During the annular solar eclipse on 26 December 2019, TROPOMI measured the penumbra in orbit 11 404 between 04:49:46 and 05:48:19 UTC. The left image in Fig.  shows the measured TOA reflectance (without solar irradiance correction) at 380 nm on 26 December 2019, R380meas, in three adjacent orbits over Southeast Asia. An apparent decrease in R380meas may be observed between 5∘ S and 25∘ N latitude, as shown by the dark shade in orbit 11 404. Note that the brightening of the sky at larger viewing zenith angles, due to the increase in multiple Rayleigh scattering, is also observed in each orbit, manifesting itself as a subtle increase in R380meas toward the east and west edges of the swaths.

Figure  shows fo at 380 nm that we calculated for the ground pixels of the TROPOMI UVIS detector in orbit 11 404. The antumbra, in which fo at 380 nm peaks at 0.976 (see Fig. ), was not captured because the antumbra was located slightly out of sight in the west. The maximum calculated fo for this orbit is 0.89 at 2.27∘ N latitude and 108.12∘ E longitude. Figure  shows that the eclipse obscuration in orbit 11 404 was not limited to the Gulf of Thailand and the South China Sea: small obscuration fractions (0<fo<0.4) could be experienced in eastern China and the northwest coast of Australia.

The right image in Fig.  shows the restored TOA reflectance at 380 nm, that is, after the correction for the eclipse obscuration (Eq. ) in orbit 11 404. The dark shade that could be observed in the left image in Fig. , resulting from the decreased R380meas in the Moon shadow, has disappeared. The appearance of the corrected R380meas in orbit 11 404 is comparable to the appearance of R380meas in orbits 11 403 and 11 405.

To analyse the reflectance correction more quantitatively, Fig.  shows the average R380meas per scan line

The line at the Earth's surface perpendicular to the flight direction defined by the satellite swath which is roughly oriented west–east.

The restored TOA reflectance during an eclipse that we showed in Sect.  can be considered the intrinsic reflectance Rint of the atmosphere–surface system, as explained in Sect. . If the optical properties of the atmosphere–surface system are not affected by the eclipse, Rint approximates the TOA reflectance as if there were no eclipse. Consequently, the eclipse obscuration fo at 380 nm can be estimated from the comparison of observations of R380meas inside and outside the Moon shadow and can be used to verify the calculated fo at 380 nm from theory.

Orbit 11 403 (east of orbit 11 404) was not eclipsed and preceded the eclipsed orbit 11 404. We compare each ground pixel of orbit 11 404 to its equivalent in orbit 11 403, i.e. for the same scan line and pixel row, such that differences in illumination and viewing geometry are negligible. That is, we compute the observed fo at 380 nm as (see Eq. ) 13fo(λ=380 nm)≈1-R380measeclipseR380measno eclipse, where the label “eclipse” indicates orbit 11 404 and the label “no eclipse” indicates orbit 11 403. We can compute Eq. () for pixels that have a comparable atmosphere–surface system. Therefore, we only compare ocean pixels, because, at the latitudes where the eclipse was measured in orbit 11 404, orbit 11 403 was mainly above the Pacific Ocean. Also, we only consider cloud-free pixels as the cloud types, and cloud fractions in the two pixels will hardly be identical. In Fig.  we showed that the difference of fo between 340 and 380 nm is insignificant (the fo curves for 340 and 380 nm are virtually indistinguishable), so the ratio R340meas/R380meas should not be affected by the eclipse for a constant atmosphere–surface system. That is, if the atmosphere–surface system of the pixel in orbit 11 404 is approximately identical to the atmosphere–surface system of its equivalent pixel in orbit 11 403, the ratio R340meas/R380meas is expected to be approximately identical regardless of the eclipse conditions. Before estimating fo from observations, we therefore apply the filter 14|R340measR380measeclipse-R340measR380measno eclipse|<0.01. Some cloudy pixels may pass the filter of Eq. (), because clouds can alter the TOA reflectance spectra at both 340 and 380 nm. The cloud fraction product FRESCO is available on the TROPOMI UVIS grid but suffers from the eclipse. For this comparison, we apply the simple cloud filter 15R340meas⋅0.95>R380meas to both orbits, which deletes the majority of the pixels with thick bright clouds. This filter is based on the fact that the TOA reflectance over the cloud-free ocean generally decreases with increasing wavelength from 340 to 380 nm see e.g.Fig. 1, while the presence of clouds may increase the TOA reflectance spectrum toward 380 nm.

Figure  shows the observed fo at 380 nm, computed with Eq. (), that passed the filters described in this section. Note the good agreement with the calculated fo at 380 nm in Fig. . The missing values result mostly from land or cloudy pixels in orbit 11 403 or 11 404. Between 0 and 10∘ N latitude, at the very west side of the swath in orbit 11 404, many pixels did not pass the filter of Eq. (), which can be explained by the thin clouds that were present (see Fig. ), but also possibly by a difference in aerosol type and concentration or ocean colour with respect to the pixels in orbit 11 403.

Figure  shows the calculated fo at 380 nm (solid line) and the observed fo at 380 nm (diamond dots) for pixel row 6 (out of 450, i.e. at the west side of the swath) and scan lines 2000 to 3500. The dashed line is the calculated fo when solar limb darkening is not taken into account (Γ=1). Taking into account limb darkening in the calculation of fo results in a much better agreement with the observed fo at 380 nm. This can also be concluded from Fig. , where we show the calculated and observed fo at 380 nm for all pixels in Fig.  plotted against the Moon–Sun disc centre distance normalized to the solar disc radius, X, computed for each of those pixels.

The density of points increases with increasing X because the Earth's surface area for which a certain value of X applies increases with increasing X. Making the filter of Eq. (15) more strict (e.g. R340meas⋅0.75>R380meas) decreases the scatter but also decreases the number of points. Another reason for the increasing scatter with increasing X is that for low fo the compared pixels may have more differences, resulting from natural variations, than caused by the obscuration ([R380meas]eclipse/[R380meas]no eclipse in Eq.  and the impact of its variations on fo are relatively large).

The AAI as derived by TROPOMI is computed from the ratio of the measured reflectances at 340 and 380 nm and the ratio of the modelled reflectances at those wavelengths, according to 16AAI=-100⋅log⁡10R340R380meas-log⁡10R340R380model, where “meas” indicates the measured TOA reflectances and “model” indicates the modelled TOA reflectances. The modelled TOA reflectances are computed for a cloud-free and aerosol-free atmosphere–surface model with the “Doubling-Adding KNMI” (DAK) radiative transfer code , version 3.1.1, taking into account single and multiple Rayleigh scattering and absorption of sunlight by molecules in a pseudo-spherical atmosphere, including polarization. The Lambertian surface albedo As in the model is assumed independent of wavelength λ and is adjusted such that the model reflectance equals the measured reflectance at 380 nm: 17R380model(As)=R380meas. The value of As that satisfies Eq. () is often referred to as the “scene albedo” or the “Lambertian equivalent reflectance (LER)”. Because As is assumed wavelength independent, it is also used to compute R340model. More details about the TROPOMI AAI algorithm can be found in . For our solar eclipse application, it should be noted that a lower R380meas results in a smaller (spectrally flat) surface contribution in the model, which increases R340model/R380model and increases the AAI.

The UV absorbing aerosol index (AAI) can be interpreted as a comparison of the measured TOA reflectance UV colour to the TOA reflectance UV colour of a cloud-free and aerosol-free atmosphere–surface model. The AAI generally increases in the presence of absorbing aerosols and can, unlike the aerosol optical depth, also be computed when the aerosol layer is above clouds. The AAI depends on various parameters such as the aerosol optical depth (AOD), single-scattering albedo (SSA), and aerosol layer height (ALH). For more details about the sensitivity of the AAI to atmosphere and surface parameters, we refer to , , , , and . In Appendix  we provide an analysis of the precision of the AAI during the solar eclipses studied in this paper.

The left image in Fig.  shows the AAI measured by TROPOMI during the annular solar eclipse on 26 December 2019, in the three adjacent orbits over Southeast Asia considered in Sect. . We use a colour scale ranging from AAI=-5 to AAI=5. This range usually covers most aerosol events. Significantly elevated AAI values are measured at the location of the penumbra: in orbit 11 404, most apparent between 20∘ S and 30∘ N latitude (see fo in Fig. ). The maximum AAI was 53.9 at 2.17∘ N latitude and 108.14∘ E longitude. The mean AAI in orbit 11 404 was 0.15. At the spiral cloud deck centred at 15∘ N latitude and 118∘ E longitude, the AAI increase is less significant. Similarly, the clouds observed in Fig.  between 10∘ S and 0∘ N latitude, and between 22 and 32∘ N, are located in the penumbra but show a less significant AAI increase.

Outside the Moon shadow, in orbits 11 403 and 11 405, the mean AAI is -1.52 and -1.48, respectively. At the locations in orbit 11 404 where fo<0.2, the mean AAI is also negative (∼-1.5). The negative mean AAI is partly caused by the scattering of light by cloud droplets, but also due to a radiometric calibration offset and degradation in the TROPOMI irradiance data . The degradation in the irradiance leads to an increase in the derived reflectance, decreasing the AAI values over time. The total AAI bias of ∼-1.5 will be solved with the release of the version 2.0.0 TROPOMI level 1b processor, foreseen for the first half of 2021. The bias is expected to be independent of viewing geometry; hence, it will not affect the relative AAI values or the conclusions of this paper.

The right image in Fig.  is similar to the left image in Fig. , but then for the corrected AAI product. That is, in Eqs. () and (), we replaced the measured TOA reflectances, R340meas and R380meas, by the restored TOA reflectances, R340int and R380int, which we computed with Eq. (). The red spot between 20∘ S and 30∘ N in orbit 11 404 that was observed in the uncorrected AAI product has disappeared. The mean of the corrected AAI in orbit 11 404 is -1.58. At the location of the thick spiral cloud deck the AAI is closer to zero. We note that no significant absorbing aerosol events can be identified in Fig. . At 12∘ S latitude and 122∘ E longitude, an AAI increase is measured in the corrected product, which could not be observed in the uncorrected image. This feature is caused by the specular reflection off the sea surface, often called the sunglint (see also Fig. ). The sunglint can also be observed in the middle of the swath of orbits 11 403 and 11 405, between 20 and 10∘ S latitude and 34 and 5∘ S latitude, respectively. explain that, when a strongly anisotropic reflector such as the sea surface is viewed from its reflective side, the AAI may increase: the model assumes a Lambertian (isotropic reflecting) surface, which increases the relative importance of the Rayleigh scattered light in the model and therefore computes a higher R340/R380 than is measured. From Eq. (), it follows that a deficit in the measured R340/R380 results in an increased AAI. Note that the shape and size of the apparent sunglint may vary per orbit, as they depend on the roughness of the sea surface (i.e. the wind speed), the presence of clouds and aerosols, and the illumination and viewing geometries.

In Fig. , we show the average R340meas/R380meas, R340model/R380model, As, and AAI of the pixels in the scan lines of orbit 11 404, before the solar irradiance correction (dotted line) and after the solar irradiance correction (solid line). The average latitudes in the scan lines are also shown. The fraction R340meas/R380meas is not affected by the solar irradiance correction, which is expected from the wavelength independence of fo between 340 and 380 nm (see Fig. ). Here, we did not detect signatures of sky colour changes in the measured UV reflectance due to secondary effects such as horizontally travelled light (see Sect.  for a detailed discussion). Before the solar irradiance correction, R340model/R380model is significantly higher than R340meas/R380meas between 20∘ S and 30∘ N where the Moon shadow resided, which increases the AAI. The high R340model/R380model is caused by the relatively low As in the Moon shadow (Fig. ), which is caused by the decrease in R380meas by fo (Fig. ). The maximum scan line average AAI is 10.7 in scan line 2672 (see bottom graph in Fig. ). After the solar irradiance correction, the AAI increase in the Moon shadow disappeared because R340model/R380model follows an approximately similar pattern to R340meas/R380meas, albeit with an offset ranging from -0.03 to -0.06, which was also observed outside the Moon shadow. We conclude that the increased AAI between 20∘ S and 30∘ N latitude in orbit 11 404 before the solar irradiance correction was caused by the relatively low As used in the model due to the reduction of the measured reflectance at 380 nm, rather than a UV colour change of the measured TOA reflectance in the Moon shadow.

Figure  shows the AAI in the scan lines of orbit 11 404, but only for pixel row 6 (see Fig. ). The solid line is the eclipse-corrected AAI and the dotted line is the eclipse-corrected AAI but without taking into account limb darkening (Γ=1). If solar limb darkening is not taken into account, the corrected AAI still shows an apparent increase between 14.9∘ S and 21.6∘ N latitude, with a maximum of AAI = 4.3 at 3.37∘ N latitude. Note that these are the latitudes at which the fo was underestimated if Γ=1 as we showed in Fig. , caused by the Moon occulting different parts of the solar disc during the eclipse (see Sect. ). In line with the discussion of the previous paragraph, an underestimation of fo at 380 nm results, after the solar irradiance correction, in too low R380meas and As, in too high R340model/R380model and, therefore, in too high AAI. We find a maximum overestimation of the AAI of 6.7 points in scan line 2671 and pixel row 4 when using Γ=1. It can be concluded that not taking into account solar limb darkening would still result in a “red spot” anomaly in the AAI map. The opposite effect occurs at the latitudes where fo was overestimated if Γ=1 in Fig. : south from 14.9∘ S and north from 21.6∘ N latitude, the AAI after the correction without limb darkening is slightly lower than the AAI after the correction where limb darkening was taken into account. We conclude that, if the artificial Moon shadow signatures are to be removed in the corrected AAI product, solar limb darkening cannot be neglected.