the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Mar 2026
Investigation of supercooled water droplet sticking efficiency during power transmission line icing using digital holography
Abstract. Transmission line icing severely threatens the safety of the power grid. Accurate prediction of the sticking efficiency (the proportion of supercooled droplets that remain on the conductor after impact, excluding bouncing and splashing) is critical for preventing and mitigating icing disasters. Traditional prediction models for sticking efficiency typically exhibit significant errors under complex conditions (e.g. varying wind speeds and precipitation intensities), thereby limiting their practical applications. To overcome this drawback, a multi-stage coupled model based on coaxial digital holography was proposed, in which supercooled droplet diameters, velocities, and collision angles were precisely measured. These measurements were integrated into a multi-stage framework that couples droplet impact dynamics and thermodynamics to compute the sticking efficiency, thereby overcoming the accuracy limitations of existing models in complex environments. Experimental results show that the new model’s prediction errors remain below 3.5 % across a range of conditions, which is a significant improvement over traditional models, underscoring its enormous potential in engineering applications.
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Status: open (until 22 Apr 2026)
- RC1: 'Comment on egusphere-2026-800', Anonymous Referee #2, 07 Apr 2026 reply
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RC2: 'Comment on egusphere-2026-800', Anonymous Referee #1, 08 Apr 2026
reply
This manuscript presents a laboratory and modeling study of the sticking efficiency of supercooled droplets on transmission lines, combining digital holography measurements with a prediction model. The topic is important and has both scientific value and clear engineering relevance. The experimental approach is generally well designed, and the use of digital holography to retrieve droplet size, velocity, and collision angle is technically sound. Overall, the study fits well within the scope of Atmospheric Measurement Techniques.
However, in its current form, the manuscript reads incomplete in several key parts. The description of the results is often too brief, and the discussion lacks sufficient depth. In particular, Sections 3 and 4 appear underdeveloped and do not fully support the main conclusions. I therefore recommend publication only after substantial revision.
Major Comments:
- The main concern is that the core results are not analyzed in sufficient detail. Section 3 mainly describes the experimental setup and selected example cases, but does not provide a systematic analysis of the measured droplet properties. Section 4 focuses on model development and validation, but the discussion remains largely descriptive. The relationships between key variables (e.g., droplet size, velocity, and collision angle) and sticking efficiency are shown in figures, but the physical interpretation is limited. In addition, the comparison with existing models lacks depth. The manuscript would benefit from a clearer explanation of why the observed trends occur and how they relate to existing theories and models.
- The proposed model consists of a dynamic phase and a thermal phase. While the formulation is generally clear, the definitions of key parameters, the citations of appropriate references, and the physical interpretation need further clarification. Several modified or fitted parameters (e.g., the modified critical Weber number) are introduced, but the underlying assumptions and their physical meaning are not sufficiently justified. These aspects should be explained more clearly.
- The manuscript reports that the prediction error is within 3.5% under various conditions. This is a strong claim. However, there is no clear description of uncertainty sources in either the measurements or the model. Moreover, uncertainties in droplet size, velocity retrieval from holography, and experimental repeatability are not quantified. A proper uncertainty analysis and robustness assessment are needed to support the reported model performance.
- Several parts of the manuscript require substantial revision in terms of clarity, structure, and formatting. In the Introduction, the presentation lacks clarity and logical flow. The background section mainly consists of a list of references without sufficient synthesis or discussion. More importantly, the key concept of sticking efficiency, which is central to the manuscript, is not clearly introduced or defined. The relationship and distinction between sticking efficiency and collection efficiency should be explicitly clarified. In addition, many references are missing where they are needed, and some citations are not formatted properly (e.g., “Jiang et al.” in Line 31). There are numerous similar issues throughout the manuscript, and a thorough check is required.
Specific comments:
- The manuscript refers to the proposed framework as a “multi-stage coupled model”, while it is consistently described and implemented as a two-stage model (dynamic and thermal phases). The use of “multi-stage” is potentially misleading and should be corrected throughout the manuscript.
- Graphical abstract (left panel): The meaning of the icons (e.g., histogram icon, arrow icon) inside the text boxes is unclear. They resemble prompt-style elements rather than scientific annotations. The arrows on both sides of the text boxes are also not clearly explained.
- Graphical abstract (right panel): It would be more effective to redesign this panel based on the experimental figures (e.g., Figs. 5-7) to better reflect the content of the study.
- Lines 68-70: Important parameters should be supported by appropriate references when they are defined and introduced. Similar issues occur elsewhere in the manuscript.
- Lines 72, 89, 104: “Where…” should not be capitalized, as it follows a comma.
- Line 139: At least five repeated experiments are mentioned, but only representative data are shown. The reproducibility of these experiments is not discussed. The uncertainty and representativeness of the selected results should be clarified.
- Figure captions: All figure captions require further clarification. They currently show trends but lack sufficient detail about the experimental conditions.
- Lines 146-150: The criteria used to evaluate the validity, reliability, and uncertainty of the measured and reconstructed results are not clearly described. It is also unclear why only one example (Fig. 4) is presented.
- Fig. 5: Please add panel labels for the right panel.
- Figs. 5-7: Please include uncertainty ranges or confidential intervals for the sticking efficiency under different experimental conditions.
Citation: https://doi.org/10.5194/egusphere-2026-800-RC2
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The manuscript presents a study of the sticking efficiency of supercooled droplets on power lines to assess icing severity. It couples dynamic aspects of droplet impact, such as velocity and collision angle, with thermal processes governing the freezing of droplets. The experimental approach employs digital in-line holography, enabling the retrieval of three-dimensional droplet properties. The topic is relevant, and the combination of detailed droplet measurements with a coupled dynamic-thermodynamic model is promising and potentially useful for improving icing predictions.
However, several aspects require clarification. In particular, key definitions are not always clearly introduced, and the derivation, interpretation, and validation of the reported model requires more clarification.
General comments:
I know that particularly the propagation can be very challenging or impossible. However, at minimum, it would be great to visualize how the fit parameters in Eq. (8) were obtained by showing the underlying dataset together with the fitted curve to get an idea on the data spread. It then can including uncertainty estimates (e.g. confidence intervals or covariance information).
It is further unclear if the three other models were applied in their respective parameter range and what the input parameters have not been described.
In the validation against real world icing the derivation of the true sticking efficiency “ηtrue” is said to be measured (line 243). How is this value measured? This is a critical point as the main claim of the paper being accurate below 3.5% relies on it. In Figures 9 to 11 it would be great to not only show the errors but also the real values for each case. Further, please state which kind of error is shown here.
Minor comments:
Technical corrections: