the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 21 Apr 2026
Propagation of interplanetary (IP) shocks near the Earth
Abstract. The solar wind monitor at the Sun-Earth L1 point has been used to estimate the arrival time of interplanetary (IP) shocks associated with coronal mass ejections (CMEs) and co-rotating interaction regions (CIRs). In standard estimates, including NASA/OMNI database, the radial propagation speed of the IP shock is assumed to be the same as the measured solar wind (proton) speed, although these speeds are known to be different in both the shock theory and CME observations. To diagnose the actual error in the arrival time of the IP shocks, we statistically compared the radial propagation speed of the IP shock with the measured solar wind speed at L1. The propagation speed is obtained from the time-of-propagation between the IP shock passage at the L1 monitoring spacecraft (SOHO and ACE) and at the Earth, the latter of which is represented by the geomagnetic sudden commencement (SC). In statistics, we limited to the IP shocks with a clear geomagnetic SC signature and with velocity profiles consistent between SOHO and ACE. During 1998–2022, 375 IP shocks satisfied such conditions. For the solar wind speed, the highest value during 15 min after the IP shock passage observed by the L1 monitoring spacecraft was used. We found the following tendencies. (1) As expected, actual arrival time of the IP shock to the Earth (represented by the geomagnetic SC) is often quite different from the predicted arrival time using the L1 velocity measurement. (2) For a majority of the cases, the geomagnetic SC is observed 0–10 min earlier than the predicted IP arrival time. (3) The speed difference is distributed asymmetrically toward faster propagation, with peak of the distribution about +10 %.
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Status: final response (author comments only)
- AC1: 'some typo (unit for speed)', Masatoshi Yamauchi, 29 Apr 2026
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RC1: 'Comment on egusphere-2026-1517', Anonymous Referee #1, 04 Jun 2026
Please read the comments about the draft in the attached document
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AC2: 'Reply on RC1 (general direcion of revision)', Masatoshi Yamauchi, 04 Jun 2026
Thank you for your instructive commons to improve the presentation. Hey are indeed very useful to revise the manuscript.
For comments that are related to the readability, we add explanation or revise (re-organize the paragraphs) accordingly. Angle analyses for Figure 1 (comment on page 5 while analyses exists in page 13) is one such example.
For comments that require new tables/figures, we will consult if we add new table/figure/number (e.g., angle analyses that is commented in page 13) or we have good reason not to include them (data availability or avoiding too much information for readability).Citation: https://doi.org/10.5194/egusphere-2026-1517-AC2 -
AC3: 'Reply on RC1', Masatoshi Yamauchi, 23 Jun 2026
To answer the comment on line 271 "You could add a plot with the angle theta of the events analyzed to see that the cleanest sample have removed all the oblique events as you state in the text", we made the angle-velocity plot as the reviewer requested. We found that this plot allows us to improve our filtering method using two independent parameters (as shown in the attached figure). Accordingly we will replace Figures 3-6 using this new criterion. Revised Figure 5 (to be new Figure 6) is also attached. With this information, Figure 6 is not longer needed.
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AC4: 'Reply on RC1 (point to point answer)', Masatoshi Yamauchi, 30 Jun 2026
Line 19: Although you are only using ACE and SOHO data, Wind spacecraft is also relevant. You could also include the references for these missions
A: We added references, including Wind.
Line 59: It would be helpful to add here a small paragraph detailing what is the meaning of the next sections.A: We added outline of how the analysis method.
line 63: These are the resolutions for all the variables used or there are differences?A: We here mentioned the time resolution of the geomagnetic index. We also explicitly mentioned that these are for solar wind data.
line 69: Please add the beginning of the period under studyA: Yes, we added for both SOHO and ACE
line 70: How did you filter this, by hand, or using some automatic/semiautomatic method?.A. I manually examined by eye because total number is < 700 samples because our purpose is to select "cleanest" examples. For such small numbers, automated method is not as good as manual judging.
line 80: There is a parenthesis missingA: Thank you, we fixed.
Figure 1: Just a suggestion for the timeline. You could remove the separation between the SOHO and ACE panels since they share the same timeline. It would make easier to check the times.
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Figure 1: Just thinking out loud, you are aligning the shock in SOHO with the shock in SYMH. I am not sure which combination is more appropriate, this one or maybe aligning the shocks in ACE and SOHO.A: Thank you for "readers' view" of layout. We now back to the "normal" time-line layout instead of time-shifted layout.
line 95 & 96: I presume that this distance and X_ACE distance are obtained from some paper. Please add the referenceA: The spacecraft location is obtained from NASA Omniweb site, and now this is explicitly mentioned the "2. Data and Method" section.
line 107: By considering only two options (angle=0 and 45) you assume that it is a shock normal to the X direction. Would it be better a small study with more angles, to reinforce this idea. Maybe you are jumping too fast in to the conclusion of a normal shockA: We moved the angle derivation method (equation (1)) to here. Accordingly, we added angle information in selecting "best" examples in the statistical analyses.
line 109 & 124: Here and after, you use 15min as a window for the IP shock passage. There is a reason for this specific number?. If so, what is it?. If you use other window, e.g. 5min, would your results changeA: After manually examined, 15 min is enough to reach the peak value and short enough not including independent increase afterward). We added this explanation. Actually, 5 min window does not change the result very much (with most enhanced result)
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lines 177 & 201 & 203 & 204 & 282-284: Are these values supposed to be the limits of the histograms?. For SOHO there are values above 12, why are you using these limits?. Maybe standard deviation or any other statistic tool would be helpful to identify the spread of the data
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line 182: As said before, you could explain this more accurate using statistic measurements. You can combine the quantitative explanation with a qualitative explanation
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line: 190: As said before, you can express it more accurate with statistics tools. Is this really a difference or is just something that came out from the type of plot?
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line 192: As you did before, why choose these numbers?. You have here -5%, If the sign of the speed ratio is negative, it is still faster?.
A: In Figures 4, and 5, we added central 80% range, average, and standard deviation. Accordingly, we clearly mentioned "central 80%" when the range values are mentioned.
line 179: The best dataset are (c) and (f), right?A: Yes, we fixed.
line 184: Are these, seconds or minutes?A: We fixed (minutes)
line 189: Why use here the log of the speed? It is better than use just VIP/VH?A: For ratio of any values (here, V1/V2), taking log-scale is the best way to linearize the horizontal axis (this makes V1/V2 binning and V2/V1 expression symmetric). For nearly 1 case, there are not big difference. This isbinningwhy we have ratio value (% off increase) at the top of each bar. We added some explanation.
Figure 3 (now is Figure 4): Correct the ylabels: "shochs"==> "shocks".
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Figure 3 (now is Figure 4): Change the order of the text within the caption. First the explanation and then the description of the panels.
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Figure 3 (now is Figure 4): Instead of using 'Even better' as the name of the sample, label them correctly, see comment beforeA : We changed the order of text in the caption, and fixed the labelling.
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Figure 4: Why using these percentages?
Figure 4: I would understand why you use here the -0.1 and 0.2 as the limits of the plots, but why 79% and 158%? Are these defined in the text?. In any case as said in Figure 3, I would show these values in a separate table explaining it in the textA: We added the explanation of % in the figure caption.
Line 198: The discussion is mainly focus on the "possible error sources" but not much in your previous results?
A: We divided the section into "possible error source" and "discussion"
line 201: How many?A: We added numbers (15=SOHO and 22=ACE out of 148)
line 202: Fig 4c is about speed not timeA: We corrected. It is Fig 3c (new Fig 4c).
line 212 (4.1 Velocity value) and 226 (4.2 Change of speeds from L1 to the Earth): The way this section is written can be improved. In the beginning it seems like your work didn't take into account this issue, but in fact you did!. Maybe written in the other way around improve it.A: We changed the section name (Possible error sources, covering subsection 4.1 to 4.3), and added a text stating that all these error are smaller than the obtained difference.
line 269: I don't fully get if these extra filtering is already implemented in Figures 3c.3f,4c and 4f, or is implemented only here. If it is the second option, you could add the plots also to see how it improvesA: With new Figure 2, the enter subsection was rewritten. New Figures 4c, 4f, 5c, 5f (old 3c,3f,4c,4f) include the extra filter.
line 271: You could add a plot with the angle theta of the events analyzed to see that the cleanest sample have removed all the oblique events as you state in the textA: Thank you very much for very important comment. We made the angle-velocity plot as the reviewer requested. We found that this plot allows us to improve our filtering method using two independent parameters (as shown in the attached figure). Accordingly we will replace Figures 3-6 using this new criterion. Revised Figure 5 (to be new Figure 6) is also attached. With this information, Figure 6 is not longer needed.
line 278 "5 Conclusion": The conclusions are a bit sparse. You can reread the discussion, since some of the ideas could be also conclusions.A: We will rewrite the conclusion.
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line 281: You would have data to support this statementA: We discussed this in the discussion section. Having two parameter (new Figure 3) instead of one indicate that "best" samples is most likely support this statement
line 309 & 310 & 313 & 314 & 315: All the tables here are labeled, Table A1, Table A2...but it is the section B of the appendix. Should be then Table B1, B2...A: Journal's LaTex package automatically assign Table A1, A2,,,, (A means Appendix, but not A).
Citation: https://doi.org/10.5194/egusphere-2026-1517-AC4 -
RC2: 'Reply on AC4', Anonymous Referee #1, 03 Jul 2026
For a faster review, could you please attach the draft with the changes implemented?
ThanksCitation: https://doi.org/10.5194/egusphere-2026-1517-RC2 -
AC5: 'Reply on RC2', Masatoshi Yamauchi, 03 Jul 2026
Thank you for your proposal to attach revision. Unfortunately, the editor's office does not allow to upload the revised manuscript. Only I can upload is new figures with significant change (New Fig 3 and Fig 5 (=old Fig 4) (Fig 1, 2, 4 and Fig=6 are corrected as was commented by the reviewer).
Here, the velocity is refined as V_SW = solar wind proton velocity, V_timing = superficial propagation speed obtained from the timings of the IP shock detection by the spacecraft (T_soho or T_ace) and geomagnetic sudden commencement, respectively, V_triangle = propagation velocity using both spacecraft through equation (1), and V_2SC = superficial propagation speed between SOHO and ACE in the -X_SGE direction.
Fig 3 caption:
(a) Scatter plot of shock angle (θ) against the simple inter-spacecraft propagation velocity (V2SC) assuming 1D shock pointing anti-sunward. The "consistent" 375 IP shocks are plotted (some shocks are outside the range and not plotted). The red-hatched area ("clean" shocks) is defined by V2SC < +50 km/s and |θ| < 40◦. The blue-hatched area ("best" shocks) is defined by−2500 km/s < V2SC < −150 km/s and |θ| < 17◦ (i.e., |tanθ| < 0.3). (b) Scatter plot of propagation velocity using the IP shock passage timing of two spacecraft (V_triangle) according to Eq. (1) and that using only one spacecraft (V_timing) for ACE. All the "clean" 278 IP shocks (red-hatched area) are plotted. (c) The same as (b) but for SOHO. (d) The same as (c) but potted only 148 "best" IP shocks. For all panels, the data are classified into three types in terms of clearness of the SC signature in the same manner as Fig. 2a.Related text:
Fig. 3a shows the scatter plot between V_2SC and θ (derived shock tilt angle). In the figure, there are many cases that indicate "backward" propagation (downstream spacecraft detected the IP shock earlier than the upstream spacecraft) indicate that the IP shock front is quite tilted toward the Y and/or Z directions. We remove these cases in the present study. Here, we allow a wider range for V_2SC compared to the solar wind speed range even for the best samples, because the inter-spacecraft time difference of the IP shock detection can be as short as 1s, with possible error of a factor of 2 or more. These different levels of "cleanness" are summarized in Table 1. A list of timings of the IP shock detection and geomagnetic SC for these 438 IP shocks, including the classification of difference sub-dataset, is listed in Appendix B (Tables A1-4).
We also remove the IP shocks in which the derived tilt angle (θ) is large. The selection (filtering) criterion is marked by dashed and solid lines in Fig. 3a. The blue-hatched area selecta IP shocks with V_2SC < +50 km/s (removing backward superficial propagation) and |θ| < 40◦ (removing obliquely aligned shock). There are total 278 examples of such "clean" shocks. This is already a fairly good dataset as shown in Fig. 3b: the derived propagation velocities using two spacecraft (V_triangle) and those using only one spacecraft (V_timing) are well correlated for ACE,
However, the agreement with V_timing for SOHO (Fig. 3c) is not as good as for ACE. This is most due to the larger distance from the upstream point to the Earth to SOHO (up to 7 × 105 km) than to ACE (up to 3 × 105 km), as mentioned in the previous section. To make even a cleaner dataset, we tighten the criterion as −2500 km/s < V_2SC < −150 km/s and |θ| < 17◦ (i.e., | tan θ| < 0.3) to form "best" set of the IP shocks (148 examples). The blue-hatched area corresponds to these best IP shocks. For this dataset, the derived propagation velocities using two different methods are well correlated even for SOHO, as shown in Fig. 3d.Fig 5 caption:
The same as Fig. 4, but for the velocity ratio between the solar wind proton velocity (VSW ) and the IP shock’s propagation velocity. The latter is calculated using the time difference and XGSE distance between the IP shock passage point at L1 and the Earth (the geomagnetic SC signature is used for timing at the Earth). Corresponding to three different points (SOHO, ACE, and estimated upstream point of the Earth by Eqs. (1) and (2)), we have three different propagation speed of the IP shock: (a)-(c) Vtiming for SOHO, (d)-(f) V_timing for ACE, and (g)-(i) Vtriangle common for SOHO and ACE. To linearize the binning of velocity ratio, we plotted against in a logarithmic scale. For examples, −0.06 and 0.06 correspond to 87% (i.e., 13% slower propagation speed than the solar wind speed) and 115% (i.e., 15% faster), respectively. These differences are written at the top of each panel.
Related text (revised part):
Fig. 5 shows the velocity ratio V_timing/V_SW for SOHO (left panels) and ACE (middle panels) as well as V_triangle/V_SW for SOHO (right panels), all in the same format as Fig. 4,,,,,.
Since we consider ratio, we linearlized the binning by taking logarithmic scale,,,,,.
These averages are unchanged if we use V_triangle (which is common for SOHO and ACE) instead of V_timing for both SOHO and ACE (ACE cases are not shown here). For SOHO’s case, the distribution becomes more symmetric but standard deviation is reduced only by 1% by using V_triangle, as shown in Figs. 5g-5i, and the number of extreme cases (i.e., more than 32% faster) does not change very much (8 shocks when using V_timing and 7 shocks when using V_triangle).
Outline is also change:
4 Possible error sources
4.4 Tiit of the shock front in the ZGSE direction
5 Summary and Discussion => some of old conclusion is moved to here
6 Conclusions => quite compact
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AC5: 'Reply on RC2', Masatoshi Yamauchi, 03 Jul 2026
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RC2: 'Reply on AC4', Anonymous Referee #1, 03 Jul 2026
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AC2: 'Reply on RC1 (general direcion of revision)', Masatoshi Yamauchi, 04 Jun 2026
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RC3: 'Comment on egusphere-2026-1517', Anonymous Referee #2, 15 Jul 2026
Major issues
The theoretical discussion of the shock has some issues, although they
can be fixed. No distinction is made between normal speed and
speed. Usually the shock speed is defined to be normal to the shock
front, which is clearly what is assumed in the Appendix. But the L1
speed is usually taken in the GSE X direction or simply it is the
total speed. Neither of these speeds correspond to the normal speed in
general. As long as the velocity vectors ahead and behind the shock
front are roughly parallel, there is a simple proportionality between
the normal and X directional/total speeds. I recommend that the
authors create a new figure that depicts the geometry. The same figure
can be used to explain the impact of the spacecraft not being on the
Sun-Earth line.For the example event shown in Figure 1, the authors argue that the 1D
shock model is failing as it predicts much slower speed than found
empirically. The shock model relies on mass conservation that is
certainly true. A likely explanation for the discrepancy is that the
shock normal is not aligned with the X direction and/or the shock is
not planar. The authors try the Parker spiral direction for the shock
front (which would be reasonable for a CIR but not for a CME) and find
that it does not work. But there are many other possibilities. In
fact the Z component of the velocity jumps from ~0 to ~50 km/s
according to both ACE and WIND measurements. This is comparable the
jump of the velocity in the X direction (50-70 km/s), which suggests
that the shock normal was tilted close to 45 degrees in the X-Z plane
(and much less in the X-Y plane). This large tilt reduces (although
does not fully eliminate) the discrepancy in the arrival times. ACE
was at around Z=1.29e5 km, while SOHO was at Z=6.7e4km, so projecting
to the Sun-Earth line reduces the distances to around 1.19e6 km for
SOHO and 1.31e6 km for ACE. This gives 646km/s (SOHO) and 624km/s
(ACE) observed shock speeds. These are consistent with each other,
suggesting that the 45 degree tilt in the X-Z plane is plausible.According to the authors the 1D shock model gives around 540 km/s
(SOHO) and 600km/s (ACE) speeds, which are still smaller for SOHO, but
consistent for ACE. Given that the compression ratios at ACE and SOHO
are drastically different (4 vs 2), there is certainly some
non-uniformity in the transverse direction, so the planar shock
assumption is probably not valid.At line 160-165 the authors decided to remove the "backward" propagating
shocks. This will only remove shocks that happen to be tilted beyond
the tilt of the line connecting the two spacecraft, but does not
limit tilts in the other way. A more neutral way would look at the
discrepancy of the propagation speeds obtained by the two spacecraft
and limit it to stay within some range (say +-10%).The authors consistently talk about tilt in the X-Y plane as the only
possibility, but in reality the tilt can be in any direction.A major missing information is comparing the observed speed with the
1D shock model. The authors keep refering to the one and only example
(which is not even analyzed correctly) why the 1D shock model is not
reliable. But what about actually doing the analysis on all the
events? There should be plots of the difference between the predicted
travel time from the 1D shock model and the observed travel time. Is
the distribution symmetric or is there still some bias? What is the
spread compared to the spread using the upstream velocity? Smaller?
Larger? The same? Is there some trend as a function of shock speed
or as a function of the assumed tilt angle?Minor issues:
Line 169: as short as 1s... Maybe 1 minute?
Line 4 and 24:
assumed to be the same as the measured solar wind (proton) speed
Add: "after the shock". All reasonable approximations discard the
plasma elements overtaken by later ones, which in effect means that
the higher speed behind the shock is used to propagate the shock.Line 38: from the different reasons -> from other reasons.
Line 43: the symmetric orbit -> symmetric orbits
Line 48: ACE is at most 3e5 km away from the Sun-Earth line,
while SOHO is up to 6e5 km. But always much less than 1e6 km.Line 66: The size of Earth is not 0.06e5 km. The radius of Earth is around
6800km, so a reasonable rounding is 7000km. The size of Earth is not well
defined. Radius or diameter are.Line 96: 700+-30 km ... 690+-20 km
-> 700+-30 km/s shock speed ... 690+-20 km/s.Line 101: Projecting these directions
-> Projecting these directions along the shock frontLine 100-105: It should be clarified that the 570+-20 km/s (not km)
and 960+-30 km/s speeds are _not_ the normal shock speed, but the speed
along the X direction.Line 158: velocity profile -> velocity profiles
Line 163: tilted in the Y direction -> tilted
There is absolutely no reason to assume that shocks can only
be tilted in the Y direction.Lines 250-260: It is incorrect to assume that the shock is always
tilting in the X-Y plane. The whole discussion needs to be changed
to be general.Figure 1: The ACE speed jumps to 480 km/s as the density increases
by about a factor of 2. It is unclear why the later increase of the
velocity to 520km/s is taken as the upstream speed, while the density
hardly changes. Is this based on the assumption that ACE does not actually
measure the speed accurately?Line 306: All shocks are "compressional". There are radially
outward propagating shocks where n_b is smaller than n_a,
and reverse shocks where n_b is larger than n_a.Line 307: It should be mentioned that epsilon is the inverse of the
shock compression ratio for outward propagating shocks.Line 336: diseased -> deceased
Figure A1: Spacecrft -> Spacecraft
Tables A1-A4: Since these belong to Appendix B, maybe they should be B1-B4.
There are no "rarefied shocks". They are reverse shocks.
Citation: https://doi.org/10.5194/egusphere-2026-1517-RC3 -
AC6: 'Reply on RC3 (for major points)', Masatoshi Yamauchi, 16 Jul 2026
Thank you very much for your instructive comments. Some of the points are already implemented in responce to the commenct by the reviewer #1. Other comments will be imlimented in the following way.
Major Comment: The theoretical discussion of the shock has some issues, although they can be fixed. No distinction is made between normal speed and speed. Usually the shock speed is defined to be normal to the shock front, which is clearly what is assumed in the Appendix. But the L1 speed is usually taken in the GSE X direction or simply it is the total speed. Neither of these speeds correspond to the normal speed in general. As long as the velocity vectors ahead and behind the shock front are roughly parallel, there is a simple proportionality between the normal and X directional/total speeds. I recommend that the authors create a new figure that depicts the geometry. The same figure can be used to explain the impact of the spacecraft not being on the Sun-Earth line.
A: Thank you for pointing out insufficient explanation. We add a new figure (new panels in Fig A1) to show the oblique shock configuration together with both spacecraft location. We also describe why we use two spacecraft timing instead of the local velocity local ratio.
Major Comment: For the example event shown in Figure 1, ,,,,
A: Thank you very much for pointing out possibility for Z tilt. For Fig 1 case, the angle estimate in the X-Z direction is 33 ± 40 degrees (velocity 730 ± 100 km/s) instead of -45 degree (velocity 660 km for SOHO and 630 km for ACE). The large error bar comes from relative Z location of the spacecraft (we need extrapolate in the z direction instead of interpolate in the y direction). We add these explanations.
Major Comment: At line 160-165 the authors decided to remove the "backward" propagating shocks. This will only remove shocks that happen to be tilted beyond the tilt of the line connecting the two spacecraft, but does not limit tilts in the other way. A more neutral way would look at the discrepancy of the propagation speeds obtained by the two spacecraft and limit it to stay within some range (say +-10%).
A: As the reviewer suggested, we also use the estimated tilt angle for filtering, as shown in Figure 3 (this is posted in the last answer to reviewer 1).
Major Comment: The authors consistently talk about tilt in the X-Y plane as the only possibility, but in reality the tilt can be in any direction. A major missing information is comparing the observed speed with the 1D shock model. The authors keep refering to the one and only example (which is not even analyzed correctly) why the 1D shock model is not reliable. But what about actually doing the analysis on all the events? There should be plots of the difference between the predicted travel time from the 1D shock model and the observed travel time.
A: Detailed analyses of "unexpected" cases will be made in the next paper. The main reason that we do not use 1D shock analyses is that ACE density value after the shock is not reliable due to saturation, as described in section 2. From our experience working on the ion instruments (calibration and analyses), we believe that the more asymmetric velocity distribution in the ACE case than the SOHO case comes from instrument difference. As described in the introduction, this paper analysed only statistically to obtain the average view, particularly how much earlier the shock arrives that the rough estimate using velocity. We are afraid of adding 1D "model speed" using the density values (reading density of 375 cases is very erroneous) as any plotting product will mislead the readers in addition o dispersing the content (mixing with unreliable "data point"), and therefore, we decided to exclude it from the analyses.
Major Comment: Is the distribution symmetric or is there still some bias? What is the spread compared to the spread using the upstream velocity? Smaller? Larger? The same? Is there some trend as a function of shock speed or as a function of the assumed tilt angle?
A: Thank you for raising these questions. We list them in the discussion for future study.
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RC4: 'Reply on AC6', Anonymous Referee #2, 16 Jul 2026
Please create plots based on shock speed using the available data. For strong shocks the density ratio is expected to be 4, so measurements do not play a significant role. For weaker shocks the difference between the after and before velocities is relatively small, so the shock speed is not that different from the "after" speed. So in both the weak and strong shock limits the effect of density is not huge. . Also, you trust SOHO density, so there is absolutely no reason not to do this for SOHO. Your paper will be much more useful if you have this included (and not just a single example).
Citation: https://doi.org/10.5194/egusphere-2026-1517-RC4 -
AC7: 'Reply on RC4', Masatoshi Yamauchi, 16 Jul 2026
We are still hesitating because we are afraid of misleading. Unlike the present study that uses only one "read" value of moment (SW speed after the shock), such an 1D shock analyses (even for "ideal" cases with shock normal pointing -X) requires three more "read" values (SW speed and density, both before and after the shock). Since the plasma is not perfect fluid even for the solar wind (this is why the particle measurement community prefers to show energy-time spectrogram rather than the moment values), moment values are often different from density values obtained by plasma frequency or Langmuir probe, particularly then the values change suddenly or spacecraft potential is not zero.
We will anyway try such a plot for the "best" 148 cases, but only for the "ideal" 1D shock model. We are not sure that we can obtain a plot with presentable quality, though.
For the same reason, we do not make 1D-shock analyses for oblique shock that requires four more unreliable "read" values (Vy and Vz, both before and after the shock). Since the particle instrument need "looking directions" that ions to enter, the anglar information is much less reliable than the total velocity. Even the Faraday cap metod first convert the angular information to electric current, and includes error particularly when the velocity (electric current inside the instrument) quickly changes. Therefore, we do not encourage any sophisticated analyses using mane moment values.
Citation: https://doi.org/10.5194/egusphere-2026-1517-AC7 -
AC8: 'Reply on RC4 (test figure attached)', Masatoshi Yamauchi, 20 Jul 2026
We attach scatter plots that compare the anti-sunward propagation speed between the 1D shock model V_1D (using density and velocity values of SOHO both before and after the shock) and the observed propagation speed V_triangle (using timing of shock passage at SOHO, ACE, and the Earth). The comparison is made both for propagation speed and the ratio to the solar wind measured by SOHO. In both plots, the 1D model speed V_1D scatters more than observed speed V_triangle. For the ratio plots, even the concentrated part around ratio 1.1 (this is similar between both) show no clear correlation between V_1D/V_sw and V_triangle/V_sw. Different symbols mean the different "estimated" tilt toward z assuming y direction is constant (which is less likely the opposite assumption), indicating that tilt toward z is not the cause for this scattering.
We believe that this comes from the difficulty in measuring correct density (this is common problem in the ion measurements during large changes, in addition to the density fluctuation). The obtained figure thus have a potential error. Solving this error problem is beyond the scope of paper (just deriving reasonable 1D-model shock velocity requires dedicated work with independent paper), and we will not show use such a potentially misleading figure in the discussion. The best compromise is to show in the appendix (only right one), explaining the reason that we do not use the 1D modelled propagation speed
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RC5: 'Reply on AC8', Anonymous Referee #2, 21 Jul 2026
Thank you for producing the plot. I attach a comparison of your V_SW vs V_shock from the paper with a clear bias and the V_triangle vs V_1D model with an added line for equal values. The distribution is now pretty symmetric, which clearly confirms that the 1D shock theory resolves the bias. This should be in the paper (well, if you want me to recommend publication :-). You may want to produce a histogram to further characterize the distribution. I hope that you did restrict the compression ratio to be between 1 and 4 and not just use any arbitrary value.
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AC9: 'Reply on RC5', Masatoshi Yamauchi, 21 Jul 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-1517/egusphere-2026-1517-AC9-supplement.pdf
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AC10: 'Reply on RC5', Masatoshi Yamauchi, 21 Jul 2026
The attached histogram "V_triagle/V_soho" is already "relatively symmetric".
After comparing this with yesterday left plot (V_triagle/V_soho vs V_1D/V_soho) and with new Figure 3d (V_triangle vs V_soho for best samples), we cannot agree with your interpretation of yesterday's right figure (V_triangle vs V_1D) as "this should solve asymmetry". So, yesterday's figure will be included in appendix with explanation of why we do not use it.Citation: https://doi.org/10.5194/egusphere-2026-1517-AC10 -
RC7: 'Reply on AC10', Anonymous Referee #2, 22 Jul 2026
None of the distributions are symmetric around 0. They are all biased towards positive values.
Citation: https://doi.org/10.5194/egusphere-2026-1517-RC7 -
AC14: 'Reply on RC7', Masatoshi Yamauchi, 22 Jul 2026
As we answered below, our result is "observational evidence" of faster propagation speed than the solar wind as "symple 1D shock model predicts". We misunderstand your meaning of !asymmetry" but now this is streamlined!
Citation: https://doi.org/10.5194/egusphere-2026-1517-AC14
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AC14: 'Reply on RC7', Masatoshi Yamauchi, 22 Jul 2026
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RC7: 'Reply on AC10', Anonymous Referee #2, 22 Jul 2026
- AC11: 'Reply on RC5 (with figure to be used)', Masatoshi Yamauchi, 22 Jul 2026
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AC12: 'Reply on RC5 (another version of the same figure above)', Masatoshi Yamauchi, 22 Jul 2026
Here is different version of the same figure (reference V_SW is taking 10 min average during 3-13 min after the shock instead of peak value within 15 min after the shock). By definition of n_after/n_before = 1 to 4, V_1D/V_SW is always > 1 (middle panel). Although the left and middle panels looks similar, they are not correlated as shown in the right panel.
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RC6: 'Reply on AC12', Anonymous Referee #2, 22 Jul 2026
Once the speeds are normalized, the ratios will be in the 1.0-1.25 range or so + noise, so the correlation is weak. But it does not change the fact that the shock arrives faster than the upstream speed would predict and the deviation is properly captured by the 1D shock model. So this positive and important results needs to be presented in the paper. Otherwise the paper presents the deviation as a mystery, which is absolutely misleading. We know that shocks propagate faster than the upstream speed, and this is confirmed quantitatively here. You can of course explain the observational uncertainties. But not presenting this result cannot be justified.
Citation: https://doi.org/10.5194/egusphere-2026-1517-RC6 -
AC13: 'Reply on RC6', Masatoshi Yamauchi, 22 Jul 2026
Thank you very much for the clarification.
Yes, our "observational" result in which shock arrives faster than the solar wind is indeed consistent with the simple 1D shock model. We make that statement clear in the main text.
Citation: https://doi.org/10.5194/egusphere-2026-1517-AC13
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AC13: 'Reply on RC6', Masatoshi Yamauchi, 22 Jul 2026
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RC6: 'Reply on AC12', Anonymous Referee #2, 22 Jul 2026
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AC9: 'Reply on RC5', Masatoshi Yamauchi, 21 Jul 2026
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RC5: 'Reply on AC8', Anonymous Referee #2, 21 Jul 2026
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AC7: 'Reply on RC4', Masatoshi Yamauchi, 16 Jul 2026
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RC4: 'Reply on AC6', Anonymous Referee #2, 16 Jul 2026
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AC6: 'Reply on RC3 (for major points)', Masatoshi Yamauchi, 16 Jul 2026
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AC15: 'Comment on egusphere-2026-1517', Masatoshi Yamauchi, 07 Aug 2026
We think we have answered all comments by the reviewers. All revised figures are ready, and we are ready for revision (we took account of almost all comments).
Citation: https://doi.org/10.5194/egusphere-2026-1517-AC15
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We forgot to add "/s" in page 5 (should be km/s instead of km) at several places when speed is estimated. This will be corrected.