Cloud heterogeneity on cloud and aerosol above cloud properties retrieved from simulated total and polarized reflectances

4.1 Cloud heterogeneity effects on polarized reflectances

As explained before, we simulated using 3DMCPOL, the polarized reflectances for the three wavelengths used in the POLDER retrieval algorithms (e.g., 490, 670 and 865 nm). Total and polarized reflectances at 490 nm for 50 m resolution are presented in Fig. 3 (second and third columns) for SZA = 60^∘. First of all, we can see that for flat cloud, the polarized reflectance field appears smoother than the total reflectance field. As polarized reflectances level off for optical thickness greater than about three, all cloudy pixels with higher optical thickness provide almost the same polarized reflectance. Therefore, cloud heterogeneity effects are visually less discernible on polarized reflectance fields compared to the total reflectance fields.

For the bumpy or fractional clouds, the polarized reflectance field appears much rougher. In the cloudbow viewing directions (second column), some parts of the cloud facing to Sun appear brighter and other parts in the shadow darker. At this small spatial scale (50 m), a large part of the total amount of pixels exhibits polarized reflectance higher than the maximum value predicted by the 1-D homogeneous cloud model (yellow pixels) and thus cannot be obtained with 1-D radiative transfer simulation: at 490 nm, their ratio reaches 41 % of the total number of pixels for the flat cloud, 52 % for the bumpy cloud and 38 % for the fractional cloud. This phenomenon of illumination and shadowing was already highlighted simply with a step cloud in Cornet et al. (2010).

In the forward direction (Θ= 60^∘) at 490 nm (third column in Fig. 3), the “shadow areas” are not dark anymore contrary to the total reflectance images (first column in Fig. 3) and appear even brighter than cloudy part. For short wavelength and forward scattering angles, molecular signal is stronger than the cloud signal and thus enhances the polarized signal in the shadow parts.

In Fig. 5, we plot the average polarized reflectances as would be measured by POLDER at 7 km × 7 km resolution as a function of the scattering angle Θ for a solar zenith angle SZA = 60^∘, and for the three wavelengths. As we can see in Fig. 5a, the main differences between homogeneous and heterogeneous clouds appear in the cloudbow direction (Θ= 140^∘) and in the forward direction (Θ < 80^∘). In the cloudbow direction, the 3-D polarized reflectances are lower than the 1-D ones for the three clouds. Similar to the total reflectances, this is mainly due to the plane-parallel bias. In these directions, the relative differences (Fig. 5b) are about −9, −12 and −35 % for the flat, bumpy and fractional cloud, respectively. We note that the relative difference is slightly lower for 490 nm because of the smoothing effects by molecular scattering above the cloud.

Figure 5(a) Polarized reflectance as a function of the scattering angle for three wavelengths (490, 670 and 865 nm) for the homogeneous cloud (1-D), the flat cloud, the bumpy cloud and the fractional cloud. (b) Relative difference between 3-D and 1-D polarized reflectances, [(Rp3-D − Rp1-D) ∕ Rp1-D × 100]. The solar zenith angle is 60^∘.

Download

In the forward scattering directions, the consequences of the 3-D effects in terms of absolute polarized reflectances appear differently depending on the wavelength. At 490 nm, the 3-D effects enhance the absolute polarization, while at 865 nm they reduce it. At 490 nm, atmospheric molecular scattering is very strong. The 3-D polarized reflectances appear greater than the 1-D ones because, as seen in Fig. 3, the polarization in the shadow parts of the cloud is enhanced by this molecular scattering. At 865 nm, the shadow parts appear dark with small positive values that reduce the negative polarization of the cloud and consequently the absolute polarization. The relative difference (Fig. 5b) is consequently positive for 490 nm (about +55 % for the fractional cloud) and negative for 865 nm (about −75 % for the fractional cloud). At 670 nm, the polarized reflectance in the shadow part is only slightly enhanced by the molecular scattering but more compared to 865 nm. Polarized reflectances thus become positive for the fractional cloud but not for the flat and bumpy clouds. Note that in the backward direction, the polarized reflectances are very weak thus no heterogeneity or 3-D effects can be detected.

Figure 5 illustrates results obtained for simulations for SZA = 60^∘ with a scattering angular range between 60 and 180^∘. For SZA = 20 and SZA = 40^∘, the plots are similar with a reduced scattering angular range comprised between 100 and 180^∘ for SZA = 20^∘, and between 80 and 180^∘ for SZA = 40^∘. Consequently, for SZA = 20 and SZA = 40^∘ the attenuation due to the plane-parallel bias is the main effect that impacts the polarized reflectances.

4.2 Consequences for droplet size distribution and cloud top pressure retrievals

The polarized signal is used as input of a POLDER retrieval algorithm developed to retrieve effective radius, effective variance and cloud top pressure. It uses the polarized information as presented in Bréon and Goloub (1998). The position of the cloudbow as well as the position of the supernumerary bows gives information on the effective radius. The amplitude of the supernumerary bows gives information on the effective variance of the cloud droplet size distribution. For cloud top pressure, the algorithm uses the information given by the molecular scattering that depends, in the forward scattering directions, on the atmospheric air mass factor (Goloub et al., 1994). The algorithm, under implementation in the POLDER operational algorithm, is based on an optimal estimation method (Rodgers, 2000) and provides errors associated to each of the retrieved parameters. It is also possible to add in the forward model variance-covariance matrix an error due to the non-retrieved parameter. Following previous computations made in Waquet et al. (2013a) for the misrepresentation of the cloud heterogeneity effects, the error added in the variance-covariance matrix on the reflectances is 7.5 % in the directions close to the cloudbow and 5 % elsewhere.

Table 2Retrieved cloud droplet effective radius (R_eff), effective variance (V_eff) and cloud top altitude (CTOP) from polarized reflectances with an optimal estimation algorithm. First column is the input, second column the retrieval for the homogeneous cloud (1-D), third column for the flat cloud, fourth column for the bumpy cloud and fifth column for the fractional cloud. The last line is the final cost function with NC meaning no convergence. The solar zenith angle is 60^∘. Note that the cloud top altitude is different according to the heterogeneous cloud leading to three different lines.

Download Print Version | Download XLSX

The retrieved values obtained with this algorithm based on the homogeneous cloud assumption, are presented in Table 2. We again use the homogeneous cloud (1-D) to check the consistency of our simulations. For all clouds, even if differences in polarized reflectances are large in amplitude, the retrieval algorithm captures the general angular features the three wavelengths, which results of small errors on the retrieved effective radius and effective variance. The algorithm is able to retrieve an effective radius of 11 µm and an effective variance of 0.02 with relative error compared to the input under 2.6 and 2.1 %, respectively (see Table 2). Indeed, as the cloud heterogeneity effects do not modify the cloudbow position and the number of supernumerary bows, the retrieval of the droplet size distribution parameters is not really affected by 3-D effects. This is a fundamental advantage of the polarized measurements compared to the bi-spectral method (Zhang et al., 2012), usually used when visible and shortwave infrared wavelengths are available. However, we note that the cost function, which is the root-mean-square-difference between the model and measurements weighted by the respective variance–covariance matrix is larger for 3-D clouds than for the homogeneous cloud. It means that the forward model (homogeneous model) used for the retrieval does not allow perfectly matching the heterogeneous cloud reflectances used as input. For the bumpy and fractional cloud, the algorithm does not even converge meaning that the forward model is not able to represent the signal within the allocated uncertainties. The main impact of cloud heterogeneities appears for cloud top pressure retrieval. In Table 2, we report the mean cloud top height for each heterogeneous cloud and the retrieved value. The 1-D homogeneous values used for control were set to the intermediate mean cloud top altitude. We note slight differences about −4 hPa (+37 m) between input and 1-D retrieval, which reveals slight differences between the radiative transfer codes used for the simulation and for the retrieval. However, differences between 3-D and 1-D are much larger, especially for the bumpy and fractional cloud with values of +62 hPa (−550 m) and +45 hPa (−390 m). As already explained, the polarized reflectance in the shortwave wavelengths (490 nm) is very high because of molecular scattering. The retrieval of the cloud top pressure is based on the amount of molecular scattering occurring above the cloud when looking in forward scattering (for scattering angle ranging between 60 and 120^∘). Consequently, as shadowing effects modify the polarized reflectances in the forward scattering directions, the cloud top pressure retrieval is impacted, especially for the fractional and bumpy cloud.

4.3 Impacts for aerosol above cloud retrieval

Polarized reflectances of POLDER are also used to retrieve aerosol optical thickness (AOT) of an aerosol layer above cloud (Waquet et al., 2009, 2013a). Waquet et al. (2013a) describes two algorithms for aerosol above clouds (AAC) retrieval using POLDER polarization measurements: (i) the research algorithm is an optimal estimation method that retrieves a large number of aerosol and cloud parameters and (ii) the operational algorithm is based on LUTs calculations and allows to retrieve the AOT at 865 nm and the Ångström exponent of aerosol above clouds. The “operational algorithm” is the one considered in the present study. The LUT calculations are performed with the successive order of scattering code that assumes a plane-parallel atmosphere (Lenoble et al., 2007). It uses assumptions of particle microphysics: six fine mode spherical aerosol models (effective radius varying between 0.09 and 0.24 µm) are considered and a constant complex refractive index of 1.47+0.01i is assumed. The errors due to the assumption made for the complex refractive index were estimated at around 20 % on average for the AOT (Peers et al., 2015) and maximal relative error may reach 25 % in case of extreme aerosol events (AOT > 0.6 at 550 nm). One additional non-spherical mineral dust model is also considered in the LUTs.

The operational algorithm uses a specific strategy to retrieve aerosol properties above clouds that depends on the aerosol type and also on the available viewing geometries (see Fig. 4 in Waquet et al., 2013a). In case of fine mode particles, the retrieval is restricted to the use of observations acquired for scattering angles smaller than 130^∘, where polarization measurements are highly sensitive to scattering by fine mode particles (such as biomass burning aerosol) and only weakly sensitive to cloud microphysics. This is illustrated in Fig. 6 with the dashed lines representing polarized reflectances for a homogeneous cloud with an aerosol layer above (dark blue and red curves) and without aerosol above (clear blue and pink curves). The increase of the polarized reflectances for scattering angles less than 130^∘ is clearly visible when an aerosol layer is present above a cloud. Non-spherical particles in the coarse mode, such as mineral dust particles, cannot be handled with this method as they do not polarize light much. When dust particles are transported above clouds, they reduce the magnitude of the primary cloud bow. The operational algorithm then includes the primary bow in order to retrieve the above cloud dust AOT. In this case, as the magnitude of the primary cloud bow primarily depends on the cloud droplet effective radius, it must be estimated or included in the retrieval process. Collocated cloud properties from MODIS at high resolution (1 km × 1 km) are used to characterize and to select the cloudy scenes within a POLDER pixel (6 km × 7 km at nadir) and the MODIS cloud products can then be used in the operational algorithm to estimate the droplets effective radius. As the magnitude of the primary cloud bow is only weakly impacted by the choice of the droplet effective variance, this parameter is assumed to be constant and equal to 0.06. Several filters are eventually applied to obtain a quality-assessed product. For instance, the retrievals are restricted to cloudy pixels associated with cloud optical thicknesses larger than 3.0, since the polarized radiation reflected by the cloud layer is then saturated and does not depend anymore on the cloud optical thickness. Criteria are also used to reject inhomogeneous and fractional cloudy pixels and to avoid cirrus cloud contamination. We refer to Sect. 3.4 in (Waquet et al., 2013a) for a detailed description of the operational algorithm.

Figure 6Polarized reflectances as a function of the scattering angle. Dashed lines are for homogeneous cloud with and without a biomass burning aerosol layer above; solid lines are for the fractional cloud with and without a biomass burning aerosol layer above. The solar zenith angle is 60^∘.

Download

In the POLDER operational algorithm, the underneath cloud is assumed to be homogeneous. Empirical criterions are used to reject heterogeneous and fractional cloudy pixels but a misclassification of the cloudy scenes is still possible. Moreover, it is also important to evaluate the AOT retrieval errors due to 3-D effects in case of fractional cloud covers. These scenes, for which aerosols and clouds are potentially mixed, remain untreated and are of primarily importance for climate studies. In the following, we investigate the possibility of using the operational algorithm to handle these scenes and we evaluate the biases observed in the polarized reflectances and in the AOT retrieval errors due to 3-D effects. In order to check the AOT value retrieved for such cases, we use the 3-D polarized reflectances generated for the fractional cloud case, with and without aerosol, and we used these 3-D simulations as inputs for the operational algorithm. Note that for the synthetic retrievals discussed here, we assumed that the operational algorithm knows the effective radius and effective variance of the cloud droplets.

Figure 73-D Polarized reflectances used as input for the aerosol above cloud algorithm (Waquet et al., 2013a) and polarized reflectances simulated with the algorithm after the convergence of the retrieval. Reflectances at all angles were used (solid line) and reflectances with only scattering angles above 120^∘ (dashed line).

Download

The 3-D polarized reflectances used as input of the algorithm and the ones simulated after the adjustment of the aerosol model and optical thickness are plotted in Fig. 7 (solid lines). When a large scattering angular range is available (between 60 and 180^∘), the algorithm works in an efficient way. The lateral polarized reflectances in scattering angular range between 80 and 120^∘ exhibit low or negative values. Consequently, no aerosol (AOT = 0) were retrieved. However, we note that the primary cloudbow is not well reproduced by the 1-D simulation provided by the operational algorithm. In the POLDER measurements, the range of sampled scattering angles varies with the geographical position. In some cases, the scattering angle range sampled by the instrument can be quite narrow. We tested the algorithm without observations acquired for scattering angles smaller than 120^∘ (dashed lines in Fig. 7). The cloudbow signal is then better matched but the inversion method retrieves erroneous AOT values of 0.31 at 670 nm and 0.28 at 865 nm instead of zero for both.

Table 3Retrieved aerosol properties for a biomass aerosol layer above the fractional cloud with the operational algorithm described in Waquet et al. (2013a). Aerosol optical thickness at 670 nm (AOT670), at 865 nm (AOT865) and Ångström coefficient for three solar zenith angles (SZA). Relative differences [(Fractional − Homogeneous) ∕ Homogeneous × 100] are indicated in bold. Last two lines, RMSE computed between the input and the recalculated polarized reflectances for the homogenous and fractional cloud.

Download Print Version | Download XLSX

A second test is made with simulated reflectances including a biomass-burning aerosol layer lofted above the fractional cloud. For the simulation, the AOT of the aerosol layer is fixed to 0.28 and 0.15, the single scattering albedo to 0.93 and 0.91 at 670 and 865 nm, respectively. In order to avoid retrieval errors related to the choice of aerosol model, we used one of the biomass burning aerosol model included in the operational algorithm. The particles effective radius is 0.15 µm and the single scattering albedo is equal to 0.91 at 865 nm. The simulated 3-D angular polarized reflectances as a function of the scattering angles are presented in Fig. 6 (solid blue and red lines). Compared to the 1-D reflectances with aerosols above cloud (dashed blue and red lines), the cloud heterogeneity effects amplify the increase of the forward signal and the decrease of the cloudbow signal. As with molecular scattering (Sect. 4.1), aerosol scattering contributes to enhance the polarized reflectances in the shadow and cloud-free parts leading to higher averaged polarized reflectances in the forward direction. In the cloudbow direction (near 140^∘), and to a lesser extent, in the side scattering (between 100 and 130^∘ in scattering angle), the polarized reflectances are additionally attenuated because of the plane-parallel biases. Note that for other solar zenith angles (not shown here), the plots are similar with a more restricted scattering angular range (between 100 and 180^∘ for SZA = 20^∘ and between 80 and 180^∘ for SZA = 40^∘). Consequently, only the attenuation due to the plane-parallel bias impacts the polarized reflectances.

The results obtained with the operational algorithm are presented in Table 3. We repeat that the same input AOT is used in the 1-D and 3-D simulations (AOT of 0.15 at 865 nm). The Ångström exponent is related to the ratio of two optical thicknesses at two wavelengths and corresponds in the retrieval to the best-selected model. As expected, the AOTs retrieved by the algorithm for homogenous clouds are close to the input one, whatever the SZA value. The retrieved AOTs only slightly overestimate the input (0.15) and are respectively equal to 0.180, 0.170 and 0.170 for SZA of 20, 40 and 60^∘. This overestimation is likely due to the approximations used in the retrieval algorithm (e.g. interpolation in the LUTs). Comparing with the retrieved values from homogeneous cloud, significant departures are observed for fractional clouds especially for SZA = 60^∘. The AOTs retrieved at 865 nm are then equal to 0.119, 0.170 and 0.280 for SZA of 20, 40 and 60^∘, respectively. For a given solar zenith angle, the viewing geometries and the angular resolution are identical for the homogeneous and fractional clouds. The differences observed in AOT between the 1-D and 3-D calculations are then necessarily due to cloud heterogeneity effects. For SZA = 40^∘, the best model that minimized the cost function is the same for the homogeneous and fractional clouds. Differences for the retrieved AOT are negligible, but we note that the RMSE between the input and recalculated reflectances is slightly larger for the fractional cloud than for the homogeneous one. For SZA = 20^∘, the operational algorithm also successfully retrieves the input aerosol model for the homogeneous and fractional cloud. However, the AOT retrieved by the operational algorithm, under the homogenous assumption, is underestimated with an error of about −33 %. For SZA = 20^∘, the range of scattering angles effectively used for the retrieval is between 100 and 130^∘. Polarized reflectances for SZA = 20^∘ are not shown but they are similar to the ones shown in Fig. 7 between 100 and 180^∘. Between 100 and 130^∘, as shown in Fig. 7, 3-D polarized reflectances are lower than the 1-D ones because of the plane-parallel biases, which explains why the AOT retrieved by the algorithm is underestimated. However, as the differences are mainly due the plane-parallel bias, which is similar for the two wavelengths, the cloud heterogeneity effects do not affect the selection of the best aerosol model. For SZA = 60^∘, the range of scattering angles used is between 60 and 130^∘. Between 60 and 90^∘, there is an increase of the forward scattering signal due to 3-D effects, which is interpreted by the operational algorithm as an increase in the AOT. We note also that 3-D effects bias the aerosol model for this case as a smaller value of Ångström exponent (corresponding to a larger effective radius) is retrieved for the fractional cloud. The retrieved AOT is thus higher (AOT of 0.28 comparing to 0.17) with a relative error up to 65 %.

Note that the operational algorithm is not applied for pixels too heterogeneous. Those are filtered using the standard deviation of the COT retrieved at 1 km by MODIS that should not exceed five. For the fractional cloud of this study, we checked the standard deviation value computed from the input cloud optical thickness (different from the retrieved one) and found seven. It is slightly above the homogeneity limit fixed in the aerosol above cloud algorithm developed for POLDER (Waquet et al., 2013a). The results presented here for aerosol above cloud retrieval can thus be seen as an upper limit for the operational algorithm.