Referee report on the article

Scale Size Estimation of Magnetosheath Jets 

by Pöppelwerth et al.

The manuscript deals with the multipoint case study of one jet observed in the magnetosheath by the three spacecraft. The estimation of the jet size and shape are based solely on the ion velocity measurements. In agreement with previous studies, the authors expect that the jet propagates in frame of the background magnetosheath plasma. It would lead to the divergence of the flow ahead the jet and convergent flow behind. Since only one event is studied, the manuscript should be considered rather as a description and demonstration of the method that can be used in a further research. The analysis itself provides questionable results and the fact that some of them are in line with already published jet properties is not enough for publication. My main objectives are stated bellow. 

Major comments

The weakness of the method is the assumption that the direction of the jet velocity does not change in course of its observation and it can lead to misinterpretation of measurements. Moreover, the data processing does not handle with uncertainties of velocity measurements that are rather large because the velocity distribution in the magnetosheath is hardly Maxwellian, especially when the jets are present. These factors result to uncertainty in a determination of the jet coordinate system and it is fully possible that the lack of divergence in front of jet discussed in the first paragraph of Discussion section is caused by these factors. A small rotation of the coordinate system probably would lead to the diverging patterns in front of the jet but it is a question whether the converging patterns at its end will persist under assumption of the constant jet velocity. 

Figure 2 is discussed only in terms of divergence or convergence of the flow prior to or after the jet passage but THE (that would be very close to the jet center - Figure 4) observes a relatively large velocity in the y direction. My understanding of the used coordinates is that it is the jet coordinate system and it is strange if its center moves with much larger velocity than its surrounding. The problem of perpendicular velocities is also clear in the discussion in lines 186-189. The authors claim the largest expansion at t_max but Figure 2 shows rather contraction in the perpendicular direction at this time.

The analyzed interval in all figures is +/- 12 s from the jet center (dynamic pressure peak). The jet duration is nearly 60 s in observations of all spacecraft (Figure 1). The estimated perpendicular size is about 1 Re, the distances of the spacecraft from the estimated jet center are lower than 0.4 Re (Figure 3) and it means that the analysis of the velocity components in Figures 2 and 3 are done inside the jet. However, the authors claim that the analysis is based on flows around the jet induced by the jet propagation through the magnetosheath plasma but such flows should be analyzed close to but outside of the jet.

Also two-point results given in the conclusion are not surprising, everyone expects that from the definition of a jet.

Minor points

Line 20 - I would suggest adding the sentence on the jet definition with corresponding reference here.

Line 23 - ……..jet occurrence “on” solar wind parameters…….

Line 30 - …with the higher velocity and density..

Line 39 - …”jets can trigger and suppress reconnection”, this connection it seems contradictory, it needs to be explained

Line 41 – I would suggest to skip  …….”for a single event”……

Line 66 – …”the central axis of this jet from evasive motion of the ambient plasma”, the sentence in this place is not clear 

Line 70 and elsewhere in the text – “spin resolution” instead of spin fit resolution

Line 95 – in the description of Fig. 2, the link to Fig. 3 is not correct

The presented work studies the scale size of a magnetosheath jet as observed by THEMIS mission. They suggest a methodological approach, and they confirm previously reported results while discussing some of the disagreements they find.

The determination of jet size is an interesting problem that requires a careful methodological approach and could be applied to other transient events apart from the jets analyzed here. Therefore, I believe the approach presented and the results shown are interesting and in principle worth publishing. Having said that, I propose some extra work to be done before the manuscript is ready for publication.

As discussed below, these could include a more careful evaluation of the assumptions (and its potential effects) made for the methodology. Furthermore, showing a couple of more events to see if the results are similar to other cases, could greatly increase the soundness of the methodology and its impact on the community.

Major

The methodology is based on some strong assumptions and there is neither an error evaluation performed, nor multiple events to verify its applicability. I list below a few of my issues with the methodology section (section 2) which are either not clearly stated or appear to be based on a strong assumption that could use some error quantification to be sufficiently motivated.

• Line 82-83: One direction vector is used, although it is very unlikely that it can fully characterize the direction. How does the result change if you use direction vectors taken from only one of the spacecraft or different pairs of them?
• Line 86: Mean velocity is defined as the average velocity of a very large window, which is also not compared if it is similar between all SCs. Also, if there is variability due to the presence of other flows this should also be affected and we can actually see THD measuring a flow increase at 16:02, almost above the threshold given in dynamic pressure. How would your result change if you remove the jet observations and other potential fast flows or if you change the window you average through?
• Line 87: Vjet is defined between all SCs, but we can see from Figure 1, that velocity is different between the different THEMIS satellites. Also, what does “mean” value at t_max? isn’t that 1 measurement, later it is suggested that it is the average value between the neighbor points, please clarify how the mean value is computed here.
• Line 87: Furthermore, the velocity of the jet can be higher in some cases than the moment product, since jets and the background population may co-exist (See Raptis et al. 2022), making the velocity observations having lower values in the data. How would a larger Vjet change your coordinate system there if you either take different measurements (pairs of SCs, maximum values, etc.) ? Also, if you assume that the velocity of the jet population is actually higher than measured due to non-Maxwellianity features (so maybe + 30-40%)?
• Line 94: Here the choice of 12 seconds before and after the tmax is not clear. Isn’t that time within the jet observation itself since the duration of the jet is larger than that? Wouldn’t that mean that for Figure 2 we just see the jet observations rather than the “before” and “after” periods of the jet flow? Something is unclear here.
• Line 95: This is the first time the word “center” is used, dropped abruptly without much explanation as to what it means or how it is derived. Some re-structuring and clarification could be useful here.
• Line 102-103: Again here, you are referring to an evasive motion, but shouldn’t that occur “after” the jet observations? if that’s only 12 seconds after tmax, aren’t these observations still referring to the jet itself, and not the plasma after its passage?
• Line 110: Here it is assumed that the propagation direction again is constant. This is not very likely to be the case as far as I am aware. How would this assumption change the result if it is not applicable? It would be nice to at least comment on that if quantification is not possible.

These are some of the aspects that either produce some kind of uncertainty to the methodology, or that they are not written clearly enough for a reader to understand the potential effects to your results. Also, in most cases, the choice made for each step is not motivated sufficiently.

Moderate/Minor

Readability of the paper: My overall suggestion here is to restructure section 2 and 3 to form clearer sections. Presently, neither of these sections are clearly separated, which forces the reader to go back and forth between the sections to understand what you are trying to say. For example, Figure 2 is only mentioned in the data and methods section, but then it is presented as part of the results in the discussion. The Gaussian fit is suddenly mentioned in the result section, which should have been mentioned before. Also, the motivation for this fit profile should have been made in the data and methods section, but currently it is shown at the end of the discussion (lines 168-173)! A re-organizing of such aspects could greatly improve the readability of the paper.

Figure 2: You mention that the top axis shows the Y’ coordinate, while the Z’ is constant. However, the values shown on the top x-axis appear to be constant on every time step. Could you explain a bit more what we are seeing here?

Lines 177-180: These two results, appear to be driven by the definition of a jet and the methodology itself. In other words, Tmax will automatically drive a dynamic pressure higher, since, well, the fit parameters at t_max have as input higher dynamic pressure pairs, so Po will be higher. Is that correct? Do I miss something? Also, the same applies for ΔR. According to my understanding, this will be the cause for every jet that has a single peak in dynamic pressure (and therefore lower values before and after it).  Could you either help me understand if I miss something here, or describe a hypothetical (or real) case for which your methodology would not result always in the same conclusion?

Edits

Line 2: Not all jets are formed at the bow shock, maybe such a general statement shouldn't be in the abstract.

Line 3-6: This sentence is very hard to read, consider splitting it.  

Line 13 and throughout the text: Consider changing θ to θ_Bn since that’s the typical symbol used.

References

Raptis, Savvas, et al. "On magnetosheath jet kinetic structure and plasma properties." Geophysical Research Letters 49.21 (2022): e2022GL100678.