the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 20 May 2026
Assessing retrieval biases in ship tracks
Abstract. Ship tracks, bright lines in clouds formed by ship exhaust, serve as "natural laboratories" for investigating aerosol-cloud interactions, one of the largest sources of uncertainty in the human forcing of the climate. Observing ship tracks has been used to help constrain the effect of anthropogenic aerosols on cloud brightness, amount and water content. The validity of these constraints relies, in part, on the accuracy of satellite retrieval algorithms used to measure cloud properties. A known source of uncertainty in these algorithms is the representation of the droplet size distribution. Standard bi-spectral retrievals (e.g. MODIS) rely on a fixed effective variance (veff) for the modified gamma distribution used to model cloud droplet dispersion. The introduction of aerosols into clean, marine clouds produces not only smaller droplets but also a narrower size distribution, contradicting this fixed assumption. This study utilises a synthetic retrieval experiment to quantify the impact of this assumption on cloud property retrievals and the derived aerosol-cloud interaction metrics. The results produced indicate that neglecting the narrowing of the droplet size distribution causes a systemic overestimation of effective radius (re) of approximately 3% in the polluted regime, while optical depth (τ) is virtually unaffected. Consequently, liquid water path (LWP) is robustly retrieved with a small bias of under 3%, which is expected due to the linear dependence of LWP on re and τ. Cloud droplet number concentration (Nd), however, suffers from a much larger overestimation of approximately 24% in freshly polluted clouds. This discrepancy is driven by the inverse dependence of Nd on the spectral width parameter k, inflating the droplet count as the true distribution narrows. This inflation of droplet number in ship tracks may exaggerate the apparent susceptibility of clouds to aerosols, potentially overstating the Twomey effect in observation-based estimates reliant on data from ship tracks. This may also lead to an overestimation the efficacy of climate intervention efforts, such as marine cloud brightening, if monitored by satellite.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(2549 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2026-2326', Anonymous Referee #3, 10 Jun 2026
- AC1: 'Reply on RC1 & RC2', Iarla Boyce, 27 Jul 2026
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RC2: 'Comment on egusphere-2026-2326', Michael Diamond, 12 Jun 2026
In this manuscript, the authors use RT calculations to explore how a hypothesized connection between effective variance and cloud droplet number concentration (Nd) can bias satellite retrievals and potentially produce misleading results about the strength of aerosol-cloud interactions (ACI). The topic is excellent and the work worthwhile. There is some very critical literature missing, however, which I think may require major revisions to incorporate. The tone also strikes me as simultaneous overconfident (in the existence of a strong, causal k-Nd linkage) and overly narrow (this would matter for all ACI studies, not just ship tracks). I expect the work to be fit for publication in AMT following adequate revisions. -Michael Diamond
General comments:
A. Critical missing literature: Lebsock & Witte (2023), in Atmospheric Chemistry and Physics, have an extensive discussion of the relationship between effective variance (via k) and Nd and propose their own correction to the adiabatic Nd calculation from effective radius (re) and cloud optical thickness retrievals. This should be discussed given the relevance to the present work; I’m very interested in knowing whether the proposed corrections based on in-situ aircraft data would substantially moderate the potential biases found in the present work.
Lebsock, M. D. and Witte, M.: Quantifying the dependence of drop spectrum width on cloud drop number concentration for cloud remote sensing, Atmos. Chem. Phys., 23, 14293–14305, https://doi.org/10.5194/acp-23-14293-2023, 2023.
B. Overly strong language: Although Lebsock & Witte (2023) do find a (noisy) relationship between k and Nd as discussed above, more conditional language about the nature of the k-Nd may be more appropriate. *If* the relationship is strong and causal (and instantaneous), then the current results about biases hold. If the real relationship is substantially weaker, however, the bias may be much less important. I’ve personally been surprised by how weak the relationship between k and Nd seems to be based on aircraft data (for example, I did a quick k, Nd correlation on ORACLES low cloud data and get values of r < 0.1, albeit with high statistical significance).
C. Generality: The authors repeatedly invoke ship tracks, but their argument applies seemingly with equal force to all studies of ACI.
Specific comments:
- Line 26: Is “obscured” the right word here? I understand you’re referring to physical adjustments that offset the Twomey effect, not factors that interfere with its reliable quantification (e.g., swelling of aerosol near cloud edges).
- Line 28: Khadri et al. (2022) is a surprising citation here; are the authors confident that paper supports this claim?
- Line 53: Do you have support for the tight relationship between Nd and k from more modern sources than Martin et al. (1994)? I’m aware of some good work out of the cloud chamber field, but in my experience this relationship has not turned up so cleanly in recent aircraft observations. That said, Lebsock & Witte (2023) are still able to derive a physically plausible relationship, as discussed above.
- Line 77-78: Citations would again be useful here.
- Equations 5 and 6: There are inconsistent physical assumptions between these equations in terms of how LWC and re vary with height above cloud base. I’d recommend sticking with the adiabatic assumptions in Grosvenor et al. (2018) given the paper’s focus.
- Line 145: I’m not sure how the results in Fu et al. (2022) support this statement.
- Lines 223-224: In the latest IPCC report, the ERFaci estimate from observations and models are very similar.
Forster, P. M., T. Storelvmo, K. Armour, W. Collins, J.-L. Dufresne, D. Frame, D.J. Lunt, T. Mauritsen, M.D. Palmer, M. Watanabe, M. Wild, and Zhang, H.: The Earth’s Energy Budget, Climate Feedbacks, and Climate Sensitivity, in: Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 923–1054, 2021. - Lines 285-288: Given the existence of Lebsock & Witte (2023), would this recommendation change to simply adopting their correction? Or is further work required?
- References (and related in-text citations): “Stevenson et al. (2012)” should be Latham et al. (2012).
Citation: https://doi.org/10.5194/egusphere-2026-2326-RC2 - AC1: 'Reply on RC1 & RC2', Iarla Boyce, 27 Jul 2026
Peer review completion
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2026-2326', Anonymous Referee #3, 10 Jun 2026
This manuscript examines how the fixed effective-variance assumption in bi-spectral cloud retrievals may bias ship-track cloud properties. The question is scientifically relevant because ship tracks are often used to infer aerosol-cloud interactions and cloud susceptibility. The manuscript has a useful central idea: a synthetic retrieval experiment can isolate the effect of droplet-size-distribution narrowing on retrieved re, tau, LWP, and Nd.
However, the current manuscript is not yet sufficiently convincing. The analysis remains highly idealized, the main sensitivity choices are not adequately justified, and the interpretation extends too far beyond what the experiment demonstrates. In particular, the results are framed as relevant to MODIS ship-track studies and marine cloud brightening, but the retrieval setup does not closely reproduce operational satellite products or real ship-track cloud variability. Substantial revision is needed to make the conclusions proportionate to the evidence.
- The title may not accurately reflect the main scope of the study. Although ship tracks are an important and typical application, the core issue examined here is the retrieval bias introduced by assuming a fixed droplet effective variance. The current title, "Assessing retrieval biases in ship tracks", may imply a broader evaluation of ship-track retrieval uncertainties than the manuscript actually provides. The authors may consider revising the title to emphasize the effective-variance assumption, with ship tracks framed as the motivating or application case.
- The practical significance of the reported bias should be evaluated relative to other uncertainty sources. The manuscript emphasizes an approximately 3% positive bias in retrieved effective radius for polluted cases, which is useful to quantify. However, it remains unclear whether this bias is large or small compared with uncertainties from other retrieval variables and assumptions, such as cloud optical depth, viewing geometry, cloud heterogeneity, partly cloudy pixels, cloud vertical structure, liquid water path assumptions, and the adiabatic Nd formulation. The authors could compare the fixed-veff-induced bias with other known uncertainty terms, or at least discuss whether the 3% re bias and the propagated Nd bias are likely to dominate over, or be secondary to, these other sources in realistic ship-track analyses. In this context, product intercomparison studies of satellite cloud retrievals may provide a useful reference for framing retrieval uncertainty; for example, Lai et al. (2019, https://doi.org/10.3390/rs11141703) discussed differences among satellite cloud optical thickness and cloud effective radius products.
- The use of veff = 0.13 as the primary retrieval assumption is a major weakness. The manuscript acknowledges that MODIS Collection 6 uses veff = 0.10 for liquid clouds, yet most of the analysis and headline conclusions are based on 0.13. This makes the reported bias closer to an upper-bound historical case than to the current operational situation. Results for veff = 0.10 should be presented as a central case in the main text, with veff = 0.13 retained only as a sensitivity or legacy comparison.
- The polluted-cloud value veff = 0.05 is treated as representative of a strongly narrowed ship-track droplet distribution, but the manuscript does not demonstrate that this value is typical for the cases to which the conclusions are applied. A sensitivity analysis over a realistic range of polluted veff values is needed. At minimum, the authors should show how re, LWP, and Nd biases change for veff values such as 0.05, 0.07, 0.10, and perhaps intermediate values representing aging ship tracks.
- The retrieval experiment does not sufficiently mimic an operational MODIS retrieval. Operational products involve exact spectral response functions, multiple absorbing bands, cloud-mask and partly cloudy pixel screening, multilayer flags, retrieval failure logic, uncertainty estimates, and quality filtering. The current Nakajima-King-style inversion is useful pedagogically, but the manuscript repeatedly interprets the results as if they directly diagnose standard satellite products. The authors should either implement a more realistic operational-like retrieval workflow or clearly state that the results are a simplified sensitivity experiment rather than a product-level bias estimate.
- The derived Nd bias depends not only on re and veff but also on assumptions in the adiabatic Nd formulation, including cloud geometric thickness, adiabaticity, vertical structure, and the spectral width parameter k. The manuscript fixes cloud thickness at 500 m and imposes LWP conservation, but real marine boundary-layer clouds and ship tracks vary substantially. Please test the sensitivity of Nd bias to cloud thickness, adiabaticity, LWP, and optical-depth ranges, or discuss why the current fixed assumptions are adequate.
- The very large Nd outliers exceeding 1200% require much more careful treatment. These cases may reflect numerical instability, LUT-edge interpolation issues, unrealistic geometry-cloud combinations, or known failure modes that would be removed by standard quality control. Please report the frequency of such cases, whether they pass realistic retrieval filters, and provide statistics both with and without them. The current use of these outliers contributes to a heavy-tailed uncertainty that may not be meaningful for practical ship-track analyses.
- The implications for aerosol-cloud susceptibility and marine cloud brightening are overstated. The manuscript's synthetic experiment isolates one retrieval-assumption bias, but MCB efficacy and observed susceptibility depend on emissions, meteorology, cloud adjustments, precipitation, entrainment, and measurement strategy. The discussion should be rewritten to present MCB relevance as a possible implication rather than a conclusion supported by this analysis.
- The manuscript needs some connection to real observations. This does not necessarily require a full observational analysis, but the authors should at least compare their assumed veff values and bias magnitudes with published aircraft, in situ, or satellite-based ship-track studies. Without this comparison, readers cannot assess whether the synthetic scenarios represent common ship-track conditions or only an extreme bounding case.
- The paper would benefit from a clearer statement of novelty. The fact that droplet dispersion affects retrieved re and Nd is already known in the aerosol-cloud and retrieval literature. The authors should more explicitly identify what is new here: the ship-track-specific quantification, the bias propagation to susceptibility metrics, the geometry dependence, or the implication for MCB monitoring. This clarification is important because the current framing sometimes presents a known retrieval assumption as if it were newly identified.
- Please check grammar and wording throughout, including phrases such as 'lead to to', 'overestimation the efficacy', 'cam become unstable', and 'maxmimising'.
- The abstract reports re overestimation of approximately 3%, while later values include 3.43% and 3.31%. Please harmonize the numbers or explain the different averaging choices.
- Please provide the LUT grid spacing, interpolation method, and treatment of retrievals near LUT boundaries similar to Liu et al. (https://doi.org/10.1016/j.aosl.2023.100337).
- Figure captions should state whether statistics include all geometries, filtered geometries, or outlier-contaminated cases.
- Please include a concise limitations subsection before the conclusion. This should explicitly list the idealized 1D, homogeneous, LWP-conserving, fixed-veff, and fixed-cloud-thickness assumptions.
Citation: https://doi.org/10.5194/egusphere-2026-2326-RC1 - AC1: 'Reply on RC1 & RC2', Iarla Boyce, 27 Jul 2026
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RC2: 'Comment on egusphere-2026-2326', Michael Diamond, 12 Jun 2026
In this manuscript, the authors use RT calculations to explore how a hypothesized connection between effective variance and cloud droplet number concentration (Nd) can bias satellite retrievals and potentially produce misleading results about the strength of aerosol-cloud interactions (ACI). The topic is excellent and the work worthwhile. There is some very critical literature missing, however, which I think may require major revisions to incorporate. The tone also strikes me as simultaneous overconfident (in the existence of a strong, causal k-Nd linkage) and overly narrow (this would matter for all ACI studies, not just ship tracks). I expect the work to be fit for publication in AMT following adequate revisions. -Michael Diamond
General comments:
A. Critical missing literature: Lebsock & Witte (2023), in Atmospheric Chemistry and Physics, have an extensive discussion of the relationship between effective variance (via k) and Nd and propose their own correction to the adiabatic Nd calculation from effective radius (re) and cloud optical thickness retrievals. This should be discussed given the relevance to the present work; I’m very interested in knowing whether the proposed corrections based on in-situ aircraft data would substantially moderate the potential biases found in the present work.
Lebsock, M. D. and Witte, M.: Quantifying the dependence of drop spectrum width on cloud drop number concentration for cloud remote sensing, Atmos. Chem. Phys., 23, 14293–14305, https://doi.org/10.5194/acp-23-14293-2023, 2023.
B. Overly strong language: Although Lebsock & Witte (2023) do find a (noisy) relationship between k and Nd as discussed above, more conditional language about the nature of the k-Nd may be more appropriate. *If* the relationship is strong and causal (and instantaneous), then the current results about biases hold. If the real relationship is substantially weaker, however, the bias may be much less important. I’ve personally been surprised by how weak the relationship between k and Nd seems to be based on aircraft data (for example, I did a quick k, Nd correlation on ORACLES low cloud data and get values of r < 0.1, albeit with high statistical significance).
C. Generality: The authors repeatedly invoke ship tracks, but their argument applies seemingly with equal force to all studies of ACI.
Specific comments:
- Line 26: Is “obscured” the right word here? I understand you’re referring to physical adjustments that offset the Twomey effect, not factors that interfere with its reliable quantification (e.g., swelling of aerosol near cloud edges).
- Line 28: Khadri et al. (2022) is a surprising citation here; are the authors confident that paper supports this claim?
- Line 53: Do you have support for the tight relationship between Nd and k from more modern sources than Martin et al. (1994)? I’m aware of some good work out of the cloud chamber field, but in my experience this relationship has not turned up so cleanly in recent aircraft observations. That said, Lebsock & Witte (2023) are still able to derive a physically plausible relationship, as discussed above.
- Line 77-78: Citations would again be useful here.
- Equations 5 and 6: There are inconsistent physical assumptions between these equations in terms of how LWC and re vary with height above cloud base. I’d recommend sticking with the adiabatic assumptions in Grosvenor et al. (2018) given the paper’s focus.
- Line 145: I’m not sure how the results in Fu et al. (2022) support this statement.
- Lines 223-224: In the latest IPCC report, the ERFaci estimate from observations and models are very similar.
Forster, P. M., T. Storelvmo, K. Armour, W. Collins, J.-L. Dufresne, D. Frame, D.J. Lunt, T. Mauritsen, M.D. Palmer, M. Watanabe, M. Wild, and Zhang, H.: The Earth’s Energy Budget, Climate Feedbacks, and Climate Sensitivity, in: Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 923–1054, 2021. - Lines 285-288: Given the existence of Lebsock & Witte (2023), would this recommendation change to simply adopting their correction? Or is further work required?
- References (and related in-text citations): “Stevenson et al. (2012)” should be Latham et al. (2012).
Citation: https://doi.org/10.5194/egusphere-2026-2326-RC2 - AC1: 'Reply on RC1 & RC2', Iarla Boyce, 27 Jul 2026
Peer review completion
Journal article(s) based on this preprint
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Alice Cicirello
Edward Gryspeerdt
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(2549 KB) - Metadata XML
This manuscript examines how the fixed effective-variance assumption in bi-spectral cloud retrievals may bias ship-track cloud properties. The question is scientifically relevant because ship tracks are often used to infer aerosol-cloud interactions and cloud susceptibility. The manuscript has a useful central idea: a synthetic retrieval experiment can isolate the effect of droplet-size-distribution narrowing on retrieved re, tau, LWP, and Nd.
However, the current manuscript is not yet sufficiently convincing. The analysis remains highly idealized, the main sensitivity choices are not adequately justified, and the interpretation extends too far beyond what the experiment demonstrates. In particular, the results are framed as relevant to MODIS ship-track studies and marine cloud brightening, but the retrieval setup does not closely reproduce operational satellite products or real ship-track cloud variability. Substantial revision is needed to make the conclusions proportionate to the evidence.