A multimodal approach to derive cloud microphysics in deep convective clouds from polarized measurements of the cloudbow

Abstract. We present a new method to derive droplet size distributions in clouds consisting of muliple modes using aircraft based polarized measurements of the cloudbow. The retrieval allows up to three modes in the droplet size distribution (DSD) and hence, is situated between a single mode retrieval and the Rainbow Fourier Transform (RFT), which derives an arbitrary distribution. While the DSDs of shallow cumulus or stratiform clouds are often well described by single mode distributions, this does not hold in the presence of drizzle or rain. Since current look-up tables of polarized phase functions used for the polarimetric fit extend only up to effective radii of about 40 µm, new Mie calculations were performed to include effective radii up to 1000 µm. In a sensitivity analysis, the uncertainty in the retrieval of large effective radii is tested as the polarized phase functions become less distinct. For effective radii up to about 800 µm, the relative mean bias is found to be less than 10 %. The relative noise (standard deviation) increases from about 4 % for typical cloud droplets of 10 µm to about 30 % around 500 µm before decreasing again towards even larger effective radii. With the found uncertainties in mind, the new multimode approach is applied to a case study of a deep convective cloud measured during the PERCUSION campaign in 2024 in the vicinity of Barbados, where a rainbow is observed in the RGB image of the camera and also the radar reflectivity shows clear signals of rain. While the single mode retrieval cannot accurately explain the measured signal close to the rainbow observation, the capability of the multimode retrieval to disentangle the signal is demonstrated qualitatively. Furthermore, the individual results from the multimode retrieval are evaluated against the droplet size distributions derived from the Rainbow Fourier Transform (RFT) and similarities are found in most cases, although the results from the RFT show instabilities with negative values in the DSD. Currently, the RFT is only capable to retrieve droplet size distributions with radii up to 100 µm, and hence is limited in regions with precipitating droplets. This is where the potential of the multimode approach comes into play as it is capable to detect modes of large effective radii up to 1000 µm, which does not only improve the result of a single mode retrieval, but might also allow to learn about physical processes such as rain initiation in deep convective clouds.