Catchment transit time sensitivity to the type of SAS function for unsaturated zone and groundwater

Türk, Hatice; Stumpp, Christine; Hrachowitz, Markus; Strauss, Peter; Blöschl, Günter; Stockinger, Michael

doi:https://doi.org/10.5194/egusphere-2025-2597

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https://doi.org/10.5194/egusphere-2025-2597

Preprints

10 Jul 2025

| 10 Jul 2025

Catchment transit time sensitivity to the type of SAS function for unsaturated zone and groundwater

Hatice Türk, Christine Stumpp, Markus Hrachowitz, Peter Strauss, Günter Blöschl, and Michael Stockinger

Abstract. Preferential flow paths in hydrological systems (e.g., macropores or subsurface pipe networks) facilitate rapid water and solute transport, leading to fast streamflow responses and markedly short transit times. While such preferential flow processes are well known in the unsaturated zone and groundwater, it remains uncertain whether catchment-scale isotope-based transport models can accurately represent these fast groundwater flow processes. In this study, we tested the hypothesis that preferential discharge of young groundwater is significant and can be captured by selecting specific StorAge Selection (SAS) functions, i.e., functions that specify if young or old water leaves a storage, at the catchment scale. We systematically compared multiple SAS parameterisations for the unsaturated zone and groundwater using a catchment scale transport model and long-term measurements of hydrogen isotopes (δ²H) data from two headwater catchments (Hydrological Open Air Laboratory, HOAL, catchment in Austria and Wüstebach catchment in Germany). The results indicated that δ²H ratios in streamflow had sufficient information content to identify preferential flow in the unsaturated zone. However, δ²H ratios in streamflow were insufficient to constrain or confirm preferential flow in groundwater, as any seasonal variation of δ²H in pore water was largely dampened by the catchments’ substantial passive groundwater storage volumes. This was further confirmed as the observed attenuated δ²H signal in streamflow could only be simulated when the volume ratio between active and passive groundwater storage was < 1 %. This damping effect affected the estimation of the longer tails (100 < T < 1000 days) of the transit time distributions, making it challenging to estimate how much of the streamwater actually is older than 100 days. In addition, weekly resolution δ²H measurements led to deceptively high-performance metrics (e.g., Nash–Sutcliffe Efficiency), even when key model parameters for groundwater age selection —such as young- versus old-water selection preferences—remain poorly constrained. As a result, the variation in the estimation of the fraction of stream water younger than 1000 days was approximately 20 % in the HOAL and 23 % in the Wüstebach catchments due to the SAS function shape holding similar model performance. These findings underscore the need for complementary data sources, such as multiple tracers, high-frequency sampling, or groundwater-level monitoring, to better constrain preferential flow processes and to reduce uncertainty in catchment-scale water transit time modelling.

Received: 03 Jun 2025 – Discussion started: 10 Jul 2025

Competing interests: Some authors are members of the editorial board of the HESS journal.

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Hatice Türk, Christine Stumpp, Markus Hrachowitz, Peter Strauss, Günter Blöschl, and Michael Stockinger

Status: final response (author comments only)

RC1:
'Comment on egusphere-2025-2597', Anonymous Referee #1, 10 Aug 2025
Thank you for the opportunity to review the manuscript entitled “Catchment transit time sensitivity to the type of SAS function for unsaturated zone and groundwater.” The authors present an interesting study comparing model performance across different setups that vary in the parameters used in the SAS function. This approach aims to deepen the understanding of catchment functioning, specifically the contributions of water from the unsaturated zone and groundwater to catchment transit times in two catchments. Overall, the manuscript addresses an important research gap by challenging an assumption in transit time distribution (TTD) modeling and has the potential to make a valuable contribution.
However, I believe that the manuscript in its current form requires major revisions before it can be considered for publication. My main concerns are as follows:
The language used throughout many sections of the manuscript is often vague and imprecise, which unfortunately leads to several hydrologically inaccurate statements. For example, there is some conflation between residence time distribution and transit time distribution (line 290), the SAS function is described as specifying if rather than how young or old water leaves the storage (line 6), and terms commonly well-defined in hydrology, such as information content (line 10) and “process”, are used incorrectly. A thorough revision of terminology is necessary, particularly in the abstract and introduction, to clarify these points and improve the manuscript’s overall precision.

The hypotheses as currently formulated are not effectively integrated into the manuscript. First, the connection between the hypotheses and the discussion is missing and could be strengthened by revising the discussion section, which currently has some weaknesses (see one of my later comments). Second, the hypotheses are not formulated in a testable manner, which limits their usefulness in framing the study.

Although the results section is generally well-written, the key messages are often difficult to discern. A clearer focus and synthesis of the main findings would greatly enhance the manuscript’s impact.

I am uncertain about the comparability of the different model setups as currently presented. The authors rely on common performance metrics such as NSE for comparison, but their stated hypotheses suggest an information theory or information content approach. If the authors choose to maintain the current comparison method, they should provide a more detailed explanation and justification for this choice. NSE also has certain limitations, which should be taken into account in this context.

The discussion would benefit from a broader perspective. Addressing questions such as the following could improve the manuscript’s relevance and clarity: What are the key findings for the research community? What are the broader implications of this work? How does this study advance process understanding in other, unstudied catchments? Under what conditions might one expect similar or different results?

While the authors refer to a previous study for a description of the model setups, I believe the manuscript would benefit from a brief summary of the underlying assumptions and structural details within the current text. This would enhance clarity for readers unfamiliar with the referenced work. Additionally, the configuration used to test passive groundwater storage requires further explanation. In particular, it would be helpful if the authors could elaborate on the rationale for choosing the specific storage volumes and clarify how mixing within this storage compartment was considered.

Some specific comments are provided below for consideration.
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Title “sensitivity”: It is not clear whether the manuscript presents a sensitivity analysis. Please clarify if such an analysis was performed; otherwise, consider revising the title accordingly.
Title “type of SAS function”: Typically, SAS function types refer to, for example, gamma or beta functions. This may not be what you mean here—please clarify the intended meaning.
Line 3: The terms fast and short are subjective and relative. Please avoid judgmental terms.
Line 3: In the phrase “such preferential flow processes,” please clarify which specific processes from the previous statements are meant—do you mean preferential flow paths?
Line 4: Please clarify the reference of the word “these.”
Line 5: Use the term significant only where statistical significance (p-value) is reported; otherwise, rephrase.
Line 5: The statement “…by selecting specific SAS functions” seems self-evident because preferential discharge of young groundwater cannot be represented without selecting an SAS function. Please refine the hypothesis so that it is testable and cannot be answered with a simple “yes.”
Line 6: Replace “if” with “how.”
Lines 6–8: It is unclear whether the functions were parameterized or if they were part of different model setups. Please clarify.
Line 10: The term “information content” implies the use of information theory; please clarify if that is the case.
Lines 10–18: This section should be improved by clearly stating the main message of the results and explicitly explaining the relationship between age and specific SAS functions.
Line 24: The term “dry period” depends on climatic context; please specify.
Line 25: Specify whether “reaching streams” refers to water after precipitation events or baseflow contributions.
Lines 28–30: As written, “this variability” (temporal) cannot be caused by spatial factors such as catchment topology. You may mean differences in temporal variability among catchments. Please reframe.
Line 33: The word “dramatically” is subjective; please remove.
Line 38: A model, by definition, cannot detect anything: consider alternative terminology. Similarly, “quantify” may not be applicable in this context.
Lines 40–41: The terms “follow” and “system” are too vague: please specify.
Line 43: Consider using “control volumes, such as catchments” instead of just “a catchment,” since the approach could also be applied to a lysimeter or a stream reach.
Line 46: A process cannot be quantified directly from a TTD; the TTD allows you to infer processes. Please check other occurrences where “process” is used in a similar way.
Line 48: Please clarify why “most” applies here.
Line 49: The message of this sentence is not sufficiently clear. Please rephrase.
Line 53: Keep terminology consistent. Use either function or model only when referring to different concepts. Here, it should be “SAS function.” Also, note that the SAS function does not directly capture storage heterogeneity; please define precisely.
Line 55: Same adjustment as above. Use function instead of model if referring to the SAS function.
Line 57: Consider rephrasing, as it is unsurprising that time-variable TTDs reflect temporal TTD variability.
Lines 59–63: Please re-check whether all cited studies actually applied SAS functions.
Lines 66–67: Please explain more clearly what is meant by “the age composition of groundwater flow to the stream.”
Line 69: SAS functions cannot be “measured”; you can parameterize them. Please revise.
Line 79: Specify what the “release of young water” refers to.
Line 80: Indicate where the “generally low longitudinal and transversal dispersivities” apply.
Lines 81–83: This sentence appears disconnected from the previous one; please rephrase for cohesion.
Line 93: Clarify whether “long-term tracer observations” were conducted in streams or in groundwater.
Line 96: The main objective could be presented in a way that connects more clearly to the underlying processes of interest rather than focusing solely on technical aspects.
Line 103: If the term “information content” is used, ensure that it is correct. If information theory was not applied, please rephrase.
Line 107: Please define what is meant by “interpretation” in this context.
Line 108: Clarify the meaning of “representation of preferential groundwater flow.”
Line 122: Please state in which catchment the “predominant soil types” are found.
Line 135: The term “catchment flow” is not defined. Do you mean streamflow?
Line 160: It is important to briefly explain the underlying assumptions and general model setup, even if they are covered in a previous publication. Currently, it is unclear how the SAS functions are integrated into the model.
Lines 178–184: The SAS function is generally time-variable. Please clarify the novelty of the approach described. Explain why the precipitation value was set as it was and define Sr,max.
Lines 195–199: Please explain why streamflow, log streamflow, flow duration curve, runoff coefficient, and δ²H were selected as variables.
Line 199: Avoid subjective terms such as “perfect.”
Line 203: Clarify what is meant by “each combination.”
Line 211: The need for stepwise calibration and the exact order of steps should be made explicit.
Lines 218–221: This information may be better placed earlier in the manuscript for clarity.
Lines 228–237: This section should more clearly describe how different passive storage volumes were implemented in the earlier-described model setup and why these volumes were selected. As it stands, the model configuration is not fully reproducible.
Lines 240–246: Please summarize the key takeaway for the reader.
Line 248: Define what is meant by “feasible parameter solutions.”
Lines 266–276: Clarify whether these results relate to the stepwise analysis, and connect them to Figure 4. The calculated fractions shown in Figure 4 should also be introduced earlier.
Line 290: The explanation (“This was due to…”) belongs to the Discussion. Also, confirm whether “residence time” here should be “transit time,” and note that this is the first mention of the term in the manuscript.
Line 313: Remove the subjective phrase “and somewhat surprisingly.”
Line 315: Specify which variability is being reduced—e.g., variability in streamflow?
Lines 351–354: Consistency with previous findings does not necessarily justify the model configurations or research hypotheses; identical results can occur in the presence of shared erroneous assumptions. Please refine this reasoning.
Lines 357–364: Please state clearly what the novelty of this section is.
Line 369: Clarify whether the described crust formation was observed directly, or if it is inferred.
Line 373: Make the link to the previous sentence explicit.
Line 376: Clarify who assumes this.
Lines 419–444: There is considerable repetition of the results in this section. Consider condensing.
Citation: https://doi.org/10.5194/egusphere-2025-2597-RC1
- AC1: 'Reply on RC1', Hatice Türk, 08 Sep 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2597/egusphere-2025-2597-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-2597-AC1
RC2:
'Comment on egusphere-2025-2597', Anonymous Referee #2, 11 Aug 2025

This is a very interesting paper that addresses the elusive role of preferential flows by introducing an additional consideration to the bucket model, which distinguishes the role of preferential flows through shape functions. It eloquently poses the paper's main questions and refers to some of them at the end, thereby focusing the paper on specific aspects of the model and its ability to capture the role of preferential flows. In that respect, this paper has a substantial contribution to the field and should eventually be accepted for publication. However, this is not a “stand-alone paper” as, without reading the previous work by Turk 2024, there is no way to establish the relation between the “bucket ratios” and the model without going over Eqs. 1-26 in the said paper. The submitted paper continues the model from Turk 2024, starting from Eq. 33, and proceeds to examine the sensitivity to the SAS function optimization, specifically to the sensitivity to the preferential flow in light of the parameter (shape function) in the said equations. However, this sensitivity is hard to understand without the full model and figures 3 and 4 in Turk 2024. Further figures are needed from Bogena et al. 2015 (figures 1 and 2) and Turk 2024 (figure 1) to visualize and understand the layout of the field and its relation to the bucket model in Figure S1. I would argue that this paper is a continuation of Turk 2024, model-wise, and it can only be understood if one reads the 2024 paper prior to this paper, and as such, narrows the potential readership of this interesting and relevant paper.

Furthermore, coming from the transport in soil and rock community, the model seems very phenomenological in nature, which I guess is standard for “bucket models”. While it makes a nice attempt to move away from the data-driven model and statistical approaches towards more mechanistic observation, there is no explicit attempt to present the causality between physical parameters to observations. This has to be done when we account for preferential flows, as these preferential flows are the outcome of specific conditions (permeability heterogeneity of the root area and groundwater, head differences within the groundwater stemming from the slope, and slope runoff on a local scale). However, the discussion on these aspects is limited to Section 4, and even there, it does not provide specific details. They are found to some extent in Bogena (2015) for Wüstebach, yet I couldn’t find them for the HOAL in Turk (2024). Why is that? This approach stays on the data side, and while the correlation it provides is an important step towards a more rigorous model, can’t there be an effort to hypothesize about the mechanisms that form the varying dominance of preferential flows and see if the data and the missing parameters might corroborate this hypothesis?
To be more specific in my request, let’s take the following example: Is there a possibility to search the literature and provide a functional form that relates how clayey soils under variation in saturation contribute to the emergence of preferential flows, and how this functional form relates to the shape function in this study? Can we compare the sensitivity of this functional form to these aspects (clay concentration, saturation) and the sensitivity of the shape function? Can it account for the model’s sensitivity to the shape function? The same can be done for the differences in slope between the two data sets presented in this study. While this is not a mechanistic model, it indicates what parameters are needed in a mechanistic model, and the sensitivity to them. This will allow this community, and adjacent communities like soil and aquifers, to frame their mathematical approaches in the context of this excellent problem, especially given the excellent datasets presented here. Datasets that urge for a more rigorous and mathematical modeling approach, in space and time, that require some input on the mechanistic origin for these probability density functions controlling the current bucket model.
Line 31: “In the light of…” or “In light of…”?
The introduction is very good, and so are the questions which represent the study aim and objective.
Figure 1. Can you provide insight on the streamflow? Maybe maps of the catchment with the locations of the sampling locations? That will help in understanding the significance and time lag of these measurements.
Figure S1: T_T should be T_r by table S 1. One must define the parameters in black.
“The darker blue box (S_s,a)” should be S_s,p
Not all symbols are defined in Table S 1, please re-check.
Maybe move Table S 1 next to Figure S 1 so it will be easier to go between them.
Line 167: α and β, do not appear in Table S 1 or Figure S 1, please define them in the right context.
The number of references to Figure S1 suggests that it should be included in the main paper rather than the supplementary material.
Equations 1 and 2: How do you define S_r,max? Is it local in time (the maximum of the soil moisture for the given rain event) or is it simply the saturation value, namely the porosity? From the equation, its unclear how this term captures the preferential flow, specifically how it relates it to physical aspects, which are not saturation (heterogeneity and head differences)
Line 223-226: Since there is no discussion on how preferential flow components like heterogeneity and head differences were implemented in the model, it is hard to understand if this is the right way to measure the model’s sensitivity to it.
Figure 2: Why is the CDF shown and not the PDF for the TTD? Indeed, one is the derivative of the other, yet the PDF allows us to see the tailing and the mean behavior more clearly. I’m also not sure if eCDF is the cumulative of , as it is not stated, and from the curvature, it’s hard to establish it.
A non-intuitive aspect is that preferential release of older water (α>1) has the highest residence time. I assume that this is due to the interplay between the ground and root area flow, which affects the fast response water in Figure S1. Therefore, as α increases above 1, less water is directed to the fast response bucket; however, there is no indication of this. Where are the equations related to each “bucket”? How do you parameterize these “buckets”?
Another aspect is that Figures 2a, b, and 3 are basically identical. I understand that they are “illustrations”, but if there is no difference among the illustrations, what is the point of showing 3 of them? Furthermore, the illustration of the different passive storage values does not provide any insight into how the analysis differs or how the results should change as a result.
Line 248: 15 parameters are identified in Table S1, and I guess there are multiple locations at which they are measured, which spans the calibration to 55 and 190 parameters, but instead of guessing, please clarify this aspect in a text, or better yet, a figure outlining the measurements in the catchment area.
Line 278: “In the HOAL catchment, the calibrated root-zone SAS shape parameter lower bound α0 = 0.14 indicated a strong preference for very young water through unsaturated root zone preferential flow pathways, suggesting that precipitation rapidly reached the stream with minimal mixing with stored water.” While the correlation is clear, I’m not sure I understand the physical aspect of it. The unsaturated root zone is controlled by capillary forces if it is indeed unsaturated and stagnant, and by the connected paths of saturated areas (or preferential flows) under unsaturated flow. As such, the mechanism I can envision is that when starting with dry conditions and high infiltration, the invaded paths, which form the latter as preferential flows, must be occupied by younger water. However, under higher saturations, preferential flows are already established within the root zone; therefore, at lower infiltration rates, the discharge will consist of older water. Is this the physical mechanism suggested by this finding? If so, please refer to it; otherwise, what is the conclusion I need to draw from this finding, and how is it related to questions 1 and 2? This aspect is discussed in lines 364-372, where the difference between the clay soil of HOAL, which promote young water through the preferential flows, in contrast to the forest cover soil in Wüstebach which promote a more uniform infiltration, and therefore reduce the preferential flow effect and increases both the residence and the storage in the subsurface which is addressed later in the paper.
Figure 6. Was there an attempt to relate the PDF (the derivative of the CDF) to the preferential flow specific length and time scales using the specific field data?
Line 316-320: In the spirit of my previous comment, the mechanism here is that it is solely controlled by the “pipeline of the preferential flows” within the groundwater, and the storage size represents the pipeline length and the extent or dominance of groundwater preferential flows? If this is the case, do we have indications for this for the HOAL and Wüstebach? Do we see that the first is more heterogeneous and therefore is more likely to lean towards preferential flows than the latter? Alternatively, it may stem from the difference in slope, where the first is steeper than the latter (as is clear from Figure 1 in Turk 2024 and Bogena 2015, respectively), which will exacerbate the inherent heterogeneity, leading to more preferential flows and shorter storage times for the HOAL case.
This is partially addressed in lines 345-350; however, the mechanism by which the dominance of preferential flows is related to the different conditions of each field is provided later in lines 364-372, favoring the first explanation. However, the second explanation is partially supported by the passive groundwater storage difference between these fields (lines 392-396). Are they both true? Equal?
These comments on the mechanism of the preferential flows and their sources are reflected in the following (lines 412-416): “An alternative explanation, however, must also be considered: it is possible that such preferential groundwater flow processes are simply absent or negligible in the HOAL and Wüstebach catchments. The current data and model structure are insufficient
to conclusively rule out either possibility. Ultimately, distinguishing between limitations in model sensitivity and the actual absence of preferential flow processes requires additional, spatially distributed tracer data and complementary hydrometric observations.” As there are no hypotheses on the mechanism leading to preferential flows that stem from the physical aspects of the fields —permeability heterogeneity of the root area and groundwater, head differences within the groundwater stemming from the slope, and slope runoff on a local scale —one cannot draw a clear conclusion. These physical considerations are evident only at the correlational level from the data, as is clear from the Turk 2024 model, and not from a causality standpoint, which would require a more rigorous consideration. This is a major weakness of this study, and an attempt to formulate a hypothesis that will drive others to see what the actual causality is is missing. Nonetheless, this statistical approach is an important step toward a rigorous model, as it points to the conditions under which preferential flows can be more dominant. An example of how the statistical approach may point towards a more rigorous model is found in lines 430-438, where the distribution tail points to the ratio between active and passive storage.
Discussion:
I extremely like how the authors pose the three questions at the beginning of the paper, yet they only return to the first two at the end of the paper. Even if the conclusion is that it is inconclusive, this should appear for completeness.
Line 399: add a space after groundwater.

Citation: https://doi.org/10.5194/egusphere-2025-2597-RC2
- AC2: 'Reply on RC2', Hatice Türk, 08 Sep 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2597/egusphere-2025-2597-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-2597-AC2

Hatice Türk, Christine Stumpp, Markus Hrachowitz, Peter Strauss, Günter Blöschl, and Michael Stockinger

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Hatice Türk, Christine Stumpp, Markus Hrachowitz, Peter Strauss, Günter Blöschl, and Michael Stockinger

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Short summary

This study shows that stream flow isotope data (δ²H) were inadequate for distinguishing preferential groundwater flow. Large passive groundwater storage dampened δ²H variations, obscuring signals of fast groundwater flow and complicating the estimation of older water fractions in the streams. Further, weekly-resolution δ²H sampling yielded deceptively high model performance, highlighting the need for complementary and groundwater-level data to improve catchment-scale transit-time estimates.


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