the incoming solar irradiance at TOA) is 0.358/0.307 = 1.168 at 340 nm and 0.528/0.239 = 2.210 at 380 nm (for SZA = 45∘). So there is almost a doubling of the relative contribution of direct illumination at 380 nm compared to 340 nm. This is due to the much smaller Rayleigh optical thickness at 380 nm which causes a stronger impact of surface BRDF on the TOA reflectance at 380 nm than at 340 nm.

The effect on the AAI of this illumination difference in combination with the BRDF is sketched in Fig. . Suppose the surface or cloud in the scene has a BRDF with a high and a low reflection part; here we explicitly exclude shadows but only consider the BRDF of a plane surface or cloud. When the satellite is viewing towards the high reflection direction at 380 nm (Fig. a) where there is a relatively large direct solar illumination, the high reflectance of the BRDF leads to a high Lambertian scene albedo (cf. Eq. ). This means that the surface will reflect both direct and diffuse radiation strongly. Then at 340 nm where there is a relatively small direct but relatively large diffuse solar illumination, the model predicts a reflectance at TOA that is too large compared to the observation; thus the AAI becomes positive. In other words, the Lambertian scene albedo that is too high has to be compensated by putting an “absorber” in the atmosphere to match the observed reflectance at 340 nm. This explains the high AAI at the large solar and viewing zenith angles observed in the large-scale effects but also the high AAI value at the bright sides of small-scale clouds. In addition, it explains the high AAI in the sunglint which is an extreme BRDF brightening effect due to Fresnel reflection at the ocean surface under clear sky conditions.

When the satellite is viewing towards the low reflection direction of the surface or cloud (Fig. b), the surface reflectance at 380 nm is low, leading to a low Lambertian scene albedo. This same low albedo is used at 340 nm to calculate the model reflectance, but since there is less direct and more diffuse illumination at 340 nm, this leads to a TOA reflectance at 340 nm that is too low. Thus the AAI becomes negative. In other words, “scatterers” have to be added to the atmosphere to compensate for the missing reflectance. In reality, these are expressions of the BRDF of the surface in combination with the different ratio between direct and diffuse illumination at 380 and 340 nm.

As part of the large-scale cloud effects, we clearly observe the cloud bow in the TROPOMI AAI orbital maps. To understand this phenomenon, we have performed a simulation of the AAI of an atmosphere with a Mie scattering cloud which has a droplet size distribution with a 10 µm effective radius. The result is shown in Fig.  for three values of the cloud optical thickness (COT), τ, at 380 nm: τ = 1, 8, and 32. In Fig. a, the BRDF of the cloud, i.e., the reflection function of the cloud without atmosphere, is shown for a solar zenith angle of 45∘ in the principal plane; in Fig. b the calculated AAI is shown for the cloud inside the atmosphere. In Fig. b, we clearly see the cloud bow appearing as sharp positive peaks in the AAI for backward scattering directions. This is to be expected on the basis of the discussion above since the cloud bow is part of the BRDF of a Mie scattering cloud. The cloud bow peaks have a similar relative strength of 0.5–1.0 AAI points for all three COT values.

In Fig. b, we observe a strong slope from negative to positive AAI values towards more forward scattering directions. We speculate that these are the small-scale effects of clouds on the AAI, as shown in Fig. . This slope towards a strongly positive AAI for larger viewing zenith angles can also be linked to the large-scale effects since we observe in Fig.  an increasing AAI for larger VZA. It appears that the AAI variation versus VZA of a cloud with a large optical thickness (τ=32) is smaller than a cloud with medium optical thickness (τ=8) and small optical thickness (τ=1).

Here we describe the three models of a cloudy atmosphere to simulate the reflectances at the top of atmosphere (TOA) needed in the AAI formula Eq. (). In Fig. , the three models are shown schematically. They have an increasing complexity, starting with the Lambertian scene model (LSM), next the Lambertian cloud model (LCM), and thirdly the scattering cloud model (SCM), consisting of anisotropically scattering particles.

The simulated reflectances are calculated using the Doubling-Adding KNMI (DAK) radiative transfer model version 3.4.1 .

This model computes the monochromatic reflectance and transmittance in a pseudo-spherical atmosphere, including polarization, using the doubling-adding method. For an arbitrary number of layers, which can have Rayleigh scattering, gas absorption, and aerosol or cloud particle scattering and absorption, this method calculates the polarized internal radiation field, as well as the TOA reflectance. For many combinations of viewing geometry, atmospheric state (cloud height, O3 column), and surface state (e.g., surface height and albedo), the TOA reflectances are calculated and stored in a LUT. Model parameter settings are summarized in Table . The atmospheric profile of pressure p, temperature T, and ozone mixing ratio is the standard midlatitude summer (MLS) profile .

Here the three different AAI retrieval methods are tested for a series of simulated scenes with clouds – but without absorbing aerosols – to investigate their sensitivity to errors in the input parameters. We note that the influence of cloud fraction and cloud optical thickness on AAI has already been discussed in and . Here we study the sensitivity of the AAI algorithm to errors in cloud height and surface albedo. An error (or uncertainty) in any of these inputs will generally result in an error (or uncertainty) in the AAI.

First a baseline scene is defined, upon which one of the parameters will be varied systematically. The baseline scene is a scene 40 % covered by a HG or a Mie scattering cloud with an albedo of 0.8, located between 3 and 4 km altitude (710 and 628 hPa). Figure  displays the effect on the AAI if the cloud height is offset. An input cloud top height of 4 km results in an AAI of zero for the SCM retrieval.

In case the cloud top pressure is wrongly estimated, for example, if an input value of 500 hPa is given instead of the true value of 628 hPa, the resulting AAI error is about -0.01, as can be read in Fig. . Apart from the generally higher AAI values for Mie clouds, the error is similar as for HG clouds. The LCM model results in a shift of about -0.1 AAI compared to the SCM, but errors are very similar to the SCM errors.

Figure  shows results for a large range of cloud pressures. Even for large errors in cloud height, the AAI bias in the SCM and LCM is limited to about ± 0.1. For the LSM, there is no dependence of AAI on cloud height since it is not an input parameter. In Fig. , the LSM AAI is shifted by about -1 with respect to the SCM AAI for HG and Mie clouds. Typical FRESCO cloud top height errors depend on cloud optical thickness. The FRESCO retrieval works well for optically thick clouds with errors of only a few hundred meters . Optically thin clouds are harder to detect, and the retrieval yields errors up to 2 km. According to Fig. , resulting errors in AAI range from almost zero to 0.1, respectively.

A similar study was conducted to analyze the AAI response to incorrect estimates of surface albedo at 380 nm, which is used in the LCM and SCM retrieval algorithms. Moreover, in this case we assume a scene with 40 % effective cloud fraction. Two cases are analyzed: one with low surface albedo As=0.05, representing forests, deserts, and ocean, and one with high surface albedo As=0.9, representing snow- and ice-covered regions . Results are shown in Fig.  and clearly show an AAI dependency on input surface albedo. The LSM retrieval shows a constant AAI value as it is not dependent on surface albedo input. Low albedo scenes are shown in Fig. a. In both the LCM and SCM retrievals, a linearly decreasing response to surface albedo is seen of about -0.3 AAI change per +0.1 change in surface albedo. A typical error in the surface albedo database is 0.03 for these types of surfaces, resulting in a potential AAI error of 0.1 index points. High albedo scenes are less sensitive to surface albedo errors on the AAI as shown in Fig. b. For surface albedo values above 0.8, the bias is roughly 0.1 AAI index points. When the surface albedo is underestimated, an AAI bias of -0.3 can be observed. As=0.8 presents a singular point since the cloudy and clear parts of the scene are no longer distinguishable, and an asymptote occurs in the AAI. Such high albedo values occur only over snow and/or ice scenes and have a typical error of 0.07, resulting in a potential AAI bias of roughly 0.1.

Two additional input parameters that potentially affect AAI retrieval accuracy are ozone column and surface elevation. Their influence on the AAI has been researched and is described in . The typical AAI errors propagated from the input parameters are summarized in Table .

The three AAI retrieval methods, LSM, LCM, and SCM, are applied to the same sample of 54 TROPOMI orbits over the Pacific Ocean, as was described in Sect. .

The LCM and SCM retrievals are dependent on external data sources for the input parameters cloud height and surface albedo. The cloud height data used are generated by the FRESCO algorithm which retrieves cloud information from the O2 A-band near 760 nm. Since this information comes from the near infrared (NIR) band, it was regridded to the ultraviolet–visible (UV–VIS) ground pixels. Availability and data quality are not always guaranteed. For example, FRESCO has larger retrieval errors for scenes with very thin clouds or little cloud cover. The surface albedo at 380 nm is taken from the OMI mode LER database which aggregates 5 years of reflectance measurements on a monthly 0.5∘ × 0.5∘ grid, based on . In order to ensure that the external input parameters remain within a valid LUT range, the following assumptions are made. If the input surface height is below 0 km (rare occurrence), it is set to 0 km to avoid extrapolation in the LUT. The most significant error would occur in the Dead Sea, as it lies 423 m below sea level. However, this is still well within the vertical resolution of the LUT. Even on the 1 km LUT resolution scale, a terrain height estimate error results in a negligible AAI bias. If the input cloud height is below 1 km (i.e., the cloud is lying on the surface), it is set to 1 km. The RT model does not allow a cloud altitude below 1 km as the thickness of the cloud layer is 1 km.

To analyze the performance of the three different AAI retrieval models, we again look at the orbital means over the Pacific. The cloud models are sparse on data in the northeastern part of the orbit. This is due to a selection based on surface albedo. Since the surface albedo database is on a 0.5∘ × 0.5∘ grid, it often does not represent the small TROPOMI ground pixels well enough, resulting in large errors. To resolve this problem, we have selected pixels only over the ocean for the LCM and SCM models by removing scenes with a surface albedo database values larger than 0.2 (mostly scenes over Alaska and Antarctica).

A thorough analysis can be performed by investigating several cross sections. In Fig. , the horizontal lines show east–west cross sections of the south, sunglint, and north in such a way that the end-of-orbit feature (“south”), the sunglint (“sunglint”), and no abnormality (“north”) are captured. The vertical lines show (from left to right) the “west”, sunglint, “cloudbow”, and “east” cross sections.

Figure  shows that the LCM and SCM retrieve a higher AAI value over a large range of latitudes compared to the LSM. The sunglint is enhanced in both models, as well as midlatitude regions (centered around scanlines 750 and 3000). As clouds typically induce a negative AAI, this increase is likely due to the improved cloud model. At extreme viewing geometries, both cloud models show a decrease in AAI. However, the SCM shifts this decrease mostly toward the regions where we find the end-of-orbit features.

Figure  shows histograms of the AAI value occurrence over the orbits for the different retrieval models. The LSM shows a sharp peak at -1.8 and shoulder-like features on the right side of the histogram which are associated with the sunglint, the positive features at the end of orbit, as well as the cloud bow and the elevated values at the eastern side of the orbit, as shown in Fig. . A clear shift in the mean is observed for the LCM (+0.3) and SCM (+0.4) retrievals. The standard deviation of the three curves are very similar at 0.5, 0.7, and 0.6 for, respectively, the LSM, LCM, and SCM. However, the shape of the curves give additional insight into the differences. The AAI value cutoff on both sides is relatively sharp in the LSM but shows a more gradual decrease in the LCM and LSM models. The left side of the LCM and SCM histograms can be traced back to the AAI decrease at the orbit ends in Fig. . The right side of the histograms relates to the increase in sunglint signal. The shoulder-like features mentioned above are less pronounced in the LCM and LSM, suggesting a more homogeneous distribution for the majority of observations.

In Fig. , we show how the three AAI retrieval models are performing in the case of absorbing aerosol presence to make sure that the absorbing aerosol signal is still captured. In January 2020, a large plume of smoke from Australian forest fires was transported thousands of kilometers eastwards across the Pacific, reaching the area that we previously used to determine the large-scale cloud effects. The smoke plume has AAI values well above 12. Apart from a small overall increase in AAI values, the smoke plume is very similar across the three models. This allows us to conclude that the absorbing aerosol signal is well captured by all three models.