This paper presents the first remote-sensing-based contrail altitude estimation algorithm. Both the image-level model and the cirrus pixel-by-pixel model are developed and compared, with an evaluation of predictive uncertainty and an assessment of the method's accuracy using individual test data and independent flight data. This study offers valuable insights for further assessing the climate impact of contrail cirrus. The paper is well-organized and well-written. I urge its publication in AMT, with some minor comments provided for the authors' consideration.

Specific comments:

Line 40: Please provide the physical explanations for why the infrared channels are used for estimating cloud top altitude.

Figure 7: The plot shows a trend where the CNN generally overestimates contrail altitude compared to the true values from CALIPSO. Are there any potential ideas for this?

Figure 10: The plot here seems to support my impression from Figure 7 that the contrail altitude can be slightly overestimated. During data collocation, you carefully considered the advection of aircraft data due to horizontal wind. Then, contrail ice crystals can sediment, which should theoretically reduce the altitude rather than increase it when compared to the flight data. Are there any reasons behind this discrepancy?

Conclusion: The RMSE is used as the metric to indicate the accuracy of the algorithm, as emphasized in the abstract. Since the developed contrail altitude retrieval method is the next step due to the biased prediction of ice supersaturation vertical extension in contrail avoidance, would it be better to also show the simple mean bias error or mean absolute error for estimating the contrail altitude?

Technical corrections:

Caption of Figure 1: "Zulu" time is equivalent to "UTC" time. However, I'm not sure if it is widely used in this research field. This applies to the entire text to be consistent with the figure.

L90: “a 50km distance of the ground-track of CALIPSO.” I assume it should refer to the supplement S1.

L132: “FlightAware (for times in 2023)”. Eventually it appears not to have been used because the focus was on the years 2018-2022.

L221: “ISS” instead of “ISSRs”.

L273: tends to be over-confident for probabilities between 0.5 and 0.9, as well as between 0.1 and 0.2.

Overall, the excellent work presented in this article is acknowledged.

Summary:

The authors use two deep learning techniques to estimate contrail cloud top height in GOES infrared imagery trained with CALIOP lidar data. Over 3000 contrails over five-year period are collocated with the lidar data to allow for the building and testing of the deep learning methods. The more successful contrail height estimate method was developed from a convolutional neural network (CNN), estimating contrail height with a root mean square error of 570 m in test data. An analysis of the CNN method results show that the predictive probability of the CNN method is generally well calibrated and has a smaller 95% confidence interval than the confidence intervals derived from flight altitude data alone. The authors also processed a 24-hour period of GOES data to show the spatial and temporal distribution of the contrail height estimates.

General comments:

The overall quality of the manuscript is good.The authors explain the methodology and results of the research concisely, and reach logical and consistent conclusions. Although the topic of the manuscript is contrail height estimation, the authors include discussion of thin cirrus height estimation that is unnecessary (considering the title of the manuscript) and confusing (especially subsection 3.2). Unless the authors can show why the cirrus altitude estimation is integral to the research presented in the main manuscript, I suggest that discussion about cirrus altitude estimation be removed from the paper. The authors make multiple references to the Supplementary Materials, so much so that it is nearly impossible to understand the manuscript without also reading those pages. As a result, the manuscript is incomplete and might not stand alone. The reader should not have to rely on the Supplementary Materials to read the principal paper. Finally, the paper lacks references to multiple concepts that should be explained in the paper (not just the Supplementary Materials). I can find no references for the various height conversions (between geometric, geopotential, and pressure altitudes), the advection of contrails, or the parallax correction used in the main paper. Add these references to the manuscript.

Specific comments:

Lines 100-104: Could not the width of contrail 2 also be the result of the geometry of the contrail relative to the CALIPSO ground track? Most of the other contrails are nearly perpendicular to the ground track, while the angle between contrail 2 and the satellite track is much more acute?

Lines 109-117: This paragraph is unclear.. The authors state “The collocation process is nearly identical at that for contrails, except that the contrail detection masks are no longer involved.”  I can’t find any mention of cloud masks up to this point.

Line 156: What are “normal” operations? Even after reading the paper, it is not clear to me what that means.

Lines 172-173: ‘…all inputs to the neural networks are “observational”…’ What is “observational” in this context? Why not say instead that the inputs are derived from the satellite radiances alone with no additional  (NWP data) used?

Figure 2 and elsewhere: It is not always clear which altitude the authors are using. In Figure 2, for example, what type of altitudes are plotted here? Geometric? Geopotential? Pressure altitudes?

Lines 194-195: What is the “thickness” of the altitude distribution? It appears in Figure 2 that the variance of the altitude distribution increases as the latitude increases, contrary to the text.

Figure 3: Why are the contrail tops generally so much higher than the ISS & SAC regions (except for summer)? It is apparent from the paper that the three profiles (Flight, ISS & SAC, Contrail top) represent entirely different times, locations, and number of observations. It would be better to make this distinction much more clear to the reader, otherwise they may be confused by this figure.

Section 3.2: The authors refer much more to the Supplementary Materials here than the manuscript itself. Many of the values stated in the text don’t match any of the values presented in Figure 4. This is very confusing! As stated earlier, I suggest the authors remove any discussion of cirrus altitude from the paper. It is superfluous and not presented well.

Figure 5: Green line, blue line, black line. Which models do they represent? A legend would make this figure much easier to understand.

Line 311: Why is “simulate” in quotation  marks? It appears to be a simulation (i.e, it imitates the appearance of) in the true sense of the word. The parallax correction is actually making the alignment of the flight tracks match better with the detected contrails.

Figure 7: Unless they looked that the Supplementary Materials, the reader would not know what “% of distance flown in 2 hours before” would mean. Some description of how this quantity was obtained must be included in the manuscript, not just the Supplementary Materials.