Review of HESS egusphere-2025-1625 “Different tracer, different bias: using radon to reveal flow paths beyond the Window of Detection” by Mortimer L. Bacher et al.

The authors have calibrated one-zone stream transient storage models (TSMs) using two different tracers: salt (NaCl) and Radon. The authors state that pairing salt tracers with Radon increases the window of detection (WoD) by up to 21 days, which is much longer than that of salt. The authors argue that including Radon improves the ability to identify the true mean value of transient storage parameters. This paper will make a nice contribution to the literature by providing new findings into measurement and modeling of stream tracer breakthrough curves.

The presentation is good but there were a few places where this reviewed got confused. To benefit the reader through an improved presentation, below are a few general comments and several specific comments for the authors to consider.   

The authors state that jointly calibrating to two tracers is an improvement, which is exciting and novel; however, it is not clear to this reviewer where the joint calibration results are presented. In the figures and captions, it appears results are based on induvial tracers. It would help the reader to specifically state which results are the joint calibration and which are individual. If Radon is relatively steady and therefore does not capture the entire BTC, why would one assume that a TSM could be calibrated using only Radon? Pairing salt with Radon creates a more representative BTC. In simple terms, better calibration data, a better chance to identify parameters. That type of statement would benefit the reader.  

Parameter “certainty” is difficult for this reviewer to understand and follow because “sensitivity” and “identifiability” seem to already cover that concept. How is certainty different than identifiability? If clearly a different metric, that makes sense. If certainty means something like identifiability, introducing a new term “certainty” just adds confusion.  

If the background was subtracted for salt, why is groundwater influx also needed for the salt TSM? If QLHS is estimated from discharge, it would help the reader that conditions are still steady state. So groundwater inflow was assumed fixed for all reaches? And then estimated by gage data (dQ/dx). And also estimated directly via calibration. Correct?

What new information is presented in Figure 9? The red flow path does not seem technically correct.  should state that this figure has been modified from Payne et al. 2009. Flow path C does not seem technically correct. You do not know if that represents tracer that bypasses measurement site. The WoD is your measurement window, not the real window in which flow paths exist. And why is C red? That adds confusion. This reviewer does not find any new information added by this figure, and it does not seem technically correct. Suggest to revise to clarify which arrow is specifically improved in this study.

This reviewer got a bit lost in the Discussion. The alternating representation and descriptions of groundwater and groundwater locations caused a tough read, and the key point seemed buried as a result. Radon helps constrain the GW inflow. Great. The salt is needed for advection and dispersion. Try to write in more simple terms where possible.    

This reviewer feels that some sort of concise recommendation from the authors would be helpful for the reader. How would this transfer to other streams or watersheds? Low versus high background Radon? This reviewer assumes this tracer approach is limited by river size; perhaps it only really applies to smaller headwater type streams? What are the limitations if streamflow is dynamic? Would this study need to be repeated for other streamflow conditions? A reader would benefit from a concise statement.

Citations look mostly complete and are well thought out. Equations appear correct. Nice work overall. 

Specific comments:

14: How do you know a longer estimated timescale would lead to a larger volume? Longer timescale does not necessarily mean more volume.

35: consider Schmadel et al. https://doi.org/10.1002/hyp.9854 for supporting definition of WoD.

58: “slug”, suggest to define as a near instantaneous injection of mass.  

62: Do not follow what “they” are. Exchange fluxes?

67: Sentence needs another look. Redundant information, consider delete.

69: switching to “duration” adds confusion for reader. You specifically mean the WoD, correct? Suggest to state the WoD for consistence as that is clearly defined. Duration of any slug is infinity; the WoD defines which portion of the slud returns real information.

84: The goal is…there are several places where qualifying words like “overarching” add to the word count and not needed.

150” “derived”? Confusing. Solute transport is simply parameterized. You are not necessarily deriving anything new.

153: well or a “completely mixed” transient storage zone.  

162: fine, but mention of the ADE if no storage is not necessary for the reader.

163: the model formulation was further modified to account for gas exchange. “Not suited” reads awkwardly.   

253: “certainty” adds confusion for this reviewer. H is entropy, but you are also calling that “certainty.” This reviewer has referred to parameter sensitivity and identifiability, but not certainty.

300: Runkel and Chapra 1993 should probably be cited here. Also, important to point out for the reader that this is steady state, meaning flow is considered steady for every slug injection. If dynamic, dA/dt + dQ/dx = qi = qout. Also, it is not clear what was needed for the TSM. You only need this equation to estimate qi and plug into the TSM. And what was the Radon concentration assumed in GW? Does qi not matter for salt because the background was subtracted?      

320: Reads as flat. A reader is left wondering what the key result is. Perhaps say that tracer results were ideal for testing this approach because there was a clear difference between surface water and groundwater concentrations. “tracers revealed spatial variability” is not necessarily novel. Suggest to add a concise statement to help the reader regarding what you see in the tracer data. For example, “pairing two tracers allowed for improved identification of parameters because surface water and groundwater are distant in this watershed.” Something like that.

334: Increased certainty? You mean improved parameter identifiability? It is not clear how certainty and identifiability are different or same. Same comment for line 348.

360: In the caption, it would help the reader to specify these are two separated calibrations with an “only salt” and “only radon”

365: unclear what Qfix, QLHS, Qout are directly from the table. So ATS is highly sensitive to Radon tracer?

410: This reviewer does not follow the main point or reason for this Figure 6, and finds this figure confusing. The GW categories are not the same as previous discuss in text. Qfix, QLHS, Qout. What is GW inflow downstream? And why is that shaded grey. The point is a few outliers are caused? Medians and percentiles are nearly the same.

415: Figure 7, it is not clear how this is different from Figure 5. New GW terminology adds confusion.

435: “Calibrating TSMs with multiple tracers better constrains model parameters.” Where are the actual results of calibrating using two tracers simultaneously? You calibrated using an individual tracer, and then calibrate to one set of combine tracer data, correct?

456: “TSM is jointly calibrated with radon and chloride.” Did you actually do a joint calibration? To suggest two tracers were used, a multi-objective function should be considered similar to Neilson with solute and temperature. This reviewer does not clearly follow where the joint results are.    

501: “critical for contextualizing” in future radon studies? How? QLHS and Qout results look very similar to this reviewer. It just provides a longer WoD.

505: Statement is not clear from Figure 6. Central tendency is all the same regardless of GW location. A reach-by-reach water balance seems critical. “Location selected for GW” is arbitrary.

519: “Previous studies have shown that large spatial-scale subsurface flow paths play a critical role in explaining water mass balances in streams.” Redundant information, and reads too vague and may add confusion for the reader. Why are the large-spatial-scale so important? It is only important for estimating an accurate WoD. Right? Meaning, your paper is about the WoD, not regional GW processes. The point the help the reader is that local groundwater fluxes control the water balance and should be quantified as part of the in-stream BTC. That is explicit and easy to understand. Suggest to write in more explicit terms specific to your study.    

540: Figure 9, should state that this figure has been modified from Payne et al. 2009. Flow path C does not seem technically correct. You do not know if that represents tracer that bypasses measurement site. The WoD is your measurement window, not the real window in which flow paths exist. And why is C red. That adds confusion. This reviewer does not find any new information added by this figure, and it does not seem technically correct.

549: Just say break the transient storage zone into two zones, each with its own exchange flux. This is important for temperature and reactive solutes. It might be critical? Too vague. And critical how? How would this help with Radon? Discussion related to two-zones is a little weak; sure, denitrification representation might improve, but how is that relevant for radon and chloride?

563: “The goal was..”

564: Radon is a solute too. Be specific here regarding which solute, which tracer.  

571: Not sure this reviewer agrees that the recommendation should always be to include Radon and chloride jointly. What is missed if Radon is excluded? Can we estimate qi from groundwater first, and then use salt once that qi parameter is set? What is Radon is non-detect? Are you assuming Radon is measurable in all streams? When longer flow paths need to be identified, sure, Radon makes sense, but there is still large uncertainty in the parameter value. Plus, a one zone may be much more of a limitation than excluding Radon. Suggest to state in simple terms that Radon can extend the WoD with paired with salt, plain and simple.         

 The authors present an interesting application of the transient storage model (TSM) in which instream tracer data is supplemented by naturally occurring radon data. The paper is generally well written and the authors have some good points. The manuscript has a number of shortcomings, however, and major revisions will be needed to develop a manuscript that warrants publication.

The authors raise two fundamental issues in the introduction that are recurring themes in the TSM literature. I haven't done much work in this arena for some time, but I have conducted other reviews where I've made similar points. Please keep in mind that many of the comments that follow are directed at the field in general rather than these particular authors.

The first issue is the alleged inability of the tracer-modeling approach to quantify "long flow paths". I can certainly think of cases where this is important -- e.g. when the stream crosses a fracture zone and water leaves the channel and doesn't return before the observation point (path C in Fig 9; lines 59/60) - but in general I would say that this concern is overblown. The importance of this issue is dependent on the overall goal of the study. If the goal is to quantify the processes that affect constituents that are present in the water column, such as the case of an accidental spill into a waterway, the "failure" of the approach is not of consequence -- the tracer mimics the constituent of concern, so if these long flow paths don't affect the tracer, they don't affect the constituent (the amount of mass in long flow paths is trivial). If your interest is the fate of molecules in the riparian zone as they interact with the stream (e.g. diffuse agricultural pollution that enters laterally), the long flow paths may be of greater importance. But I would argue that the typical stream tracer approach isn't an appropriate means to address this latter scenario.

Further, if one is concerned about long flow paths, why use slug additions that by definition have a short window of detection? Its important to note that 100% of the data sets used to establish the transient storage paradigm were based on continuous tracer injections wherein tracer concentrations are allowed to reach a steady-state plateau. Under this approach, plateau will be achieved when all flow paths that return to the stream have had sufficient time to do so (thereby eliminating the problem associated with path B). Unfortunately many contemporary investigators have utilized slug additions as a means of streamlining the field effort, and this simplification comes with a price.

The second fundamental issue is the much celebrated parameter identifiability/equifinality problem raised by numerous investigators. The point I'd like to make here is that the "failure" to develop unique estimates of the transient storage parameters does not necessarily indicate a "problem" with the "traditional" tracer based modeling approach. The common explanation for parameter identifiability problems is that the approach is somehow inadequate. An equally plausible explanation in many cases is that transient storage simply isn't important in the reach of interest. In the extreme case, consider data from a straight, lined canal. If you applied the approach in this situation and were unable to identify the transient storage area and exchange rate, would you blame the approach, or conclude that transient storage is unimportant? For the case of a natural stream reach, there may be identification issues simply because these flow paths aren't relevant when viewed in terms of constituent mass.

As someone who has worked for years trying to help numerous researchers analyze problematic data sets, its my opinion that the transient storage approach is adequate when applied to a quality data set. Most problems arise when the data is sparse in critical parts of the breakthrough curve, the investigators have inaccurate estimates of streamflow, and/or the data is simply noisy (due to poor lab analyses, incomplete mixing, etc). 

specific comments:

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1) abstract "...the amount and location of groundwater inflow, which is not explicitly accounted for in TSM".  This is incorrect, TSMs consider inflow (e.g. ql in equation 1).

2) line 32  "solute tracer experiments are biased towards faster flow paths". To reiterate, if it doesn't affect the tracer, it doesn't affect the constituent of interest (at the scale studied). The tracer is simply reproducing what constituent molecules would experience.

3) line 40 "TSMs assume a uniform, steady-state ..flow".  This is incorrect -- the lateral inflow term can be used to implement non-uniform flow. Consideration of unsteady flow is rare, but possible:

Runkel, R.L., McKnight, D.M., and Andrews, E.D., 1998. Analysis of transient storage subject to unsteady flow: Diel flow variation in an Antarctic stream, J North American Benthological Society, 17(2), 143–154, 10.2307/1467958.

also, I don't agree with "effectively infinite dimensions" (nor does your text on line 154, "finite-size, well-mixed storage zone")

4) line 45, "The parameter values derived from TSMs provide a means of comparing solute transport within a single stream or across multiple streams". Could cite:

Runkel, R.L., 2002. A new metric for determining the importance of transient storage, J. North American Benthological Society, 21(4), 529–543, 10.2307/1468428.

5) lines 50-55. Again, it depends on your objective; for most cases I'm not convinced adding the radon data really helps. I find the idea of supplementing the tracer data with other auxiliary data the most promising approach for separating surface and subsurface (hyporheic) storage. I think you allude to using radon data for this purpose later in the paper. For more of my thoughts (as if you haven't had enough :-), see:

Runkel R.L., McKnight, D.M., and Rajaram, H., 2003. Modeling hyporheic zone processes, Advances in Water Resources, 26(9), 901–905, 10.1016/S0309-1708(03)00079-4

6) line 79-80. "When surface water exchanges with subsurface transient storage zones and contacts radium-bearing minerals in the streambed, radon activity increases as a function of the time spent in the hyporheic zone". Radon in the stream could come from this contact w/ streambed materials AND/OR groundwater inflow. I'm guessing the streambed part is modeled using the production term (gamma, equation 2) and the groundwater part is handled through the lateral inflow term. More description of how this is handled should be added, including what you're using to set the lateral inflow concentration.

7) line 108-110. "Each reach length was at least 20 times the Wetted Channel Width to control for expected variations in solute transport that occur as a function of reach selection".  Similar metrics for reach length are often mentioned in regard to complete mixing of the tracer with depth and width, but I'm guessing you're alluding to the Dahmkohler number. You may want to clarify this.

8) line 120. "Discharge was calculated for the resulting BTCs using dilution gaging".  I assume this required some relationship between conductivity and chloride, which is fine. But you may want to try this method as a check:

McCleskey, R. B., Runkel, R. L., Murphy, S. F., & Roth, D. A. (2025). Stream discharge determinations using slug additions and specific conductance. Water Resources Research, 61, e2024WR037771. https://doi.org/10.1029/2024WR037771. 

I'm happy to help and provide an updated spreadsheet if interested.

9) line 128. "Radon sampling sites were co-located with BTCs observations" - was there 1 sample per site?  This paper is all about the radon yet we don't get to see the data - please add.

10) line 187-188. Here you refer to D, alpha, Ats; Table 1 has D, A, Ats

11) line 188-189. Is it a uniform distribution or a logarithmic one?, I'm confused...

12) line 195, "intersection of behavioral parameter sets" - I like this approach...

13) calibration approach described in section 2.4 and various flow approaches described later in the paper.

I don't agree with the approach of fixing velocity and A, and estimating Q for several reasons. I highly recommend fixing Q and estimating A.  A few subpoints:

- why not use the Q from the slug additions? I think your three Q methods overly complicate things and these complications aren't relevant to what you're trying to show (the utility of adding radon data). I suggest using the Qfix approach and dropping the others. If you're worried about uncertainty in your slug estimates, develop a linear regression between the Q estimates and distance and use the regressed values at each site.

- fixing A does nothing to reduce "potential issues of equifinality" (line 205). The main channel area is by far the easiest parameter to estimate via simulation as it controls the velocity and thus the timing of the BTC. When estimating A, Ats, alpha and D using nonlinear regression, the A parameter always has the narrowest 95% confidence interval and is the parameter estimated with the most certainty. Equifinality problems usually arise when there's not enough data in certain parts of the BTC to uniquely identify D, Ats, and alpha. Wagner and/or Harvey have papers (book chapters?) which show the sensitivity of various parts of the BTC for various parameters and there's always ample info to estimate A. By fixing A (and/or velocity) you're ignoring this information and biasing your other parameter estimates. If you insist on fixing A/velocity, I suggest using the center of mass rather than the peak as this more truly represents the average reach velocity (see Runkel 2002 ref above), especially if there's an extended tail.

14) lines 215-220.  Degassing is a function of turbulence which is effected by velocity and thus Q. Stream width (surface area) is also important. Why not use the value estimated at the most similar Q?

15) line 334. "radon provided more information on groundwater inflow". With all the uncertainty involved (e.g. degassing rate, radon inflow concentration, radon analyses) why would these estimates of inflow be better than your dilution gaging? The Qfix approach is the way to go.

16) line 402. "parameter interactions became evident when inflow was at the most downstream points".  Back on line 310 you mention all of the inflow entering over 1 meter long area; it's my experience that these abrupt changes can cause numerical problems -- you may not 'see' these problems at sites farther away from the observation point (the Crank-Nicolson method usually 'recovers'), but this one at the downstream end could be a numerical artifact. I suggest spreading the inflow over several 1-m segments (maybe 10 m).

17) line 470. "This suggests that obtaining narrow, well-constrained estimates for groundwater inflow, ATS, or α from calibrating the TSM with radon will remain challenging unless at least one of these parameters is further constrained" -- this is easily done - fix Q and save the modeling approach for the more empirical/abstract parameters!!!

Rob Runkel

18 July 2025