Physically 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 quantitative monitoring remains challenging because conventional ground-based instruments provide spatially limited point observations and cannot resolve three-dimensional fog structure, while passive satellite retrievals have insufficient vertical resolution and difficulty separating fog from low cloud. Millimeter-wavelength cloud radar (MMCR) can penetrate fog and provide fine spatiotemporal resolution, but many radar Vis retrievals rely on empirical reflectivity–visibility relations. This study develops a physically constrained, observation-calibrated single-wavelength Ka-band MMCR retrieval that links reflectivity, liquid water content (LWC), geometric median radius, extinction, and Vis through lognormal droplet-size-distribution moments. A segment-wise mass-absorption LWC power law and an extinction-oriented radius power law are fitted to same-source FM-120 extinction-matching pseudo-targets, achieving a mean absolute fractional extinction error of 9.37 % on the development dataset. In ten spring-2025 DNQ3-conditioned cases, the present retrieval attains a mean absolute error of 0.092 km, while the local FM-120 and Liu et al. (2019) relations yield broadly comparable ranges and the Gultepe et al. (2009) relation departs more strongly. This method improves the physical self-consistency of single-band MMCR fog Vis retrieval without requiring auxiliary in-situ observations and provides technical support for three-dimensional coastal fog monitoring and traffic meteorological early warning.