The CAR instrument flew aboard the UW CV-580 research aircraft (Fig. 2a) and obtained the bidirectional reflectance distribution function (BRDF) over an extensive and persistent stratocumulus cloud deck with an overlaying smoke aerosol layer. The aircraft was also equipped with other instruments to measure gases, aerosols, and radiation (see Appendix A by Peter V. Hobbs in the work of Sinha et al., 2003). Figure 2b shows a cutaway drawing of CAR. The instrument is approximately 72 cm long, 41 cm wide, and 39 cm deep; it weighs 42 kg. CAR was designed primarily to image the sky and surface at an instantaneous field of view (IFOV) of 1∘ through a 190∘ plane as shown in Fig. 2c. CAR measures both transmitted and reflected radiances at 14 narrow spectral bands located in the ultraviolet, visible, and near-infrared spectrum (0.340–2.303 µm; Fig. 2d). This combination provides a convenient and efficient means of obtaining complete BRDFs for any surface type at a landscape level and ensures that surface albedo, which is an angular-weighted integration of the reflection function over a hemisphere, can be derived from these measurements covering the required angular range (Nicodemus et al., 1977; Kimes et al., 1987).

During the BRDF measurements over the marine stratiform clouds, the instrument obtained unique views of the cloud–aerosol system, scanning from zenith to the horizon and then from the horizon to nadir, covering the entire 360∘ range of azimuthal directions as the aircraft flew in a circular flight track (see Gatebe et al., 2003; Fig. 3). The quick-look red–green–blue (RGB) image in Fig. 3 (R = 1.04 µm, G = 0.87 µm, and B = 0.47 µm) illustrates measurements taken from 12:27 to 12:54 UTC. The Sun can be seen in the sky at about a 33∘ view zenith angle, which also corresponds to the solar zenith angle, and a bright cloud system is seen on the image from view zenith angles of 90–180∘. The horizon coincides with the 90∘ view zenith angle, which is easily identified by the contrast between the sky and surface. In this image, the principal plane is defined by the vertical plane containing the Sun and the plane that is equidistant between two solar disks.

Note that the circular flight track during the BRDF measurements above the clouds (∼ 650 m) is about 4 km in diameter, and with an aircraft bank angle of 20–30∘, which is compensated by CAR to help maintain the full 180∘ view from zenith to nadir, the plane took ∼ 3 min to complete an orbit. Marine stratiform clouds are generally characterized by a well-defined cloud-top height corresponding to a strong boundary layer inversion. Given this viewing geometry of the cloud–aerosol system, the CAR measurements permit the retrieval of aerosol optical properties above clouds separated into above and below the aircraft, plus the cloud optical properties, using the color ratio method. These measurements provide the best data for validating above-cloud aerosol retrieved from satellite measurements, analogous to the validation of cloud-free aerosol retrievals from satellites, which is typically done with observations from the AErosol RObotic NETwork (AERONET) ground-based sun-photometer network (Holben et al., 1998).

The color ratio (CR) method has been used to simultaneously retrieve the above-cloud aerosol optical depth (ACAOD) and aerosol-corrected COD from OMI (Torres et al., 2012) and MODIS observations (Jethva et al., 2013, 2016). The technique is physically based on the reduction of the ultraviolet (UV), visible (VIS), and near-infrared (NIR) radiation reaching the top of atmosphere due to particle absorption above cloud. The effects of aerosol absorption have a spectral signature, in which the absorption strength is found to be stronger at shorter wavelengths than at longer wavelengths. This produces a strong color effect in spectral measurements, and hence it is called the color ratio method. The method employs the VLIDORT V2.6 polarized radiative transfer model (Spurr, 2006) for the simulation of lookup table (LUT) reflectances. VLIDORT treats the outgoing radiance in a pseudo-spherical geometry. Therefore, it is expected that the aerosol radiance simulation at slant geometry, i.e., a viewing zenith angle > 70∘, may not carry the same accuracy as the case with lower viewing angles. This may result in less accurate retrievals at extreme viewing geometries. Additionally, larger retrieval errors at lower cloud optical depth measurements and heterogeneity in aerosol and cloud fields also add to the apparent dependence on scattering angle.

The aerosol microphysical–optical properties of carbonaceous smoke model and radiative transfer configurations assumed in the radiative transfer simulations are shown in Table 2. The aerosol model used here in the ACAOD inversion is identical to the one employed in Jethva et al. (2016), wherein the MODIS retrievals of ACAOD were found to be in very good agreement (RMSE ∼ 0.05 % and 99 % matchups within predicted uncertainty) with those directly measured from an AATS sun photometer. The results imply that the aerosol microphysical–optical properties assumed in the inversion based on the long-term ground-based AERONET inversion at an inland site in Mongu are suitable for ACAOD retrievals over the adjacent Atlantic Ocean. The retrieved ACAOD at 470 and 860 nm is converted to its value at 500 nm according to the spectral extinction assumed in the selected aerosol models.

The near-UV-based color ratio algorithm has been applied to the long-term record of OMI to derive a global product of ACAOD (Jethva et al., 2018). The ACAOD product has been validated against airborne measurements taken from the HSRL-2 lidar operated during the ORACLES campaign conducted over the southeastern Atlantic Ocean. On the other hand, the ACAOD derived from the visible–near-IR observations of MODIS was validated against the direct AOD measurements acquired from the airborne NASA Ames Airborne Tracking Sun Photometer (AATS) and the Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research (4STAR) sun photometers operated during different field campaigns (Jethva et al., 2016; Schmid et al., 2003). In both OMI and MODIS validation studies, the satellite-retrieved ACAOD product was found to agree well with the airborne measurements within the expected uncertainty limits associated with the inversion technique, which mainly arises from the chosen aerosol model and its absorption properties.

Here, the CR method was applied to CAR observations, which include direct and diffuse solar radiance (or sky radiance), at eight spectral channels (see Fig. 4.). The direct solar component is given by the extraterrestrial solar radiance attenuated by atmospheric absorption and scattering. On the other hand, sky radiance results from single- and multiple-scattering processes due to the interaction of sunlight with aerosols and gas molecules. Atmospheric gas molecules (e.g., nitrogen, oxygen, carbon dioxide, ozone, water vapor) and aerosols are likely to strongly affect the solar radiance in the visible and near-infrared regions. The attenuation (scattering and/or absorption) by each atmospheric constituent is strongly dependent on wavelength and can be determined through the optical thickness using simple parametric models (e.g., Zibordi and Voss, 1989). In the case of CAR measurements close to the Sun (solar aureole), the signal from the direct solar radiance measurements saturates the detectors, and therefore pixels that are especially close to the solar direction (scattering angles are ≤ 10∘) should be excluded from any retrieval (Gatebe et al., 2010). The sky radiance distribution seen here is typical of clear skies (cloud-free), whereby the radiance of a point in the sky depends both on its position relative to the Sun (i.e., azimuth angle) and on its air mass number (i.e., zenith angle). The sky radiance distribution is generally symmetrical about the principal plane, wherein the maximum value of the sky radiance for each wavelength is observed. This is illustrated in Fig. 4e at 45∘ ≈ 315∘, 90∘ ≈ 270∘, and 135∘ ≈ 225∘ for λ > 0.4 µm. The minimum values of sky radiance are found to be in the area directly opposite to the Sun's position.

The CAR observations are indicative of the presence of absorbing aerosols above the clouds due to apparent brightening and darkening, which is evident when looking at the measured sky radiances and the cloud bidirectional reflectance factor (BRF) (see Fig. 4). Aerosol loading has a strong influence, especially in the forward scattering directions (relative azimuth angle (φ) < 90∘ and φ > 270∘), with reflectances in the shorter wavelengths (e.g., 0.38 µm) larger by a factor of > 2 relative to the longer wavelengths (e.g., 1.22 µm; Fig. 4e). The asymmetry depicted in Fig. 4e is largely attributed to aerosol scattering and not to Rayleigh scattering, as the latter is expected to exhibit a symmetrical distribution in either scattering direction. More interestingly, there seems to be a strong aerosol absorption signal above clouds. It is well known that clouds reflect uniformly across the visible–near-IR spectrum; however, the presence of absorbing aerosols above clouds (in this case smoke transported from southwestern Africa) induces an overall absorption or darkening in the UV and shorter visible wavelengths, thus resulting in a strong reflectance gradient from the UV to blue to near-IR spectrum, with ∼ 35 % reduced reflectance at 0.34 µm compared to that at 1.04 µm, as seen in Fig. 4f. Overall, the positive spectral gradient seen in Fig. 4f is normally associated with cloud darkening at the shorter wavelengths (see Gautam et al., 2016).

To examine 3D influences in CAR retrievals, we performed 1D and 3D radiative transfer simulations using a Monte Carlo model that powers the online simulator of 3D radiative processes that was created as part of the I3RC (Intercomparison of 3D Radiation Codes) project and is publicly available at http://i3rcsimulator.umbc.edu/ (last access: 14 February 2021). This model was validated through I3RC intercomparison experiments (e.g., Cahalan et al., 2005) and was used in several other studies (e.g., Várnai et al., 2013). The key simulation parameters are listed in Table 3; additional details and the results of the simulations are discussed in Sect. 3.4.

Figures 5 and 6 show the full BRF of low stratiform clouds at selected wavelengths of 0.472 and 0.870 µm, respectively, from each of the 16 different cases described in Sect. 2. The two wavelengths form the basis of the color ratio method for the simultaneous retrieval of above-cloud aerosol optical depth (ACAOD) and cloud optical depth (COD). The spectral BRF of stratiform clouds observed in the 16 cases is highly anisotropic due to a combination of factors ranging from cloud heterogeneity (including sub-pixel heterogeneity) to solar illumination geometry, sensor viewing geometry, and cloud parameters such as optical thickness and effective radius (see Cornet et al., 2018). The 16 cases have a range of solar zenith angles (23∘ < SZA < 36∘). Measurements span an area of ∼ 55 km (N–S) × ∼ 12 km (E–W), with most cases (nine cases: cases h–p) concentrated over a much smaller area (∼ 8 km × ∼ 4 km) (see Fig. 1). The observations were taken at approximately the same altitude (Table 1, cases a–d: 1420–1541 m above mean sea level or a.m.s.l.; cases h–p: 1608-1616 m a.m.s.l.), implying that corresponding pixels for different cases have a similar measurement scale. The only exceptions (cases e–f) were taken at different altitudes during the aircraft spiral from 1814 to 3369 m a.m.s.l.. The cloud-top height was ∼ 1000 m a.m.s.l. (Sinha et al., 2003), and the cloud geometrical thickness was at most 300 m (see Melnikova and Gatebe, 2018; Sect. 2.2). Based on these characteristics, the 16 cases may be classified into three groups (see Table 1). Group 1 includes cases a–d with SZA ≈ 24∘; measurements were taken close to each other in time at Δt < 16 min with an altitude at ≈ 1508 m, and the location is about the same as shown in Fig. 1. Group 2 includes cases e–g with SZA ≈ 24∘, Δt < 6 min, altitude approximately variable from low to high, and at the same location near the Namibian coastline as shown in Fig. 1. Group 3 includes cases h–p with SZA ≈ 34∘, Δt < 23 min, and altitude ≈ 1614 m; the location is about the same as shown in Fig. 1. Since stratiform clouds are formed and maintained by a balance of various marine boundary layer processes (see Duynkerke and Teixeira, 2001; Wood, 2012; Feingold et al., 2017), the variations in the BRF patterns with time, especially where other parameters are similar, are possibly linked to the formation of open cells caused by drizzle–cloud dynamical interactions, inevitably leading to changes in the cloud liquid water path and BRF. The pronounced circular brightness feature (see cases h–p, Fig. 5, λ = 0.470 µm; Fig. 6, λ = 0.870 µm) shows a cloud bow (or primary rainbow), which is typical of water clouds (see Gatebe et al., 2003, wherein case h was analyzed in detail). Figure 7 shows the derived spectral albedo (with atmosphere) for all 16 cases at λ = 0.470 µm and λ = 0.870 µm (see Table 4 for the spectral albedo, with atmosphere, for all the wavelengths). Clearly, Group 3 cases had a higher spectral albedo and were optically thicker, while Group 2 cases from near the Namibian coastline had the lowest spectral albedo (with atmosphere). It is interesting to note that the spectral albedo remains almost constant in Group 2 cases despite the change in measurement scale during the spiral. In the following subsections, we will examine how the surface reflectance anisotropy impacts retrievals of the optical depth (both clouds and aerosols) using the color ratio method.

Figure 8 shows the retrieved AOD for aerosol layers located above the aircraft level (AOD_sky) derived from the observed diffuse sky radiance by CAR. The retrievals were performed using a single-channel fit at 470 nm between the observed sky radiance aerosol lookup table, accounting for the variations in AOD and geometry. Note that the aerosol model used for AOD_sky retrievals was the same for the inversion of AOD below aircraft (AOD_cloudtop). It is complicated to characterize and model the anisotropic effects of reflecting clouds with varying optical depths on the hemispherical diffuse sky radiances measured by CAR. Therefore, we adopted a simple approach to account for these effects, at least partially, by retrieving AOD above the aircraft and assuming an averaged underneath-cloud optical depth field retrieved from the AOD_cloudtop inversion for each CAR BRDF case. For the most part the hemispherical distribution of retrieved AOD_sky along the azimuth direction is found to be smooth and nearly uniform, suggesting that the sky retrievals of AOD are not significantly affected by cloud anisotropy and that the simple approach of assuming an averaged value of COD for the full azimuthal scan works reasonably well in capturing the cloud effects on the sky radiances. The angular pattern in cases a–d is similar and in good agreement with the airborne direct sun-photometer measurements, as discussed later (Fig. 12 and Table 1).

The retrieved AODs below the aircraft (AOD_cloudtop) for all 16 CAR BRDF cases are shown in Fig. 9. The white areas in each polar plot are devoid of AOD_cloudtop retrievals because there is no cloud detection and/or the observations fall outside the color ratio vs. reflectance lookup table domain including extreme viewing geometry. In almost all cases (a–p), the retrieved AOD_cloudtop shows a dependence on viewing zenith angle, whereby lower (higher) AOD_cloudtop values are associated with slant (near-nadir) viewing angles (see also Fig. 11 – scatter plots of AOD_cloudtop vs. COD). Such a gradient in the retrieved AOD_cloudtop can result from the limitations of the radiative transfer calculations at slant angles and the fact that CAR observations are interpreted within the lookup table after linearly interpolating between aerosol geometry nodes. The nodes in geometry used in the RT calculations include solar view zenith angles (sza_nodal), view zenith angles (vza_nodal), and relative azimuthal angles (raa_nodal) (see Table 2). Another salient feature of the retrieved AOD_cloudtop field is the intermittent patches of high AODs that extend in the viewing zenith direction along an azimuthal plane. A careful qualitative inspection of this feature with BRFs measured at 0.47 µm (see Fig. 5) and 0.87 µm (Fig. 6) reveals that the higher AODs are spatially collocated with relatively lower values of BRF, indicating that these observations belonged to clear-sky, partially cloudy sky, or thin heterogeneous scenes for which the assumption of fully overcast thick homogeneous pixels made in the CR algorithm breaks down. Under such situations, it is expected that the uncertainty in the retrieved AOD_cloudtop would be larger than the expected errors due to other algorithmic assumptions. This issue is explored further in Sect. 3.4 under the influence of 3D effects on the retrieved AOD_cloudtop and COD.

Another important observation in Fig. 9 is the increasing magnitudes of AOD above cloud for cases e, f, and g. Table 1 shows that the altitude of aircraft for these three cases was recorded as 1533 ± 2, 1814 ± 259, and 2646 ± 223 m a.m.s.l. It is expected that as the aircraft altitude moves higher in the atmosphere, the CAR sensor would see an aerosol layer of greater geometrical thickness, thereby resulting in greater aerosol extinction and AOD. The retrieved AOD_cloudtop for these cases precisely demonstrates this effect by showing increasing magnitudes for higher aircraft altitudes.

The color ratio algorithm, along with the above-cloud AOD, also co-retrieves aerosol-corrected cloud optical depth, which is shown in Fig. 10. Unlike aerosol fields seen both above and below the aircraft level with homogeneous distributions, the cloud optical depth fields retrieved from most of the cases show a great deal of variability along the azimuthal plane. Except for cases m, n, o, and p, all other cases (a through l) show overall higher cloud optical depth in the backscattering directions in the bottom hemisphere opposite to the Sun and between the azimuth angles 90 and 270∘. Unlike polar-orbiting satellite observations at a fixed geometry for a given overpass, the CAR measurements offer a complete picture over all the viewing directions relative to the Sun direction. This unique observational geometry provides increased information content that could allow quantification of the effects of angular reflectance distribution in remote sensing retrieval algorithms.

Figure 11 shows scatter plots of AOD_cloudtop vs. COD for view zenith angles 0–30∘ (blue), 30–60∘ (green), and 60–90∘ (red), which show very interesting patterns. The retrievals of AOD_cloudtop are found to exhibit a systematic dependence on COD (similar to an exponential decay function), especially the blue and green dots, and larger values of AOD_cloudtop correspond to lower values of COD crawling along the x axis on the right as COD increases. An exception to this rule are the retrievals made at higher view zenith angles of 60–90∘ (red), for which the retrieved ACAOD remains low (< 0.2) despite an increase in the COD, which seems unrealistic and confirms some of the limitations of the color ratio method. Another exception is seen in cases e, f, and g, for which AOD_cloudtop vs. COD shows no clear dependence on viewing zenith angle and COD was around 5, indicating that these observations belonged to clear-sky, partially cloudy sky, or thin heterogeneous scenes for which the assumption of fully overcast thick homogeneous pixels made in the CR algorithm breaks down. The relationship between the two retrieved quantities appears to be confined for COD < 10, after which both retrievals are found to be unrelated to each other. Such observed dependence was expected as noticed in the color ratio algorithm introduced in Jethva et al. (2013). Uncertainties in satellite ACAOD inversion are known to be larger at lower CODs. This is because the retrieval domain space, i.e., color ratio versus reflectance at a longer wavelength, at lower CODs becomes narrower with steep changes in the color ratio, especially at COD < 10. Therefore, any uncertainty in the assumptions made in the retrieval algorithm, i.e., single-scattering albedo, an assumption of fully overcast pixels, and linear interpolation between the nodes whereby reflectances and the ratio of a joint aerosol–cloud scene behave nonlinearly, would result in the amplification of error in the retrieved ACAOD. These artifacts are more pronounced at lower values of both ACAOD and COD, for which uncertainties in the retrieved ACAOD could reach 40 % to 80 % at COD < 10 and ACAOD < 0.5 typically observed in the present CAR AOD retrievals (Jethva et al., 2013, Table II). Figure 11 results also suggest a strong inverse relationship between the AOD_cloudtop and COD for cases in which COD < 10 and a weaker inverse relationship for COD > 10. Additionally, studies (e.g., Torres et al., 2012; Jethva et al., 2018) have estimated uncertainty limits in ACAOD for a typical range of satellite viewing geometry (i.e., solar zenith angle 20–40∘, viewing zenith angle 0–40∘, and relative azimuth angle 100–150∘), while varying the single-scattering albedo and aerosol layer height. The error estimates of ACAOD, not reported in these papers, were found to be nearly stable as a function of geometry in the stated ranges. A nearly uniform retrieval of sky-looking AOD (above aircraft and clouds) shown for different CAR profiles in Fig. 8 further demonstrates the stability of the algorithm for a viewing zenith range 0–60∘. At slant angles > 60∘ and around the edge of the scan, the limitation of radiative transfer calculations due to its pseudo-spherical treatment in the RT code restricts the accuracy of AOD inversion. However, we note that no explicit cloud screening was performed on the measurements. All measurements go through the ACA algorithm whereby if they fit into the retrieval domain, i.e., color ratio vs. reflectance at 860 nm, then a corresponding retrieval of ACAOD and aerosol-corrected COD is obtained. It is possible that heterogeneity in aerosol and cloud fields in the observed scene can introduce uncertainty in the retrievals. For instance, a mixture of cloudy and cloud-free scenes observed in a particular measurements can affect both AOD and COD inversions.

Figure 12 shows the two main aerosol above-cloud-retrieved parameters, namely AOD_sky, when CAR views upward while flying above the cloud field, and the AOD below aircraft (AOD_cloudtop), when CAR views downward and measures the cloud field averaged over all the viewing directions (see also Table 1, columns 6–9). The summation of AOD_sky and AOD_cloudtop provides the column AOD above the stratocumulus cloud fields (ACAOD), as retrieved from CAR measurements over marine stratus clouds during SAFARI 2000 in the southeast Atlantic region. In addition to the two aerosol above-cloud parameters retrieved from CAR, Fig. 12 also shows simultaneous COD retrievals using CAR measurements and AOD retrievals from the AATS sun photometer that made coincident measurements of AOD on the UW CV-580 flights. The AOD retrievals from AATS are based on direct sun-photometer measurements and therefore represent aerosol loading above the aircraft level.

In the case of the flight transects shown in Fig. 1, the AATS AOD retrievals were largely obtained above the marine stratocumulus clouds. However, when the cloud top is well separated from the aircraft, i.e., the altitude of the aircraft is higher than that of the cloud tops, the AATS measurements do not capture the aerosol layer below the aircraft as the instrument is always pointing upwards toward the Sun. Therefore, the reported AOD data from AATS are not representative of the total column AOD above clouds unless the aircraft is flying at the same altitude at which the cloud top is located. Often, the altitude difference is not negligible; for example, during the SAFARI flights shown in Fig. 3, there was a clear separation of ∼ 600 m between the aircraft and cloud top. Specifically, the CAR-retrieved AOD_cloudtop captures this missing aerosol layer caught between the aircraft and cloud top, which is in addition to the AOD_sky retrieved above the aircraft level. The latter quantity is equivalent to that retrieved by AATS, whereas AOD_cloudtop is the remainder of the column AOD that we retrieve from CAR in this study. For these reasons, Jethva et al. (2016), in validating MODIS-retrieved ACAOD for the same 13 September 2000 AATS flight, extrapolated the airborne measurements from the respective altitudes to cloud top using detailed profile measurements and an associated altitude–AOD polynomial in order to make the comparisons between satellite and airborne measurements consistent.

To illustrate the various retrievals, we consider flight measurements from cases h–p. The CODs associated with marine stratocumulus clouds (cases h–m) vary between 15 and 20 (Fig. 12). These retrievals (for cases h–m) are based on relatively homogeneous clouds observed during the three separate circular measurements obtained from transects a–d, e–g, and h–p. These relatively homogeneous and similar sets of circular transects are also noted in the BRF polar plots shown in Fig. 6h–m. The simultaneous retrievals of Sky_AOD show moderately high aerosol loading, with an AOD of 0.5 across circles h–m, which is in very close agreement with the AATS_AOD retrievals. Consistency in AOD retrievals (above the aircraft level) between the two disparate measurement approaches, i.e., AATS and CAR, is generally found throughout the data obtained from the 16 cases (a–p), as indicated by the high correlation (R2 = 0.92) between the two retrievals shown in Table 1. However, the central distinction here is that the CAR approach also allows us to directly retrieve aerosols above clouds that are present below the aircraft level (AOD_cloudtop). For instance, in case h, the AOD_cloudtop is 0.18 and the Sky_AOD is 0.50, implying that the total above-cloud column AOD is 0.68 or 31 % higher relative to the AATS_AOD retrieval. Overall, we find AOD_cloudtop ranging between 0.18 and 0.41 from the 16 cases shown in Fig. 12, indicating a notable enhancement of the overall presence of aerosols above clouds. These observations show that a significant aerosol layer is not captured by the aircraft sun photometer, indicating the strength and effectiveness of nearly simultaneous multiangular measurements scanning the sky and surface, as demonstrated in this study using CAR measurements.

Numerous earlier studies indicate that passive remote sensing of both cloud and aerosol properties can be significantly impacted by three-dimensional (3D) radiative processes (e.g., Marshak and Davis, 2005; Wen et al., 2006; http://i3rc.gsfc.nasa.gov/Publications.htm, last access: 14 February 2021). Since the impact of 3D effects is different for different observations and retrieval algorithms (e.g., Cornet et al., 2018), we next examine the impact of 3D effects on the CAR aerosol and cloud retrievals discussed above. Our goal is not to provide quantitative estimates of 3D effects; instead we examine whether 3D effects are likely to play a substantial role in shaping the behavior of CAR-retrieved cloud and aerosol optical depths.

Our tests consider the scene shown in Figs. 5k, 6k, 9k, and 10k to be representative of heterogeneous areas with potentially significant 3D effects. The figures show that around the 60∘ azimuth angle, CAR observed a roughly 300 m wide and very long trough in which the retrieved COD drops by roughly 50 % (Fig. 10k), while the retrieved AOD_cloudtop increases by roughly 50 % (Fig. 9k). Figures 9, 10, and 11 show that this behavior is not unique and that in many cases with COD values below 10 or sometimes even 20, the retrieved AOD values increase sharply as COD decreases. In principle, this behavior appears consistent with earlier findings that showed 3D effects to increase retrieved AOD values for pixels that were surrounded by brighter (thick cloud-covered) areas (e.g., Wen et al., 2013).

As discussed in Sect. 2.3, we examined the impact of 3D radiative effects through Monte Carlo simulations whose results are listed in Table 5. In each row of this table, the left column indicates whether or not below-CAR aerosols (BCAs) were considered, what the cloud optical depth was at the trough center, and whether the simulations considered 1D or 3D radiative processes. The indicated uncertainties come from Monte Carlo simulation noise.

Since COD retrievals are shaped mainly by the 0.87 µm reflectance values, 3D BRFs exceeding 1D BRFs by about 25 % for COD = 7 indicate that 3D radiative processes significantly enhance CAR BRFs and thus the COD values retrieved in the center of the trough, which means that 3D effects make the COD drop in the trough appear less deep than it really is. This behavior is consistent with earlier studies showing that radiative smoothing (caused by the diffusion of photons scattered from thick to thin areas) makes horizontal cloud variability appear less strong than it really is. Several studies proposed counteracting this effect by artificially roughening the retrieved COD fields (e.g., Marshak et al., 1998; Zinner et al., 2006), but these methods have yet to gain wide usage. By performing additional simulations, we found that if we decreased COD at the center of the trough from 7 to 4.7, 3D simulations would yield 0.87 µm BRF values around 0.32, thus resulting in hypothetical retrievals yielding COD = 7 (similar to the actual CAR retrievals). We note, however, that the value of 4.7 depends on our assumption of cloud-base altitude (hence cloud geometrical thickness), so it is somewhat uncertain.

Regarding aerosol retrievals, we first examine how 3D radiative processes affect the key signal of our ACAOD retrievals, which is the impact of below-CAR aerosols (BCAs) on the BRF(0.47 µm) / BRF(0.87 µm) color ratio (CR) values. Specifically, we compare the CR values for the BCA and no BCA cases and check whether the CR difference is similar in 1D and 3D radiative simulations. 1CR3D(BCA)-CR1D(no BCA)/CR1D(BCA)-CR1D(no BCA)=1.052±0.02 While the calculations above use the retrieved value of COD = 7 at the center of the linear trough, we also tested whether the results change if the 3D simulations use COD = 4.7 instead. 2CR3D, COD=4.7(BCA)-CR1D(no BCA)/CR1D(BCA)-CR1D(no BCA)=1.075±0.02 These results indicate that 3D processes strengthen the impact of BCAs on CR values by about 3 %–10 %.

To estimate the impact of these CR changes on retrieved ACAOD values, we examined the nonlinearity of the CR–ACAOD relationship using additional 1D Monte Carlo simulations. These simulations used the same setup as in Table 2, except that below-aircraft ACAOD values were increased by 20 %. The simulations (identified by the subscript IBCA) gave BRFIBCA(0.47 µm) = 0.24523 ± 0.00004 and BRFIBCA(0.87 µm) = 0.32069 ± 0.00006, yielding CRIBCA = 0.76469 ± 0.00027. Comparing the impact of original and increased BCA amounts on CR gives 3(CRIBCA-CRnoBCA)/(CRBCA-CRnoBCA)=1.1900±0.0089. This indicates that a 20 % enhancement in ACAOD causes a 19 % enhancement in the CR signal, which implies that a 10 % change in CR is consistent with a 10 % × 20 / 19 = 10.5 % change in ACAOD. Considering the uncertainties, we can say that the 3 %–10 % impact of 3D effects on CR values corresponds to a 3 %–11 % impact on retrieved ACAOD values.

To understand this result, we need to consider both the radiative smoothing discussed above for COD retrievals and the 3D process often called “bluing” (e.g., Marshak et al., 2008). Bluing occurs when nearby thick clouds reflect more sunlight than the clouds in the field of view do, and some of the extra reflection is then scattered into the instrument field of view by air molecules and aerosol particles that reside between the cloud and the sensor. As expected, Table 5 reveals that 3D processes do indeed enhance BRFs: for COD = 7, BRF3D values exceed the corresponding BRF1D values at both 0.47 and 0.87 µm. However, the table also reveals that given a certain 0.87 µm BRF value, 3D and 1D processes yield fairly similar 0.47 µm BRFs and thus color ratios: BRF0.47µm,COD=4.7,3D ≈ BRF0.47µm,COD=7,1D and CR3D,COD=4.7 ≈ CR1D,COD=7.

The weak impact of 3D effects on CR is likely due to two factors. First, while the bluing process implies a larger molecular and aerosol scattering enhancement at 0.47 µm than at 0.87 µm (i.e., a higher CR), this is partially compensated for by the aerosol absorption cross section being larger at 0.47 µm than at 0.87 µm. Second, many of the 3D effects that cause the enhancements apparent in Table 5 are likely caused by the in-cloud radiative smoothing process discussed above, which causes similar relative enhancements in the trough BRFs at 0.47 and 0.87 µm: cloud droplets, which cause radiative smoothing through multiple scattering, have similar scattering properties at 0.47 and 0.87 µm.

We note that simulations (not shown) indicate that 3D effects would have a similar or even weaker influence on ACAOD retrievals over the linear trough if the measurements were taken not by CAR flying only 600 m above the clouds but by a satellite passing overhead. This is because the compensating effect of aerosol scattering and absorption and the spectrally neutral in-cloud radiative smoothing cause 3D relative enhancements that are spectrally quite neutral.

Overall, the results discussed above imply that 3D radiative processes had a significant impact on retrieved cloud optical depths, but also that the 3D impact on retrieved ACAOD values is fairly small and is not the main reason for the retrieved ACAOD values increasing over thin clouds.