Clouds play a crucial role as intermediary factors in maintaining the balance of atmospheric radiation energy and water cycle. The particle size distribution (PSD) and the optical and microphysical properties of clouds are intricately linked. Therefore, precise determination of PSD is pivotal for analyzing the interactions among different atmospheric components. Polarized remote sensing, a novel atmospheric detection technology, can be utilized to retrieve the PSD of water clouds. Multi-directional observation information can be leveraged to retrieve PSD. However, current methods overlook sensor scattering angle coverage and actual cloud characteristics. The fixed-resolution sampling method within the field of view (FOV) neglects the influence of sensor imaging characteristics and cloud heterogeneity. Therefore, conducting studies aimed at enhancing the accuracy of water PSD inversion based on sensor imaging and cloud characteristics is important for atmospheric research.

In PSD retrieval research using polarized multi-angle observation data, the selection of inversion scale significantly influences the number of available observation angles and the cloud’s heterogeneity. To address these limitations, we propose a dynamic scale PSD retrieval method based on multi-angle polarized data, leveraging the polarized radiation characteristics of water clouds and radiation transmission theory. We conduct a quantitative evaluation of retrieval feasibility at various scales within satellite imaging geometry and cloud characteristics. Our method utilizes an optimal pixel merging strategy at a pixel-by-pixel level to improve inversion resolution while maintaining accuracy, ultimately applying the inversion method to directional polarization camera (DPC) observation data. Results indicate that, unlike the fixed retrieval scale of 25 pixel×25 pixel used in POLDER (polarization and directionality of the Earth’s reflectance) product, our method dynamically adjusts the inversion scale between 1 pixel×1 pixel and 7 pixel×7 pixel, leading to improved retrieval resolution. Thus, the optimization strategy for inversion scale in this study aims to strike the best balance between inversion success rate and accuracy, employing a dynamic selection method on a pixel-by-pixel basis. Tailored to the imaging characteristics of domestically produced DPC data, we devise the technical flowchart depicted in Fig. 1. Initially, we establish a polarized scattering phase function library for various water cloud droplet PSDs. By considering the number of observed angles within the water cloud “rainbow” effect among DPC observations, we determine the initial inversion scale. Simultaneously, we iteratively optimize the inversion resolution based on the number of observed angles and cloud attribute information within the scale. Finally, by leveraging multi-angle polarized observation data, we achieve the inversion of water cloud droplet size distributions at the optimal inversion scale.

Compared with moderate resolution imaging spectroradiometer (MODIS) cloud effective particle radius products, the spatial distribution shows good consistency. As depicted in Fig. 8, the inversion results of overlapping areas between MOD06_L2.A2022068.0220.061.20220 and DPC are contrasted within the case study region. Figures 8(a) and 8(b) vividly depict that the values and distributions of cloud effective particle radius from DPC and MODIS exhibit remarkable similarity. However, Fig. 8(c) reveals substantial disparities in inversion values between the two, primarily in fragmented cloud regions, whereas variances in stable cloud cluster areas are negligible. In Fig. 9, we perform a quantitative statistical analysis of the inversion results within overlapping areas. Using regression equations derived from fitting, our inversion results yield smaller values for cloud effective particle radius compared to MODIS products, especially for radius of 5?12 μm. This trend aligns with comparisons between POLDER and MODIS. For larger particles, both DPC and inversion results surpass those of MODIS, possibly due to lower sensitivity of polarization to larger particles, leading to increased inversion errors for this particle size range. In histogram analysis, the proportion of inversion results with errors less than 2.05 μm exceeds 50%. Considering significant differences in imaging time between DPC and MODIS, substantial shifts in cloud position, variations in shape, and disparities in sensor resolution and inversion methods, significant errors in pixel-by-pixel comparisons are expected. However, these deviations are acceptable. Therefore, analyses indicate our method can yield more detailed inversion results while maintaining high accuracy.

The dynamic inversion resolution method improves upon conventional techniques by considering the variations in scattering angle coverage across different regions and the effect of cloud structures on satellite wide FOV imaging. By carefully considering observational conditions and the real-time state of clouds at a pixel level, this method avoids loss of accuracy and success rate stemming from arbitrary resolution selection in PSD inversion. Additionally, it reduces uncertainties from geometric variations in multi-angle imaging and cloud heterogeneity during inversion. Consequently, our study provides significant benefits in enhancing the accuracy and success rate of cloud PSD retrieval. In conclusion, our research explores ways to enhance the efficiency of utilizing domestic multi-angle polarized data and improve the accuracy of PSD inversion.