We focus on the retrieval from the GOSAT/TANSO-CAI. GOSAT is mainly designed to measure the carbon dioxide loading using the TANSO Fourier Transform Spectrometer. In addition, the satellite carries the Cloud and Aerosol Imager (CAI) with four channels (380, 674, 870, and 1600 nm), ranging from UV to SWIR bands for cloud screening and aerosol detection. We firstly simulate the synthetic measurements from the CAI in four spectral bands (Nλ=4) based on the improved Pstar model. Moreover, we define a 5×5 pixel region as one subdomain, i.e., Nu/v=5, though there is no limitation in these definition if the computer resource is allowed. The geometric information is determined by the mean values of the CAI observations at the solar zenith angle of 27∘ ±1, satellite zenith angle of 30∘ ±1, and relative azimuth angle of 150∘ ±1 at the subdomain (Hashimoto and Nakajima, 2017).

The simulated true AOT values at 500 nm for each mode are given as 0.02, 0.1, 0.2, and 0.3, respectively. The total AOT is the sum of each AOT in a random mixture. We defined the soot fraction in fine aerosol as randomly ranging from 0.5 % to 1.5 %. In the ocean surface, a moderate wind speed of 5 m s-1 is assumed. From the widely used suite compiled by the NASA Ocean Biology Processing Group, and based on the large statistical ocean color sample of MODIS, we selected two representative classes of oceanic scenarios: the Linai region, in which the water is typically clear, with climatological values of Chl, a_443, and bbp_443 being about 0.056 mg m-3, 0.017, and 0.0014 m-1, respectively, and the Yellow Sea, in which the water is typically coastal, with climatological values of Chl, a_443, and bbp_443 being about 3.00 mg m-3, 0.35, and 0.039 m-1, respectively, where a_443 denotes the total absorption coefficient of ocean at 443 nm, and bbp_443 is the total backscattering coefficient of oceanic particulates at 443 nm. It should be noted that the used Chl products are derived by the OCI algorithm of Hu et al. (2012), and a_443 and bbp_443 products are derived by the quasi-analytical algorithm (QAA) method of Lee et al. (2002), respectively. We assume the aerosol and oceanic-substance spatial distributions to be homogeneous in the 5×5 pixel regions. In total, we have 64 atmospheric cases of simulated observation data with a Gaussian random noise of 2 % standard deviation as measurement errors for each oceanic condition. Then eight parameters of each pixel, i.e., AOTs of fine, sea spray, and dust; the volume soot fraction in fine aerosol; wind speed; and concentrations of Chl, sediment, and CDOM for the whole subdomain, are determined simultaneously using Eq. (4). The soot fraction in fine aerosol is defined as the retrieval parameter owing to its high absorption effects. The a priori conditions are randomly defined in a ±50 % range of the true values, except for the soot fraction, which has a fixed value of 0.01. To investigate the feasibility of the multi-pixel method in the retrieval, we analyzed the simulation data, adopting different γ values of 0.0, 0.1, 0.5, 1.0, 1.5, 2.0, and 3.0. The general simulation and retrieval setup are summarized in Tables 1–2.

Figure 1 shows the retrieved AOT and spectral Rrs values with true conditions as well as the statistical results of the retrieved relative error and root-mean-square deviation (RMSD) at different values of γ for the open ocean. Note that Fig. 1a–g show only the retrievals of 0.0 and 3.0 at γ, which denote the use of no spatial smoothness constraint, i.e., the traditional single pixel method, and allowed a variation of about 1.35 times the retrieved parameters constrained from neighboring pixels, respectively. The results indicate that the accuracy of the retrieved AOT of each mode is generally improved by using the spatial smoothness constraint, i.e., the multi-pixel method, to correct the retrieval bias induced by measurement errors. Specifically, the retrieved relative error and RMSD of the fine AOT decrease from 30.51 % and 0.031 to 13.45 % and 0.018, respectively, when the γ values change from 0.0 to 3.0 (Fig. 1h–i), which indicates the effectiveness of the multi-pixel method in aerosol retrieval. Coarse aerosols (sum of sea spray and dust) can also be well derived, which is partly due to the adoption of the SWIR channel observation (Fig. 1e), even though larger errors are shown for the inversion of each coarse aerosol, i.e., AOT of sea spray and dust (Fig. 1b–c), compared with the true values. Additionally, due to the more significant improvement in the retrieval of the fine AOT, the multi-pixel scheme contributes to a better estimation of the total AOT (Fig. 1f). In contrast, the soot fraction is difficult to retrieve due to its low sensitivity to measurements, even though an UV channel observation, i.e., 380 nm, is implemented by the CAI, for which the retrieval results are highly dependent on the a priori value (1 % in this case; Fig. 1d). In regard to the spectral Rrs, we find that the multi-pixel method helps to facilitate the consistency of the retrieval with the true values (Fig. 1g) in comparison to those derived by the single pixel method, and this finding is similar to that of Xu et al. (2016) over open oceans. The low values of Rrs at 860 nm and at 674 nm also support the reasonability of our previous black ocean assumption in those bands in the two-channel aerosol inversion (Nakajima and Higurashi, 1997). However, the underwater influence in the retrieval of aerosols at UV channels over the open ocean is suggested to be considered due to the higher backscattering effect of ocean body.

Over coastal waters, the sediment and CDOM, which exist with higher concentrations in the ocean and show generally similar inherent optical properties to the fine aerosol and soot, exert non-negligible effects on the aerosol retrieval. Compared with the inversion of fine AOT over the open ocean (Fig. 1a), the retrieval in the low-aerosol loading over coastal regions shows larger biases when using the traditional single-pixel method, mainly due to the contamination of oceanic sediment (Fig. 2a). Nevertheless, retrieval errors can be effectively reduced using the multi-pixel scheme, with the relative error and RMSD decreasing about 27.4 % and 0.02234 (Fig. 2k–l), respectively. This improvement is also due in part to the better estimation of the spectral Rrs (Fig. 2j). It is demonstrated that the retrieved accuracy of the coarse AOT is generally similar to that in clear waters (Fig. 2e), which is partly attributable to the utilization of SWIR measurements that are not sensitive to sediment and can be used in the atmospheric correction over turbid waters (Wang and Shi, 2007). Moreover, it remains difficult to retrieve the absorptive soot over coastal waters, even when using the multi-pixel constraint (Fig. 2d). With regard to the underwater retrieval, significant improvements are evident in the inversion of oceanic substances, particularly for the sediment and CDOM, after implementing the spatial smoothness constraint (Fig. 2g–i). Such improvements also contribute to the better retrieval of the spectral Rrs, with the relative errors in the first three CAI bands decreasing from 41.87 %, 17.76 %, and 15.94 % to 22.87 %, 8.09 %, and 8.23 %, respectively. Generally, there are higher averaged kernel matrix values for fine and coarse aerosols, sediment, and CDOM than those for the soot fraction, Chl, and the wind speed in the non-glint cases during the retrieval. It should be noted that we used relatively accurate a priori values for the AOT estimation in a range of ±50 % of the true conditions, however, the retrieved sea spray and dust will have larger biases when xa exceeds true values more largely, owing to the limited spectral information of CAI and similar optical properties of these two modes. However, their sum, i.e., the total coarse AOT, can still be determined well and exhibits no obvious dependence on the a priori conditions.

The above results demonstrate the effectiveness of the multi-pixel scheme in the retrieval of aerosols over homogeneous atmosphere–ocean areas. To consider the retrieval under inhomogeneous conditions, we conducted further inversion experiments in two situations. First, we assumed that the aerosol loading and oceanic substances change continuously from coastal to open ocean, with a large spatial variation in the 5×5 pixel subdomain. Results indicate that the multi-pixel strategy still performs better retrieval in this case, as shown in Fig. 3a–c, particularly for the estimation of fine aerosols. Similar to the retrievals over the homogeneous region, the spectral Rrs can be better derived using the multi-pixel scheme, especially over coastal regions (low values of the Rrs at 380 nm and high values of the Rrs at 674 nm), but the traditional single-pixel method tends to yield larger bias estimations for the retrieval (Fig. 3c). Another inversion experiment is performed for the retrieval over land (with a higher aerosol loading and soot fraction) and coastal ocean interface regions in the subdomain. In this simulation, the land surface is assumed to be reddish-brown fine sandy loam with spectral reflectance values of 0.1098, 0.2775, 0.3630, and 0.4790 for the four CAI bands, and values are selected from the ECOSTRESS spectral library (https://speclib.jpl.nasa.gov/library, last access: 15 February 2019). For the aerosol retrieval over land, we make simultaneous determinations of the AOT and spectral surface reflectance (Ag) with randomly defined a priori values of Ag in a range of ±10 % of the true conditions and assumed spectral uncertainties of 0.02, 0.02, 0.02, and 0.001 for the CAI channels, respectively. The results indicate that the single-pixel method generally overestimates the fine and coarse AOT values over sand due to the high ground reflectance. However, the retrieval accuracy over the sand surface improves significantly by constraining the spatial aerosol variation in the subdomain, which also benefits from the better AOT estimation over the coastal ocean region (Fig. 3d–e). With regard to the retrieval of the soot fraction (SF; Fig. 3f), it remains difficult to derive over-ocean areas with a high dependence on the a priori value (red line of Fig. 3f), whereas absorptive soot can be better estimated over land regions due to the high reflectance of the ground surface by providing more significant information to the retrieval. Moreover, the multi-pixel scheme promotes the inversion of the SF, particularly in high aerosol conditions, which is similar to the research of Hashimoto and Nakajima (2017) conducted over the whole land regions. The performance of retrieval for absorptive soot with dependence on the aerosol loading over the land, where the better retrievals are identified in the condition of fine AOT at 500 nm over 0.1 (Fig. 3f) in this study, also supports the finding that errors of retrieved single scattering albedo decrease with increasing AOT for the AERONET (Dubovik et al., 2000). It is interesting that the retrieved accuracy of the SF nearest to the coastal line over the ocean (solid circles of Fig. 3f) tends to be improved using the multi-pixel method, though it is slightly improved. This improvement is more significant in the homogeneous aerosol distribution and dominated fine-mode conditions over the land–ocean interface region, as shown in Fig. 4. The availability of retrieval for the absorptive soot over the dark surface, i.e., the ocean region, benefits from the spatial smoothness constraint from the better-derived SF over the bright surface, i.e., sand ground, where the surface albedo is near or over the neutral reflectance defined by Kaufman (1987). We then derived the relationship between the neutral reflectance (An) in which the apparent reflectance does not change with AOT and the single scattering albedo (ω), asymmetry factor (g), and phase function (P(cos⁡Θ)) of aerosols based on the single scattering and two-stream approximation over land, calculated as follows: An=πωP(cos⁡Θ)μμ0t^(μ)+t^(μ0);t^(μ)≡m1-ω121+32gμ, where μ and μ0 are the cosines of the satellite and solar zenith angle, respecitvely. It is demonstrated that the neutral reflectance of band 2 of the CAI is ranged from 0.232 to 0.275 when the asymmetry factor and phase function are 0.7 and 0.0142, respectively, corresponding to the single scattering albedo of 0.935 and 0.950 with the soot fraction of 2.05 % and 5.10 %, which is generally similar to the threshold values of the retrieved SF in Figs. 3f and 4b. However, these threshold values are just the specific case used in this study and are also dependent on the ratio of fine AOT in real conditions.

Following the simulation retrieval experiment performed using synthetic spectral measurements, we then apply the proposed algorithm to the real CAI data for deriving aerosols over the ocean. Radiometric correction was conducted as prescribed in Shiomi et al. (2010). With regard to the ancillary data, we use the surface pressure and wind speed data from the National Centers for Environmental Prediction (NCEP) to correct the Rayleigh scattering and sea surface reflectance, respectively, as well as the relative humidity data to account for the effect of aerosol hygroscopic growth. The gas absorption is processed by a correlated k-distribution approach (Sekiguchi and Nakajima, 2008) where several main absorptive gases are considered, and the column ozone data are adopted from the ozone monitoring instrument (OMI). In particular, we used a relatively high spatial smoothness constraint with a γ value of 1.0 for each horizontal orthogonal direction in the multi-pixel scheme. Moreover, to keep the consistency between each subdomain, the boundary conditions of Bu/v used in Eq. (4) are determined by the retrieved results derived from the neighbor subdomains.

Figure 5 compares the spatial distributions of retrieved fine, coarse (sum of sea spray and dust), and total AOTs using single- and multi-pixel methods. Results show that the derived AOTs by the single-pixel approach have a generally similar spatial distribution to those retrieved by the multi-pixel method, which the fine aerosol dominates. However, irregular dotted variations with abnormal retrieval results are shown in some pixels (black box in Fig. 5) when conducting the single-pixel retrieval. Although it is difficult to support these irregular dotted distributions being real, the investigation of the posterior error in those pixels demonstrates that the retrieved uncertainties are generally higher than those of other pixels (not shown). Such kinds of occasionally irregular dotted variations derived by the single-pixel method have also been identified in the aerosol retrieval over land (Hashimoto and Nakajima, 2017), which we rather consider to be caused by errors in the single-pixel inversion that tends to be affected by various observation noises. On the contrary, the multi-pixel scheme is more robust to these factors, so the irregular dotted variation of retrieved AOT can be effectively improved when considering the spatial smoothness constraint during the retrieval, as shown in Fig. 5d–f, which allows reduction of the retrieval errors constrained by adjacent pixels.

Another retrieval experiment is performed on the monitoring of the Asian dust event from the CAI. Studies have demonstrated that dust aerosols carried by the dust storm in East Asia exert significant influence on the local ecosystem and environmental pollution (Huang et al., 2014). Figure 6 shows the spatial distribution of retrieved fine and coarse AOTs from the CAI on 27 April 2012 over the Yellow Sea. In order to have a better validation for the current algorithm, the MODIS standard Level 2 aerosol products derived using more channels, with the satellite overpass time about 3 h later than that of the CAI, are also adopted as comparison. Results show that a relatively obvious transport belt for fine aerosols between the south of the Shandong Peninsula and the middle of the Yellow Sea is derived by the CAI (Fig. 6a); meanwhile, significant dust storms are determined in the north of Yellow Sea (Fig. 6d), where the retrieved coarse AOTs at 500 nm are over 1.5 in the high-density areas. It is demonstrated that the derived AOTs for fine and coarse aerosols are generally consistent with the MODIS standard aerosol products with similar spatial distributions (Fig. 6c and f). In addition, the derived AOTs from the CAI with the multi-pixel method (Fig. 6b and e) around the Shandong Peninsula are in more agreement with MODIS aerosol products than those retrieved by the single-pixel approach, which implies the effectiveness of the multi-pixel scheme in the inversion of aerosols, particularly for fine aerosol. It should be noted that the derived fine AOT values from the CAI seem to be generally lower than those obtained using MODIS products over the Yellow Sea. Although our algorithm divides the coarse aerosols into sea spray and yellow sand, it is more appropriate to use their sum, i.e., coarse AOTs, than the yellow sand as the indicator of the Asian dust transport, since the retrieval errors of coarse AOTs determined by the CAI are much lower than those of individual yellow sand particles, as shown in Fig. 2c and e. Such a deficiency in distinguishing the sea spray and dust is expected to be better improved using the upcoming Cloud and Aerosol Imager 2 (CAI2) with seven channels (340, 380, 443, 550, 674, 869, and 1630 nm) by providing more measurement information.

Retrieval of aerosols over extremely highly turbid waters is still a challenging problem due to the significant contamination from the backscattering of oceanic particulates, currently. Taking the Hangzhou Bay (HZB) as a sample region, the total suspended particulate matter can be over 1000 mg L-1 sometimes (He et al., 2013), which contributes a substantial proportion into the satellite signals as a result of the aerosol being generally difficult to accurately derive. In order to investigate the feasibility of the multi-pixel scheme in the retrieval of the AOT over highly turbid water, we try to apply the current algorithm in such a circumstance. Figure 7 shows the comparison of the retrieved total AOT by using the single- and multi-pixel method with or without using the SWIR band of the CAI, i.e., 1600 nm, with those from the MODIS aerosol products in December–March 2013 over the East China Sea. It should be noted that there are several high-error observation belts for band 4 in this image (Fig. 7f) due to some instrument problems, but the data are available for most regions including the HZB. Results demonstrated that the retrieved AOTs by the CAI with or without using the SWIR measurement are all consistent with those of the MODIS aerosol product (Fig. 7c) beyond the coastlines, however, the estimated AOTs from the CAI using different strategies around highly turbid regions show large differences. Generally, the derived AOTs without using SWIR measurements (Fig. 7a) demonstrate obviously higher values than those retrieved by adding SWIR information (Fig. 7d) near coastal region. This is because the satellite reflectance at SWIR channels is much less sensitive to the suspended sediment than that at visible bands in turbid waters, so the aerosols can be estimated without significant contamination of sediment (Wang and Shi, 2007) based on the SWIR observation. Although we simultaneously conduct the oceanic sediment retrieval in the algorithm, it is still difficult to use four spectral measurements to estimate at least five free variables (AOT of fine, sea spray and dust, sediment, and CDOM) in the high backscattering surface condition, where the retrieval could be degenerated. Nevertheless, such a deficiency can be improved using the multi-pixel scheme even though the SWIR measurements are not used (Fig. 7b), which indicates the potentiality of the multi-pixel strategy in the aerosol retrieval over highly turbid waters, particularly for those multispectral instruments without the SWIR observation.

To further investigate the feasibility of this algorithm, two in situ data from the AERONET, i.e., the Ieodo Station and Gageocho Station, are used for the validation. To examine the dependence of this retrieval on the a priori information, we set fixed values of xa for all cases. We selected the retrieved AOTs from the pixel closest to the AERONET site in the subdomain. The results indicate that the retrieved AOT values for fine and coarse aerosols, as well as the total aerosols, are all consistent with those of the AERONET observations without significant dependence on the a priori information (Fig. 8). It should be noted that the simultaneous retrieved AOTs for fine and coarse aerosols are denoted in same color. Generally, increased accuracy in the determination of AOTs is demonstrated by using the multi-pixel method (shown by circles), with the retrieved relative errors of the AOT for fine, coarse, and total aerosols decreasing from 26.19 %, 96.70 %, and 27.64 % to 23.52 %, 86.83 %, and 22.40 %, as well as the RMSD, which varied from 0.1062, 0.05660, and 0.1129 to 0.06838, 0.04960, and 0.08738, respectively, in comparison to those derived by the single-pixel scheme (shown by crosses). As in the simulation inversion experimental results shown in Figs. 1–3, the multi-pixel scheme tends to be more effective in the retrieval of fine aerosols than of coarse aerosols from the CAI measurements. However, we still identify a few cases in which the retrieved errors have increased using the multi-pixel scheme, which inspires us to make further studies on the better definition of γ values for each retrieved parameter or the pixel resolution of the subdomain. It should be noted that we neglect the multiple scattering influence between neighbor pixels caused by the adjacent effect in the retrieval, since the effect is generally small for the CAI instrument with moderate spatial resolution. Nevertheless, we have to consider the adjacent effect for the extremely high spatial resolution imagers using a 3-D radiative transfer model.