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

Li, Xiaojie; Ge, Jinming; Qiu, Yucheng; Lv, Qiaoyi; Song, Wei; Zhang, Jie; Zhang, Chi; Liu, Bochun; Wang, Jiapeng; Xia, Hongwei; Zhu, Yuhang

doi:10.5194/egusphere-2026-1032

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https://doi.org/10.5194/egusphere-2026-1032

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30 Mar 2026

| 30 Mar 2026

Status: this preprint is open for discussion and under review for Atmospheric Measurement Techniques (AMT).

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

Xiaojie Li, Jinming Ge, Yucheng Qiu, Qiaoyi Lv, Wei Song, Jie Zhang, Chi Zhang, Bochun Liu, Jiapeng Wang, Hongwei Xia, and Yuhang Zhu

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.

Received: 24 Feb 2026 – Discussion started: 30 Mar 2026

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Xiaojie Li, Jinming Ge, Yucheng Qiu, Qiaoyi Lv, Wei Song, Jie Zhang, Chi Zhang, Bochun Liu, Jiapeng Wang, Hongwei Xia, and Yuhang Zhu

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CC1:
'Comment on egusphere-2026-1032', Liping Liu, 12 May 2026 reply
This manuscript presents a physically constrained retrieval framework for fog visibility using single-frequency Ka-band millimeter-wave cloud radar observations, addressing the key limitation of traditional radar-based visibility inversion methods’ reliance on empirical parameterizations. The study aligns well with the scope of Atmospheric Measurement Techniques and demonstrates both clear innovation and practical value for fog monitoring in transportation and maritime operations.
However, several issues related to the methodological assumptions, algorithm adaptation for sea fog conditions, and quantitative evaluation of critical data processing steps need to be addressed prior to publication. The following points summarize my concerns and suggestions.
General comments
The theoretical derivation (Eqs. 3–7) assumes that fog droplet size distribution (DSD) follows a lognormal distribution. The authors briefly mention bimodal/multimodal DSD as a limitation for future work in the conclusion, without any assessment of its prevalence or impact on algorithm performance. This may undermine the reliability of the methodology. The authors may need to provide a statistical analysis of the occurrence frequency and characteristics of bimodal/multimodal DSD in the 5-year FM-120 dataset collected at the Data Observation Base, discuss the physical mechanism by which bimodal DSD disrupts the coupling relationships between radar reflectivity (Z), liquid water content (LWC), geometric mean radius (rm), and extinction coefficient (βext), and clearly define the applicability boundary of the proposed algorithm under non-lognormal DSD conditions.

The authors adopt the LWC retrieval algorithm from Ge et al. (2023), which was originally developed for general liquid water clouds. Sea fog exhibits distinct microphysical characteristics compared to clouds, including smaller droplet sizes, lower LWC values, and shallower vertical extents, which may significantly affect algorithm performance. The authors can describe in detail all adaptations made to the original LWC algorithm specifically for sea fog conditions, particularly the 10-bin segmentation method mentioned in Section 3.1.

The authors state that "Doppler and ground clutter suppression techniques are further employed to eliminate ground clutter effects" (Section 2) without details on the specific algorithms used, parameter settings, or effectiveness evaluation. The authors should describe the exact clutter suppression algorithms used and their specific parameter settings.

Minor points and comments
Define all symbols on their first use in the text, including K* and the constant c in Eq. (11).

Improve the discrimination of the legend lines in Figure 7(e) and directly label the fractional error of each retrieval method within the figure.

Add a new table summarizing the basic characteristics of the 10 validation sea fog events, including start/end time, minimum visibility, maximum LWC, and fog type.

Revise the sentence "thereby avoiding purely empirical formulations" in the abstract to "thereby reducing reliance on purely empirical site-specific formulations" for greater accuracy.

Replace "global scale" with "near-global scale" when referring to satellite observations in Section 1, as satellite sensors do not provide complete coverage of the polar regions.

Provide a brief definition of the trust region reflection (TRR) algorithm or add a relevant reference in Section 3.1 for readers unfamiliar with this optimization method.

Revise the overclaim "applies to diverse fog types" in Section 6 to "shows promise for application to diverse fog types, pending further validation" since the method has only been tested on advection sea fog.

Discuss whether the overall fractional error of 36.61% meets the accuracy requirements for operational fog early warning in the transportation and maritime sectors in Section 4.

Explain the criteria used to select the 10 validation sea fog events and provide a clear definition of what constitutes a fog event in this study in Section 5.

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Citation: https://doi.org/10.5194/egusphere-2026-1032-CC1
RC1:
'Comment on egusphere-2026-1032', Anonymous Referee #1, 22 May 2026 reply
Review for egusphere-2026-1032
The authors present a retrieval algorithm for visibility from conventional cloud radars. Visibility is retrieved from deriving Liquid Water Content (LWC) directly, and effective droplet radius rm empirically from Ka-band cloud radar measurements. The retrieval is applied to ten fog cases in Xiang’an (District Xiamen, China). Retrieved visibility results are evaluated with co-located local automated visibility measurements, and compared to retrieved values derived from empirical estimates. The authors claim a reduced fractional error using their method. In addition, a sensitivity analysis is performed, exploring the retrieval's sensitivity to scattering assumptions (Rayleigh vs Mie scattering) and the microphysical parameters LWC and rm. While the manuscript surely addresses a relevant topic, the presented results do not convince me of the feasibility or applicability of the proposed method. I recommend rejecting the manuscript in its current form based on the following long list of substantial concerns.
General comments
the authors base their results on a small sample size of only 10 pre-selected cases, even though a large dataset of 5 years would be available for further analysis. It remains unclear and is not discussed how the retrieval performs in cases, when fog presence is not confirmed by independent measurements, or when clouds or precipitation occur. In both manuscript scopes (methodology validation and ‘proof-of-concept’), a larger, more diverse statistical sample would need to be considered with a more thorough discussion of the limitations of the approach – in which cases does it work well, and when are there large uncertainties?

The authors claim that their novel method “exhibited consistent Vis variation trends” (L271) with “superior stability and smaller retrieval errors compared to the traditional empirical methods” (L294). Yet, based on results illustrated in Figs 7(e) or Fig. 9(a), the correlation between observed and retrieved visibility seems very low (Fig. 9), and variability does not correspond to independent vis-meter measurements (Fig 7). Reasons for mis-matches often seem speculative.

There are a number of methodological limitations to the approach in itself which the authors mention in part:
Deriving LWC from single-frequency radar has high uncertainties as outlined in numerous state-of-the-art publications as the problem of retrieving two moments of the drop-size distribution with one measurement is ill-defined. The authors remain vague how much this uncertainty affects (and inhibits) the accuracy of their visibility retrieval.

The authors introduce numerous empirical formulas throughout the manuscript (e.g., L 183; L 268) without backing up how they were derived, or if state-of-the-art approaches were used. This should be clarified throughout the manuscript.

DSD is assumed to be log-normally distributed (L 114). The measured DSDs could be analyzed in more detail to evaluate this assumption for the presented cases.

The metrics (“fractional error”) that the authors use to evaluate the success of their retrieval is not introduced. It remains unclear how exactly this error is derived from the retrieval.

Specific Comments
L2: more precise information is needed on which conventional techniques the authors refer to here

L7: also see comments above; the authors use the same radar measurement to infer LWC and visibility, thus, the information is not ‘independent’

L 13: also see above; the number of analyzed cases is statistically not high enough to thoroughly validate a novel method.

L 16: I do not think that this statement is supported by the presented analysis and high fractional error of 33.6%.

Line 24: a more original reference should be added here (the authors mention the classical Koschmieder Law, developed in the 1920s (Horvath, 1971) further down in the manuscript.)

Line 36: A sentence should be added that a sensitivity to small hydrometeors is only given if Ze is not dominated by large hydrometeors in the radar volume. The authors need to discuss the additional sources of retrieval uncertainty when larger hydrometeors are present in the observed column (see general comments above).

L 54: unclear which approaches the authors refer to

L 81: information on the radial scanning patterns should be added as it remains unclear whether the radar is in zenith or scan mode.

L 89: variables should be introduced to the equation and units are missing.

L 101: The authors mention that vis-meter and cloud radar do not measure from exactly the same location. This mis-match requires a clear statement (and discussion) that the authors assume that fog microphysical properties at the surface are the same as at 30.2m height (first range).

L 138: should be Eqs 5-7

L 153: Did the authors consider correcting radar Ze for gas attenuation, and, if so, how?

L 154: unclear what is meant by „microphysical coupling“. Z depends on two parameters, N_T and σ. If a relationship of r_m from Z alone is established, more assumptions are used than "lognormal size distribution" alone which would have to stated more clearly and discussed in more depth.

L 166: „physical transformation“ is unclear

L 176: unclear and very general; the authors should illustrate an example to outline the uncertainties originating from their LWC retrieval.

L 183: unclear why a power-law correlation is assumed, and under which conditions this empirical relation was derived – shouldn’t LWC also affect this relation?

L 184: sentence should be split to facilitate readability.

Fig 2: reference missing in the text.

L 188: which effect will this have on the visibility retrieval? Would it lead to an over- or under-estimation of visibililty in low reflectivity conditions?

L 203: It is unclear if the authors interpolated the dsd from fm-120 and then did the integration of the extinction coefficient, or directly used the points of the size bins, which don't seem to sample the extinction efficiency sufficiently, as seen in Fig 4.

L 207: unclear – which parametrization?

Fig 5: I find this 3D figure difficult to read. I suggest to instead use 2d projections of error vs rm and error vs LWC.

L 212: not clear which figure this refers to.

L 217: blind zone has not been introduced before, unclear what the authors refer to.

L 224: Is this derived from the DSD observations?

L 237: More information is needed on how this empirical relation is derived, and how large uncertainties are.

Fig 6: color scale should be centered around 0.

L 268: unclear how this formula was derived.

7: I find it hard to connect visibility time-series with the radar panels. Sub-panel (e) – which distance does the blue-dashed line correspond to?

L 290: Unclear, as previously described that Fig 3 shows large deviations for small Z values.

L 292: This statement needs to be highlighted more precisely in Sec. 4, as it is not evident to me from the presented analyses.

L 306: This is not backed up by the analysis as it was previously mentioned that temporal variability is dampened in the retrieval (L 272), and spatial variations of fog visibility were not evaluated by independent measurements.

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Citation: https://doi.org/10.5194/egusphere-2026-1032-RC1

Xiaojie Li, Jinming Ge, Yucheng Qiu, Qiaoyi Lv, Wei Song, Jie Zhang, Chi Zhang, Bochun Liu, Jiapeng Wang, Hongwei Xia, and Yuhang Zhu

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Short summary

Fog sharply reduces visibility and threatens shipping, traffic and aviation. Traditional visibility measurements perform poorly in dense fog. We developed a new method to estimate fog visibility using millimeter-wave cloud radar based on physical fog properties, not empirical formulas. Tests on ten real sea fog events show our method is more accurate and stable. It provides reliable fog monitoring, improves safety, and supports better fog forecasting and early warning for coastal areas.


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