Fog can reduce horizontal visibility below 1 km and create substantial hazards for transportation, aviation, port operations and maritime traffic. Yet monitoring its three-dimensional structure remains difficult. Ground instruments such as optical visibility meters and fog droplet spectrometers can provide accurate point measurements, but they do not map the horizontal or vertical distribution of fog. Active laser instruments can profile the atmosphere, although their signals may be severely attenuated in dense fog. Passive satellite imagers offer broad coverage but have limited vertical resolution and can struggle to distinguish fog from low cloud. Millimeter-wave cloud radar can penetrate fog, detect small hydrometeors and provide fine spatial and temporal resolution, making it a promising tool for resolving fog structure.

The research was conducted at the Datan Observation Base in Xiang’an District, Xiamen, using a YLUKA2 solid-state Ka-band dual-polarization cloud radar, a DNQ3 forward-scattering visibility meter and an FM-120 fog droplet spectrometer. The radar operated at 34.50–35.50 GHz, with a nominal spatial resolution of 30 m and a maximum detection range of 30 km. Its antenna was installed about 25 m above ground, and it performed continuous sector scans between 60 and 300 degrees at a 2-degree elevation angle. Clear-sky observations were used to characterize and subtract ground clutter, although residual contamination remained a limitation for near-range retrievals. The DNQ3, positioned approximately 153 m from the radar along a 150-degree azimuth, measured near-surface visibility using infrared pulses with a central wavelength of 0.87 micrometers.

The FM-120 supplied the droplet observations needed to constrain the retrieval. From 2019 through 2023, it measured droplets from 2 to 50 micrometers in 30 non-equidistant size bins at 1 Hz. After quality control, the development dataset contained 236,037 contributing one-second records aggregated into 4,234 valid one-minute spectra from 28 fog events. Each spectrum was classified as narrow unimodal, broad unimodal, shoulder, bimodal or uncertain. Shoulder spectra formed the largest group at 41.83%, followed by broad-unimodal spectra at 33.54%. Bimodal spectra accounted for 6.38% overall, but their prevalence increased as visibility declined: they represented 4.22% in dense fog with visibility of 200–500 m and 24.07% in very dense fog with visibility of 100–200 m. The 50–100 m interval had an estimated bimodal fraction of 35.90%, but only three events contributed to that interval, so the authors did not use it for robust quantitative inference.

These changing droplet-size distributions demonstrated why a single radar reflectivity value cannot be converted directly and uniquely into visibility. For fog droplets observed in the millimeter-wave band, radar reflectivity is proportional to the sixth moment of the droplet-size distribution, while visible-light extinction depends on the second moment and the size-dependent Mie extinction efficiency. Liquid water content is related to the third moment, and effective radius combines the second and third moments. Mathematical moment relations can connect reflectivity, liquid water content and radius, but they cannot determine both liquid water content and geometric median radius from a single-frequency measurement because droplet number concentration and distribution width remain unknown. The authors addressed this non-uniqueness with two observation-calibrated steps: a segment-wise mass-absorption method for liquid water content and attenuation correction, followed by an extinction-oriented power law relating geometric median radius to linear reflectivity.

For the liquid-water stage, the researchers adapted a self-consistent radiative-transfer algorithm in which one-way attenuation from fog water is proportional to liquid water content. A bounded reflective trust-region least-squares solver searched for parameters that reconstructed measured reflectivity while accounting for accumulated liquid-water attenuation. Because liquid water path can vary markedly within a fog profile, profiles were divided into independently fitted segments, generally spanning four to 10 range gates. Different starting vectors were used depending on whether the maximum reflectivity in a segment was above or below −15 dBZ. Once liquid water content had been retrieved, the accumulated attenuation could be used to correct the measured reflectivity. This stage required no auxiliary in-situ liquid-water measurement, but the study did not have independent reference measurements with which to validate that intermediate retrieval.

The radius stage was designed to reduce extinction errors that could arise from a conventional radius–reflectivity fit. For every FM-120 development row, the researchers searched candidate geometric median radii from 1.00 to 20 micrometers in increments of 0.01 micrometer. Each candidate was inserted into a moment-closure equation to find the radius whose predicted extinction most closely matched the same row’s size-dependent Mie extinction. These extinction-matching values were pseudo-targets derived from reflectivity, liquid water content and the same-source droplet spectrum, not independent observations of geometric median radius. An unweighted least-squares fit to the pseudo-targets yielded the selected power-law relation. On the development dataset, this relation had a mean absolute fractional extinction error of 9.37%, compared with 10.88% for a direct radius relation. The largest improvement occurred between −15 and 0 dBZ, where the error decreased from 12.25% to 4.96%.

Two structural assumptions limited the method. First, it approximated the extinction efficiency of visible light at 550 nm as a constant value of 2, the large-droplet asymptote rather than an exact representation across the small-droplet range sampled by the FM-120. This created a weak-reflectivity bias because predicted radii in cases below −40 dBZ were predominantly under 5 micrometers, where the actual Mie efficiency differs more strongly from 2. In that interval, the closed-form extinction was lower than the same-source FM-120 reference, with a mean signed residual of −25.32%. Because visibility is inversely proportional to extinction, this pattern tended to produce visibility overestimation. Second, the single-lognormal closure became less exact as droplet distributions became more complex, particularly below 200 m visibility. Calibrating the radius relation against extinction rather than radius absorbed part of this distribution-shape error, but it could not eliminate it.

Sensitivity calculations further showed that liquid water content exerts more influence on retrieved extinction than the estimated median radius. In the retrieval equation, a 10% increase in liquid water content raises extinction by 8.1%, whereas a 10% increase in radius lowers it by 4.1%. When both parameters were varied over multipliers from 0.50 to 2.00, the calculated relative extinction response ranged from −67.7% to +209.4%. Radius and liquid-water errors can partly compensate because the variables enter with opposite exponents. Drizzle presents a separate weakness: droplets larger than 100 micrometers can strongly raise radar reflectivity while contributing comparatively little to the median radius inferred from an FM-120 dataset limited to 50-micrometer droplets. The resulting retrieval error depends on competing effects between the mass-absorption liquid-water estimate and the radius closure, and the study did not quantify that trade-off with dedicated drizzle observations.

In a case on 2 March 2025, warm, humid southerly flow produced an advection sea fog that developed rapidly after 18:00 local standard time and reached maximum intensity around 21:00. Fog returns extended to approximately 10 km, the fog top exceeded 350 m and peak reflectivity approached 0 dBZ. At 20:29, the highest-reflectivity regions were concentrated south and southwest of the observation site, where the underlying topography and man-made structures could promote turbulence and droplet coalescence. Across 10 selected events in which DNQ3 visibility stayed below 1 km for at least 30 minutes without other precipitation, the new retrieval had a mean absolute error of 0.092 km and a relative error of 42.86%. A local FM-120 relation produced errors of 0.123 km and 50.53%, the Liu et al. relation produced 0.160 km and 85.30%, and the Gultepe et al. relation departed most strongly, with 0.533 km and 310.63%.

Those error statistics do not establish a definitive ranking of the methods. The radar sampled a volume at an altitude of roughly 30 m over the ground at the matched range, whereas the DNQ3 measured visibility about 1.5 m above ground. The instruments also relied on different scattering principles, and droplet sedimentation could improve near-surface visibility without producing a comparable change in the radar sample. DNQ3 observations helped select the events and identify the radar gate whose temporal pattern most closely matched the meter, making this a conditioned comparison of reasonable ranges and local consistency. The samples were also limited to spring warm fog at one southeastern coastal site; radiation fog, orographic fog and other climate regions were not tested. Independent in-situ liquid-water measurements, standardized hydrometeor phase observations, more completely collocated validation, dual-wavelength radar and measurements across more fog regimes were identified as necessary next steps.

Subject of Research: Physically constrained coastal fog visibility retrieval from single-frequency Ka-band cloud radar observations

Article Title: Physically constrained retrieval of fog visibility from millimeter-wavelength cloud radar observations

Article References: Li, X., Ge, J., Qiu, Y., Lv, Q., Song, W., Zhang, J., Zhang, C., Liu, B., Wang, J., Xia, H., & Zhu, Y. (2026). Physically constrained retrieval of fog visibility from millimeter-wavelength cloud radar observations. Atmospheric Measurement Techniques, 19(20), 6607-6623. https://doi.org/10.5194/amt-19-6607-2026

Image Credits: AI Generated

DOI: 10.5194/amt-19-6607-2026

Keywords: coastal fog, visibility retrieval, Ka-band radar, millimeter-wave radar, droplet size distribution, liquid water content, light extinction, remote sensing, fog microphysics, weather monitoring, Physically, constrained