## general comments ##

This paper presents an interactive visualization system that allows for the sensitivity analysis of model parameters along warm conveyor belt trajectories. For a set of WCB trajectories, the impact of 40 model parameters on the impact of QR is assessed visually in multiple ways. The research questions that motivate the work are well phrased and are addressed later by the method as well as in the case study. The work is of high importance for gaining a deeper understanding of NWP models.

pro:

+ insightful application of visualization methods to a complex meteorological problem (model parameter sensitivity during WCB ascent)

+ well-discussed case study that reveals interesting observations

+ the construction of the visualization components is described well

+ useful comparative tools are provided (similarity measure by time warping, temporal alignment)

con:

- some visualization choices require more justification or discussion (regarding perception)

- the trajectory input could be described more formally to avoid ambiguities

I enjoyed reading the paper. It is well written, addresses a relevant problem for model analysis, and describes its visualization system well, making the work reproducible. In summary, I recommend to:

* consider switching from a saturation-encoding to polar area charts for the spheres or discuss perceptual limitations

* discuss options for achieving scalability in the trajectory plots regarding many model parameters

* consider adding the suggested references

* make exposition improvements (size of figures, color map legends, axis labels, unambigious math symbols)

## specific comments ##

# Pie charts

The sensitivity to certain variables was color-coded by saturation at a certain time by placing a spherical glyph with one segment per variable at the respective location in space.

- The glyph was called a "pie chart", which suggests that a quantitative attribute is mapped to the slice angles, which was not the case. I would suggest using a different name for the glyph, in order to avoid the usually negative associations related to the inaccurate angle perception of pie charts.

- The meaning of the slice hue was not clear from the beginning. Please add color bars as in Fig. 8 also to Figs. 1 and 2.

- Using saturation for quantitative data is not an ideal encoding, since psychophysical experiments showed that it ranks rather low on the effectiveness scale (see the book "Visualization Analysis and Design" by Tamara Munzner).

- Instead of encoding a quantitative attribute by the saturation of a fixed-size pie segment, I would suggest to consider using a polar area chart instead. The polar area chart likewise uses pie segments with fixed angle, but the radius of the segment is varied according to the quantitative attribute. Thereby, the quantitiative data is mapped to a positional encoding (i.e., the radius), which ranks higher on the effectiveness scale, and where differences between different radii can be perceived easier. Since small values lead to tiny segments, it would be imaginable to use a full glyph with maximal radius, as it is done now, which is depicted with the desaturated hue. And then, each pie segment could be filled from the center towards the outside by a fully saturated segment where the radius of the fully-saturated segment encodes the quantitative data. The saturation of a pixel could be calculated in the fragment shader based on the distance to the glyph center and the quantitative value that is to be encoded. If I'm not mistaken, it should be straightforward to implement this shading on the existing spherical glyphs. I would leave it to the authors to decide if they want to try this alternative encoding or whether they would like to discuss the perceptual limitations of their current saturation-based encoding.

# Preattentive encoding on 3D trajectories

- The distortion of the oriented patterns on the sphere impedes the effectiveness (Fig 6c). This is perhaps not a crucial feature and could possibly be removed.

- Along the 3D trajectories, multiple quantitative attributes are color-mapped, each with its own single-hue color map. While the individual encodings are pre-attentive, the task of finding locations in the image, where both encodings have high values at the same time, or where one is high and the other is low, is not pre-attentive anymore. If the user wants to find places, where two variables have high values at the same time, then it would be better to highlight those areas on the trajectory with a separate pre-attentive encoding, for example by high-lighting such regions. This could be considered if this task should be further supported. Since the displayed set of trajectories is usually relatively small, it is not a crucial improvement.

# Curve plots

The temporal alignment is a nice idea. I also liked the time warping to find similar sequences. (Not a question, just a comment.)

- Please add little labels for the x-axis to indicate that this axis encodes time.

- The curves were simplified using LTTB if there are more vertices than pixels. It was mentioned that this reduces the performance penalty of drawing too many points. I would be curious by how much the performance is improved by this optimization.

- Instead of mean (using a curve) and the stdev (using color-coding), one could display the full distribution of all trajectories in a trajectory density plot. 

- It was mentioned that the scalability of the approach is limited when there are too many model parameters to display. It would be imaginable to achieve scalability by including table lenses. A table lense distinguishes between selected and non-selected model parameters. The non-selected model parameters would encode less information in a box with smaller height, while the selected ones encode more information in a box with larger height. Implementing this is not a necessity, but it could be mentioned that standard approaches exist to achieve scalability of the presented method.

# 3D View

- In Figure 1, I find it difficult to estimate the altitude of the surface precipitation. From the text, I would think that it should be on the ground, but since the drop shadows are not cast onto the surface precipitation it appears to float above the ground. Perhaps the drop shadows could also be cast onto the color-coding on the surface.

- Is the vertical scaling of the clouds and the WCB trajectories equal? The clouds seem rather flat compared to the high vertical ascent of the WCBs.

# Meaning of derivative activations

- When we see on the trajectory that at a certain location the sensitivity to a certain variable is high, does this immediately mean anything, or could it be that this particular variable is actually not present? For example, for a variable to actually exhibit a change, many other conditions might have to be right. Couldn't it be that the change that would have a strong influence on QR would actually never occur in a certain weather situation? Or are certain changes on one variable easier to occur than certain changes on another variable? If this is the case, is there some room for an extension of the diagnostic tool in the future?

# Literature on trajectory data visualization

The most relevant literature is already mentioned. The field of trajectory visualization is quite large, so there could always be additional references added. Here are two directions that could be interesting, a survey and a multi-parameter analysis method along trajectories.

- survey on movement data visualization: https://doi.org/10.3390/ijgi8020063

- time activity curves: https://doi.org/10.1109/VISUAL.2019.8933578  and  https://doi.org/10.1111/cgf.14093

# Formal description

- The input to the method could be described a bit more formally: Given is a set of trajectories X={x_1(t),..., x_n(t)} with attributes a_i^j(t), etc. This could make the dimensionality of inputs and outputs a bit clearer, emphasizing that this is about the analysis of multi-variate data along trajectories.

- The symbol "n" is ambigiously used, namely for the number of bands and for the normal (also in the appendix). I suggest adding a vector (\vec) over the normal and the tangent. 

- Also consider using a single terminology, i.e., decide on "bands" or "sectors", instead of mixing the terms.

- In appendix B, I would suggest to call the "up" vector "\vec k" or something else with only one letter.

# Case study

- It was said that "location and ascent rate" of WCB trajectories were used as distinction criteria for the clustering. Have those two scalars been added in a weighted combination of some sort? If so, what were the weights?

- The bending of lines in Figure 11 looks in some cases a bit odd. If there is a problem with this encoding along lines with high curvature, it might be worth mentioning this as limitation.

- Several figures could be made a bit larger (from Fig 10 onwards).

- In Figure 12, I find it difficult to see a difference in da_cnn_4 for the slantwise and convective trajectories. The green shades look rather similar to me.

Review of Neubauer et al. 2023 “Visual analysis of model parameter sensitivities along warm conveyor belt trajectories using Met.3D (1.6.0-multivar0)” for Geoscientific Model Development

General:

This study proposes a novel visualisation system that allows to investigate interactively the sensitivities of prognostic variables to model parameters along warm conveyor belt trajectories, and thereby helps to gain a deeper understanding of subgrid-scale processes in numerical weather prediction models.  They apply their tool to the well-known cyclone “Vladiana” and show that the rain water density along the WCB trajectories is sensitive to parameters related to rain sedimentation and local rain production from collision of cloud droplets, and that the magnitude of the sensitivities differs for different regions and for convectively vs. slantwise ascending trajectories. The topic is relevant, the results are interesting, and the paper is well written.

Below are some minor comments that can mostly be addressed with some additional sentences for clarification.

Minor comments

• Abstract and conclusions: Please also include some key findings about your case study. In the conclusion it would be nice if you could come back to the questions posed in the introduction and summarise the results.
• It is difficult to understand Fig. 1 at this point in the paper, without watching the supplementary videos and before reading sections 2 and 3. Please add further details in the caption: What is the starting time of the WCB trajectories? What is QR (it has not yet been defined when Fig. 1 is mentioned) and what are the units of QR? What is sensitivity_max and what are the units of the sensitivities? What is shown in the curve plots, i.e., what is shown on the x and y axes, what are the black lines and the blue shading? What do the colours in the pie charts show? Please add colour bars to the figure. Even with the added information, you might consider moving the plot to the data and method section (where you nicely explain the different fields) to make it easier understandable, or to mention that the details will be explained in the data and method section.
• I find the term “pie charts” quite confusing, as I first expected the slices to have different sizes to illustrate relative sizes of data. Furthermore, I find it rather difficult to capture the values in the pie charts based on the colour saturation, could you make the difference between low and high values larger?
• Data, first paragraph: Over which time interval are the WCB trajectories calculated (and shown in the figures)?
• Line 321: “Sensitivities to CCN parameters and to k_r are ranked higher in the southern group.“ I see the symbol dk_r in Fig. 9a, but where are the sensitivities to the CNN parameters? I don’t see any of the CCN parameter names from Table C2 in Fig. 9a.
• Fig. 9: From the text in the figure caption, one might infer that precipitation from above is more important for the southern than for the northern group, but according to the text it is the other way around.
• Fig. 10: I find it confusing that you refer to the absence of something in turquoise in the caption. Should the turquoise cloud droplets (or their absence) be found in the pie or in the underlying map? If it should be in the pie, maybe you could highlight the outer border of this (grey) segment with turquoise lines. Otherwise, the reader does not know to which variable the grey part of the pie belongs.
• You mention Fig. 12 before Fig. 11, could you exchange them?
• Line 355: “… convective trajectories in the foreground and slantwise trajectories in the background” _– Do you mean group 1 and 2, respectively?
• Figs. 10, 11, 12, 13, 14 (and in other places in the paper): It would make the text easier understandable if you could be more specific with the wording and more often write “sensitivities of QR to xxx” (in the figure caption and in the text).

Typos and wording

• Appendix Table C2, description of inv_z: parenthesis sign “)” after “sedimentation” not needed.
• Line 175: “Figure 3a,d shows …”: Do you mean Figure 3c,f?
• Line 296: “different group”: different groups
• Line 326: “…, we compare the maximum sensitivity of QR to any parameter in Fig. 8.” I find this phrase difficult to understand. Maybe better something like “…, we investigate where along the trajectories any of the parameters is associated with the maximum sensitivity (Fig. 8).”
• Line 332: Parenthesis should include “Video 2”.
• Line 345: “more sensitive … along convective trajectories …” – Maybe add: “than along slantwise trajectories”.
• Lines 368-370: Part of the phrase is repeated.