I applaud the authors' effort to analyse subsurface storm flow (SSF), given that this is an underresearched topic. In general, the experimental setup is sound, but still the findings are heavily biased (as often in hydrological research). This bias results from the fact that we can rather easily analyse 100 storms to quantify the influence of storm characteristics and antecedent moisture conditions. From this must follow, even without analysing the data, that storm and antecedent conditions have an influence. This, however, does not answer the question of whether this influence is large at all (as put forward in the manuscript), because the influence of other drivers was not analysed. They could have, and likely have, a much larger influence, but we cannot analyse 100 soils, 100 forest types, or 100 catchment sizes as easily as 100 storms, and then still do not capture the strong interaction of soils, forest types, and catchment sizes. This bias, which does not diminish the scientific value and quality of this study, should be prominently displayed because, very likely, subsequent modelling based on the study results will conclude that soils, forest use, or catchment size have only a minor effect, although the scientific foundation to support this is weak or even lacking.

The study, like all studies, depends on assumptions. The assumptions were justified. However, I missed a critical assessment of how much the findings were influenced by the assumptions and would differ under deviating assumptions. In particular, I found the definition of rain events (break 6 h) critical, given that the duration of runoff events was much longer, with the falling limb of the hydrograph lasting 240 h. These short rain events were visible on the hydrograph, but they were not independent of the previous rain that caused the falling limb. The authors use the antecedent soil moisture conditions (ASI) to correct for this discrepancy between definitions of rain events and runoff events, but I wonder whether this attempt to correct one deficit by introducing another yields helpful and applicable findings. This notion can be supported by several arguments:

• Whether a peak in rain intensity becomes visible in the hydrograph or not depends on the catchment size. Event definition and ASI cannot replace catchment size.
• I would expect the most prominent SSL event to occur when a large rain falls on very dry soil because then the largest contrast in hydraulic conductivity, differing by several orders of magnitude, will result above and below the wetting front. Hence, a low ASI will promote SSL, which is opposite to what happens when one rain event is split into two. Splitting a rain in two will thus cause an erroneous relation to ASI.
• For surface runoff events on very small plots with the falling limb lasting only minutes, it was found that even a break of 23 h was not sufficient to classify the second part as a separate rain because the hydrograph continued as if no break had occurred (for details see Auerswald and Gu, 2021). A modelling as a separate event at a higher ASI would have produced a different shape of the hydrograph that did not agree with the measured hydrograph.

Details

L 18-19: No; rainfall and moisture were the only variables analysed. Hence, it is not known whether they primarily control SSF.

L 22: This number is misleading because it depends on definitions and assumptions that are not explicitly stated in the abstract.

L 35: Doesn't the condition "overlain by a more permeable layer" always exist due to the wetting front? Isn't the more general condition leading to SSF that conductivity plus sorptivity (sensu Philip) is smaller than rain intensity?

L 56: The event is not yet defined. Furthermore, this sentence suggests that the events of precipitation and SSF agree, whereas later, SSF lasts much longer than precipitation.

L 72: ASI is not defined yet (only in the abstract).

L 86: I would argue that the complex relationships are a result of a complex definition of rain events being part of an SSL event.

L 121: Does 'concave' apply along or across the slope? To me, Fig. 1 suggests a convex shape across the slope (diverging water), not a concave slope. I may misinterpret Fig. 1.

L 125: The unit should be mm/yr.

L 130 ff: The soil material is either described as periglacial deposits or as colluvium. Both terms appear to be used interchangeably. In my understanding, both are different (Pleistocene vs. Holocene; existing along the entire slope vs. existing in toe-slope positions; coarse stones are possible vs. coarse stones are usually depleted compared to upslope soils).

L 160: I wonder why Robinia is defined to the species level while all other trees are only defined to the genus level.

Table 1: Depth is not clear. Is this the upper or the lower boundary or the midpoint? It may be worth noting whether the size classes follow the 2/50, the 2/63 or any other system.

L 218 ff: This is a strange definition of an event that must yield a complex behaviour, as complained about on L. 86. Please note that for erosion events, also a minimum dry period of 6 h is until today a generally accepted requirement going back to Wischmeier (1959), who developed this from only 20 m long plots. These two identical definitions of a dry period separating runoff events are in conflict because the travel time of surface runoff is several orders of magnitude shorter than that of SSF.

L 264: 'Non-triggering' is also a strange category. It assumes that rain does not contribute to SSF when it does not trigger a noticeable peak in SSF. From water balance considerations, the non-triggering events during the falling limb of the hydrograph should also contribute to SSF. Or where else does the water go? Ignoring these events must increase the unexplained fraction of SSF.

L 277: Shouldn't it read "trenchflow rate"? The omission of the term 'rate' is particularly confusing, as rates are often abbreviated with lowercase letters, while sums are abbreviated with uppercase letters.

L 281: This assumption is in conflict with the general understanding of hydrology, which suggests that soil moisture changes due to rain. Why not use V_tot/(P_tot-VWC change)? This would lead to a more realistic estimate of the contributing area.

L 301: Why should the average VWC be important and not the total? In your assessment, H_tot is constant, and hence the difference between average and total does not appear. However, when transferring your results to different catchments, the difference becomes important. I would even expect that a contrast leasing to contrasting conductivities is important. A contrast would neither be captured by the average nor the total but by SD or similar metrics.

L 313: Why is D used here and not H_tot? Is there a difference between the two? Explain.

L 318 + 328: Shouldn't ASI minus PWP (permanent wilting point) be used instead of arbitrarily adjusting ASI? From a theoretical perspective, ASI should not be the correct parameter. Furthermore, I do not see a justification for a fractional adjustment factor to correct this.

L 334: This is clearly a spurious correlation that cannot be interpreted because an identical variable is used on both sides of the equation (see Pearson, 1897, or specifically in hydrological research: Kenney, 1982). For some specific cases, a correction exists (Kenney, 1982; Kanaroglou, 1996).

Fig. 8: Many of these correlations are at least partly spurious because both sides of the equation contain common elements. E.g., the calculation of P_tot depends on the intensities. The significance, as denoted, is then meaningless. This makes interpretation of the figure impossible because the degree to which common numbers were used on both sides differs (I5 contributes considerably less to P_tot than I60; hence, the difference between correlation coefficients may only be due to a different fraction of the spurious component). Furthermore, the table is clearly multiple testing, which would require an adjustment to maintain the alpha level. Less adjustment would be necessary if the authors did not weaken the statistical power of their analysis by testing parameters like I5 or I10, for which I can see no hydrological argument as to why these parameters should generally drive SSF. Also, no confidence intervals are given. Hence, it cannot be decided whether one correlation coefficient is larger than the other. The text wrongly assumes that the larger value is always better.

L 440: Does the area really change, or does this only reflect the shortcomings of Eqn 1?

Table 3: r² and the parameters of Eqn 4 are spurious. How can the r² of Eqn 5 be calculated when the text says that Eqn 5 was obtained by rearranging Eqn 4? Is r² then the Nash-Sutcliffe efficiency? Calculation Eqn 5 directly would be advantageous because it avoids the spurious step.

L 4 66: No confidence intervals are given to support this statement.

L 478: same remark as above

L 508-509: Where is this shown? A test like the Hotelling test must be applied to support such a statement. I am unsure whether the Hotelling test can be applied to Spearman's correlation or if an analogous test exists. If not, Spearman appears unsuitable for the intended task.

Fig. 19: Again, confidence intervals would be required to support the interpretation made in the text.

L 738: This statement is only true for SSF volume as defined in this study. Whether this is generally true remains unknown.

L 742: The contributing area was unfortunately not quantified. Only a minimum area was quantified. By omitting the adjective, a wrong impression is given (not to mention that the adjective is wrong as well, because the equation makes an unrealistic assumption).

L 764: R. C.?

L 767: and beta.

Table A1: The assumed porosities for the two lowest depths of T3-B3 are very unlikely. For the measured bulk density, this would only be possible if the density of the solids were 3.2 kg/L, which is considerably above that of the main minerals in soils. Something else must be wrong in the calculations if they require unreasonable porosity to yield reasonable results. In contrast, the measured porosities are in line with the measured BDs.

References:

Auerswald, K., Gu Q.-L.: Reassessment of the hydrologic soil group for runoff modelling, Soil and Tillage Research, 212, 2021. https://doi.org/10.1016/j.still.2021.105034

Kanaroglou, P.S.: On spurious correlation in geographical problems, The Canadian Geographer, 40, 194–202, 1996.

Kenney, B.C.: Beware of spurious self-correlations!, Water Resources Research, 18, 1041–1048, 1982.

Pearson, K.: Mathematical contributions to the theory of evolution – On a form of spurious correlation which may arise when indices are used in the measurement of organs, Proceedings of the Royal Society of London, 60, 489–498, 1897.

Wischmeier, W. H.: A rainfall erosion index for a universal soil-loss equation, Soil Sci. Soc. Am. Proc., 23, 246–249, 1959.

Review of „Influence of rainfall event characteristics and antecedent conditions on subsurface stormflow response of two forested hillslopes”

The authors analyze the relationships between rainfall and subsurface stormflow using a comprehensive data set from two trenched hillslope sites, which is of great potential interest to hillslope hydrologists. It is evident that the authors put considerable effort into data collection and processing. They also provide a comprehensive exploratory analysis of the data, and their findings appear to corroborate earlier studies in other research catchments. However, some aspects of the analysis seem questionable, which also affects the conclusions that are drawn. These aspects are elaborated on below.

From a general perspective, the study would benefit from a clear perceptual model of hillslope hydrology underlying the analysis. The correlation analysis presented here probably does not aim at investigating the general causality of rainfall and runoff, which is not in question, but quantifying their possible relationships under different conditions. An exploratory data analysis alone, however, is limited in its explanatory power, if not combined with a perceptual model that enables testable hypotheses. The manuscript does not clearly describe on which perceptual model the analysis is based. For example, the authors derive a quadratic increase of runoff with rainfall, which is hardly physically interpretable over the entire range of possible flow conditions. A large part of the analysis uses the concept of variable contributing area/MCA, but also the concept of varying subsurface runoff coefficients is used, which implies a fixed-size catchment area. It would be interesting to see whether the trench data allow determining which concept is more realistic. In addition, an estimate of the catchment area based on topographic analysis would be extremely helpful to compare rainfall and runoff volumes in millimeters, even if used only as an upper bound.

Another point is that the analysis is based on field data, yet measurement uncertainty is not addressed, and there is no discussion of how it might affect the results. The authors select data for the analysis, but the criteria for this selection are not made fully clear (only two of three trenches are used, “outliers” are removed without further explanation, selective data ranges in figures).

The manuscript is thus not suitable for publication in its present form; a critical revision of the analysis would be needed. The data and data processing, however, are very valuable for further research. Independent of the further progress with the present manuscript, I would encourage the authors to consider preparing a data publication in ESSD or a similar journal, in order to increase “our ability to generalize the findings and explore the influence of a broader range of storm sizes, intensities, antecedent wetness conditions and different hydrogeologic settings.”

Major Comments

L 117: Only two of three trenches were used in the analysis. Please provide more reasoning why T2 was excluded. Even if not as comprehensive, it could provide further insight to the matter, and with your automatic analysis, it should not be too much work to analyze the data as well.

L 301 to 306: This approach gives much more weight to sensors located far from others, and can exceed the actual soil volume that is sensed by the device. In your case, the sensor at 150 cm depth has more weight than the two sensors at the top combined. The soil moisture in the upper soil layer would typically be more dynamic, and perhaps also more influential on hydrological processes. Including soil moisture from a lower layer with an even higher weight might thus dampen the contrast in VWC across events. Integrating over an interpolated profile might be an alternative.

L 314f: While in Eq. 2 sensors from six depths are averaged, yet here only three are used? Furthermore, the weighted averaging described above considered the midpoints between sensors. Following this approach, the total depth would be in the middle of 60 and 150 cm, and not 75 cm. This is not consistent.

 L 317: “if the ASI is too large, the effect of the initial conditions can be over-represented” – how is “too large” defined? The goal of this study is to investigate the effect of initial conditions, so how can you know that it is “over-represented”? This would only be possible if you knew about the relationship beforehand.

L 333ff, eq. 4 and 5: Eq 4 has P_tot on both sides, and thus results in spurious correlation. Eq 5 separates V_tot and P_tot, so this problem does not occur. This quadratic model could also be fitted to the data without taking the detour of eq. 4. But, more importantly, what is the physical interpretation of this? Is there a limit to this quadratic growth, or will there be a point where, say, 10 mm of rainfall produce 100 mm of flow (for a respective rainfall duration)?

L356ff, Fig 5: Unclear what aggregation by association means. Please describe that clearly in the text. It appears that intensities were averaged over events - why not take the maximum? Please add to the caption that the axis in a) has a gap, and that the axes in a and b are not the same scale.

L 403, Fig. 8: Have you also analyzed the correlation of ASI alone?

L 418-427, Figs. 9, 10: The manually plotted trends can be dangerous, if they imply a different kind of relationship than actually supported by the data. Both variables involve measurement uncertainty, which will influence the locations of the data points. Conclusions about the difference of the two sites cannot be drawn from this. On the linear scale, the patterns do not look too different, and also on the log scale, the dashed line from T1 could be made fit to T3.

L 443: Why should the subsurface runoff coefficient not be “very small” in some cases? How are these events characterized in terms of rainfall, not SSF metrics? For small rainfall events, this would be plausible, because of interception, or soil storage.

L 449f: How many events were included in this selection (% of all events)?

How do you justify analyzing only a selected subset of the data? Including other data would probably give very different results, which is evident when comparing Fig 14 against Figs 9 and 10. The full data show a plateau, although the log scale makes comparison difficult. The relationships in the data thus are essentially different when looking at the entire range, compared to the quadratic relationship this analysis is tailored to. This seems very questionable. Even more so, as a quadratic relationship suggests that the SSF volume increases faster with increasing rainfall. Without limitation, this implies that the SSF volume surpasses the rainfall volume at some point, which is not physically possible (compare comment on eqs. 4 and 5).

L 494: The role of rainfall intensity is not so evident for me in Fig. 16. Between 20 mm and 30 mm, the Q_dmax values cover a wide range. There is not a clearly discernible pattern with regard to VWC_i and I_30? For example,  at T1, which has more events in this range, the Q_dmax for medium intensities and medium VWCs range between ~150 and 650 l/h.

L 563f: Interception storage does not seem to be subordinate in view of your statements regarding the non-triggering rainfall events. Would interception not be the main explanation for the triggering threshold and the seasonality in "Fig." 19?

L 571 – 576: Would considering the soil moisture deficit, i.e. the water volume required for saturation, be a more useful proxy here than ASI? The minimum water volume available for SSF (and overland flow) would then be P_tot - Interception - Soil Moisture Deficit.

L 576: I do not agree that the goal of hydrological research should be limited to "obtaining the best fit".  I would favor to include our physical understanding in the data analysis and the interpretation. The "optimum depth" is site dependent because of soil properties like thickness or porosity, which are known to vary across sites.

L 584f: “P_tot –V_tot relationship is poor” - This statement is not clearly supported by the data. Figures 9 + 10 indicate a positive correlation of V_tot and P_tot also above 40 mm, at least at the linear scale, and possibly also a difference between antecedent soil moisture conditions. There is some scatter, and there are admittedly only a few data points in that rainfall range, but a trend is visible, and it is also what one would have expected (more rain, more flow).

L 597: Is the 5 to 12 mm threshold really backed up by these citations? Quoting from Tromp- van Meerveld and McDonell 2006a: "Our analyses suggest that there is a clear threshold for significant (>1 mm) subsurface stormflow to occur; significant subsurface stormflow occurred only during rainstorms larger than 55 mm". Fu et al. 2013, Fig. 7 shows a threshold of 5 mm per 0.5 h, not total volume. Noguchi et al. 2001, Table 2 show that the smallest storm event analysed had 15.6 mm total precipitation.

L 611f: This raises the question of what the physical meaning of this would be. Do you consider the soil to drain below the initial soil moisture level during the SSF event?

L 616ff : Either the contributing area changes, or the runoff coefficient of the catchment area changes. They are mutually exclusive. Which kind of field observations of contributing area are you referring to?

L 619ff: Are there alternative possible explanations? For small events, could there have been increasing accumulation of water in downslope direction, resulting in a small SSF volume at the trench, but not enough for a detectable rise in groundwater level? Or overland flow that infiltrated downslope? Or spatially variable rainfall?

L 623ff: On the contrary, one could also argue that without knowledge about the contributing area and about specific discharge, the observed volumes are not interpretable in terms of the local water balance.

L 635 - 643: Although you might not be wrong, I do not fully get the point here. First, is the "barrier" you are referring visible in Fig. 10? Is it the part of the hand-drawn curve between 10 and 20 mm of P_tot? If so, it might be an artifact of the manually drawn trend line. If I understand your argumentation correctly, the increasing rainfall results in an increased contributing area, which in turn might add additional "barriers", or sinks, to the flow field. Why would then the volume not increase just due to the additional rainfall received by the former smaller contributing area?

L 725: Please elaborate the discussion of this point, as this contradicts your finding of higher runoff coefficients in winter.

L 739ff: This conclusion is not supported by your data. The two sites may differ in the precipitation threshold, but they do not really show a different pattern in rainfall-runoff response, see Fig 14. An apparent difference in behavior could be artificially created by the manual trend lines in the semilogarithmic plots of Figs. 9 and 10, at least for wet conditions. The different scale of the x-axis for the linear-linear plots could also add to this misconception.

L 775f: You probably should not simply adjust the lab-measured porosities because the Topp equation gives a different result. On the one hand, you measured porosities in the lab in order to use the CRIM because Topp cannot account for temperature effects, which you claim to be important. In cases where the two differ, you ignore the measured data, including the reported bulk densities, and take some arbitrary value? Also, the increase in porosity at greater depth at T1 is questionable. How would your results change if the actually measured porosities are used?

Minor Comments

L 67: Maybe word it the other way round, making V_tot the dependent variable

L 74: I am not sure whether it is helpful to portray the findings as “complex”. We indeed know about the threshold behavior, which is partially depending on soil moisture conditions. Otherwise, SSF is proportional to the rainfall volume and intensity, which is logical considering their causal relationship.

L 76: Soil characteristics including macropores should be mentioned here as well.

L 116ff: Perhaps consider adding some photographs of the trenches?

L 134: “ to the base of the trench” at xy m: mention the depth of the trench here

L 144: “silt (loam)” – what is it? Silt and loam are describing different particle size distributions

L 175: “the end of the study period (27 May 2024–25 June 2024)” – are the dates indicating the study period, or the time of installation of the weir? If the latter, you may just omit the parentheses and add “from.. to”

L 201: Please provide your definition of outliers.

L 272f: Instead of I_5, would computing I_10, i.e. maximum rainfall rate in 10 minutes, not help to increase the sample size? It would not touch the significance of the analysis in my opinion, since trench flow was also recorded in 10-minute intervals, but would add ~25% to the number of events at both sites.

L 274f: Please explain this more clearly. Was I_m derived from the others, or were all averaged to get something else?

L380, Fig 7: More explanation needed, in caption and in text. Why are the numbers for subevents/simple events for the same site differing between variables?

L 409: “P_tot > 40–50 mm“– Choose one number that defines "very large" events.

L 428f: Does this refer to the correlation of V_tot and P_tot? Above, the Spearman correlation was used. Uclear why you are showing Pearson here.

L 464, Fig. 14: The x-axis of the right panel is cut off before 15. Please show the full range, or at least point to it in the caption.

L 495: What are the correlations of events > 20 mm?

L 496: “were associated with fairly high rainfall intensities” – and high total rainfall volumes.

L 539: Results not shown? Consider putting these in supplementary material.

L 569-571: Perhaps mention that this corroborates similar findings of many earlier studies, and cite them.

L 603: “In contrast…” - Is this an additional threshold to the ≈ 2 mm one, or is the threshold here at ≈ 15 mm? Please clarify.

L 605: Does this mean that the observations at T1 do not match these results?

L 610: T3 is in Fig 12. Would the 40 mm not apply to both T1 and T3?

L 706f: This would imply that no fast SSF response can be expected in case of large and intense rainfall in wet conditions. What else is expected then - overland flow?

L 710 ff: The different configurations of flow paths - across sites and  across conditions - is the important factor in SSF dynamics. Thus, perhaps consider discussing the methodological issues first and then these 'complexities', rather than putting them 'beside'.

L 733: Which are these “few” studies, and how do their findings relate to yours? Please elaborate.

Technical Corrections

L 69: 2006a or b?

L 69-70: Noguchi et al. … matrix flow: Check wording

L 71-72: how … was present: Check Wording

L 126: temperature and precipitation ARE

L 134: Is the range 2 to 256 mm, or are all greater than 2-256 mm? Consider omitting the “>” and check style guide how to indicate range of numbers

L 271 and elsewhere: P_tot etc. - Check style guide if subscript should be italicized

L 405, Fig. 8: row header reads “Time lag”, column header “lag time”

L 418-427, Figs. 9, 10: Consider making one figure with two panels (also applies to other figures)

Figs 15, 16, 17, 18: Circles in figures are larger than in the legend, which makes the figure unreadable.

L 499: “QΔmax ranging from 130 to 638 mm/h” – check unit

Fig 17, 18: Mention log scale in caption

Fig 19: Is this deemed to be a table? Give more details in the caption and/or the table: these are statistical values of selected data - "trimmed means". Also indicate the number of events in each season after trimming.

L 592: Year missing in citation.

L 598: 2006 a or b?

L 601: Consider replacing "= ca" with ≈, or with words " is approx."

L 604: Figs 10 and 11, should be 9 and 10?

L 710, and others: Consider combining parentheses to avoid “)(“