Aerosol-cloud interactions (ACI) continuously consist one of the largest uncertainties in climate radiative forcing and projections. This study combines a large ensemble of satellite observations, reanalysis meteorology, shipping data and a trajectory model to extensively use natural experiments, aims to develop understanding of the impact of non-linearity nature of clouds on ACI effect derived from ship tracks. Ship tracks are widely used in previous studies for decades to understand ACI, because its excellence in ruling out the confounding factors of metrological co-variability, however an assumption of linear gradients of cloud properties was made. This study uncovers a systematic bias caused by this assumption, resulting in a new finding that liquid water path adjustment in ACI is much weaker than we thought, once the bias is corrected for. This study reconciles dispute between many previous studies in liquid water path adjustment, with both increase, decrease and neutral reported. The scope fit well with ACP. The manuscript is very well written, the results are scientific interesting and politically meaningful with implication in geoengineering. I am happy to recommend for publication, once the concerns as below are addressed.

Specific comments:

1) It is a clever design that the study used null experiment to isolates the response of the cloud to the aerosol perturbation, and removes any effects due to the ship track geometries and alignment with non-linear gradients in the unperturbed. I wonder how representative is for the null experiment, since it was done with one particular year (2019) of meteorology and cloud images, for example, how much difference it could be for the correct LWP if choose 2017 for the null experiment instead of 2019? Some discussion of this uncertainty would help improve the robustness (and uncertainty range due to interannual variability of meteorology) of study and the new estimate of the corrected LWP adjustment.  

2) It is nice that authors extensively discuss the new finding of this study compared against recent studies from satellite observations, e.g., (Manshausen et al., 2023; Manshausen et al., 2022); (Toll et al., 2017; Toll et al., 2019). But, it would also be nice to see some discussion of this new finding compared against modelling studies. For example, how does the corrected LWP compared against global climate models, and some high resolution simulations. On particular, (Glassmeier et al., 2021) used cloud-resolving simulation to also show that LWP adjustment could be overestimated by ship-track studies. Do you study confirmed their simulation with observational evidence, and how much agreement there is between your observation and their cloud-resolving simulation? Furthermore, in line-270 (ish), you find that LWP shows very little evolution over time, while Glassmeier et al. discuss that LWP adjustment would develop along the time (see their Fig.3). Does your new finding suggest that the cloud-resolving simulation also need significant improvement in the underlying fundamental processes?

3) It would be also nice to see some discussion of this new finding aligning with some recent satellite observation studies over stratocumulus and trade cumulus regimes, which is the focus of this study. For example, although (Malavelle et al., 2017) showed a negligible LWP adjustment using an Icelandic volcanic plume covering diverse cloud regimes, recently (Chen et al., 2024) used a Hawaii volcanic natural experiment over a trade cumulus regime and showed a slight but consistent decrease of LWP in various meteorological conditions.

4) I can understand that the length of ship-track could be seen as a time-axis for ACI developing. However, I think this could only be true when the shipping routes are near-perpendicular to the prevailing wind. What about if they are near-parallel to each other, then the ACI signal could be a mixture of different time-scales? Would this influence your analysis, e.g. Fig.2 and Fig.5?

5) Details of ERA5 data should be provided in Method. Would spatial resolution of ERA5, if I am correct would be around 25km, influence your analysis, give that your defined ship-track is about 10km central region?

Editorial suggestions:

1) Removal the paragraph at line-160 (ish). Because it confused me when you show it here before explicitly introduce null experiment and tell about why, also you will talk about this point in the paragraph line-180, which is clearer.

2) Line 398: calling à cooling

References:

Chen, Y., Haywood, J., Wang, Y., Malavelle, F., Jordan, G., Peace, A., Partridge, D. G., Cho, N., Oreopoulos, L., Grosvenor, D., Field, P., Allan, R. P., and Lohmann, U.: Substantial cooling effect from aerosol-induced increase in tropical marine cloud cover, Nature Geoscience, 10.1038/s41561-024-01427-z, 2024.

Glassmeier, F., Hoffmann, F., Johnson, J. S., Yamaguchi, T., Carslaw, K. S., and Feingold, G.: Aerosol-cloud-climate cooling overestimated by ship-track data, Science, 371, 485-489, 10.1126/science.abd3980, 2021.

Malavelle, F. F., Haywood, J. M., Jones, A., Gettelman, A., Clarisse, L., Bauduin, S., Allan, R. P., Karset, I. H. H., Kristjánsson, J. E., Oreopoulos, L., Cho, N., Lee, D., Bellouin, N., Boucher, O., Grosvenor, D. P., Carslaw, K. S., Dhomse, S., Mann, G. W., Schmidt, A., Coe, H., Hartley, M. E., Dalvi, M., Hill, A. A., Johnson, B. T., Johnson, C. E., Knight, J. R., O’Connor, F. M., Partridge, D. G., Stier, P., Myhre, G., Platnick, S., Stephens, G. L., Takahashi, H., and Thordarson, T.: Strong constraints on aerosol–cloud interactions from volcanic eruptions, Nature, 546, 485-491, 10.1038/nature22974, 2017.

Manshausen, P., Watson-Parris, D., Christensen, M. W., Jalkanen, J.-P., and Stier, P.: Invisible ship tracks show large cloud sensitivity to aerosol, Nature, 610, 101-106, 10.1038/s41586-022-05122-0, 2022.

Manshausen, P., Watson-Parris, D., Christensen, M. W., Jalkanen, J. P., and Stier, P.: Rapid saturation of cloud water adjustments to shipping emissions, Atmos. Chem. Phys., 23, 12545-12555, 10.5194/acp-23-12545-2023, 2023.

Toll, V., Christensen, M., Gassó, S., and Bellouin, N.: Volcano and Ship Tracks Indicate Excessive Aerosol-Induced Cloud Water Increases in a Climate Model, Geophysical Research Letters, 44, 12,492-412,500, 10.1002/2017gl075280, 2017.

Toll, V., Christensen, M., Quaas, J., and Bellouin, N.: Weak average liquid-cloud-water response to anthropogenic aerosols, Nature, 572, 51-55, 10.1038/s41586-019-1423-9, 2019.

The study uses ship locations and reanalysis wind data to identify the location of ship plumes (also non-visible ship tracks). With that, the cloud properties of LWP and Nd are compared between the track and its surroundings. The authors create a null experiment in which they assume as if the ships were sailing in a different year. This allowed them to remove inherent systematic biases caused by the geometry of the ship tracks with respect to the cloud fields. They find that the nonlinearity of the cloud properties gradients across the ship tracks leads to a systematic bias which results in an overestimation of the LWP response to Nd. This finding is very important since other studies are using the approach of comparing cloud properties between the in-plume and outside-the-plume. The null experiment approach further allows the authors to correct for this overestimation, resulting in a lower LWP adjustment than previously estimated by other studies. It also provides a new evidence using a cleaver method of the possible LWP response to Nd, given the large range of estimates in various studies.

The paper is well-written and I support its publication. I have several questions, mainly regarding the methodology, which I would like the authors to clarify.

1. I would expect that within 30-60 km (across track in the study is 30-60 km) cloud properties would be roughly similar on average. Such a distance is considered to be meso-scale and therefore I would not expect large variations due to varying synoptic conditions. What is the cause of the background gradients that you find across the tracks?

2. Why are both the null and 2018 LWP response to Nd are positive? It seems like there is some fundamental cause. In line 256, you write that it is the correlation between cloud properties and wind. What could be the mechanism causing this? Is it related to more surface fluxes at high wind speed?

3. Figure 1 can be a bit confusing. The dotted lines in (a) and (b) are either crossing the midpoint (the track) or bouncing upward/downward. Consider choosing a different color or symbol.

4. Related to Figures 1 and 3, it is clear why concave (convex) matters, but if you have the observations at the track and on the sides, why do you look at the gradient from one side of the track to the other? Shouldn't it be enough from the center to one of the sides? And even so, you have the observations at the center (inside the track), so why do you interpolate over it? I assume that it’s me not fully understanding the point, but others might too, and therefore I think it would be better to explain it more explicitly.

5. The results are being compared to a few key studies which they are strongly related to. Nevertheless, I think it would be beneficial to expand the discussion to studies that used modeling as well. In addition, you mention that the time scale of the LWP response is an important factor. In this context, I suggest discussing the results with respect to Glassmeier et al., 2021 study (doi:10.1126/science.abd3980).

6. In the radiative forcing calculation, is it 60°N-60°S or 90°N-90°S? Are you considering only scenes with the clouds you sampled and ignoring clear scenes and scenes with other cloud types when computing the mean forcing? It should be clear how exactly you derived the forcing.

7. In line 358, you write that the cross-track gradients in LWP do not average out to zero. So why don’t you calculate the gradients for individual ship tracks and then average them? You explain in Section 2.3 that this is done to avoid errors (which you calculate using a bootstrapped method). Maybe these errors are negligible compared to the averaging bias?

Minor comments:

Figure 4b: the label of the colorbar might has a typo.

Line 283: "subsections" instead of "sections.

Line 357: Clarify the meaning of "Nd enhancement before 5 hours”. Why before?

Lines 360-363: Sentence is not clear.

Line 369: Seems like “be” is missing.

Line 398: "cooling" instead of "calling”?