the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 30 Mar 2026
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.
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Status: final response (author comments only)
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CC1: 'Comment on egusphere-2026-1032', Liping Liu, 12 May 2026
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AC3: 'Reply on CC1', Jinming Ge, 02 Aug 2026
We sincerely thank Dr. Liping Liu for the thorough and constructive community comment. These suggestions have substantially improved the clarity, rigor, and presentation of our manuscript. Below we address each point in detail. Reviewer comments are shown in italic and our responses in bold.
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AC4: 'Reply on CC1', Jinming Ge, 02 Aug 2026
We sincerely thank Dr. Liping Liu for the thorough and constructive community comment. These suggestions have substantially improved the clarity, rigor, and presentation of our manuscript. Below we address each point in detail. Reviewer comments are shown in italic and our responses in bold.
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AC3: 'Reply on CC1', Jinming Ge, 02 Aug 2026
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RC1: 'Comment on egusphere-2026-1032', Anonymous Referee #1, 22 May 2026
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.
Citation: https://doi.org/10.5194/egusphere-2026-1032-RC1 -
AC1: 'Reply on RC1', Jinming Ge, 02 Aug 2026
We sincerely thank the reviewers’ careful and constructive evaluation of our manuscript. Although the manuscript was not accepted in the previous round, we have carefully considered all the comments, conducted additional analyses, and provided further clarifications to address the raised concerns and strengthen the scientific rigor of our study. Yes, single reflectivity measurement cannot uniquely determine fog properties, especially the DSD and radius, which we had stated in the revised version. However, the fundamental premise of our approach is that accurate retrieval of Liquid Water Content (LWC) through the mass absorption method provides the physical basis for estimating fog extinction. Since LWC primarily determines the extinction capacity of fog, it serves as the key variable controlling visibility reduction. The optical depth is subsequently derived by incorporating the assumed droplet size distribution, particularly the effective droplet radius, which enables the final estimation of visibility. In the revised version, we clarify that the FM-120 measurements are used as upstream, sample-internal development evidence rather than independent validation data. Specifically, the radius parameter is estimated based on a relationship established from pseudo-targets, rather than from directly observed independent measurements. Accordingly, all diagnostics derived from the same samples are explicitly labeled as sample-internal development assessments. We have also modified the manuscript to limit the interpretation of the ten 2025 fog events to evaluating local consistency and physical plausibility of the retrieved properties, rather than independent validation of retrieval performance. The Conclusion section has been further strengthened by explicitly acknowledging the need for future evaluation using held-out events, diverse fog regimes, stricter temporal and spatial collocation strategies, and improved treatment of drizzle contamination and deviations from the assumed lognormal droplet size distribution.
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EC1: 'Comment on egusphere-2026-1032', Chao Liu, 02 Jun 2026
As we can see from the discussion session, really constructive community comments were posted by an expert. After reviewing the CC posted, the comments are well qualified to be considered as referee comments, and the manuscript can be processed for the next step.
Citation: https://doi.org/10.5194/egusphere-2026-1032-EC1 -
AC2: 'Reply on EC1', Jinming Ge, 02 Aug 2026
Thank you very much for overseeing the review of our manuscript and for the constructive feedback from the expert referee. We have carefully considered all the comments, which have substantially improved the clarity, rigor, and presentation of our work. We greatly appreciate the time and effort devoted to this detailed assessment. We hope the revised version now meets the standards for publication in Atmospheric Measurement Techniques and look forward to the next steps in the editorial process.
Citation: https://doi.org/10.5194/egusphere-2026-1032-AC2
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AC2: 'Reply on EC1', Jinming Ge, 02 Aug 2026
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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
Minor points and comments