On the sensitivity of cloud effective radius retrieval based on spectral method to bi-modal droplet size distribution: A semi-analytical model

- Effects of bi-modal droplet size distribution on cloud effective radius retrieval investigated.
- Retrieval tends to underestimate the effective radius of bi-modal size distribution.
- The underestimation is larger for 3.7 µm MODIS band than 2.1 µm band.

The bi-spectral solar reflective method is widely used to infer cloud optical thickness (τ) and effective radius (re) from satellite cloud reflectance observations. An important assumption often made in this method is that cloud droplet size distribution (DSD) follows the monomodal Gamma or Lognormal distributions, with a fixed variance. However, it is known that the warm rain processes, e.g., collision-coalescence, can broaden cloud DSD and even lead to bi-modal size distribution. In this study, a semi-analytical model is developed to better understand the retrieved re based on the monomodal DSD assumption when the true DSD is bi-modal. The results based on this model agree well with the results from rigorous radiative transfer simulations. The model reveals that the re retrieval based on the monomodal DSD assumption tends to underestimate the re of the true bi-modal DSD. This bias is due to the nonlinear relationship between cloud droplet single-scattering albedo and cloud droplet size. The degree of this underestimation is found to increase with re and the width of the DSD. The model also indicates that the underestimation more strongly affects the 3.7 µm band than in the 2.1 µm band retrievals; leading to smaller 3.7 µm band re retrieval than that based on 2.1 µm. It is also demonstrated through numerical tests that cloud optical thickness retrieval shows little sensitivity to the cloud microphysics assumption and is relatively accurate. This is probably because the asymmetry factor of cloud droplet varies within a relatively small range, and therefore limits the impact of cloud microphysics on τ retrieval. This study has several implications, in particular for understanding the potential impact of drizzle on cloud re retrieval. Future work is needed to evaluate the model in more realistic cloud field.