Physical Constrained Retrieval of Fog Visibility from Millimeter-Wavelength Cloud Radar Observations

Abstract. Fog severely degrades visibility (Vis) and poses substantial risks to transportation and aviation, yet its quantitative monitoring remains challenging, because conventional optical and passive remote sensing techniques lose sensitivity under dense fog conditions. Millimeter-wave cloud radar (MMCR) provides a promising alternative due to its strong penetration capability and fine spatial resolution; however existing Vis retrieval algorithms largely rely on empirical parameterizations, resulting in considerable uncertainties. In this study, we develop a physically constrained fog Vis retrieval framework that explicitly links radar reflectivity(Z) to fog microphysical properties through radiative transfer theory. Visibility is inferred by estimating the extinction coefficient from independently derived fog liquid water content (LWC) and effective droplet radius (re), thereby avoiding purely empirical formulations. The method is applied to a Ka band MMCR observations at the Datan Observation Base (DOB) Fujian province, China. LWC is retrieved using a mass-absorption based algorithm developed in our previous study. A power-law relationship between the geometric mean radius (rm) and radar reflectivity (Z) is then established using 5 years of droplet size distribution data from an FM-120 fog droplet spectrometer, enabling a reasonable estimation of re from observation. Based on the obtained LWC and droplet size parameters, the extinction coefficient (βext) and Vis are subsequently derived. Validation against ten sea-fog events in spring 2025 demonstrates that the proposed algorithm achieves a fractional error of 36.61 %, outperforming commonly used empirical approaches, which exhibit errors ranging from 38.61 % to 77.08 %. These results indicate that our proposed framework provides a more reliable and physically interpretable solution for high-precision fog visibility retrieval using single-frequency MMCR observations.