We thank Nima Zafarmomen for these comments.  Please see the original comments below in plain type, and our responses in bold.  

1) While ERRA is introduced as a novel approach to estimate impulse response functions in nonlinear, nonstationary, and heterogeneous systems, the paper could benefit from a more detailed explanation of how ERRA compares to or improves upon traditional models. Could you clarify the specific advantages of using ERRA over simpler regression-based methods, especially in terms of its handling of nonlinearity and nonstationarity?

Our study does not introduce ERRA, per se; that was done by Kirchner (HESS 28, 4427-4454, 2024), as a specific application of a more general approach to impulse response functions in nonlinear, nonstationary, and heterogeneous systems (Kirchner, Sensors 22, 3291, 2022).  Sections 4 and 5 of Kirchner (2022) present benchmark tests of the handling of nonlinearity and nonstationarity, and illustrates the consequences of ignoring nonlinearity and nonstationarity, using synthetic data.  Sections 3 and 4 of Kirchner (2024) illustrate similar principles using applications to real-world hydrological data.  Together, these sections comprise over 20 pages in print, so it would not be appropriate to repeat them here.  We can, however, refer readers to the relevant sections and figures in these previous publications.

2) The study discards certain catchments due to unreasonable Q/P ratios or the presence of dams. How does the exclusion of these data points affect the generalizability of the results, particularly in arid regions where water scarcity issues might be more prominent? Could this exclusion introduce a bias towards more typical hydrological conditions?

These catchments were excluded for quality control reasons. In any of the climatic regions of Iran, if the average measured Q is greater than 0.8 times the average measured P – implying that evapotranspiration is less than 0.2 times P – this is a clear indication that there must be substantial errors in the measurements of Q, P, or both. Thus there should be no impact on the generalizability of the results, because one should not be trying to generalize from clearly erroneous data. In any case, this criterion only excluded 154 basins out of 1155, so the overall impact on our results should be small (but again, excluding erroneous data is clearly the right thing to do).

We excluded catchments that were substantially affected by dams (as revealed in satellite imagery), because discharge below dams reflects both dam management decisions (which are not trying to study) and natural hydrological processes (which are the focus of our investigation). We need to exclude records below dams if we want to see the behavior of the physical system, without the confounding effects of dam operations. We don't think this affects the generalizability of our results, because as far as we know, the physical processes relating precipitation to streamflow presumably are not different in basins where people subsequently decide to build dams, and basins where they don't.

3) The study highlights the interactions between groundwater depth, topography, and climate but doesn't fully explore potential synergistic or antagonistic effects between these factors. Could you provide more in-depth analysis on how these interactions vary across different climatic zones, particularly in extreme arid versus humid regions?

In the discussion section, we already provide a detailed analysis of how shallow groundwater in humid regions leads to higher runoff peaks, while deeper groundwater in arid regions promotes infiltration and reduces runoff, highlighting the synergistic effects of aridity and groundwater levels. We emphasize the role of the aridity index (AI) in influencing these interactions, with the combination of AI, topography, and groundwater depth shaping runoff behavior in different climatic contexts.

Statistically, one can test for interactions by including interaction terms in regression models like those reported in Table 1.  We tested for such interactions, and none were statistically significant, which is why we didn't report them.  We can of course add a comment that explains this.

4) The paper states that larger catchment areas tend to have lower peak heights of runoff response. However, the correlation is weak, suggesting that catchment area is not the dominant factor. Could further sensitivity analysis be done to isolate the contribution of catchment area to the runoff response, especially considering regional variations in topography?

It is intuitive that larger catchments have lower runoff-response peak heights, because different precipitation events from different parts of the catchment with different travel times are ultimately mixed at the gage. What our multiple regression analysis exactly does is to isolate the contribution of catchment area to streamflow response by removing linear trends of confounding factors. Our analysis shows that catchment size does not seem to be as important as initially thought, with slope being a more important topographic feature (at least in this data set). Some potentially important factors, such as subsurface permeability or available water storage capacity, cannot be taken into account because we have no data for them. This may account for some of the scatter in the regression results.

5) While the study acknowledges the role of groundwater over-extraction in shaping runoff responses, it could expand on the anthropogenic effects in the regions studied. Could the authors include a more detailed discussion on how land use changes, agricultural practices, or urbanization might affect runoff response in the context of groundwater depletion?

Usually, changes in agriculture/landuse affect only a very small portion  of most catchments on decadal time scales, and thus do not alter the rainfall-runoff relations significantly. For the relatively short time period between 2000 and 2018 we don't expect drastic changes in landuse.

Broadly our conceptual model indicates the direction of expected effects of groundwater decline, however a quantitative analysis of how groundwater decline impacted the presented relations is out of the scope for the current analysis.

6) The study uses temporal averages of groundwater depth but does not account for potential seasonal or inter-annual variations in groundwater levels. How might fluctuations in groundwater depth over time influence runoff response, and would incorporating temporal variability improve model accuracy?

In many locations, the seasonal and inter-annual variations in groundwater levels are a small fraction of the average groundwater depth.  Thus we would expect their effects to be difficult to detect, particularly given the seasonal and interannual variations in other forcing factors, such as precipitation and vapor pressure deficit.  Such an analysis is beyond the scope of the current work.

I highly recommend the authors consider citing recent work on hydrological modeling for irrigation, specifically studies integrating satellite-based vegetation indices to improve runoff prediction accuaract. For example, studies like 'Assimilation of Sentinel‐based Leaf Area Index for Modeling Surface‐Groundwater Interactions in Irrigation Districts'

The goal of our analysis is not to predict runoff, but to understand runoff generation processes and to characterize the relationship between precipitation and streamflow, as modulated by landscape characteristics (including groundwater levels). The challenge with using vegetation indices such as LAI and NDVI is that they are strongly influenced by variations in climatic aridity, which is also a direct driver of rainfall-runoff relationships.  Thus in our analysis we consider variations in climatic aridity to be the root driver of both vegetation patterns and the sensitivity of runoff to rainfall (which is of course also modulated by vegetation, as an intermediary in the climate-vegetation-streamflow causal chain). 

We thank Nima Zafarmomen for these further comments, which are reproduced below, with our responses in bold.

1)    The authors note that statistical tests for interaction effects did not produce significant results, suggesting limited “synergistic” or “antagonistic” interplay among aridity, groundwater depth, and slope. However, in highly heterogeneous catchments—or in regions experiencing rapid anthropogenic alteration—interaction terms can become obscured. I recommend you divide catchments into clusters (e.g., extreme-arid vs. semi-arid vs. humid) and re-running a separate regression or partial correlation for each climate cluster. This might reveal region-specific interactions between groundwater depth, slope, and aridity that are masked when grouping all basins together.

Thanks for this suggestion. We will consider this approach when revising the manuscript.  We note, however, that cutting the data set into pieces will reduce the statistical power in each piece, and that the effects of aridity will be less obvious in clusters that have been selected according to aridity itself (and thus which encompass narrow ranges of aridity). 



2)    The authors excluded basins with dams and those with suspect Q/P data ratios, defending that choice to remove clearly erroneous or management-driven data. However, large-scale dam construction and data anomalies often co-occur with water scarcity or over-exploitation. I suggest provide a short subsection or appendix explaining how many catchments were removed in each climatic zone, along with summary statistics. This detail can help readers assess whether certain regions or aridity classes became underrepresented.

We all agree that data that is obviously incorrect cannot be included in a serious analysis and that including or excluding certain basins will not resolve the intrinsic sampling bias that arises from working with natural point measurements. Note that the distribution of stream gages is also not uniform across the country and is subjected to management decisions.  We will be as transparent as possible about the data collection and sample selection in our revised manuscript. 

3)    The manuscript treats declining groundwater primarily as a static or background phenomenon, with the authors explaining that assessing interannual variability is out of scope. However, in many arid and semi-arid regions of Iran, agricultural water demand (and thus groundwater pumping) can fluctuate seasonally. Even a concise paragraph on how seasonal groundwater extraction might alter infiltration/runoff partitioning would be valuable. The authors could highlight existing studies or anecdotal evidence (e.g., “dry-season pumping draws down water tables, potentially diminishing baseflow and altering subsequent runoff peaks once the next rainy spell arrives”).

Thanks for this comment.  We will see what we can do.

4)    The current study uses daily time steps and annual-mean groundwater depths. Some of Iran’s rainfall occurs in short bursts during transitional seasons, while over-extraction of groundwater might be strongest in the growing season. Suggest a follow-up framework in which the ERRA approach is applied to seasonal subsets of data to assess whether monsoon-like precipitation events or dry-season extraction produce distinct RRD signatures. Even if the authors have limited time series to do this robustly, a short mention of how seasonal segmentation might provide additional clarity on the processes would strengthen the broader relevance of the work.

Thanks for this comment.  This might indeed make an interesting follow-up study but is outside the scope of the present paper.  

5)    ERRA gives an empirical characterization of rainfall-to-runoff “impulse response,” but readers might also want a conceptual link to classic infiltration, saturation excess, and variable source area processes. Add a brief conceptual figure or paragraph illustrating how deeper vs. shallower groundwater can shift the infiltration capacity or the areal extent of saturated areas, and how that shift emerges quantitatively in the RRD peaks. Even a high-level conceptual depiction would help tie the empirical results back to established hydrological theory.

Thanks for this suggestion. We will consider whether it would be helpful to include a conceptual diagram illustrating the different flow paths under different climatic conditions, although we don't want to go beyond what the available data can show.

We thank the reviewer for these helpful and insightful comments. Below we provide a point-by-point response to the individual questions/suggestions.

The reviewer’s comments are marked in normal font and our responses are in bold.

It was a please to read the manuscript on “Climatic, topographic, and groundwater controls on runoff response to precipitation: evidence from a large-sample data set”. The study analyzes the potential controls of the effectiveness of runoff generation per unit of precipitation over a large number of catchments in Iran using recently developed Ensemble Rainfall-Runoff Analysis. The authors examine catchment area, aridity, and slope and groundwater depth as potential controls. The study provides important insights on the controls of runoff generation in arid and semi-arid environments.

Thank you!

The manuscript is well-written and structured. I suggest to additionally highlight the importance of such studies in the arid environments. Moreover, I recommend a more rigorous selection of representative groundwater wells that might be the reason behind its lower importance. Please find my detailed comments below.

Detailed comments

Choice of the representative groundwater well: From the description in the manuscript, it was not clear how groundwater wells were linked with corresponding surface catchments. In my opinion the choice of a representative well is not straightforward, especially in case of complex hydrogeological settings and large surface catchments. This might also be the reason for the relatively weak correlations between runoff peak height and groundwater depth (Line 242). I suggest to use hydrogeological maps (e.g., hydraulic conductivity) to identify representative wells out of more than 13,000 wells available for the study.

We understand that selecting a representative well is challenging, particularly in complex hydrogeological settings and large catchments. For this reason, we did not select representative wells but instead calculated the temporal mean groundwater depth for all well level time series that were available in each catchment, and averaged these to obtain a catchment mean value.

Introduction: The novelty can be additionally highlighted in the Introduction by outlining possible differences in the controls of runoff response between arid and temperate climates. While in the temperate climates several large sample studies (e.g., Norbiato et al., 2008 (https://doi.org/10.1016/j.jhydrol.2009.06.044); Tarasova et al., 2018 (https://doi.org/10.1029/2018WR022588); Zheng et al., 2023 (https://doi. org/10.1029/2022WR033226)) investigated potential controls of variable runoff response, in the arid environments such studies are indeed missing.

We will add a new paragraph to the revised manuscript highlighting the lack of studies on streamflow response particularly in arid landscapes. 

Line 33-35: A somewhat more differentiated argument could be useful here, summarizing the main findings of these large list of studies that are named here.

In the revised manuscript, we will clarify that storage levels include both groundwater and soil moisture, and will add appropriate references.

Line 37-38: It might be worth mentioning here Tromp-van Meerveld and McDonald, 2007 (doi:10.1029/2004WR003778) here.

Thank you very much for drawing our attention to this.  We will reference it in the revised manuscript.

Line 46: It might be worth mentioning here the work of Botter et al. 2013 (https://doi.org/10.1073/pnas.1311920110)

We will reference this the revised manuscript.

Line 66: Please correct the reference here.

This is standard citation for an un-dated reference where the author is an organization rather than an individual.

Line 76: It is not quite clear what is meant by a “reasonable catchment”? Please clarify. Moreover, please indicate if the catchment area was provided by the corresponding authorities and if it was used to test the accuracy of the delineated catchments.

 The term "reasonable catchment" referred to gages for which the watershed delineation process failed. We will revise the wording in our revised manuscript stating that “we excluded gages for which the watershed delineation process failed."  

Line 78: Please motivate the choice of this dataset. Was it tested in Iran or in the comparable environments?  Please also specify its spatial resolution.

CHELSA is a widely used global precipitation dataset at daily resolution. Although the dataset has not been specifically tested in Iran, it has been validated in a range of similar semi-arid and mountainous regions. The dataset has a spatial resolution of 30 arc-seconds (approximately 1 km), which allows for detailed analysis of rainfall patterns at a high regional scale, making it ideal for extracting daily rainfall time series for each catchment in the study.

Line 79-81: Please clarify if the Q/P criteria was used to avoid anthropogenically affected areas, or to eliminate catchments with erroneous Q and P observations.

We used the ratio of Q/P in a first step to eliminate basins with obviously wrong hydrographs. We will revise the text in our manuscript to make this point clearer.

Line 85: Please clarify if only one groundwater well per catchment was used.

Our analysis does not rely on a single groundwater well per catchment. Instead, we first calculated the temporal mean groundwater depth for every well within a catchment and then average these individual well means to derive an overall mean depth to groundwater for each catchment.

 

Figure 2: I suggest to display maximum 2 years of time series. Otherwise, the differences between stations are not really visible.

We recognize the suggestion to display a shorter time series for better visibility of station differences. However, we chose to present the entire time series to capture long-term trends, including regions where streamflow is gradually declining. Limiting the display to only two years could obscure important patterns and hydrological changes crucial to our analysis. However, we will add a plot showing the detailed time series for the timespan  2000-2002 to the supporting information of the revised manuscript.

CC3 was re-submitted as RC2, and our response can be found there.

We thank Abdolreza Bahremand for these helpful and insightful comments. Below we provide a point-by-point response to the individual questions/suggestions.

The reviewer’s comments are marked in normal font and our responses are in bold.

I am pleased to see that this paper is a practical application of the Ensemble Rainfall-Runoff Analysis (ERRA) method, as presented in the impressive paper by Professor Kirchner, 2024 HESS. The paper is concise and well-structured, making it an enjoyable read with no redundant text or sections. It makes a valuable contribution to the understanding of runoff response in arid and semi-arid regions, particularly in Iran, by employing the innovative Ensemble Rainfall-Runoff Analysis (ERRA) method. The use of a large-sample dataset (211 catchments) spanning diverse climatic and topographic conditions enhances the generalizability of the findings.

My comments: 

1. I wonder why you did not analyze whether Q/A (runoff per unit area) shows a statistically meaningful relationship with slope, groundwater depth, and aridity index. Wouldn't this provide a useful benchmark alongside the ERRA analysis? Even if the correlations are weak, wouldn’t presenting this analysis address potential reader curiosity and offer additional insight?

Thank you very much for this suggestion. Like RRD peak height, total discharge per unit area is negatively correlated with basin area and groundwater depth, and positively correlated with mean topographic slope.  But in contrast to RRD peak height, runoff per unit area is positively correlated with aridity index, while RRD peak height is negatively correlated with aridity index. This behavior is indeed interesting and will be discussed in the revised manuscript.

2. I noticed that some of the results cannot be well explained by traditional runoff mechanisms, such as Hortonian or saturation excess runoff, as described in textbooks and literature. I wonder if you avoided discussing these mechanisms for this reason or simply felt no need to include such a discussion. Similarly, you avoided mentioning or justifying the results, particularly those related to the aridity index using the Budyko approach. I’m not sure how to best address this, but I thought it might be worth mentioning for further consideration if it aligns with the focus of the paper.

Runoff mechanisms are difficult to see in daily streamflow dynamics, and an exploration of runoff mechanisms would require much more detailed information on soil moisture, groundwater dynamics, etc. In any case our main objective here is to see how runoff behavior correlates with possible drivers, not to attribute runoff behavior to specific mechanisms.

3. While readers familiar with Professor Kirchner's excellent work (HESS 2024) may understand ERRA, those encountering it for the first time will likely find the current explanation insufficient (section 2.3).

We will somewhat expand our explanation of the Ensemble Rainfall-Runoff Analysis method in the revised manuscript

4. You classify groundwater depth into shallow, intermediate, and deep based on percentiles (25%, 50%, and 25%, respectively), but you do not provide the actual depth ranges for these categories.

Thank you very much for this useful comment. We will add the ranges corresponding to the four quartiles to the revised manuscript.

5. Could you clarify whether all 211 catchments are non-nested, or if some share nested relationships? If applicable, please explain how this was considered in the analysis.

Thank you for raising this point. 47% of our catchments contain no overlap with other catchments, and only 27% of the analyzed catchments overlap with other catchments by more than 20% of their drainage areas. We will add this information to the text of our revised manuscript.

6. Don’t you think that erosive features and geomorphologic parameters (such as drainage density) could play a significant role in shaping runoff response, and their inclusion or acknowledgment in the study would have added depth to the analysis? Currently nothing has been mentioned about them in the paper.

We recognize that factors such as drainage density could play an important role in shaping the runoff response. However, due to the lack of detailed stream maps for the study basins, we were unable to estimate drainage density (DD). However, our analysis includes slope, which is a typical geomorphic variable.

7. You could have acknowledged the potential influence of geology in your discussion. (In general, geology has been largely ignored in the paper. The word "geology" and any of its derivatives are mentioned only once, in line 194). For example, you could have noted that geological heterogeneity (e.g., variations in bedrock permeability and soil type) may contribute to variability in runoff response but was not included due to data limitations or scope constraints. Including examples from the literature, such as Izadi et al. (2020) Investigating the Effects of Lithological Units on Runoff Coefficient (A case study of 18 watersheds in three climatic regions of Iran) (in Persian, but with figures and an English abstract that clearly illustrate the impact of lithological units on runoff coefficients in Iranian watersheds), would have highlighted the importance of geology in hydrological processes. 

We agree with the reviewer that geology, infiltration coefficients and permeability have a significant effect on runoff generating processes. We will expand our discussion on the potential effects of these geological factors, including a discussion with respect to the findings of Izadi et al. (2020).

8. I believe the literature review on studies involving Iran data could be more extensive, although I appreciate the paper's current concise structure.

We will reference additional studies in Iran in the introduction of the revised manuscript 

9. Corrections for Figure 1:

Scale Unit: The unit for the scale should be "km" (lowercase "k" and "m") instead of "Km". This follows the standard scientific notation for kilometers.

Legend Label: The word "Legend" can be deleted from the map. The legend itself (color-coded circles) is sufficient to indicate what the colors represent, and the label is redundant.

Legend Symbols: The legend in Figure 1a currently uses colorful squares to represent the groundwater depth classifications (shallow, intermediate, deep). However, the map itself uses colorful circles. The legend should be updated to use circles instead of squares to match the map symbols. This will avoid confusion.

Geographic Coordinates: The geographic coordinates around the map (latitude and longitude) are missing the degree symbol (°). The coordinates should be labeled with the degree symbol (e.g., 30°N, 50°E) to conform to standard geographic notation.

10. Please ensure consistency in the formatting of axis labels by using parentheses for units in Figure 2, as done in the other figures.

Thank you very much for catching these “glitches” in the figures. We will revise the figures according to your suggestion labeling units in square brackets.

11. In several parts of the discussion (e.g., Sections 3.1, 3.2, and Conclusion), you have used "peak" without specifying "RRD peak", which could lead to misunderstandings. For example, readers might mistakenly interpret the findings in terms of peak discharge, which could contradict general hydrological knowledge (e.g., larger catchments typically have higher peak discharges, but the study finds that larger catchments have lower RRD peaks). To avoid confusion, you should consistently use "RRD peak" instead of "peak" throughout the manuscript. 

Thank you very much for this comment. We will adjust the terminology in our revised manuscript always using RRD peak height, when referring to the peak of the RRD curve.